Math part 4 question 7

Math Part 4 Question 7

Answers

Answer 1

For the given function f(x) = (x - 4)² - 3, the following statements are correct -

B: relative minimum at (4,-3).

C: decreasing interval from (-∞, 4).

E: increasing interval is (4, ∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -

f(x) = (x - 4)² - 3

f'(x) = 2(x - 4)

2(x - 4) = 0

x = 4

So, the only critical point of the function is x = 4.

Plug in the value of x = 4 in the equation -

(4 - 4)² - 3

0 - 3

-3

Since f''(4) is positive, the critical point at x = 4 is a relative minimum.

Therefore, the function has a relative minimum at (4, -3).

To find the increasing and decreasing intervals, we can look at the sign of the first derivative -

f'(x) = 2(x - 4)

For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).

For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).

Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).

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Related Questions

The exchange rate from euros to dollars is one euro =$1.2 complete these convertions euros 160 to dollars $76.80to euros

Answers

One euro is equivalent to $1.2 in dollars thanks to the $1.2/euro conversion rate. The EUR/USD exchange rate is another name for this rate.

What is a rate of exchange?

A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia. We can multiply the quantity of euros by the conversion rate to convert 160 euros to dollars:

1 euro Equals $1.22; 160 euros = $192.

Hence, 160 euros are equal to $192.

We can divide the amount in dollars by the conversion rate to convert $76.80 to euros:

64 euros are equal to $76,80 at the exchange rate of $1 to the euro.

Hence, 64 euros are equal to $76.80.

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Two angles of a quadrilateral measure 180° and 50°. The other two angles are in a ratio of 2:11. What are the measures of those two angles?

Answers

The measures of those two angles are, 20° and 110°

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Two angles of a quadrilateral measure 180° and 50°.

And, The other two angles are in a ratio of 2:11.

Since, The other two angles are in a ratio of 2:11.

Hence, ,Measures of both angles are, 2x and 11x.

Now, We know that;

Sum of all interior angles of a quadrilateral are 360°.

Hence, We get;

⇒ 180 + 50 + 2x + 11x = 360

⇒ 230 + 13x = 360

⇒ 13x = 360 - 230

⇒ 13x = 130

⇒ x = 10

Thus, Measures of both angles are,

2x = 2 × 10 = 20°

and 11x = 11 × 10 = 110°

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simplify using trig identities
(cos2x-1) / (sin2x)

Answers

As a result, the formula is (cos 2x - 1) / (2 sin x cos x)

What are an equation and an expression?

A mathematical expression shows the worth of something by combining numbers, factors, and functions. A mathematical assertion known as an equation involves setting two expressions equivalent to one another.

We can start by using the identity:

cos 2x = cos² x - sin² x

We can rearrange this to get:

cos² x = cos 2x + sin² x

Substituting this into the expression we want to simplify, we get:

(cos² x - sin² x - 1) / (sin 2x)

We can then use the identity:

sin 2x = 2 sin x cos x

Substituting this into the expression, we get:

(cos² x - sin² x - 1) / (2 sin x cos x)

We can simplify the numerator using the identity:

cos² x - sin² x = cos 2x

Substituting this into the expression, we get:

(cos 2x - 1) / (2 sin x cos x)

Therefore, the simplified expression is:

(cos 2x - 1) / (2 sin x cos x)

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HELP DUEEE TONIGHT!!!!!

a group of 175 adults were asked whether they exercise and whether they are vegetarian. their responses are summarized in the following table.​

Answers

im not sure if im right at all but ,

a) 44%
b) 40%
c) 28%
d) either one of the no's.

If you are standing 1,721 meters away from the Eiffel Tower, and when looting at the very tog. the angle of elevation is \( 10.37^{\circ} \), can you determine the height of the Eiftel Tower. If wo ca

Answers

The height of the Eiffel Tower is approximately 311.6 meters.

Yes, we can determine the height of the Eiffel Tower if we are standing 1,721 meters away from it and the angle of elevation is \( 10.37^{\circ} \). We can use the tangent function to find the height of the Eiffel Tower. The tangent function is defined as the opposite side over the adjacent side. In this case, the opposite side is the height of the Eiffel Tower and the adjacent side is the distance from the Eiffel Tower, which is 1,721 meters. The equation for the tangent function is:

tan( \( 10.37^{\circ} \) ) = height / 1,721

We can rearrange the equation to solve for the height of the Eiffel Tower:

height = tan( \( 10.37^{\circ} \) ) * 1,721

Using a calculator, we can find the value of tan( \( 10.37^{\circ} \) ) and multiply it by 1,721 to get the height of the Eiffel Tower:

height = 0.181 * 1,721

height = 311.6 meters

Therefore, the height of the Eiffel Tower is approximately 311.6 meters.

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For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.)

Answers

The composite functions and their domains are:
(a) (fog)(x) = 30x + 8, domain: all real numbers
(b) (gof)(x) = 30x + 40, domain: all real numbers
(c) (fof)(x) = 36x + 56, domain: all real numbers
(d) (gog)(x) = 25x, domain: all real numbers

The composite functions are formed by substituting one function into another. We can find the composite functions for f(x)=6x+8 and g(x)=5x by following these steps:

(a) (fog)(x) = f(g(x)) = f(5x) = 6(5x) + 8 = 30x + 8

The domain of (fog)(x) is the set of all real numbers, since there are no restrictions on the values of x.

(b) (gof)(x) = g(f(x)) = g(6x+8) = 5(6x+8) = 30x + 40

The domain of (gof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

(c) (fof)(x) = f(f(x)) = f(6x+8) = 6(6x+8) + 8 = 36x + 56

The domain of (fof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

(d) (gog)(x) = g(g(x)) = g(5x) = 5(5x) = 25x

The domain of (gog)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

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Anthony plants flowers from seed and each day measures the height of the flowers compared to the soil line. He records his measurements in a scatter plot. Anthony calculates the equation of the least squares regression line: Predicted Height =0.56 ⋅ Days in Soil − 3.16 Use the drop-down menus to complete the statements below about what this linear model tells you about the height of a flower.

Answers

From the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

What is an equation?

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Two expressions joined by an equal sign form a mathematical statement known as an equation. The expression on the left and the expression on the right is shown to be equal in relation to one another.

LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" symbol in the statement. It will be taken into account as an expression.

Given,

The predicted height = 0.56

Days in soil = 3.16

The y-axis of the plot is the height of the line compared to the soil line.

The x-axis gives the number of days.

from the equation of the least squares regression line, we get the above predicted height and the days in the soil.

y  = mx+b is the equation of a line.

Then, we can say that,

m = slope = 0.56

b = y-intercept = 3.16

Therefore from the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

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Find the exact value by using a sum or difference identity.
sin (185° -65°) please please help me :/

Answers

I'm not 100%

sure

:))))))))))))))))))))))))

1 year ago Wags the dog was 3 years more than 3 times the age of Scratch’s the cat. In the 2 years time Scratch will be 2 more than one quarter of Wags age. Find Wags and Scratch’s approximate ages today?

Answers

After solving the problem we found that Wags is approximately 15 years old and Scratch is approximately 5 years old today.

The solution uses algebraic equations and substitution to solve for the ages of Wags and Scratch, which is based on the concept of solving systems of linear equations.

Let's assume that Wag's age today is represented by W, and Scratch's age today is represented by S.

From the first piece of information, we can set up the following equation:

W - 1 = 3 + 3(S - 1)

Simplifying:

W - 1 = 3S - 6

W = 3S - 5

From the second piece of information, we can set up the following equation:

S + 2 = (1/4)(W + 2) + 2

Simplifying:

S + 2 = (1/4)W + 2.5

Substituting W = 3S - 5:

S + 2 = (1/4)(3S - 5) + 2.5

Solving for S:

S + 2 = (3/4)S - (5/4) + 2.5

S + 2 = (3/4)S + 3/4

1/4 S = 1 1/4

S = 5

Substituting S = 5 into W = 3S - 5:

W = 10 + 5

W = 15

Therefore, Wags is approximately 15 years old and Scratch is approximately 5 years old today.

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Answer this
………………..

Answers

The slope of the linear equation is; 0.5

The y-intercept of the Linear Equation is: 4.75

Yes the equation is proportional

What is the graph of the linear Equation?

The equation we are given is expressed as;

y = ¹/₂x + 4³/₄

When x = 0,

y = ¹/₂(0) + 4³/₄

y = 4.75

When x = 1,

y = ¹/₂(1) + 4³/₄

y = 5.25

When x = 2,

y = ¹/₂(2) + 4³/₄

y = 5.75

When x = 3,

y = ¹/₂(3) + 4³/₄

y = 6.25

If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5

Thus, slope = 0.5

y-intercept = 4.75

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Calculate the fluid intake in milliliters for the following meal
(assume a cup = 6oz and a glass = 8oz)
1/3 glass of orange juice
1/2 cup of tea
1/2 pt milk
1 tuna fish sandwich
1 popsicle (3oz)

TOTAL = _____ mL

*I need this answered quickly please and thank you.*

Answers

The total fluid intake for the meal is 493.055 mL

How to calculate the total fluid intake for the meal

Converting:

1/3 glass of orange juice

= (1/3) x 8 oz = 2.67 oz

= 79.027 mL (rounded to 3 decimal places)

1/2 cup of tea

= (1/2) x 6 oz

= 3 oz = 88.720 mL (rounded to 3 decimal places)

1/2 pint of milk

= (1/2) x 16 oz

= 8 oz = 236.588 mL (rounded to 3 decimal places)

1 tuna fish sandwich = no fluid intake

1 popsicle (3oz)

= 3 oz

= 88.720 mL (rounded to 3 decimal places)

Total fluid intake

= 79.027 mL + 88.720 mL + 236.588 mL + 0 mL + 88.720 mL

= 493.055 mL (rounded to 3 decimal places)

Therefore, the total fluid intake for the meal is 493.055 mL.

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Question 7 Explain how you can use composition of functions to prove that the functions f(x)=(2)/(3)x-8 and g(x)=(3)/(2)x+12 are inverses.

Answers

To prove that the functions f(x)= (2)/(3)x-8 and g(x)=(3)/(2)x+12 are inverses, we can use composition of functions. We can do this by setting f(g(x)) = x and g(f(x)) = x and showing that they are equivalent.

First, let's look at f(g(x)). We can substitute g(x) into the equation for f(x), so we have: f(g(x)) = (2)/(3)((3)/(2)x+12)-8. Simplifying, we have: f(g(x)) = (4x+48)/6 - 8. Distributing the 4 and rearranging, we have: f(g(x)) = x.

Now let's look at g(f(x)). We can substitute f(x) into the equation for g(x), so we have: g(f(x)) = (3)/(2)((2)/(3)x-8)+12. Simplifying, we have: g(f(x)) = (2x-32)/3 + 12. Distributing the 2 and rearranging, we have: g(f(x)) = x.

Therefore, we have shown that f(g(x)) = x and g(f(x)) = x, which means that f(x) and g(x) are inverses of each other.

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given a line and a point not on the line , find a plane
containing the point and parallel to the given line
Geometry

Answers

To find a plane containing a point P not on a given line l and parallel to l, we can follow these steps:

Choose any point Q on the line l.

Find the vector v that connects point Q to point P, i.e., v = P - Q.

Find the direction vector d of the line l.

Take the cross product of the direction vector d and the vector v, denoted by d x v.

The plane that contains point P and is parallel to line l can be represented by the equation ax + by + cz = d, where (a, b, c) is the vector d x v, and x, y, and z are the coordinates of any point on the plane.

Here's an example to illustrate the process:

Let's say we have a line l that passes through points A(1, 2, 3) and B(4, 5, 6), and a point P(7, 8, 9) not on the line. We want to find a plane containing point P and parallel to line l.

Choose any point Q on the line l. Let's choose Q(1, 2, 3) for convenience.

Find the vector v that connects point Q to point P: v = P - Q = (7-1, 8-2, 9-3) = (6, 6, 6).

Find the direction vector d of the line l: d = (4-1, 5-2, 6-3) = (3, 3, 3).

Take the cross product of the direction vector d and the vector v: d x v = <3, 3, 3> x <6, 6, 6> = <0, 18, -18>.

Write the equation of the plane: 0x + 18y - 18z = d. Since the plane is parallel to line l, we know that the coefficients of x, y, and z are all 0, except for the coefficients of y and z, which are the components of the vector d x v. Therefore, the equation simplifies to 18y - 18z = 0, or y - z = 0.

So the plane containing point P(7, 8, 9) and parallel to the line passing through points A(1, 2, 3) and B(4, 5, 6) can be represented by the equation y - z = 0.

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Using the following regression output, test the following hypotheses. Use a=0. 1: variable coefficient constant 4. 162 units 15. 509

Answers

As our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero.

The hypotheses that we want to test are:

H0: The coefficient for the variable is equal to zero.

H1: The coefficient for the variable is not equal to zero.

Using the given output, we can see that the coefficient for the variable is 15.509, and the standard error of the coefficient is 5.123. The t-value for the coefficient is calculated by dividing the coefficient estimate by its standard error, so:

t = 15.509 / 5.123 = 3.032

To test the hypothesis, we can compare the calculated t-value with the critical value of the t-distribution with n-k-1 degrees of freedom (where n is the sample size and k is the number of independent variables), at a significance level of 0.1 and using a two-tailed test.

Since the sample size and number of independent variables are not provided, we cannot determine the degrees of freedom or the critical value directly. However, we can use a t-distribution calculator or look up the critical value from a t-distribution table. For example, with n=50 and k=2 (based on the given output), the critical value for a two-tailed test at a significance level of 0.1 is approximately ±1.645.

Since our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero. In other words, there is evidence to suggest that the variable has a significant effect on the outcome being predicted by the regression model.

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What are the solutions to the quadratic equation x^2-3x+4=0

Answers

Answer:

[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]

[tex]x=\frac{3}{2} + i\frac{\sqrt{7}}{2}[/tex]

Step-by-step explanation:

We can use the quadratic formula to solve the equation:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -3, and c = 4. Substituting these values into the formula, we get:

x = (3 ± sqrt((-3)^2 - 4(1)(4))) / 2(1)

x = (3 ± sqrt(9 - 16)) / 2

x = (3 ± sqrt(-7)) / 2

Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Therefore, the answer is:

[tex]x=\frac{3}{2}+i\frac{\sqrt{7} }{2}[/tex]

[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]

how do I do this I'm confused truly can u help me

Answers

Answer:

1st one: (x-7)

2nd: (-x+7)

3rd: (5x+3)

Step-by-step explanation:

1: you subtract like terms so first you do 3x-2x which is x and do -2-5 and get -7 so its (x-7)

2: do 2x-3x and get (-x) and then do 5-(-2) and get 7 so the answer is (-x+7)

3: first do 2x+3x and get 5x and then do 5+(-2) and get 3 so the answer is (5x+3)

Answer:

Step-by-step explanation:

( 3x - 2 ) - ( 2x + 5 ) = 3x - 2 - 2x - 5  = x - 7

( 2x + 5 ) - ( 3x - 2 ) = 2x + 5 - 3x + 2 = - x + 7

( 2x + 5 ) + ( 3x - 2 ) = 2x + 5 + 3x - 2 = 5x + 3

A baker needs 15lb of cream cheese that contains 20% fat to fill a big order. But his supplier delivers one cream cheese that contains 10% fat, and another that contains 35% fat. How many pounds of each should a baker combine to fill the order?

Answers

.10x + .35x = 15(.20)
.45x = 3
x = 3/4.5
x = 6.67 or 6 2/3lbs

The parametric equations of a curve are:
2x=
cotθ
-
cscθ and
4y=2cscθ-
2cotθ
Find the Cartesian equation ( y = f(x)) for
the curve

Answers

The Cartesian equation ( y = f(x)) for the curve is y = -x.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the given parametric equations. We can do this by rearranging the equations and solving for θ in terms of x or y, and then substituting that value into the other equation.

First, let's rearrange the first equation to solve for cotθ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x

Next, let's rearrange the second equation to solve for cscθ:
4y = 2cscθ - 2cotθ
2cscθ = 4y + 2cotθ
cscθ = 2y + cotθ

Now, let's substitute the value of cscθ from the second equation into the first equation:
2y + cotθ - cotθ = -2x
2y = -2x
y = -x

Therefore, the Cartesian equation of the curve is y = -x.

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Company C had 60 defective batteries out of 10,800. If Company C also manufactures 15,000 new batteries next month, how does this company compare to the others? Explain.

Answers

The expected number of defective batteries out of 15,000 batteries is of:

83.3.

Then this expected amount is compared to the number of different batteries of the other companies.

How to obtain the number of defective batteries?

The number of defective batteries is obtained applying the proportions in the context of the problem.

Company C had 60 defective batteries out of 10,800, hence the proportion of defective batteries is of:

60/10,800.

Out of 15,000 batteries, the expected number of defective batteries is of:

60/10,800 x 15,000 = 83.3.

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HELP geometry IXL need help

Answers

The value of ST in the given triangle is is √73.

What is Pythagoras' theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: In a triangle

TR = 8

SR = 3

ST =?

We apply here Pythagoras theorem and we get

SR² + TR² = ST²

3² + 8² = ST²

9 + 64 = ST²

73 = ST²

ST = √73

Hence, the value of ST is √73.

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Suppose a novel infectious disease reaches the portland-metro area. This disease takes 9 days to recover from, and has a basic reproduction number of R0=4.5. Suppose the disease is 0.3% fatal. We'll model the disease outbreak with an SIR model.
i) Find a value for N, the total population of the portland-metro area.
ii) Determine the values of a and b, the constants for the SIR model.
iii) Suppose on day 0, there are 5 cases of the disease. If 15% of the initial population has immunity to the disease, determine the initial values S(0), I(0) and R(0).
iv) Solve the SIR model numerically, over a time interval that shows the whole course of the disease outbreak. Create a graph showing S, I and R vs time. The remaining questions can all be answered by reading and interpreting the graph:
v) How many people ultimately will be infected?
vi) How many will die from the disease?
vii) When is the peak of the outbreak?
viii) When is the outbreak is over?
ix) For this disease, what is the herd immunity threshold? Find the time at which the number of R individuals reaches the herd immunity threshold.
x) How many people die of the disease, after the herd immunity threshold is reached?

Answers

The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.

i) The total population of the Portland-metro area, N, can be determined by looking up the population of the city, county, and other areas that make up the metro area.

ii) To determine the values of a and b, we need to look at the basic reproduction number, R0. For an SIR model, the constant a is equal to the basic reproduction number (R0=4.5), and the constant b is equal to (a/N).

iii) To determine the initial values S(0), I(0) and R(0), we can use the equation S(0)=N-5-0.15N, I(0)=5, and R(0)=0.15N.

iv) To solve the SIR model numerically, we need to create a differential equation for each variable (S, I, and R) and use numerical integration to solve the system. Then, a graph can be created to show the values of S, I, and R over time.

v) From the graph, we can see that the total number of people infected is equal to the peak of the I(t) curve.

vi) The total number of people that die from the disease is equal to the peak of the R(t) curve.

vii) The peak of the outbreak is at the time when the I(t) curve has its highest value.

viii) The outbreak is over when the I(t) curve reaches 0.

ix) The herd immunity threshold is reached when the R(t) curve reaches a value equal to the basic reproduction number (R0).

x) The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.

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Express the following as a linear combination of u =6, 1,6), v= (1,-1,4) and w = (1,4,7). (23, 10, 23) =_______ U-________ V+_________ +w

Answers

Given vectors are, u = (6,1,6), v = (1,-1,4) and w = (1,4,7) and a vector (23, 10, 23).We need to express (23, 10, 23) as a linear combination of u, v and w.


To find the coefficients, we use matrix notation.
Let A be a matrix containing u, v and w as its column matrices, and X be a matrix containing the coefficients.
Then,AX = B Where A = [u | v | w]X = [a | b | c]B = (23, 10, 23)
Therefore, [u | v | w][a | b | c] = (23, 10, 23)⇒ a(u1) + b(v1) + c(w1) = 23a(6) + b(1) + c(1) = 23⇒ 6a + b + c = 23⇒ a(u2) + b(v2) + c(w2) = 10a(1) - b(1) + c(4) = 10⇒ a - b + 4c = 10⇒ a(u3) + b(v3) + c(w3) = 23a(6) - b(4) + c(7) = 23⇒ 6a - 4b + 7c = 23
The above system of linear equations can be solved using Gaussian elimination method.
The row echelon form of the augmented matrix [A | B] is, [6 1 1 | 23][1 -1 4 | 10][0 0 2 | 9]
The solution is, c = 9/2, b = -3, and a = 1/2.
Therefore, (23, 10, 23) = (1/2)u - 3v + (9/2)w can be written as a linear combination of u, v and w.

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What are the other three angle measures is <1 has a measure of 45

Answers

The other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

What is the quadrilateral?

A quadrilateral is a polygon with four sides and four angles. In other words, it is a closed figure that has four straight sides and four vertices (corners).

If <1 has a measure of 45 degrees, then the sum of the angle measures in the quadrilateral must be 360 degrees. Let's call the other three angles in the quadrilateral <2, <3, and <4.

Then we can use the fact that the opposite angles in a quadrilateral add up to 180 degrees to write two equations:

<1 + <3 = 180 (opposite angles)

<2 + <4 = 180 (opposite angles)

We also know that <1 = 45, so we can substitute that in the first equation:

45 + <3 = 180

Solving for <3, we get:

<3 = 135

Now we can substitute the values of <1 and <3 into the sum of angle measures equation:

45 + <2 + 135 + <4 = 360

Simplifying, we get:

<2 + <4 = 180

This is the same equation as the opposite angles equation, so we know that <2 and <4 are also opposite angles. Therefore, we can conclude that:

<2 = <3 = 135 degrees

<4 = 45 degrees

Hence, the other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

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Julie and Barry Spinos purchased a house for $96,400. They made a 25 percent down payment and financed the remaining amount at 5. 50 percent for 30 years. Their monthly payment is $410. 66. How much of the first monthly payment is used to reduce the principal?

Answers

The first monthly charge has about $78.78 allotted in the direction of reducing the principal.

The total buy charge of the house is $96,400 and the Spinoses made a 25% down payment, because of this they paid $96,400 x 0.25 = $24,100 in advance.

Therefore, the final quantity that they financed is $96,400 - $24,100 = $72,300.

They financed this amount at 5.50% for 30 years, which gives us the following method for calculating the monthly payment (P):

P = (r * PV) / (1 - (1 + r)^(-n))

in which:

r = month-to-month interest rate  PV = present value  n = overall range of payments  

Substituting the values, we get:

P = (0.00458 * 72,300) / (1 - (1 + 0.00458)^(-360))

P ≈ $410.66

We recognise that the monthly payment is $410.66 and we will calculate the interest portion of the primary monthly price as follows:

interest = balance * monthly interest price

interest = $72,300 * (5.50% / 12) ≈ $331.88

To calculate the amount of the primary monthly charge this is used to lessen the fundamental, we subtract the interest component from the total monthly payment:

$410.66 - $331.88 ≈ $78.78

Thus, the first monthly charge has about $78.78 allotted in the direction of reducing the principal.

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Pls help!! Which graph represents the following ellipse.

Answers

A graph that represents the following ellipse (x + 1)²/16 + (y - 3)²/36 = 1 is: C. graph C.

What is the equation of an ellipse?

Mathematically, the standard form of the equation of an ellipse is given by mathematical expression:

x²/a² + y²/b² = 1  

Where;

a represents the major axis.b represents the minor axis.

This ultimately implies that, the major axis of this ellipse is the x-axis. By critically observing the graph (see attachment), we can logically deduce the following values:

a = √16 = 4.

b = √36 = 6.

In conclusion, the standard form of the equation of this ellipse is given by (x + 1)²/16 + (y - 3)²/36 = 1.

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ive been trying to do this since this morning and can't, I need help
a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?

Answers

The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units'

Given data ,

Let the exponential growth equation be represented as x ( t )

Now , the average percentage change from the year 2000 - 2009 is calculated by

The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )

The total number of years = 9 years

So , the average percentage change = total percentage / number of years

On simplifying , we get

The average percentage change = 12.21 / 9 = 1.35667 %

b)

The population in 2009 was 37,000,000

So , the population growth rate r = 1.35667 %

And , the population in the years 2015 is given by

The number of years n = 6 years

x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶

On simplifying , we get

x ( t ) = 37,000,000 ( 1.013567 )⁶

x ( t ) = 40,115,896

Hence , the population in the year 2015 is 40,115,896

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help plsssssssssssssssssss

Answers

Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]

Step-by-step explanation:

     Both 3 and 9 are not irrational numbers, so the first option is incorrect.

     The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.

     The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;

                 [tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]

      They do, so this answer option is correct.

Complete a dilation with scale factor of 1/2 around the origin and then reflect over the y-axis. What are the new ordered pair of A’?

Answers

The new ordered pair of A’ are (-1, -2.25). Hence the correct option is b.

What are cο-οrdinates?

A cοοrdinate system in geοmetry is a technique that uses οne οr mοre integers οr cοοrdinates tο establish the accurate pοsitiοning οf geοmetrical οbjects οn a manifοld, such as Euclidean space. When lοcating a pοint οr οbject οn a twο-dimensiοnal plane, cοοrdinates—pairs οf numbers—are utilized.

The x and y cοοrdinates serve as a representatiοn οf a pοint's lοcatiοn οn a 2D plane. a grοup οf numbers used tο denοte certain lοcatiοns. The figure usually cοnsists οf twο integers. The frοnt-tο-back and tοp-tο-bοttοm distances are represented by the first and secοnd numbers, respectively. When there are 12 units belοw and 5 abοve, as in (12.5), the ratiο is 1.

Tο cοnduct a dilatiοn with a scale factοr οf 1/2 arοund the οrigin, multiply each pοint's cοοrdinates by 1/2. If the initial cοοrdinates οf pοint A are (x, y), then the dilated pοint A' cοοrdinates are:

A' = (1/2 * x, 1/2 * y)

We negate the x-cοοrdinate while keeping the y-cοοrdinate cοnstant tο represent the dilated pοint A' οver the y-axis. As a result, the final cοοrdinates οf A" are:

A'' = (-1/2 * x, 1/2 * y)

As a result, Anew "'s οrdered pair is (1/2 * x, 1/2 * y)

= ((1/2 × -2), (1/2 × -5))

= (-1, -2.25)

Thus, the new ordered pair of A’ are (-1, -2.25). Hence the correct option is b.

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zearn homework got 10 lessons to catch up on i will give some points if u help me with all my work

Answers

Answer: 1yd= 36in

1/3x36in

Solve the compound inequality and give your answer in interval notation. 8x-6>-30 OR -2x+4>=12

Answers

The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

A compound inequality contains at least two inequalities that are separated by either "and" or "or.  The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities.

The compound inequality 8x - 6 > -30 OR -2x + 4 >= 12 can be solved by solving each inequality separately and then combining the results.

Solve 8x - 6 > -30:
8x - 6 > -30
8x > -24
x > -3

Solve -2x + 4 >= 12:
-2x + 4 >= 12
-2x >= 8
x <= -4


The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

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Answer:-4.5

Step-by-step explanation:

-6+-30=-36

-36 divided by 8= -4.5

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