Answer:
no, no, yes, yes
Step-by-step explanation:
You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.
GraphThe attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.
(4, -5) . . . not a solution
(-1, 8) . . . not a solution
(7, 11) is a solution
(0, -3) is a solution
Please help! Select the equation that represents the following linear graph:
If [tex]y = \frac{(1 + x)u}{(1 + x)v} [/tex]
Find dy/dx
The value of dy/dx is ( v du/dx - u dv/dx)/v²
From the question, we have
y = (1+x)u/(1+x)v
y = u/v
dy/dx = d/dx(u/v)
d/dx(u/v) = ( v du/dx - u dv/dx)/v²
Derivatives:
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.
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Find the focus and the directrix of the parabola with the equation y = - 1/12 (x - 4) 2. (A) Focus = (4, -1), directrix is y = -5 (B) Focus = (4,2), directrix is y = 5 (C) Focus = (4,1), directrix is y = -5 (D) Focus = (4, -1), directrix is y = 5
The focus of parabola is (4 , -1) and directrix is 5
The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Focus: The point (a, 0) is the focus of the parabola
Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
Given equation of parabola is :
y = - 1/12 (x - 4) - 2
Comparing it with standard equation,
h = 4
k = 2
a = -1/12
using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)
=> focus = (4 , 2+(12/4×-1))
=> focus = (4 , 2-3)
=> focus = (4 , -1)
and directrix is : y = 2-(1/4×-1/12)
y = 2 + 12/4
y=2 + 3 => 5
So, the focus is (4,-1) and directrix is 5
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The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft. What is the mean height of the low tides? (I need to show work.)
The mean height of the low tides is 1.21 ft
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft
The mean of a sample is given by the formula =
summation of all observation / number of observation
mean = (x₁ + x₂ + x₃ + x₄)/ 4
mean = -0.22 + 2.64 - 0.22 + 2.64 / 4
mean = 4.48 / 4 = 1.21
Therefore, the mean height of the low tides is 1.21 ft
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Lightest weight
750g
0.7kg
7.5kg
705g
7.05kg
Answer:
.7 kg
Step-by-step explanation:
1. Convert answers in grams into kilograms
1000g = 1 kg
750g = .75kg
705g = .705 kg
2. Find smallest number of kg
= .7 kg
What transformation takes the graph of f(z) - 4z +9 to the graph of g (z) = 4x+7?
translation 2 units right
translation 2 units left
translation 2 units down
translation 2 units up
The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)
What transformation rule is used to transform a given function?
In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.
Horizontal translation
g(x) = f(x - k), where k > 0 for a translation in + x direction.
Vertical translation
g(x) = f(x) + k, where k > 0 for a translation in + y direction.
After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down. Then, we find the following transformation formula:
g(z) = f(z) - 2
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At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The table complete table that shows equivalent ratios is:
Toss Dollars
5 2
30 12
45 18
See image in the attachment that shows the points on a coordinate plane.
What are Equivalent Ratios?The ratios that give the same value when we compare them together are regarded as equivalent ratios.
For example, 2:3 is an equivalent ratio to 4:6, because 4/6 can be simplified as 2/3.
If it cost $12 to toss 30 rings, the ratio of dollars to number of toss would be: 12:30 = 2:5.
Let x = number of toss
Let y = amount in dollars
The equation that models the equivalent ratios can be written as y = 2/5x.
Therefore, when we have 2 dollars (y = 2):
2 = 2/5(x)
10 = 2x
10/2 = x
x = 5 toss
When we have 45 tosses (x = 45):
y = 2/5(45)
y = 18 dollars
The table of equivalent ratios would be:
Toss Dollars
5 2
30 12
45 18
The points, (5, 2), (30, 12), and (45, 18) are shown on the coordinate axes in the diagram below, where y = dollars, and x = toss.
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Find the coordinates of the point which divide the lines joining the following pairs of points in the given ratio
a. (5,8) and (-1,3) 2:3
b.(4,7) and (3,-2) 4:5
The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then
(x,y)=( (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n )
Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3
Therefore, we have
P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))
P(x,y)=(2.6,6)
Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
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solve the absolute value inequality.
|-3x|-7≥ 11
Answer:
x ≥ 6
Step-by-step explanation:
|-3x| - 7 ≥ 11 The absolute value of -3x is 3x
3x - 7 ≥ 11 Cancel the 7 by adding it on both sides
3x ≥ 18 To get x by itself divide 3 on both sides
x ≥ 6
I can determine if a function is linear or
nonlinear.
4. Determine if the table represents a
linear or nonlinear function.
Answer:
1st Table : Linear
2nd Table : Non-Linear
Step-by-step explanation:
To determine if the function is Linear or not , we find the change in y with a certain change in x
So for the 1st Table:
When x changes from x = 2 to x = 4 increased by 2
Then y changes from y = 3 to y = 0 decreases by 3
When x changes from x = 4 to x = 6 increased by 2
Then y changes from y = 0 to y = -3 decreases by 3
Since change in y is the same for the same change in x , Then the Function is Linear
So for the 2nd Table:
When x changes from x = 1 to x = 2 increased by 1
Then y changes from y = 1 to y = 4 increased by 3
When x changes from x = 2 to x = 3 increased by 1
Then y changes from y = 4 to y = 9 increased by 5
Since change in y is not the same for the same change in x , Then the Function is Non-Linear
Glad to Help
Find the slope of the line
Answer:
-3
Step-by-step explanation:
we sure y2-y1/x2-x1 to find slope
6+6/-4+0
12/-4
-3 is the slope
Hopes this helps please mark brainliest
If y vaires directly with x and y= 12 when x= 15. What is the value of x when
y=16?
The value of x=20, according to the given question.
What is meant by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to the given data in the question,
We know that y varies directly with x like that,
y=kx..................(1)
y=12 when x=15.
Now, we have to find the value of x when y=16.
Then, putting the given values of x & y in the eq. (1), and determine the value of k.
12=k(15)
[tex]k=12/15\\k=4/5\\[/tex]
Now, putting the value of k in the second statement in eq.(1), where only y's value is given.
[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]
Hence, the value of x=20.
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The equation for line t can be written as y+3= 1/2(x–7). Line u, which is perpendicular to line t, includes the point (3,3). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation of a line u perpendicular to line t and passes through (3, -3) is y = -2x + 3
How to represent the slope of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptLine t has equation as y + 3 = 1 / 2 (x - 7).
Line u is perpendicular to line t and it passes through (3, -3).
The products of the slope of perpendicular lines is equals to negative 1.
Therefore,
m₁ m₂ = -1
1 / 2 m₂ = -1
m₂ = -2
Therefore, the equation of the line have a slope of -2.
let's find the y-intercept using (3, -3)
-3 = -2(3) + b
b = -3 + 6
b = 3
Therefore, the equation in slope intercept form is y = -2x + 3.
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Help me please it’s confusing
Answer: 1/6
Step-by-step explanation:
To subtract fractions, you must have a common denominator. To do this, the common multiple of 3 and 2 is 6. So 2/3 is multiplied by 2/2 and 1/2 is multiplied by 3/3. The multiplication is valid since we multiplied by one, it didn't alter the value but rather it put it into an alternate, equivalent form.
The probability that a vehicle entering the Lu-
ray Caverns has Canadian license plates is 0.12; the
probability that it is a camper is 0.28; and the proba-
bility that it is a camper with Canadian license plates
is 0.09. What is the probability that
The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:
0.3214 = 32.14%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
The probabilities that compose the formula are listed as follows:
P(B|A) is the probability of the event B happening, given that the event A has already happened.[tex]P(A \cap B)[/tex] is the probability of both the events, A and B, happening.P(A) is the probability of the event A happening.The events in this problem are given as follows:
Event A: Camper.Event B: Canadian license plates.The probabilities are given as follows:
P(A) = 0.28, P(A and B) = 0.09.
Hence the conditional probability is obtained as follows:
P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.
Missing InformationThe probability asked is that a camper entering the Luray Caverns has Canadian license Plates.
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2. Determine if the diagram is a function.
Why or why not?
Please
Answer:
IT IS A FUNCTION
It is specifically a Surjective/ onto Mapping/function
Step-by-step explanation:
surjective or onto function is when y has an image in x
Answer:
The graph is a function
Step-by-step explanation:
-For every input (x) there is only one output value (y)
Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.
Ex.
X: 2, 4, 7 , 2, 5 This is not a function. More than one input for each output.
Y: 1, 2, 4, -3, 7
Ex.
X: 5, 6, -5, 8 this is a function. Exactly one input for every output.
Y: 1, 4, 5, 9
Are These acute obtuse or right
11. Corey bought 25 gallons of gas to fill up his pickup truck. He paid for the part of the total with a $25 gift card and was left owing $26. How much did he pay per gallon for the gas?
Answer:
I believe that the answer is $2.04, per gallon.
Step-by-step explanation:
I added the $25 he paid with the gift card, and the $26, which was $51 that Corey paid in total. Corey had gotten 25 gallons and they want to figure out how much he paid for each gallon. So we take the total he spent divided by the number of gallons he had gotten. So 51/25=2.04
Hope this helps!!!!
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample. "Two supplementary angles are not congruent."
The counterexample for "Two supplementary angles are not congruent." is
angle 100° and angle 80° are supplementary angels
angle 90° and angle 90° are supplementary angels
The instances show supplementary angles that are not congruent
What is counter examples?A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.
Counterexamples provides instances that opposes the statement
In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement
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Simplify: 3√50+ √24 - 2√72
A. 3√6 +2√2
B. 3√9+2√5
C. 3√2+2√6
D. 10√2+2√6
Answer:
Step-by-step explanation:
13+(-3)^2+4(-3)+1- {-10-(-6)}
_________________________
[4+5}/ [4^2-3^2(4-3)-8]+12
15/3=5
GCF ( 160, 320, 480)
The greatest common factor of 160, 320 and 480 will be 160.
What is the Greatest Common Factor?The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.
In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)
Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.
Factorize number 160
160 = 2×2×2×2×2×5
Factorize number 320
320 = 2×2×2×2×2×2×5
Factorize number 480
480 = 2×2×2×2×2×3×5
The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.
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Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
Step-by-step explanation:
the list of your answer options has a different sequence than the picture.
I assume the picture shows us the correct sequence.
the correct answer is
D : the y-values are all greater than our equal to 2
why ?
because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.
so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.
Dylan has a bag of 1256 rubber balls to hand out as prizes at a town festival. There are 13 games at the festival. About how many rubber balls should he give each game?
Answer The answer is 96 but as a fraction 96 8/13
Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.
i bet u cant solve it
For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
As given in the question,
Given :
Pair of parallel lines are AG and BH.
CF is the transversal.
Transversal CF intersect line AG at point D and
Transversal CF intersect line BH at point E
Four pair of corresponding angles
Two pair of alternate interior angles
Corresponding pair of angles in the pair of parallel lines are congruent.
∠ADE ≅ ∠BEF
∠ADE and ∠BEF are corresponding angles.
Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
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=
4(7x), what is the value of a(-2)
The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.
As given in the question,
Given expression is equal to :
f(x) = 4 ( 7x )
Calculate the value of the given function for x = -2 is given by :
Substitute value of x = -2 we get.
f(-2)
= 4 ( 7 ( -2) )
Seven is positive and 2 is negative , multiplication of positive to negative is always negative.
So, 7 ( -2 ) is -14 Substitute in above equation we get,
= 4 ( -14 )
= -56
Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to
f( -2 ) = -56.
The complete question is :
If f(x) = 4 (7x) , what is the value of f(-2)?
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Hailey used math to describe design in nature:
the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals.
Math shows the world is designed, and that design is _______.
The math shows the world is designed, and that design is symmetry and spirals.
How is math found in nature What is the significance of mathematical patterns in nature?
Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.
Here,
If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.
Hence, the math shows the world is designed, and that design is symmetry and spirals.
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Complete sheet below
Answer:
1: D
2: B
3: A
D: C
Step-by-step explanation:
. You get an auto loan at 3.5% interest for 5 years; please answer the following.
A. You can afford a $250 per month car payment; how expensive a car can you afford?
B. You purchase a car for $8000 with a $2000 down payment, what are your monthly payments?
Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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A particle moves with velocity dx/dt in the x-direction
and dy/dt in the y-direction at time t in seconds, where
dx/dt = 3t² and dy/dt = 12t.
Find the distance traveled by the particle from time
t=0 to t= 3.
Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.
How to get distance/displacement using velocity?
Velocity is defined as the rate of change of position or the rate of displacement.Velocity = dx/dt that is change in position x with respect to time t.Integration is anti derivative for any quantity. Hence to get displacement using velocity, integrate to with respect to 't' and substitute values of t accordingly.According to given data:
A particle moves with velocity (dx)/(dt) = 3t² in x- direction
and (dy)/(dt) = 12t in y-direction
Integrating both sides of these derivatives with respect to t
x= ∫3t² dt = (3t³)/3 + A = t³ + A
where A is integration constant
y= ∫12t d t = (12t²)/2 + B = 6t² + B
where B is integration constant
At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.
Therefore, the difference in position of a from t = 0 t = 3 is
27 + A - (0 + A) = 27 units.
Similarly,
At t = 0 , we get y = B and at t = 3 we get
y = 6 * 3² + B = 54 + B
Therefore, the difference in position of y from t = 0 tot t = 3 is
54 + B - (0 + B) = 54 units.
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The production of a gold mine decreases by 5% per year.
What is the approximate half-life for the production decline?
Based on this approximate half-life and assuming that the
mine's current annual production is 5000 kilograms, about
what will its production be in 10 years?
Answer:d
Step-by-step explanation:d