How do you decide which operations to use when writing an equation?​

Answer:

The terms are rearranged, so the Commutative Property is correct.

Answer: (3,-13)

Step-by-step explanation:

[tex]f(x)=-x^2-4\\x=3[/tex]

Step-by-step explanation:

We need to find the circumference of the equation.

One circle circumference is a circle full rotation.

[tex]c = \pi(d)[/tex]

[tex]d = 2r[/tex]

[tex]c = 2r\pi[/tex]

R is 14.

[tex]c = 28\pi[/tex]

We need a rotation 10times so

[tex]10 \times 28\pi = 280\pi[/tex]

Using linear regression, the function that best fits the data in the scatter-plot is given by:

f(x) = 1/2x + 1.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the context of the problem.

The scatter-plot in this problem contains these following points:

(-16, -7), (-9, -5), (-3, -3), (1, 2), (5, 4), (8, 3) and (14,6).

Inserting these points into a calculator, the equation is given by:

f(x) = 0.46835x + 1.

Approximating the slope to 1/2 considering the given options, the function is given by:

f(x) = 1/2x + 1.

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D has a value of 13 using vertical angles.

What is a vertical angle?

Assuming that C and D constitute vertical angles

The formula is C = (-3x) + 58 and D = x - 2.

We must ascertain what D's measurement is.

Vertical angles are really a pair of opposing angles created when two lines cross.

A and B in the figure represent vertical angles. C and D are also.

Angles vertically are always congruent. Accordingly, in this illustration, A, B, and C, D

Therefore, value of C = D (-3x)+ 58 = x – 2

By assembling,

(-3x )- x = (-2) - 58

By doing more math, 4x = 60 (-4x = - 60)

4 x = 60/4 x = 15 when both sides are divided.

So, ∠D = (x - 2) and  

= 15 - 2 

So, ∠D = (x - 2) and  

Consequently, D has a value of 13 using vertical angles.

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Answer:

A composite number is a whole number greater than 1 with more than two factors.

Step-by-step explanation:

The equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation of the function:

p(x) = 140,000(0.965)ˣ

Which is the annual population decrease of giraffes in the wild of 3.5% due to development.

Plug x = 1.0085

[tex]\rm p(x) = 140,000(0.965)^{1.0085}[/tex]

S(p(x)) = 140,000(0.965)ˣ(1.0085)ˣ

S(p(x)) = 140,000(0.9732)ˣ

Thus, the equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.

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Solving the questions from the given equations

1)the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2

2) The cost per head per month is $23.4

3) The cost per head per month is $39

What is Equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

1) The grains use feed for one horse = 4.5pound

The cost of 1 bag of grain = $27 per 50lb

The cost of 1lb grain = $0.54

Now the monthly cost of the grain will be:

Cost/head/day x # of days in month = Cost/head/month

$0.54 x 30 = $16.2

Hence, the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2

2) The amount of grain use to feed for one head = 1.5pound

If the grain is feed twice a day = 1.5 x 2

                                                   = 3.0

The cost of the grain = $13 per 50lb

The cost of 1lb grain = 13 / 50

                                  = $0.26

The cost of grain feed in one day = 0.26 x 3

                                                        = $0.78

The cost of per head per month =

0.78 x 30 = $23.4

Hence, The cost per head per month is $23.4

3)The amount of grain use to feed for one head = 2.5pound

If the grain is feed twice a day = 2.5 x 2

                                                   = 5pounds

The cost of the grain = $13 per 50lb

The cost of 1lb grain = 13 / 50

                                  = $0.26

The cost of grain feed in one day = 0.26 x 5

                                                        = $1.3

The cost of per head per month =

1.3 x 30 = $39

Hence, The cost per head per month is $39

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(tan x + cot x) sin x * cos x is 1

(tan x + cot x) sin x * cos x

= (tan x + 1 / tan x) sin x * cos x               because cot x = 1 / tan x

= (((tan x) ^2 + 1) / tan x) sin x * cos x             because (tan x) ^2 +1= (sec x) ^2

= (sin x / cos x) tan x

= tan x / tan x

= 1

The graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted

The slope of the line = 4/3

The line is passing through the point = (1,3)

Here we have to use the point slope form the line

The point slope form of the line = [tex](y-y_{1} )= m(x-x_{1})[/tex]

Where m is the slope of the line

[tex](x_{1},y_{1} )[/tex] is the coordinate of the point

Substitute the values in the equation

(y-3) = 4/3 (x-1)

y-3 = (4/3)x - 4/3

y = (4/3)x - 4/3 + 3

y = (4/3)x + 5/3

We got the slope intercept of the line.

Plot the graph using the slope intercept form of  the line

Hence, the graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted

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We will establish simple proportions. If [tex]16[/tex] miles takes [tex]20[/tex] minutes, how many minutes for [tex]12[/tex] miles?

That makes [tex]12[/tex] miles in [tex]15[/tex] minutes.

Answer: B. Function g is the result of f being translated left 2 units and up 4 units. and C. The graph of function f opens upward.

Step-by-step explanation:

It is translated 2 units to the left and 4 units up because in the function of a(x-h)^2k, h represents the function going left of right and k representing the function going up and down. a represents it stretching if it is greater than 1 and compressing if less than 1 and if it is negative it reflects over the x axis however here nothing changed for the a so it did not stretch nor compress nor reflect over the x axis

The measurement that does not represent the dimension of the triangle is 15, 30 and 45cm

The measurement that does represent the dimension of the triangle is 4, 8 and 10 cm.

Two triangles are similar if the ratio of the side lengths of the triangle are equal.

The ratio of the length of the triangles are 6 cm : 12 cm : 15 cm

Express the ratio in its simplest form - 2 cm : 4 cm : 5 cm

Ratio of 12, 24 cm and 30cm in its simplest form - 2 : 4 : 5

Ratio of 10, 20 and 25cm in its simplest form - 2 : 4 : 5

Ratio of 18, 36, 45cm in its simplest form - 2 : 4 : 5

Ratio of 15, 30 and 45cm in its simplest form - 1 : 2 : 3

Ratio of 4, 8 and 10 in its simplest form - 2 : 4 : 5

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Step-by-step explanation:

Make the facts and then you can get the answer easily

Answer:

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35

Step-by-step explanation:

Given a simple random sample, the size is 40 senators.

Since the relevant statistic is the sample mean, 60.35 years.

Calculate t as:

*Significance level is 0.05.

Area of 0.05, one-tail yields t=1.685.

Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35

Answer:

x = 70

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the interior angles and equate to 540

x + 160 + 110 + 105 + 95 = 540

x + 470 = 540 ( subtract 470 from both sides )

x = 70

The speed of the particle at time t=4 is 5 units.

We are given the x(t) vs time curve.

To find:

Speed of particle at t = 4

We know that the slope of x-t curve represents the speed of the particle.

To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4

Slope = y₂ -y₁ / x₂ - x₁

Slope = 40 - 10 / 6 - 0

Slope = 30 /6

Slope = 5

From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.

So the value of speed is also 5 units.

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Answer: if you are talking about mixed number form the answer is 1 1/11 the improper/exact form would just be twelve over eleven (12/11)

Step-by-step explanation:

The mystery number is y = 0.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), operations, variables, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Let's assume the mystery number to be y.

When we multiply it by 1, add 5, and finally subtract by 2 we obtain 3.

Using the statement we obtain the expression,

y × 1 + 5 - 2 = 3

y + 5 - 2 = 3

y + 3 = 3

Subtracting 3 from each side of the equation,

y + 3 - 3 = 3 - 3

y = 0

Hence the mystery number is 0.

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1) Judging by the picture, which resembles a construction done with a compass with the same distance, therefore we can tell a regular polygon.

2) We can also trace some line segments then we'll have a:

It is to be noted that the distance between P and ρ is: [tex]\approx[/tex] 15.52

This solution is arrived at using the Line Segment theorem. See further explanation below.

The length of the line segment connecting two points in a plane is defined as the distance between two points. The method for calculating the distance between two locations is often written as

[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]

Hence, since we have ρ is to contain two points, we will solve as follows:

Distance between ρ and P where ρ is (0, -3) and (7,4)

we have to multiply the coordinates.

To multiply coordinates, you have to multiply the corresponding values.

That is

[tex]x_{1} \times x_{1} [/tex]

and

[tex]y_{1} \times y_{1}[/tex]

In this case:

x1 = 0

[tex]x_{1} = 0[/tex]

also

[tex]x_{1} = 7[/tex]

[tex]y_{1} = - 3[/tex]

also

[tex]y_{1} = 4[/tex]

Hence, for

[tex]x_{1} = 0 \times 7 = 0[/tex]

for

[tex]y_{1} = - 3 \times 4 = 12[/tex]

Hence, solving for the distance between P and ρ, we'd use coordinates of P as = (4, 3); and coordinates of ρ as = (0, -12)

Recall that distance is given as

[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]

Hence,

d = √((0-4)² + (-12-3))²)

[tex]d = \sqrt{{(( {0 - 4}^{2} }) + { (- 12 - 3)}^{2} } [/tex]

Expand the brackets

[tex]d = \sqrt{ { - 4}^{2} + ( { - 15}^{2} } )[/tex]

[tex]d = \sqrt{16 + 225} [/tex]

[tex]d = \sqrt{441} [/tex]

d = 15.5241746963

Approximately,

d = 15.52

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a. Trapezoidal Rule- 9.413607

b. Midpoint Rule-9.393861

c. Simpson's Rule -9.400407

a. We use n=8 for this integral, .Δt=4-0/8=0.5

Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]

#For the Trapezoidal Rule:

[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]

=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]

=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]

=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]

≈9.413607

Hence, the approximate integral value using Trapezoidal rule is 9.413607

b.For the Midpoint Rule, we calculate the integral as:

[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]

x1 is the midpoint of the ith interval.

From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are

[0.25,0.75,1.25,2.25,2.75,3.25,3.75]

We therefore have the integral value as:

=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]

Hence, the approximate integral value using the Midpoint Rule is 9.393861

c. For the Simpson's Rule, we calculate the integral rule as follows:

Hence, the approximate integral value using the Simpson's Rule is 9.400407

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The value of x is 2 is and y is -1 is after solving equation by elimination method

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

5x + 7y=3 .....(i)

-5x + 7y=-17......(ii)

Solve equation ii and iii

-5x + 7y=-17

5x + 7y=3

14y = -14

y = -1

put the value of y in equation 1

5x + 7y=3

5x + 7(-1)=3

5x - 7 = 3

5x = 10

x =2

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An integer exists a whole number that can be positive, negative, or zero and is not a fraction.

Unlike fractional numbers, integers can only be positive, negative, or zero. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Any number that exists a part of a collection of all the aforementioned number categories is considered an integer. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

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Number of bags= 16

Bag weight= 1.8 pounds

Then, number of pounds is

= 16x 1.8 = 28.8 pounds of cherries

Mean = Sum of points/ number of points

Median

Answer:

4 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Make them equivalent

4 [tex]\frac{2}{3}[/tex]  if I multiply the numerator (top) and the denominator (bottom) by 2 I get

4[tex]\frac{4}{6}[/tex]

4 [tex]\frac{5}{6}[/tex] is greater than 4 [tex]\frac{4}{6}[/tex]

Answer:

k = -2.

Step-by-step explanation:

By the Factor Theorem, if x - 1 is a factor then p(1) = 0.

So, p(1) = (1)^2 + 1  + k = 0

k = -1 - 1

k = -2.

Answer: 65 min

 7 pounds

Step-by-step explanation:

The error interval of the area a of the shaded region

What is Error Interval?

Error intervals are the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated.

Given,

Area of the circle  = 67.1cm²

Area of the square  = 12.3cm²

According to the question:

The formula for the area of the shaded

region on the diagram is:

Area of the circle - Area of the square

Putting the value of Area of circle and Area of square

= 67.1cm² - 12.3cm²

= 54.8cm²

The Error interval of area a = 54.8 + 0.5   and 54.8 - 0.5

                                             = 54.85        and 54.75

Hence, Area of shaded region is 54.85< a < 54.75        

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