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f(1) = 10

Given f(x) = 3x + 7

To find f(1), replace x by 1 in the equation above

f(1) = 3(1) + 7

= 3 + 7

= 10

To find the acale factor we need to solve the following equation:

This comes from the fact that the biggest sides of both triangles have to be realted.

Therefore the dilation factor is 0.4.

Given that the volume of gas kept at constant pressure varies inversely with the temperature T and when the temperature is 50 degrees, the volume is 20 cubic feet.

We have to find the volume of gas when the temperature is 100 degrees.

Since it is given that volume varies inversely with the temperature. It means

Substitute T1 = 50, V1 = 20, T2 = 100.

Thus, the volume of gas when the temperature is 100 degrees is 10 cubic feet.

N 11

Remember that

The law of sines

In this problem

Solve for x

sinX=(14.9*sin71)/25.5

If the relation between the book read by Alexa and the number of months she takes to read them is directly proportional, then, if x is the number of months she took to read 120 books, you can write:

By solving for x and simplifying, you obtain:

Hence, Alexa read 120 books in 20 months

We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.

We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:

where v is speed, d is distance and t is time, we know that for the first jet:

Where d₁ represents the distance of the first jet from the starting point. For the second jet:

Where d₂ represents the distance of the second jet from the starting point.

We also know that:

As:

Thus, we have that:

This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).

The AAS triangle congruence postulate proves that these triangles are congruent .

In the question,

two triangles are given that are triangle ABC and triangle PQR .

Consider the triangle ABC and triangle PQR .

we can see that

(i) angle C = angle R           .....given in the figure

(iii) angle B = angle Q         .... given in the figure

(ii) side BC = side QR          ....given in the figure

From the above three statements we conclude that

ΔABC ≅ ΔPQR

both the triangles KLM and PQR are congruent by AAS Congruence Postulate .

Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .

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The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.

The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.

The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.

Slope m = (y2-y1) / (x2-x1)

Let,

(x1, y1) = (-1, -1)

(x2, y2) = (2, 4)

Slope (m) = ((4) - (-1)) / ((2) - (-1))

                = 5/3

y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))

                         => y+1 = 5/3(x + 1)

                         =>y = 5/3(x+1)-1

Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.

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Answer

39 child tickets were sold that day

Step-by-step explanation

Variables

• x: child tickets sold

• y: adult tickets sold

Given that four times as many adult tickets as child tickets were sold, then:

If 1 child ticket cost $5.70, then x child tickets will cost 5.7x dollars.

If 1 adult ticket cost $9.20, then y adult tickets will cost 9.2y dollars.

Given that the theater sold tickets for $1657.50, then:

Substituting the first equation into the second one and solving for x:

Answer:

which one

Step-by-step explanation:

don't forget to follow rate like

The given function is

If we evaluate the function when x = 0, we get

The slope-intercept form of the line is

where m is the slope and b is the y-intercept

so we only need to substitute the values into the equation

m=2

b= -5

the equation is

Let's solve the given logarithmic expression:

We get,

Therefore, m = 3.

ANSWER

B. 9.99 + 1.29n ≤ 50

EXPLANATION

The total amount of money she spends at the store has to be at most, the value of the gift card $50. This is the cost of the album, 9.99, and then 1.29 for each song. If the total number of songs is 'n', then for n songs, she'll spend 1.29n. In total she spends: 9.99 + 1.29n at the store. The equation is

The surveyors are really interested in all registered boters in Huntsville, therefore the first answer is F.

Since they are only doing a sample of people with phones the real population is all registered voters with telephones, therefore the second answer is C.

The sample for this survey is the 550 voter surveyed.

To find the proportion of people who said they vote for brown we divide the number of this people by the total of people surveyed:

Therefore the proportion was 0.4418

Given the graph represents the amount of water in the aquarium versus time.

A) As shown in the graph :

as the time increases the amount of water in the aquarium decreases

The rate of water decreasing =

so, the rate = 60 litres per minute

Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:

Now, let's use the given area and solve it for x:

Since the "path" already has fence, the amount of fence needed is 2x:

Given a point (x, y), let's evaluate the transformations:

- Translation 6 units to the right.

Means moving the point 6 units in the horizontal direction; to the right.

The new point will be (x + 6, y).

- Translation 2 units down.

Means moving the point 2 units down; in the vertical direction.

The new point will be (x + 6, y - 2).

Answer: (x + 6, y - 2).

Step 1

Given;

Required; To find out how many balls are thrown at him if he catches 14 balls.

Step 2

There are two approaches to determine the number of balls thrown at Marcus

Approach 1

Draw the table;

we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.

Answer=35 balls

Approach 2

Hence, 35 balls were thrown at Marcus

Answer:

Explanation:

Here, we want to know the table that represents a function

For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.

What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value

Now, looking at the table given:

In this problem we have that

m by supplementary angles

so

mmtherefore

the answer is

Part 2

the transformations that produce triangle ABC are

1) A dilation from the with scale factor of 2

2) A reflection across the x-axis

3) A translation of

Answer:

Explanation:

In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).

So, by Pythagorean theorem, we can write the following equation

Now, we can expand the left side

Then, subtract x² from both sides

Subtract 64 from both sides

Finally, divide by 16

Therefore, the value of x is 12

Solution:

The future price p(t), in dollars, can be modelled by the exponential function;

(a) The current price is;

ANSWER: $800

(b) The price 8 years from today;

ANSWER: $975

Horizontal addition

Row 1 a + 12 + b +6 =37

Row 2

Row 3

Row 4

Now Let us add the columns

Column 1

Column 2

Column 4

Column 2

Hence, Video games under 10-12 is c=17, gotten from column 2

Vertical total under 16-18 is h=35 gotten from column 4

Hence, the horizontal total of the video game is 52

Since h is gotten, we can solve for 7 to 9 vertical total

Hence, the 7 to 9 vertical total is 29

Hence, Darts under 7 to 9 is 4

Darts under 13 to 15 is b

Hence, Darts under 13 to 15 is 15

Basket ball under 13 to 15 is e

Hence, Darts under 13 to 15 is 14

Video Games Horizontal total is d,

Hence, the Horizontal total of the Video game is 52

Basketball horizontal total is f

40+e=f

Hence, the horizontal total of the Video game is 54.

Hence, the above table fill the empty space

We have to solve this equation:

We can solve it for D by adding 37 on both sides of the equation as this won't change the equality:

Answer: D = 77

• Line x = -2 is a vertical line that passes through point x = -2

Given the point ( 3;-5)

• We know that perpendicular lines have opposite reciprocal slopes , so the slope of the line will be

• m = 1/2

• so , the standard formula for a line : y = mx +c

at point ( 3-5) , we will have :

-5 = 1/2(3) + c

Therefore c = -5 -3/2

= -13/2

• Our y- intercept will be -13/2

• Finally , our equation of the line will be :

y = 1/2x -13/2

The error is in the distribution property application, in the way the signs are multiplied.

We will look at it in detail:

When (-2) is multiplied by (-12h) it should end with a positive sign, as (-a)*(-b)=a*b

By rotating the shape of the graph, we get the following cylinder:

So we have a cylinder with:

• radius r = 4,

• height h = 6.

The volume of the cylinder using π = 3.14 is given by:

The solid obtained is a cylinder of volume 301.44.

1. The hypothesis tested are given as follows: A. H0:μdiff=0 vs. Ha:μdiff≠0.

2.

3. Based on the p-value, we do not have enough evidence that the null model is not a good fit for our observed data.

4. The 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015 is of (-8.34, 12.54).

At the null hypothesis, it is tested if there has not been change, that is, if the mean is of zero, hence:

H0:μdiff=0

At the alternative hypothesis, it is tested if there has been change, hence:

Ha: μdiff≠0

Considering a two-tailed test, as we are testing if the mean is different of a value, with 10 - 1 = 9 df, and a significance level of 1 - 0.99 = 0.01, the critical value is of:

|t| = 3.25.

The test statistic for the t-distribution is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The parameters in this problem are given as follows:

[tex]\overline{x} = 2.1, s = 10.159, n = 10, \mu = 0[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{2.1 - 0}{\frac{10.159}{\sqrt{10}}}[/tex]

t = 0.65.

Considering a two-tailed test, with t = 0.65 and 10 - 1 = 9 df, the p-value is of:

0.2660.

The confidence interval is given as the estimate plus/minus the multiplication of the critical value and the standard error.

Hence the lower bound of the interval is of:

2.1 - 3.25x10.159/sqrt(10) = -8.34.

The upper bound of the interval is of:

2.1 + 3.25x10.159/sqrt(10) = 12.54.

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Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets