Answers : • center c and scale factor 2• center a and scale factor 5• center c and scale factor 1• center a and scale factor 2

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.

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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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

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

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.

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.

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:

Let's solve the given logarithmic expression:

We get,

Therefore, m = 3.

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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SOLUTION

Density is calculated as

The side lengths of the aluminium cube has been given as 0.5 m

The volume becomes

so the volume is 0.125 cubic-meters.

The mass becomes

Hence the answer is 337.5 kg

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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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

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).

1) Let's visualize it to better understand:

A right rectangular prism is made from

2 faces 6 x 7

4 faces 20 x 6

Since we have rectangles, we can write calculating the area of each rectangle.

S base = 2 (6x 7) ⇒ S base = 84 cm²

S faces = 2 (20 x 6) ⇒ S faces = 240 cm²

S faces = 2 (20 x 7) ⇒ S faces = 280 cm²

2) Then the total surface area

84+240+280=604 cm²

To study population growth, we use the following formula

Where,

Let's replace the values above, and solve for t.

The given function is

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

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

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:

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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

The diagram below shows all the possible outcomes from rolling a pair of six sided dice.

The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.

Total number of outcomes = 36

Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3

Thus, the probability of rolling a sum greater than or equal to 11 is

3/36 = 1/12

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

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

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

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

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 a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?

The equation 4x +8=28 could be used to describe a scenario like this below:

In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?

Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.

With that equation you can find that:

4x +8=28

4x+8 -8 =28-8

4x=20

x=5

5 cans of soda.

• 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