Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13

In 2000 there were 419 million people 65 or older

In 2017 there were 656 million people 65 or older

a)

To calculate the absolute change in the number of people 65 and older you have to subtract the initial number (on year 2000) from the final number (in year 2017)

The absolute change is 240millions

b)

The relative change is the percentage of change. To calculate it you have to calculate the difference between the final number and the initial number, divide the result by the initial number and multiply it by 100

The relative change is 57.30%

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

Let's use the distance formula to solve for the distance between the two given points!

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

Now, we input the points:

(5-(-2) + (-2-4)

(which will equal...)

(7) + (-6)

Now we input the solutions we got here to the distance formula:

[tex]d =\sqrt{(7)^2 + (-6)^2[/tex]

(we simplify....)

[tex]7^2 = 49\\(-6)^2 = 36[/tex]

input these solutions into the distance formula again...

[tex]\sqrt{49 + 36} = \sqrt{85}[/tex]

85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.

Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is [tex]\sqrt{85}[/tex].

To find the value of x, use the vertical angle theorem.

Vertical angles are congruent.

Thus we have:

6x - 10 = 5x + 1

Solve for x.

6x - 10 = 5x + 1

Add 10 to both sides:

6x - 10 + 10 = 5x + 1 + 10

6x = 5x + 11

Subtract 5x from both sides:

6x - 5x = 5x - 5x + 11

x = 11

To find the value of y, use corresponding angles thoerem.

When two parallel lines are crossed by a transversal, the angles in matching corners are correponding angles.

Corresponding angles are congruent.

Thus, we have:

y = 6x - 10

Substitiute x for 11:

y = 6(11) - 10

y = 66 - 10

y = 56°

ANSWER:

x = 11, y = 56°

Step 1:

Write the two systems of equations

y = 3x = 2

3x = y - 3

Step 2:

Substitute y from the first equation into the second equation

Final answer

NO SOLUTION

Answer:

4/15

Step-by-step explanation:

4/15 = 0.26666666...

We are given that Mike reads 5 pages an hour. This is the quotient of pages with respect to time. In this case, the time is the independent variable and the number of pages is the dependent variable since the number of pages depends on the time interval that is considered.

A circle has 360°

since the diameter cuts in half the circle

The measure of the arc of half the circle (semicircle) measure arcAB is

AB=180°

Then correct answer is

option a

Since we have the value for selling each shirt, the earnings that came from the hats sold and the total earnings we can complete equation using a linear equation in which the cost of each shirt will represent the slope and the y-intercept will be the earnings that came from the hats, like this:

then clear the equation for x in order to find how many shirts were sold

The system of equations has 3 cases

1. y = ax + b, y = ax + c

Since the coefficient of x and y are the same, and the y-intercepts are different, then

The two lines are parallel

2. y = ax + b, y = dx + c

Since the 2 lines have different coefficients of x, then

The two lines are intersected

3. y = ax + b, y = ax + b

Since the two lines have equal coefficients of x and equal y-intercepted, then

The two lines are coincide (same line)

6. a)

Since the system of equations is

The coefficients of x not equal

Then from case 2 above

The two lines are intersected

6.b

Since the system of equations is

The coefficients of x are equal

The y-interceptes not equal

Then from case 1 above

The two lines are parallel

Step 1:

Write the function

Step 2:

Factorize both the numerator and the denominator.

Step 3:

A hole is a common factor between the numerator and the denominator.

Hole: x + 5 = 0

x = -5

Final answer

Hole is -5

Answer:

seven and one-tenth.

Explanation:

To name decimal number, we first name the values before the decimal point, in this case, seven

Then, we add an and that corresponds to the decimal point

Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.

Therefore, the name of the decimal number 7.1 is:

seven and one-tenth.

From the figure, the radius of the sphere is:

The volume of the sphere is given by the formula:

Using the value of the radius:

Approximating to the nearest cubic inch:

ther

Answer:

Step-by-step explanation:

first find seconds in an hour

60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour

then multiply 8 by 3600 to see how many feet per hour

28,800

we need miles so there are 5280 feet in a mile

28800/5280 is 5.45454545 or 5.455 miles per hour

To be able to determine which among the choices is a proportion, you check if each side has the same common ratio.

A. 8/10 = 6/8

Ratio: 0.80 = 0.75 (Not Proportional)

B. 3/4 = 12/15

Ratio: 0.75 = 0.80 (Not Proportional)

C. 4/6 = 9/12

Ratio: 0.67 = 0.75 (Not Proportional)

D. 6/9 = 8/12

Ratio: 0.67 = 0.67 (Proportional)

Since the ratio of each side of letter D is equal, Letter D is the one that is in Proportion.

Answer: No solutions

Step-by-step explanation:

[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]

However, as absolute value is non-negative, there are no solutions.

The formula to calculate compound interest is given to be:

where:

The following parameters are given in the question:

We can substitute these values into the formula to calculate the final amount as follows:

Solving, we get:

The amount after 17 years is $154,577.64

To solve this problem I'll use proportions.

2 1/8 cups ------------------------ 1/2 cup of chocolate.

x ----------------------- 1 cup od chocolate chips

x = (1*2 1/8) / 1/2

x = 17/8 / 2

x = 4 % cups of peanuts

Randy and Wade started riding a bike at noon. Noon is 12 pm. Both of them are heading towards each other and 60km.

let

speed of wade = x

speed of Randy = 4 + x

They met each other at 1:30 pm. 12 pm to 1:30 pm is 1 hour 30 minutes(1.5 hours). Both of them will cover a total distance of 60km.

Therefore,

speed of wade = 18km/hr

speed of Randy = 4 + 18 = 22km/hr

To estimate each number by rounding it to the nearest ten, we will look at the unit digit,

If it is less than 5, then we replace it by 0 and keep the ten-digit as it

If it is 5 or more, then we will replace it by 0 and add the ten-digit by 1

Let us do that with every number

28, the unit digit is 8 which is greater than 5, then replace it by 0 and add 2 by 1

28 rounded to 30

51, the unit digit is 1 which is less than 5, then replace it by 0

51 rounded to 50

76, the unit digit is 6 which is greater than 5, then replace it by 0 and add 7 by 1

76 rounded to 80

Now let us multiply them

The product of the given numbers is 120,000

You have that the movie aspect ratio is 2.15 : 1, that is, you have following relation between width and height:

2.15/1 = 2.15 = 215%

that is, the widht is 2.15 times the height, or the width is 215% longer than height.

In order to determine what is the percentage of the image shown, you calculate the percentage that widht is more longer than height. You have a TV of 62.72 width and 35.28 in height:

62.72/35.28 = 1.77 = 177%

that is, width of TV is 1.77 times longer than height, or width is 177% longer.

Hence, on TV will be not possible to watch the complete image. And the percentage shown is of 177%.

It is the movement on the number line is right right left

The option (d) is correct .

Given,

The movement on the number line for the calculation

21 - (- 15) + (- 30)

To find the which of the following correctly represents the movement of calculation?

Now, According to the question:

21 - (- 15) + (- 30)

21 + 15 - 30 = 6

right right left

Hence, It is the movement on the number line is right right left

The option (d) is correct.

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Given a rectangular box with an open top and square base, the dimensions of the box are:

The volume can be calculated as:

The area of the sides is:

The area of the base:

There are 4 lateral sides and 1 base (the top is open), so the total surface area is:

We have a fixed volume of 2048 in³, then:

Using this result on A_total:

To find the minimum surface area, we take the derivative:

Now, we calculate the minimum total area using a:

The basic form of the equation is;

4p (x- h)= (y - k)²

where (h, k) is the vertex and p is the distance from the vertex to either of its directrix or the focus

But, focus is = (1, -4) adn directrix = 2

So, the perpendicular point is :

(1.5 , -4)

p = -0.5

Putting all the values into the formula

4p (x- h)= (y - k)²

4(-0.5)(x - 1.5) = (y - (-4)²

simplify

-2(x - 1.5) = (y + 4)²

-2(x - 1.5) = y² + 8y + 16

Divide through the equation by -2

x - 1.5 = (-1/2) y² - 4y - 8

Add 1.5 to both-side of the equation

The given expression is

where x=3

the dot in the expression means multiplication

substitute into the expression above we have

Applying BODMAS

Therefore the value of the expression is 72

As given by the question

There are given that the measuring circle.

Now,

From the given circle, the length of the MN is 28 units, because the half of the length of the MN is 14. So just multiply by 2 into half of the given value.

Hence, the length of MN is 28 units.

Now,

For the measure of MN:

The measurement of the angle MN is 74 degrees.

Hence, a measure of arc MN is 74 degrees. and the length of segment MN is 28 units.

Given the equation:

Where y represents the total length of the road (in miles), and x represents the number of days the crew has worked.

(a) What was the road’s length when the crew started working?

When the crew started working we have x = 0. Then:

The road's length is 53 miles.

(b) What is the change per day in the road’s length?

The change per day in the road's length is 2 miles/day.

The values of the composition of the functions are:

(f o g)(x) = -x³ - x + 1

(g o f)(x) = -x³ - x - 1

To find the value of the composition of a given function, the inner function is first evaluated, then the output of the inner function is then replaced into the outer function and simplified.

Given the functions:

(f o g)(x) = f(g(x))

Substitute -x for x into the function f(x) = x³ + x + 1:

f(g(x) = (-x)³ + (-x) + 1

f(g(x) = -x³ - x + 1

(g o f)(x) = g(f(x))

Substitute x³ + x + 1 for x into the function g(x) = -x:

g(f(x)) = -(x³ + x + 1)

g(f(x)) = -x³ - x - 1

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For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.

Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".

Kareem needs to save $13,800 in total

He already got $3000 from his uncle.

Thus, he needs $13,800 - $3000 = $10,800 more

He will need to save up $10,800 in 3 years, that is 3 x 12 = 36 months

To find the amount he must save each month, we will divide $10,800 by 36: