The figure shows the measures of various angles of a roof and it supports. Find the measure of angle 1, the angle between an eave and a horizontal support beam.

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

Answer:

19

Explanation:

We know that the diagonals of a rectangle are always equal, therefore RT = SW.

So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;

The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).

Given: c = 20, a = 8, and b = x. Find x.

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

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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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°

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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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

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.

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.

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.

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].

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

Given:

Total student = 4

Joe, Sofia, Hayden, and Bonita.

Find-:

Probability he draws Sofia then Joe.

Explanation-:

Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

The formula of probability:

For Sofia.

Total number of possible outcomes = 4

Favorable outcomes for Sofia = 1

So probability for Sofia :

After the first student set it aside.

For Joe.

Total number of possible outcomes = 3

A favorable outcome for Joe = 1

So probability for Joe.

So probability for Sofia then joe is:

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

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

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".

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

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%

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.

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

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

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:

4/15

Step-by-step explanation:

4/15 = 0.26666666...

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

Kyah, this is the solution to the exercise:

People = 200

Capacity of each table = 8 people

In consequence, we need:

Number of tables = People/Capacity of each table

Replacing by the values we know:

Number of tables = 200/8

Number of tables = 25

a)

Every 63 years, the amount of titanium halves.

441 years later means how many halving?

441/63 = 7 halving

We start off with 1000 and do 7 halving to get the amount of Titanium-44 after 441 years.

after 441 years, the amount of titanium remaining would be 7.8125 kg

b)

Let's find the point where the remaining titanium would be 1 kg.

That would be:

t is the time we are looking for. We can solve this using Ln(natural log):

There is basically 9.965 halving. That would make the years approximately:

9.965 * 63 (half life) = 627.795 years (approx)

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

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: