Translate the figure 2 units left and 2 units down.

Solution

The given coordinate

Therefore

Options A and B can't be the answer since

Then Option C there is a calculation error there

Option D

Now

Given:

The total students in the bus initially, T=50.

15 students got off the bus at the first stop and 8 students got off at the second bus stop.

Now, the students left in the bus is

Therefore, 27 students are left in the bus.

Solution

Step 1:

There are three types of systems of linear equations in two variables, and three types of solutions.

1. An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.

2. An inconsistent system has no solution.

3. A dependent system has infinitely many solutions.

Step 2

Solve the systems of the equations using the substitution method

Final answer

The system is dependent so there are infinite solutions.

Equivalent

We want to get the standard deviation of the distribution;

From which we can compute;

When we input the values, we have

Given:

The vertex of the parabola is (1,2).

The point passes through the parabola = (3,10).

Required:

We need to find the equation of the parabola.

Explanation:

Consider the standard form equation for the parabola.

where (h,k) is the vertex.

Substitute (h,k) =(1,2) in the equation.

Substitute x =3 and y=10 in the equation to find the value of a.

Subtract 2 from both sides of the equation.

Substitute a =2, h=1 nad l=2 in the equation of the parabola.

Final answer:

The standard form equation for the function:

The equation is;

Here, we want to select an equation which when graphed with the equation shown will give a a system with infinite solutions

For us to have a system with infinite solutions, the value on the left hand side of the equation for y must be equal to the value of y on the right hand side

What we simply mean that the equation that would be plotted will be the same as that already plotted

We have this as;

This will make the two y equal and thus gives an equation with infinitely many solutions as the y value on both sides will be equal

Answer:

D.

Explanation:

To graph the function, we need to identify some points in the graph. Then

Therefore, we will use the points (0, -8), (1, -3), (2, 0), (3, 1), and (4, 0) to graph the function. So, the graph is

Therefore, the zeros are 2 and 4 because (2, 0) and (4, 0) are the points where the graph crosses the x-axis. Thus, the answer is D.

Solution

Calculate the cost of admission for a group of 2 people

C rep Cost (in dollars) of admission per person

p rep group of people

find the cost of admission for group of 2 people

So the answer is 50 dollars

From an airplane that is flying at an altitude of 3,000 feet, the ange of depression of an airport ground signal measures 27" Find to the nearest foot, the distance between the airplane and the airport signal.​

see the attached figure to better understand the problem

we have that

sin(27)=3,000/D ------> by opposite side divided by the hypotenuse

solve for D

D=3,000/sin(27)

The balcony is composed by a semicircle with radius r=5 units and a right triangle with a leg equal to 8 units.

Then, in order to find the perimeter, we need to find the missing leg of the triangle and the semi-circunference of the semicircle. So, let's draw a picture of our triangle:

We can find the missing leg by means of Pythagorean theorem, because,

which gives

Then, by subtracting 64 to both sides, we have

and by applying square root to both sides, we obtain

Now, let's find the semicircunference. For a complete circle, the circunference formula is given by

where r denotes the radius. Then, the semicircunference is half this value, then, in our case, we have

Then, the semicircunference is

Then, the perimeter of the balcony is the sum of the 2 legs of the triangle plus the semi-circunference, that is,

Therefore, by rounding to the nearest whole number, the perimeter is: 30 feet.

On the other hand, the area of the balcony is equal to the area of the triangle plus the area of the semicircle. Then, the area of the triangle is given by

and the area of the semicircle is half the area of the complete circle, so we have

Therefore, the area of the balcony is given by

Hence, by rounding to the nearest whole number, the area of the balcony is: 87 square feet

Notice that if we have a function

g(x)= x-10

and a function

f(x)= -4/x

The composition

In scatter plot

when the y variable increses as the x variable increases

this represents a positive correlation

then in the figure we have a positive correlation

Extra

Giving the case where x variable increases and y decreases this means Negative Correlation

Giving the case where the dots have no pattern this means no correlation

Last month: 1 batch of cookies and 1 batch of brownies (7 eggs in total)

The month before: 2 batches of brownies and 3 batches of cookies (18 eggs in total)

Where c and b are the numbers of eggs needed to make a batch of cookies and brownies, respectively. From equation (1):

Using this in (2):

Finally, from (1):

He needs 4 eggs to make a batch of cookies and 3 eggs to make a batch of brownies.

2(x-9) = 7

Let the unknown number = x

The difference between the unknown number and 9:

x - 9 = 7

Twice the difference betweenn the unknown number and and is equal to 7:

2(x-9) = 7

Since we were asked to teranslate and not solve, the translation into an equation becomes:

2(x-9) = 7

9:

Step 1: Write out the formula for the volume of a cube

Step 2: Write out the given value of the side of the square and substitute it into the formula

Step 3: Write out the formula to find the number of cubes of a given volume that can fill the container of a given value

Step 4: Write out the volume of the glass case and the cube and substitute them into the formula in step 3

Therefore,

Hence, the number of cubes is 4

The right option is C

we have the expression

using a trigonometric substitution

Let

substitute in the original expression

Remember that

Remember that

using the triangle

Find out the value of H

Applying the Pythagorean Theorem

H^2=(3x)^2+1^2

H^2=9x^2+1

H=√(9x^2+1)

substitute

simplify

therefore

the answer is

I’m here to help you. Just give me a few mins to look over your question.

Step 01:

Data

Equally size of pie

Ms Winston:

1/4

Ms Smith:

1/8

Miss Kwan:

Step 02:

Class

3 / 4 of pie

Let me do some algebra, it will be self explanatory.

I have basically moved cx to the left, and b to the right, now let me do more algebra

Now the Second method is the graphing the equation and finding the values of x, that follow the graph.

Answer:

first option

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint M is calculated as

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

use this formula with (x₁, y₁ ) = G(x, y ) and (x₂, y₂ ) = H (78.8, 4 )

and equate to x/ y coordinates of midpoint , that is

[tex]\frac{x+78.8}{2}[/tex] = 43.3 ( multiply both sides by 2 to clear the fraction )

x + 78.8 = 86.6 ( subtract 78.8 from both sides )

x = 7.8

and

[tex]\frac{y+4}{2}[/tex] = 20 ( multiply both sides by 2 to clear the fraction )

y + 4 = 40 ( subtract 4 from both sides )

y = 36

the coordinates of G (7.8, 36 )

Total amount of gasoline used for his journey = 12.38 + 11.45 = 23.83 gallons of gasoline .

Solution

- The smaller angle is (6x + 6) while the larger angle is (9x + 9) by observation.

- Thus, we can find the value of x since we also know that the larger angle is 108 degrees.

- After finding x, we can find the measure of the smaller angle.

- Thus, we have:

Final Answer

The measure of the smaller angle is 72 degrees

Let "x" represent the number of adult tickets sold

And "y" represent the number of child tickets sold

C is the total ticket sales.

The total profit can be calculated as to number of adult tickets multiplied by its unit price plus the number of child tickets multiplied by its unit price:

If in one afternoon the movie theter made C=$146 on ticket sales and we knoe that y=10 children tickets were sold, you can calculate the number of adults tickets by replacing the given values in the equation and solving it for x:

They sold 8 adult tickets on said afternoon.

In figure A:

21 ^2 + 28^2 = C ^2

928 = c^2

therefore side c = 30.36cm

since we need to find the area of a square inscribed in a triangle , we have a right triangle with sides 21cm, 28cm and 30.46cm :

3/4 c + c +4/3c = 30.5

37/12 c = 30.5

c = 30.5 *12 /37

c = 377/37 =9.89

Therefore :

Area of a square = 9.89^2= 97.8 cm^2

We can multiply the terms of top, then we have

now, in the denominator, we have

then, we obtain

Now, we can see that

and

and also

by combaning these results, the answer is

So,

Given that n is the middle number of three consecutive even integers, we can write:

n - 2: The previous number to n.

n: The middle number.

n + 2: The next number to n.

The sum of these three numbers is the sum we're asked to find. That is:

SSS theorem: All three corresponding sides are congruent.

Therefore, Consider the 2 triangles to the right:

GI = SR

HG = QS

HI = QR

So:

Δ GHI ≅ Δ SQR by the SSS postulate

Answer: Δ GHI ≅ Δ SQR

Use the product rule:

d/dx = [f(x)*g(x)] = f(x) * d/dx g(x) + d/dx f(x) * g(x)

-4e^x csc^2(x) + 4e^x cot(x)

The first thing that you must see

is that 3, is a common factor of 48, and 243.

Then we factor by r³, and we get the following

If we apply the difference of squares we get

Then, the elements that are NOT factos are 3r⁵,7r-16 and 7r+16, so the answers would be a,b,e

A translation right 5 units and up 4 units.

We will have that the expression A & B are given by the following equations respectively:

&

Now, we solve for "x" the number of sales:

So, for no amount of months is salary A better than salary B.