A student cafeteria has 24 tables, tables X has 4 seats each, tables Y has 6 seats each, and tables Z has 10 seats each. The total seating capacity of the cafeteria is 148. For a student meeting, half of tables X, 1/4 of tables Y, and 1/3 of tables Z will be used, for a total of 9 tables. Determine X, Y, and Z. ( Answer the final answer in a full sentence. )

Explanation

We are given the following:

We are required to determine the value of cos 16° from the diagram given.

We know that according to the trigonometry ratio rules:

So, we have:

Hence, the answer is:

Looking at the triangles, we see that they have two congruent sides, and the angles between them are congruent too.

Then, the two triangles are related by side-angle-side (SAS), so the triangles are congruent (SAS theorem).

• What are you being asked to find? define your variables

We are being asked to find the number of goats and ducks that there might be in the farmhouse.

• What are you given?

•

From the information given by the question, we know that there are as many as 12 animals and that they have as many as 34 legs.

• Create & solve a system

from the given information we can write two expressions, one for the total number of animals, which equals 12, and another for the number of legs, let's call x to the number of goats and y to the number of ducks.

We know that there are a total of 12 animals, this is the number of goats plus the number of ducks, then we can write the expression:

goats + ducks = 12

x + y = 12

0.

And we know that there are 34 legs since a duck has 2 legs and a goat has 4, the number of legs of all the ducks would be the number of ducks times 2 and the number of legs of all the goats is 4 times the number of goats, then we can express the equation:

goat's legs + duck's legs = 34

4x + 2y = 34

Then, the system of equations that we have to solve is:

1. x + y = 12

2. 4x + 2y = 34

Now let's solve the system of equations, by following these steps:

Solve for y from the first equation:

x+y=12

x-x+y=12-x

y=12-x

Replace the expression y=12-x into the second equation and find the value of x.

4x + 2y = 34

4x+2(12-x)=34

4x+2*12-2x=34

4x+24-2x=34

2x+24=34

2x+24-24=34-24

2x=10

2x/2=10/2

x=5

Now that we know that x equals 5, let's replace it into the expression y=12-x, to find the value of y:

y=12-x

y=12-5=7

Then, x equals 5 and y equals 7

• Explain your solution

•

In the farmhouse could there be a total of 5 ducks and 7 goats

done

The form of the linear equation is

m is the slope

b is the y-intercept

The given equation is

Compare it with the form above to find m and b

Since the coefficient of x is -2, then

m = -2

Since m is the slope of the line, then

The slope of the line is -2

The answer is B

The opposite angles of a parallelogram are equal, therefore:

Opposite sides of a parallelogram are parallel and equal so:

∠TSQ and ∠RQS are alternate interior angles, therefore:

Use the next trigonometric identities:

Then, the sec(90º - θ) is:

The sin(θ) is:

Then:

First answer:

Second Answer:

The coordinates of the Y'' after reflection of poligon X'Y'Z' over the x axis: (-2, -4)

The scatter plot shows a positive correlation because the points show a linear-trend describing that when x-values (weight) increases then y-values (calories) also increases.

Hence, the relationship is a Positive correlation.

First, draw a schematic representation of that situation:

The shortest distance between the starting point (Linus's house) and the endpoint (Charlie's house) is a straight line. Since a right triangle is formed with the sides of length 7 blocks and 3 blocks, we can use the Pyhtagorean Theorem to find the length of the hypotenuse:

Therefore, the shortest distance between those two points would be 7.6 blocks.

We know that the rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then

where (X1,Y1) and (X2,Y2) are points of our model.

So, in this case we have that:

So, the correct answer is: the rate of change for the sales tax is $0.08 per dollar.

When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.

In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:

Answer: h(3x) = 27x²-4

The circumference of a circle is given by the formula

however we also knos that the diameter can be written as

meaning that the formula for the circumference can also be written as

then the circumference for the given information is:

Let's assum that each person drives 120 miles per week.

Then for person A we have:

for person B we have:

finally, for person C:

Then, if person A changes to person B's car, we have that the save is:

if person B buys person C's car, then the save is:

therefore, the savings on gas will be different for both of them and person C is incorrect.

2)Since person A saved 2 gallons, then the new car for Person C must save 2 gallons for each mile traveled.

Then we have the following equation:

where 'x' represents the number of gallons consumed in 120 miles. then, solving for x we have:

therefore, person C will need to buy a car that uses 1 gallon for eah 120 miles traveled

Answer:

Step-by-step explanation: it is that

Let's begin by identifying key information given to us:

New size: Height = 18 in, Width = ?

Old size: Height = 2 in, Width = 1 in

We will get the width of the new photo by following the explanation below:

Therefore, the width of the enlarged photo is 9 inches

A function is a relation between variables y and x,

where theres only a y value for every x value

In this case x=1 . For every value of x = 1 ,there are infinite values for y , it can take any value , negative or positive.

So this is NOT a function

Solution

final answer is.

Choice A, C ,D

Answer:

is not correct because the lcm will be 16 and u will get 21/16

26 gallons

1) We can write this information setting up a proportion

miles gallons

120 10

312 x

2) Assuming the pace hasn't changed, then we can consider that as proportional:

120x = 312 * 10

120x= 3120

x = 3120/120

x =26

3) So 26 gallons are going to be needed for those 312 miles.

Answer:

C. 39 feet

Step-by-step explanation:

[tex]{ \tt{h(t) = - 16 {t}^{2} + 48t + 3 }}[/tex]

- Let us find the limits of the function

[tex] { \tt{ \frac{d \{h(t) \}}{dt} = - 32t + 48 }} \\ [/tex]

- So, let us differentiate for the second time;

[tex]{ \tt{ \frac{d {}^{2} \{h(t) \} }{dt {}^{2} } = - 32}} \\ [/tex]

- So, at maximum height; d{h(t)}/dt is 0;

[tex]{ \tt{ - 32t + 48 = 0}} \\ { \tt{ - 32t = - 48}} \\ { \tt{t = 1.5 \: seconds}}[/tex]

- Therefore; maximum height is;

[tex]{ \tt{h(t) = - {16t}^{2} + 48t + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = - 16(1.5) {}^{2} + 48(1.5) + 3}} \\ { \tt{h(1.5) = - 36 + 72 + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = 39 \: feet}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The given data set is 21,31,26,24,28,26.

Arranging the data set in the ascending order,

21,24,26,26,28,31.

The data set contains 6 numbers,

The median can be determined by taking the average of 3rd and 4th term of the data set,

Thus, the required median is 26.

The range can be determined by taking the difference between the highest and the lowest value of the data set,

Thus, the range of the data set is 10.

The interquartile range of the data set can be determined by taking the difference of quartile 1 and quartile 3.

Thus, the required interquartile range is 4.

We will have:

The fraction is approximately 11.

Note that 10 dimes = $1

Also 4 quarters = $1

That means, 100 dimes equals $10

Also, 44 quarters =

Solution

For this case we can do the following:

1)

2)

3)

4)

5)

Answer:

x = 33

Step-by-step explanation:

Creating an equation

The angles shown are corresponding angles

Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.

Corresponding angles are congruent ( equal to each other )

This means that 124 = 4x - 8

Solving for x

124 = 4x - 8

==> add 8 to both sides

132 = 4x

==> divide both sides by 4

33 = x

The angles in the question are vertically opposite angles and Vertically opposite angles are equal.

Therefore,

Therefore,

While completing the race, Ned spent 63 min walking if the ratio of time walking to jogging was 9:1, how many minutes did he spend completing the race?

Let

x-----> time spent walking

y -----> tiime spent jogging

we have

x/y=9/1

x=9y -----> equation A

we have

x=63 min

substitute in the equation A

63=9y

solve for y

y=7 minutes

therefore

teh answer is

Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.

we have that

the rule of the translation is

(x,y) -------> (x-6, y-7)

Applying the rule to the coordinates of triangle ABC

A(3,4) ------> A'(3-6,4-7)

A'(-3,-3)

B(7,7) ------> B'(7-6, 7-7)

B'(1,0)

C(8,1) --------> C'(8-6,1-7)

C'(2,-6)

Answer:

A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.

Explanation:

Given the compound inequalities:

First, solve both inequalities:

Thus, the number line should be the one that represents the solution:

• For x≤8, there is a ,closed circle on 8, and ,shading to the left.

• For x≥11, there is a ,closed circle on 11, and ,shading to the right.

Therefore, the correct description will be:

A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.

The last option is correct.