A tabletop in the shape of a trapezoid has an area of 5,550 square centimeters. Its longer base measures 115 centimeters, and the shorter base is 85 centimeters . What is the height?

Given:

Line ST is perpendicular to line PR.

[tex]m\angle PQV=32^\circ[/tex]

To find:

The measure of angle SQU.

Solution:

Line ST is perpendicular to line PR.

[tex]m\angle SQR=90^\circ[/tex]

If two lines intersect each other, then the vertically opposite angles are equal.

[tex]m\angle UQR=m\angle PQV[/tex]       (Vertically opposite angle)

[tex]m\angle UQR=32^\circ[/tex]

Now,

[tex]m\angle SQR=m\angle SQU+m\angle UQR[/tex]

[tex]90^\circ=m\angle SQU+32^\circ[/tex]

[tex]90^\circ-32^\circ=m\angle SQU[/tex]

[tex]58^\circ=m\angle SQU[/tex]

Therefore, the correct option is D.

Answer: x = 10

Step-by-step explanation:

The Pythagorean's theorem says that for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:

A^2 + B^2 = H^2

In this case, we have:

A = (x - 4)

B = (x - 2)

H = x

Then we have the equation:

(x - 4)^2 + (x - 2)^2 = x^2

Now we need to solve this for x, first let's simplify it.

(x^2 - 2*x*4 + 16) + (x^2 - 2*2*x + 4) = x^2

2*x^2 - 12*x + 20 = x^2

2*x^2 - 12*x + 20 - x^2 = 0

x^2 - 12*x + 20 = 0

The solutions of this equation are given by the Bhaskara's equation, such that for an equation like:

a*x^2 + b*x + c = 0

The solutions are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then the solutions for our equation are:

[tex]x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4*1*20} }{2*1} = \frac{12 \pm 8 }{2}[/tex]

Then the two possible solutions are:

x = (12 - 8)/2 = 4/2 = 2

Notice that if x = 2, then the length of the catheti will be:

A = 2 - 4 = -2

B = 2 - 2 = 0

This has no sense, so we can discard this solution.

The other solution for x is:

x = (12 + 8)/2 = 10

x = 10

Then:

H = 10

A = 10 - 4 = 6

B = 10 - 2 = 8

This solution makes sense, then x = 10.

Answer:  I think its 324

Step-by-step explanation: $9.00 X 36 = 324

Answer:Sandra =  18c

Step-by-step explanation:

Given that Kurt has c comic books

And

Sandra has 18 times as many comic books as Kurt.

We can say the expression to show how many comic books Sandra has will be

Kurt =  c

Sandra =  18c

Addition Property of Equality

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.

The construction correctly finds the best location of the warehouse is shown in option C (Construction Y because point E is the circumcentre of triangle LMN and due to its exact equidistant location from the three stores at L, M, and N, Point E is the ideal location for the warehouse.)

The location that is equally spaced from the three vertices and where the perpendicular bisectors of a triangle's sides intersect.

Calculation for distance of the three stores from warehouse:

Precisely one circle crosses through all three, which are all on the same line. Finding the centre of the circle that goes through all three of the points is equivalent to finding the point that is equally distant from each of the three points (since all points on a circle are equidistant from the centre).

L, M, and N are our points. To create the triangle, draw the lines LM, LN, and MN. The junction of any two of the lines' perpendicular bisectors, point E, will serve as the circle's centre.

Due to the fact that E is the triangle's LMN's circumcenter, as demonstrated in Construction Y.

Therefore, given that it is precisely equidistant between the three stores at L, M, and N, this is the optimal location for the warehouse.

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Answer:

the answer is C.

Step-by-step explanation:

construction X, because point E is the circumcenter of angle LMN.

Answer:

21

Step-by-step explanation:

Dr James ordered 56 pizzas for the teachers.

Of the pizzas ordered, 2/7 of them were pepperoni,

Number that were pepperoni = 2/7 × 56 pizzas

= 16 pizzas were pepperoni

19 were cheese , and the rest were veggie pizzas.

How many of the slices were veggie?

The number of veggie slices is calculated as:

Veggie slices = Total number of pizzas - ( Number of Pepperoni + Number of Cheese)

= 56 - ( 16 + 19)

= 56 - 35

= 21

The number of veggies is 21

Answer:

b) 13

Step-by-step explanation:

67 - 55 = 12

55 - 46 = 9

46 - 34 = 12

34 - 25 = 9

25 - x = 12

rearrange that so,

25 - 12 = x

x = 13

Answer:

b) 13

Step-by-step explanation:

67 - 12 = 55

55 - 9 = 46

46 - 12 = 34

34 - 9 = 25

pattern: subtract 12, subtract 9

the pattern tells us to subtract 12, so take take 25 and subtract 12 from it:

25 - 12 = 13

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

A is 10

B is 13

C is [tex]\sqrt{43.65}[/tex]

D is [tex]\sqrt{74}[/tex]

Answer:

Perimeter of the rectangle = 44 units

Step-by-step explanation:

Let the coordinates given are the vertices A(-7, 6), B(3, 6), and C(3, -6) of the rectangle.

Since, opposite sides of a rectangle are equal in length,

Fourth vertex of the rectangle will be D(-7, -6)

Length of AB = 3 - (-7) = 10 units

Length of BC = 6 - (-6) = 12 units

Length of CD = 3 - (-7) = 10 units

Length of AD = 6 - (-6) = 12 units

Therefore, perimeter of the rectangle = 2(Length + width)

                                                               = 2(12 + 10)

                                                               = 44 units

Answer:

B. $79.45

Step-by-step explanation:

The equation for simple interest is I = PRT, where I = interest earned, P = principal/amount invested, R = rate as a decimal, and T = time in years.

For this example, we'll calculate the interest earned, then add to the principal to get the total amount of money in her account.

I = (70)(0.045)(3)

I = 9.45

70 + 9.45 = $79.45

Please let me know if you have questions.

Answer:   sorry about that your answer would come out to be -8/15

which i believe is less than x

Step-by-step explanation:    

Answer:

x < -11/6

Step-by-step explanation:

and boom

Answer:

x = 3

Step-by-step explanation:

y = 5x

x + y = 12

x + 5x = 12 (substitute 5x in the place of y)

6x = 12

x = 12/6

x = 3

Answer:

Step-by-step explanation:

y=5x

+5(y)=(12-x)+5  which distributing is +5y= +60-5x

y=5x

+5y=+60-5x

6y=60

y=10

10=5x

x=2

Answer: Combination 2,3,4 (going down)

Step-by-step explanation:

These are the equations

1. 3.97(5)+5.25=25.1 this is (10 cents over cant buy)

2. 2.75(7)+2.4(2)= 24.05 (good)

3. 5.25(2)+2.4(6)= 24.9 (good)

4. 3.97(3)+2.75(4)= 22.91 (good)

5. 5.25(2)+2.75(6)= 27 (two dollars over cant buy)

The distance of from Sally's house to Dave's house is 5 miles. Therefore, option B is the correct answer.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, Sally lives 3 miles due west of Jenny, and Jenny lives 4 miles due north of Dave.

Distance is

c²=3²+4²

c²=9+16

c²=25

c=5 miles

The distance of from Sally's house to Dave's house is 5 miles. Therefore, option B is the correct answer.

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Answer:

f(2) = 22

Step-by-step explanation:

To find f(#), plug the number into each x of the equation.

f(x) = 10x + 2

f(2) = 10(2) + 2

Simplify the parentheses by multiplying.

f(2) = 20 + 2

Add.

f(2) = 22

Hope this helps!

Answer: $80

Step-by-step explanation:

Answer:

The percentage of the original price that was discounted is 21.33%

Step-by-step explanation:

The original price of a bicycle was $375. Now it is on sale for $295.

The discounted price of a product is calculated as the percentage of discount that you want to apply multiplied by the price of the product. This is the amount of money that is discounted. But to calculate the sale price, the original price of the product must be subtracted minus the discounted quantity.

So, this expressed in this case is:

375-x*375=295

The value of x is the discount that you want to calculate expressed in decimal number. This result will then be multiplied by 100 to obtain the discount expressed as a percentage.

Isolating the value of x you get:

-x*375=295-375

-x*375=-80

x=(-80)÷(-375)

x=0.2133

As a percentage, it is 0.2133*100= 21.33%

The percentage of the original price that was discounted is 21.33%

Answer:

Step-by-step explanation:

length of semichord=2/1=1 cm

[tex]d=\sqrt{3^2-1^2} =\sqrt{8} =2\sqrt{2}[/tex]

or d≈2.83

Answer:

0

Step-by-step explanation:

The x-value in the y-intercept must be zero. This is because the y-intercept is where a line or function intersects with the y-axis. All points on the y-axis have an x-value of 0. Therefore, all y-intercepts will have an x-value of 0 and look like (0,b).

Answer: x and y intercepts are the points in which your line crossing x axcis and y axcis . For the streight line given by  linear function y=ax+b we find coordinates of the point A represent x intercept  using value for the second coordinate y=0 then return this value to linear function

0=ax+b       subtract b from both sides

-b     -b

-b=ax          divide by a which id different then 0

-b/a=x

X-itercept is a point A(-b/a, 0)

For y intercept point B (x.y) our first coordinate x=0, return this value to the linear function y=ax+b

y=a*0+b  

Y=0+b

y=b

y intercept is a point B(0,b)

For the special types of linear equations:

1. When a=0 liner function is y=b we have parallel lines with x axcise, crosing only y axcise and there are only y intercept B(0,b)

2. When a=0 and b=0 linear function is y=0, which is equation of the x axcise. In this case y intercept is the orgin point O(0,0) and x-intercepts is are all points of the x axcise A(x,0); x can be any real number. This means infinite many x intercept points.

3. When a is not 0 and b=0 we have x intercept point A(0,0) and y intercept point B(0,0).

4. For the linear equation x=c, c is constant value, we have parallel line with y axcise crosing x axcise at the point A(c,0) and there is no y intersect because there are parallel lines

Step-by-step explanation:     Example y=2x+6. For x intercept  y=0, return to linear function and in the place oy poot its value  

               0=2x+6    subtract  6

              -6      -6

              -6=2x          divide by 2

              -3=x                                                                                                      

X intercept points is a point A(-3,0)                                                                                                                        

For the y intercept point B(x,y)  x=0, return to linear function and in the place of x poot its value

              y=2x+6

              y=2*0+6

              y=0+6

              y=6

x intercept is a point B(0,6).

Answer:

The cost per highlighter is $0.60

Step-by-step explanation:

I know this because to find the cost of each highlighter you would divide $2.40 by 4 so the answer would be $0.60.

Please give brainliest I'm trying to level up

Answer:

$0.60

Step-by-step explanation:

$2.40/4= 0.6 = $0.60

Answer: The answer I got was A) 2.5

Step-by-step explanation:

Hope this Helps!!!

Ok first of all fort nite is you know second I did some calculations its not five so the thing I cant find out is what 5.5  rounded is so what ever 5.5 rounded to is your answer so if you find out what 5.5 is rounded to youll have your answer! I hope this helps