The perimeter of a rectangular field is 168 feet. The field is 36 feet wide. How long is the field

When two line segments are congruent, what it really means is that the length of the line segments are equal. Congruent is usually interchanged with the word equal since it means the same: equal lengths. However, congruent is very specific in the sense that it means “equal lengths”. When we say equal alone, it may refer to different properties, congruent however is very specific.

Now the answer to this question should be:

B. AB overbar congruent to CD overbar

Not similar, not equal, and definitely not element. What we mean in this case is “equal lengths”, therefore the perfect word is congruent.

The possible lengths of sides of the rectangle will be  [tex](6,22)[/tex] or [tex](22,6)[/tex] .

Area is the space which is occupied by any [tex]2D[/tex] surface.

Area of rectangle [tex]=Length\ *\ Breadth[/tex]

Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]

We have,

Perimeter of rectangle [tex]=56[/tex] feet

Area of rectangle  [tex]=132[/tex] squared feet

Let,

Length of rectangle [tex]=x[/tex]

Breadth of rectangle [tex]=y[/tex]

So,

Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]

                                   [tex]56=2(x+y)[/tex]

                                  [tex]28=(x+y)[/tex]

⇒                                 [tex]x=28-y[/tex]     [tex]........(i)[/tex]

Now,

Area of rectangle [tex]=Length\ *\ Breadth[/tex]

                        [tex]132=x\ *\ y[/tex]           [tex]........(ii)[/tex]

Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],

[tex]132=(28-y)y[/tex]

[tex]132=28y-y^2[/tex]

⇒[tex]y^2-28y+132=0[/tex]

Now using Middle term split method;

[tex]y^2-28y+132=0[/tex]

[tex]y^2-22y-6y+132=0[/tex]

[tex]y(y-22)-6(y-22)=0[/tex]

[tex](y-6)(y-22)=0[/tex]

⇒

[tex](y-6)=0[/tex]

⇒  [tex]y=6[/tex]

[tex](y-22)=0[/tex]

⇒  [tex]y=22[/tex]

So,

Now if we take [tex]y=6[/tex], then

[tex]x=28-6[/tex]

[tex]x=22[/tex]

And,

if we take [tex]y=22[/tex], then

[tex]x=28-22[/tex]

[tex]x=6[/tex]

So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .

Hence, we can say that he possible lengths of sides of the rectangle are  [tex](6,22)[/tex] or [tex](22,6)[/tex] .

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20

5

30

Step-by-step explanation:

Answer:

16 cm approximately

Step-by-step explanation:

We are given that a telephone pole cast shadow that is 34 m long .We are given that a statue that is 36 cm long and shadow of statue is 77 cm long.

We have to find the length of telephone pole

Let height of pole

Using direct proportion

[tex]\frac{x}{34}=\frac{36}{77}[/tex]

By multiply property of equality then we get

[tex]x=\frac{36}{77}\times 34[/tex]

x=[tex]\frac{1224}{77}[/tex]

x=15.896 cm

Hence, the height of telephone pole=15.896 cm=16 cm approximately

Final answer:

The number of adult tickets sold for the school play is 93, calculated by setting up an equation based on the information that the total tickets sold were 279 and student tickets were two times the number of adult tickets.

Explanation:

The question asks us to determine the number of adult tickets sold when a total of 279 tickets were sold for the school play, and the number of student tickets is two times the number of adult tickets sold. We can set up an equation to solve this problem.

Let A be the number of adult tickets, and S be the number of student tickets. The problem gives us two equations:

S = 2A (The number of student tickets is two times the number of adult tickets)

A + S = 279 (The total number of tickets sold is 279)

Substituting the first equation into the second gives us:

A + 2A = 279

3A = 279

A = 279 / 3

A = 93

Therefore, 93 adult tickets were sold for the school play.

divide the ratio:

8/20 = 0.4

0.4 = 40%

To find the number of adults needed for 48 children at a daycare with an adult to child ratio of 3:16, we set up a proportion and solve for the unknown number of adults. We cross-multiply and divide to find that 9 adults are required.

The question asks us to calculate how many adults are needed for 48 children in a daycare center given an adult to child ratio of 3:16. To solve this, we need to set up a proportion based on the ratio and solve for the number of adults needed.

We have the ratio of adults to children as 3:16, which means for every 3 adults, there are 16 children. To find out how many adults are needed for 48 children, we set up the proportion:

3 adults / 16 children = x adults / 48 children

Now we cross-multiply and solve for x:

(3 adults) / (48 children) = (16 children)

144 = 16x

x = 144 / 16

x = 9

Therefore, 9 adults are needed to take care of 48 children at the daycare center.

Answer:

The discount on the purchase of a T-shirt and a pair of jeans costing $62.50 with a 20% discount policy is $12.50.

A store's discount policy offers 20% off for purchases over $50. The question involves calculating the discount amount when a T-shirt and a pair of jeans are purchased together for $62.50. To determine the discount, we simply multiply the total purchase amount by the discount rate.

Step-by-Step Calculation:

First, confirm the purchase amount qualifies for the discount. The combined cost of the T-shirt and jeans is $62.50, which is above $50, so the purchase qualifies for the discount.

Calculate the discount by multiplying the total purchase amount by the discount rate: $62.50 × 0.20 (which is the same as 20%).

Discount Amount = $62.50 × 0.20 = $12.50.

Therefore, the amount of the discount the customer would receive on the purchase of the T-shirt and jeans is $12.50.

multiply jeans by shirts by shoes

 so 4 x 6 x 2 = 48 different combinations

Answer: The values for a, b, h, and k are a = 5, b = 3, h = 0, k = -3.

Step-by-step explanation: In this problem, we know ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and (0, -1). We are asked to determine the values of a, b, h, and k.

We were also then provided with the equation for vertical eclipse:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y -k)^2}{a^2}[/tex]

Before we begin, we need to first define our values for a, b, h, and k.

The first step, we need to determine the center of the eclipse. We can use the midpoint formula to determine the midpoint between the vertices along the major axis: (0, 8) and (0, -2).

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

[tex]M = (\frac{0 + 0}{2} , \frac{-2 + 8}{2} )\\M = (0, 3)[/tex]

We now know that our center (h, k) is (0, 3). Which means our values for h and k are 0 and 3. Next, we have to determine our values for a and b. Considering the center of our eclipse is not at the center, we can use one of our vertices to determine our value for a.

[tex]V_{1}[/tex] = (h, k±a)

(0, 8) = (0, 3±a)

3 ± a = 8

±a = 5

Now, we know that a = 5.  For us to get b, we need to use this formula: [tex]c^2 = a^2 - b^2[/tex]. Let's rewrite this formula, so we can focus on getting our b-value.

[tex]c^2 - a^2 = -b^2[/tex]

For us to use this formula, we need to determine our c value. To find our c-value, we have use of our foci points: (h, k±c). C is the units away/further from the center towards our foci points.

(0, 3±c) = (0, 7)

3 + c = 7

7 - 3 = c

4 = c

Now, we know that our value for c is 4. Now, let's plug into the formula.

[tex](4)^2 - (5)^2 = -b^2\\16 - 25 = -b^2\\\frac{-9}{-1} = \frac{-b^2}{-1} \\\sqrt{b^2} = \sqrt{9} \\b = 3[/tex]

Our value for b is 3. If we put into our eclipse formula:

[tex]\frac{(x-0)^2}{3^2} + \frac{(y -(-3))^2}{5^2}[/tex]

angles in a triangle = 180 degrees

70 +35 = 105 degrees

180-105 = 75 degrees

 3rd angle  = 75 degrees