An isosceles triangle has a base of 8 feet and a height of 6 feet. What is the length of one of the two congruent sides? Work and a diagram would be appreciated using the Pythagorean Theorem

Answer:

it is a right triangle

Step-by-step explanation:

by Pythagorean theorem

Given the dimensions of locker box are length = 6 feet, width = 4 feet, and height = 10 feet.

Wayne wants to cover the box, so we need to find its total surface area. The box is in the shape of rectangular prism.

We know the formula for total surface area of rectangular prism is given as follows :-

[tex] Total \;Surface \;Area = 2*(lw + wh + hl) [/tex]

T.S.A. = 2·(6 x 4 + 4 x 10 + 10 x 6) = 2·(24 + 40 + 60) = 2·(124) = 248 feet²

Surface Area = 248 squared feet

To cover the locker with waterproof covering, we needed to find the surface area of the box. As we multiplied two dimensions at a time in the formula, so the units are "squared feet".

Hence, option A is correct i.e. squared feet or ft².

Answer: x=9

Step-by-step explanation:

In the given picture, we have a circle in which we have given two congruent arcs [tex]\overarc{RS}\text{ and }\overarc{TS}[/tex]

And [tex]\overline{RS}=59\text{ and }\overline{ST}=10x-31[/tex]

Since, we know that congruent arcs have congruent chords.

Therefore,  [tex]\overline{RS}=\overline{ST}[/tex]

[tex]59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9[/tex]

To solve the problem we must know the Chord's Equidistant From The Center Of A Circle Theorem.

If two chords of a circle are equidistant from the center then they are congruent to each other and their corresponding arcs are also congruent.

The value of x is 9.

Chord RS and chord ST are equidistant from the center. therefore,

RS = ST

[tex]59 = 10x-31\\ 59+31 = 10x\\ 90 = 10x\\\\ x= \dfrac{90}{10}\\\\ x= 9[/tex]

Hence, the value of x is 9.

Learn more about Equidistance chords:

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The value of cos (11pi/6), is -sqrt(3)/2.

To determine the exact value of cos (11π/6), we first need to understand the trigonometric values at certain angles. In this case, 11π/6 radians is equivalent to 330 degrees. Using the unit circle, we know that at 330 degrees, cosine is equivalent to -√3 / 2.

Answer:400

Step-by-step explanation:

1 foot = 12 inch

300 by 12 = 3600

3600 divided by 9 inches = 400

You're welcome L0L

Answer:

The data we have is:

He works for $8 an hour.

He mows lawns for $10 an hour.

He wants to work no more than 20 hours per week, and wants to hearn at least $120 week.

So if S is the number of hours he works in the store, and M is the number of hours that he mowns lawns, we have the inequalities:

S + M ≤ 20

S*$8 + M*$10 ≥ $120

So let's choose a possible solution:

Let's select M = 12 and S = 0

in this way, he worsk

0h + 12 h = 12 h that is less than 20 hours, and he wins:

0*$8 + 12*$10 = $120, which is the minimum amount of money that he wants to win.

and we have a lot of other possible solutions:

S= 1, M = 12

S = 2, M= 12.. and so on.

Answer:

C. [tex]75000\text{ cm}^3[/tex]

Step-by-step explanation:  

We have been given a container and we are asked to find the volume of our given container.

We can see that our container is made of two cuboids, so we will use volume of cuboid formula to solve our given problem.

[tex]\text{Volume of cuboid}=\text{Length*Breadth*Height}[/tex]

We can from provided image that the base cuboid (bigger) has lengths 25 cm, 40 cm and 40 cm.

The height of smaller cuboid will be 25 cm (50 cm -25 cm). The other two sides of smaller cuboid are 35 cm and 40 cm.

[tex]\text{The volume of container}=\text{Volume of the bigger cuboid + Volume of the smaller cuboid}[/tex]

Upon substituting our given values in volume formula we will get,

[tex]\text{The volume of container}=\text{25 cm*40 cm*40 cm}+\text{25 cm*35 cm* 40 cm}[/tex]

[tex]\text{The volume of container}=40000\text{ cm}^3+35000\text{ cm}^3[/tex]

[tex]\text{The volume of container}=75000\text{ cm}^3[/tex]

Therefore, the volume of our given container is [tex]75000\text{ cm}^3[/tex] and option C is the correct choice.

Final answer:

Two-thirds of each poster are not covered with opaque paper. Multiplying (2/3) by 5 gives us 10/3, which can be converted to 3 and 1/3, indicating that three whole posters plus one-third of another are not covered.

Explanation:

If one third of each of 5 same sized posters is covered with opaque paper, then two thirds of each poster are not covered. To find what fraction of the posters are not covered by opaque paper, you apply multiplication. You start with one poster: one-third covered means two-thirds are not covered. Represent this as 2/3. Since the question concerns 5 identical posters, you multiply the fraction of one poster (2/3) by the number of posters (5).

Mathematically, this looks like:

(2/3) × 5 = 10/3

However, 10/3 represents more than one whole, and it can be converted into a mixed number to represent the total unobstructed fraction of the posters. This is 3 and 1/3, meaning that in total, you have three whole posters and one-third of another poster not covered by opaque paper.

The ranges in the frequency table are inclusive on the lower end and exclusive on the upper end.

To create a frequency table using equal intervals for the average number of movies per person, we first need to determine the intervals and then count how many countries fall into each interval.

Let's use intervals of 1.

Frequency Table:

Average Number of Movies | Number of Countries

0.5 - 1.4 | 4 (Turkey, Japan, UK, Finland)

1.5 - 2.4 | 3 (Austria, Germany, Spain)

2.5 - 3.4 | 4 (Sweden, Denmark, Switzerland, France)

3.5 - 4.4 | 2 (Norway, Canada)

4.5 - 5.4 | 1 (US)

To know more about frequency table click here :

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Answer:

The volume of cone -shaped tent is 226.08 cubic ft.

Step-by-step explanation:

Given : A cone-shaped tent has a diameter of 12 ft and a height of 6 ft.

To find : What is the volume of the tent?

Solution : The formula of volume of cone is

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

where, r is the radius

we have given diameter = 12 =2r

r=6 ft

h is the height h=6 ft

[tex]\pi =3.14[/tex]

Substitute the value in the formula,

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

[tex]V=\frac{1}{3}\times (3.14)\times 6^{2}\times 6[/tex]

[tex]V=\frac{1}{3}\times 3.14\times 36\times 6[/tex]

[tex]V=226.08 ft^3[/tex]

Therefore, The volume of cone is 226.08 cubic ft.

Answer:

The domain is all possible values of 'x' that would make the function true. As you can see from the graph, this function goes out to infinity both ways, so all values of 'x' will satisfy the function, so your answer should be:

Step-by-step explanation:

Final answer:

To simplify the expression 5.5a - 1 + 21b + 3a, combine like terms to get 8.5a + 21b - 1, which is the simplified form of the original expression.

Explanation:

To simplify the expression 5.5a - 1 + 21b + 3a, we need to combine like terms, which are terms that have the same variable raised to the same power. Here, 5.5a and 3a are like terms, and they can be combined by addition. There are no like terms for 21b or the constant -1, so they remain as they are.

Step 1: Combine the coefficients of like terms 5.5a and 3a: 5.5a + 3a = 8.5a.

Step 2: Rewrite the simplified expression with the combined like term: 8.5a + 21b - 1.

This is the simplified form of the original expression.