What is the value of the function at x=−2?



y=−4

y = 0

y = 2

y = 3

Final answer:

In an isosceles triangle, the angles opposite the two equal sides are themselves equal, and the sum of all angles always adds up to 180 degrees within plane geometry.

Explanation:

A rule about the angle measures of an isosceles triangle is that the angles opposite the two equal sides are themselves equal. An isosceles triangle has at least two sides of equal length, and the angles opposite these sides are called the base angles. Since the sum of angles in any triangle in Euclidean (plane) geometry must add up to 180 degrees, knowing two angles are the same allows us to easily calculate the third angle.

For example, if an isosceles triangle has two equal angles of 50 degrees each, the remaining angle must be 180 - (50 + 50) degrees, which is 80 degrees. This is different from a spherical triangle, where the sum of the angles can be greater than 180 degrees due to spherical geometry. It's also worth noting that these rules apply only to plane geometry, which is the study of shapes on a flat plane.

Answer:

Possible length range of third side is between 3<x<21.

Step-by-step explanation:

Sum of two sides of triangle cannot be equal or less than third side. Therefore, one side length of a triangle must be between subtract and sum of other two sides. Than, range of third side is:

[tex](12-9)<x<(12+9)\\3<x<21[/tex]

Final answer:

In the expression 3 to the power of 4, the base is '3', the exponent is '4', and the value of the expression is 81 after multiplying the base by itself for the number of times indicated by the exponent.

Explanation:

The expression given is 3 to the power of 4, which is written in mathematical terms as 34. The base of this expression is the number that is being multiplied by itself, which in this case is "3". The exponent is the number that indicates how many times the base is multiplied by itself, and here it is "4".

Finally, the value of the expression is the result of carrying out the multiplication that the exponent indicates, so for 3 raised to the 4th power, it's 3 x 3 x 3 x 3, which equals to 81.

To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.

To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:

Square the length of one side: 12 x 12 = 144

Multiply the result by 2: 144 x 2 = 288

Take the square root of the result: √288 ≈ 16.97 inches

Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.

Final answer:

The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.

Explanation:

The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the square are both 12 inches long. So, we have:

hypotenuse² = side1² + side2²

hypotenuse² = 12² + 12²

hypotenuse² = 144 + 144

hypotenuse² = 288

To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:

hypotenuse = √(288)

hypotenuse = 16.97 inches (rounded to the nearest inch)

Answer:

126

Step-by-step explanation:

No Following

Answer:

750

Step-by-step explanation:

for others

750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity

We need to find how many gallons of 80%

8x, since we don't know how many gallons

mixed with 250 gall of 40%: 0.40(250)

and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:

8x+0.4(250)=0.7x+0.7*250

Multiply on both sides of the equation

0.8x+100= 0.7x+175 Subtract 100 on both sides

0.8x= 0.7x+75

Subtract 0.7 on both sides

0.1x= 75

Divide both sides by 0.1

x= 750

You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

Hence,  750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

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Final answer:

Joanna's wind chime is suspended from the centroid of the triangular piece, which is the intersection point of the triangle's three medians and serves as its center of gravity.

Explanation:

The anchor point where Joanna has suspended the flat wooden triangular piece of the wind chime is known as the centroid of the triangle. The centroid is the point where the three medians of the triangle intersect, and it is always located inside the triangle. A median of a triangle is a line segment connecting a vertex to the midpoint of the opposing side. The centroid is also the triangle's center of gravity, meaning it is the balance point where the triangle can be suspended and remain in equilibrium. For any given triangle, the centroid will be found at a point that is one-third of the distance from each vertex to the midpoint of the opposite side.

Answer:

{I got 60} just took the test not 118 or 48 but thanks lol

Answer:

Option [tex]42.1\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle

see the attached figure to better understand the problem

Step 1

Find the area of the square

Remember that

The area of the square is

[tex]A=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=14\ in[/tex]

substitute

[tex]A=14^{2}=196\ in^{2}[/tex]

Step 2

Find the area of the circle

Remember that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex]

substitute

[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]

Step 3

Find the area of the region

[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]

Answer is 32. hope i helped.

Answer:

32 units

Step-by-step explanation:

Verified by test results

Hope this helps:)

Answer:

The variable "x" is the number of square tables and the variable "y" represents the number of round tables.

The committee needs 12 square tables.

Step-by-step explanation:

You know that the equation is 150 = 8*x + 6*y. You also know that 8 people can fit on a square table and 6 people can fit on a round table. Then 8 people multiplied by the amount of square tables plus 6 people by the amount of round tables should add 150 people. So in the previous equation the variable "x" is the number of square tables and the variable "y" represents the number of round tables.

If the number "y" of round tables is 9, you can replace this value in equation 150 = 8*x + 6*y, with 150 = 8*x + 6*9. Solving this last equation, you can calculate the value of the variable "x", that is, calculate the amount of square tables needed.

150= 8*x + 6*9

150= 8*x + 54

150-54= 8*X +54 - 54

96 = 8*x

[tex]\frac{96}{8} =\frac{8}{8} *x[/tex]

12=x

So, the committee needs 12 square tables.

The number of square tables that's needed will be 12 square tables.

The equation given is 150 = 8x + 6y and this represents the number of each type of table that's needed for 150 people.

Since 6 people are already give for the round tables, then to solve the square tables will be:

150 = 8x + 6y

150 = 8x + (6 × 9)

150 = 8x + 54

Collect like terms

8x = 150 - 54

8x = 96

Divide both side by 8

8x/8 = 96/8.

x = 12

Therefore, the number of square table that's needed will be 12 square tables.

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Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

Answer:

a conjecture, a postulate, and a definition

Step-by-step explanation:

A premise is an assumption something is true.  When completing a proof, we must use already established truths to get us from one step to another; these can be theorems, postulates, conjectures, or definitions.  However, premises themselves cannot be used to prove something.

you don't show the options but it should look something like this:

195 +15d = 360

answer:

subtract 195 from each side

15d = 165

d = 165/15  =11

 he needs to walk 11 dogs

The equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and number of dogs is 11.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Frank needs a total of $360 to cover his expenses of the week. He earns $195 a week working at a restaurant and also walks dogs to supplement his income, frank charges $15 per dog that he walks.

The equation, which can be used to find the number of dogs d that frank needs to walk to cover his expenses,

[tex]15d+195=360[/tex]

Solve it further to find the number of dogs d,

[tex]15d+195=360\\15d=360-195\\d=\dfrac{165}{15}\\d=11[/tex]

Thus, the equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and the number of dogs is 11.

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From the information, A is a right triangle, B is an acute triangle and C is an acute angle.

A polygon with three sides, angles, and vertices is called a triangle.

Given that, triangle side lengths, we need to identify the triangle as acute, right or obtuse,

How to solve the triangle?

It will be a right triangle if a² + b² = c², It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².

1) a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25

This is a right triangle.

2) a² + b² = 5² + 6²

= 25 + 36 = 61

c² = 7² = 49

61 > 49 = аcute triangle.

3) a² + b² = 8² + 9²

= 64 + 81 = 145

c² = 12² = 144

145 > 144 = аcute triangle.

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To write the given numbers as words, you can break them down into groups of three digits from right to left and then write each group separately. For example, 38 is written as thirty-eight.

To write the numbers as words, we can break them down into groups of three digits from right to left. Here are the numbers written as words:

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To write the given numbers as words, we break them down into their place values. 38 can be written as thirty-eight, 116 as one hundred sixteen, 573 as five hundred seventy-three, 1.821 as one thousand eight hundred twenty-one, 754.322 as seven hundred fifty-four thousand three hundred twenty-two, and 6.615.010 as six million six hundred fifteen thousand ten.

In order to write the given numbers as words, we can break them down into their place values. Let's analyze each number:

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