The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?

Answer:

∠AOB and ∠COD are vertical angles

∠DOE and ∠COD are complementary, adjacent

∠AOB and ∠AOD are supplementary, adjacent.

Step-by-step explanation:

Let's start with ∠AOB and ∠COD.

Looking at this, we can see they are the same angles formed by two lines that intersected. These are vertical angles as they are opposite each other.

∠DOE and ∠COD together form the angle ∠EOC, which is a right angle. Complementary angles are any of two that add up to 90°, so these two angles are complementary. They are also adjacent because they are right next to each other.

∠AOB and ∠AOD together form the angle ∠BOD, which has a measure of 180°. Supplementary angles are any of two that add up to 180°, so ∠AOB and ∠AOD are supplementary. They are also adjacent as they are touching/right next to each other.

I hope this helped!

Answer:

The proportion of college students who work​ year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58​% of college students work​ year-round.

A random sample of 400 college​ students, 232 say they work​ year-round.

To test the researcher's claim use a one-proportion z-test.

The hypothesis can be defined as follows:

H₀: The proportion of college students who work​ year-round is 58%, i.e. p = 0.58.

Hₐ: The proportion of college students who work​ year-round is 58%, i.e. p ≠ 0.58. C

Compute the sample proportion as follows:

 [tex]\hat p=\frac{232}{400}=0.58[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0[/tex]

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 [tex]p-value=2\times P(z<0)=2\times 0.5=1[/tex]

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work​ year-round is 58%.

Answer:

9m(n)^3 +14m(n)^2

Step-by-step explanation:

6m(n)^3 - m(n)^2 + 3m(n)^3 + 15m(n)^2

=> 6m(n)^3 + 3m(n)^3 + 15m(n)^2 - m(n)^2

=> 9m(n)^3 +14m(n)^2

Answer:

A. [tex] 3 {}^{9} [/tex]

Step-by-step explanation:

[tex]3 {}^{4} \times {3}^{5} = {3}^{4 + 5} = 3 {}^{9} [/tex]

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{3^9}[/tex]

Step-by-step explanation:

[tex]3^5 \times 3^4[/tex]

Apply the law of exponents : [tex]a^b \times a^c = a^{b+c}[/tex]

The exponent product rule states that, when multiplying two exponents that have the same base, you can add the exponents.

[tex]3^{5+4}[/tex]

[tex]3^9[/tex]

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = [tex]C(n,k)[/tex] not nk

Answer:

True

Step-by-step explanation:

apec

Answer: On the 20th day, he will give $5242.88

Step-by-step explanation: This is a geometric series with elements:

initial value ([tex]a_{0}[/tex]) = 0.01

ratio = 2

At the twentieth day means the 20th term, i.e. n = 20.

To determine that term, use the formula: [tex]a_{n} = a_{0}.r^{n-1}[/tex]

Substituing terms:

[tex]a_{20} = 0.01.2^{20-1}[/tex]

[tex]a_{20} = 0.01.2^{19}[/tex]

[tex]a_{20} = 0.01.524288[/tex]

[tex]a_{20} = 5242.88[/tex]

Then, on the 20th day, your uncle gave to you $5242.88

Answer:

6.1

Step-by-step explanation:

use law of cosines

d² = e² + f² - 2ef cos D

d² = 9² + 10² - 2(9)(10) cos 37

d² = 81 + 100 - 143.75

d² = 37.25

d = 6.1

Answer:

Option D is the correct option.

Step-by-step explanation:

Given,

Diameter ( D ) = 10 meters

Radius ( r ) = 10 ÷ 2 = 5 meters

Height ( h ) = 8 meters

Volume = ?

Now, let's find the volume of the given cylinder:

[tex]\pi \: {r}^{2} h[/tex]

Plug the values

[tex] = 3.14 \times {5}^{2} \times 8[/tex]

Evaluate the power

[tex] = 3.14 \times 25 \times 8[/tex]

Calculate the products

[tex] = 628 \: {m}^{2} [/tex]

Hope this helps...

Best regards!!

Answer:

[tex]-24x^4+6x^3+25x^2+16[/tex]

Step 1:

We need to place the numbers in descending order of the power. Here, [tex]-24x^4[/tex] has the largest power, so that number goes first. We keep doing this until we end up with our final expression, placed in order based on the powers.

[tex]-24x^4+6x^3+25x^2+17-7+6[/tex]

Step 2:

We can see that the last three numbers, 17, -7, and 6, don't have variables or powers, so we simplify by adding (and subtracting) them.

[tex]17-7=10\\10+6=16[/tex]

Our final equation:

[tex]-24x^4+6x^3+25x^2+16[/tex]

Answer:

54

Step-by-step explanation:

im not that good so u should cheek it first

Answer: 9a + 249

Step-by-step explanation: 9a + 249 and a would be one cause these numbers are independent

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Gradient formula :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]let \: (x1 \: , \: y1) \: be \: ( - 2 \: , \: 0)[/tex]

[tex]let \: (x2 \: , \: y2) \: be \: (0 \: , \: 4)[/tex]

[tex]m = \frac{4 - 0}{0 - ( - 2)} [/tex]

[tex]m = \frac{4}{2} [/tex]

[tex]m = 2[/tex]

Answer:

2

Step-by-step explanation:

The formula you use to find the slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

First, you want to substitute

[tex]\frac{4-0}{0--2}[/tex]

Which simplifies to

[tex]\frac{4-0}{0+2}[/tex]

Because two negatives equal a positive

The next step is to add and subtract

[tex]\frac{4}{2}[/tex]

Which simplifies to

[tex]\frac{2}{1}[/tex]

Which equals

2.

Hope this helped, if you have any questions, feel free to ask.

Have a good day! :)

Answer:

No amplitude

Period is pi

Step-by-step explanation:

Step-by-step explanation:

Answer:

The answer is C.) (2, -5)

Answer: Combination

There are 56 committees possible

============================================

Explanation:

The reason why we know we'll use a combination (instead of a permutation) is because order does not matter. There are no ranking positions on a committee. No one person has a special job compared to the other. The ordering of a committee doesn't matter. All that matters is the entire group itself. For instance, if we had people A,B,C then the committee ABC is the same as CBA and BAC. We would have to introduce a different person, say person D, to get a new committee group.

We have n = 8 people overall to choose from and r = 5 slots to fill. Use the combination formula to get

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_8 C _5 = \frac{8!}{5!*(8-5)!}\\\\_8 C _5 = \frac{8!}{5!*3!}\\\\_8 C _5 = \frac{8*7*6*5!}{5!*3!}\\\\_8 C _5 = \frac{8*7*6}{3!}\\\\_8 C _5 = \frac{8*7*6}{3*2*1}\\\\_8 C _5 = \frac{56*6}{6}\\\\_8 C _5 = 56\\\\[/tex]

We can conclude there are 56 different committees possible.

Answer:

The answer is B CPCT

Step-by-step explanation:

In an isosceles triangle ΔHKJ with

Construct KM, a bisector of the base HJ.

to prove:

in ΔKHM and ΔKJM

bisects      [Given]

Segment bisectors states that a line or segment which cuts another line segment into two equal parts.

then, by definition of Segment bisector :

       [Given]

Reflexive property of congruence that any geometric figure is congruent to itself.

  [by definition of Reflexive property of congruence]

SSS(Side-Side-Side) Postulates states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

therefore, by SSS postulates

ΔKHM  ΔKJM

By CPCT [Corresponding Part of congruent Triangle]

         proved!

hope i helped

-lvr

Answer:

C: 40 teaspoons.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a straight proportion question. Many things can be solved with a proportion. This is a good example of what is possible.

Formula

3 teaspoons       x

======              =========

36 cookies        480 cookies

Notice that in the end, the units of teaspoons will be left. Multiply both sides by 480

3 teaspoons * 480 cookies

=======================            =  X

36 cookies

Notice the cookies cancel

3 teaspoons * 480

===============     =  x

36

x = 1440/36 teaspoons.

x = 40 teaspoons

answer: C

Answer:

1,1,3,1,1

Step-by-step explanation:

Answer:

0       1

1        1

2       3

3       1

4       1

Step-by-step explanation:

You would just count how many 0 there are in the set and there are 1 and you would put in by 0. For 1 there are 1, for 2 there are 3, for 3 there are 1, and for 4 there are 1.

Answer:

y=x+2

Step-by-step explanation:

I have included a graph with the equation and both points on it (click/tap on it to see the full picture.)

Answer: y= x+2

Step-by-step explanation:

Answer:

poop

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

last option

Step-by-step explanation:

Again, 1 cm represents 8 / 2 = 4 feet so the width is 4 * 4 = 16 and the length is 6 * 4 = 24.

Answer:

64/9

Step-by-step explanation:

(8/3) ^2

( 8/3) * (8/3)

64/9

64/9 is the answer <3<3 Hope this helps

by bargaining with the owner, vying for discounts or insisting on multiple products for a complimentary value deal

Answer:

C. Test for Goodness-of-fit.

Step-by-step explanation:

C. Test for Goodness-of-fit would be most appropriate for the given situation.

A. Test Of  Homogeneity.

The value of q is large when the sample variances differ greatly and is zero when all variances are zero . Sample variances do not differ greatly in the given question.

B. Test for Independence.

The chi square  is used to test the hypothesis about the independence of two variables each of which is classified into number of attributes. They are not classified into attributes.

C. Test for Goodness-of-fit.

The chi square test is applicable when the cell probabilities depend upon unknown parameters provided that the unknown parameters are replaced with  their estimates and provided that one degree of freedom is deducted for each parameter estimated.

Answer:

T = 3(2)ᵈ⁻¹

Step-by-step explanation:

This is a geometric series, where the first term is 3 and the common ratio is 2.

T = 3(2)ᵈ⁻¹

This can be rewritten as:

T = ³/₂ (2)ᵈ

Answer:

10KB = 1MB

Step-by-step explanation:

Since 1KB => 2*10bytes

1MB => 2*20bytes

Therefore 10KB => 1MB

Answer:

Octahedron  Answer B) in your list

Step-by-step explanation:

The octahedron is the three dimensional figure that contains 8 equilateral triangles as its faces. It looks like 2 pyramids with square base and lateral equilateral triangles joined by their square bases

Answer:

C

Step-by-step explanation:

apeeeex

Answer:

x + 2y ≤ 12

x + 2y = 12

Step-by-step explanation:

The teachers can not give more than 12 hours of homework so this is the answer. those are the 2 equations you can use. It under 12 hours or equal to 12 hours.

Answer:

Part A: x + 2y ≤ 12.

Part B: y = -1/2x + 6.

Part C: (0, 0).

Step-by-step explanation:

Part A: The total hours of homework have to be 12 hours, and it has to be either 12 hours or less. So, we have ≤ 12.

They take 1 math course with x hours of homework, so in total, that is 1 * x = x hours of math homework.

They take 2 science courses with y hours of homework, so in total, that is 2 * y = 2y hours of science homework.

The inequality would then be x + 2y ≤ 12.

Part B: x + 2y = 12

2y = -x + 12

y = -1/2x + 6

You can  use the Math is Fun: Function Grapher and Calculator to find the graph of the line, shown below.

Part C: Since the inequality uses a ≤ symbol, we know that the shading will be underneath the line. An appropriate point below the line includes (0, 0). We will test out whether it works as a point included in the inequality.

x + 2y ≤ 12

0 + 2 * 0 ≤ 12

0 + 0 ≤ 12

0 ≤ 12

Since this is a true statement, (0, 0) holds true for the inequality.

Hope this helps!

Answer:

(x - 1)² + (y - 2)² = 20

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given the endpoints, then the centre is at the midpoint

C = [ [tex]\frac{-3+5}{2}[/tex], [tex]\frac{0+4}{2}[/tex] ] = (1, 2 )

The radius is the distance from the centre to either of the 2 endpoints.

Use the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)

r = [tex]\sqrt{(-3-1)^2+(0-2)^2}[/tex]

  = [tex]\sqrt{(-4)^2+(-2)^2}[/tex]

  = [tex]\sqrt{16+4}[/tex]

  = [tex]\sqrt{20}[/tex]

Thus equation of circle is

(x - 1)² + (y - 2)² = ([tex]\sqrt{20}[/tex] )² , that is

(x - 1)² + (y - 2)² = 20

Answer:

Step-by-step explanation:

1.  4x = angle 4

x = angle 1

Angle 1 + angle 4 = 180

4x + x = 180

5x = 180

2. 55 = angle 2

angle 1 = 68

angle 3 = 55 + 68 = 123 = 180 - 123 = 57

Angle 4 = 57

Hope this helped,

kavitha