NEED HELP ASAP

X and y are in direct proportion, when x is 8, y is 12. Which of the following is not a

Nat2105 [25]

Answer:

d.

Step-by-step explanation:

if x varies directly as y,

x = ky

8 = 12k

12k = 8

k = 8/ 12

k = 2/3,

x = 2/3 y

now substitute the value of any of the numbers of each pair, and check if it works:

for e.g, find x when y = 15

x = 2/3y

x = 2/3 × 15

x = 10

since you obtain x = 10 when y = 15, the pair is a possible corresponding value of x and y. now do the same for the rest .

ii) x = 2/3y

x = 2/3 × 3, when y = 3

x = 2

hence, this is also a possible pair of x and y values.

iii) x = 2/3y

x = 2/3 × 9 when y = 9

x = 6

again, a possible pair of x and y values.

iv) x = 2/3y

x = 2/3 × 20 when y = 20

x = 40/3

here, when y = 20, x is not 15. it is 40/3.

thus, it can be determined that this is not a possible pair of x and y values.

please try to understand and have a great day!

8 0

1 year ago

In sentence 7, the phrase by all accounts is best

hram777 [196]

In sentence 7, the phrase by all accounts is best replaced by however.

Correct option is A

The sentence that precedes 7 states something that is in contrast with it.
Therefore 'by all accounts' in sentence should be changed to 'however' as it is generally used to present something that is different from or contrasts with the previous statement.
Thus A is the best answer. The other options are incorrect because they do not convey the contrast that is required in the given context.

What is a phrase in grammar?

In syntax and grammar, a phrase is a group of words which act together as a grammatical unit.
For instance, the English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy".
Phrases can consist of a single word or a complete sentence.

Learn more about Phrases

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5 0

1 year ago

What is the factored form of x^3 + 125?

Lerok [7]

$x^3+125=x^3+5^3$

Sums of cubes can be factored as

$a^3+b^3=(a+b)(a^2+ab+b^2)$

So

$x^3+125=(x+5)(x^2+5x+25)$

7 0

3 years ago

Read 2 more answers

Write the linear equation that goes through the points (2, 20) and (-3, 8). *

Lyrx [107]

Answer:

2.4x+15.2

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

10 months ago