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3 years ago

9

The graph of the equation y equals 1/2 x - 3 determine the value of y for the point (4,y).

1 answer:

oksano4ka [1.4K]3 years ago

3 0

The answer is b. If your problem is y=1/2x-3

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Find the y-intercept of the following equation. Simplify your answer.<br> 10x + y = 8

vredina [299]

Answer: 8

Explanation:

Form: y = mx + b

Where:
m is the slope
b is the y-intercept

We have:
10x + y = 8
y = -10x + 8

Thus, the y-intercept is 8

4 0

2 years ago

<img src="https://tex.z-dn.net/?f=0%20%3D%20%20%20-%204.9t%20%7B%7D%5E%7B2%7D%20%20%2B%2027t%20%2B%202.4" id="TexFormula1" title

marta [7]

$0 = - 4.9t {}^{2} + 27t + 2.4$
Convert decimals to fractions

$0 = - \frac{49}{10} t {}^{2} + 27t + \frac{12}{5}$
Multiply both sides by 10

$0 = - 49t {}^{2} + 270t + 24$
Move expression to the left.

$0 + 49t {}^{2} - 270t - 24 = 0$
Remove zero.

$49t {}^{2} - 270t - 24 = 0$ Solve the quadratic equation.

$t = \frac{ - ( - 270) + - \sqrt{( - 270) {}^{2} - 4 \times 49 \times ( - 24) } }{2 \times 49}$
Remove parenthesis and calculate.

$t = \frac{270 + - \sqrt{72900 + 4704} }{98}$
Add the numbers

$t = \frac{270 + - 77604}{98}$
Separate the solutions

$t = \frac{270 + \sqrt{77604} }{98} \\ t = \frac{270 - \sqrt{77604} }{98}$
The final solution are
$t1 = \frac{270 - \sqrt{77604} }{98} , t2 = \frac{270 + \sqrt{77604} }{98}$

7 0

3 years ago

In the adjoining figure, area of trangle ABC is

Zepler [3.9K]

Answer:

$PQ=4\ cm$

Step-by-step explanation:

see the attached figure with the letter D to better understand the problem

we know that

The segment side AD is the height of triangle ABC

so

Triangles PBQ and ABD are similar by AA Similarity Theorem

The area of triangle ABC is equal to

$A=\frac{1}{2}(BC)(AD)$

we have

$A=48\ cm^2\\BC=12\ cm$

substitute

$48=\frac{1}{2}(12)(AD)$

$AD=8\ cm$

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional

so

$\frac{BP}{AB}=\frac{PQ}{AD}$

substitute the given values

$\frac{BP}{2BP}=\frac{PQ}{8}$

$\frac{1}{2}=\frac{PQ}{8}$

$PQ=4\ cm$

3 0

3 years ago

What is the value of \dfrac{d}{dx}\left(\dfrac{2x+3}{3x^2-4}\right) dx d ( 3x 2 −4 2x+3 )start fraction, d, divided by, d, x

stellarik [79]

Answer:

4.

Step-by-step explanation:

We are asked to find the value of expression $\frac{d}{dx}(\frac{2x+3}{3x^2-4})$ at $x=-1$ .

First of all, we will find the derivative of the given expression using "Quotient Rule of Derivatives" as shown below:

$(\frac{f(x)}{g(x)})'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{(g(x))^2}$

$\frac{d}{dx}(\frac{2x+3}{3x^2-4})$

$\frac{\frac{d}{dx}(2x+3)*(3x^2-4)-(2x+3)*\frac{d}{dx}(3x^2-4)}{(3x^2-4)^2}$

$\frac{2*(3x^2-4)-(2x+3)*(6x)}{(3x^2-4)^2}$

$\frac{6x^2-8-12x^2-18x}{(3x^2-4)^2}$

$\frac{-6x^2-18x-8}{(3x^2-4)^2}$

Therefore, our required derivative is $\frac{-6x^2-18x-8}{(3x^2-4)^2}$ .

Now, we will substitute $x=-1$ in our derivative to find the required value as:

$\frac{-6(-1)^2-18(-1)-8}{(3(-1)^2-4)^2}$

$\frac{-6(1)+18-8}{(3(1)-4)^2}$

$\frac{-6+18-8}{(3-4)^2}$

$\frac{4}{(-1)^2}$

$\frac{4}{1}$

$4$

Therefore, the value of expression $\frac{d}{dx}(\frac{2x+3}{3x^2-4})$ at $x=-1$ is 4.

6 0

3 years ago

Use the image to determine the height of the girl.

sergey [27]

Answer:

72 in

Step-by-step explanation:

We know that 120 in is equal to the sum of the given height expressions.

(9x) +(7x-8) = 120

16x = 128 . . . . . . add 8 and simplify

x = 8 . . . . . . . . . . divide by 16

9x = girl's height = 9·8 = 72 . . . . inches

The height of the girl is 72 inches.

8 0

3 years ago