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4 years ago

Which graph matches the equation y+6=3/4(x+4)?

Mathematics

2 answers:

Scilla [17]4 years ago

7 0

Answer:

The equation of the function is

$\rightarrow y+6=\frac{3}{4} \times (x+4)\\\\4 \times (y+6)=3 \times (x+4)\\\\4 y+24=3x+12\\\\3x-4y=24-12\\\\3x-4y=12\\\\\frac{3x}{12}+\frac{4y}{-12}=1\\\\\frac{x}{4}+\frac{y}{-3}=1$

The function will cut x axis at (4,0) and y axis at (0,-3).

To draw a line you need two distinct points.

Draw a line passing through (4,0) and (0,-3).

Sloan [31]4 years ago

6 0

Answer:

Step-by-step explanation:

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lapo4ka [179]

3w+8=50

3w=50-8=42

w= 42/3=14

7 0

3 years ago

A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32

olga2289 [7]

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

32*t = 32

t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

4 0

3 years ago

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 2.2 2.2% with a standard deviation of 6.3 6.3%.

Svet_ta [14]

Answer:

a) 0.625; b) 16.879; c) 8.442

Step-by-step explanation:

Since this is a normal distribution, we want the value of the mean, μ: 2.2; and the value of the standard deviation, σ: 6.3.

For the 40th percentile, we look in a z chart. We want to find the value as close to 0.40 as we can get; this is 0.4013, and it corresponds to a z score of z = -0.25.

Our formula for a z score is $z=\frac{X-\mu}{\sigma}$ . Using our values, we have

-0.25 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(-0.25) = X-2.2

-1.575 = X-2.2

Add 2.2 to each side:

-1.575+2.2 = X-2.2+2.2

0.625 = X

For the 99th percentile, the value in the z chart closest to 0.99 is 0.9901, which corresponds to a z score of z = 2.33:

2.33 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(2.33) = X-2.2

14.679 = X-2.2

Add 2.2 to each side:

14.679+2.2 = X-2.2+2.2

16.879 = X

For the IQR, we find the values for the 75th percentile (Q3) and the 25th percentile (Q1). The value in a z chart closest to 0.75 is 0.7486, which corresponds to a z score of z = 0.67:

0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(0.67) = X-2.2

4.221 = X-2.2

Add 2.2 to each side:

4.221+2.2 = X-2.2+2.2

6.421 = X

The value in a z chart closest to 0.25 is 0.2514, which corresponds to a z score of z = -0.67:

-0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(-0.67) = X-2.2

-4.221 = X-2.2

Add 2.2 to each side:

-4.221+2.2 = X-2.2+2.2

-2.021 = X

This makes the interquartile range

6.421--2.021 = 8.442

8 0

3 years ago

What is $65.25 - 15% =?

ella [17]

Answer:

$55.36

Step-by-step explanation:

15% of 65.25 is 9.89

then that'd be 65.25 - 9.89 = 55.36

hope this helps/is right.

6 0

3 years ago

Read 2 more answers

Combine like terms to create an equivalent expression.

zvonat [6]

Answer:

ytg4f3udy2iujsjwrhubygjrkgthjeyiulk4g;5tpyoih5jeklg5g45h5y4mjtgrety87gi3h4h5gt4f526h37uj65y

Step-by-step explanation:

5 0

4 years ago