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2 years ago

Select the correct answer.

Mathematics

1 answer:

earnstyle [38]2 years ago

3 0

The equations are both the same with a slope of 2 and y-intercept of 3.

<h3>Solution to system of equation</h3>

A line is the distance between two points. Given the equations below;

2y - 4x = 6

y = 2x + 3

___________

y - 2x = 3

y = 2x + 3

The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.

Learn more on equation of a line here: brainly.com/question/13763238

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X y

Darina [25.2K]

Answer:

Part 1) The rate of change is $\frac{17}{15}$

Part 2) The initial value is 68

Part 3) The function rule to the linear model is $y=\frac{17}{15}x+68$

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

step 1

Find the slope

take two points from the table

(0,68) and (15,85)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{85-68}{15-0}$

$m=\frac{17}{15}$

In a linear function , the slope is the same that the rate of change

therefore

The rate of change is $\frac{17}{15}$

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the table

For x=0, y=68

therefore

The y-intercept is

$b=68$

The y-intercept is also called the initial value

therefore

The initial value is 68

step 3

Determine the function rule to the linear model

$y=mx+b$

we have

$m=\frac{17}{15}$

$b=68$

substitute

$y=\frac{17}{15}x+68$

8 0

3 years ago

I would really appreciate help with the following, along with work shown so I can understand how these were solved.

Alja [10]

First, you have to know the double angle formula:

sin 2A = 2 sin A cos A

cos 2A = cos² A − sin² A = 2 cos² A − 1 = 1 − 2 sin² A

tan 2A = 2 tan A / (1 − tan² A)

Next, find the other leg: 17^2-15^=64, √64 is 8, so the unknown leg length is 8.

sinα=15/17, cosα=8/17, tanα=15/8

sinβ=8/17, cosβ15/17, tanβ=8/15

Plug these values in the above formula, you'll have your answers.

For the half angles, know the half-angle formula:

sin(B/2) = ± √(1 − cos B)/2

cos(B/2) = ± √(1 + cos B)/2

tan(B/2) = (1 − cos B) / sin B = sin B / (1 + cos B)

refer to this website for details:

https://brownmath.com/twt/double.htm

For the power reduction formula, please search for it. I tried to copy and paste here, but it wouldn't paste.

for number 4, factor the quadratic equation into (cscx-8)(cscx+1)=0

cscx=8 or cscx=-1

You may not have the csc button on your calculator. Recall that csc is 1/sin, so sinx=1/8 or sinx=-1, so x is either 7.18 or 270 degrees

6 0

3 years ago

-54/-9 - (-5)= need help ASAP

Semenov [28]

So the answer is 13.5

Look at the attached picture⤴

Hope it will help u..

4 0

3 years ago

Read 2 more answers

When using technology what is the second step in constructing a copy of angle SUN

iVinArrow [24]

First, draw a circle with point U as the center point and point S as the end of the radius. Then, draw another circle with point D as the center point and the radius length equal to US. Next, draw ray DE away from angle SUN. Finally, draw angle SUN.

5 0

2 years ago

A regular decagon has a side length of 4 centimeters long if the decagon is divided into 10 congruent triangles each has an appr

ratelena [41]

Area of decagon is given by:
Area=1/2(nsr)
where:
n=number of sides
s=side length
r=height
thus the area will be given by:
Area=1/2(10*4*6.2)
Area=124 cm^2

4 0

3 years ago