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1 year ago

What is the Y-Intercept of the line that has a slope of -4 and passes through the point (4,-6)

Mathematics

2 answers:

svlad2 [7]1 year ago

8 0

The y intercept is the y intercept which is 2

IrinaVladis [17]1 year ago

6 0

Answer:

Y-intercept = 22

Step-by-step explanation:

The equation of a line in slope-intercept format is given by the equation y=mx+c

where m is the slope and c the y-intercept.

(The y-intercept is the value of y when x = 0)

Slope given as -4

And we know it passes through the point(4,6) ie at x=4, y =6

Substitute in above equation to get value of c, the y-intercept

6 = -4(4) + c

6 = -16 + c

c = 22

And this is the y-intercept

The equation of the line is y = -4x + 22

See attached figure for graph

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the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.

laila [671]

The perimeter of a rectangle is <u>length + length + width + width</u>.

We know that the length of a rectangle is 3cm more than its width, which gives us the equation: (l for length and w for width)

l = 3 + w

We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

98 = 2l + 2w (equation for perimeter of a rectangle as noted above)

We can divide both sides of this equation by 2 to get:

49 = l + w

Now we'll stick l = 3 + w into the above equation, which gives us:

49 = 3 + w + w

which simplifies to 49 = 3 + 2w.

Now we'll subtract 3 from both sides:

49 - 3 = 46

3 + 2w - 3 = 2w

which gives us 46 = 2w.

Dividing both sides by 2 gives us 23 = w.

Substituting w = 23 into the equation l = 3 + w gives us:

l = 3 + 23

l = 26cm.

Let's check our answer. 26cm is 3cm more than 23cm. 26cm + 26cm + 23cm + 23cm gives us 98cm. The length is 26cm and the width is 23cm.

7 0

3 years ago

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

Artist 52 [7]

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $44,500

Sample mean, $\bar{x}$ = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = $9,500

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}$

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37$

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income than the national average

5 0

3 years ago

Which value is NOT a solution of the inequality -2x + 5<7?

Ivenika [448]

Answer:1

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

-2*x+5-(7)<0

Step by step solution :

STEP

Pulling out like terms

1.1 Pull out like factors :

-2x - 2 = -2 • (x + 1)

Equation at the end of step

STEP

2.1 Divide both sides by -2

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2 Subtract 1 from both sides

x > -1

Inequality Plot :

2.3 Inequality plot for

-2.000 X - 2.000 > 0

One solution was found :

x > -1

5 0

3 years ago

Read 2 more answers

A plumber charges $52.50 per hour plus a $75.00 service charge. Your father's firm hired him to fix some leaky pipes.

Setler79 [48]

Cost as a function of hours is:

c(h)=52.5h+75

4 0

3 years ago

Hiya Guys , Can you help me if you do one answer each Ill give you a thanks and Stars / Rating and A Brainlist , please help !!!

Volgvan

Answer:

I don't know I'm sorry I will tell you another answer asks me to

6 0

3 years ago