2) find an equation of the line theough the given
points. Give the final answer in slope-intercept form.
(2,-2) (-1,4)

Answers

Answer 1

Answer:

y = -2x + 2

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (2, -1)

Points on the y-axis (y1, y2) = (-2, 4)

To find the equation of line in slope intercept form;

First of all, we would determine the slope of the line.

Mathematically, slope is given by the formula;

[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]

[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

Substituting into the equation, we have;

[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]

[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]

[tex] Slope, m = \frac {6}{-3} [/tex]

Slope, m = -2

Next, we would use the following formula to find the equation of the line;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - (-2) = -2(x - 2)

y + 2 = -2x + 4

y = -2x + 4 - 2

y = -2x + 2 = mx + c


Related Questions

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Lower Bound Upper Bound Frequency
56 64 11
65 73 15
74 82 14
83 91 4
92 100 11

Required:
a. What is the sample standard deviation?
b. What is the sample variance?

Answers

Answer:

[tex]\sigma = 12.5[/tex] ---- sample standard deviation

[tex]\sigma^2 = 157.2[/tex] ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

[tex]x_1 = \frac{56 + 64}{2} = 60[/tex]

[tex]x_2 = \frac{65 + 73}{2} = 69[/tex]

And so on

So, the table becomes:

[tex]\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}[/tex]

Calculate the mean

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}[/tex]

[tex]\bar x = \frac{4191}{55}[/tex]

[tex]\bar x = 76.2[/tex]

The variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}[/tex]

[tex]\sigma^2 = \frac{8488.8}{54}[/tex]

[tex]\sigma^2 = 157.2[/tex]

The sample standard deviation is:

[tex]\sigma = \sqrt{\sigma^2[/tex]

[tex]\sigma = \sqrt{157.2[/tex]

[tex]\sigma = 12.5[/tex]

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

[tex]\sigma^2 = 157.2[/tex]

A researcher suspects that people who are abused as children tend to be more prone to severe depression as young adults. She prepares a questionnaire that measures depression and that also asks many personal questions about childhood experiences. Think about how an appropriate description of the purpose of this research would be written (to be read by subjects) in order to obtain their informed consent. You must balance the conflicting goals of not deceiving the subjects about what the questionnaire will tell about them and not biasing the sample by scaring off people with painful childhood experiences.Based on this criteria, which of the statements is an appropriate description of the purpose of the research, that would be read by subjects in order to obtain their informed consent? Pay close attention to the wording of each description. a. The purpose of this research is to study whether people who are abused as children tend to be more prone to severe depression as young adults. b. The purpose of this research is to study whether childhood abuse tends to cause severe depression in young adults. c. The purpose of this research is to study whether severe depression is a result of people having bad experiences in childhood. d. The purpose of this research is to study how childhood experiences are related to risk of depression. e. The purpose of this research is to study different experiences people have had in childhood.

Answers

Answer:

d. The purpose of this research is to study how childhood experiences are related to risk of depression.

Step-by-step explanation:

This answer satisfies the requirements of the question as it uses mild language that will not scare off respondents while also maintaining transparency and truthfulness. This can be seen in wordings such as;

a. Childhood experiences: Instead of explicitly using the term child-hood abuse which can scare off respondents, this phrase uses a milder form of the word that is also not dishonest in itself.

b. Risk of depression: Instead of using heavy terms such as "severe depression," or shady terms like "bad expreciences," the phrase, "risk of depression," helps the subjects to honestly identify what the question is about in a mild way.

Which of the following will have 6 at unit place?  a.19² b.11² c.24² d.13²​

Answers

i wanna say the answer is c)24^2

factor x^2-8x-48 completely

Answers

Answer: (X-12)(x+4)

The middle number is -8 and the last number is -48.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -8

Multiply together to get -48

Can you think of the two numbers?

Try 4 and -12:

4+-12 = -8

4*-12 = -48

Fill in the blanks in

(x+_)(x+_)

with 4 and -12 to get...

(x+4)(x-12)

Answer:

(x+4)(x−12)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { (x - 12)(x + 4 )}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{2} - 8x - 48[/tex]

[tex] = {x}^{2} + 4x - 12x - 48[/tex]

Taking [tex]x[/tex] as common from first two terms and [tex]12[/tex] from last two terms, we have

[tex] = x \: (x + 4) - 12 \: (x + 4)[/tex]

Taking the factor [tex](x+4)[/tex] as common,

[tex] = (x - 12)(x + 4)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

hi pls help me now i'll gibe you brainest,thank you​

Answers

Answer:

64 cm^3

Step-by-step explanation:

answer for question no 5

length , breadth and height of the cube are always equal .So

here length = 4 cm

volume of a cube = l^3

=4^3

=64 m^2

On a
paper, graph y < -2x Then determine which answer matches
the graph you drew.

Answers

Answer:

theres the graph

Step-by-step explanation:

Use the limit definition of the derivative to find the instantaneous rate of change of
f(x)=5x^2+3x+3 at x=4

Answers

[tex]f'(4) = 43[/tex]

Explanation:

Given: [tex]f(x)=5x^2 + 3x + 3[/tex]

[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]

Note that

[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]

[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]

[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]

Substituting the above equation into the expression for f'(x), we can then write f'(x) as

[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]

[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]

[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]

Therefore,

[tex]f'(4) = 10(4) + 3 = 43[/tex]

Belief in UFOs A survey found that of people believe that they have seen a UFO. Choose a sample of people at random. Find the probability of the following. (a) At least 3 people believe that they have seen a UFO.(b) 2 or 3 people believe that they have seen a UFO.

Answers

Answer:

b is the answer am not sure you know

Answer:

a) 3/10

b)3/10

Step-by-step explanation:

let the sample of people be 10

so,

a) total outcome=10

favourable outcome=3

P(seeing a UFO)= 3/10

b) total outcome=10

favourable outcome=2 or 3

P(seeing a UFO)= 2/10+3/10-(2/10

5/10-2/10

=3/10

If 5(y-2) - 3(y + 4) = 0, then y
IS
A. -1
B. 3
C. 7
D. 11​

Answers

Answer:

Y is -1.

Step-by-step explanation:

If you substitute the values, you find that that's the correct answer.

11 because you distribute the 5 to y and -2 and distribute the -3 to y and 4 so it would be (5y-10) and (-3y-12) combine like terms which would end in 2y and -22 set up as 2y=-22 and solve getting 11

What is the solution to the HELP HELP equation m+4
m2
-?
m2-16
4-m
Om =-4
O m = -2
Om = 2.
Om = 4

Answers

Answer:

m = -2

Step-by-step explanation:

[tex]\frac{m}{m+4} + \frac{4}{4-m} = \frac{m^2}{m^2-16}\\\\\frac{m}{m+4} + \frac{4}{-(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex]                      [tex][ \ ( 4 - m) = - (m -4) \ ][/tex]

[tex]\frac{m}{m+4} + \frac{-4}{(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex]                        [tex][ \ \frac{a}{-b} = \frac{-a}{b}\ ][/tex]

[tex]\frac{m}{m+4} - \frac{4}{m-4} = \frac{m^2}{m^2-16}\\\\[/tex]                         [tex][ \ \frac{x}{y} + \frac{-a}{b} = \frac{x}{y} - \frac{a}{b} \ ][/tex]

[tex]\frac{m(m-4)-4(m+4)}{(m-4)(m+4)} = \frac{m^2}{m^2-16}\\\\\frac{m^2 -4m -4m-16}{(m^2-16)} = \frac{m^2}{m^2-16}\\\\[/tex]                     [tex][ \ T aking \ LCM \ and \ simplifying\ ][/tex]

[tex]m^2 - 8m -16 = m^2[/tex]                           [tex][ \ \frac{a}{b} = \frac{c}{b} => a = c \ ][/tex]

[tex]m^2 - m^2 - 8m - 16 = 0\\\\0 -8m = 16\\\\-8m = 16 \\\\m = \frac{16}{-8} = -2[/tex]

Which is an x-intercept of the continuous function in the
table?
-2
-1
0
1
2
3
f(x)
-10
48
46
44
-2
0
(0, -6)
(3.0)
O (-6.0)
(0, 3)

Answers

Answer:

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

so

In the table we have

(-1, 0)(−1,0) is a x-intercept, because

For x=-1x=−1 the value of the function is equal to zero

(-6, 0)(−6,0) is a x-intercept, because

For x=-6x=−6 the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

(-1, 0)(−1,0)

(-6, 0)(−6,0)

Julie borrowed 3500 for 3years at a seven and a half simple interest rate how much interest rate is that​

Answers

Answer:

787.50

Step-by-step explanation:

interest=3500*7.5*3/100

interest=35*7.5*3

interest=787.50

giving brainliest please answer

(answer D is) Marco's, George, Andy, Rubens


A
B
C
D
?​

Answers

A is right. Every 2nd person

please help. question in picture ​

Answers

Answer:

Step-by-step explanation:

28
Here are two rectangles.
Р
e
B
D
S
R
QR = 20 cm
BC = PQ
The perimeter of ABCD is 52 cm
The area of PQRS is 90 cm?
Find the length of AB.

Answers

9514 1404 393

Answer:

  21.5 cm

Step-by-step explanation:

Consider rectangle PQRS. Its area is ...

  A = LW

  90 cm² = PQ×QR = PQ×(20 cm)

  (90 cm²)/(20 cm) = PQ = 4.5 cm . . . . . . BC has this value, too

__

Consider the perimeter of ABCD. It is given by ...

  P = 2(L +W)

  52 cm = 2(AB +BC) . . . . substitute known value for P

  26 cm = AB +4.5 cm . . . . use known value for BC, divide by 2

  21.5 cm = AB

A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly 16% of all applications were from minority members, and exactly 15% of the 2100 open positions were filled by members of the minority.

Required:
a. Find the mean of p, where p is the proportion of minority member applications in a random sample of 2100 that is drawn from all applications.
b. Find the standard deviation of p.

Answers

Answer:

a) The mean is of [tex]\mu = 0.16[/tex]

b) The standard deviation is of [tex]s = 0.008[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Question a:

Exactly 16% of all applications were from minority members

This means [tex]p = 0.16[/tex], and thus, the mean is of [tex]\mu = p = 0.16[/tex]

b. Find the standard deviation of p.

2100 open positions, thus [tex]n = 2100[/tex].

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.16*0.84}{2100}}[/tex]

[tex]s = 0.008[/tex]

The standard deviation is of [tex]s = 0.008[/tex]

In one hour Dele walks 8km. How
long will it take her to walk 14km at
the same rate?

Answers

Answer:

1.45 h

Step-by-step explanation:

common factor of 8 and 14 is 2.

every 2km dele takes 15 minutes.

we know this because 15 minutes is 1/4 of an hour and 2km is 1/4 of 8km

14km/2km = 7

7*15 minutes = 1.45 hours

Answer:

1.75 hours/ 1hr 45 min

Step-by-step explanation:

1hr = 8 Km

?? = 14 Km

= (14km × 1hr)/ ( 8km)

= 1.75hours

= 1hr 45min

Am I correct? If not which of the answers is correct?

Answers

Answer:

Yea you are right.

Step-by-step explanation:

If the length of a rectangle is four times its width and the perimeter of the rectangle is 90 yd, whats its area?

Answers

Answer:

324 yds ^2

Step-by-step explanation:

If length=l and width=w, you could write an equation to find the length and width. Then use that to find the area. L=4w. There are two of each side in the rectangle. 4w+4w+w+w=10w. 10w=90. w=9. 4w=36. L=36. 36*9=324yds^2

Write down in terms of n, an expression for the nth term
of the following sequences:
a) 6 2 -2 -6 -10
b) -8 -15 -22 -29 -36

Answers

Answer:

[tex]{ \bf{(a).}} \\ { \tt{ {n}^{th} = a + (n - 1)d }} \\ { \tt{ {n}^{th} = 6 + (n - 1) \times - 4 }} \\ {n}^{th} = 10 - 4n \\ \\ { \bf{(b).}} \\ { \tt{ {n}^{th} = - 8 + (n- 1) \times - 7 }} \\ { \tt{ {n}^{th} = -1 - 7n}}[/tex]

Find cos 0, tan 0, and csc0 where 0 is the angle shown in the figure. Give exact values, not decimal approximations. (plz help!)​

Answers

Step-by-step explanation:

everything can be found in the picture

In a recent year, 31.6% of all registered doctors were female. If there were 53,000 female registered doctors that year, what was the total number of registered doctors?

Answers

Answer:

The total number of registered doctors was 167,722.

Step-by-step explanation:

Total number of doctors:

The total number of doctors is given by x.

31.6% of all registered doctors were female. 53,000 female doctors.

This means that:

[tex]0.316x = 53000[/tex]

What was the total number of registered doctors?

We have to solve the above equation for x. So

[tex]x = \frac{53000}{0.316}[/tex]

[tex]x = 167722[/tex]

The total number of registered doctors was 167,722.

3 tons of topsoil cost $2,040.00. What is the price per pound?

Answers

Answer:

$0.34/pound

Step-by-step explanation:

1 ton = 2000 pounds

3 tons = 6000 pounds

-------------------------

2040/6000 = $0.34/pound

PLEASE HELP ME WILL MARK YOU IF YOU HELP(please answer all of them >_<)

Answers

Answer:

See below.

Step-by-step explanation:

Problem 2.

Left figure: 2 sides and included angle: SAS

Middle figure: 2 angles and included side: ASA

Right figure: 3 sides: SSS

Problem 3.

CPCTC = corresponding parts of congruent triangles are congruent

An employer has a staff of eighty actuaries, ten of whom are student actuaries. A student actuary is allowed a total of ten weeks off per year (52 weeks in a year) for studying, vacation, and sick days. A non-student actuary is given four weeks off a year. It is assumed that all actuaries use all of the weeks off allocated to them. The actuary Mr. Taylor is at work today. What is the probability that he is a student?

Answers

Answer:

0.1111

Step-by-step explanation:

From the given information;

Number of staffs in the actuary = 80

Out of the 80, 10 are students.

i.e.

P(student actuary) = 10/80 = 0.125

number of weeks in a year = 52

off time per year = 10/52 = 0.1923

P(at work || student actuary) = (50 -10/52)

= 42/52

= 0.8077

P(non student actuary) = (80 -10)/80

= 70 / 80

= 0.875

For a non-student, they are only eligible to 4 weeks off in a year

i.e.

P(at work | non student) = (52-4)/52

= 48/52

= 0.9231

P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)

P(at work) =  (0.125 × 0.8077) + ( 0.875 × 0.9231)

P(at work) = 0.1009625 + 0.8077125

P(at work) = 0.90868

Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)

P(he is a student) = (0.125 × 0.8077) ÷ 0.90868

P(he is a student) = 0.1009625 ÷ 0.90868

P(he is a student) = 0.1111

c+12<16
what will be the answer

Answers

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Find the area of the following shape:

Answers

Answer:

36cm^2

Step-by-step explanation:

total area: 6x(4+3)=42

total area excluding the space: 42-(2x3)=36

Answer:

36 cm squared

Step-by-step explanation:

To solve this problem, I first construct a line. (shown in yellow in the first photo)

I then find the area of the top rectangle. (6 cm * 4 cm = 24 cm squared.)

Next, I find the area of the lower rectangle. But...to do that I have to find the length of the line that I constructed. To do this, I do  6cm-2cm=4cm.

Then I can find the area of the lower rectangle. (4cm*3cm=12cm squared.)

add up the area of both of the rectangles and.........12+24=36 cm squared

Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. ∆ARE ≅ ∆_____ by _____

Answers

Answer:

add a picture so i can see .

Step-by-step explanation:

PLEASE HELP ME OUT

Find the value of n in the equation 8 + 2n = 14.

n=____​

Answers

N=3 explanation: subtract 8 from 14 then divide it by two

(x+4)(x^2-5x+3) multiply the polynomials

Answers

9514 1404 393

Answer:

  x^3 -x^2 -17x +12

Step-by-step explanation:

Use the distributive property and collect terms.

   (x +4)(x^2 -5x +3) = x(x^2 -5x +3) +4(x^2 -5x +3)

  = x^3 -5x^2 +3x +4x^2 -20x +12

  = x^3 -x^2 -17x +12

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