Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17

Answers

Answer 1

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula. we get

[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]

[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]

[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-5=2(x-(-7))[/tex]

[tex]y-5=2(x+7)[/tex]

[tex]y-5=2x+14[/tex]

Adding 5 on both sides, we get

[tex]y-5+5=2x+14+5[/tex]

[tex]y=2x+19[/tex]

Therefore, the equation for the given data is [tex]y=2x+19[/tex].


Related Questions

20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]

Answers

Ques20. 66
Ques21. 8x+20y
Ques22. 132

A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.

Answers

Answer: [tex]\dfrac{8}{3}\ m[/tex]

Step-by-step explanation:

Given

Length of the plank is [tex]6\ m[/tex]

Foot of the flank is [tex]4\ m[/tex] away from the wall

Lizard climbs 2 m up the wall

from the figure, the two triangles are similar

[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]

So, the distance from the wall is

[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]

A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley

Answers

The image of this question is missing and so i have attached it.

Answer:

dd/dt = 4.47 ft/s

Step-by-step explanation:

From the image attached, let's denote the following;

d = horizontal distance beneath pulley

h = height of pulley

l = diagonal from the pulley to the head of the person

v = velocity of rope rising

Using pythagoras theorem;

l² = d² + h²

Differentiating with respect to time and considering h = c^(te) gives;

2l(dl/dt) = 2d(dd/dt)

We are given;

d = 20 ft

h = 10 ft

v = 4 ft/s

We know that velocity in this case is change in diagonal distance with time. Thus;

v = dl/dt = 4 ft/s

From earlier, we saw that;

2l(dl/dt) = 2d(dd/dt)

Thus, reducing it gives

(dl/dt)(l/d) = dd/dt

Now, l² = d² + h²

l = √(d² + h²)

Also, v = dl/dt = 4

Thus;

4(√(d² + h²))/d = dd/dt

4(√(20² + 10²))/20 = dd/dt

dd/dt = 4.47 ft/s

Find the values of the unknown angles marked with letters. please help me- it is about alternate angles
100 points!!!
a ?
b ?
c ?
d ?

Answers

Answer:

Step-by-step explanation:

Find either c or d first. Those are easy and everything will fall into place after those 2 are found.

c: angle c is supplementary with 115. That means that they add up to equal 180; therefore, 115° + c° = 180° so c = 65°.

d: angle d is supplementary with 70. Therefore, 70° + d° = 180° so d = 110°.

a and c are same side interior, so they are also supplementary. That means that a = 115°.

b and d are also same side interior, so they are also supplementary. That means that b = 70°.

Please help me. if I don’t complete my course I’m getting sent back to my parents house, and I need to complete this course
This is similar polygons, and the lessons I get don’t help

Answers

For the first question, yes, they are similar. Each of the corresponding sides has a ratio of 4:1 from the first polygon to the second, meaning they are similar. For the second question, the ratio is 1.6:1, and if we multiply the 10 on the bottom polygon by 1.6, we get 16, which is the answer.

For real though, I’m hoping you don’t get sent back there. I’m assuming you dislike it there, so good luck with your course. I’m here to help if you need it.

#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?

Discriminant = b2 – 4ac

–8
4
8
16

Answers

Answer:

16

Step-by-step explanation:

the quadratic equation –3 = –x2 + 2x can be changed into :

x²-2x-3= 0

a=1, b= -2 , and c = -3

so, the discriminant = (-2)²-4(1)(-3)

= 4 + 12 = 16

Triangle ABC is a right triangle.

Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.

Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40

Answers

Answer:

x + 90 + (x minus 10)= 180° can be used to find the value of x.

Answer:

A) X+90+ (x-10) - 180

C) 2x+80 = 180

D) x+90 = 2x+40

Step-by-step explanation:

DJVJNNSMKAJABJSHSNSB

Answers

Could u explain more

using appropriate properties , find 7/5 × 5/12 − 3/12 × 7/5 − 1/15

Answers

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]

Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?

Answers

Add the ratio: 3 + 5 = 8

Divide total students by that:

32/8 = 4

The ratio for girls is 3, multiply the 4 by 3:

4 x 3 = 12

There are 12 girls

Answer:

12

Step-by-step explanation:

If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:

[tex]\frac{3}{8}[/tex] of 32

= [tex]\frac{3}{8} * 32[/tex]

[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]

There are 12 girls.

Rhombus LMNO is shown with its diagonals.

Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.

Angle MNO measures 112°. What is the measure of angle LMN?

Answers

Answer:

hope this help

Step-by-step explanation:

Answer:

90

51

10

Step-by-step explanation:

Match the answers……………..

Answers

9 in 8956 = 900

9 in 95675 = 90000

9 = 9 in 124569

9 in 68795 = 90

90000 = 9 in 2549652.........

hope it helps...

Check if -2 is the solution of equation 2 – x = 4x + 3​

Answers

Answer:

7x the answer i think

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]

Step-by-step explanation:

We are asked to check is -2 is the solution of the following equation.

[tex]2-x= 4x+3[/tex]

We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.

[tex]2- (-2) = 4(-2)+3[/tex]

Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Let's start with the left side.

[tex]2+2= 4(-2)+3 \\[/tex]

[tex]4= 4(-2)+3[/tex]

Now solve the right side. Remember to multiply first.

[tex]4= -8+3[/tex]

[tex]4= -5[/tex]

[tex]4\neq -5[/tex]

4 is not equal to -5, so -2 is not the solution for this equation.

Independent Practice


Find the first, fourth, and eighth terms of the sequence.


an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline


A.
0.667; 4.5; 364.5


B.
3; 0.375; 0.0234375


C.
0.5; 13.5; 1093.5


D.
0.5; 121.5; 280.5

Answers

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

Help anyone can help me do the question,I will mark brainlest.​

Answers

Answer:

a) 30

b)600pi

Step-by-step explanation:

For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30

Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi

A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?

Answers

Answer:

[tex]Expected = 0.09375[/tex]

Step-by-step explanation:

Given

[tex]Balls = 4[/tex]

[tex]n = 4[/tex] --- selection

Required

The expected distinct colored balls

The probability of selecting one of the 4 balls is:

[tex]P = \frac{1}{4}[/tex]

The probability of selecting different balls in each selection is:

[tex]Pr = (\frac{1}{4})^n[/tex]

Substitute 4 for n

[tex]Pr = (\frac{1}{4})^4[/tex]

[tex]Pr = \frac{1}{256}[/tex]

The number of arrangement of the 4 balls is:

[tex]Arrangement = 4![/tex]

So, we have:

[tex]Arrangement = 4*3*2*1[/tex]

[tex]Arrangement = 24[/tex]

The expected number of distinct color is:

[tex]Expected = Arrangement * Pr[/tex]

[tex]Expected = 24 * \frac{1}{256}[/tex]

[tex]Expected = \frac{3}{32}[/tex]

[tex]Expected = 0.09375[/tex]

if an angle is 10 degree less than its complement, find the angle.

Answers

Let one be x

Other one is x-10

ATQ

[tex]\\ \sf \longmapsto x+x-10=90[/tex]

[tex]\\ \sf \longmapsto 2x-10=90[/tex]

[tex]\\ \sf \longmapsto 2x=90+10[/tex]

[tex]\\ \sf \longmapsto 2x=100[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{100}{2}[/tex]

[tex]\\ \sf \longmapsto x=50[/tex]

[tex]\\ \sf \longmapsto x-10=50-10=40[/tex]

see attached photo, please help asap!!!

Answers

Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

I need help plz help

Answers

We know

[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]

[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto x=47(0.9)[/tex]

[tex]\\ \sf\longmapsto x=42.3[/tex]

Item 1 Which fraction is equivalent to 3.47? 3_23/50 3_47/100 3_12/25 I don't know.

Answers

the second one. because 3 is a whole number. the place for 4 is over 10 and the number of 7 is over 100. so we use the last one which is 100. for example, 47/100 means 0.47 and 4/10 means 0.4 while

Answer: 3 and 47/100

Step-by-step explanation:

need help asap pls !

Answers

Answer:

L={∅}

Step-by-step explanation:

HELP ME PLEASEEEE

TAXI RATES A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. Write an expression for the cost of the ride
if you travel x miles in the taxi with no traffic delays.

Answers

Step-by-step explanation:

C(x) = 2.50 + 5(0.40x)

<=> C(x) = 2.50 + 2.00 x

The required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

Given that,
A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. To determine an expression for the cost of the ride, if travel x miles in the taxi with no traffic delays to determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the number of miles be x,
The total charge be C(x)
Now accoding to the condition total charge could be the sum of the cost of every fifth mile and $2.40. So, every fifth mile = x / 5
Now,
C(x) = 2.40 + 0.40 * x/5

Thus, the required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Find the sum of the second multiple of 9 and the fifth multiple of 6.​

Answers

Answer:

48

Step-by-step explanation:

9,18

6,12,18,24,30

18 + 30 = 48

find the missing segment in the image below​

Answers

Answer:

3

Step-by-step explanation:

Intercept theorem

DE // CB ⇒ [tex]\frac{AD}{AC} = \frac{AE}{AB}[/tex]

⇒ [tex]\frac{6}{6+?} =\frac{4}{4+2}[/tex]

⇒ ? = 3


PLEASE HELP IM TRYING TO FINISH THIS BY NEXT MONDAY AND IVE BEEN STUCK ON THIS

Answers

Answer:

Step-by-step explanation:

Choice A is the only one that is applicable.

Answer:

A. F(x) has 1 relative minimum and maximum.

Step-by-step explanation:

[tex]{ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}[/tex]

As x and F(x) tend to positive and negative infinity:

[tex]{ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}[/tex]

❎So, B and C are excluded.

Roots of the polynomial:

[tex]{ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}[/tex]

, D is also excluded.

✔, A

You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.

Answers

Answer:

$61.50

Step-by-step explanation:

14.25(4) + 4.50

= 57.00 + 4.50

= 61.50

Answer hurry which one 1 2 3 or 4?

Answers

Answer:

Option: 1

Step-by-step explanation:

Let,

Footprints that Adele will find be = f

So, Footprints that Yumiko finds = 2f = f + f

Since,

As given that,

Yumiko finds 16 Footprints so it will be,

2f = f + f = 16

And,

f = 16 / 2

= 8

Which is half of Footprints found by Yumiko.

So the bar model 1 represents it correct.

Answer:

option 1

Step-by-step explanation:

i did the quiz

Monica makes tomato sauce with the plants she grows in her garden. She uses 3 basil leaves in her sauce for every 8 tomatoes. She is making a big batch of sauce with 32 tomatoes from her garden.

Answers

Answer: 12 Basil leaves

Step-by-step explanation:

Given

Monica uses 3 basil leaves for every 8 tomatoes

For 32 tomatoes she needs

[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]

Thus, she needs 12 basil leaves.

Mark all the relative minimum points in the graph.

Please help I don't understand what to do.​

Answers

Answer:

Step-by-step explanation:

The thing to remember is that absolute can be relative but relative can't be absolute. In other words, absolute min is the very lowest point on the graph and there's usually only one (unless there are 2 absolute mins that have the same y value) while relative mins can occur at several points on a graph. That means that the only relative min point on the graph occurs at (-3, 4); the absolute min occurs at (5, -6).

What would -4|5+-3| be

Answers

Answer:

-8

Step-by-step explanation:

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