y = m x + b for a trend line that passes through the points (2, 18) and (–3, 8). Which value should he use as b in his equation

Ruchi is incorrect because 2.81×10⁴ is around 30,000. so the units must be smaller than feet.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

As it is given that the measurement that Ruchi wrote is 2.81×10⁴ ft². And, the area of 2.81×10⁴ ft² is 28,100 ft² which is nearly 30,000 ft², while the size of an average house is 2,300 ft². Therefore, the area that is written by Ruchi is too big compared to an average kitchen.

Hence, Ruchi is incorrect because 2.81×10⁴ is around 30,000 so the units must be smaller than feet.

Learn more about Units conversion:

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The expression that is equivalent to 5y⁻³ is start fraction 5 over y cubed end fraction.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

In order to find the expression that is equivalent to 5y⁻³, we need to use exponential properties,

[tex]5y^{-3}\\\\=\dfrac{5}{y^3}[/tex]

Hence, the expression that is equivalent to 5y⁻³ is start fraction 5 over y cubed end fraction.

Learn more about Expression:

https://brainly.com/question/13947055

Answer:

option C 5/y^3

Step-by-step explanation:

To help Carmen find the total after 3 years

We'll have to use the annual compound interest formula: A = P(1 + r)ⁿ

A = Final balance (?)

P = Principal balance (6000)

r = Rate (0.028)

n = years (3)

A = 6000(1 + 0.028)³

A = 6000(1.028)³

A = 6000(1.086373952)

A = 6518.243712

Round that to the nearest cent, and we get $6,518.24 as the answer.

Answer:

Step-by-step explanation:

Hello.

First, let's clarify what the G.C.F. means.

It means "Greatest Common Factor"

So, let's find the Greatest Common Factor of 15 and 48.

First, let's list all the factors of 15:

1, 3, 5, 15

Here are the factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Therefore, the GCF of 15 and 48 is 3.

I hope it helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

Answer:

∠ ABC = 51°

Step-by-step explanation:

the inscribed angle ABC is half the measure of its intercepted arc AC , so

5x + 11 = [tex]\frac{1}{2}[/tex] (16x - 26) ← distribute parenthesis

5x + 11 = 8x - 13 ( subtract 8x from both sides )

- 3x + 11 = - 13 ( subtract 11 from both sides )

- 3x = - 24 ( divide both sides by - 3 )

x = 8

Then

∠ ABC = 5x + 11 = 5(8) + 11 = 40 + 11 = 51°

Answer: x=sqrt21, y=sqrt70

Step-by-step explanation:

Based on the calculations, the width of the rectangular prism is equal to 1,352.91 meters.

Given the following data:

Mathematically, the surface area of a rectangular prism is given by this formula:

[tex]A =2(wl+hl+hw)[/tex]

Where:

A is the surface area.

Substituting the given parameters into the formula, we have;

[tex]460 =2(w0.05+0.12(0.05)+0.12w)\\\\460=2(0.17w+0.006)\\\\460=0.34w+0.012\\\\0.34w=460-0.012\\\\0.34w=459.988\\\\w=\frac{459.988}{0.34}[/tex]

w = 1,352.91 meters.

Read more on rectangular prism here: brainly.com/question/3867601

Problem 1

Answer: The roots are x = 0, x = 2, x = -3

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

Explanation:

The term "root" is another way of saying "zeros of a function" or "x intercept".

To find the roots, set each factor equal to zero and solve for x.

x-2 = 0 solves to x = 2, while x+3 = 0 solves to x = -3

========================================================

Problem 2

Answer: Roots are x = 1, [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex]

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

Explanation:

Factor by grouping

x^3 - x^2 + 5x - 5 = 0

(x^3 - x^2) + (5x - 5) = 0

x^2(x - 1) + 5(x - 1) = 0

(x^2 + 5)(x - 1) = 0

x^2 + 5 = 0 solves to the roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex]

x-1 = 0 solves to x = 1

Note: [tex]i = \sqrt{-1}[/tex]

1) Wat are the real zeros of the function y=x(x-2)(x+3):

Answer: [tex]x_{1} = -3 ; x_{2} = 0; x_{3} =2[/tex]

To find the x-intercept, set y = 0:

x( x -2 ) ( x + 3) = 0

Apply the Zero Product Property:

x - 2 = 0 or x + 3 = 0

x = 2 or x = -3

Find the union of solutions:

x = 0 or x = 2 or x = -3

2) Find all of the solutions of the equation

x^3 -x^2 +5x - 5 = 0

Answer: x = 1 or no real solution

Apply grouping:

[tex](x^{3} -x^{2} ) + *(5x-5)=0[/tex]

Factor out common factor:

[tex]x^{2} (x-1) +5(x-1)=0[/tex]

Factor out --> [tex](x-1)(x^{2} +5) =0[/tex]

Apply zero product property:

[tex]x - 1 =0[/tex] or [tex]x^{2} +5 =0[/tex]

x - 1 = 0

Rearrange variables to the left side of the equation--> x=1 or no real solutions.

Answer:

5(a+5b)*(a-5b)

Step-by-step explanation:

Answer:

5 (a+5b)( a−5b)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Measure all three aspects--the length, width and height--of an object to get a three-dimensional measurement.

D = 437FT × 4 FEET

multiply the values in order to get the dimension

Answer:

y = -2x + 5

Step-by-step explanation:

to figure this out you may plug this equation into y = mx + b with b being the unknown

this goes to

-7 = -2(6) + b

then multiply 6 to -2

-7 = -12 + b

then add 12 to both sides

5 = b

b is 5 so that means the equation is

y = -2x + 5

Answer:

35m

Step-by-step explanation:

The formula to find the volume of right circular cylinder is: V=πr^2*h

We know the following info:

V = 5390m^3

r = 7m

So the equation would be 5390 = 3.14*7^2*h

so h = 35m

Answer:

h ≈ 35.01m

Step-by-step explanation:

V=Лr²h

r =7m

v = 5390³

h= V / Лr²

h= 5390 / Л7²

=35.01409m

Answer:

30°

Step-by-step explanation:

AB || DC (Given)

-> AB || DF

-> x = 30° (alternate angles)

The graph looks like an absolute function.

If we were to compare the function [tex]y= |x|[/tex] to this graph (see image attached), we see that the function in the graph has only shifted two to the right.

To write in function form, when shifting the graph horizontally

In this case, since we want to shift over two spots horizontally, we get the function is

 y = |x -2|

Now we want to find the function that is increasing and decreasing over the same interval.

The only function that looks the most similar is y = 4|x-2|.

The reason for that is because the y = 4|x-2| is just a stretched version of y= |x-2| meaning the point where it is increasing or decreasing should stay the same. Look at the second image I attached.

Hope it helps!

Answer:

1/2 mile

Step-by-step explanation:

30miles / 60 minutes = (30/60) miles / 1 minute = (1/2) mile / 1 minute

Answer:

49/30

Step-by-step explanation:

To find the mean, add up 2.2 + 1 1/5 + 1 1/2 to get 49/10

Then divide that by 3 (it says four Douglas trees but you only put 3 types)

49/10 divided by 3 is 49/10 times 1/3, which is 49/30

Answer:

[tex]7 + x = 15 \\ x = 15 - 7 \\ x = 8[/tex]

So; No

Answer:

1. pt. A) 96:38

pt. B) Because they are the same values, just flipped

2. pt. A) 38:46

pt. B) 19:23

Step-by-step explanation:

hope this helped

Answer:

100 - 5n

Step-by-step explanation:

100 - 5n

Hope this helps!

» Variables y and x have a proportional relationship, where y = 9 when x = 3. What is the value of x when y = 36? Enter your answer in the box.

— — — — — — — — — —

Since variables y and x have a proportional relationship, then the equation is in the form y=kx.

First, we need to find the constant of variation (k) by substituting the given to the equation of variation.

The constant of variation (k) is 3. So, find the value of x when y = 36.

Hence the unknown value (x) is 12.

Answer:

3 dollars

Step-by-step explanation:

4/15 of 30 = $8
2/5 of 30 = $12
7/30 of 30 = $7

8 + 7 + 12 = $27

30 - 27 = $3

They only had 3 dollars left after spending everything else they had.

Answer:

3/30

Step-by-step explanation:

4/15 so times 15 by 2 and 4 by 2 to get 8/30

leave 7/30 alone

2/5 five times 6 is 30, since you multiplied 5 by 6 you have to do 2 x 6 which is 12, 12/30

now you can add bc a common denominator 12 + 7 + 8 = 27

30 - 27 = 3, so 3/30ths was spent on souvenirs.

Answer:

See below. (C*a) + (P*b) = M

Step-by-step explanation:

amount of students = 45

amount of candy per student = 1

amount of popcorn per student = 1

Let "S" be the total amount of students

Let "C" be the total amount of candy

Let "P" be the total amount of popcorn

Let "T" be the total number of snacks

Let "a" be the price per candy

Let "b" be the price per popcorn

Let "M" be the total amount of money spent at the game

The price of the candy is unknown.

The price of the popcorn is unknown.

The total amount of money spent at the game is unknown.

(C*a) + (P*b) = M

I am not sure what you are asking for but, here is what I drew up for you. Hope this helps!

Answer:

x = 27.048

Step-by-step explanation:

sin(x) = 7/15

15 sin(x) = 7

15sin = 0.2588, so

0.2588(x) = 7

Then, divide both sides by 0.2588

x = 27.048

Answer:

Step-by-step explanation:

305ml × 10 = 3,050ml

3,050ml = 3.05L

Answer:

It would be -6, 5 but i dont see that for an option so pick -6,-5

Step-by-step explanation:

Answer:

x = 57.8°

explanation:

[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]

[tex]\hookrightarrow \sf sin(x) = \dfrac{11}{13}[/tex]

[tex]\hookrightarrow \sf x = sin^{-1}(\dfrac{11}{13} )[/tex]

[tex]\hookrightarrow \sf x = 57.8[/tex]

Answer:

57.8° (nearest tenth)

Step-by-step explanation:

Use the sine trig ratio:

[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]

where:

Given:

[tex]\implies \mathsf{\sin(x)=\dfrac{11}{13}}[/tex]

[tex]\implies \mathsf{x=\arcsin\dfrac{11}{13}}[/tex]

[tex]\implies \mathsf{x=57.8 \textdegree \ (nearest \ tenth)}[/tex]

Answer:

[tex]y = - \frac{ {x}^{2} }{16} [/tex]

Step-by-step explanation:

First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards

Equation of a Parabola with center (h,k) >

[tex](x - h) {}^{2} = - 4p(y - k)[/tex]

Where p is the distance of the vertex to focus/ or distance to vertex to directrix

This emans that the vertex is halfway of (-4,0) and x=4.

Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that

The vertex is halfway between (-4,0) and (4,0).

So the vertex is (0,0).

Plugging that in we get,

[tex] {x}^{2} = - 4py[/tex]

The distance to the vertex or either the focus or directrix is 4 so p=4

[tex] {x}^{2} = - 4(4)y[/tex]

[tex] {x}^{2} = - 16y[/tex]

[tex]y = - \frac{ {x}^{2} }{16} [/tex]

Answer:

One solution

(2,0) is the point

Step-by-step explanation:

If the graphs of the equations intersect, then there is one solution that is true for both equations.

When the lines intersect, the point of intersection is the only point that the two graphs have in common, so the coordinates of that point are the solution for the two variables used in the equations.

The point of intersection is (2,0), because that is the point that both lines intersect at.