Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.

Justin states that the ratio is 4:1.
Desiree insists the ratio is 24:6.

They both ask Luke to tell them which ratio is correct. Which statement below would be the best answer for Luke?

Answer: The slope is -2

Step-by-step explanation:

It is important to remember that the equation of the line in Slope-Intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you can observe that the given equation of the line [tex]y=-2x+3[/tex] is written in Slope-Intercept form.

Therefore, you can identify that the slope "m" is:

[tex]m=-2[/tex]

And the y-intercept "b" is:

[tex]b=3[/tex]

Answer:

32

Step-by-step explanation:

The formula is base x hight.

The base is 8.

The hight is 4.

You just multiply the two.

8x4=32

Simple. :)

Hope this helps!

Answer: 42 inches squared

Step-by-step explanation:

To find the total area you will find the area of the rectangle and then add that to the area of the triangle. (Remember a triangle is half of a rectangle!) First we will find the area of the rectangle...

4x8=32 inches squares

Now let’s find the area of the triangle, find the rectangle then divide it in half...

5x4=20 inches squared

20/2=10 inches squared

Now add 32 to 10 and you’ll have your answer!

32+10=42 inches squared

Answer:

79.2kg

Step-by-step explanation:

So first step is to find 10% of 88, which is 8.8. And 88kg is higher than his normal weight, so his original weight would be lower than 88kg. So you subtract. 88-8.8=79.2. His normal weight is 79.2kg.

Answer:

[tex]\large\boxed{\dfrac{2s-6}{s+3}}[/tex]

Step-by-step explanation:

[tex]s^2-9=s^2-3^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(s-3)(s+3)\\\\s^2+6s+9=s^2+2(s)(3)+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\=(s+3)^2[/tex]

[tex]\dfrac{s^2-9}{2s}\div\dfrac{s^2+6s+9}{4s}=\dfrac{s^2-9}{2s\!\!\!\!\diagup_1}\cdot\dfrac{4s}{s^2+6s+9}\\\\=\dfrac{(s-3)(s+3)}{2s\!\!\!\!\!\diagup_{_1}}\cdot\dfrac{4s\!\!\!\!\!\diagup^{^2}}{(s+3)^2}=\dfrac{2(s-3)(s+3)}{(s+3)(s+3)}\qquad\text{cancel}\ (s+3)\\\\=\dfrac{2(s-3)}{s+3}=\dfrac{2s-6}{s+3}[/tex]

ANSWER

p=-1

EXPLANATION

The given equation is

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

We compare with the general equation of the parabola with vertex at the origin.

[tex]{y}^{2} =4px[/tex]

Comparing the right hand side we have,

[tex]4px = - 4x[/tex]

Divide both sides by 4x

[tex] \frac{4px}{4x} = \frac{ - 4x}{4x} [/tex]

This implies that,

[tex]p = - 1[/tex]

The y-axis runs vertically, so changing the y-coordinate moves a figure up or down. Adding a number to the y-coordinate shifts the image up, while subtracting a number shifts the figure down.

So to translate 3 units down, we just subtract 3 from the y-coordinate.

Instead of (-2, 1) it's now (-2, -2) since 1 - 3 (units) = -2

Now, another way to say "reflect across the y-axis" is to say "reflect across the line x=0" since the line created by graphing x=0 is the same as the y-axis.

An image that is a reflection across the y-axis, or across the line x=0, will have opposite x-coordinates from the pre-image but identical y-coordinates.

Therefore, the rule for reflecting an image across the y-axis can be described as (x, y) → (−x, y).

So using our translated point (-2, -2) it now becomes (2, -2).

You didn't provide an image, however, all you need to find is the translated and reflected point that lies on (2, -2).

Answer:

( 2 , 1 )

Step-by-step explanation:

literally have no idea how the other person got -2 as the second answer lol

its 1 not -2 , ik cause i had this problem on my acellus and had to guess until i got it

Answer:

Length: 139 feet

Width: 104 feet

Step-by-step explanation:

The formula for the perimeter of a rectangle can be given by [tex]P = 2l + 2w[/tex]. We are given the perimeter of the pool along with the width.

[tex]P = 486[/tex]

[tex]w = l - 35[/tex]

From here, all we have to do is plug back into the original formula:

[tex]486 = 2l + 2(l - 35)[/tex]

Which can be further simplified as:

[tex]486 = 2l + 2l - 70[/tex]

[tex]486 = 4l - 70[/tex]

From here, all we have to do is add 70 to both sides of the equation and divide by four:

[tex]556 = 4l[/tex]

[tex]139 = l[/tex]

To make sure that this answer is accurate, we can find that the width of the rectangle should then be 104 (given by 139 - 35). All we have to do is plug back into the original equation:

[tex]P = 2l + 2w[/tex]

[tex]P = 2(139) + 2(104)[/tex]

[tex]P = 278 + 208[/tex]

[tex]P = 486[/tex]

And the substitution works, so the length of the rectangle would be 139 feet and the width would be 104 feet.

Answer:

Length = 139 and Width = 104 .

Step-by-step explanation:

Given: The perimeter of a rectangle swimming pool is 486 feet. The width of the pool is 35 feet less than the length.

To find: Find the length and the width​ .

Solution: We have given that

Let the length = x

According to question

The width of the pool is 35 feet less than the length.

width = x-35

perimeter = 2(length + width)

plugging the values

486   = 2(x + x-35)

486  =  2x + 2x - 70

486  = 4x - 70

On adding by 70 both side

486 +70 = 4x-70 +70

556 = 4x

On dividing by 4 both side

139 = x

so, length = 139 .

    width = x -35 =  139- 35 = 104

Therefore,  length = 139 and width = 104.

Answer:

First Option

Step-by-step explanation:

Given expression is:

[tex]\sqrt[4]{x^{10}}[/tex]

The radicand's exponent will be made multiple of 4 to make the calculations easy

So,

[tex]= \sqrt[4]{x^8 * x^2}[/tex]

The 4 outside the radical means that the power that will be multiplied with the exponents will be 1/4

So,

[tex]= x^{(8*\frac{1}{4})} * x^{(2*\frac{1}{4})}\\=x^2 \sqrt[4]{x^2}[/tex]

As x^2 couldn't be solved using radical, it will remain inside the radical.

So the correct answer is first option..

Answer: First option.

Step-by-step explanation:

Knwing that we must find which is the equivalent expression of the expression [tex]\sqrt[4]{x^{10}}[/tex], it is important to remember the Product of powers property, which states the following:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

The we can rewrite the expression:

 [tex]=\sqrt[4]{x^8x^2}[/tex]

Remember that:

[tex]\sqrt[n]{a^n}=a[/tex]

Then we get this equivalent expression:

 [tex]=x^2(\sqrt[4]{x^2})[/tex]

Answer:

[tex]\boxed{\math{\frac{1}{9}\text{ lb}}}[/tex]

Step-by-step explanation:

[tex]\text{Size of one serving} = \dfrac{\text{Total size}}{\text{No of servings}} = \dfrac{\frac{2}{3}\text{ lb}}{\text{6 servings}}\\\\\text{Change the 6 to a fraction and change divide to multiply}\\\\\dfrac{2}{3} \div 6 = \dfrac{2}{3} \times \dfrac{1}{6}[/tex]

[tex]\text{Cancel the 2s}\\\\\dfrac{2}{3} \times \dfrac{1}{6} = \dfrac{1}{3} \times \dfrac{1}{3}\\\\\text{Multiply numerators and denominators}\\\\\dfrac{1}{3} \times \dfrac{1}{3} = \dfrac{1}{9}\\\\\text{Each serving contains }\boxed{\mathbf{\frac{1}{9}\textbf{ lb}}}[/tex]

Answer:

c.45 degrees

Step-by-step explanation:

90 -180= 90

90÷2=45

For this case, we have by definition, that the four internal angles of a square measure 90 degrees. If we draw the diagonals of the square we have that the angles are divided between 2, that is, they go to measure 45 degrees.

So, according to this definition we have to:

[tex]Angle\ 3 = \frac {90} {2}\\Angle\ 3 = 45[/tex]

Answer:

The angle 3 is 45 degrees

Option C

Answer:

2t + n + 3d = 65

3t + 2n + 5d = 85

t + n + td = 40

Step-by-step explanation:

tubs of popcorn = t

plates of nachos = n

drinks = d

The Smiths: 2t + n + 3d = 65

The Langes: 3t + 2n + 5d = 85

The Radfords: t + n + td = 40

So, the correct answer would be the one including all 3 of these equations. :)

Answer:

The system of equations are:

[tex]2t + n + 3d = 65[/tex]

[tex]3t + 2n + 5d = 85[/tex]

[tex]t + n + 2d = 40[/tex]

Step-by-step explanation:

Consider the provided information.

let "t" represents tubes of popcorn, "n" represents nachos and "d" represents drink.

The Smiths ordered two tubs of popcorn, one plate of nachos, and three drinks. They spent $65. Which can be represents as:

[tex]2t + n + 3d = 65[/tex]

Langes ordered three tubs of popcorn, two plates of nachos, and five drinks. They spent $85. Which can be represents as:

[tex]3t + 2n + 5d = 85[/tex]

The Radfords ordered one tub of popcorn, one plate of nachos, and two drinks. They spent $40. Which can be represents as:

[tex]t + n + 2d = 40[/tex]

Thus, the system of equations are:

[tex]2t + n + 3d = 65[/tex]

[tex]3t + 2n + 5d = 85[/tex]

[tex]t + n + 2d = 40[/tex]

Step-by-step explanation:

1. x = acceptable weight of candy bar

2. |x - 12| ≤ 0.45

3. x - 12 ≤ 0.45, x - 12 ≥ -0.45

x ≤ 12.45, x ≥ 11.55

4. The acceptable weight range for each candy bar is between 11.55 grams and 12.45 grams.

⇒The Interval in which we have to find the function is Negative is (-1,1].

→(-1,1]=Semi closed or Semi Open Interval, Point -1, is not included in the set, but 1 is included in the set.

 ⇒ The meaning of negative here is,that either for positive or negative value of x , the value of f(x), that is y Should be negative.

⇒y is negative in third and fourth Quadrant.

Graph -(2), is the function , in which the function is negative for the interval (–1, 1].

Answer:

The value of the expression for x=2 is 2.

Step-by-step explanation:

Consider the provided expression.

[tex]4(x - 3) + 5x - x^2 [/tex]

We need to find the value of expression for x=2.

Substitute the value of x=2 in provided expression and simplify as shown.

[tex]4(2 - 3) + 5(2) - 2^2 [/tex]

[tex]4(-1) + 10 - 4 [/tex]

[tex]-4 + 6 [/tex]

[tex]2 [/tex]

Hence, the value of the expression for x=2 is 2.

The numerical value of the expression 4(x - 3) + 5x - x² when x = 2 is 2.

Given the expression in the question:

4(x - 3) + 5x - x²

x = 2

To evaluate the expression 4(x - 3) + 5x - x² for x = 2, repalce all the occurences of x in the expression with 2 and simplify:

4(x - 3) + 5x - x²

Plug in x = 2:

4(2 - 3) + 5(2) - (2)²

Subtract 3 from 2:

4(-1) + 5(2) - (2)²

Take the square of 2:

4(-1) + 5(2) - 4

Multiply 4 and -1:

-4 + 5(2) - 4

Multiply 5 and 2:

-4 + 10 - 4

Add the 3 numbers:

2

Therefore, the value of the expression is 2.

Learn more about algebraic expressions here: https://brainly.com/question/28959918

#SPJ6

Answer:

32 Minutes

Step-by-step explanation:

Together the two clerks can file 21 files per minute (10+11=21).

Therefore to file 672 folders would take 32 minutes (672/21=32)

Answer:

425/85*100 = 500 thus: 500-425 =75 Tickets.

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

The exact volume of the cylinder is [tex]\( 3380\pi \)[/tex] cubic meters.

To find the exact volume V of a cylinder, we use the formula:

[tex]\[ V = \pi r^2 h \][/tex]

where:

- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,

- r is the radius of the cylinder, and

- h is the height of the cylinder.

Given:

- Radius (r=13) meters, and

- Height (h=20) meters.

Substitute these values into the formula:

[tex]\[ V = \pi \times (13)^2 \times 20 \]\[ V = \pi \times 169 \times 20 \][/tex]

[tex]\[ V = 3380\pi \][/tex]

The exact volume of the cylinder is 10,613.2 cubic meters.

To find the volume of a cylinder, we use the formula: Volume = πr²h, where π (pi) is approximately 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

Given:

Radius (r) = 13 meters

Height (h) = 20 meters

Calculate the area of the base (circle) using the formula A = πr².

A = 3.14 × (13)²

A = 3.14 × 169

A = 530.66 square meters

Multiply the area of the base by the height of the cylinder.

Volume = 530.66 × 20

Volume = 10,613.2 cubic meters

So, the exact volume of the cylinder is 10,613.2 cubic meters.

Answer:

To easily solve this question, we must realize that the graph of the relation is very similar to that of the expression

y = √(x-a) , where a>0

If we take a look at the image attached, we have plotted the graph of

y = √(x-1) , and its correspondent inverse function.

This means that the answer is the first option

Answer:

False

Step-by-step explanation:

You need 3 points to name a plane.  2 points is required to name a line

Answer:

It would be CUB

Step-by-step explanation:

Answer:

slope = -2

y-intercept = (0,2)

y = -2x + 2

Step-by-step explanation:

In order to find the slope, we must use the formula y2-y1/x2 - x1. But in order to do so, we will have to find two perfect points.

perfect point #1: (-2,6)

perfect point #2: (2, -2)

Now, we simply input the corresponding points into our formula.

-2 - 6 = -8

2 - (-2) = 4

-8/4 = -2

So, the slope of the graph is -2

In order to find the y-intercept we must look at where the line intersects in the y axis. Looking back at our graph, we can determine that the line intersects at (0,2)

The slope-intercept form is y = mx + b, m represents the slope and b represents the y intercept. Therefore after inputting the slope and y-intercept we should get y = -2x + 2

Answer:

The sum of the two expressions is 5x^2 + 4x - 5

Step-by-step explanation:

Rewrite

3x2 - 5x+1

2x2 +9x-6

as

3x^2 - 5x+1

2x^2 +9x-6                          " ^ " indicates exponentiation

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

5x^2 + 4x - 5

Answer:

[tex]5x^2+4x-5[/tex]

Step-by-step explanation:

[tex]3x^2-5x+1 \ and \ 2x^2 + 9x -6[/tex]

Add both the polynomials

To add both the polynomials we combine like terms

[tex]3x^2-5x+1 +2x^2 + 9x -6[/tex]

3x^2 and 2x^2 are like terms . it becomes 5x^2

-5x and 9x are like terms . it becomes 4x

[tex]3x^2-5x+1 +2x^2 + 9x -6[/tex]

[tex]5x^2+4x-5/tex]

Answer:

x = 16 and z = 84

Step-by-step explanation:

The 2 given angles are vertical and congruent, hence

7x - 16 = 6x ( subtract 6x from both sides )

x - 16 = 0 ( add 16 to both sides )

x = 16

Hence 6x = 6 × 16 = 96°

z and 6x form a straight angle and are supplementary, hence

z + 6x = 180

z + 96 = 180 ( subtract 96 from both sides )

z = 84

Answer:

Surface Area of Cone = 200π cm^2

Surface Area of Right Prism = 17.5 ft^2

Step-by-step explanation:

32. We are given a figure of a cone and we are to find its surface area.

We know that the formula for the S.A. of cone is given by:

Surface Area of cone = [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex]

Substituting the given values in the above formula.

Surface Area of cone = [tex]\pi \times 8(8+\sqrt{15^2+8^2} )[/tex] = 200π cm^2

25. We are to find the surface area of a right prism.

Surface Area of Right Prism = Base Perimeter × height + 2(Base Area)

Base Perimeter = 2(4 + 1.5) = 11 ft

Height = 0.5 ft

Base Area = 4 × 1.5 = 6 ft

Substituting these values in the above formula.

Surface Area of Right Prism = 11 × 0.5 + 2(6) = 17.5 ft^2

Answer:

Surface area of cone = 200π cm

Surface area of prism =  17.5 ft²

Step-by-step explanation:

To find the slant height of cone

slant height l = √(r² + h²)

= √(8² + 15²)  = 17

To find the surface area of cone

Surface are = πr² + πrl

 = π*8² + π*8*17

 = 64π + 136π

 = 200π cm²

To find the surface area of prism

l = 4 ft

b = 1.5 ft and h = 0.5 ft

Surface area = 2(lb + lh + bh)

 = 2[(4* 1.5) + (4*0.5) + (1.5*.5)

 = 2(6 + 2 +0.7.5)

 = 17.5 ft²

Answer:

-2√2, or ≈-2.83

Step-by-step explanation:

Well, when t = 1.75, our equation should be [tex]d=4\sin{(\pi \cdot1.75)}[/tex].

Note that [tex]\pi\cdot1.75=\frac{7\pi}{4}[/tex]. Using the unit circle (attached), we can find that the value of sine at [tex]\frac{7\pi}{4}[/tex] radians is exactly [tex]-\frac{\sqrt2}{2}[/tex]. Plugging that value back into our equation gives us

[tex]d=4\cdot\left(-\frac{\sqrt2}{2} \right)=-\frac{4\sqrt2}{2}=-2\sqrt2[/tex]

So our answer is [tex]d=-2\sqrt2[/tex], in whatever units we're using to measure height.

Answer: 0.38 Meters

Step-by-step explanation:

plug 1.75 in for t and solve, do not convert into units as you need the height so meters is accurate.

d=0.38

Answer:

[tex]\frac{1}{8}[/tex] of the phones in office has both a speaker phone and a conference-call capability

Step-by-step explanation:

Since total number of phones in the office is not given, the answer will be "in that terms".

let it be x

So built in speaker phones is (1/4)x

Hence conference call phones would be (1/2)(1/4x) = (1/8)x

Hence "1/8th of the phones in office has both a speaker phone and a conference-call capability"

Answer:

(1/8)x phones have both speaker phone and a conference call capability

Step-by-step explanation:

Let the total phones be x

It is given that one forth of the phones have in built speaker = (1/4)x

It is also given that one half of the phone having built in speaker also have conference call capability = (1/2) of (1/4)x

                                           = (1/8)x

Therefore, (1/4)x - (1/8)x

              =  (1/8)x

(1/8)x phones have both speaker phone and a conference call capability.

a) y = x - 4

First, to find the rate of change [slope], do rise\run: -y₁ + y₂\-x₁ + x₂. Doing this will result in the slope being 1, and the ONLY answer that has a slope of 1, is the top choice.

Slope-Intercept Formula: y = mx + b [m represents slope].

I am joyous to assist you.

Answer:

6x-15

Step-by-step explanation:

3*2x= 6x

3*5=15

6x-15

Answer:

6x - 15

Step-by-step explanation:

3(2x - 5)

Distributive property

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

= 6x - 15

Answer:

Step-by-step explanation:

Look at the picture.

Answer:

2g{4} hahah sike

Step-by-step explanation:

Answer:

[tex]5\sqrt{2}[/tex]

Step-by-step explanation:

Here we are given two coordinates and we are required to fin d the distance between them not by using the distance formula but by using Pythagoras theorem.

Let us see how we do that.

We will take the help of graph in this. We draw a line parallel to x axis passing through H (-2,-3) and a vertical line passing through I(3,2)

Let us assume that these two lines intersect at point J whose coordinates will be (-3,-3)

Now using scale of the graph we can see that Distance HJ = 5 units and IJ= 5 units and ΔHIJ makes and Right angle triangle where ∠IJH = 90°

Hence we can apply Pythagoras theorem in this.

[tex]HJ^{2}+JI^{2}=HI^{2}[/tex]

[tex]5^2+5^2=HI^{2}[/tex]

[tex]HI^{2}=25+25[/tex]

[tex]HI^{2}=50\\HI=\sqrt{50}\\HI=\sqrt{25*2}\\HI=5\sqrt{2}\\[/tex]

Please refer to graph in attachment for further clarification.