There are 5 pencils and 8 pens. What is the ratio of pens to pencils?

Answer:

slope: (y₂ - y₁) / (x₂ - x₁)

(5 - 2) / (-1 - 1) = 3/-2 = -3/2

y = -3/2x + b

5 = -3/2(-1) + b

5 = 3/2 + b

b = 3.5

y = -3/2x - 7/2

(5.83 - 1.42) / (4.22 + 0.72) = 4.41/4.94

y = 4.41/4.94x + b

5.83 = (4.41/4.94)(4.22) + b

5.83 = 3.76724696 + b

b = 2.06275304

y = 4.41/4.94x + 2.06

(the numbers are really wacky so i hope thats right, so sorry if it isn't)

Answer:

Actual distance between the 2 priers = 90 MI

Step-by-step explanation:

Ratio of Scaled drawing to actual dimension = 2 : 15

2 cm represents 15MI

2cm ≡ 15 MI

∴ 1 cm ≡ (15/2) MI

1 cm ≡ 7.5 MI

scaled distance of priers in drawing = 12cm

∴ 12 cm ≡ 7.5 × 12

= 90 MI

∴ Actual distance between the 2 priers = 90 MI

Answer:

It took 11.04 hours  by Stephanie.

Step-by-step explanation:

Concept

distance = speed*time

time = distance/time

_________________________________

Given

for Steven

time  = 10 hours

speed = 53 miles per hour

Distance for steven = 53*10 = 530 miles

_____________________________________

Now ,

as Stephanie also traveled the same distance as steven

Distance = 530 miles

speed = 48 miles per hour

time = 530/48 hour = 11.04 hours

Thus, It took 11.04 hours  by Stephanie.

In other way

since distance traveled by Steven and Stephanie are same

let time taken by Stephanie be x hours

Distance traveled by steven = Distance traveled by Stephanie

53*10 = 48*x

x = 530/48 = 11.04 hours

equation = 53*10 = 48*x

Answer:

x < 6

Step-by-step explanation:

Given

- 3x + 51 > 13 + 7x - 22 ( simplify right side )

- 3x + 51 > 7x - 9 ( subtract 7x from both sides )

- 10x + 51 > - 9 ( subtract 51 from both sides )

- 10x > - 60

Divide both sides by - 10, reversing the symbol as a result of dividing by a negative quantity.

x < 6

Answer:

Dimensions of the rug = 13 ft × 26 ft

Step-by-step explanation:

Dimensions of the room = 21 ft × 34 ft

Area of the room = 21 × 34 = 714 ft²

Cynthia wants to leave a uniform strip of floor around the rug.

Let the width of the rug = x ft

Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft

Area of the rug = (21 - 2x)×(34 - 2x) square feet

338 = (21 - 2x)×(34 - 2x)

338 = 714 - 68x - 42x + 4x²

4x² - 110x + 714 - 338 = 0

4x² - 110x + 376 = 0

2x² - 55x + 188 = 0

2x² - 47x - 8x + 188 = 0

x(2x - 47) - 8(x - 47) = 0  

(x - 4)(2x - 47) = 0

x = 4, [tex]\frac{47}{2}[/tex]

For x = 23.5 area of the rug will be negative.

Therefore, x = 4 ft will be the width of the rug.

Dimensions of the rug will be 13 ft × 26 ft. 

Answer:

I guess that you want to model the elevation of Lake Sam Rayburn.

During the summer, it is 165 ft above the sea level (the sea level is our position 0ft).

If it does not rain, the elevation of the lake decreases by 0.5ft each week.

So if we assume that there is no rain, we can write the elevation fo the lake as a linear relationship with slope equal to -0.5ft and y-intercept equal to 165ft.

L(w) = 165ft - 0.5ft*w

Where w is the number of weeks without rain, if we have 0 weeks without rain, then the level of the lake remains constant at 165ft above sea level,

L(0) = 165ft - 0.

Answer:

The approximate area, of the baseball diamond is 8192 ft²

Step-by-step explanation:

The given coordinates of the baseball diamond are;

(0, 64), (64, 0), (0, -64), and (-64, 0)

The length of one unit of the coordinate plane = 1 foot

Therefore, we note that, there are two points with x-coordinate = 0 at which the y-coordinates = 64 and -64

Similarly here are two points with y-coordinate = 0 at which the x-coordinates = 64 and -64

The length of the segment are therefore the vertices of a square as we have;

A(0, 64), B(64, 0), C(0, -64), and D(-64, 0)

∠DBA = ∠DCA = tan⁻¹(64/64) = tan⁻¹(1) = 45°

∠DBA + ∠DCA = ∠ABC = 90°

The shape of the diamond is a square

The length, l of the side of the square is given by the relation;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

When, (x₁, y₁) = (0, 64), (x₂, y₂) = (64, 0)

We have;

[tex]l = \sqrt{\left (0 -64 \right )^{2}+\left (64-0 \right )^{2}} = 64\cdot \sqrt{2}[/tex]

The

The area, A, of the baseball diamond is therefore;

A = Area of a square = (Length of the side of a square)² = (64·√2)² = 8192 ft²

The area, of the baseball diamond = 8192 ft².

Answer:

19

Step-by-step explanation:

FH is FG = GH    which is 4+15=19

Answer:

Simplify the expression.

30.9ft

Step-by-step explanation:

you ' re welcome ! grandma loves you < 33 ; )

Answer:

3x +2 +X = X+5

4x + 2 = X + 5

3x = 3

X = 1

Step-by-step explanation:

brain list me plzzz I need it

x = 1

3x + 2 + x = x + 5

3x + x - x = 5 - 2

3x = 3

x = 3 : 3

x = 1

Answer:

274

Step-by-step explanation:

First stop of Caroline = At 36 mile marker

Destination of Caroline = At 353 mile marker

Distance left to be covered = 353 - 36 = 317 miles

Given that Caroline decides to stop at an attraction [tex]\frac{3}{4}[/tex] of the way after she stops for gas.

i.e. at a distance [tex]\frac{3}{4}[/tex] of 317 miles away from the Gas stop.

[tex]\frac{3}{4} \times 317 = 79.25\times 3 \approx 238\ miles[/tex]

So, Caroline stops at a point which is around 238 miles away from the gas station.

To calculate the Mile marker of her stop, we need to add the mile marker of gas station and the distance of her stop from gas station.

Mile marker location at her stop = 36+238 = 274

Answer:

Answer:-4e-9

[tex]3e - 19 - 7e + 10[/tex]

Start by combining like terms. I put like terms in parentheses so you can see them, but they are not needed.

[tex] = (3e - 7e) + ( - 19 + 10)[/tex]

[tex] = - 4e - 9[/tex]

That's it.

Answer: (-3,7)

Step-by-step explanation:

Flip the signs

Answer:

6/x^2

Step-by-step explanation:

Simplify the following:

2/x^2 + 4/x^2

2/x^2 + 4/x^2 = (2 + 4)/x^2:

(2 + 4)/x^2

2 + 4 = 6:

Answer: 6/x^2

Answer:

6/x²

Step-by-step explanation:

[tex]\frac{2}{x^{2} } + \frac{4}{x^{2} } \\\\[/tex]

= (2+4) / x²

= 6/x²

Hello there! :D

Firstly, I want you to understand an important concept. This has something to do with absolute value. So, although distance is a number, it is neither positive nor negative. It does not necessarily involve value. So, what we are looking for today will not have a negative sign in front of it. We are simply looking for distance!

Let's start with ST, because the distance between those is smaller and therefore I can better explain this to you. T is at the point 19.1, and S is at the point 14. We need to find the amount of distance between the two. How do we do that?

Subtraction! In order to find this value we can subtract the smaller number from the larger number.

19.1-14= 5.1

ST is 5.1

Now we can look at the distance between TR. We are actually going to add numbers together! We know that T is 19.1. If we were to put a dot at zzero and measure that distance, it would be 19.1. What is the distance from R to zero? That's right! The same principle is there. If we had a dot at zero and we're measuring from 4, the distance would be 7.5 (even though it is negative on the number line).

So, we can add these numbers together!

19.1+7.5= 26.6

TR is 26.6

I hope this helped you and you have a wonderful day,

Kai xx

Answer:

The elevator is now on the 2nd floor.

Step-by-step explanation:

15 - 18 = -3

-3 + 5 = 2

Answer:2nd floor

Step-by-step explanation:

since the elevator is on the 15th floor and you go down 18 that’s equals negative 3 then you go back up 5 floors and you add 5 to negative 3 which leaves you with the 2nd floor

Answer:

B,D,F

Step-by-step explanation:

I got it correct on edge

Answer:

24m

Step-by-step explanation:

factor the equation to get 6x4m which gets you 24m

Answer: option 3. 24m

Step-by-step explanation:

concept to know: (a+b)²=a²+2ab+b²  

                             (a-b)²=a²-2ab+b²

 (2m+3)²-(2m-3)²

=(4m²+12m+9)-(4m²-12m+9) ⇔ Use the formula mentioned above

=4m²+12m+9-4m²+12m-9 ⇔ take off parentheses

=4m²-4m²+12m+12m+9-9 ⇔ move the like term together

=24m ⇔ combine like term

Hope this helps!! :)

Please let me know if you have any question

Answer:

#1 : -2=n

#2: x=-3

#3: v=8

Step-by-step explanation:

the pictures are the explination

i hope they help

sorry if they dont

im a bad explainer

Use the distance formula to determine the distance between two points.

√ 37

Answer:

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

Step-by-step explanation:

I hope this helps!

16/6

Step-by-step explanation:

51/3= 16/3

therefore:

16/3÷2

16/3×1/2

16/6

Answer:

b = 6

I hope this helps!

Answer:

each of them costed at least 16 dollars only because if you divide 94 and six your answer would be 15.6666666667 and if you round that it would be sixteen. I am confused what else the question is asking. I apologize if it did not answer your question

Answer:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Step-by-step explanation:

So we have the rational function:

[tex]f(x)=\frac{x}{x-7}[/tex]

The domain restrictions of rational functions are the zeros of the denominator.  In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.

So, solve for the denominator by setting it to 0:

[tex]x-7=0[/tex]

Add 7 to both sides:

[tex]x=7[/tex]

So, our domain is all real numbers except for 7.

(When x=7, we have 7/0, which is undefined.)

Therefore:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Answer:

the picture has it all!

whatever equals zero is not the domain and whatever doesnt equal zero is the domain!

hope i helped :)

Answer: 2x -5 less than or equal to 124

Answer:

See below.

Step-by-step explanation:

So we have the graph of:

[tex]x^2+y^2=8[/tex]

As given, the graph is a circle with a radius of 2√2 and a center of (0,0)

Part 1)

The domain of a function is the span of x-values it covers and the range of a function is the span of y-values it covers.

From the graph, we can see that the x-values the graph covers goes from -2√2  to +2√2. The graph includes these values.

Thus, the domain is, in interval notation:

[tex][-2\sqrt2,2\sqrt2][/tex]

From the graph, we can see that the y-values the graph covers also goes from -2√2 to 2√2.

Therefore, like the domain, the range in interval notation is:

[tex][-2\sqrt2,2\sqrt2][/tex]

Part 2:

First of all, we can use the vertical line test to prove that the graph is indeed not a function.

Algebraically, we have to do some more.

First, recall what it means when an equation is not a function. It means that one x maps onto two or more ys.

In other words, to prove that the equation is not a function, we can substitute an x for a value and solve for y.

For instance, let's use 0 for x (and 0 is within the domain). Thus:

[tex]x^2+y^2=8\\(0)^2+y^2=8[/tex]

Simplify:

[tex]y^2=8[/tex]

Take the square root of both sides:

[tex]y=\pm\sqrt8\\y=\pm2\sqrt2[/tex]

In other words, when x is 0, y can be either -2√2 or 2√2. So we have two different y-values with the same x-coordinate.

[tex](0,-2\sqrt2)(0,2\sqrt2)[/tex]

Therefore, the equation is not a function.

Answer:

w=-9

Step-by-step explanation:

14-9=5, but this is addition, so you must do a negitive

-9+14=5

Answer:

[tex]\Large \boxed{a=\frac{-1}{4} }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{3}{a} \cdot x - 4 = 20[/tex]

Let x = -2.

[tex]\displaystyle \frac{3}{a} \cdot (-2) - 4 = 20[/tex]

Solving for a.

[tex]\displaystyle \frac{-6}{a}- 4 = 20[/tex]

Adding 4 to both sides.

[tex]\displaystyle \frac{-6}{a} = 24[/tex]

Multiplying both sides by a, then dividing both sides by 24.

[tex]\displaystyle \frac{-6}{24} = a[/tex]

Simplifying.

[tex]\displaystyle \frac{-1}{4} = a[/tex]

Answer: Choice C) Star shaped symbol

We can rotate the star symbol 90 degrees to have it line up with its original image. The before and after images would be identical after doing such a rotation. So this figure has rotational symmetry.

The other figures would change if we rotated them some angle x such that [tex]0 < x < 360[/tex], so they do not have rotational symmetry.