toni can carry up to 18 lb in her backpack l. Her lunch weighs 1 lb, her gym clothes weigh 2 lb, and her books (b) weigh 3 lb each. How many books can she carry in her backpack?

[tex]-\frac{1}{3}x[/tex] + y = -1   ⇒   y = [tex]\frac{1}{3}x[/tex] - 1

To graph this line, plot a point at the y-intercept (0, -1), than plot the next point using the rise over run from the slope [tex](\frac{1}{3})[/tex] by counting up 1 and to the right 3 of the y-intercept.  This gives you a second point of (3. 0).  Draw a line through those two coordinates.

Answer: Plot (0, -1) and (3, 0) and draw a line through them.

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y = 4 +  [tex]\frac{1}{3}x[/tex]    ⇒   y =  [tex]\frac{1}{3}x[/tex]  + 4

Same as above.  Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).

Answer: Plot (0, 4) and (3, 5) and draw a line through them.

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You should end up with two PARALLEL lines.  Since the lines never intersect, there are no solutions to this system of equations.

Answer: No Solution

Angle A and Angle BCA are corresponding angles and equal.

Angle x and Angle BCA are VERTICAL angles and equal.

Therefore Angle A = Angle BCA = Angle x = 62 degrees.

The slope of this line is -3/4

In order to find this, we look for two points on the line and then use the slope formula. Two points that are on the line are (0, 2) and (4, -1). Plug these into the following formula.

m (slope) = (y2 - y1)/(x2 - x1)

m = (-1 - 2)/(4 - 0)

m = -3/4

Let losses = X

They won 13 more than 3 times as many so wins =  3X +13

Now you have wins  + loses  = total games:

X +3X + 13= 109

Combine like terms:

4x + 13 = 109

Subtract 13 from each side:

4x = 96

Divide each side by 4:

x = 96 / 4

X = 24

Wins = 3X +13

3(24) +13 = 72+13 = 85

Wins = 85 games

Losses = 24 games

Sal is 10 years old. If you want to check you can do 10*4+5 and get 45

To find your pay for a week, multiply the total hours worked (h) by the hourly wage ($10). For example, working 40 hours would yield a total pay of $400. A $2 per hour raise increases your hourly wage to $12 and represents a 20% pay increase.

To calculate your pay if you work h hours in one week at a rate of $10 per hour, you simply multiply the number of hours worked by the hourly wage. This can be expressed in the following formula:

Total pay = Hourly wage  imes Number of hours worked

So, if you work h hours, your total pay will be:

Total pay = $10/hour  imes h hours

This means that if you work 40 hours in a week, for example, your total pay would be:

Total pay = $10/hour  imes 40 hours = $400

If your boss is impressed with your work and gives you a $2 per hour raise, your new hourly wage would be $12 per hour. The percentage change in pay in this case is 20%, calculated by dividing the raise amount by the original wage ($2/$10 = 0.20 or 20%).

The equation for the direct variation is y = 1.2x

In order to find this, we start with the base for any direct variation equation.

y = kx.

Now we use the ordered pairs to find the value of k to model the equation.

y = kx

24 = k(20)

1.2 = k

Now that we know this, we can model the equation as y = 1.2x and test for the other values --- each of which work in the newly written equation.

Answer:

its actually 0.8x

Step-by-step explanation:

im saying this for future people

96 days

12 x 8 = 96

to check I did:

8 x 1 = 8

8 x 2 =16

etc.

I did the same thing with 12,

To find out how many days it will be until Ben and Isabel exercise together again, we need to determine the least common multiple (LCM) of their exercise intervals. The LCM of 12 and 8 is 24.

To find out how many days it will be until Ben and Isabel exercise together again, we need to determine the least common multiple (LCM) of their exercise intervals. Ben exercises every 12 days, while Isabel exercises every 8 days.

To find the LCM of 12 and 8, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 12 are 12, 24, 36, 48, 60, 72, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and so on. The smallest number that appears in both lists is 24.

Therefore, Ben and Isabel will exercise together again in 24 days.

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17.28  dollars is the answer

12.8 * 1.35 =17.28

Therefore Marissa spent $17.28 on potatoes.

A perpendicular bisector must go through the midpoint of a line, in this case AB. Since Audra opened her compass to more than half way she needs to close it partially until she is on the midpoint.

Answer:

Given that Audra was drawing a perpendicular bisector of segment AB with a compass. She started with line segment AB. Then, she placed her compass point on A and opened the compass more halfway to B.

Her next step will be "Using the width of the compass from the previous step, draw two arcs to the left and right of both A and B".

Step-by-step explanation:

Expanded form

0.200 + 0.050 + 0.003

Standard (word) form

zero and two hundred fifty three

hope that helps :)

253/1000 and 253% is the answer to your question :)

The formula of a midpoint:

[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have:

[tex]M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7[/tex]

Substitute

[tex]\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4[/tex]

5 X 4 = $ 20 $ Your answer is 20.

The solution to the given equation 18n - 7p - 15n = 5p for n is n = 4p. Thus, the option D is correct.

The equation is given as follows:

18n - 7p - 15n = 5p

Combine like terms by subtracting 15n from 18n:

(18n - 15n) - 7p = 5p

3n - 7p = 5p

Move the term containing n to the other side of the equation by adding 7p to both sides:

3n - 7p + 7p = 5p + 7p

3n = 12p

Solve for n by dividing both sides of the equation by 3:

(3n)/3 = (12p)/3

n = 4p

Therefore, the solution to the equation 18n - 7p - 15n = 5p for n is n = 4p.

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

[tex]Answer:\ (x+1)(x-1)(x^2+1)[/tex]

30 bass and 5 perch, so then you will bet minimal costs

the answer is -1 hope this helps

The slope of this line is -1

We can see here that the volume of the 612 g piece of aluminum is approximately 226.67 cm³.

Density is a physical property of matter that measures how much mass is contained in a given volume of a substance. In other words, it quantifies how closely packed the particles (atoms, molecules, or ions) are within a material. Density is typically expressed in units such as grams per cubic centimeter (g/cm³) in the metric system or pounds per cubic inch (lb/in³) in the imperial system.

To find the volume of a 612 g piece of aluminum, you can use the formula for density:

Density = Mass/Volume

You have the density (2.70 g/cm³) and the mass (612 g), and you want to find the volume. Rearrange the formula to solve for volume:

Volume = Mass/Density

Inputting  the values:

Volume = 612g/2.70g/cm³

​

Calculate the volume:

Volume = 612/2.70

Volume ≈ 226.67cm³

So, the volume of the 612 g piece of aluminum is approximately 226.67 cm³.

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Answer:

y=x^2+6

you need to add in the exponent

Ask google for help on that.

Answer:

12a+2b

Step-by-step explanation:

2(x - 2) = 3(x + 9)

Distributive property.

2x - 4 = 3x + 27

Subtract 2x from both sides.

-4 = x + 27

Subtract 27 from both sides.

-31 = x

It appears as though you're to figure out the quotient some way (as by using a calculator), then verify that the product of quotient and divisor gives the dividend.

2. 96 ÷ 6 = 16

... (6×10) + (6×6) = 96

... 6 × 16 = 96

4. 84 ÷ 6 = 14

... (6×10) + (6×4) = 84

... 6 × 14 = 84

6. 104 ÷ 4 = 26

... (4×20) + (4×6) = 104

... 4 × 26 = 104

8. 102 ÷ 6 = 17

... (6×10) + (6×7) = 102

... 6 × 17 = 102

10. 64 ÷ 4 = 16 . . . . Ken will make 16 gift bags, each containing 4 pens.

1. Speed = 3.33333 Meters per second, 400/120=3.33333, average speed = total distance/elapsed time

2. Velocity = 3.33333 Meters, 400/120, V = distance / time

3. Acceleration = -0.222222[tex]m/s^2[/tex], acceleration = (velocity2 - velocity1) / time

acceleration = net_force / mass

Answer:

2 A. 400÷120=3.33

2 B. d/t=v

400/120=3.33 N E

3.

3.3m/s/15s=0.22m/s^2

downhill= negative slope=negative acceleration(slowing down)

86,700,000 − 3.45 × 10^7

= 8.67 × 10^7  − 3.45 × 10^7

= (8.67 - 3.45) × 10^7

= 5.22 × 10^7

Hope it helps

By Subtracting the given expression 86,700,000 − 3.45 × [tex]10^7[/tex] we get Option b) 5.22 × [tex]10^7[/tex].

To subtract 3.45 × [tex]10^7[/tex] from 86,700,000, we need to perform a mathematical operation involving exponents.

To perform the subtraction, we start by rewriting the numbers in scientific notation form, where a number is expressed as a product of a coefficient and a power of 10.

Given expression: 86,700,000 - 3.45 × [tex]10^7[/tex]

Step 1: Rewrite 86,700,000 in scientific notation:

86,700,000 = 8.67 × [tex]10^7[/tex]

Now, the expression becomes: 8.67 × [tex]10^7[/tex] - 3.45 × [tex]10^7[/tex]

Step 2: Subtract the coefficients:

8.67 - 3.45 = 5.22

Step 3: Keep the common base (10) and subtract the exponents:

[tex]10^7[/tex] (common base) - [tex]10^7[/tex] = [tex]10^7[/tex]

Combining the coefficient and the exponent, we get the final result:

5.22 × [tex]10^7[/tex] (option b)

When we subtract numbers in scientific notation, we first need to make sure both numbers have the same exponent. In this case, we converted 86,700,000 to scientific notation as 8.67 × [tex]10^7[/tex]. Then, we subtracted the coefficients, which gave us 5.22. The exponent remains the same, which is [tex]10^7[/tex]. So, the final answer is 5.22 × [tex]10^7[/tex].

The correct option is b) 5.22 × [tex]10^7[/tex].

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Complete Question

Choose the correct answer form the given options:

Subtract. 86,700,000 − 3.45 × [tex]10^7[/tex]

a) 5.22 5.22×[tex]10^6[/tex]​

b) 5.22×[tex]10^7[/tex] ​

c)​ 5.22×[tex]10^8[/tex] ​

Estimation is useful in calculating the total cost of items in a grocery store basket.

An example of a real-life multiplication situation where estimation makes sense is calculating the total cost of items in a grocery store basket. Let's say you have a basket with 3 apples that cost $1.50 each and 2 yogurts that cost $2.75 each. To estimate the total cost, you can round the prices to the nearest dollar and multiply: 3 x $2 + 2 x $3 = $6 + $6 = $12. This estimation gives you a rough idea of the total cost without needing to calculate exact values.