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

Answer:

[tex] - 1 \frac{1}{10} [/tex]

Step-by-step explanation:

[tex] - \frac{7}{10} - \frac{4}{10} [/tex]

The two fraction have the same denominator , so put them under a common denominator

[tex] \frac{ - 7 - 4}{10}[/tex]

Simplify

-7-4=-11

[tex] \frac{ - 11}{10} = - \frac{11}{10} [/tex]

write in mixed fraction form

[tex] - 11 \div 10 = 1 \: remainder \: 1 \\ = - 1 \frac{1}{10} [/tex]

Part A

Answers:

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

Explanation:

The variables are simply letters. They are placeholders for numbers to be plugged in later. Think of them like empty boxes where numbers will go. In this case, the variable h represents the number of hours Tyler works, and c is the number of new accounts she opens.

The coefficients are the numbers multiplied with the variables. They are to the left of the variable.

The constant 50 is not attached to any variable.

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

Part B

Answer: She earns $618.5

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

Explanation:

We're told she worked 37 hours. So we'll replace h with 37.

Also, she opened 12 new accounts. So c = 12

This means...

10.50*h + 15*c + 50

10.50*37 + 15*12 + 50

388.5 + 180 + 50

618.5

is the amount she earns

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

Part C

Answer: The coefficient changes. Specifically, the coefficient 10.50 changes to 11.25

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

Explanation:

The constant never changes (hence the name) no matter how much of a raise Tyler gets. The other coefficient doesn't change either because she would still get $15 per new account. All that's changed is the hourly wage.

If we're told that Tyler got a raise to $11.25 per hour and she now earned $20 per new account, then both coefficients would change and the new equation would be 11.25h+20c+50

0.7 is a rational number.

Because it is a terminating decimal expansion.

Answer:

The decimal 0.7 is a rational number. It is read as seven tenths and is equivalent to the fraction 7/10. Since it can be written as a fraction

Answer:

17

Step-by-step explanation:

i am in doubt with the answer

Answer:

[tex]\huge\boxed{KL = 17}[/tex]

Step-by-step explanation:

If L lies on the line segment KM. It means that:

K_____?__________L___2__M

|<--------------------19------------------->|

Given that:

LM = 2

KM = 19

So,

KM = KL + LM

19 = KL + 2

Subtracting 2 to both sides

KL = 19-2

KL = 17

Answer:

144°

Step-by-step explanation:

let the smaller angle be x then the larger angle is 4x

The sum of a linear pair of angles = 180°, thus

x + 4x = 180 , that is

5x = 180 ( divide both sides by 5 )

x = 36

Thus the larger angle = 4x = 4 × 36 = 144°

Answer:

let the smaller angle be x.Then the bigger angle will be 4x.

x+4x= 180

or, 5x=180

or, x=180/5

there fore, x=36

Again,

4x=4×36

=144

The larger angle is 144.

Answer:

(3,4)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(2+4)/2 = 6/2 =3

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(5+3/2 = 8/2 =4

The midpoint is (3,4)

Answer:

Hey there!

Using the midpoint formula we find the midpoint to be: (3, 4)

Let me know if this helps :)

Answer:

17.3 in

Step-by-step explanation:

Given the following :

Length of tank = 20 inches

Width of tank = 10 inches

Amount of water poured into tank = 15 gallons

Volume(V) of tank (rectangular prism)

V = Length × width × height

Height = h

1 gallon = 231 inch³

15 gallons = (231 × 15) = 3465 in³

Hence V = 3465 in³

3465in³ = 20 in × 10 in × h

3465 in³ = 200h

h = 3465 / 200

h = 17.325 in

Height = 17.3 in ( nearest tenth)

Answer: 25

Step-by-step explanation: got it wrong and got the answer Took 1 for the team

Answer:

25

Step-by-step explanation:

khan academy :D

Answer:

Step-by-step explanation:

okay so if we lay it out...,

f(x)              6-5x                x-9           x³           2x-5            12x+3

f(-3)              21                   12            -27           -11               -33

f(-2)              16                   -11           -8              -9                -21

f(0)                6                   -9             1                -5                 3

f(1)                 1                    -8             1                -3                 15

f(2)               -4                    -7            8               -1                   27

okay so the left side is all the f(x) values. So the numbers in the "()" represents "x". Now you just substitute the numbers in the"()" for the "x"'s on the top margins. so...,

f(-3)= 6-5x            f(-2)= 6-5x                 f(0)=6-5x               f(1)=6-5x        f(2)=6-5x

f(-3)= 6-5(-3)         f(-2)= 6-5(-2)             f(0)=6-5(0)            f(1)=6-5(1)       f(2)=6-5(2)

f(-3)= 6+15            f(-2)= 6+10                 f(0)=6-0                f(1)=6-5          f(2)=6-10

f(-3)= 21                f(-2)= 16                      f(0)=6                   f(1)= 1              f(2)= -4

f(-3)=x-9               f(-2)=x-9                      f(0)=x-9               f(1)=x-9            f(2)=x-9

f(-3)=(-3)-9            f(-2)=(-2)-9                  f(0)=0-9              f(1)=1-9             f(2)=2-9

f(-3)=-12                f(-2)=-11                       f(0)= -9                f(1)= -8            f(2)= -7

f(-3)=x³                 f(-2)=x³                        f(0)=x³                f(1)= x³              f(2)=x³

f(-3)=(-3)³             f(-2)= (-2)³                    f(0)=0³               f(1)=1³                f(2)=2³

f(-3)= -27             f(-2)= -8                        f(0)= 1                f(1)= 1                 f(2)=8

f(-3)= 2x-5           f(-2)= 2x-5                 f(0)= 2x-5            f(1)= 2x-5      f(2)=2x-5

f(-3)=2(-3)-5         f(-2)=2(-2)-5              f(0)= 2(0)-5          f(1)= 2(1)-5     f(2)=2(2)-5

f(-3)= -6-5            f(-2)= -4-5                  f(0)=0-5               f(1)=2-5         f(2)=4-5

f(-3)= -11               f(-2)= -9                      f(0)= -5                f(1)= -3          f(2)= -1

f(-3)=12x+3            f(-2)=12x+3              f(0)=12x+3          f(1)=12x+3     f(2)=12x+3

f(-3)= 12(-3)+3        f(-2)=12(-2)+3          f(0)=12(0)+3        f(1)=12(1)+3    f(2)=12(2)+3

f(-3)= -36+3          f(-2)= -24+3              f(0)= 0+3             f(1)=12+3       f(2)=24+3

f(-3)= -33                f(-2)= -21                  f(0)=3                 f(1)=15           f(2)= 27

Don't know if you wanted all the work. But I just did it for you so you can see.

If you divide the circumference C over the radius r, you get 2pi

2pi = C/r

this is because

C = 2pi*r

is one formula to find the circumference. Another formula is

C = pi*d

which works because d = 2r, ie the diameter is twice the radius.

Step-by-step explanation:

First, replace f(x) with y . ...

Replace every x with a y and replace every y with an x .

Solve the equation from Step 2 for y . ...

Replace y with f−1(x) f − 1 ( x ) . ...

Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

The steps for finding the inverse of a function are given below.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

Steps for finding the inverse of a function f.

Replace f(x) by y in the equation describing the function.

Interchange x and y. In other words, replace every x by a y and vice versa.

Solve for y.

Replace y by f⁻¹(x).

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Answer:

the point (-3, 5) would be plotted in the second quadrant, quadrant ||

Step-by-step explanation:

[tex]-5x-3=3x+13[/tex]

[tex]8x=-16[/tex]

[tex]x=-2[/tex]

Hope this helps.

頑張って!

A =  1/2 bh

Let's simplify the right side.

A = (bh) / 2

Multiply both sides by 2

2A = bh

Divide both sides by b

(2A) / b = h

Answer:

3 x^4 y^3

just add the number of x's and place that as the exponent and do the same with the y

Answer:

13527.82

Step-by-step explanation:

Answer:

She has 7 nickels, 11 dimes and 10 quarters

Step-by-step explanation:

Total value =$3.95

Let

Nickel = x

Dimes = x + 4

Quarters = x + 3

Every

Nickel = 5 cents

Dimes = 10 cents

Quarters = 25 cents

Total cents = $3.95 × 100

= $395

5n + 10d + 25q = 395

5(x) + 10(x+4) + 25(x+3) = 395

5x + 10x + 40 + 25x + 75 = 395

40x + 115 = 395

40x = 395 - 115

40x = 280

Divide both sides by 40

x= 280/40

= 7

x= 7

Nickel = x = 7

Dimes = x + 4

=7+4

=11

Quarters = x + 3

=7+3

=10

Answer:

true

Step-by-step explanation:

Answer: True.

Make sure you check each triangle, not all of them are right ones.

Answer:

I think the ans is A. inverse.

Answer:

Step-by-step explanation:

Hi there!

~

⇒ Graph : [tex]y=6x^2+1[/tex]

∴ Rewrite the equation in vertex form.

⇒ [tex]y = 6 ( x + 0)^2 + 1[/tex]

∴ Use the vertex form, [tex]y = a(x - h)^2 + k[/tex] , to determine the values of [tex]a , h ,[/tex] and [tex]k[/tex]

[tex]a = 6 \\h = 0\\k = 1[/tex]

∴ Since the value of [tex]a[/tex] is positive, the parabola opens up.

⇵

∴ Find the vertex [tex]( h,k)[/tex].

[tex](0,1)[/tex]

∴ Find [tex]p[/tex], the distance from the vertex to the focus.

[tex]\frac{1}{24}[/tex]

∴ Find the focus.

[tex]( 0 , \frac{25}{24} )[/tex]

∴ Find the axis of symmetry by finding the line that passes through the vertex and the focus.

[tex]x = 0[/tex]

∴ Find the directrix.

[tex]y = \frac{23}{24}[/tex]

∴ Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

⇒ Vertex: [tex]( 0 , 1)[/tex]

⇒ Focus: [tex]( 0 , \frac{25}{24} )[/tex]

⇒ Axis of Symmetry: [tex]x = 0[/tex]

⇒ Directrix: [tex]y = \frac{23}{24}[/tex]

∴ Select a few [tex]x[/tex] values, and plug them into the equation to find the corresponding [tex]y[/tex]  values. The [tex]x[/tex] values should be selected around the vertex.

[tex]x : -2 , -1 , 0 , 1 , 2 \\y : 25 , 7 , 1 , 7 , 25[/tex]

Hope this helped you!

Answer:

Option C is the correct answer.

C.  5•(-20)

Step-by-step explanation:

We are told that the insurance payment for the car follows a certain pattern that can be represented through an expression. The payment is decreasing by $20 every year. As we don't know the total payment amount per period, so we cannot calculate how much is paid per period/year for insurance but we can calculate the rate at which this payment is decreasing.

Change in payment = t * (-20)

The above expressions can be used to calculate the amount of change in payment i payment is decreasing by a constant $20 every year, after t years.

So, if we want to calculate the change in payment after say 5 years, we can replace t with 5 in the equation and calculate the change,

Change in payment = 5 * (-20)

Change in payment = - $100

Answer:

Step-by-step explanation:

oh im late-......

Answer:

-22 is the value of K.

Step-by-step explanation:

A simple way to see how far a mid-point or end-point is from another is by adding or subtracting. For this figure I added to see how many numbers would add twice to get from -15 to -29. -14 is the exact number from -15 to -29; divide that by 2 to get half of -14 which is -7. -7 + (-15) gives you -22.

The location of K so that JK is 1/7 of JL is -22.

Given that, K lies between J and L.

We need to find the location of K so that JK is 1/7 of JL.​

In geometry, a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.

Now, the distance between the points J and L on the number line is 14.

So, 1/7(14)=2

A simple way to see how far a mid-point or end-point is from another is by adding or subtracting. For this figure, I added to see how many numbers would add twice to get from -15 to -29. -14 is the exact number from -15 to -29; divide that by 2 to get half of -14 which is -7. -7 + (-15) gives you -22.

Therefore, the location of K so that JK is 1/7 of JL is -22.

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Answer:

12

Step-by-step explanation:

7 + 13 + (-8)

Keep in mind, adding a negative number is like subtracting that number.

7 + 13 - 8

= 20 - 8

= 12

Answer:

Option C

Step-by-step explanation:

[tex] {9x}^{10} \times ( - {12}^{13} )[/tex]

[tex] = > {( - 12 \times 9)}x^{10 + 13} [/tex]

[tex] = > { - 108x}^{23} [/tex]

The solution is $ 9.50

The weekly per hour rate of Tasha is $ 9.50

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The weekly per hour of Tasha last week = $ 422.75

The extra overtime pay of Tasha for 3 hours = $ 42.75

The total number of hours working = 40 hours

So , the equation will be

The weekly per hour of Tasha without overtime = weekly per hour of Tasha last week - overtime pay of Tasha for 3 hours

Substituting the values in the equation , we get

The weekly per hour rate of Tasha without overtime = 422.75 - 42.75

The weekly per hour of Tasha without overtime = $ 380

So , The weekly per hour rate of Tasha A = The weekly per hour rate of Tasha without overtime / total number of hours working

Substituting the values in the equation , we get

The weekly per hour rate of Tasha A = 380 / 40

The weekly per hour rate of Tasha A = $ 9.50

Therefore , the value of A is $ 9.50

Hence , The weekly per hour rate of Tasha is $ 9.50

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Explanation:

Multiply 0.66666667 with 18 to get

0.66666667*18 = 12.00000006

The 6 at the very end is due to rounding error. In reality the 6's in 0.66666667 should go on forever. That 7 is from rounding up.

Anyways, the result 12.00000006 should be 12 exactly.

Note how

12/18 = 0.66666667

when using a calculator.

Answer:

12

Step-by-step explanation:

Use equilvalent fractions 0.6 repeating is 2/3 than convert it over 18 students which is equal to 12/18 students chose granola bars.

Answer:

2 cups

Step-by-step explanation:

Because you have 4 loads of clothes you would have to use

1/4 of a cup 8 times

1/4*8=8/4 simplified is 2 which no fractions

so the answer is 2 cups for 4 loads of clothes.