Stephanie is driving a new route from her house to her job, which is 12 1⁄4 miles away. On this route, she will pay a toll every 3 1⁄2 miles, and the cost of each toll is $1.35.
1. How many tolls will Stephanie pay?
2. What is the total cost of a one-way trip?

Answer:

Hence the expression [tex]$$(m+11)(m-4)=m^2+7m-44$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$[/tex]

Answer: D

Step-by-step explanation:

See attached image.

There are 84 possible student body governments

The given parameters are:

Senior = 7

Junior = 3

Sophomore = 4

The number of student body governments is calculated as:

n = Senior * Junior * Sophomore

This gives

n = 7 * 3 * 4

Evaluate

n = 84

Hence, there are 84 possible student body governments

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30+20+50 = 100 ml total. 20 ml is orange juice.

So, 30/100 reduce by dividing top and bottom by 30 gives

3/10 is the proportion of orange juice in the fruit cocktail.

Hope this helps! :)

Answer:

3/10

Step-by-step explanation:

First, find the total amount of liquid for a drink with 30 mls of orange juice
Assume volumes can be added
30+20+50 = 100 ml
the percentage/proportion of orange juice in the drink is the number of mls of orange juice divided by the total volume
so
30/100
which can be reduced to 3/10

Answer:

(C) 496

Step-by-step explanation:

area = 100 yd × 372 yd = 37,200 yd²

37,200 yd² / 75 yd² = 496

Answer: (C) 496

Answer:

56.8 m²

Step-by-step explanation:

This shape is clearly a trapezium / trapezoid. So :  

Area of a trapezium is given by the formula :

[tex]\frac{a+b}{2} h[/tex]

Substitute values given in diagram :

a = 4.2

b = 10

h = 8

[tex](\frac{4.2+10}{2} )8[/tex]

7.1 × 8 = 56.8

Units will be m² as this is area

Giving us our final answer of 56.8 m²

The flow rate of the given fluid in the pipe is gotten as; 3/2 liters per minute

We are told that a pipe fills 11/15 liters in 22/45 minutes.

Now, to get the flow rate of this pipe, we will use the formula;

Flow rate = Quantity of fluid/Time

Thus;

Flow rate = 11/15 ÷ 22/45

⇒ 11/15 * 45/22

⇒ 3/2 liters per minute

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Answer:

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Step-by-step explanation:

Surface area of a cube

SA = 6s²  (where s is the side length)

Given the side length of the box is 15 inches:

⇒ SA of box = 6 · 15² = 1350 in²

Surface Area of blocks with 3 inch side lengths:

⇒ SA = 6 · 3² = 54 in²

⇒ SA of 27 blocks = 27 · 54 = 1458 in²

Surface Area of blocks with 4 inch side lengths:

⇒ SA = 6 · 4² = 96 in²

⇒ SA of 27 blocks = 27 · 96 = 2592 in²

Surface Area of blocks with 5 inch side lengths:

⇒ SA = 6 · 5² = 150 in²

⇒ SA of 27 blocks = 27 · 150 = 4050 in²

Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.

To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:

[tex]\implies \dfrac{\textsf{SA of 27 blocks}}{\textsf{SA of box}}=\sf \dfrac{4050}{1350}=3[/tex]

Summary

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Answer: [tex]6.2 *10^9[/tex]

Step-by-step explanation:

Scientific notation is large numbers expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

So the first number cannot be 6200 or 62 or 0.6, it has to be 6.2 because 6.2 > 1 and 6.2 < 10

count your numbers right of the decimal and you should get:

[tex]6.2 *10^9[/tex]

Answer: A pair of congruent, corresponding sides

Step-by-step explanation:

This will make the triangles congruent by either AAS or ASA.

A pair of congruent, corresponding sides will make the triangles congruent by either AAS or ASA property.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Consider it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. A Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written.

For ΔABC ≅ ΔDEF, since all of their corresponding elements like angle and sides congruent.

The ASA congruent rule state that If corresponding two angles and one corresponding side of two triangles are of same measurement, then the considered pair of triangles are congruent.

This will make the triangles congruent by either AAS or ASA property.

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The angle through which ΔABC is rotated is; Option A: 48°

Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.

In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°

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The measure of angle QS based on the information given when Point R is between points Q and S is 11x + 35.

From the information given,

PR = 3x + 7

QR = 8x + 28

The value of QS will be:

PR + QR

= (3x + 7) + (8x + 28)

= 11x + 35

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Answer:

B and D

Step-by-step explanation:

check where the points are. If they are in shaded triangle they are solutions

Answer:

Step-by-step explanation:

Since the new line is parallel to the one that has a slope of 1, we can write:

y = 1x + b for the new line

Remember that y=mx+b, where m is the slope and b the y-intercept, the value of y when x=0.

We need to find a value of b that forces the line through point (1,-1).  Use (1,-1) in the equation and solve for b:

y = 1x + b

-1 = 1*(1)+b

b = -2

The equation of the line parallel to one with slope of 1 and going through point (1,-1) is:

y = 1x - 2

Answer:

- Please see the attached picture for full solution!:)

------------------ HappY LearninG<3 -------------

Answer:

x = -26

Step-by-step explanation:

[tex]5^7^x^+^5 =125^2^x^-^7\\\\5^7^x^+^5 =5^3^(^2^x^-^7^)\\\\5^7^x^+^5 =5^6^x^-^2^1[/tex]

∴ 7x + 5 = 6x - 21

7x - 6x + 5 = -21

x = -21 - 5

x = -26

Answer: 6

Step-by-step explanation:

    We will set up a proportion to solve. Let x be equal to ?.

[tex]\displaystyle \frac{3}{5} =\frac{x}{x+4}[/tex]

    Now, we will cross-multiply.

3 * (x + 4) = 5 * x

3x + 12 = 5x

12 = 2x

6 = x

A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the opposite sides are equal and parallel to each other. We can write,

AD ≅ BC

Since BX ≅ DY, therefore, we can write,

AB = CD

AX + XB = DY + YC

XB = DY, cancelling both the sides,

AX = YC.

Also, XY is the common side.

Since all the sides are equal also the angle are equal, therefore, it can be written,

AXDY ≅ CYXB

Given the area of CYXB is 71.5 square units. Therefore,

ABCD = CYXB + AXDY

ABCD = 2(CYXB)

ABCD = 143 square units.

Hence, the correct option is D.

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Answer:

7x - 9x = 26

Step-by-step explanation:

9 times a number = 9x

7 times the number = 7x

=26 because it says so

and 9x subtracted from 7x is 7x - 9x

By using the concepts of direct and inverse trigonometric expressions, the angles that represents the trigonometric function cos 5/6 are θ₁ ≈ 33.557° and θ₂ ≈ 326.443°.

Cosine are trigonometric functions whose period is 360°. Cosine is positive both for the first and fourth quadrants. Thus, the two angles associated to the given trigonometric expression are by inverse trigonometric functions:

θ₁ ≈ 33.557°, θ₂ ≈ 326.443°

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The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

The lines are given as:

y = -14x + 3 and y = -32x+3

Substitute y = -32x+3 in

-32x+3 = -14x + 3

Evaluate the like terms

-18x = 0

Divide by -18

x = 0

Substitute x = 0 in y = -14x + 3

y = -14(0) + 3

Evaluate

y = 3

Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

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Answer:

y = 3x - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6

y = 3x - 6 ← equation of line L

Answer:

pretty 5

Step-by-step explanation:

5

hahaha

got it on khan

A scale factor is defined as the ratio between the scale of the new object and the original object.

If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.

A scale factor is defined as the ratio between the scale of the new object and the original object.

We have,

The original measurement = x

The scale factor = m

The scale factor figure measurement = y

Now,

A scale factor is defined as the ratio between the scale of a given original object and a new object,

This means,

m = y/x

y = mx

This means,

The scaled figure measurement is the multiplication of the scale factor with the original measurement

Thus,

If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.

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Answer:

l = (S/pi)-r^2

Step-by-step explanation:

Just rearrange the equation.

S = pi*l + pi * r^2

S-pi*r^2 = pi*l

l = (S-pi*r^2)/pi

l = (S/pi)-r^2

The density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

Remember that density is defined as the quotient between mass and volume.

We know that the mass of the solid is 10.0 grams.

And the volume of the solid is given by the difference between the volume of the water alone (15.0 mL) and the water with the solid (17 mL).

V = 17mL - 15mL = 2mL

Then the density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

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The value of a is (c) 86

The given parameter is:

Angle C = 86

By vertical angle theorem, we have:

Angle A = Angle C = 86

This implies that:

Angle A = 86

The arc A subtends angle A

This means that:

Arc A = 86

Hence, the value of a is (c) 86

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The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, [tex]ME=0.02[/tex]

Population proportion, [tex]p=0.50[/tex]

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\large\textsf{(We will solve for your given question as well because it}\\\large\textsf{pops up in solving for your question.)}[/tex]

[tex]\huge\textbf{Solving for your original answer:}[/tex]

[tex]\mathbf{5 + 10x = 20}[/tex]

[tex]\mathbf{10x + 5 = 20}[/tex]

[tex]\huge\textbf{SUBTRACT 5 to BOTH SIDES:}[/tex]

[tex]\mathbf{10x + 5 - 5 = 20 - 5}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{10x = 20 - 5}[/tex]

[tex]\mathbf{10x = 15}[/tex]

[tex]\huge\textbf{DIVIDE 10 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{10x}{10}=\dfrac{15}{10}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{x = \dfrac{15}{10}}[/tex]

[tex]\mathbf{x = \dfrac{15\div5}{10\div5}}[/tex]

[tex]\mathbf{x = \dfrac{3}{2}}[/tex]

[tex]\mathbf{x = 1 \dfrac{1}{2}}[/tex]

[tex]\mathbf{x = 1.5}[/tex]

[tex]\huge\textbf{Therefore, the overall answer should be:}[/tex]

[tex]\huge\boxed{\star\boxed{\mathsf{\ x= \dfrac{3}{2} \ }}\star}[/tex]

[tex]\huge\textbf{And to answer your question, the very}\\\\\huge\textbf{first step in solving for this equation}\\\\\huge\textbf{[5 + 10x = 20] is:}[/tex]

[tex]\huge\boxed{\textsf{Option D. Subtract 5 to both sides}}\huge\checkmark\\\\\\\\\\\large\text{Look at the explanation above to see how we chose that.}\\\\\large\text{Remember: addition opposite is subtration \& subtraction opposite}\\\large\text{is addition, whereas multiplication is division \& divsion is}\\\large\text{is multiplication.}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035

We want to find the option that is equal to the repeating decimal 0.353535.

Option A; 35 + 0.35 + 0.0035

When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.

Option B; 0.0035+ 0.000035 + 0.00000035

When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.

Option C; 0.35 + 0.0035 + 0.000035

When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.

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Answer:

1.) C - 0.35+0.0035+0.000035+...

2.) The first term of the geometric series is 0.35.

3.) The common ratio of the geometric series is 0.01

4.) The simplified fractional representation of 0.353535... is 35 / 99

Step-by-step explanation:

Edge

The equation of the trend line is y = 3x + 15

Start by entering the table of values in a graphing calculator.

From the graphing calculator, we have the following summary:

The equation of the trend line is represented as:

y = bx + a

Where

b = SP/SSX = 52.5/17.5 = 3

a = MY - bMX = 25.5 - (3*3.5) = 15

This gives

y = 3x + 15

Hence, the equation of the trend line is y = 3x + 15

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