1: What number must be multiplied by (5x + 6) to result in the expression 20x + 24?

2: On the first day of a road trip, you drive x miles.
On Day 2, you drive 10 more than twice the miles driven on Day 1.
On Day 3, you drive 100 miles less than Day 1.

Write an expression to represent the miles driven on each day of the road trip, then write a final simplified expression representing the total miles driven in three days.
a) Day 1:
b) Day 2:
c) Day 3:
d) Final simplified expression to represent total miles driven in three days:

e) Look at your expression for c) Day 3: "100 miles less than Day 1." Describe a real-word situation to explain why order matters when writing this expression.

Answers

Answer 1

1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.

2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:

a) Day 1: x

b) Day 2: 2x + 10

c) Day 3: x - 100

d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.

e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.

What is a mathematical expression?

A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).

Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.

1) Multiplication:

(20x + 24) ÷ (5x + 6) = 4

Check:

4(5x + 6) = 20x + 24

2) Road Trip Expressions:

Day one driving distance = x miles

Day two driving distance = 2x + 10

Day three driving distance = x - 100

Total distance = x + 2x + 10 + x - 100

= 4x + 10 - 100

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Related Questions

6. Which of the following is true about the line given by 8x - 2y = 24?

A) The slope is negative.
B) The y-intercept is negative.
C) The x-intercept is 8.
D) The line does not pass through quadrant III.

Answers

Answer:

Step-by-step explanation:

put equation in slope-intercept formula (y=mx+b)

8x-2y=24

-8x -8x

-2y=-8x+24

divide each side by -2

y=4x-12

the "b" in the formula is the y-intercept which is -12, therefore B is correct

Reagan went to the playground. She played on the swings for 24 minutes and went on the slide for 13 minutes. It was 4:28 P.M. when Reagan left the playground. What time was it when Reagan arrived at the playground?

Answers

Answer:

If she played on the swings for 24 minutes and on the slide for 13, then she was at the playground for 37 minutes.

If she left the playground at 4:28, then you want to subtract 37 minutes from 4:28.

4:28 - :37 = 3:51.

She arrived at the playground at 3:51

Step-by-step explanation:

Hope it helps! =D

Answer:

3:51 p.m.

Step-by-step explanation:

Add the two amounts of time:

24 minutes + 13 minutes = 37 minutes

She was at the park for 37 minutes. She arrived at the park 37 minutes before 4:28 p.m.

Now we subtract 37 minutes from 4:28 p.m.

Remember that 1 hour = 60 minutes, so when you borrow 1 hour to do the subtraction, you add 60 minutes to the minutes of the time of day.

Borrow 1 hour from 4 hours as 60 minutes. You end up with 3 hours. Then add the 60 minutes to the 28 minutes to get 88 minutes.

4:28 p.m. is the same as 3:88 p.m.

4:28 p.m. 3:88 p.m.

- 0:37 -----> - 0:37

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

3:51 p.m.

Answer: 3:51 p.m.

Lupe wrote two different fractions with the same denominator. both fractions were less than 1. can their sum equal? can their sum be greater than 1?

Answers

Answer: it depends on the number you took

Step-by-step explanation:

solve the equation a^2x^2 = abx + 2b^2 using completing the square method

Answers

The solution to the equation is

x = b/a ± √(b^2/a^2) / a.

What is the equation?

Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:

a²x² = abx + 2b²

Which is

a²x² - abx - 2b² = 0

Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.

We need to find the square of half of the coefficient of the x term, which is -ab/2a.

So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:

a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0

This gives us the left side of the equation as

(ax - b/a)² = b²/a².

We can then take the square root of both sides:

ax - b/a = ±√(b²/a²)

Finally, we can add b/a to both sides to get the solution:

x = b/a ± √(b²/a²) / a

Answers

Answer: B strange and harrowing story.

Step-by-step explanation: Based on the description of the stranger's face in the novel, it is likely that the captain would expect the stranger to tell a strange and harrowing story. The stranger's face is described as "wild" and "ghastly," which suggests that the story he is about to tell may be disturbing or unsettling in some way. The captain may also expect the story to be emotionally intense, given the stranger's appearance and demeanor.

Given U(-6, 7), V (1, -7), W (6, 4), and X (10, y). Find y such that
UV LWX.

Answers

To find the value of y such that the quadrilateral UVLWX is a parallelogram, we need to find the coordinates of the fourth vertex (X) such that the opposite sides of the quadrilateral are parallel.

The coordinates of U and V are (-6,7) and (1,-7), respectively. The vector UV connecting these two points is given by (1-(-6), -7-7) = (7, -14).

The coordinates of W and X are (6,4) and (10,y), respectively. The vector WX connecting these two points is given by (10-6, y-4) = (4, y-4).

For the sides UV and WX to be parallel, the vector UV must be proportional to the vector WX. This means that the ratio of the x-components must be equal to the ratio of the y-components. In other words, we have the following equation:

(7/4) = (-14)/(y-4)

Solving for y, we get:

y = -7

Therefore, the value of y such that the quadrilateral UVLWX is a parallelogram is y = -7.

Which of the following characteristics are true of all parallelograms? Select all that apply

Answers

Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram.

Parallel sides with two opposed pair?Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.

The complete question is,

Which of the following attributes of a parallelogram leads to the conclusion that every square can be categorized as a parallelogram? Choose each option that applies.

four equal sides

two pairs of diametrically opposed equal angles

diagonals are cut in half.

two sets of parallel, opposed sides.

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The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms. About 21,000 cubic feet of road salt is used during a typical snow storm.

a. What is the total volume of the storage shed?
b. How many snow storms can the town expect to handle before the storage shed needs to be refilled with additional road salt?

Answers

The volume of the storage shed is 125600 ft³.

The storage shed will be refilled after using 125600 ft³ of salt.

How to find the volume of the storage shed?

The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms.

The volume of the storage shed can be found as follows;

volume of a cylinder = πr²h

where

r = radiush = height

Therefore,

r = 40 / 2 =20 ft

h = 100 ft

volume of the storage shed = 3.14 × 20² × 100

volume of the storage shed = 3.14 × 400 × 100

volume of the storage shed = 125600 ft³

Therefore, the storage shed can handle 125600 ft³ of salt before it needs to be refilled.

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Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes. At this rate, how long would it take to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches?

Answers

Answer:

Step-by-step explanation:

To figure out how long it would take Fine Floors to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches, we first need to determine how many square yards of carpeting are needed for the room. We can start by converting the dimensions of the room from feet and inches to yards, since that's the unit of measurement we're working with.

To convert feet to yards, we divide by 3. For example, 11 feet is equal to 11/3 = 3.67 yards. To convert inches to yards, we divide by 36 (since there are 36 inches in a yard). For example, 9 inches is equal to 9/36 = 0.25 yards.

So the length of the room in yards is 3.67 + 0.25 = 3.92 yards, and the width of the room in yards is 13/3 + 4/36 = 4.33 + 0.11 = 4.44 yards.

To determine the total area of the room in square yards, we multiply the length and width: 3.92 * 4.44 = 17.38 square yards.

Now that we know how many square yards of carpeting are needed for the room, we can use that information to calculate how long it would take Fine Floors to install the carpeting. Since we know that Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes, we can use that as the ratio for our calculation.

To calculate how long it will take to install 17.38 square yards of carpeting, we use the proportion:

(15 sq. yards) / (4 hours 30 minutes) = (17.38 sq. yards) / (x hours)

Cross multiplying and solving for x, we find: x = (4 hours 30 minutes) * (17.38 sq. yards) / (15 sq. yards)

So it would take Fine Floors approximately 5 hours and 11 minutes to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches.

If a new video game costs the store $25 and they sell it for 37.50, what was the percent markup?

Answers

The percent markup of the supplied statement is equal to 50% after the problem is solved.

How much of a markup should I use?

There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.

Exactly how is markup determined?

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

According to the given information:

Cost price of game=$25

Selling price of game=$37.50

Profit = selling price - cost price

Profit = 37.50 - 25

Profit / markup percentage = (profit /cost price ) * 100

= (12.50/25) * 100

= 50%

The percent markup of the supplied statement is equal to 50% after the problem is solved.

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is 11^2 x 5^4 a factor of 11^3 x 5^4

Answers

No, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

To see this, you can divide 11^3 x 5^4 by 11^2 x 5^4 and see that there is a remainder.

11^3 x 5^4 = (11 x 11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

11^2 x 5^4 = (11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

75125 / 75125 = 1 with a remainder of 0.

Therefore, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?

Answers

Jayden tosses it 57 times!

-50 POINTS- Already asked 3 times someone help pls. Don’t guess either.

Answers

Answer:

To find the coordinates of the point on the x-axis that is reflected over the x-axis from the point P, you can use the formula (x, -y). In this case, the x-coordinate of point P is 4, so the x-coordinate of the reflected point will also be 4. The y-coordinate of point P is 7, so the y-coordinate of the reflected point will be -7. Therefore, the coordinates of the reflected point are (4, -7).

A pizza shop sold 18 medium pizzas. The number of large pizzas sold was 3 times as many as the number of medium pizzas sold. How many pizzas did the pizza shop sell altogether?

Answers

Answer:

18 × 3 = 54

18 + 54 = 72

Therefore, the answer is 72.

18x3 +18 = 54+ 18 = 72. 72 pizzas were sold

How many triangles can be formed with the angle measures: 20, 100, and 60 degrees?

Answers

There are infinite many triangles that can be formed with the angle measures 20, 100, and 60 degrees

How to determine the number of triangles

From the question, we have the following parameters that can be used in our computation:

Angles = 20, 100, and 60 degrees

The above parameters are angles

When only angles are given, the triangle can have as many side lengths as possible

This means that there are infinite many triangles

Answers

Let x be the number of ounces of Solution A that the scientist uses, and let y be the number of ounces of Solution B that she uses. We can set up the following system of equations to represent the given information:

0.65x + 0.90y = 140 * 0.80 = 112
x + y = 140

To solve this system of equations, we can first multiply the second equation by -1 and add the resulting equations:

-1 * (x + y = 140)
-x - y = -140

0.65x + 0.90y = 112
-x - y = -140

-0.35x - 0.10y = -28

Next, we can divide both sides of the second equation by -0.1 to get rid of the fractional coefficient:

-0.35x - 0.10y = -28
(-0.1/-0.1) * (-0.35x - 0.10y) = (-0.1/-0.1) * -28
-3.5x - y = -28

Finally, we can add the resulting equations to eliminate one of the variables:

-3.5x - y = -28
0.65x + 0.90y = 112

0.35x + 0.90y = 84

Dividing both sides by 0.35, we find that x = 240.

Substituting this value back into the equation x + y = 140, we find that y = -100. Since y represents the number of ounces of Solution B, this is not a valid solution. This means that there is no solution to the system of equations, and the scientist cannot obtain a mixture that is exactly 80% salt using these two solutions.

List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)

Answers

Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.

n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.

What is span in vector space?

In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.

The vectors that are in the same span should be a multiple of the vectors

V₁ = (8 2 7 ), V₂ = (-6 4 0 )

Now, V₁ + V₂ = (2 6 7).

So, The five vectors in the span of V₁ and V₂ is,

2×(2 6 7).

= (4 12 14).

- 2×(2 6 7).

= (- 4 - 12 - 14).

3×(2 6 7).

= (6 18 21)

- 3×(2 6 7)

= (- 6 - 18 - 21).

5×(2 6 7).

= (10 30 35).

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need some help with this

Answers

The length of the missing side is 54.

What is Triangle?

Triangle is a closed polygon consisting of three sides, three vertices and three angles.

Similar triangles are those triangle for which the ratio of corresponding sides is same without affecting the shape.

Given that ΔABC and ΔPQR are similar.

Let x be the side length of PR.

Ratio of their side lengths are equal.

AB : PQ = BC : QR = AC : PR

5 : 45 = 8 : 72 = 6 : x

Take the ratios 8 : 72 = 6 : x

⇒ 8 / 72 = 6 / x

Cross multiplying,

⇒ 8x = 72 × 6

⇒ 8x = 432

⇒ x = 432 / 8 = 54

Hence the side length missing is 54 units.

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-2 3/4, -1 3/4, -3/5 < o > -2 3/4, -3/5, -1 3/4 cual es menor?

Answers

Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.

What is fraction?

An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.

Here,

Given:

2 [tex]\frac{3}{4}[/tex], -1 [tex]\frac{3}{4}[/tex], 3/5 , -2 [tex]\frac{3}{4}[/tex], -3/5, -1 , [tex]\frac{3}{4}[/tex],

Therefore , by seeing the above given numbers ,

We compare above number

and we get to know ,

The 5th number 3/5, comes out to be smallest number from the following given numbers.

Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.

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A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line. Please Help Best helped will get brainiest Promise PLS HELP !!!!!!!!!!!!!!!!!!!

Answers

Answer:

y - 1 = 3/2 (x + 10)

Step-by-step explanation:

Point-slope form of the equation of a line is a fill-in-the-blank shortcut to write an equation. If you know a point and the slope of a line you can fill in that info and voila! you have the equation.

Here is Point-slope equation:

y - Y = m(x - X)

Because the point given (-10,1) is in the form (X,Y), fill in -10 for X and 1 for Y.

The slope given is 3/2, fill that in for m.

y - Y = m(x - X)

y - 1 = 3/2 (x - -10)

y - 1 = 3/2 (x + 10)

The equation is

y - 1 = 3/2 (x + 10)

Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.

Answers

the is answer is probably c

the answer makes sense

A(n)___ is a convex in which both pairs of opposite side are parallel

Answers

4th option: parallelogram

gretchen buys a sweater at a clearance sale for $35.74. The original price of the sweater was $59.99. Find the percent discount.

Answers

Answer:

59.5765%

Step-by-step explanation:

$35.74/$59.99

Find the value of each variable for each circle. Show your work

Answers

The values of the variables in the circles are

Circle 1: a = 34 degreesCircle 2: a = 58 degrees, b = 90 degrees and c = 61 degrees

How to determine the values of the variables in the circles?

From the question, we have the following parameters that can be used in our computation:

Circles and missing angles (see attachment for the figures)

Circle 1

To determine the unknown variable (a), we make use of the following theorem

The angle subtended by an arc at the circumference is twice the angle subtended at the circumference

Mathematically, this means that

a = 2 * 17 degrees

Evaluate the product

a = 34 degrees

Circle 2

To determine the unknown variable (a), we make use of the following theorem

The angle at the circumference in a semicircle is 90 degrees.

Mathematically, this means that

b = 90 degrees

Also, we have

a + 122 degrees = 180 degrees

Evaluate

a = 58 degrees

Using the theorem in (a), we have

b + a/2 + c = 180

This gives

90 + 58/2 + c = 180

Evaluate the like terms

c = 61 degrees

Hence, the angle c is 61 degrees

Answers

-5+2 -3 3
——- = — = - — // hope this helps!
-1+3 2 2

Sevati's collection has 14 fewer magazines in it than Alita's collection. They have 50 magazines
collection? How many magazines are in Alita's collection?
Select the person with more magazines: Alita
Select a label for each bar. Drag the bar representing Sevati's magazines to the right to draw a model that represents the scenario.
Enter expressions to complete the model.
Alita's
magazines
Sevati's
magazines.
x-14
14
X
Enter the expression that represents the number of magazines in Alita's collection.
Enter the expression that represents the number of magazines in Sevati's collection. x-14
Enter an expression for the number of magazines they have together.
Enter the number of magazines in Sevati's collection.
How
-50
50

Answers

Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.

what is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Let's examine the writing of expressions. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

given

If x is the alita collection,

then sevati is equal to x - 14 + x = 50.

Sevati's collection of magazines is represented by the formula 2x - 14 = 50, hence the alita collection is equal to 2x = 36

x = 18

Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.

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Rewrite the function f(x)=-4(x-4)^2+26 in the form f(x)=ax^2+bx+c

Answers

Answer: -4x^2 + 32x - 38

Step 1.
(x-4) ^2 = x^2 - 8x+ 16

Step 2.
(-4) x^2 - 8x+ 16

-4(x^2-8x+16) = -4x^2 + 32x - 64

Step 3.
-4x^2 + 32x - 64 + 26 = -4x^2 + 32x - 38

Summary
Suppose a quadratic expression in standard form has a value of c = 0. Can this quadratic expression be
factored? How do you know?

Answers

Answer:

yesx is a factor

Step-by-step explanation:

You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.

C = 0

When the constant is zero, the equation becomes ...

ax² +bx = 0

Factoring out x, we have a factored form as ...

x(ax +b) = 0

showing that the equation can always be factored.

Suppose a young couple deposits $1000 at the end of each quarter in an account that earns 7.6%, compounded quarterly, for a period of 8 years. After the 8 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, how much will they have in the account (to help with their child’s college expenses)?

Answers

If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.

How the future value is computed?

The future value for this investment is computed in two separate solutions.

We have used an online finance calculator to facilitate the process.

The future value denotes the present deposits compounded at an interest rate.

Initial Deposits:

N (# of periods) = 32 quarters (8 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $0

PMT (Periodic Deposit) = $1,000

Results:

FV = $43,489.87

Sum of all periodic payments = $32,000.00

Total Interest = $11,489.87

Subsequent Deposits:

N (# of periods) = 76 quarters (19 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $43,489.87

PMT (Periodic Payment) = $200

Results:

Future Value (FV) = $215,293.42

Sum of all periodic payments = $15,200 ($200 x 76 quarters)

Total Interest = $156,603.55

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40= x²-y²
21= xy
find x and y

Answers

On solving the provided question, we can say that - the equation, 21 = xy; 40 = [tex]x^2-y^2[/tex] x= 2 and y = 2

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

21 = xy;

40 = [tex]x^2-y^2[/tex]

x= 2

and

y = 2

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