c = 1/2 ab^2
Solve for b

The old/Original value of the book before 30% increase in price  is $70

Let us assume the old price of book before30% increase be x

Then the new price of the book after 30% increase would be x+ 30% of x

Which can be simplified as x+ 0.30x

Which further can be simplified 1.30x

As we are provided with the new price of book, we have to equate the above linear equation with the new price of the book

1.30x = $91

To solve the equation we need to move 1.30 from left hand side to right hand side which would change from  to

X= 91/1.30

X=$70

Hence the old value of the book before 30% increase in price   is $70

Correct question is if  30% increase in price of a book and the new price of a book is $91.00. What was the original price of the book?

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Answer:

Not complete, please recheck the question

Answer:

55%

Step-by-step explanation:

She has ridden 22 out of 40 miles

22/40 is 0.55

0.55 = 55%

She has eight more miles or 45% left to go.

Answer:

It is C.

Step-by-step explanation:

Since 10 is to the power of negative five the number would be smaller than it was originally.

Based on the start-up expenses to the sole proprietorship, the amortization amount reported as an "other expense" on Schedule C (Form 1040) for the first year of business will be $111.

Before the amortization amount can be calculated, a deduction of $5,000 should be made because the start-up costs were less than $50,000.

The amount to be amortized is therefore:

= 7,500 - 5,000

= $2,500

The amount to be amortized will be amortized over 15 years. As the business started on May 1, 2021, there are only 8 months left in the year.

The amortization amount is:

= (2,500 x 8 months) / ( 15 x 12 months a year)

= $111

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Hello, :)

Points are (-3,0) , (-2,2), (0,1) and (1,2)

f(0)=1

Answer: $563.2

Step-by-step explanation:

h=hours. T=total money earned in a week. o=overtime pay

o=12.8/2

o=6.4

T=12.8(40)+6.4(h-40)

T=512+6.4h-256

T=512-256+6.4h

T=6.4h+256

T=6.4(48)+256

T=307.2+256

T=$563.2

The vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

The function is given as:

y = -2/3|x - 1|

The above function is an absolute value function

An absolute value function is represented as:

y = a|x - h| + k

Where the vertex is

Vertex = (h, k)

By comparing y = a|x - h| + k and y = -2/3|x - 1|, we have

(h, k) = (1, 0) --- vertex

a = -2/3

Because a = -2/3 is negative, then the vertex is a maximum

Hence, the vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

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Answer:

18

Step-by-step explanation:

bc it is asking for the absolute value

Answer:

8.6

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]

Define the points:

Substitute the defined points into the formula:

[tex]\implies d=\sqrt{(7-0)^2+(5-0)^2}[/tex]

[tex]\implies d=\sqrt{7^2+5^2}[/tex]

[tex]\implies d=\sqrt{49+25}[/tex]

[tex]\implies d=\sqrt{74}[/tex]

[tex]\implies d=8.6\;\;\sf (nearest\: tenth)[/tex]

Therefore, the length of one of the diagonals of the rectangle is 8.6.

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

The graph of f(x) = 2x^2 - 4x + 5 is a minimum

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the function is given as

f(x) = 2x^2 - 4x + 5

The above equation is a quadratic equation.

A quadratic equation is represented as:

f(x) = ax^2 + bx + c

By comparison, we have

a = 2

b =-4

c = 5

If the value of a is positive, the graph is a maximum.

Since the value of a is 2, then it means that the graph is a minimum

Hence, the graph of f(x) = 2x^2 - 4x + 5 is a minimum

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Answer:

I'm pretty sure it's 5:4 or 5/4. I think this because there are 5 peaches and four oranges.

According to the solving the relationship between d and r are:

d = 2.5*r

r = d/2.5

The relation in mathematics refers to the relationship between two or more types of values. Assume that x1 and x2 are two ordered pair sets. If set x is related to set y, the values of set x are referred to as domain, whereas the numbers of set y are referred to as range.

A base relation is simply a physical table that is maintained in a database. In contrast, a view is formed from base relations but it doesn't physically exist in the database; it only exists as either a structural definition that pulls data from a number of different base relations.

Given : 5 daises to 2 roses

d ∝ r

where d=daises and r=roses

d = kr

k = d/r

k = 5/2

k = 5.2

So,

d = 2.5 x r...............equation(1).
making r subject in eq (1)

r = d/2.5 ........................equation(2)

According to the solving the relationship between d and r are:

d = 2.5*r

r = d/2.5.

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The responses to the questions involving the solution and equations of a straight line are;

6. The slope is -0.5

7. The equation is; y = x + 4

8. y = 7 - 0.25•x

9. The balance after m months is modeled by the equation;

B = 1,800 - 150•m

10. The slope is the monthly payment on the loan

6. The points on the graph in question 6 are; (0, 4), and (4, 2)

The slope is given by the ratio of the rise to the run of the graph as follows;

[tex]Slope = \frac{2 - 4}{0 - 4} = - 0.5[/tex]

7. The equation in slope and intercept form is found as follows;

The given points are;

(-1, 3), and (-3, 1)

The slope and intercept form is presented as follows;

y = m•x + c

The point and slope form is presented as follows;

y - y1 = m•(x - x1)

Where m is the slope of the graph

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

Which gives;

y - 3 = 1 × (x - (-1)) = x + 1

y = x + 1 + 3 = x + 4

The equation of the graph in slope and intercept form is; y = x + 4

8. The points are; (-4, 8), (4, 6)

Which gives;

m = (6 - 8)/(4 - (-4)) = -2/8 = -0.25

Therefore;

y - 8 = -0.25•(x - (-4)) = -0.25•x - 1

y = -0.25•x - 1 + 8 = -0.25•x + 7

9. The amount Zachary purchased the computer on loan = $1,800

The balance after 3 months = $1,350

The balance after 5 months = $1,050

Therefore;

The points on the graph of the equation that models the balance are therefore;

(0, 1,800), (3, 1,350), (5, 1,050)

Which gives;

B - 1800 = ((1,350-1,800)/(3-0))•(m - 0)

B - 1800 = -150•m

The equation that models the balance, B, after m months is therefore;

10. The slope, ((1,350-1,800)/(3-0)) = -150, signifies the amount by which the balance reduces each month, which is the same as the amount Zachary pays each month, (the monthly payment).

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Answer:

(0,-4)

Step-by-step explanation:

I'm pretty sure it would be (0,-4) though it may be counted wrong. A whole 180° is like if you start from the highest point, you'd be at the lowest point right after the turn. It doesn't really matter the direction with 180° in this case cause it's going to be the same outcome anyways. (Or so I'd think).

Answer: 225 yd³

Step-by-step explanation:

6*4*3=72

3*17*3=153

153+72=225 yd³

Answer:

Step-by-step explanation:

Answer:

first translate triangle FDE down 5 units

second reflect it over the y axis

The image

Step-by-step explanation:

Answer:

Adjective

Those are describing words

The 61% of 407 estimates 248. 27

Percentage can be defined as the ratio of a number to 100

Example;

The percentage of 55 is expressed as;

= 55/ 100

From the information given, we have to determine 61% of 407

This is expressed as;

= 61/ 100 × 407

= 0. 61 × 407

= 248. 27

Thus, the 61% of 407 estimates 248. 27

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The number of heavy equipment operators employed is 26 while number of laborers employed is 6

Let x be the number of heavy equipment operators employed

Thus, If thirty-two people were hired, then we can say that;

32 - x represents the number of laborers employed

Thus, the equation to solve for x would be;

136x + 80(32 - x) = 3960

136x + 2560 - 80x = 3960

216x + 2560 = 3960

216x = 3960 - 2560

216x = 1400

x = 1400/216

x ≅ 6

Thus;

32 - x = 32 - 6 = 26

Thus, we conclude that number of heavy equipment operators employed is 26 while number of laborers employed = 6

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Answer:4

Step-by-step explanation:

7+4=11

15-4=11

Answer:

0 = 3 or No Solution

Step-by-step explanation:

a) Simplify both sides of the equation

−2(y + 1) + 5y = 3(y + 1) − 2

(−2)(y) + (−2)(1) + 5y = (3)(y) + (3)(1) + −2

−2y + −2 + 5y = 3y + 3 + −2

(−2y + 5y) + (−2) = (3y) + (3 + −2)

3y + −2 = 3y + 1

3y −2 = 3y + 1

b) Subtract 3y from both sides

3y − 2 − 3y = 3y + 1 − 3y

−2 = 1

c) Add 2 to both sides

−2 + 2 = 1 + 2

0 = 3 or No Solution

Answer: jus subtract untill u find x

Step-by-step explanation:

whether u do to one side do to the other

Answer:

Step-by-step explanation:

You want the maximum possible number of solutions to the equation

  ||ax -b| +c| = d

The values of 'a' and 'b' represent a vertical scale factor and a horizontal shift, so don't really contribute to the number of possible solutions. That means we can consider only the equation ...

  ||x| +c| = d

Positive c

We know |x| is always positive, and may have the same value for two different values of x. For positive 'c', the outside absolute value function does nothing, so the equation is effectively ...

  |x| = d-c

For d < c, there can be no solutions. For d = c, there will be one solution, and for d > c, there will be two solutions.

Negative c

When 'c' is negative, then sum |x| +c may have either sign. This gives rise to another pair of possible solutions, for a total of four solutions.

The attached graph shows the two cases. The red graph shows the left side expression with c > 0; the purple graph shows the left side expression with c < 0. The orange horizontal line represents a value of 'd'. The number of intersection points with that horizontal line is the number of possible solutions to the given equation.

For c > 0, there are two possible solutions.

For c < 0, there are four possible solutions.

Encontrando un factor comun entre los 3 números dados, concluimos que cada pedazo de tronco debe medir 3 metros, y se obtendran 10 pedazos en total.

Sabemos que los troncos miden 15, 9, y 6 metros, si los queremos cortar en pedazos de igual longitud, de tal forma que nada se desperdicie, entonces debemos encontrar un factor comun entre esos 3 numeros.

Los podemos reescribir como:

15 = 3*5

9 = 3*3

6 = 2*3

Entonces el unico factor comun entre las 3 longitudes es 3.

El tronco de 15 metros dará:

15/3 = 5 pedazos de tronco.

El tronco de 9 metros dará:

9/3 = 3 pedazos de tronco.

El tronco de 6 metros dará:

6/3 = 2 pedazos de tronco.

Sumando eso obtenemos 5 + 3 + 2 = 10 pedazos en total.

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Answer:

  5 trumpet players

Step-by-step explanation:

Given there are 10 fewer trumpet players than saxophone players, and the number of saxophone players is 3 times the number of trumpet players, you want to know the number of trumpet players.

Let t represent the number of trumpet players. Then 3t is the number of saxophone players, and the difference in numbers is ...

  3t -t = 10

Collect terms and divide by the coefficient of t:

  2t = 10

  t = 5

There are 5 trumpet players.

__

Additional comment

Check: There are 3 times as many sax players, so 15 of those. That's 10 more than the number of trumpet players.

You could have written the equation as ...

  t +10 = 3t . . . . . . 10 more than the number of trumpets

Sometimes, when ratios are given:

  t : s = 1 : 3

you can think in terms of "ratio units." Here, the difference is 3-1 = 2 ratio units, corresponding to a difference of 10 players. Then the multiplier of the ratio is 10/2 = 5:

  t : s = 1 : 3 = 5 : 15 . . . . . . 5 trumpets and 15 saxophones.

Answer:

I don't know I think it's b

Answer:

B

Step-by-step explanation:

h(x) is a discrete function, so its domain and range only contain individual points.

h(x) contains the points (-5, -2), (-4, 2), (0, 6), (2, -4), and (4, 4)

Look at the y-coordinates: -2, 2, 6, -4, 4

Arrange them in order: -4, -2, 2, 4, 6 ==> B