The price of a math book is $50 but you only have $35 with you. If you get a discount of 20% how much money do you need to borrow from a friend so that you can but the book?

Answer:

the answer is 715

Step-by-step explanation:

Answer:

715

Step-by-step explanation:

5*100

5*40

5*3

then add all together

Make sure to use order of operations

➷ 40 + 25 = 65

75 - 65 = 10

The correct answer would be B. $10

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Answer:

No, because the median test score decreased 5 points.

Step-by-step explanation:

The middle line is is the median so, if the pre-test is 60 and the post-test is 55 then there is a 5 point difference.

The difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To subtract the two rational expressions [tex]\( \frac{5x}{x^2-x-6} \) and \( \frac{4}{x^2+4x+4} \)[/tex], we need to find a common denominator.

First, factor the denominators:

1. x²-x-6 = (x-3)(x+2)

2. x²+4x+4 = (x+2)²

The common denominator will be (x-3)(x+2)(x+2).

Now, rewrite the expressions with the common denominator:

1. [tex]\( \frac{5x}{(x-3)(x+2)} \)[/tex]

2. [tex]\( \frac{4}{(x+2)^2} \)[/tex]

To subtract, the numerators remain the same, so the expression becomes:

[tex]\[ \frac{5x}{(x-3)(x+2)} - \frac{4}{(x+2)^2} \][/tex]

To combine the fractions, we need to rewrite the first fraction with the common denominator:

[tex]\[ \frac{5x(x+2)}{(x-3)(x+2)(x+2)} - \frac{4(x-3)}{(x-3)(x+2)(x+2)} \][/tex]

Now, we can subtract the fractions:

[tex]\[ \frac{5x(x+2) - 4(x-3)}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 10x - 4x + 12}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \][/tex]

So, the difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To find the difference between the two rational expressions, we first need to factorize the denominators and simplify where possible. Let's break it down step by step:

1. Factorize the denominators:

[tex]\(x^2 - x - 6 = (x - 3)(x + 2)\) \(x^2 + 4x + 4 = (x + 2)^2\)[/tex]

2. We rewrite the expressions with common denominators:

  [tex]\(\frac{5x}{(x - 3)(x + 2)} - \frac{4}{(x + 2)^2}\)[/tex]

3.  To simplify these, we need a common denominator, The least common denominator is [tex]\((x - 3)(x + 2)^2\).[/tex], so to get it, we multiply (x + 2) with Expression 1 and  (x - 3) with Expression 2 on both numerator and denominator. We get:

  [tex]\(\frac{5x(x + 2)}{(x - 3)(x + 2)^2} - \frac{4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

4. We combine the fractions:

[tex]\(\frac{5x(x + 2) - 4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

  [tex]\(= \frac{5x^2 + 10x - 4x + 12}{(x - 3)(x + 2)^2}\) \(= \frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\)[/tex]

So, the difference between the two rational expressions is [tex]\(\frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\).[/tex]

Answer:

6

Step-by-step explanation:

Given equation is [tex]f(x)= x(x+1)^2 (2x-3)(x+2)^2[/tex].

Now we need to find about what is the degree of the give function.

We know that degree of polynomial function is the highest exponent of the variable (x).

So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.

Second choice will be easier.

Degree of [tex]x[/tex] = 1

Degree of [tex](x+1)^2[/tex] = 2

Degree of [tex](2x-3)[/tex] = 1

Degree of [tex](x+2)^2[/tex] = 2

Hence degree of the given polynomial function = 1+2+1+2=6

D. Shifted 4 units left and 2 units down

The answer to your problem is d.

Answer:

86.7

Step-by-step explanation:

2 x 10.2 x 4.25 = 86.7

To find the volume you need to multiply all these 3 values.

After multiplying it all that amount will be the answer.

The volume of the given dimensions is [tex]\(86.7\)[/tex] cubic units.

To find the volume, we multiply the three given dimensions together. The dimensions given are [tex]\(2\)[/tex], [tex]\(10 \frac{1}{5}\)[/tex], and [tex]\(4 \frac{1}{4}\)[/tex].

First, we need to convert the mixed numbers to improper fractions:

1. Convert [tex]\(10 \frac{1}{5}\)[/tex] to an improper fraction:

[tex]\[ 10 \frac{1}{5} = 10 + \frac{1}{5} = \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \][/tex]

2. Convert [tex]\(4 \frac{1}{4}\)[/tex] to an improper fraction:

[tex]\[ 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4} \][/tex]

Next, multiply the three dimensions together.

First, convert the whole number [tex]\(2\)[/tex] to a fraction:

[tex]\[ 2 = \frac{2}{1} \][/tex]

Now, multiply the fractions:

[tex]\[ \frac{2}{1} \times \frac{51}{5} \times \frac{17}{4} \][/tex]

[tex]\[ \frac{2 \times 51}{1 \times 5} = \frac{102}{5} \][/tex]

[tex]\[ \frac{102 \times 17}{5 \times 4} = \frac{1734}{20} \][/tex]

[tex]\[ \frac{1734}{20} = 86.7 \][/tex]

Answer :

D

Solution :

14ft + 17ft = 30ft

31ft = 30ft

Answer:

(x-3)²

Step-by-step explanation:

x²-6x+9

x² can be written as (x)²

9 can be written as 3²

(x)²-6x +(3)

we can break 6x as 2(3)(x)

by using square formula

(a+b)²= a²-2ab+b²

Putting all the values back in expression we get

(x)²-2(3)(x)+(3)²

by closing formula we get

(x-3)²

Answer:

(x-3)2

Step-by-step explanation:

i took the test

Answer:

9m

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2  where s is the side length

We know the surface area is 486 and the side length is z

486 = 6z^2

Divide each side by 6

486/6 = 6z^2/6

81 = z^2

Take the square root of each side

sqrt(81) = sqrt(z^2)

9 = z

Each side has a length of 9m

Answer:

Step-by-step explanation:

[tex]\dfrac{5^{11}}{5^x}=5^4\qquad\text{multiply both sides by}\ 5^x\\\\5^{11}=5^4\cdot5^x\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\5^{11}=5^{4+x}\iff11=4+x\qquad\text{subtract 4 from both sides}\\\\11-4=4-4+x\\\\7=x\to x=7[/tex]

Answer:

26 is the answer

Step-by-step explanation:

Your answer is D. 2 seconds because her distance from the floor is consistent. Every push-up is 2 seconds apart, therefore it’s D.

well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.

B)

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x[/tex]

A)

Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.

Final answer:

Dorian's claim is incorrect because dividing 10,200 votes by 30% (or 0.30) gives 34,000 votes, which is the correct total number of votes cast in the mayoral election. Therefore, the calculation shows that the total votes are much higher than Dorian's claim of 3,060 votes.

Explanation:

A. Dorian's claim that the total number of votes cast in the mayoral election was 3,060 is not reasonable because if the losing candidate received 10,200 votes which represented 30%, then the total votes should be much higher than 3,060. To find the total, you would divide the number of votes the candidate received by the percentage they represent.

B. To find the total number of votes cast in the mayoral election, you would set up the equation 10,200 = 0.30 * Total Votes. Dividing 10,200 by 0.30 gives the total number of votes cast, which is 34,000.

Equation: Total Votes = 10,200 votes / 0.30 = 34,000 votes

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 20) and (7, 22). Substitute:

[tex]m=\dfrac{22-20}{7-5}=\dfrac{2}{2}=1[/tex]

[tex]y-20=1(x-5)[/tex]

[tex]y-20=x-5[/tex]         add 20 to both sides

[tex]y=x+15[/tex]

[tex]7x - (2x)2 + {x}^{3} [/tex]

[tex]7x - 4x + {x}^{3} [/tex]

[tex]3x + {x}^{3} [/tex]

[tex]3( - 2) + { (- 2)}^{3} [/tex]

[tex] - 6 + - 8[/tex]

[tex] - 14[/tex]

Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

The equation x + y = 10 represents a linear relationship that spans all real numbers in both x and y directions. Thus, the domain and the range for this function are both all real numbers.

The equation for the set F is x + y = 10, which is a straight line on a graph. This line extends infinitely in both directions, meaning that there is no restriction on the possible values of x (the domain) and y (the range). Therefore, the correct answer for both domain and range would be 'All Real Numbers'.

To visualize this, imagine you plug in any number for x and solve the equation for y. Similarly, you can do the same, guessing a y-value and solving for x. No matter the number chosen, there will always be a corresponding number on the other side, whether positive, negative, or zero.

Remember that a domain is the set of all inputs (or 'x' values) that a function can accept, and a range is the set of all possible outputs (or 'y' values) that the function can produce. In this example, the function can handle and generate all real numbers, so its domain and range are all real numbers.

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I hope this helps.

-8y+7x

Answer:

[tex]7x-8y[/tex]

Step-by-step explanation:

We have been given an expression [tex](-3y-x)-(5y-8x)[/tex]. We are supposed to simplify our given expression.

Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:

[tex]-3y-x-1*5y-1*-8x[/tex]

[tex]-3y-x-5y+8x[/tex]

Now, let us combine like terms.

[tex]-x+8x-5y-3y[/tex]

[tex]7x-8y[/tex]

Therefore, the simplified form of our given expression would be [tex]7x-8y[/tex].

Answer:

Broke paints [tex]216\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the outsides of the square walls and triangular ceilings of her tree house is equal to the area of four squares and four triangles

so

[tex]A=4[(6)^{2} +\frac{1}{2}(6)(6)]\\ \\A=4[36+18]\\ \\A=216\ ft^{2}[/tex]

The surface area of the square walls and triangular ceiling she painted is 216 ft²

The surface area of the painted region can be found as follows:

area of the square = l²

where

Therefore,

l = 6 ft

area of the square = 6² = 36 ft²

Area of the triangular region = 1 / 2 bh

where

Therefore,

area of the triangular region = 1 /  2 × 6 × 6 = 36 / 2  = 18 ft²

Therefore,

area of the painted region = 18(4) + 36(4) = 144 + 72 = 216 ft²

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[tex]f(x)=\sqrt{x}[/tex] is the Square Root Function. These are the characteristics of the graph of the square root function:

Since the function [tex]g(x)=\sqrt{x}-2[/tex], then this stands for the form:

[tex]g(x)=f(x)-c[/tex]. This form tells us that the graph of f has been shifted c units downward where the value c = 2 in this problem. The graphs of both functions are shown below. The red one is [tex]f(x)[/tex] while the blue one is [tex]g(x)[/tex]

Answer:

Step-by-step explanation:

The parent function is

[tex]f(x)=\sqrt{x}[/tex]

Remember that a parent function is the simplest function of its type, like this case the function [tex]f(x)[/tex] is the simplest form of radical functions.

The transformed function is

[tex]g(x)=\sqrt{x}-2[/tex]

Notice that the difference between these two functions is that [tex]g(x)[/tex] has 2 units less on the vertical or dependent variable, such transformation indicates a vertical translation downwards.

Therefore, the transfomation made is a vertical translation 2 units downwards.

Answer:

$35.97

Step-by-step explanation:

the regular price is 59.95

40% discount so

let's say the price now is x and i am gonna do fractions

x/59.95 = 40%/100

100 x X = 100x  

59.95 x 40 = 2398

i divide 2398 by 100 which equal 23.98

40% is 23.98 and then i do 59.95 - 23.96 = 35.97

DONE!

The discount amount on the watch is $23.98 and the sale price after applying the 40% discount off the regular price of $59.95 is $35.97.

When a jewelry store is having a going-out-of-business sale, and all merchandise is marked 40% off the regular price, we can calculate the amount of the discount and the sale price using percentage formulas. For example, if a watch has a regular price of $59.95, we multiply this price by 40% (or 0.40) to find the discount amount.
To find the discount amount: $59.95 times 0.40 = $23.98

Next, to find the sale price, we subtract the discount amount from the regular price.
To find the sale price: $59.95 - $23.98 = $35.97

Therefore, the discount amount is $23.98, and the sale price of the watch is $35.97.

Answer:

Answer: 572

Step-by-step explanation:

Answer:

Do you mean like a "degree" of a circle?

Step-by-step explanation:

Answer:

Are you talking about the degrees of a circle?

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

It is the famous Pythagorean theorem which is this equation:

a^2 + b^2 = c^2,

where a and b are the legs and c is the hypotenuse.

Answer:

Pythagorean theorem

Step-by-step explanation:

Answer:

Answer:

y=−4x is a direct variation with the constant of variation +(−4)

Any equation in (or modifiable into) the form y = a . x

is a direct variation with constant a

Step-by-step explanation:

Answer:

-61

Step-by-step explanation:

-42-34=-76= -61

Unfilled circle on 3, filled circle on 0, line connecting the circles.

•—————o

0 3

The values of x that have the absolute value less than 3 are plotted in the figure attached.

The number line should be represented in the straight line that have the zero point in the middle, having the positive and negative numbers that should be listed on the other side.

Given that to plot all values of x that have the absolute value less than 3,

It can be written as |x| ≤ 3

We can say that,

The values of x that have the absolute value greater than 3 are -3 and 3. It should be located into the equal intervals.

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Answer:

y = 4(2^x)

Step-by-step explanation:

To write the exponential values, compare the y values. Notice they are multiples of 8 and they are increasing. This means the base is likely 2 or 4 since each of these numbers has the same multiples. Our options also only include base 2 and 4.

Try 4^1 = 4 and 4^4 = 256.

Try 2^1 = 2 and 2^4 = 16.

None of these give the exact values in the points. This means there is an initial value multiplied to them as well.

When x = 1 and the base is 4, the value is too small. But when x = 4, the value is too large. This cannot be reconciled.

When x = 1 and x = 4 for the base 2, both values are too small and could be multiplied by the same number to get the right values.

2*4 = 8

16*4 = 64

The initial value is 4 so the function is [tex]y = 4(2^x)[/tex]