At the carpet store where you work, a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size. The carpet ,pad,and installation will cost $17.50 per square yard. To the nearest dollar,how much will it cost to carpet the room?

For this case we have that by definition, the equation of the line in slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have:

[tex](x1, y1): (- 8,11)\\(x2, y2): (4,3.5)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {3.5-11} {4 - (- 8)} = \frac {-7.5} {4 + 8} = \frac {-7.5} {12 } = - \frac {\frac {15} {2}} {12} = - \frac {15} {24} = - \frac {5} {8}[/tex]

Thus, the equation will be given by:

[tex]y = - \frac {5} {8} x + b[/tex]

We substitute a point to find "b":

[tex]11 = - \frac {5} {8} (- 8) + b\\11 = 5 + b\\b = 11-5\\b = 6[/tex]

Finally:

[tex]y = - \frac {5} {8} x + 6[/tex]

Answer:

[tex]y = - \frac {5} {8} x + 6[/tex]

Answer:

So our answers could be any of these depending on the form wanted*:

[tex]y=\frac{-5}{8}x+6[/tex]

[tex]5x+8y=48[/tex]

[tex]y-11=\frac{-5}{8}(x+8)[/tex]

[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]

*There are other ways to write this equation.

Step-by-step explanation:

So we are given two points on a line: (-8,11) and (4,7/2).

We can find the slope by using the formula [tex]\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y+2) \text{ is on the line}[/tex].

So to do this, I'm going to line up my points vertically and then subtract vertically, then put 2nd difference over 1st difference:

( 4  ,  7/2)

-(-8 ,    11)

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

12      -7.5

So the slope is -7.5/12 or -0.625 (If you type -7.5 division sign 12 in your calculator).

-0.625 as a fraction is -5/8 (just use the f<->d button to have your calculator convert your decimal to a fraction).

Anyways the equation of a line in slope-intercept form is y=mx+b where m is the slope and b is y-intercept.

We have m=-5/8 since that is the slope.

So plugging this into y=mx+b gives us y=(-5/8)x+b.

So now we need to find b. Pick one of the points given to you (just one).

Plug it into y=(-5/8)x+b and solve for b.

y=(-5/8)x   +b with (-8,11)

11=(-5/8)(-8)+b

11=5+b

11-5=b

6=b

So the equation of the line in slope-intercept form is y=(-5/8)x+6.

We can also put in standard form which is ax+by=c where a,b,c are integers.

y=(-5/8)x+6

First step: We want to get rid of the fraction by multiplying both sides by 8:

8y=-5x+48

Second step: Add 5x on both sides:

5x+8y=48 (This is standard form.)

Now you can also out the line point-slope form, [tex]y-y_1=m(x-x_1) \text{ where } m \text{ is the slope and } (x_1,y_1) \text{ is a point on the line }[/tex]

So you can say either is correct:

[tex]y-11=\frac{-5}{8}(x-(-8))[/tex]

or after simplifying:

[tex]y-11=\frac{-5}{8}(x+8)[/tex]

Someone might have decided to use the other point; that is fine:

[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]

So our answers could be any of these depending on the form wanted*:

[tex]y=\frac{-5}{8}x+6[/tex]

[tex]5x+8y=48[/tex]

[tex]y-11=\frac{-5}{8}(x+8)[/tex]

[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]

let's use the conjugate of the denominator and multiply top and bottom by it, recall the conjugate of a binomial is simply the same binomial with a different sign in between.

[tex]\bf \cfrac{2\sqrt{x}-3\sqrt{y}}{\sqrt{x}+\sqrt{y}}\cdot \cfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\implies \cfrac{2\sqrt{x}\sqrt{x}-2\sqrt{x}\sqrt{y}~~-~~3\sqrt{x}\sqrt{y}+3\sqrt{y}\sqrt{y}}{\underset{\textit{difference of squares}}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}} \\\\\\ \cfrac{2\sqrt{x^2}-2\sqrt{xy}-3\sqrt{xy}+3\sqrt{y^2}}{(\sqrt{x})^2-(\sqrt{y})^2}\implies \cfrac{2x-5\sqrt{xy}+3y}{x-y}[/tex]

Answer:

[tex]\dfrac{2x-5\sqrt{xy}+3y}{x-y}\\[/tex]

Step-by-step explanation:

In Rationalize the denominator we multiply both numerator and denominator by the conjugate of denominator.

In Conjugate we change the sign of middle operator.

Example: Congugate of (a + b) = a - b

Now Solving the given expression,

[tex]\dfrac{2\sqrt{x} - 3\sqrt{y}}{\sqrt{x} + \sqrt{y}} = \dfrac{2\sqrt{x} - 3\sqrt{y}}{\sqrt{x} + \sqrt{y}}\times \dfrac{\sqrt{x} - \sqrt{y}}{\sqrt{x} - \sqrt{y}}\\\\\Rightarrow \dfrac{(2\sqrt{x} - 3\sqrt{y})(\sqrt{x} - \sqrt{y})}{( \sqrt{x} + \sqrt{y}){(\sqrt{x} - \sqrt{y}})}\ \ \ \ \ \ \ \ \ \ \ [\because (a-b)(a+b)=(a^{2} +b^{2})]\\\Rightarrow \dfrac{2x-2\sqrt{xy}-3\sqrt{xy}+3y}{x-y}\\\\ \Rightarrow \dfrac{2x-5\sqrt{xy}+3y}{x-y}\\[/tex]

Answer:

25

Step-by-step explanation:

Those parallel lines tell us our triangles are similar. So that means the corresponding sides are proportional.

So we have that x corresponds to x+15 and

40 corresponds to 24+40.

So we have this proportion to solve:

[tex]\frac{x}{x+15}=\frac{40}{24+40}[/tex]

Let's simplify what we can:

[tex]\frac{x}{x+15}=\frac{40}{64}[/tex]

Cross multiply:

[tex](64)(x)=(x+15)(40)[/tex]

Multiply/distribute:

[tex]64x=40x+600[/tex]

Subtract 40x on both sides:

[tex]24x=600[/tex]

Divide both sides by 24:

[tex]x=\frac{600}{24}=25[/tex]

x=25

Answer:

x = 25.

Step-by-step explanation:

24/40 = 15/x

x = (40*15) / 24

x = 600/24

= 25.

Answer:

your y-intercept is 0 and slope is 4 so any line with zero slope it will be horizontal

Answer: On mine it is D

Step-by-step explanation:

It is the small one facing up

Answer:

Step-by-step explanation:

p^8 q^6 / p ^4 q^3

In this expression the base of numerator and denominator is same:

We will change the division into multiplication and the denominator will become numerator will negative exponents:

p^8 q^6 * p ^-4 q^-3

Now simplify the terms with same base

The exponents of the same base will be added

=p^8+(-4) q^6+(-3)

=p^8-4 q^6-3

=p^4 q^3

The answer is p^4 q^3....

[tex]\huge{\boxed{5}}[/tex]

The Pythagorean theorum states that when [tex]a[/tex] and [tex]b[/tex] are sides and [tex]c[/tex] is the hypotenuse, [tex]a^2 + b^2 = c^2[/tex]

So, let's plug in the values. [tex]3^2 + b^2 = (\sqrt{34})^2[/tex]

Simplify. The square of a square root is the number inside the square root. [tex]9 + b^2 = 34[/tex]

Subtract 9 from both sides. [tex]b^2 = 25[/tex]

Get the square root of both sides. [tex]\sqrt{b^2} = \sqrt{25}[/tex]

[tex]b=\boxed{5}[/tex]

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=3,\ hypotenuse=\sqrt{34}[/tex]

Let's mark the other leg as x.

Substitute:

[tex]3^2+x^2=(\sqrt{34})^2[/tex]      use (√a)² = a

[tex]9+x^2=34[/tex]            subtract 9 from both sides

[tex]x^2=25\to x=\sqrt{25}\\\\x=5[/tex]

The scale factor of the dilation is:

                           [tex]1\dfrac{1}{2}[/tex]

Scale factor--

It is a fixed amount by which the each  of the dimension of the original figure is multiplied in order to obtain the dilated image of the figure.

Here we see that there is a enlargement dilation.

( since the side of the image increases after the dilation)

Let the scale factor be k.

From the figure we see that:

The side of length 6 units is transformed to get a side of length 9 units.

i.e.

[tex]6\times k=9[/tex]

i.e.

[tex]k=\dfrac{9}{6}\\\\i.e.\\\\k=\dfrac{3}{2}\\\\i.e.\\\\k=1\dfrac{1}{2}[/tex]

Answer:

Exponential decay

Step-by-step explanation:

b = 0.73

Since the b is less than 1 (b<1), the rate is decreasing.

Answer with explanation:

Size of the sample = n =225

Mean[\text] \mu[/text]=48.5

Standard deviation [\text] \sigma[/text]= 1.8

[tex]Z_{90 \text{Percent}}=Z_{0.09}=0.5359\\\\Z_{score}=\frac{\Bar X -\mu}{\frac{\sigma}{\sqrt{\text{Sample size}}}}\\\\0.5359=\frac{\Bar X -48.5}{\frac{1.8}{\sqrt{225}}}\\\\0.5359=15 \times \frac{\Bar X -48.5}{1.8}\\\\0.5359 \times 1.8=15 \times (\Bar X -48.5)\\\\0.97=15 \Bar X-727.5\\\\727.5+0.97=15 \Bar X\\\\728.47=15 \Bar X\\\\ \Bar X=\frac{728.47}{15}\\\\\Bar X=48.57[/tex]

→Given Confidence Interval of Mean =48.8

→Calculated Mean of Sample =48.57 < 48.8

So, the value of Sample mean lies within the confidence interval.

Answer:

sample answer

Step-by-step explanation:

To find the margin of error, multiply the z-score by the standard deviation, then divide by the square root of the sample size.

The z*-score for a 90% confidence level is 1.645.

The margin of error is 0.20.

The confidence interval is 48.3 to 48.7.

48.8 is not within the confidence interval.

Answer:

[tex]xy(1+2y\sqrt{x}+\sqrt{y})[/tex]

Step-by-step explanation:

Given expression,

[tex]\sqrt{x^2y^2}+2\sqrt{x^3y^4}+xy\sqrt{y}[/tex]

[tex]=(x^2y^2)^\frac{1}{2} + 2(x^3y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]

[tex]\because (\sqrt{x}=x^\frac{1}{2})[/tex]

[tex]=(x^2)^\frac{1}{2} (y^2)^\frac{1}{2} + 2(x^3)^\frac{1}{2} (y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]

[tex](\because (ab)^n=a^n b^n)[/tex]

[tex]=x^{2\times \frac{1}{2}} y^{2\times \frac{1}{2}} + 2(x^{3\times \frac{1}{2}})(y^{4\times \frac{1}{2}})+xy\sqrt{y}[/tex]

[tex]\because (a^n)^m=a^{mn}[/tex]

[tex]=x^1 y^1 + 2x^{1\frac{1}{2}} y^2 + xy\sqrt{y}[/tex]

[tex]=xy+2x.(x)^\frac{1}{2} y^2 + xy\sqrt{y}[/tex]

[tex]=xy+2xy^2\sqrt{x}+xy\sqrt{y}[/tex]

[tex]=xy(1+2y\sqrt{x}+\sqrt{y})[/tex]

Answer:

B is the right option

Step-by-step explanation:

On edg :))

Sample Response: First, the like terms had to be combined using the lowest common denominator (LCD). Then the subtraction property of equality was used to isolate the variable term. Finally, both sides of the equation were multiplied by the reciprocal of the coefficient to solve for a.

Answer:

11.8294Step-by-step explanation:

Answer:

Step-by-step explanation:

How many deciliters are equivalent to 5 cups?

2.1097 deciliters

11.85 deciliters

118.5 deciliters

210.97 deciliters

ANSWER IS 11.85

Let see.

Numbers which are bigger than 0 are defined as positive numbers and have a prefix of + (plus).

Numbers which are smaller than 0 are defined as negative numbers and have a prefix of - (minus).

Let say number a is equal to the expression,

[tex]a=3xy[/tex]

Since y is negative we can change its prefix to -,

[tex]a=3x\cdot(-y)[/tex]

Any number (in this case 3x) multiplied by negative number will produce a negative number.

Therefore the sign or prefix of number a will be -.

Hope this helps.

r3t40

When you multiply a positive number and a negative number, the result is a negative number. Therefore, the sign of 3xy, when x > 0 and y < 0, is negative.

The question is asking for the sign of the product of two numbers, x and y, when x is positive (x > 0) and y is negative (y < 0). In mathematics, when you multiply a positive number and a negative number, the result is always a negative number.

So, the product of x and y or 3xy in this case, would be negative. This is due to the principle that the product of different signs (in this case, positive and negative) is always negative.

https://brainly.com/question/34274159

#SPJ3

Answer:

The numbers are

[tex]6+2\sqrt{15}i[/tex]   and  [tex]6-2\sqrt{15}i[/tex]

Step-by-step explanation:

Let

x and y -----> the numbers

we know that

[tex]x+y=12[/tex] -----> [tex]y=12-x[/tex] ------> equation A

[tex]xy=96[/tex] ----> equation B

substitute equation A in equation B and solve for x

[tex]x(12-x)=96\\12x-x^{2}=96\\x^{2} -12x+96=0[/tex]

Solve the quadratic equation

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2} -12x+96=0[/tex]  

so

[tex]a=1\\b=-12\\c=96[/tex]

substitute

[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(1)(96)}} {2(1)}[/tex]

[tex]x=\frac{12(+/-)\sqrt{-240}} {2}[/tex]

Remember that

[tex]i^{2}=\sqrt{-1}[/tex]

[tex]x=\frac{12(+/-)\sqrt{240}i} {2}[/tex]

[tex]x=\frac{12(+/-)4\sqrt{15}i} {2}[/tex]

Simplify

[tex]x=6(+/-)2\sqrt{15}i[/tex]

[tex]x1=6+2\sqrt{15}i[/tex]

[tex]x2=6-2\sqrt{15}i[/tex]

we have two solutions

Find the value of y for the first solution

For [tex]x1=6+2\sqrt{15}i[/tex]

[tex]y=12-x[/tex]

substitute

[tex]y1=12-(6+2\sqrt{15}i)[/tex]

[tex]y1=6-2\sqrt{15}i[/tex]

Find the value of y for the second solution

For [tex]x2=6-2\sqrt{15}i[/tex]

[tex]y2=12-x[/tex]

substitute

[tex]y2=12-(6-2\sqrt{15}i)[/tex]

[tex]y2=6+2\sqrt{15}i[/tex]

therefore

The numbers are

[tex]6+2\sqrt{15}i[/tex]   and  [tex]6-2\sqrt{15}i[/tex]

Answer:

An angle is 90° if and only if it is a right angle.

Explanation:

The statement is: If an angle is 90°, then it is a right angle.  

The converse of this statement would be:

If an angle is a right angle, it is 90°.

Clearly, both the conditional and converse of this statement is true.

The prime polynomial out of the given options is 3x^3 + 3x^2 - 2x - 2.

Out of the given polynomials, the polynomial that is prime is 3x3 + 3x2 - 2x - 2.

A polynomial is considered prime if it cannot be factored into a product of lower degree polynomials with integral coefficients.

In this case, the polynomial 3x3 + 3x2 - 2x - 2 is a cubic polynomial and cannot be factored further, so it is prime.

Answer:

c. Keeping the movie and paying the purchase price and late fees is the cheaper option.  

Step-by-step explanation:

1. If Susan takes a cab and pays late fees

            Cost of cab = $10.00

Late fees = 5 × 1.50 =   7.50

                   TOTAL = $17.50

2. If Susan keeps the movie

Purchase price of movie = $9.99

       Late fees = 5 × 1.50 =   7.50

                           TOTAL = $17.49

Keeping the movie and paying the purchase price and late fees is the cheapest option.

a. is wrong. Taking a cab is the more expensive option.

b. is wrong. Susan contracted to return the movie, so she should try to do so.  

c. is correct. This is a statement of fact, not a judgement call.

d. is wrong. Susan contracted to pay the late fees if she did not return the video (but she should still return it).

Answer:

Choice B: y = 1/2x + 8

Step-by-step explanation:

Given

slope = 1/2

y-intercept = (0,8)

Put in y = mx + b form

slope is indicated by m

y-intercept is indicated by b

y = 1/2x + 8

Answer

y = 1/2x + 8

Answer: B.  [tex]y=\dfrac{1}{2}x+8[/tex]

Step-by-step explanation:

We know that the equation of a line in slope-intercept form is given by :-

[tex]y=mx+c[/tex], where m is the slope of the line and c is the y-intercept of the line.

For the given graph , we have

y-intercept = (0,8)

i.e. c=8

Slope =[tex]\dfrac{1}{2}[/tex]

i.e. m=8

Then, the equation of the given line in slope-intercept form will be :-

[tex]y=\dfrac{1}{2}x+8[/tex]

Answer:

The constant variation, and the price of one ticket is 8.  

Step-by-step explanation:

Answer:

x =27

Step-by-step explanation:

5(x + 1) = 4(x + 8)

Distribute.

5x + 5 = 4x + 32

Move x term onto one side.

x + 5 = 32

Move integer onto one side.

x = 27

Although I am unsure what this question has to do with Mathematics, Joe Bob could simply say "How often do you work out in a week?"

[tex]x^2-y^2=(x-y)(x+y)\\\\x^2-y^2=3\cdot12=36[/tex]

Answer:

-6*F

Step-by-step explanation:

-15+9=-6

Answer:

The answer is 7

Step-by-step explanation:

The expression is 10-(1/2)^4 * 48

Here PEMDAS rule applies:

where,

P= parenthesis

E= exponent

M= multiplication

D= division

A= addition

S= subtraction

So according to this rule first we will solve parenthesis and exponent.(PE)

10-(1/2)^4 *48

(1/2)^4 means, multiply 1/2 four times:

1/2*1/2*1/2*1/2=1/16

Therefore the expression becomes:

10-1/16*48

Now we have MD which is multiplication and division:

1/16*48 = 3

Now after solving the multiplication and division the expression becomes:

10-3.

After subtracting the terms we have:

10-3=7

Thus the answer is 7....

Answer:

-89

Step-by-step explanation:

9x + 4b + 9y +4c + 4a​ (9x+9y)+(4a+4b+4c) =9(x+y)+4(a+b+c)

but :   a+b+c = -2 and x+y = -9

9x + 4b + 9y +4c + 4a​ = 9(-9)+4(-2) = - 81 -8 =-89

Ah, all you have to do is combine 2/5m and 3/5m.

In this case:

=2/5m - 4/5 - 3/5m

=-1/5m - 4/5

=-m/5-4/5

Answer:

[tex]\frac{-1}{5}m-\frac{4}{5}[/tex]

Step-by-step explanation:

You are given:

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

Reorder using commutative property (putting like terms together):

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

Now we are going to bring down the -4/5 (there is nothing to do there).

(2/5)m and -(3/5)m have the same denominator all we have to do is figure out what is 2-3 which is -1

[tex]\frac{-1}{5}m-\frac{4}{5}[/tex]

x>7

Step-by-step explanation:

when dividing by a (-)

the inequality sign changes

Answer:

"The student should have switched the direction of the inequality sign to get –5> x for a final answer."

and the second one is:

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

Step-by-step explanation:

i got that on edge

Answer:

The average rate of change is 1.275

Step-by-step explanation:

The average rate of change of f(x) from x=a to x=b is given by:

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

The money Terry invested is modeled by the function [tex]f(x)=0.01(2)^x[/tex] where x represents number of days.

The average rate of change from day 2 to day 10 is given by:

[tex]\frac{f(10)-f(2)}{10-2}[/tex]

[tex]f(10)=0.01(2)^{10}=10.24[/tex]

[tex]f(2)=0.01(2)^{2}=0.04[/tex]

The average rate of change becomes:

[tex]\frac{10.24-0.04}{8}[/tex]

[tex]=\frac{10.2}{8}=1.275[/tex]

Answer:

The average rate of change is 1.275

[tex]\bf \left( \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 5\cdot 2}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3} \right)^2 \times \left( \cfrac{5^0}{2^{-3}} \right)^3\times 2^{-9}\implies \left( \cfrac{5\cdot 2}{ 3} \right)^2 \times \left( \cfrac{1}{2^{-3}} \right)^3\times 2^{-9}[/tex]

[tex]\bf \left( \cfrac{10}{ 3} \right)^2 \times \left( 2^3 \right)^3\times 2^{-9}\implies \left( \cfrac{10}{ 3} \right)^2 \times 2^9\times 2^{-9}\implies \cfrac{10^2}{3^2}\times 2^{9-9} \\\\\\ \cfrac{100}{9}\times 2^0\implies \cfrac{100}{9}\times 1\implies \cfrac{100}{9}[/tex]