Consider the equation 5 + x = n. What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation.

Answer:

x = -12

Step-by-step explanation:

x - 8 = -20

+8        +8

perpendicular slopes are those that are flipped and opposite signs to the original slope

Answer: 5%

Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.

$2/40 = .05 = 5%

The interest rate is 5%.

Point C must be the center of the circle, since all of the radii connect there.

Answer:

Seven forward, seven opposite. It's like saying a footballer runs from 0 yd line to 50 yd line then turns around and runs 50 yards again, ends up right back at the 0.

Answer:

a

Step-by-step explanation:

got it right on test

Step-by-step explanation:

[tex]n!=\underbrace{1\cdot2\cdot3\cdot...\cdot n}\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\=======================\\_nP_r=\dfrac{n!}{(n-r)!}\\\\_8P_5=\dfrac{8!}{(8-5)!}=\dfrac{8!}{3!}=\dfrac{3!\cdot4\cdot5\cdot6\cdot7\cdot8}{3!}=4\cdot5\cdot6\cdot7\cdot8=6,720\\=======================\\_nC_r=\dfrac{n!}{r!(n-r)!}\\\\_{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{4!\cdot5\cdot6\cdot...\cdot12}{4!\cdot8!}=\dfrac{5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}=495[/tex]

Answer:

6 bags

Step-by-step explanation:

this is super confusing

i don't think so.....

sorry

This answer explains how to determine the volume of an open box created by cutting squares from each corner of a piece of cardboard, discussing the relations between variables, volume calculation, domain restrictions, and a guess-and-check method for maximizing volume.

Variables: In the open box scenario, let's assume the size of the square cut from each corner is 'x'.

Relation to Dimensions: After cutting and folding, the length of the box would be (6ft - 2x), the width would be (6ft - 2x), and the height would be 'x'.

Product for Volume: The volume formula is length x width x height. Substituting the expressions, we get V = x(6 - 2x)(6 - 2x).

Domain: The domain for the volume function would be 0 < x < 3 (as the size of the cut cannot exceed half of the side length).

Guess and Check: To find the maximum volume, you can test values within the domain like x = 1, 1.5, 2, 2.5, and 3 to determine the optimal cut size and corresponding dimensions and volume.

what are we supposed to evaluate, here? i dunno what your asking us to do

Answer:

Step-by-step explanation:

Remarks

They want only the exponential equation, here's the point.

Equation

[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]

What this gives you is the equation for a rise every  500 feet. To figure out the %

Use

[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]

Example

Let h = 1000 feet

101 / (1 + 1.8/100) ^ (1000/500)

101 / (1.018)^2

101 / 1.036324

97.46

Now take this number and use the second formula

% = (101 - 97.46)/101 * 100%

% = 3.54%

The answer should be 3.6% (2 * 1.8%)

This is close enough. The question does say approximately.

1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.

Answer:

[tex]\large\boxed{3x-4y=30}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{2}x-\dfrac{2}{3}y=5\qquad\text{multiply both sides by LCM(2, 3) = 6}\\\\6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x-6\!\!\!\!\diagup^2\cdot\dfrac{2}{3\!\!\!\!\diagup_1}y=6\cdot5\\\\(3)(x)-(2)(2y)=30\\\\3x-4y=30[/tex]

Answer:

The solution in the attached figure

[tex]sin(A)=\frac{12}{13}[/tex]

[tex]sin(B)=\frac{5}{13}[/tex]

[tex]cos(A)=\frac{5}{13}[/tex]

[tex]cos(B)=\frac{12}{13}[/tex]

[tex]sin(A)=cos(B)[/tex]

[tex]sin(B)=cos(A)[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

sin(A)=cos(B) and cos(A)=sin(B)

because

[tex]A+B=90\°[/tex] -------> by complementary angles

step 1

Find sin(A)

The function sine of angle A is equal to divide the opposite side angle A by the hypotenuse

[tex]sin(A)=\frac{BC}{AB}[/tex]

substitute the values

[tex]sin(A)=\frac{12}{13}[/tex]

step 2

Find sin(B)

The function sine of angle B is equal to divide the opposite side angle B by the hypotenuse

[tex]sin(B)=\frac{AC}{AB}[/tex]

substitute the values

[tex]sin(B)=\frac{5}{13}[/tex]

step 3

Find cos(A)

The function cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse

[tex]cos(A)=\frac{AC}{AB}[/tex]

substitute the values

[tex]cos(A)=\frac{5}{13}[/tex]

[tex]cos(A)=sin(B)[/tex]

step 4

Find cos(B)

The function cosine of angle B is equal to divide the adjacent side angle B by the hypotenuse

[tex]cos(B)=\frac{BC}{AB}[/tex]

substitute the values

[tex]cos(B)=\frac{12}{13}[/tex]

[tex]cos(B)=sin(A)[/tex]

Answer:

B.) -1/3

Step-by-step explanation:

According to the rational root theorem, rational roots will be of the form ...

±(divisor of the constant)/(divisor of the leading coefficient)

= ±(one of {1, 2, 3, 4, 6, 12})/(one of {1, 2, 4})

You will note that 3 is not among the possible denominators, hence -1/3 is not a possible rational root.

the answer is b cause its is correct

You would need to multiply the quantity of shrubs bought by the price of each one, so 4p and add that to the price of the soil to get the total cost

The equation becomes 4p + 17.50 = 53.50

Now solve for p:

4p +17.50 = 53.50

Subtract 17.50 from both sides:

4p = 36

Divide both sides by 4:

p = 36/4

p = 9

The answer would be: 4p + $17.50 = $53.50; p = $9.00

Answer:

$87.95

Step-by-step explanation:

1. multiply the stock (92) time 4.4% (or 0.044)

    92*0.044 = 4.048

2. subtract 4.048 from 92

    92-4.048 = 87.952

3. Round to the nearest cent (2 in the thousandth place means the 5 stays the same)

    87.95

Answer:

40 feet

Step-by-step explanation:

The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.

3x - 4 = 3(4) - 4 = 12 - 4 = 8

x² -1 = (4)² - 1 = 16 - 1 = 15

2x² - 15 = 2(4)² - 15 = 32 - 15 = 17

Add the sides together, 8 + 15 + 17 = 40 feet

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

[tex]r=\frac{3}{1-cos(theta)}[/tex]

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at  x = -3. Choice D fits this criteria

Answer:

D

Step-by-step explanation:

edge

The answer is C because you multiply 8×8.95 to get your lowest range, and 8×15.79 to get your highest range.

Since this is subtraction, everything must be turned negative in the second polynomial.

(6x^2 - 5x) - (2x^2 + 3x - 2)

6x^2 - 5x - 2x^2 - 3x - (-2)

6x^2 - 5x - 2x^2 - 3x + 2

Now, reorder the terms to make it easier.

6x^2 - 2x^2 - 5x - 3x + 2

Now, just combine like terms.

4x^2 - 5x - 3x + 2

4x^2 - 8x + 2

There’s the answer!

Please consider marking this answer as Brainliest to help me advance.

Answer:

B

Step-by-step explanation:

Note that the absolute value always returns a positive value, that is

| - 2 | = | 2 | = 2

given

2| u | - | v | with u = - 9 and v = - 2, then

2 | - 9 | - | - 2 |

= 2 × 9 - 2 = 18 - 2 = 16 → B

Answer:

A. [tex]9\sqrt{10}[/tex]

Step-by-step explanation:

The given expression is   [tex]-6\sqrt{10}+5\sqrt{90}[/tex]

Remove the perfect square from the second radical.

[tex]=-6\sqrt{10}+5\sqrt{9\times10}[/tex]

[tex]=-6\sqrt{10}+5\sqrt{9} \times \sqrt{10}[/tex]

This implies

[tex]=-6\sqrt{10}+15\sqrt{10}[/tex]

[tex]=(-6+15)\sqrt{10}[/tex]

[tex]=9\sqrt{10}[/tex]

The correct choice is A

Answer:

[tex]A=2,002.9\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular polygon is equal to

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

where

r is the apothem

P is the perimeter

step 1

Find the perimeter

The perimeter of a regular nonagon is

[tex]P=ns[/tex]

where

n is the number of sides (n=9)

s is the length side (s=18 cm)

substitute

[tex]P=9*18=162\ cm[/tex]

step 2

Find the apothem

The apothem in a regular polygon is equal to

[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]

we have

[tex]s=18\ cm[/tex]

[tex]n=9[/tex]

substitute

[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex]

[tex]r=9cot(20\°)=24.73\ cm[/tex]

step 3

Find the area of the regular nonagon

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

substitute

[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]

Answer:

You will need 7 more pennies.

Step-by-step explanation:

Answer:

7 more pennies.

Step-by-step explanation:

Quarters are .25 each and you have 2 so that is .50.

Dimes are .10 each and you have 12 so that is 1.20

Pennies are .01 each and you have 23 so that is .23.

Added together and you get 1.93. So all you need is 7 pennies to get 2 dollars.

To find the sales tax rate, you need to find what percentage of the base price the difference in cost is.

First, subtract 22.99 from 24.10:

24.1-22.99=1.11

Now, divide 1.11 by 22.99:

1.11/22.99=0.0483

Multiply 0.0483 by 100 to convert the decimal to a percentage:

0.0483*100=4.83

The sales tax rate was 4.83%.

Hope this helps!!

Answer:

1.

Horizontal Asymptote is y = 0

2.

Vertical Asymptote is x = -4

3.

No Slant Asymptote

4.

Hole at (5, 0.14)

5.

x-intercepts:

x-intercept [tex](-\frac{1}{2},0)[/tex]

y-intercepts:

y-intercept  [tex](0,\frac{1}{16})[/tex]

6.

Domain is [tex]{x|x\neq -4,5}[/tex]

Step-by-step explanation:

1. Horizontal Asymptotes

* If the degree of the numerator is less than the degree of the denominator (this is our case since multiplying will give the numerator a degree of 2 and denominator a degree of 3), then y = 0 is the only horizontal asymptote

Horizontal Asymptote is y = 0

2. Vertical Asymptotes

* To get VA (vertical asymptote), we set the denominator equal to zero.

Before doing this, we see that we can cancel out (x-5) from both numerator and denominator so the denominator becomes (x+4)^2. Now we find VA:

[tex](x+4)^2=0\\x+4=0\\x=-4[/tex]

Vertical Asymptote is x = -4

3. Oblique asymptotes

* If the degree of numerator is less than the degree of the denominator (this is our case as explained above), then there is no slant asymptote.

No Slant Asymptote

4. Holes

There is hole in a rational function if there is the same factor in both numerator and denominator (before simplifying, only after factoring). Set that equal to 0 and solve. Then, cross out the common factor and put the x-value into the function and get the y-value of the hole.

We can see that there is a factor of (x-5) in both the numerator and denominator. We set it equal to 0 and solve for x:

[tex]x-5=0\\x=5[/tex]

Putting x = 5, we get:

Y value of hole = [tex]g(x)=\frac{2x+1}{(x+4)^2}\\g(5)=\frac{2(5)+1}{(5+4)^2}\\g(5)=0.14[/tex]

Hole at (5, 0.14)

5. Intercepts

To get x-intercepts, we set y = 0 (g(x) = 0) and for y-intercepts we set x = 0.

x-intercepts:

[tex]0=\frac{2x+1}{(x+4)^2}\\2x+1=0\\2x=-1\\x=-\frac{1}{2}[/tex]

x-intercept [tex](-\frac{1}{2},0)[/tex]

y-intercepts:

[tex]y=\frac{2x+1}{(x+4)^2}\\y=\frac{2(0)+1}{(0+4)^2}\\y=\frac{1}{16}[/tex]

y-intercept  [tex](0,\frac{1}{16})[/tex]

6. Domain

This is the set of allowed x-values of the function. We simply disregard any value that would make the denominator equal to 0.

So we have:

x - 5 = 0, x = 5

and

(x+4)^2 = 0, x = -4

Domain is the set of all real numbers x EXCEPT x = -4 and x = 5

Domain is [tex]{x|x\neq -4,5}[/tex]

Answer:

The answer is (c) ⇒ the value is 6.6667

Step-by-step explanation:

∵ [tex]\lim_{x\to \2} _2\frac{x^{5}-32}{x^{3}-8}[/tex]

∵ 32 = 2^5 , 8 = 2³

∴ [tex]\lim_{x \to \2}_2 \frac{x^{5}-2^{5}}{x^{3}-2^{3} }[/tex]

* by using the rule:

[tex]\lim_{x\to\a}_a \frac{x^{n}-a^{n}}{x^{m}-a^{m}}=\frac{n}{m}(a)^{n-m}[/tex]

∴ [tex]\frac{5}{3}(2)^{5-3}=\frac{5}{3}(2)^{2}=\frac{20}{3}[/tex]

∴ 20/3 = 6.6667 ⇒ answer (c)

Answer:

The correct option is c.

Step-by-step explanation:

The given limit is

[tex]lim_{x\rightarrow 2}\frac{x^5-32}{x^3-8}[/tex]

It is can be written as

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}[/tex]

According to the property of limits,

[tex]lim_{x\rightarrow a}\frac{x^n-a^n}{x^m-a^m}=\frac{n}{m}(a)^{n-m}[/tex]

In the given limit, a=2, n=5 and m=3. Using the above property of limits we get

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{5-3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{2}[/tex]

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

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{20}{3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=6.6667[/tex]

Therefore the correct option is c.

Answer:

The null and alternate hypothesis would be

H0:   pm = pf  

H1:   pm < pf  

Test is left tailed

The test statistic: z = -0.98

The p-value: 0.1365

We fail to reject the null hypothesis

Conclusion:  There is not enough evidence to support the claim that the proportion of men who own cats is less than the proportion of women who own cats

Step-by-step explanation:

The null and alternate hypothesis would be

H0:  pm = pf

Ha:  pm < pf    

because they say that the test claim is the proportion of men is smaller less than the proportion of women.  The null hypothesis always get the statement of equality (the equals sign).  In this case, the alternate hypothesis is the claim.  

The test is left tailed because the alternate hypothesis has a <  sign.  It's strictly less than a value, so it's one tailed, and the < or > sign points to the area of rejection, so in this case, it's pointing left

The test statistic is calculation is attached as a photo  

The p-value is found by looking it up on the chart using z = -0.98

Since 0.1365 > 0.005, we fail to reject the null hypothesis

Because we fail to reject the null, there is not enough evidence to support the claim

We perform a hypothesis test for the difference between two proportions. The null hypothesis states the proportion of men owning cats equals the one of women, while the alternative hypothesis says it's smaller. We do a one-tailed test, and if the p-value<=0.005, we reject the null hypothesis.

In order to test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at a .005 significance level, we need to perform a hypothesis test for the difference between two proportions.

The null hypothesis (H0) is that the proportion of men who own cats (pM) equals the proportion of women who own cats (pF), while the alternative hypothesis (H1) is that pM smaller than pF. So they are:

H0: pM = pF

H1: pM < pF

Basing on the samples, 25% of 40 men and 35% of 40 women owned cats. We are making a one-tailed (left-tailed) test because we want to know if pM is less than pF.

The test statistic and p-value have to be calculated using these formulas or a statistical software. If the p-value is less or equal to .005 (our alpha), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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Answer:

B

Step-by-step explanation:

Use the Heron's formula for the area of the triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]

Since [tex]a=11.5,\ b=13.7,\ c=12.2,[/tex] then

[tex]p=\dfrac{11.5+13.7+12.2}{2}=18.7.[/tex]

Hence,

[tex]A=\sqrt{18.7(18.7-11.5)(18.7-13.7)(18.7-12.2)}=\sqrt{18.7\cdot 7.2\cdot 5\cdot 6.5}=\\ \\=\sqrt{11\cdot 1.7\cdot 9\cdot 4\cdot 0.2\cdot 5\cdot 5\cdot 1.3}=30\sqrt{11\cdot 1.7\cdot 0.2\cdot 1.3}=30\sqrt{4.862}\approx 66.1\ un^2.[/tex]

Answer:

Choice b is correct.

Step-by-step explanation:

We have given the sides of triangle.

a = 11.5, b = 13.7 and c  = 12.2

We have to find the area of the triangle.

The formula to find the area of the triangle when three sides are given is:

A = √p(p-a)(p-b)(p-c)

where p = (a+b+c) / 2

p = (11.5+13.5+12.2)/2

p = 18.7

A = √18.7(18.7-11.5)(18.7-13,7)(18.5-12.2)

A = 30√4.862 units²

A≈ 66.1 units²