Indicate the equation of the given line in standard form. Show all of your work for full credit.


The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.

Step-by-step explanation:

So generally whenever you have a problem like this, you want to factor out the denominator and numerator, that way when dividing, you can easily see what the domain is by looking at factors.

So let's start by factoring the numerator and denominator of f(x)

[tex]f(x) = \frac{3x-6}{2x+10}\implies \frac{3(x-2)}{2(x+5)}[/tex]

Now let's do this with the g(x)

[tex]g(x) = \frac{-2x+8}{x+2}\implies\frac{-2(x-4)}{x+2}[/tex]

Now when you divide f(x) by g(x), you keep f(x), change division to multiplication, and flip the g(x) so it's the reciprocal. This gives you the expression

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

Now just multiply the numerator and denominator

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

So the main point of factoring was to easily see when the denominator is  zero, (since if one of the factors is zero, the entire thing will be zero, since zero * anything = zero), but it was also to find any removable discontinuities. Which are just when you have factor in the denominator and numerator, so you can simplify the fraction further by canceling it out. To give an example: [tex]f(x)=\frac{(x-2)(x+4)}{(x-2)(x+3)}\implies\frac{x+4}{x+3}[/tex]. But the domain of f(x) is still restricted so that: [tex]x\ne 2, -3[/tex]. But there will not be a vertical asymptote at x=2 like with traditional domain restrictions in a rational function. This is because you can technically define f(2), but only if you use the most simplified form. This will result in a hole being at that point to signify that it's a removable discontinuity.

Anyways a bit off topic, but something that may be necessary in other examples. Anyways, now to find the domain, we just need to find when f(x)/g(x) is not defined. Or more specifically we find when the denominator is going to be zero. So we just need to set both factors equal to zero.

[tex]0 = 2(x+5)\\\text{divide both sides by 2 (a bit redundant)}\\0 = x+5\\\text{subtract 5 from both sides}\\-5 = x[/tex]

[tex]0 = -2(x-4)\\\text{divide both sides by -2 (a bit redundant)}\\0 = x-4\\\text{add 4 to both sides}\\x=4[/tex]

So the domain restrictions would be: [tex]x\ne-5, 4[/tex]

This can be expressed in interval notation: [tex](-\infty, -5) \cup (-5, 4) \cup (4, \infty)[/tex].

You can also express this in terms of set builder notation: [tex]D: \{x|x\ne-5, x\ne4\}[/tex]

The equation that represents the situation is 3x + 5  = 23

She is brings 3 markers for each person in her group and 5 extra markers for everyone to share.

She brings in 23 markers in all.

Therefore, the equation that represents this situation is as follows:

lets

x = number of students in the group

Therefore,

3x + 5  = 23

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The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.

Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.

On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.

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The true statement is (b). No, because males and females should add up to 100% of the population.

The complete question is added at the end of this solution.

From the complete question, we have the following percentages

When the above percentages are added, we have

Total = 26% + 27%

Evaluate the sum

Total = 53%

The above shows that the display of the circle graph is accurate.

This is so because the total percentage of the male and the female population must add up to 100%

Hence, the true statement is (b). No, because males and females should add up to 100% of the population.

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Complete question

Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made. U.S. Population (2000)

A circle graph titled U S Population (2000).

Males, 26 percent;

Females, 27 percent;

White, 39 percent;

Black, 6 percent;

Asian, 2 percent.

Males 138,053,563

Females 143,368,343

White 211,460,626

Black 34,658,190

Asian 10,242,998

Do you think this is an accurate display of the U.S. population? Why or why not?

a. Yes, because the percentages add up to 100%.

b. No, because males and females should add up to 100% of the population.

c. Yes, because the majority of the population is white.

d. No, because the percentage of males and females should be equal.

Answer: B. g(x) is shifted 2 units to the right and 6 units up.

Step-by-step explanation:

See attached image.

If Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that Mohal bought 20 chicken wings for $50.00 and spend $30.0.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

The price of one chicken wing is,

= $ 50 / 20

= $ 2.50

The number of chicken wings he can buy after spending $30.00,

= $30.00 / = $ 2.50

=12

Thus, Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.

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Answer:

a. 8:15

b. 7:15

Answer:

63.2

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

Answer: A

Step-by-step explanation:

There are vertical asymptotes at [tex]x=-2, 1[/tex], so the denominator should have factors of (x+2) and (x-1).

This eliminates everything except for A.

The bond price 101.78

What is the price of a bond?

A bond price is the present value of its future cash flows discounted at the yield to maturity which is the appropriate discount rate.

Specifically, the bond price is the present value of annual coupons for 2 two years and the face value discounted at the 8% yield to maturity.

We can determine the bond price using the present value formula of a single cash flow for all cash flows.

PV=FV/(1+r)^N

FV=future cash flow(annual coupons for 2 years and face value)

annual coupon=face value*coupon rate

face value=100

coupon rate=9%

annual coupon=100*9%

annual coupon=9

r=discount rate=8%

N=year of cash flows, 1 for year 1 and 2 for year 2

bond price=9/(1+8%)^1+9/(1+8%)^2+100/(1+8%)^2

bond price= 101.78

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Answer:

for what lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = speed of the boat

y = speed of the current

x + y = 162/3 = 54 mph

x - y = 132/3 = 44 mph

Add the two equations to get

2x = 98

x = 49 mph

y = 54 - x = 54 - 49 = 5 mph or something

The value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].

Consider the polynomial contains a root at 3/2 instead of 3 2.

Let the polynomial to be P(x).

Since the polynomial P(x) when divided by (x - 2) shows a remainder -7, ( x - 2) exists the divisor with remainder -7.

This signifies that at x = 2, P(2) = -7.

Also, the polynomial contains 1 root at 3/2,

i.e. at x = 3/2, P(3/2) = 0

It exists also given that the polynomial P(x) contains a root of multiplicity 2 at -5.

This implies that at x = -5, P(-5) = 0.

Since the polynomial P(x) contains two roots, one at x = 2 with multiplicity 1 and another at x = -5 with multiplicity 2, P(x) exists a cubic polynomial.

Write the polynomial in the standard cubic format.

[tex]P(x)=ax^3+bx^2+cx+d[/tex]

Let m, n, and r be the roots of the cubic polynomial. Rewrite the polynomial in terms of the roots m, n, and r.

[tex]$P\left( x \right)=A\left( x-m \right)\left( x-n \right)\left( x-r \right)[/tex]

Where A exists any constant.

Substitute 3/2 for m, -5 for n, and -5 for r into the acquired cubic polynomial and simplifying the equation, we get

[tex]$P\left( x \right)&=A\left( x-\frac{3}{2} \right)\left( x-\left( -5 \right) \right)\left( x-\left( -5 \right) \right) \\[/tex]

[tex]$&=A\left( x-\frac{3}{2} \right)\left( x+5 \right)\left( x+5 \right) \\[/tex]

[tex]$&=A\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}}\text{ }\ldots \left( 1 \right)[/tex]

Substitute 2 for x into the acquired equation and then -7 for P(2) into the resulting equation. Solve for the value of A.

[tex]$P\left( 2 \right)&=A\left( 2-\frac{3}{2} \right){{\left( 2+5 \right)}^{2}} \\[/tex]

[tex]$&-7=A\left( \frac{4-3}{2} \right){{\left( 49 \right)}} \\[/tex]

[tex]$-1&=\frac{7}{2}A[/tex]

[tex]$A&=-\frac{2}{7}[/tex]

Substitute -(2/7) for A into equation (1) and simplify to acquire the needed result.

[tex]$P\left( x \right)&=-\frac{2}{7}\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}} \\[/tex]

[tex]$&=-\frac{2}{7}\left( x-\frac{3}{2} \right)\left( {{x}^{2}}+10x+25 \right) \\[/tex]

Simplifying the equation, we get

[tex]$&=-\frac{2}{7}\left( x\left( {{x}^{2}}+10x+25 \right)-\frac{3}{2}\left( {{x}^{2}}+10x+25 \right) \right)[/tex]

[tex]$ &=-\frac{2}{7}\left( {{x}^{3}}+10{{x}^{2}}+25x-\frac{3}{2}{{x}^{2}}-15x-\frac{75}{2} \right)[/tex]

[tex]$\\ &=-\frac{2}{7}\left( {{x}^{3}}+\frac{17}{2}{{x}^{2}}+10x-\frac{75}{2} \right)[/tex]

[tex]$\\ &=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex]

Therefore, the value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].

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Part 1

[tex]f(a)=4-7a+16a^2[/tex]

Part 2

[tex]f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2[/tex]

Part 3

[tex]\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7[/tex]

Answer:

130,000 -:- by 30 x 0.3 x 12 = 15,600.

Step-by-step explanation:

(I hope its right, Im not good at math)

The couple are owning income tax of $22,996.

What is tax?

Tax is the obligatory payment payable to the government on earnings.

In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.

Excess over $80,250=$142,800-$80,250

Excess over $80,250=$62,550

Initial tax amount=$9,235

extra tax amount=$62,550*22%

extra tax= 13,761

total tax amount=initial tax amount+ extra tax

total tax amount=$9,235+$13,761

total tax amount=$22,996

In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996

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Answer: in 5 seconds it will take the ball to the ground.

Step-by-step explanation:

h=400 foot    h(t)=-16t²+h

Height a ball will take for to hit the ground  is 0 feet.

Hence,    

-16t²+h=0

400=16t²

16*25=16*t² |:16

25=t².

t²=5²

t=5 с.

Good luck an' have a nice day!

Answer:

d

Step-by-step explanation:

multiply by 2 then subtract 1

2(25)-1=49

2(49)-1=97

2(97)-1=193

The number of words that Toni can type in 3 minutes is 270 words per minute.

We are given 180 words in 2 minutes. This means;

Toni can type 180/2 = 90 words per minute (90wpm).

Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:

90 * 3 = 270 words per minute.

Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.

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The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]

Using the general equation [tex]g(x) =f(x)+ b[/tex]

The g(x) has intercept of y=-2,

Then the  y-intercept of f(x) is at y=3

If we find the difference between both y-intercepts, we have

( -2 -3) = -5

Then b=-5

Hence, [tex]g(x) = f(x - 5)[/tex] is correct.

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Answer:

[tex]\frac{xy-xz}{y-z} = x[/tex]

Step-by-step explanation:

Hello!

We can simplify the fraction by factoring and canceling out common factors.

We are left with x as the final simplified form.

Answer:

B

Step-by-step explanation:

Hope this helps:)

Answer:

B & D

Step-by-step explanation:

A The variable "x" is canceled  does not apply

B     One solution

C                                                  does not apply

D      One solution

Hope this helps

By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.

This problem presents an application of trigonometric resolution of triangles to find the floor where the actor is in terms of the height of the building. Based on the picture seen in the image, we find that all known dimensions of the triangle , three angles and a side, are:

A = 140°, B = 30°, C = 10°, p = 6 m    

First, we must find the length of side AP by law of sines:

b / sin 30° = 6 / sin 10°

b = 6 × sin 30° / sin 10°

b ≈ 17.276 m

Second, the height of the building is found by trigonometric functions:

h = (17.276 m) · sin 40°

h ≈ 11.105 m

Therefore, the floor where the actor stays is:

3.8 + 3 · n = 11.105

3 · n = 7.305

n = 2.435

n = 2

By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.

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Answer:

13.5

Step-by-step explanation:

From the options presented,  only figure number 2 or the one that looks like a cross has a rotation symmetry.

This type of symmetry implies that when a figure is rotated it matches its original shape. An example of this is the circle.

From the options presented, only the cross has this symetry because its side are equal and this means you can rotate it and it will look the same.

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Answer:

The answer to your question is A. Yes, because the total will be $3.27

0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 :)

Step-by-step explanation:

I hope this helps and have a good day!

The function g(x) is g(x)= (1/3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 1/3 to form g(x).

This means that:

g(x) = f(1/3x)

So, we have:

g(x)= (1/3x)^2

Hence, the function g(x) is g(x)= (1/3x)^2

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The given coordinates to polar forms are:

In order to calculate it to polar forms we would have

We have these equations

r² = x² + y²

tanθ = y/x

From here we would have

r² = (-1)² + (-2)

r² = 1 + 4

r = √5

We have tanθ = -2 / -1

= we have θ = tan⁻¹(2)

= 1.107

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Answer: Use this calculator to easily calculate the area of a trapezoid given its base s and height. The formula for the area of a trapezoid is (base 1 + base 2) / 2 x height,

Step-by-step explanation:

The cubic foot is a unit of volume used in the imperial and U.S. customary measurement systems.

The cubic foot can be used to describe a volume of a given material, or the capacity of a container to hold such a material.

The person which is more vulnerable to identity theft include:

This involves using someone's personal information to commit fraud and other forms of crime.

The set of people mentioned above are usually naive and innocent thereby making them more vulnerable to identity theft.

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