Find the slope and y-intercept.

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 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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A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.

Given that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.

So, the combination for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

                                                                        =  17576000

Therefore, 17576000 license plates can be made.

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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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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

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

The output voltage of the op-amp circuit shown is -5v.

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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Answer:

C

Step-by-step explanation:

We can use process of elimination

D is incorrect because the roots are 3 and -4 and there are no negative roots visible

B is wrong because the roots -3 and -6 are both negative

You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6

For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate

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 function illustrates that the bill for someone who uses 600 kilowatt will be $80.

It should be noted that a function simply means an expression that defines the relationship between a variable and another variable. In this case, one can infer that functions are essential in the formulation of relationship between the variables that are given.

Based on the information given, it should be noted that it was stated that the power company calculates a person's monthly bill from the number of kilowatt-hours.

The bill for someone who uses 600 kilowatt will be:

= 0.1(x - 400) + 60

= 0.1(600 - 400) + 60

= 0.1(200) + 60

= 20 + 60

= 80

In conclusion, the bill will be $80.

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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

Answer:

Answer number 1

......................

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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Answer:

[tex]\frac{169}{49}[/tex]

Step-by-step explanation:

Square the top and bottom numbers in the fraction

13^2 = 169

7^2 = 49

169/49

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

Step-by-step explanation:

See attached image.

Answer:

x = 24°

Step-by-step explanation:

If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.

Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".

∠EFH = 2x

∠JHG = 24°

∠GHF = x

∠EFH = ∠JHF                                  <----- Opposite interior angles are equal

∠EFH = ∠JHG + ∠GHF                   <----- Break ∠JHF into 2 angles

2x = 24 + x                                      <----- Insert values

x = 24                                             <----- Subtract x from both sides

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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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!

Answer:

2635

Step-by-step explanation:

the first two stand for 1000

so

2000

is the first part

the second numeral stands for 100

there are 6 of them

so

600

is the second part

the third numeral stands for 10 and there are 3 of them

thus

30

is the third part

there are 5 lines so the last part is 5

so your answer is 2635

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]

Answer:

A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION

f

(

x

)

=

b

x

An exponential function with the form

f

(

x

)

=

b

x

,

b

>

0

,

b

≠

1

, has these characteristics:

one-to-one function

horizontal asymptote:

y

=

0

domain:

(

−

∞

,

∞

)

range:

(

0

,

∞

)

x-intercept: none

y-intercept:

(

0

,

1

)

increasing if

b

>

1

decreasing if

b

<

1

Step-by-step explanation:

hope it helps you

The value of g(3) is g(3) = 4

The function value is given as:

g(x)

The notation g(3) implies that:

We determine the value of g(x) when x = 3

From the graph, the function has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the value of g(3) is g(3) = 4

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the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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 value of the angle TSU is.97°. Therefore, none of the given options are correct.

From the information given, the value of UZ will be:

= YZ - YU

= 63 - 26

= 37°

UZ = TZ = 37°

Therefore, the value of TSU will be:

= 23° + (37° × 2)

° 23° + 74°

= 97°

In conclusion, the correct option is E.

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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:

Step-by-step explanation:

hello :

 f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x        (f g)(x) = 4x......(answer : A)

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:

13.5

Step-by-step explanation: