which expression is equal to (x+5)(-3x^2+15x-1)?
a. -3x^3+74x-5
b. -3x^3+30x^2-76x-5
c. -3x^3-76x-5
d. -3x^3+30x^2+74x-5

Answer:

14

Step-by-step explanation:

To subtract 3x2 + 4x – 5 from 7x2 + x + 9, we will take the difference of the two polynomials to have;

7x2 + x + 9 -(3x2 + 4x – 5)

= 7x²+x+9-3x²-4x+5

= 7x²-3x²+x-4x+9+5

= 4x²-3x+14

Further subtracting 4x²-3x from the resulting polynomial will give us;

4x²-3x+14 - (4x²-3x)

= 4x²-3x+14-4x²+3x

= 4x²-4x²-3x+3x+14

= 14

Therefore the final answer is 14

Subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9 yields the polynomial 4x^2 - 3x + 14. The difference polynomial is 4x^2 - 3x + 14.

When subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9, you need to subtract the coefficients of like terms.

Starting with 7x^2 + x + 9 - (3x^2 + 4x - 5), you subtract the corresponding coefficients:

(7x^2 - 3x^2) + (x - 4x) + (9 + 5)

This simplifies to:

4x^2 - 3x + 14

So, the resulting polynomial is 4x^2 - 3x + 14 after subtracting.

In this polynomial, the highest degree term is 4x^2, the linear term is -3x, and the constant term is 14. The difference is a quadratic polynomial with a leading coefficient of 4, a linear term with a coefficient of -3, and a constant term of 14.

This polynomial represents the result of subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9.

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Answer:

Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are  (0, 14) and (10, 1)

Option B is correct.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because 2/5 × 4x=8/5 and 2/5×9=18/5

ita in d

Answer:

The number of years will it take to accumulate the amount in the account is 15 years .

Step-by-step explanation:

Given as :

The principal invested = p = $4000

The rate of interest = r = 8.75% compounded annually

The amount accumulate after t years = A = $14,000

Let The years of accumulation = t years

From Compounded Interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, $14000 = $4000 × [tex](1+\dfrac{\textrm 8.75}{100})^{\textrm t}[/tex]

Or, [tex]\dfrac{14000}{4000}[/tex] = [tex](1.0875)^{\textrm t}[/tex]

Or, 3.5 =  [tex](1.0875)^{\textrm t}[/tex]

Taking log both side

[tex]Log_{10}[/tex]3.5 = [tex]Log_{10}[/tex]  [tex](1.0875)^{\textrm t}[/tex]

Or, 0.54 = t [tex]Log_{10}[/tex]1.0875

or, 0.54 = t × 0.036

∴ t = [tex]\dfrac{0.54}{0.036}[/tex]

I.e t = 15

So, The number of years will it take = t = 15 years

Hence, The number of years will it take to accumulate the amount in the account is 15 years . Answer

Answer:

(x, y ) → (x + 2, y - 4 )

Step-by-step explanation:

Compare the coordinates of 2 corresponding points in the original and the image, that is

B(- 5, 4 ) → B'(- 3, 0 )

To translate from B → B'

We require a shift of 2 units right in the x direction and 4 units down in the y direction, that is

(x, y ) → (x + 2, y - 4 ) ← translation rule

I'm assuming there should be a dollar sign here. This is the same as saying "$3 for one pound". A unit rate has some amount per 1 unit of something else. In this case, the 1 unit is 1 pound.

A different example of a unit rate is writing 40 miles per hour. This is the same as saying the car drives 40 miles in 1 hour. The unit here is the "1 hour".

Answer:

Given: $1.00 for 2 lemons $3.00 for every pound $4.00 for 3 slices of pizza $6.0

Step-by-step explanation:

The square root of -100 is 0 + 10i or simply 10i in the form of a complex number, representing the imaginary part along the complex plane's imaginary axis.

The square root of a negative number is not a real number, but rather a complex number denoted by the imaginary unit i for the square root of -1. To find the square root of -100, express -100 as the product of its prime factors: [tex]\(-100 = -1 \times 2^2 \times 5^2\)[/tex]. Then, applying the properties of square roots, break it down: [tex]\(\sqrt{-1} \times \sqrt{2^2} \times \sqrt{5^2}\)[/tex].

The square root of -1 is represented as i, while the square roots of [tex]\(2^2\)[/tex] and [tex]\(5^2\)[/tex] are 2 and 5, respectively. Combining these results, the square root of -100 is 0 + 10i, or simply 10i in complex number form, indicating that it lies on the imaginary axis of the complex plane.

It's important to note that the square root of a negative number results in a complex number with a real part of 0 and an imaginary part that represents the square root of the positive value of the number. In this case, the square root of -100 yields an imaginary component of 10i, indicating the distance from 0 along the imaginary axis in the complex plane, demonstrating the nature of complex numbers when dealing with square roots of negative values.

Answer:

-1/81

Step-by-step explanation:

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Answer:

-1/81

Step-by-step explanation:

Answer:

[tex]25^o[/tex]

Step-by-step explanation:

Let

x ----> the angle in degrees

we know that

[tex]sin(x)=0.42[/tex]

Find the measure of angle x

Using a calculator

[tex]x=sin^{-1}(0.42)=24.83^o[/tex]

Round to the nearest degree

[tex]x=25^o[/tex]

a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

Solution:

Given that,

Use the set of ordered pairs below to answer each question.

{(4, 20),  (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}

So we must find GCF of the ordered pairs

GCF of 4 and 20:

The factors of 4 are: 1, 2, 4

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

GCF of 8 and 4:

The factors of 4 are: 1, 2, 4

The factors of 8 are: 1, 2, 4, 8

Then the greatest common factor is 4

GCF of 2 and 3:

The factors of 2 are: 1, 2

The factors of 3 are: 1, 3

Then the greatest common factor is 1

GCF of 15 and 3:

The factors of 3 are: 1, 3

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

GCF of 6 and 15:

The factors of 6 are: 1, 2, 3, 6

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

GCF of 6 and 30:

The factors of 6 are: 1, 2, 3, 6

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6

GCF of 1 and 5:

The factors of 1 are: 1

The factors of 5 are: 1, 5

Then the greatest common factor is 1

GCF of 6 and 18:

The factors of 6 are: 1, 2, 3, 6

The factors of 18 are: 1, 2, 3, 6, 9, 18

Then the greatest common factor is 6

GCF of 0 and 3:

The factors of 0 are: All Whole Numbers

The factors of 3 are: 1, 3

Then the greatest common factor is 3

Summarizing the results:

(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

So let us find the factors of second cordinate and check

For (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20

Thus first coordinate 4 is factor of second cordinate

For (8, 4) the factors of 4 are 1, 2, 4

Thus first coordinate is not a factor of second cordinate

For (2, 3), the factors of 3 are 1, 3

Thus first coordinate is not a factor of second cordinate

For (15, 3), the factors of 3 are 1 and 3

Thus first coordinate is not a factor of second cordinate

For (6, 15) , the factors of 15 are 1, 3, 5, 15

Thus first coordinate is not a factor of second cordinate

For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Thus first coordinate 6 is factor of second cordinate

For (1, 5) , the factors of 5 are 1 and 5

Thus first coordinate 1 is a factor of second cordinate

For (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18

Thus first coordinate 6 is factor of second cordinate

For (0, 3) , the factors of 3 are 1 and 3

Thus first coordinate is not a factor of second cordinate

Summarizing the results:

The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Therefore,

(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

To find the ordered pairs with a GCF of 3, divide the second coordinate by the first to find pairs where the first is a factor of the second, and check the second coordinate for prime numbers.

To find the ordered pairs whose first and second coordinates have a greatest common factor of 3, we can go through each pair and check the GCF. The pairs that have a GCF of 3 are (6, 15), (6, 30), and (0, 3).

To find the ordered pairs whose first coordinate is a factor of its second coordinate, we need to divide the second coordinate by the first coordinate and check if the result is a whole number. The pairs that meet this condition are (2, 3), (15, 3), and (0, 3).

To find the ordered pairs whose second coordinate is a prime number, we need to check if the second coordinate is divisible only by 1 and itself. The pair that meets this condition is (2, 3).

Answer:

y=-2x-2

Step-by-step explanation:

y-4=-2(x+3)

y=-2x-6+4

y=-2x-2

Answer:

B

Step-by-step explanation:

Given

5 - 2x + 7y = 4 ( subtract 5 from both sides )

- 2x + 7y = - 1 ( add 2x to both sides )

7y = 2x - 1 ( divide all terms by 7 )

y = [tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{7}[/tex] → B

Answer:

B. [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]

Step-by-step explanation:

We have been given an equation [tex]5-2x+7y=4[/tex]. We are asked to choose the equation that is equivalent to our given equation.  

We will convert our given equation in point-slope form of equation.

[tex]5-2x+2x+7y=4+2x[/tex]

[tex]5+7y=4+2x[/tex]

[tex]5-5+7y=4-5+2x[/tex]

[tex]7y=-1+2x[/tex]

[tex]7y=2x-1[/tex]

Divide both sides by 7:

[tex]\frac{7y}{7}=\frac{2x}{7}-\frac{1}{7}[/tex]

[tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]

Therefore, equation [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex] is equivalent to our given equation and option B is the correct choice.

Answer: 21

Step-by-step explanation:

28-(28/100)*25=28-7=21

The polynomial in standard form is [tex]\( -3x^3 + 6x^2 + 5x + 1 \)[/tex], which corresponds to option A.

Here are the step-by-step instructions to put the given polynomial in standard form:

1. Rearrange the terms by descending order of exponents: Start by rewriting the polynomial with the terms arranged from highest degree to lowest degree.

[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]

2. Check for any missing terms: Make sure that each degree of x from highest to lowest is represented. In this case, all terms are present.

3. Double check the arrangement: Ensure that the terms are arranged correctly with respect to their exponents.

[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]

Thus, the polynomial in standard form is:

[tex]\[ -3x^3 + 6x^2 + 5x + 1 \][/tex]

Therefore, the correct answer is option A.

Complete Question:

Put the polynomial in standard form

[tex]$$5 x-3 x^3+1+6 x^2$$[/tex]

Choose the correct option

A: [tex]$-3 x^3+6 x^2+5 x+1$[/tex]

B: [tex]$1+6 x^2+5 x-3 x^3$[/tex]

C: [tex]$6 x^2+5 x-3 x^3+1$[/tex]

D: [tex]$-3 x^3+5 x+6 x^2+1$[/tex]

Answer:

[tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].

Step-by-step explanation:

We have to determine that in which quadrant the angle [tex]\theta[/tex] lies if [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].

The horizontal axis i.e. x-axis and the vertical axis i.e. y-axis divides the coordinate plane into four zones, the zone with x and y both positive is the first quadrant and rotating about the origin in anticlockwise we will find 2nd, 3rd and 4th quadrant one by one.

In the first quadrant all the trigonometrical functions [tex]\sin \theta[/tex], [tex]\cos \theta[/tex] and [tex]\tan \theta[/tex] are positive.

In the second quadrant only  [tex]\sin \theta[/tex] is positive.

In the third quadrant only [tex]\tan \theta[/tex] is positive i.e. [tex]\sin \theta[/tex] and [tex]\cos \theta[/tex] are negative.

In the fourth quadrant only [tex]\cos \theta[/tex] is positive.

Therefore, [tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex]. (Answer)

If both sin 0 and cos 0 are negative, the angle 0 lies in the third quadrant because only in this quadrant are both sine and cosine functions negative.

The question asks in which quadrant does 0 lie given that sin 0<0 and cos 0<0. In the context of trigonometric functions in the Cartesian coordinate system, the sin of an angle is negative in the third and fourth quadrants, and the cos function is negative in the second and third quadrants. As such, if both sin 0<0 and cos 0<0, it indicates that the angle 0 must lie in the third quadrant. This is because it is the only quadrant where both the sin and cos of an angle are negative. Therefore, the angle 0 lies in the third quadrant.

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Answer: t ≈ 20 years

Step-by-step explanation:

Since it is compounded continuously , we will use the compound interest formula:

A = P[tex]e^{rt}[/tex]

Where A is the amount when tripled

P is the initial amount

r is the rate

t is the time

since the investment is tripled , it means the A = 3P.

From the question:

A = 3P

P = $6000

r = 5.5%

t = ?

Substituting into the formula , we have

3P = P[tex]e^{rt}[/tex] , that is

3(6000) = 6000[tex]e^{0.055t}[/tex]

Dividing through by 6000 , we have

3 = [tex]e^{0.055t}[/tex]

Take the In of both sides in order to remove the exponential , that is

In 3 = 0.055t

divide through by 0.055

t = In 3 / 0.055

Therefore :

t = 19.97476888

t≈ 20 years

Answer:

(27 - n) times 3 is the expression Kyle should use.

Step-by-step explanation:

If Lee ran for 3 times longer than Kyle ran on Wednesday, then we have to figure out how long Kyle ran on Wednesday. If Kyle ran n fewer minutes than he ran on Tuesday, then we need to figure out how long he ran on Tuesday. If Kyle ran 27 minutes on Tuesday, the we need to subtract n from that to get how long Kyle ran on Wednesday. We can't figure that out with an undefined variable, therefore, that will just have to be 27 - n in the equation. If Lee ran for 3 times that, we need to multiply that by 3. 27 - n would have to be done first, so we will put that in parenthesis. We put all of that together to get (27 - n) times 3. Hope this helps!

KL is equal to JM because the quadrilateral is a parallelogram.

7x-2=12x-22

5x=20

x=4

KL=7(4)-2=26

answer: x=4, KL=26

Answer:

[tex]\frac{9}{4}\ or\ 2\frac{1}{4}\ square feet[/tex]

Step-by-step explanation:

On the first day the moss covered

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

                         [tex]=\frac{3}{2}\ square\ feet[/tex]

One the second day the moss covered [tex]=3\frac{3}{4}[/tex] square feet

                                                      [tex]=\frac{15}{4}\ square\ feet[/tex]

Extension of moss cover on second day

= Moss covered second day - Moss covered first day

[tex]=\frac{15}{4}-\frac{3}{2}\\=\frac{15}{4}-\frac{3\times2}{2\times2} \\=\frac{15}{4}-\frac{6}{4}\\=\frac{9}{4} \\=2\frac{1}{4}\ square\ feet[/tex]

Answer:

3.47 + 1.8 = 5.27 lbs of fruit Randy bought in all

Answer:

width of garden=b=10 ft

length of garden=l=10+14=24 ft

Step-by-step explanation:

given area of garden=240 ft^2

length of garden=l

width of garden=b

ac/ ques, l=b+14

area of garden=lb

240 ft^2=(b+14)b

put b=10 form hit and trial method

240=(10+14)10=(24)10=240

width of garden=b=10 ft

length of garden=l=10+14=24 ft answer

Start by simplifying both fractions

[tex]

\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4} \\

\dfrac{48}{64}=\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4}

[/tex]

As you can see both fractions simplify to a same value hence the equality

[tex]\dfrac{24}{32}=\dfrac{48}{64}[/tex]

stands.

Hope this helps.

Ralph read 27 books and Homer read 6 books.

Step-by-step explanation:

Given,

Total books read = 33

Let,

Books read by Ralph = x

Books read by Homer = y

According to given statement;

x+y=33     Eqn 1

Ralph read three more than four times as many as Homer.

x = 4y+3    Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](4y+3)+y=33\\4y+3+y=33\\5y=33-3\\5y=30[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{30}{5}\\y=6[/tex]

Putting y=6 in Eqn 2

[tex]x=4(6)+3\\x=24+3\\x=27[/tex]

Ralph read 27 books and Homer read 6 books.

Keywords: linear equation, substitution method

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Answer:

The slope is dy/dx= -1/2

Step-by-step explanation:

Y-3= -1/2(X -2)

Y= -1/2x +2/2 +3

Y= -1/2x +1+3

Y= - 1/2x +4

The slope dy/dx= -1/2

Answer:

The group will need to take a minimum of 5 buses to carry all the people to the trip

Step-by-step explanation:

Given:

Number of 7th grade students going on the trip = 178

Number of chaperones going on the trip = 20

Number of people each bus can hole = 42

To find the number of buses the group will have to take.

Solution:

Let minimum number of buses the group will have to take = [tex]x[/tex]

using unitary method:

If 1 bus can hold = 42 people

Then, [tex]x[/tex] buses can hold = [tex]42x[/tex] people

Total number of people for the trip = [tex]178+20=198[/tex]

The total number of people that can go in [tex]x[/tex] buses must be greater than or equal to 198 in order to carry all the people to the trip.

Thus we have the inequality:

[tex]42x\geq198[/tex]

Solving for [tex]x[/tex]

Dividing both sides by 42.

[tex]\frac{42x}{42}\geq\frac{198}{42}[/tex]

[tex]x\geq4.71\approx 5[/tex]   [As number of buses must be in whole number]

Thus, the group will need to take a minimum of 5 buses to carry all the people to the trip.

The number of buses needed for a field trip is 5 buses.

To determine how many buses are needed for 178 7th grade students and 20 chaperones going to the aquarium, where each bus holds 42 people, we first calculate the total number of passengers: 178 students + 20 chaperones = 198 people. We then divide this total number by the bus capacity. However, since we can't have a fraction of a bus, if there is any remainder after division, we must round up to the next whole number. So the inequality to represent this situation is:

Calculate total passengers:
178 students + 20 chaperones = 198 people

Divide by bus capacity to find the number of buses needed:
198 ÷ 42 = 4.714...

Round up to the next whole number, which means 5 buses will be needed.

Answer:

y=-1

Step-by-step explanation:

-5y+8=-3y+10

-5y-(-3y)+8=10

-5y+3y=10-8

-2y=2

y=2/-2

y=-1

Answer:

A. 3 cm

Step-by-step explanation:

The smallest face has the sides 4 cm and 8 cm. If the water is 4 cm from its top, then the height of the water is [tex]16-4=12[/tex] cm and the volume of the water is

[tex]V_{water}=4\cdot 8\cdot 12=384\ cm^3[/tex]

The largest face has the sides 8 cm and 16 cm. If the container is placed on its largest face, then the volume of the water is

[tex]V_{water}=8\cdot 16\cdot h \ cm^3,[/tex]

where h is the height of the water.

Equate volumes of the water:

[tex]8\cdot 16\cdot h=384\\ \\h=\dfrac{384}{8\cdot 16}=3\ cm[/tex]

Therefore, the water is 3 cm from the bottom.

Answer:

y=3x+6

Step-by-step explanation:

Parallel means same slope.

y-y1=m(x-x1)

y-9=3(x-1)

y=3x-3+9

y=3x+6

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y=3x+6.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

Since the line is parallel to y=3x+2, the slope of the line will be the same as this line, therefore, will be equal to 3. The equation of the required line will be,

y = 3x + c

Now, the value of constant, c can be found by substituting the point in the equation of the line, therefore,

9 = 3(1) + c

9 = 3 + c

c = 6

Hence, the equation of the line will be y=3x+6.

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Answer:

Package A: [tex]g=18p[/tex] and Package B: [tex]g=12p[/tex]

Step-by-step explanation:

Here is the complete question: A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks. Write an equation for package A and B that represents the total number of glue sticks is "g" in "p" package.

Given: There are 2 packages .

Package A has 18 glue sticks

Package B has 12 glue sticks

As given let "g" be the total number of glue sticks in "p" packages.

Package A:

Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]

∴ [tex]g=18\times p= 18p[/tex]

∴ [tex]g=18p[/tex]

Package B:

Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]

∴ [tex]g=12\times p= 12p[/tex]

∴ [tex]g=12p[/tex]