Brad wants to open a new savings account. He finds one that returns 3% on his investment each year.

Question 1
Assign a variable to each of the following pieces of information

Final balance
Initial investment
Return rate

Answer:

-2y+6 or -2(y-3)

Step-by-step explanation:

-3y+6+y=-2y+6

Answer:

$240

Step-by-step explanation:

The amount in the account after 3 years will be 16171.45701

What is a deposit?

It is a financial term that means money held at bank. It is a sum of  money which you pay when you start renting something. The deposit is a money which we put in our bank account. It is made for funds and we can withdraw that money anytime. If you take a loan the money can be deposited is in the form of collateral amount. Demand and time are two types of deposits made by businesses or individuals. The amount of money that is paid to an account is known as deposit. The sum of money that is given in advance as a part of a total payment is termed as deposit. It is a transaction involving the transfer of money to a bank account. It is an another way for safekeeping.

Given p=periodic payment=$100/week

r= interest rate=2.4%, compounded weekly

t=3 years

n=52 weeks

b= future value= P([tex](1+r/n)^{nt}[/tex]-1)/(r/n)

=100([tex](1+2.4/5200)^{156}[/tex]-1)/(2.4/100×52)

=16171.45701

After 3 years the amount in the account will be 16171.45701.

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Answer:

A

Step-by-step explanation:

It's A because in order to have an equation, you need a equal sign and a variable and an expression is a base of algebra and i see your in middle school and have you ever seen a inequality sign in a algebraic expression?

An inequality sign is not part of an algebraic equation

Option A

Explanation :

Any algebraic equation will have an equal sign

For example , Algebraic equation is

[tex]y=3x+2[/tex]

This algebraic equation have = sign

The above algebraic equation have expression 3x+2

Also the above algebraic equation have variable 'x'  and 'y'

So , an algebraic equation have = sign , variables and expression

If we have inequality sign then we call it as inequality not an equation

An inequality sign is not part of an algebraic equation

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By proving that triangles DEA and EFB are congruent due to the Side-Angle-Side postulate and demonstrating that AE is parallel to FB as well as AD parallel to BC, we can conclude that EABC is a parallelogram.

To prove that quadrilateral EABC is a parallelogram, we can use the properties of triangles and the definition of a parallelogram. According to the given information, E is the midpoint of DA and F is the midpoint of DB. Additionally, we know that E, F, and C are collinear and that FC is congruent to EF.

Leveraging these pieces of information, we observe that triangle DEA is congruent to triangle EFB because they have a side (EF or DE), an angle (at point E, since DE is an extension of EF), and another side (EA or FB, which are halves of DA and DB, respectively) in common (Side-Angle-Side postulate).

Since the two triangles are congruent, angle DEA is congruent to angle EFB, and angle DAE is congruent to angle FEB. These congruent angles imply that line AE is parallel to line BF. Since E and F are midpoints, AE is half of DA and BF is half of DB. If we continue the line AE to meet CD at point A and the line BF to meet CD at point B, EA will be parallel to FB, and AD will be parallel to BC, meeting the definition of a parallelogram.

EABC is a parallelogram because opposite sides are parallel and equal due to the Midpoint Theorem.

Given:

E - midpoint of DA

F - midpoint of DB

E, F, C collinear, FC ≅ EF

To Prove: EABC is a parallelogram.

Proof:

1. By the Midpoint Theorem, EF || AB and EF = 1/2 * AB. (Midpoint Theorem)

2. Since E, F, C are collinear and FC ≅ EF, EC bisects EF at C. Therefore, AB || EC. (Definition of a parallelogram)

3. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = AB, EC = 1/2 * AB. Similarly, EF = 1/2 * AB. Hence, EC = EF. Therefore, EA || BC. (Midpoint Theorem)

4. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = BC, EC = 1/2 * BC. Similarly, EF = 1/2 * BC. Hence, EC = EF. Therefore, EB ≅ AC. (Midpoint Theorem)

Therefore, EABC is a parallelogram.

Answer:

A. x + 4

Step-by-step explanation:

f(x) = 4x⁴ − 21x³ − 46x² + 219x + 180

Plug in the zero of each binomial.  If it's also a zero of f(x), then that binomial is a factor of f(x).

f(-4) = 936

f(-3) = 0

f(5) = 0

f(-3/4) = 0

The binomial (x + 4) is not the factor of the polynomial. Then the correct option is A.

The algebraic factors with exactly two terms are known as binomial components. Although binomials are simple to solve and their roots are identical to those of polynomials, binomial factors are intriguing.

The polynomial is given below.

⇒ 4x⁴ – 21x³ – 46x² + 219x + 180

Let's check all the factors.

If the factor does not satisfy the polynomial, then the binomial is a factor of the polynomial.

For x + 4 = 0, then we have

The value of the polynomial at x = -4, will be

⇒ 4(-4)⁴ – 21(-4)³ – 46(-4)² + 219(-4) + 180

⇒ 4(256) – 21(-64) – 46(16) + 219(-4) + 180

⇒ 1024 + 1344 – 736 – 876 + 180

⇒ 2548 – 1612

⇒ 936

Thus, the binomial (x + 4) is not the factor of the polynomial.

Then the correct option is A.

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Answer:

63 miles left

Step-by-step explanation:

253+157=410

473-410=63

Answer:

Katherine invested $12,000

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest,

P = principal,

r = rate (as decimal),

t = time (in years).

In your case,

t = 1 year,

r = 0.06 (or 6%)

P + I =$12,720, thus

[tex]12,720-P=P\cdot 0.06\cdot 1\\ \\12,720-P=0.06P\\ \\12,720=P+0.06P\\ \\1.06P=12,720\\ \\P=\dfrac{12,720}{1.06}\\ \\P=\$12,000\\ \\I=\$12,720-\$12,000=\$720[/tex]

Bart should;

Multiply 6(400), 6(10), and 6(2) ⇒ 2nd

Multiply each addend by 6 ⇒ 4th

Find the sum of (2400 + 60 + 12) ⇒ 5th

Step-by-step explanation:

Let us revise the distributive property

Bart used place value and the distributive property to rewrite the

expression 6(412)

His work is shown 6(412) = 6(400 + 10 + 2)

We need to know what Bart should do to find the product

∵ 6(412) = 6(400 + 10 + 2)

- Multiply each number in the bracket by 6 in the right hand side

∴ 6(400 + 10 + 2) = (6)(400) + (6)(10) + 6(2)

∴ 6(400 + 10 + 2) = 2400 + 60 + 12

∴ He should to multiply each addend by 6 and then find the sum of

  (2400 + 60 + 12)

Bart should;

Multiply 6(400), 6(10), and 6(2)

Multiply each addend by 6

Find the sum of (2400 + 60 + 12)

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Answer:

The one up is right  but  just to make it easier it is B, D, E

Step-by-step explanation:

Got it right on edge 2021

Hope it helps :)

Answer:

4/9

Step-by-step explanation:

(4/9)/(7/9) is equal to (4/9)*(9/7) because "keep change flip." So we keep the first number, change division into multiplication, and flip 4/9 (basically find the reciprocal) and that is 9/4. Thus,  (4/9)*(9/7) is equal to 4/9 because the 7's cancel.

I hope this helped!

Answer: 4/7

Step-by-step explanation: In this problem, we have 4/9 ÷ 7/9. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

So here, 4/9 divided by 7/9 can be rewritten as 4/9 × 9/7.

Now we are simply multiplying fractions.

To multiply fractions, we multiply across the numerators and multiply across the denominators.

Image provided.

Notice however that 36/63 is not in lowest terms so we divide both the numerator and denominator by 9 and we get the equivalent fraction 4/7.

Therefore, 4/9 divided by 7/9 = 4/7.    

Answer: 87 children and 51 adult

Step-by-step explanation:

Let x be child admission and let y be adult admission.

We know that x+y=138 based on the fact that 138 tickets were sold.

We also know that 6.3x+9.9y=1053 based on the information.

Let y=138-x

Then, 6.3x+9.9(138-x)=1053

6.3x+1366.2-9.9x=1053

-3.6x+1366.2=1053

-3.6x=-313.2

x=87

138-87=y=51

87 children's and 51 adult tickets were sold.

Answer:

x=0

Step-by-step explanation:

4(x+1)=2x+4

4x+4=2x+4

4x-2x+4=4

2x+4=4

2x=4-4

2x=0

x=0/2

x=0

Answer:

yes it's a solution

Step-by-step explanation:

the guy before me explained it well

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Step-by-step explanation:

we have to caalculate the distance between Dustin's home and work

So

Given

Speed =s = 55 miles per hour

Time = t = 2 hours and 15 minutes

Converting time into fraction

Time = 2.25 hours

We know that

[tex]s = \frac{d}{t}\\d = s * t\\d = 55 * 2.25\\d = 123.75\ miles[/tex]

So the distance is 123.75 miles

The car travels 25 miles per gallon

We have to calculate the total number of gallon first

So,

[tex]No.\ of\ gallons = \frac{Miles}{Miles\ per\ gallon}\\=\frac{123.75}{25}\\=4.95\ gallons[/tex]

So the total amount is:

[tex]2.75*4.95\\= 13.6125\ dollars[/tex]

Total amount is $13.6125. Dividing it by total distance will give us the cost of each mile

So,[tex]Cost\ of\ mile = \frac{Total\ amount}{Distance}\\= \frac{13.6125}{123.75}\\=0.11\ dollars[/tex]

Hence,

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Keywords: Speed, Distance

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Answer:

Three zeros [tex]x=-4,\ x=1,\ x=6[/tex]

x-intercepts: (-4,0), (1,0), (6,0)

Step-by-step explanation:

Plot the graph of the function [tex]y=x^3-3x^2-22x+24[/tex] on the coordinate plane. This graph intersects the x-axis at three different points (see attached diagram):

This means [tex]x=-4,\ x=1,\ x=6[/tex] are zeros of the function [tex]y=x^3-3x^2-22x+24[/tex]

Answer:

D

because i think

Answer:

4000

Step-by-step explanation:

Answer: 4,000.

Hope this helps!

Answer:

the solution is, x=2

Step-by-step explanation:

we have

y= 3x

y=2x+2

so we can write,

3x=2x+2

3x-2x=2

x=2

Answer:

m(the slope) = -2

Step-by-step explanation:

First, you want to use the slope formula. This can be written as (Y[subscript2]-Y[subscript1])/(X[subscript2]-X[subscript1]). This may seem a bit confusing but I hope it will make sense to you. The subscripts basically mean which Y value or X value you are taking. In this case, you could rewrite the equation as this: (18-8)/(1-6). The 18 is the Y value of the second point, so it is Y[subscript2]. Now all you need to do is simplify the equation.

(18-8)/(1-6)

10/-5

(-1)10/5

(-1)2

-2

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have two points (-4, -4) and (-1, 0).

Substitute:

[tex]d=\sqrt{(-1-(-4))^2+(0-(-4))^2}=\sqrt{(-1+4)^2+(0+4)^2}\\\\=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Answer:

11 yards

Step-by-step explanation:

The volume of a cone formula is:

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

Where V is the volume,

r is the radius (half of diameter)

h is the height

Given,

h = 15

V = 475.17

We find the radius (r) first by substituting given values:

[tex]V=\frac{1}{3}\pi r^2 h\\475.17=\frac{1}{3}\pi r^2 (15)\\475.17=5\pi r^2\\r^2=30.25\\r=5.5[/tex]

The radius (r) is 5.5 yards

We need the diameter, which is DOUBLE THE RADIUS, so diameter would be:

Diameter = 5.5 * 2 = 11 yards

Answer:

C. Sea level

zero represent in this situation is Sea level.

Integers come in three types:

Given:

An eagle is flying 30 feet above sea level = +30 feet

and, spots a fish swimming 2 feet below sea level. = -2 feet

So, using integers the zero represent the Sea Surface,

Hence, zero represent in this situation is Sea level.

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F(n) = 5n

You are being told n is the number of tables, and there are 15 tables:

f(15) = 5(15)

F(n) = 75

You need 75 candles.

5 pounds of peanuts should be mixed with cashews

Step-by-step explanation:

The given is:

The price of one pound of peanut is $1.5

The price of one pound of cashew is $4.5

10-pound mixture is obtained that will sell for $3.00 per pound

We need to find how many pounds of peanuts should be mixed with cashews

Assume that x represents the number of pound of peanuts, and y represents the number of pounds of the cashews

∵ x pounds of peanuts should be mixed with y pounds of cashews

∵ The mixture obtained is 10 pounds

∴ x + y = 10 ⇒ (1)

∵ The price of each pound of peanut = $1.5

∵ The price of each pound of cashew = $4.5

∴ The selling price of the mixture = 1.5x + 4.5y

∵ The selling price of one pound of mixture = $3

∵ The mixture is 10 pounds

∴ The selling price of the mixture = 3 × 10 = 30

- Equate the two expressions of the selling price of the mixture

∴ 1.5x + 4.5y = 30 ⇒ (2)

Now we have system of equations to solve it

Multiply equation (1) by -4.5 to eliminate y

∵ -4.5x - 4.5y = -45 ⇒ (3)

- Add equations (2) and (3)

∴ -3x = -15

- Divide both sides by -3

∴ x = 5

∵ x represents the number of pounds of peanuts

∴ The number of pound of peanuts is 5

5 pounds of peanuts should be mixed with cashews

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Answer:20592

Step-by-step explanation:

Because you multiply 5 times 2288

Leo has 2574 red marbles.

Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.

It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.

Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.

Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.

Step-by-step explanation:

[tex]7 = \pi {r}^{2} [/tex]

Were you given an input for r?

If not then:

7/pi = about 2.23

[tex] \sqrt{2.23} = about \: 1.5[/tex]

r = about 1.5

Answer:

13.406

The drawing will help

Answer:

13.406

Step-by-step explanation:

The number of people who can still have a hot dog is 82 people

Given:

Total hot dogs bought = 8 dozens

Total hot dogs bought = 8 × 12

= 96

Number of hot dogs his pet ate = 14

Number of guests who are hotdog = Total hot dogs bought - Number of hot dogs his pet ate

= 96 - 14

= 82

Therefore, the number of people who can still have a hot dog is 82 people

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Answer:

-12 feet per second

Step-by-step explanation:

average rate of change over [0.75, 1.25] = [tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex]

f(1.25) - f(0.75) = 4 - 10 = -6

1.25 - 0.75 = 0.5

[tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex] = [tex]\frac{-6}{0.5}[/tex] = -12

The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.

We have,

To find the average rate of change of the function f(t) over the interval [0.75, 1.25], you can use the following formula:

Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)

Calculate f(1.25):

f(1.25) = -16(1.25)^2 + 20(1.25) + 4

Calculate f(0.75):

f(0.75) = -16(0.75)^2 + 20(0.75) + 4

Plug these values into the formula:

Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)

Calculate the numerator:

Average Rate of Change = [(-16(1.25)^2 + 20(1.25) + 4) - (-16(0.75)^2 + 20(0.75) + 4)] / (1.25 - 0.75)

Simplify the numerator:

Average Rate of Change = [-25 + 25 + 4 - (-9 + 15 + 4)] / (1.25 - 0.75)

Further, simplify:

Average Rate of Change = (4 - (-9 + 15 + 4)) / (1.25 - 0.75)

Continue simplifying:

Average Rate of Change = (4 - 10) / (1.25 - 0.75)

Calculate the final result:

Average Rate of Change = (-6) / (0.5)

Average Rate of Change = -12 feet per second

Thus,

The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.

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Answer:

5

Step-by-step explanation:

0.3*10=3

10/5=2

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

3+2=5

Answer:

C) y+6=3/2(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

m=slope & (x1, y1) is a point on the line

m=(y2-y1)/(x2-x1)

m=(-3-(-6))/(4-2)

m=(-3+6)/2

m=3/2

y-(-6)=3/2(x-2)

y+6=3/2(x-2)

Option 3

The point slope form of the given points (2, -6) and (4, -3) is [tex]y+6=\frac{3}{2}(x-2)[/tex]

Given that two points are (2, -6) and (4, -3)

We have to find the point slope form

The point-slope of the line is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where m is the slope of the given line.

So now to write the given points in point intercept form we need to find the slope, m

The slope of line is given as:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\text { Here } x_{1}=2 ; y_{1}=-6 ; x_{2}=4 ; y_{2}=-3[/tex]

Plugging in the values, we get

[tex]m=\frac{-3-(-6)}{4-2}=\frac{3}{2}[/tex]

So, the slope of the given line is [tex]\frac{3}{2}[/tex]

Now, we need to find the point slope form. For that purpose we can use either of the points, but since in the answer options they have used the 1st point we will do so too.

Therefore, the point slope form is:

[tex]\begin{array}{l}{y-(-6)=\frac{3}{2}(x-2)} \\\\ {y+6=\frac{3}{2}(x-2)}\end{array}[/tex]

From the given options we can see that the correct answer is option 3.