The balance y (in dollars) of your savings account after t years is represented by y=300(1.05)'. The beginning balance of your friend's account is $340, and the balance increases by $10 each year. a. Compare the account balances by calculating and interpreting the average rates of change from t=2 to t=6.​

Answers

Answer 1

Answer:

My balance grows faster than my friends balance.

Step-by-step explanation:

My balance

[tex]y=300(1.05)^t[/tex]

where

t = Time

Average rate from t=2 to t=6 is given by

[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{300(1.05)^6-300(1.05)^2}{4}\\ =\mathbf{17.82}[/tex]

My friend's balance is given by

[tex]y=340+10t[/tex]

Average rate is given by

[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{(340+10\times 6)-(340+10\times 2)}{4}\\ =\mathbf{10}[/tex]

My balance grows faster than my friends balance.


Related Questions

equation
2x-1/4+x/3=2

Answers

Answer:

x=27/28

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−14+x3=2

Step 1: Simplify both sides of the equation.

2x−14+x3=2

2x+−14+13x=2

(2x+13x)+(−14)=2(Combine Like Terms)

73x+−14=2

73x+−14=2

Step 2: Add 1/4 to both sides.

73x+−14+14=2+14

73x=94

Step 3: Multiply both sides by 3/7.

(37)*(73x)=(37)*(94)

x=27/28

Answer:

x=27/28

Ella purchased a game that was on sale for 12% off. The sales tax in her county is 6%. Let y represent the original price of the game. Write an expression that can be used to determine the final cost of the game.

A y − 0.12y

B 0.06(0.88y)

C 1.06(0.88y)

D y − 0.88y + 0.06y

Answers

Answer:

The expression that can be used to determine the final cost of the game is

1.06(0.88 y) ⇒ (C)

Step-by-step explanation:

If the price of an item is discounted, that mean its new price will be less its initial priceThe taxes on item, makes its new price greater than the initial price because tax is add

Let us solve the problem

∵ Ella purchased a game that was on sale for 12% off

→ That means the new price will (100% - 12%) of the initial price

∵ y represented the initial price of the game

→ Multiply y by (100% - 12%) to get the new price

∴ The new price = y (100% - 12%)

∴ The new price = y (88%)

→ Change 88% to normal number by divide it by 100

∴ The new price = y ([tex]\frac{88}{100}[/tex])

The new price = 0.88 y

∵ The sales tax in her county is 6%

→ That means the final cost will be (100% + 6%) of 0.88 y

∴ The final cost = (100% + 6%) × (0.88 y)

∴ The final cost = 106% × (0.88 y)

→ Change 106% to normal number by divide it by 100

∴ The final cost = [tex]\frac{106}{100}[/tex] × (0.88 y)

The final cost = 1.06(0.88 y)

The expression that can be used to determine the final cost of the game is 1.06(0.88 y)

Answer:

C. 1.06(0.88y)

Step-by-step explanation:

mr george has a bank balance of 42 dollar at the start of the mouth.after he depostite 6 dollar the new balance is

Answers

Answer:

48 dollars.

Step-by-step explanation:

If Mr. George starts with 42, and adds 6, his new balance should equal 48 because you add the two numbers.

$42-$6=$36 i believe

Find the distance between the pair of points, round to the nearest tenth if necessary.

Answers

Step-by-step explanation:

distance between the two points is given by formula

d=

[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } = \sqrt{( - 2 - 4)^{2} + {( - 3 - 0)}^{2} } = \sqrt{( - 6)^{2} + ( - 3)^{2} } = \sqrt{36 + 9} = \sqrt{45} = \sqrt{9 \times 5} = 3 \sqrt{5} [/tex]

Evaluate the expression for x=5, y=-3 and z=7 *
7 – 3y – 3z

Answers

Answer:

-5

Step-by-step explanation:

i tried my best but this is the result

Can y’all help me please:)

Answers

Answer:-9

Step-by-step explanation:

that is the answer

(5x10₃) x (9x10₇)
answered in standard form

Answers

Answer:

5x9x10^10

Step-by-step explanation:

your question is incomplete

One day, the principal announces the cancelation of classes to two teachers, each whom sends this to two other teachers, and so on. Suppose that text messages were sent in five rounds, counting the principal’s text message as first, how many text messages were sent in all?

Answers

Answer:

62

Step-by-step explanation:

2 + 4 + 8 + 16 + 32 = 62

If each person sends 2 texts each, then you basically multiply by 2 every round

Find the distance from P(6,-9) to the origin.
Please helppp

Answers

Answer:

10 units

Step-by-step explanation:

Distance from P(6, -9) to O ( 0, 0 ) PO

Let

X1 = 6          X2 = 0

Y1 = -9         Y2 = 0

Formula of Distance

[tex]\sqrt{(x2 - x 1) + (y2 - y1)}[/tex]

[tex]\sqrt{6^{2} +(-9^{2}) }[/tex]

[tex]\sqrt{100}[/tex]

10 units

Solve for x.
–2(x - 1) - x + 3 = -1
Anyone wanna help?

Answers

x=2
explanation:
simplify to get -3x+5=-1
calculate to get -3x= -1-5
-3x=-6
x=2

Answer:

-2(x-1) - x + 3 = -1

First if all, we operate the parenthesis knowing that [tex]a(b+c) = ab + ac[/tex]:

-2(x-1) - x + 3 = -1 ---->.-2x -2*(-1) - x + 3 = -1

Now, we operate:

.-2x -2*(-1) - x + 3 = -1 ----> -2x + 2 - x + 3 = -1

Now we operate another time to put all the x together and the independent terms too:

-2x + 2 - x + 3 = -1 ----> -3x + 5 = -1

We substract 5 at both sides to have only the x at one side:

-3x + 5 = -1 ----> -3x + 5 - 5 = -1 - 5 ----> -3x = -6

As both sides have a minus (-) we can eliminate it:

-3x = -6 ----> 3x = 6

We divide both sides by 3 to have only a x:

3x = 6 ----> 3x/3 = 6/3 ----> x = 2

Now, we know that x=2. We can also verify it by replacing it on the first equation:

-2(x-1) - x + 3 = -1 ---> -2(2-1) - 3 + 3 = -1 ---> -2(1) - 2 + 3 = -1 ---> -2 - 2 + 3 = -1

Now we know it's true, as we have replaced it and we got he answer.

What is the slope of a line perpendicular to the line whose equation is
12x – 9y = 135. Fully reduce your answer.

Answers

Answer:

The slope is -9/12

Step-by-step explanation:

First find the slope of the given line:

12x - 9y = 135 → -9y = -12x + 135 → y = 12/9 - 15

The perpendicular slope is a slope that is the reciprocal and is the opposite charge of the given slope.

So the answer would be -9/12, which is 12/9 but flipped upside down and is negative.

The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, squared, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=

Answers

Answer:

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

Step-by-step explanation:

Given the polynomial function p(x)=x^3+7x^2-36

We are to write it as a product of its linear factor

Assuming the value of x that will make the polynomial p(x) to be zero

Let x = 2

P(2) = 2³+7(2)²-36

P(2) = 8+7(4)-36

P(2) = 8+28-36

P(2) = 0

Since p(2) = 0 hence x-2 is one of the linear factors

Also assume x = -3

P(-3) = (-3)³+7(-3)²-36

P(-3) = -27+7(9)-36

P(-3) = -27+63-36

P(-3) = 36-36

P(-3) = 0

Since p(-3) = 0, hence x+3 is also a factor

The two linear pair are (x-2)(x+3)

(x-2)(x+3) = x²+3x-2x-6

(x-2)(x+3) = x²+x-6

To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.

x^3+7x^2-36/x²+x-6 = x+6

Hence the third linear factor is x+6

x^3+7x^2-36 = (x-2)(x+3)(x+6)

Answer:

x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)

Step-by-step explanation:

Here we want to rewrite the polynomial

P(x) = x^3 + 7x^2 - 36

As a product of linear factors given that we have one of the roots already as (x + 3)

What we shall do here is to divide the polynomial by x + 3

Please check attachment for long polynomial division

From the division, the other factor is x^2 + 4x -12

So we can rewrite the polynomial as;

x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)

So let’s now write x^2 + 4x -12 as a product of its linear factors

x^2 + 4x -12 = x^2 + 6x -2x -12

= x(x + 6)-2(x + 6)

so we have;

(x -2)(x + 6)

Therefore;

x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)

Irma is just learning to play the Happy Fairies video game. In the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens. Irma had a total of – 5 points. Then, her fairy house fell over in the wind and she got – 3 points. How many total points does Irma have now?

Answers

Answer: -8 points

Step-by-step explanation:

From the question, we are informed that Irma is just learning to play the Happy Fairies video game and that in the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens.

We are told that Irma had a total of –5 points, then, her fairy house fell over in the wind and she got –3 points.

Her total points now will be the addition of -5 and -3. This will be:

= -5 + (-3)

= -5 - 3

= -8

Note that minus multiplied by plus is minus.

Answer: -8

Step-by-step explanation:

Is this equation an example of a literal equation? Why?

Answers

Answer:

yes this is...,.,.,.....

A pack of 8 pairs costs 9:80. What is the cost of one pair of socks?​

Answers

Answer:

1 1/2

Step-by-step explanation:

Answer:

$1.26

Step-by-step explanation:

  9.80/8 = 1.22500

1.22500 rounded up = 1.26

Find the vertex and the axis of symmetry of the graph of y=-6(x+4)^2 – 3.

Answers

Answer:

vertex = (- 4, - 3 ), equation is x = - 4

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = 6(x + 4)² - 3 ← is in vertex form

with (h, k ) = (- 4, 3 ) ← vertex

The equation of the axis of symmetry is a vertical line passing through the vertex, with equation

x = - 4

i need help with this geometry

Answers

The answer would be C because it is askeing

What’s 5 divided by 6.2

Answers

5 divided by 6.2 is 0.80

Answer:

8

Step-by-step explanation:

Because you need to round 0.8064516129 to the nearest tenth

Examine the diagram. It is not drawn to scale.
In the diagram shown, mZ1 = 30° and m25 = 120°.
What is the sum of the measures of 24, 25, and 26?
4
1
2
5
on
degrees
Identify the following angle measures.
m22= v degrees
m24 =
v degrees
3
3
m26 =
v degrees
6

Answers

Answer:

Examine the diagram. It is not drawn to scale.

A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6.

In the diagram shown, m∠1 = 30° and m∠5 = 120°.

What is the sum of the measures of ∠4, ∠5, and ∠6?

✔ 360

degrees

Identify the following angle measures.

m∠2 =  

✔ 60

degrees

m∠4 =  

✔ 150

degrees

m∠6 =  

✔ 90

degrees

Step-by-step explanation:

Examine the diagram. It is not drawn to scale.

In the diagram shown, mZ1 = 30° and m25 = 120°.

What is the sum of the measures of 24, 25, and 26?

4

1

2

5

on

degrees

Identify the following angle measures.

m22= v degrees

m24 =

v degrees

3

3

m26 =

v degrees

6

I HOPE YOU GET IT RIGHT IK ITS THE ANSWERS I ALWAYS DO IT!!!!!!❤

The values of m∠2, m∠4 and m∠6 are 60°, 150° and 90° respectively.

What is an angle?

An angle is formed from the intersection of two or more lines. Angles less than 90 degrees are called acute angles, angles greater than 90° are called obtuse angles while angles with a measure of 90° are called right angles.

From the diagram:

m∠1 + m∠4 = 180° (sum of angles in a straight line)

30 + m∠4 = 180°

m∠4 = 150°

m∠2 + m∠5 = 180° (sum of angles in a straight line)

120 + m∠2 = 180°

m∠2 = 60°

m∠1 + m∠2 + m∠3 = 180° (sum of angles in a triangle)

30 + 60 +  m∠3 = 180°

m∠3 = 90

m∠3 + m∠6 = 180° (sum of angles in a straight line)

90 + m∠6 = 180°

m∠6 = 90°

The values of m∠2, m∠4 and m∠6 are 60°, 150° and 90° respectively.

Find out more on angle at: https://brainly.com/question/25770607

HELP pleaseee i’m beggingggg

Answers

Answer:

35 1/3°54 2/3°

Step-by-step explanation:

Angle AOB and BOC create a complementary angle. This means when two angles sum up to 90°. We can write an equation for this problem;

(x + 8) + 2x = 90

~Remove parenthesis

x + 8 + 2x = 90

~Combine like terms

3x + 8 = 90

~Subtract 8 to both sides

3x = 82

~Divide 3 to both sides

x = 82/3 or x = 27 1/3

Use what have for x to solve for the angle measures.

Angle AOB:

x + 8

(27 1/3) + 8

35 1/3°

Angle BOC:

2x

2(27 1/3)

54 2/3°

Check.

35 1/3 + 54 2/3 = 90°

Best of Luck!

0.72...0.702 put < or > between the numbers in each pair​

Answers

Answer:

0.72>0.702

Step-by-step explanation:

In JL, K is the midpoint. The coordinates of J are (2, 2), and the
coordinates of Kare (10, 11). What are the coordinates of L?

Answers

(6,6.5) u can do the math simply

1/3 multiplied by 1 1/2

Answers

Answer:

0.5

Step-by-step explanation:

Please help! I’ll give brainliest to anybody who answers correctly!

Answers

I think you add 3 to the second number

Factor the expression
x^2 − 14x + 45 completely.

Answers

Answer:

(x+5) (x+9)

Step-by-step explanation:

In order to the trinomial

x

2

+

14

x

+

45

Begin by finding the factors for the first term

x

2

=

x

x

Place those factors as the first term in each parenthesis

(

x

_

)

(

x

_

)

Since both signs of the trinomial are positive you will be adding the factors and both signs will be positive.

(

x

+

_

)

(

x

+

_

)

Now determine the factors of the third term

45

=

1

45

,

3

15

,

5

9

We need the factors that will add up to the middle term

14

=

5

+

9

Place these factors as the second term in each of the parenthesis.

(

x

+

5

)

(

x

+

9

)

(x-5)(x-9) is the factored form of the expression  x²-14x+45

The given expression is x²-14x+45

x is the variable in the expression

x square minus forteen times of x plus forty five

Plus and minus are operators in  the expression

x²-9x-5x+45

Now let factor out the expression

x(x-9)-5(x-9)

(x-5)(x-9)

Hence, the factored form of the expression is (x-5)(x-9)

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

Plz help me
Find the rational approximation of square root 7 to the nearest tenth.

Answers

Answer:

2.6

Step-by-step explanation:

Plz help me I’ll give brainliest!!

Answers

Answer:

k = 1

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (4, 1 )

with k = 1

5 ice cream cones cost $7.25. At this rate, how much do
3 ice cream cones cost? Plus what is the cost per ice cream cone

Answers

Answer:

i

Step-by-step explanation:

. 7.25 divided by 3 is 2.416666666 on the calulater. and the cost per cone is 1.45. so each cone is 1.45 per each and the cost per cone of 3 is 2.416666666 for the calulater. I hoped I helped if I didn't I'm sorry

For your trip to Austin you know you are going to travel 182 miles and your car can do that in 14 gallons. How far can your car travel on 8 gallons of gas?​

Answers

First, you need to create a unit rate.
The car travels 182 miles on 14 gallons of gas.
To create a unit rate, you would have to divide 14 by 182.

182 mi 13 mi
———— = ———-
14 gal 1 gal

Then, you would need to multiply the numerator and denominator by 8 because the question is asking how far the car can travel on 8 gallons of gas.

13 mi x 8 104 mi
——— = ————
1 gal x 8 8 gal

So, your answer is the car travels 104 miles on 8 gallons of gas.

what rational number lies between 4/3 and 1.666666​

Answers

Answer:

−26 and −16 is −14.

Step-by-step explanation:

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