Given a+b=7 and a–b=3, find:

2^a*2^b

Answer:

x=√-16

Step-by-step explanation:

Since x^2+16=0

Substrate 16

X^2=-16

Square root of both sides

X=√-16

So therefore the final answer is

X=√-16

Answer:

25155000

Step-by-step explanation:

by formula

100

2. 5850000×4.3

100

100

3. 25155000

Arnold will have to pay $689546.98 after 30 years of taking out a loan.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The given problem is the case of compound interest.

The values for different parameters are as follows,

P = 195000

r = 4.3%

And t = 30 years

Now, substitute all the corresponding values in the expression for amount given below as,

A = P(1 + r/100)ⁿ

   = 195000(1 + 4.3/100)³⁰

   = 689546.98

Hence, the total amount to be paid after 30 years is given as $689546.98.

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Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

[tex]a_n=a_1\cdot r^{n-1}[/tex]

[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]

[tex]\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}[/tex]

[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]

[tex]r=\frac{3}{4}[/tex]

[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]

[tex]a_1=8[/tex]

[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]

[tex]a_n=8\left(\frac{3}{4}\right)^{n-1}[/tex]

[tex]\mathrm{Geometric\:sequence\:sum\:formula:}[/tex]

[tex]a_1\frac{1-r^n}{1-r}[/tex]

[tex]\mathrm{Plug\:in\:the\:values:}[/tex]

[tex]n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}[/tex]

[tex]=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]

[tex]=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}[/tex]

[tex]=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

[tex]=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}[/tex]

[tex]=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32[/tex]

[tex]=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}[/tex]

[tex]=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}[/tex]               ∵ [tex]\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}[/tex]

[tex]=32\cdot \frac{4^{25}-3^{25}}{4^{25}}[/tex]

[tex]=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}[/tex]

[tex]=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}[/tex]        ∵ [tex]\mathrm{Factor}\:32:\ 2^5[/tex],  [tex]\mathrm{Factor}\:4^{25}:\ 2^{50}[/tex]

so

[tex]=\frac{4^{25}-3^{25}}{2^{45}}[/tex]        ∵ [tex]\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}[/tex]

[tex]=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}[/tex]      

[tex]=32-\frac{3^{25}}{2^{45}}[/tex]            ∵  [tex]\frac{4^{25}}{2^{45}}=32[/tex]

[tex]=32-0.024[/tex]        ∵  [tex]\frac{3^{25}}{2^{45}}=0.024[/tex]

[tex]=31.98[/tex]            

Therefore, the sum of the first 25 terms in this geometric series: 31.98

Answer: The radius is 11.5 meters (to the nearest tenth)

Step-by-step explanation: The circle with center H has an arc TX that measures 24 meters, and also the angle subtended by YX equals 120°.

The length of an arc is given b the formula;

Length of arc = (∅/360) x 2πr

Where the length of the arc is 24 and ∅ is 120, the formula becomes;

24 = (120/360) x 2(3.14) r

24 = (1/3) x 6.28 r

By cross multiplication we now have,

(24 x 3)/6.28 = r

72/6.28 = r

11.4649 = r

r ≈ 11.5

Therefore, the radius is approximately 11.5 meters

Answer:

The image will be congruent to the pre-image because n = 1.

Answer:

Awsner number 2

Step-by-step explanation:

[tex]width: 2x^2-3\\height:7\\S=7(2x^2-3)\\S=14x^2-21[/tex]

Answer:

each clinic serves about 300 people

Step-by-step explanation:

Population of 24742 is served by 83 clinics

Then each clinic will serve

24742/83 =298.157

≈ 300

Answer:

c. 300

Step-by-step explanation:

24,742/83

298.0963855

Approximately 300

Answer:

t = 10n + 25

Step-by-step explanation:

At the end of n weeks, the total amount that Melissa would have can be found by the function, t = 25 + 10n.

Melissa made $25 from washing her mother's car and keeps it aside.

She then makes $10 every week. This means that in n number of weeks, the amount she would have made from chores is:

= Amount per week x number of weeks

= 10 x n

= 10n

The total she would then have in n weeks is:

= Amount saved from mother + Amount earned from chores in n weeks

= 25 + 10n

This total is t, so the total function is t = 25 + 10n.

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Answer:

Kayla will not have enough because the total will be $225.67

Step-by-step explanation:

2 * 9.98 = 19.96

3 * 24.99 = 74.97

19.96 + 25.99 = 45.95

45.95 + 74.97 = 120.92

120.92 + 89.99 = 210.91

0.07 * 210.91 = 14.76

210.91 + 14.76 = 225.67

Kayla will not have enough because the total will be $225.67

Since there is a budget of $200. The sales tax rate is 7%

Also, the following items should be purchased

2 T-shirts, $9.98 each

1 pair of pants, $25.99

3 dresses, $24.99 each

1 pair of shoes, $89.99

So, the calculations should be

2 of 9.98 = 19.96

3 of 24.99 = 74.97

Now the total should be

19.96 + 25.99 = 45.95

45.95 + 74.97 = 120.92

120.92 + 89.99 = 210.91

0.07 of 210.91 = 14.76

And, finally

210.91 + 14.76 = 225.67

Therefore, Kayla will not have enough because the total will be $225.67

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Answer:

- 6 - 3i

Step-by-step explanation:

Given

(- 3 - 2i) - (3 + i) ← distribute both parenthesis

= - 3 - 2i - 3 - i ← collect like terms

= - 6 - 3i

An employee at a cell phone store sold 40 phones for $450 each, totaling $18,000 in sales. Based on her commission rate of 2.5%, she earns $450 in commission for the week.

The subject of this question is how to calculate the employee's commission based on her sales. First, we need to calculate the total sales the employee made. She sold 40 phones at $450 each, so her total sales would be 40 * $450 = $18,000.

Next, we need to figure out what 2.5% of her total sales is because this is her commission rate. The calculation would be $18,000 * 2.5/100 = $450.

So, the employee's commission for this week is $450.

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Answer:

4/5

Step-by-step explanation:

To find the slope given two points

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

   = (-1 -3)/(-3 -2)

    =-4/-5

    = 4/5

We can use the points (2,3) and (-3,-1) to solve.

Slope formula: y2-y1/x2-x1

= -1-3/-3-2

= -4/-5

= 4/5

Best of Luck!

Answer: 9ft² and 12.25ft²

Step-by-step explanation:

The range of the possible areas will be 9 square feet and 12.25 square feet. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space.

On a coordinate plane, the x-axis is labeled Side length and the y-axis is labeled Perimeter or area.

A line representing the perimeter goes through points (0, 0), (1, 4), (2, 8), (3, 12).

Then the equation of line will be

y = [(12 – 8) / (3 – 2)]x

y = 4x

A curved line representing the area goes through points (0, 0), (2, 4), (3, 9), and (4, 16).

y = x²

Andrew wants to build a square garden, and needs to determine how much area he has for planting.

The perimeter of the garden is between 12 and 14 feet.

Then the value of the side length corresponding to 12 and 14 will be

For y = 12, we have

12 = 4x

 x = 3

Then the area will be

y = 3²

y = 9 square feet

For y = 14, we have

14= 4x

 x = 3.5

Then the area will be

y = 3.5²

y = 12.25 square feet

Then the range of the possible areas will be 9 square feet and 12.25 square feet.

Then the correct option is B.

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Answer:

$5.5 per hour

Step-by-step explanation:

You divide the cost  by the number of hours

Answer:

About 10 minutes, which is 1/6 of an hour.

Step-by-step explanation:

Answer:

-3r -16

Step-by-step explanation:

2 (r - 3) - 5(r + 2)

Distribute

2r-6 - 5r - 10

Combine like terms

-3r -16

Answer:

lateral surface area means surface area of vertical walls.

there are 3 vertical walls and each is a rectangle.

hence

lateral surface area = 3 × area of one wall

= 3× ( 8×5 )

= 3 × 40

= 120 square units

Answer: x=1,y=0

Step-by-step explanation:

X-2y=1.....equation 1

2x-y=2.....equation 2

X=1+2y.......equation 3

Substitute equation 3into 2

2(1+2y)-y=2

2+4y-y=2

2+3y=2

3y=2-2

3y=0

Y=0/3

Y=0

Substitute for y=0 in equation 1

X-2y=1

X-2(0)=1

X-0=1

X=1

X=1 & Y=0

Answer:

x=1

y=0

Step-by-step explanation:

Answer:

answer is a

Step-by-step explanation:

the volume is everything on the inside of the tank

surface area would only be the amount of water it take of cover one side

area would just be the size of the glass on bottom

the perimeter would just be the length of all four edges of each side of the fish tank

For the maximum amount of water it takes to fill a rectangular fish tank, we need to know the volume of the fish tank.

Option A is the correct answer.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The volume of any container gives us the maximum amount the container can hold.

Now,

For the maximum amount of water it takes to fill a rectangular fish tank, we need to know the volume of the fish tank.

Thus,

The volume of the fish tank gives us the maximum amount it can hold.

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Answer:

y - 1 = -4(x+3)

Step-by-step explanation:

We will use the point slope form of a line

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is the point

y - 1 = -4(x--3)

y - 1 = -4(x+3)

Answer:

40

Step-by-step explanation:

Answer: D) 1/14

Work Shown:

There is 1 orange marble out of 7 total. The probability of picking an orange marble is 1/7. Let A = 1/7 which we'll use later.

The probability of flipping tails is 1/2 because 1 side is tails out of 2 sides total. Let B = 1/2

Multiply A and B

A*B = (1/7)*(1/2) = (1*1)/(7*2) = 1/14

This represents the probability of getting an orange marble and flipping tails.

We are able to multiply the probabilities because the two events (picking a marble and flipping a coin) are independent.

Answer:

The answer would 1/14 :)

Step-by-step explanation:

Answer:

what are the statements lol

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

There are only two angle measures here, an angle, a bunch of congruent copies, and its supplement, with a bunch of congruent copies.

∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7 are all supplementary to ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8

Answer: 2(x + 2) + 2 = 2(x + 3) + 1

Steps:

2x + 6 = 2x + 7

Subtract 6 from both sides

2x + 6 - 6 = 2x + 7 - 6

Simplify

2x = 2x + 1

Subtract 2x from both sides

2x - 2x = 2x + 1 - 2x

Simplify

0 = 1

The sides are not equal.

NO SOLUTION

Answer:

1, 2, and 5

Step-by-step explanation:

Answer:

There were 25 pizzas made last week.

Step-by-step explanation:

It is given that 64% of the pizzas had extra cheese and 16 pizzas had extra cheese. So it means that 64% is equals to 16 pizzas. In order to find how many pizzas were made, you have to find the remaining percentage of pizzas without extra cheese by subtracting 64% from 100% :

100 - 64 = 36 % of pizzas without extra cheese

64 % = 16 pizzas

1 % = 1/4 pizza

36 % = 9 pizzas

We have found out that 9 pizzas were made without extra cheese. The total pizzas were made last week is 25 pizzas (including extra cheese and no extra cheese) :

Total = Extra Cheese + No extra cheese

= 16 + 9

= 25 pizzas

Answer:

The solution is D, -11.

Step-by-step explanation:

Answer:

8 ads

Step-by-step explanation:

To start off, we know we have a budget of $500 which means we cannot go above that amount. Ads cost $75 each but in our case they are now 20% cheaper. Lets figure out the new price of the ads. Remember to change 20% into its decimal form (20% -> 0.2)

75 x 0.2 = 15

Now we subtract 15 from 75 to get our new ad price.

75 - 15 = 60

Now to figure out how many ads we can get with a budget of $500, we simply divide 500 by 60. Don't forget to round the answer to the nearest whole number since we cannot go over our budget.

500 / 60 = 8 ads

The measure of angle VU is 240°.

Given that arc SV has a measure of **120°** and angle STV is **82°**, we can find the measure of angle VU.

1. The central angle STV is equal to the measure of arc SV. Therefore, ∠STV = 120°.

2. The sum of angles around a point (360°) is equal to the sum of the central angle and the inscribed angle. So, ∠VU + ∠STV = 360°.

3. Solving for ∠VU:

  - ∠VU + 120° = 360°

  - ∠VU = 360° - 120°

  - ∠VU = 240°

Therefore, the measure of angle VU is 240°.