Riley is saving up to buy a new television. She needs a total of $1,164.38. Riley has saved $200.66 already and earns $80.31 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?

The value of [tex]x[/tex] is 29.

The formulae for the surface area ([tex]A_{s}[/tex]) and volume ([tex]V[/tex]) are, respectively:

[tex]A_{s} = 2\cdot (h\cdot l + w\cdot l + h\cdot w)[/tex] (1)

[tex]V = w\cdot h \cdot l[/tex] (2)

Where:

According to the statement, we must equalize (1) and (2) and substitute the remaining variables:

[tex]2\cdot (h\cdot l + w\cdot l + h\cdot w) = w\cdot h\cdot l[/tex]

[tex]2\cdot h\cdot l + 2\cdot w \cdot l + 2\cdot h\cdot w = w \cdot h \cdot l[/tex]

[tex]2\cdot \log_{2}x\cdot \log_{4}x+2\cdot \log_{3}x\cdot \log_{4}x+2\cdot \log_{2}x\cdot \log_{3}x = \log_{2}x\cdot \log_{3}x\cdot \log_{4}x[/tex]

By applying logarithm properties, we simplify the expression:

[tex]2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right) = \log_{2}x \cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right)[/tex]

[tex]2\cdot \left[\frac{1}{\log_{2}4}+\frac{1}{\log_{2}3\cdot \log_{2}4}+\frac{1}{\log_{2}3}\right] = \left(\frac{1}{\log_{2}3\cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]2\cdot \left(\frac{\log_{2}3+\log_{2}4+1}{\log_{2}3\cdot \log_{2}4} \right) = \left(\frac{1}{\log_{2}3 \cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]\log_{2}x = 2\cdot (\log_{2}3 + \log_{2}4+1)[/tex]

[tex]\log_{2}x = \log_{2}9 + \log_{2}16 +2[/tex]

[tex]x = 9 + 16 + 4[/tex]

[tex]x = 29[/tex]

The value of [tex]x[/tex] is 29.

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Nota - The statement of this question presents typing mistakes and is also incomplete, the corrected form is presented below:

A right rectangular prism whose surface area and volume are numerically equal has edge lengths [tex]\log_{2} x[/tex] (height), [tex]\log_{3}x[/tex] (width) and [tex]\log_{4}x[/tex] (length). What is [tex]x[/tex]?

Answer:

M = -2 1/4

Step-by-step explanation:

You can use the formula y2 - y1 / x2 - x1 to get your answer.

y2 is 18 and y1 is 9. x2 is 6 and x1 is 10 so plugging that into the formula above you will get 18 - 9 / 6 - 10.

18 - 9 is 9 and 6 - 10 is -4

9/-4 = M (M is short for slope)

M = -2 1/4

Hope this worked for you.

Answer:

1st , 2nd , and 4th

Step-by-step explanation:

Answer:

7.22 x 10^5

Step-by-step explanation:

Remember that the decimal is always to the right of the ones place.

1. Move it one place to the left and multiply by 10 to compensate.

2. Move it two places to left and multiply by 10^2.

3. Move the decimal point three times and multiply 10^3 to compensate, and the pattern continues until you reach the very last digit, the 7.

4. Numbers after the 7 that are not zeros will be after the decimal point.

so, 7.22 x 10^5

Answer:

(2;5)

Step-by-step explanation:

Elimination:

Let's first multiply the first by 2 to clear fractions and write them both in standard form:

[tex]\left\{ {x-2y=-8} \atop {2x+y=9}} \right. \\[/tex]

Eliminate x: Multiply the first by 2, then subtract the equations:

[tex]2I-II: 2x-4y-2x-y=-16-9\\-5y=-25 \rightarrow y= 5[/tex]

Eliminate y: Multiply the second by 2, then add equations:

[tex]I+2II: x-2y +4x+2y = -8+18\\5x=10 \rightarrow x=2[/tex]

Subtsitution

Solve the first for y (oh, what a coincidence, it's done already!) and replace the value in the second.

[tex]\frac12x +4 = -2x+9 \rightarrow \ x+8=-4x+18\\x+4x = 18-8 \rightarrow 5x=10 \rightarrow x=2[/tex]

Then let's plug this value into a convenient one - let's say, the first - and find y from there:

[tex]y=\frac12\cdot 2 +4\rightarrow y =1+4 \rightarrow y=5[/tex]

If anyone tries saying it's not substitution, bring the system in standard form, as you did for the elimination method, then solve again for y.

Answer:

2 months

Step-by-step explanation:

To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.

When solved, x=2. This means that after 2 months the cost of each will be the same.

Answer:

16, 32, and 64

Step-by-step explanation:

The number is being doubled every time.

Answer:

  £2.76

Step-by-step explanation:

The cost of Amy's purchase is ...

  16×(£0.14) = £2.24

Her change from £5.00 is ...

  £5.00 -2.24 = £2.76 . . . . Amy's change

Answer:

A & B

Step-by-step explanation:

A rational number is a number that can be written as a fraction or a terminating or repeating decimal. An irrational number is one that cannot be written as a fraction, or one that goes on forever without terminating or repeating in any way. Let's check all of our options and find the ones that are irrational.

Our first option (A) looks irrational! The "..." shows us that it goes on forever, and it doesn't look like it repeats. So this option is irrational.

Our next option is B, the square root of 24. What is the square root of 24? Well, if we look it up on a calculator, we get 4.89897948557..., and it looks like this one doesn't terminate or repeat either. So option B is also irrational.

Option C is the square root of 121. The square root of 121 is 11, which can be written as a fraction (11/1) and is a terminating decimal. So it's rational.

Our last option is D, and it is written already as a fraction, so we know for sure that it's rational. If we divide it out, we get 0.44444... with the 4 going on forever. It's a repeating decimal, and repeating decimals are rational.

So our final answers for which are irrational are A & B.

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;

Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.

Therefore,

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

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x + -13 = 22

Reorder the terms:

-13 + x = 22

Solving

-13 + x = 22

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.

-13 + 13 + x = 22 + 13

Combine like terms: -13 + 13 = 0

0 + x = 22 + 13

x = 22 + 13

Combine like terms: 22 + 13 = 35

x = 35

Simplifying

x = 35

Hi there!

a. A stratified sample can be used by dividing the tenants into two groups: those who have children and those who do not have children. Then, a Sample Random Sample FROM EACH stratum can be conducted for a total of 16 tenants surveyed.

b. Using a cluster sample in this situation could introduce undercoverage or selection bias if there is a distinction between those on some floors and those on others. For example, tenants on lower floors might be more opposed to a playground  (ex: noise, crowd, etc.) in comparison to those on higher floors.

Answer:

x = 5

Step-by-step explanation:

24 - 8x = -16

Subtract 24 from both sides.

-8x = -40

Divide both sides by -8.

x = 5

Answer:

5

Step-by-step explanation:

24 - 8x = -16

24 + 16 = 8x

8x = 40

x = 40/8

= 10/2

= 5

Answer:

You can use the exponential rule where

[tex](n^x)^y=n^{xy}[/tex]

Therefore,

[tex](a^3)^{-2}=a^{3*(-2)}=a^{-6}[/tex]

[tex]\\ \rm\leadsto (a^3)^{-2}[/tex]

[tex]\\ \rm\leadsto a^{-6}[/tex]

[tex]\\ \rm\leadsto \dfrac{1}{a^6}[/tex]

Answer:

EZ

Step-by-step explanation:

A. 15 Percent

B. 40 Percent

Answer:

A) 15% B) 40%

Step-by-step explanation:

Answer:

(4 + d) × 2

Step-by-step explanation:

Answer:

(serial number, model number)Step-by-step explanation:

Answer:

C=66, C=25 1/7

Step-by-step explanation:

i

C=pi(d)

C=22/7*21

C=66

ii

C=pi(d)

C=22/7*16

C=25 1/7

Answer:

x=5

Step-by-step explanation:

Step-by-step explanation:

sum of 2 angles on a straight line = 180°

therefore,

y + 120 = 180

y = 180 - 120 = 60

y = 60°

now apply angle sum property of triangle

now,

50 + x + y = 180

50 + x + 60 = 180

110 + x = 180

x = 180 - 110

x = 70

therefore, x = 70 & y = 60

hope this answer helps you dear! take care

Answer:

x = 70°

y = 60°

Step-by-step explanation:

hope it helps u

plzz plzz pLZZ MARK AS BRAINLIEST

[tex]\\ \sf\longmapsto (x-2)(x+1)[/tex]

[tex]\\ \sf\longmapsto x(x+1)-2(x+1)[/tex]

[tex]\\ \sf\longmapsto x^2+x-2x-2[/tex]

[tex]\\ \sf\longmapsto x^2-x-2[/tex]

Using similar triangles formed by the fence, and the house, the top of which the property line passes, the height of the house can be determined.

Reasons:

The given parameters are;

Height of the fence = 12 foot

Length of the shadow cast by the fence = 25 foot

Distance of the house from the property line = 60 feet

The maximum allowable height for the house.

Solution:

Using similar triangles, we have;

[tex]\displaystyle \frac{Height \ of \, fence}{Length \ of \ fence \ shadow} = \mathbf{\frac{Height \ of \, house}{Distance \ of \ house\ from \ property \ line}}[/tex]

Which gives;

[tex]\displaystyle \frac{12}{25} = \mathbf{\frac{Height \ of \, house}{60}}[/tex]

[tex]\displaystyle Height \ of \ house = \frac{12}{25} \times 60 = 28.8[/tex]

The height of the house = 28.8 feet

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Please find attached the drawing of the question created with MS Visio, obtained from a similar question online.

Answer:

>

Step-by-step explanation:

Squares eventually get bigger then when you multiply

Answer:

You can make as many as you want, infinitely smaller but you need to specify the size of the brownies

Step-by-step explanation:

Answer:

2400

Step-by-step explanation:

60(customers/day) x40(days) = 2400 customers in 40 days

Answer:

500: starting amount

(1 + 0.02): interest/growth rate

x: time

Step-by-step explanation:

we have 9x - 7 ≤ 28 + 4x

⇔9x - 4x ≤ 28 +7

⇔5x ≤ 35

⇔x ≤ 7

ok done. Thank to me :>

Answer:

1. 3 tacos per person

2. 8 chairs per table

3. 6 avocados per bag

Step-by-step explanation:

1. Divide 45 by 15 to get the unit rate: # of taco per person.

45 = 15x

45/15 = 15x/15

3 = x

3 tacos per person

2. Divide 72 by 9 to get the unit rate: # of chairs per table.

72 = 9x

72/9 = 9x/9

8 = x

8 chairs per table

3.  Divide 42 by 7 to get the unit rate: # of avocados per bag.

42 = 7x

42/7 = 7x/7

6 = x

6 avocados per bag

Answer:

see explanation

Step-by-step explanation:

The following statements are true

The domain of f(x) is all real numbers

The range of f(x) is all real numbers

f(2) = 4

locate x = 2 on the x- axis, go vertically up to meet the line at (2, 4 ) , then

f(2) = 4