Kaltlin has a patio that is in the shape of a rectangle with an area of 1500 ft?. She has decided to expand the patio so that it can hold mpatio will be a larger rectangle. The current patio has a length of 50 ft and a width of 30 ft. She plans on making the new length 2 timesthe new width 2 times the current width.

The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is:

f(x) = 3x⁵

The domain of the function: D = all real number

The range of the function: R = all real number

x-intercept = 0

y-intercept = 0

Increasing interval: x ∈ [0, ∞)

Decreaing interval: x ∈ (-∞, 0]

Symmetry = The function is not symmetric

End behavior:

x → ∞, y →∞

x → -∞, y → -∞

Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

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The dimensions of this cuboid are 2 cm, 11 cm, and 17 cm respectively.

Mathematically, the volume of a cuboid can be calculated by using this following formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula, we have;

Volume = 2 × (x + 3) × (x + 9)

374 = 2 × (x² + 9x + 3x + 27)

374 = 2 × (x² + 12x + 27)

Dividing both sides by 2, we have:

187 = x² + 12x + 27

Rearranging the equation, we have:

x² + 12x + 27 - 187 = 0

x² + 12x - 160 = 0

Next, we would solve the quadratic equation by using the factorization method as follows:

x² + 12x - 160 = 0

x² + 20x - 8x - 160 = 0

x(x + 20) - 8(x + 20) = 0

(x - 8)(x + 20) = 0

x = 8 or x = -20

Since the dimensions cannot be negative, the value of x is equal to 8.

Check:

x² + 12x - 160 = 0

8² + 12(8) - 160 = 0

64 + 96 - 160 = 0

160 - 160 = 0 (True).

For the dimensions, we have:

Width = x + 3 = 8 + 3 = 11 cm.

Height = x + 9 = 8 + 9 = 17 cm.

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Answer:

3

Step-by-step explanation:

Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once

Answer:

five blocks away

Step-by-step explanation:

because 4 +1 =5

please if it is wrong let me know so I can correct

Answer: y = -3x - 2

Step-by-step explanation:

slope intercept form: y=mx+b

Answer: 0.01 more

Step-by-step explanation:

60% sure!

Answer: Following the pattern, the prediction for the next numbers is as follows:

Confirmation by calculator use:

Therefore the predicted numbers are the correct one.

Answer:

A

Step-by-step explanation:

When distributing, you multiply the outside number to each number in the inside as well as looking at the operation inside the parenthesis. Hope this helps!

The mistake is that, what we have to prove is taken as a known fact.

A theorem is a statement that can be proved or has already been proved true by a logical argument.

"there is no smallest negative integer" is taken as a fact

but it is the part of the theorem that we have to prove,

Therefore, we can conclude that the mistake in the given proof is what we have to prove is taken as a known fact.

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Answer: 4x+6/x^2

Step-by-step explanation:

The total number of pages in the book is 180.

Total number of pages:

It refers the number of pages in the prescribed book.

And if we want to find the total number of pages, then we have to add the read pages and the remaining pages.

Given,

Jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday.

Here we need to find the total number of pages in the book.

Let us consider x be the number of pages in the book.

The portion of book read by Jimmy on Monday is 2/15

The portion of book read by Jimmy on Tuesday is 1/3

The portion of book read by Jimmy on Wednesday is 2/9

The portion of book read by Jimmy on Thursday is 3/4

And the remaining pages to read on Friday is 14

So, the total of all is:

=> x (2/15 + 1/3 + 2/9)

=> x (6 + 15 + 10)/45

=> 31x/45

So, for Thursdays, he reads 3/4 of the remainder of the book.

He has (1 - 31/45)x left that is 14x/45.

So, he reads 3/4 of this; which is

=> 3/4(14x/45) = 42/180x.

Therefore, until Thursday he has read

=> 31/45x + 42/180x.

We know that here 180 would be a common denominator;

Now we have to convert these fractions,

Then we have,

124/180x + 42/180x = 166/180x

Up to this point, he has 14 pages left;

Therefore, this means he has read 14 pages less than x, the total number of pages.

Then the given equation is written as,

166/180x = x-14

0 = 14/180x - 14

Adding 14 to each side gives us, then we get,

14 = 14/180x

14(180)/14 = x

180 = x

Therefore, there are 180 pages in the book.

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Answer:

Step-by-step explanationFrom your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.:

The original price of the sweater is $48.

Given that, Kate used a 30% off coupon to purchase a sweater.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The cost of sweater is $33.60

Let the original price of the sweater be x

Now, x-30% of x=33.60

⇒ x-30x/100 = 33.60

⇒ x -3x/10 =33.60

⇒ 7x/10 =33.60

⇒ 7x=336.0

⇒ x=48

Therefore, the original price of the sweater is $48.

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Answer:

y=3/5x-7

Step-by-step explanation:

when lines are parallel they have the same slope and the slope of the first line was 3/5

Hello!

Let's consider the equation given:

 ⇒the coefficient before the x is the slope

When lines are parallel:

 ⇒the slopes are equal

Since the line given has a slope of 3/5

 ⇒ the line parallel is [tex]y = \dfrac{3}{5} x - 7[/tex]    <==Answer

Hope that helps!

Given:

Radius of circular swimming pool = 15ft

Radius of the path around the pool = 3ft

radius of outer edge of the pool = 15 + 3 = 18ft

To find the circumference of the outer edge of the path around the pool, use the formula below:

where,

r = 18 ft

pi = 3.14

Thus, we have:

Therefore, the circumference of the outer edge of the path around the pool is 113.04 ft

ANSWER:

113.04 ft

The time that both gongs will strike together again after striking simultaneously at 12 noon is 2 : 34 pm.

The time the gongs will strike together again can be determined by calculating the least common multiple of 22 and 77. The multiple of a number is the product of a number and another number. For example, a multiple of 2 is 10. The least common multiple is the smallest multiple that is common to two or more numbers.

The least common multiple would be determined using the prime factorisation method.

Prime factors of 22 = 2 x 11

Prime factors of 77 = 7 x 11

The least common multiple = 2 x 7 x 11 = 154

The next time both gongs would strike at the same time is 154 minutes or 2 hours 34 minutes

12 noon + 2 hours + 34 minutes = 2 : 34 pm

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Answer:

x=1

Step-by-step explanation:

1. distribute through the parentheses

8x-6=2

2. Combine like terms

8x=8

3. Divide by 8

x=1

Hello!

Let's solve:

  [tex]\text{Copy down the equation}\\2(4x-3)=2\\\\\text{Multiply 2 into the equation in the parentheses}\\8x - 6 = 2\\\\\text{Add 6 to both sides of the equation}\\8x-6+6=2+6\\8x=8\\\\\text{Divide by 8 on both sides}\\\dfrac{8x}{8} =\dfrac{8}{8} \\\\x=1[/tex]

Answer: x = 1

Hope that helps!

Answer:

Step-by-step explanation:

u will have 1 niche of water in 2 hours

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on then the 7th term of the series 6, 12, 24, ........... is 384

Let the first term (a) be 6.

The given series is in geometric progression,

we know that, 7th term = a × [tex]$$r^{7-1}[/tex] = a[tex]$ r^6[/tex]= [tex]6 \times(2)^{6}[/tex] = 384

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on.

Here, a is the first term and r is the common ratio.

The nth term of a Geometric Progression Formulas is [tex]$T_n=a r^{n-1}$[/tex]

Common ratio [tex]$=\mathrm{r}=T_n / T_{n-1}$[/tex]

Therefore, the correct answer is 384.

The complete question is:

Find the 7th term of the series 6,12,24,....?

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Answer:

Let b represent the number of hours babysitting, and let l be the number of hours landscaping. We have this system of equations:

[tex]7b + 8l = 134[/tex]

[tex]b = l + 2[/tex]

The value of k is -1 of tangent over the parabola.

Equation of a line: y = (2 + x - k) ÷ 2, in line form of y = mx + c.

Equation of the parabola: x² = (y - 6x - 3) ÷ 2

Given,

y = (x ÷ 2) + (1) - (k ÷ 2)

where, m = 1 ÷ 2 and c = (1 - k) ÷ 2

For parabola equation in parabola form,

y = 2x² + 6x - 3

y = 2(x² + 3x - n) - 3

n = (b ÷ 2)²

n = (6 ÷ 2)²

n = 9

y = 2(x² + 3x - 9 + 9) - 3

y = 2(x² + 3x + 9) - 9 - 3

y = 2(x² + 3x + 9) - 12

y = 2(x + 3)² - 12, Hence the parabola equation is in vertex form.

Now, comparing the above vertex form with the parabola equation,

x² = 4ay

(x + 3)² = (y ÷ 2) + 6

where a = 1 ÷ 2

Now using the condition of tangency c = a ÷ m

c = (1 - k) ÷ 2

m = 1 ÷ 2

a = 1 ÷ 2

(1 - k) ÷ 2 = (1 ÷ 2) ÷ (1 ÷ 2)

1 - k = 2

k = -1

Therefore, the value of k is -1.

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If you use excel solver for this analysis, the number of different variable cells should you use are 12

Option- C

The right answer is 12.

Given that,

There are four buses that transport children to the district's three main schools. You are aware of the price of transporting each student to each school.

Since there are four buses and three schools according to the supplied description, each bus has three school alternatives, thus 4*3=12, bearing in mind that there must be the least expensive route to transport all of the students to their schools.

There must therefore be 12 separate variable cells employed.

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You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

C = 2πr

If we substitute 125ft for r and use 3.14 to approximate π

we get a circumference of:

C = 2 * 3.14 * 125

C = 6.28 *125

C = 785ft

We can now convert the circumference in feet to inches as follow;

As we know that 1ft = 12inches

∴ 785ft = 12(785) inches = 9,420 inches.

To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:

=[tex] 9,420in\ X \ \frac{1\ flower}{6 in} [/tex]

=[tex] \frac{9,420}{6 } \ flower [/tex]

=1,570 flowers

Hence You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

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The interest rate for the loan is 20%.

The interest rate represents the percentage or the proportion of the interest over the total loan.

The interest is the finance charge for the credit extended by the pay lender.

The interest rate, R = Interest x 100/Principal x Time, where the simple interest equals principal x rate x time.

The total amount borrowed = $500

The total finance charge = $100

The period of the loan = 1 year

The interest rate

= $100 x 100/$500 x 1

= 20%

Thus, the pay lender is charging an interest rate of 20% per annum.

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What is the interest rate?

For a random sample of 130 mortgages with 20 delinquents on their current payment, the mean of the sampling distribution of the proportion of delinquent payments is not possible to say because population proportion is not known.

A random sample refers to a randomly selected subset of the population. In random sampling, each member of the population has an equal chance of selection, reducing the risk of selection bias. Random sampling ensures that the conclusion drawn from the sample should approximate the results obtained if entire population had been measured. The mean of the sampling distribution is the mean of the population from which results were sampled. As the population proportion (fraction of  the population with certain characteristic) is unknown, the mean cannot be determined.

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The answer to the given expression 2⁴· [(2²·2⁴)⁻³/2¹⁴] would be 2⁻²⁸ which is determined by the laws of the exponents.

The product rule is an exponent rule that states that when you multiply similar bases, the add exponents.

For example, (a²)·(a³) = a²⁺³ = a⁵

In the power rule, elevating one exponent to a second multiplies the exponents.

For example, (a²)³ = a²ˣ³ = a⁶

The given expression would be as

⇒ 2⁴· [(2²·2⁴)⁻³/2¹⁴]

As per the laws of the exponents, the solution would be as :

⇒ 2⁴· [(2²⁺⁴)⁻³/2¹⁴]

⇒ 2⁴· [(2⁶)⁻³/2¹⁴]

⇒ 2⁴· (2⁻¹⁸/2¹⁴)

⇒ 2⁴· (2⁻¹⁸⁻¹⁴)

⇒ 2⁴· (2⁻³²)

⇒ 2⁴⁻³²

⇒ 2⁻²⁸

Therefore, the answer would be 2⁻²⁸.

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The correct answer to the question would be:

D. The manufacturer tests every 500th smartphone off the production line.

When the radius of a cylinder is 6 ft. and it is increasing at the rate of 2 feet per minute, its volume will change at rate of 509.14 ft³/minute.

Given a cylinder with:

r = radius

h = height = 3/2 . r

The volume of the cylinder is:

V = πr².h

Substitute h = 3/2 . r,

V = πr².(3/2 r)

V = 3/2 . πr³

Take the derivative with respect to t:

dV/dt = 9/2 . πr²  . dr/dt

Substitute dr/dt = 2 ft./minute and r = 6 ft.,

dV/dt = 9/2 . π.6²  

dV/dt = 9/2 . π.6²  = 509.14 ft³/minute.

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Answer:

[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

Step-by-step explanation: