Miss Kito is building a rectangular pen for her lea.She will use the side of her house for one wall of the pen;therefore she will not need any fencing on that side.On the other three sides, she will use special fencing that costs $12 per foot . She wants the entire enclosed area to be 2400 square feet. Lastly,she needs four corner that costs $5 each ?

Let x represent the length of each side of the pen perpendicular to the house and let y represent the length of the side of the pen parallel to the house.Write a function c(x) for the cost of the materials for the llama pen in terms of x. Simplify

Please explain and thank you

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

1.875

Step-by-step explanation:

mark brainlist pls

ANSWER

Date: 3/31/2013

• Initial principal: ,$100,000

• Interest: ,$3,980

• Ending principal: ,$103,980

Date: 3/31/2014

• Initial principal: ,$103,980

• Interest: ,$4,138.40

• Ending principal: ,$108,118.40

Date: 3/31/2015

• Initial principal: ,$108,118.40

• Interest: ,$4,303.11

• Ending principal: ,$112,421.51

Date: 3/31/2016

• Initial principal: ,$112,421.51

• Interest: ,$4,474.38

• Ending principal: ,$116,895.89

Date: 3/31/2017

• Initial principal: ,$116,895.89

• Interest: ,$4,652.46

• Ending principal: ,$121,548.35

Date: 3/31/2018

• Initial principal: ,$121,548.35

EXPLANATION

The initial balance is $100,000 and it is said that this balance grows by 3.98% each year. For the first year 3/31/2013 the values are:

• Initial principal: ,$100,000

• Interest: here we have to find 3.98% of the initial principal:

so the interest is $3,980

• Ending principal: is the initial amount plus the interest of the first year:

The ending principal for the first year is $103,980.

Now we have to do the same for the next 4 years. The initial principal will be the ending principal of the previous year. The interest is the 3.98% of the initial principal of the same year and the ending principal is the initial principal plus the interest. So for the second year 3/31/2014:

• Initial principal: ending principal of 2013 = ,$103,980

• Interest:

the interest is $4,138.40

• Ending principal:

the ending principal is $108,118.40

Next year, 2015:

• Initial principal: ending principal of 2014 = ,$108,118.40

• Interest: 3.98% of initial principal:

• Ending principal:

Year 2016:

• Initial principal: ending principal of 2015 = ,$112,421.51

• Interest:

• Ending principal:

Year 2017:

• Initial principal: ending principal of 2016 = ,$116,895.89

• Interest:

• Ending principal:

Finally, the initial principal of 2018 is the ending principal of 2017: $121,548.35

Answer: the answer would be that there is 20 cups in a gallon to find measurements like that ok so 4×4=16 so there is 4 cups in a quarter so it says 1 and a quarter of a gallon or 1 and 1/4 so 16 × 0.25=4 then now you can see that the calculation is correct so then 5×4=20 so 20cups is your answer

hope i helped

Step-by-step explanation:

Step-by-step explanation:

x- intercept is the x coordinate when y is 0

4x + 7(0) = 6

4x = 6

x = 1.5

(1.5, 0)

y- intercept is when x is 0

4(0) + 7y = 6

7y = 6

y = 6/7

( 0, 6/7)

I hope this helps!!!

Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

Step-by-step explanation:

only smile for youuuuuuuu

Answer:

I only smile for the money, lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

k - 4 = 3

   9

k/9  = 3(9) + 4

k = 31/9

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

8 + b = -5

  -4

8 + b = -5 (-4)

8 +  b = 20

b = 20 - 8

b = 12

k = 31/9

b = 12  

k - 4 = 3

  9

k/9  = 3(9) + 4

k = 31/9

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

8 + b = -5

 -4

8 + b = -5 (-4)

8 +  b = 20

b = 20 - 8

b = 12

Answer: 68y+106=36-y

Answer: (4,5,7) ,(7.2,-4),(-4,-7.2),(3,5.2)

Step-by-step explanation:

Answer:

it's C

Step-by-step explanation:

Answer:

I think the answer would be 96cm³

Step-by-step explanation:

have a great rest of ur dayy

Answer

35

Step-by-step explanation:

4.55/.13=35. Also, Heidi could do 35x13. I hope this helps!

Answer:

∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)

Step-by-step explanation:

Start with the Maclaurin series for cos x.

cos x = ∑ₙ₌₀°° (-1)ⁿ x²ⁿ / (2n)!

Substitute ⅓ x².

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓ x²)²ⁿ / (2n)!

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓)²ⁿ x⁴ⁿ / (2n)!

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)

Multiply by 8x.

8x cos (⅓ x²) = ∑ₙ₌₀°° 8x (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)

8x cos (⅓ x²) = ∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)

if you are given two points (x1,y1) and (x2,y2), you can calculate the slope using the following formula

we need to identify two points to use the formula above

we can see that, when x = 0 , then y = 5

and when x = -7 then y = 0

so the points are (0,5) and (-7,0)

we can use those points to replace them in the formula

Thus, the slope of the line is 5/7

Answer:

-15-13=

-28

-11-9-7

-27

Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.

An angle bisector is the line segment that bisects the angle into two equal halves.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

Ray BE is a bisector of angle CBA,

∠CBE = ∠EBA = 60°

∠EBD = ∠EBA - ∠DBA

∠EBD = 60 - 30 = 30

So,

∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]

Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements is true if ray BE is a bisector of angle CBA?

A. Ray BD is a bisector of angle CBA.

B. ∠EBD is congruent to ∠CBE.

C. Ray BE is a bisector of angle ABE.

D. ∠EBD is congruent to ∠DBA.

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

The rational function that might have the given graph is \(y = - \frac{x}{(x+1)\cdot (x-1) }\).

Step-by-step explanation:

This graph shows a rational function whose numerator is a first order polynomial and denominator is a second order, due to the presence of vertical asymptotes at \(x = -1\) and \(x = 1\). The lead coefficient of the numerator must be 1, since horizontal asymptote must be \(y = 0\) and intercept must be \(0\), since \(y(0) = 0\).

Then, we conclude that a rational function that might have the graph is:

\(y = - \frac{x}{(x+1)\cdot (x-1) }\) (1)

We present the proof that given function is appropriate.

Answer:

Step-by-step explanation:

28=-6x-12+2x

28+12=-6x-12+12+2x

40=-4x

x=-10

Answer:

x = -10

Step-by-step explanation:

\(28 = - 6x - 12 + 2x\)

Collect like-terms (also, when moving the terms to the other side, make sure to change their sign into the opposite of the previous one):

\(6x - 2x = - 12 - 28\)

\(4x = - 40\)

Divide both sides of the equation by 4 to make x the subject:

\(x = - 10\)

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

Answer:

The answer is Ahope this helps

Answer:

(A)  " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 .   That value is the unit rate. "

Step-by-step explanation:

Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

The values of the composite functions are

(1) (f + g)(x) = 4x² + 2x - 2

(2) (fg)(x) = 8x³ - 4x² - 2x + 1

(3) (fⁿ)(x) = (4x² - 1)ⁿ

From the question, we have the following functions that can be used in our computation:

f(x) = 4x² - 1

g(x) = 2x - 1

Using the above as a guide, we have the following:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x² - 1 + 2x - 1

Evaluate the like terms

(f + g)(x) = 4x² + 2x - 2

(fg)(x) = f(x) * g(x)

(fg)(x) = (4x² - 1) * (2x - 1)

Evaluate the products

(fg)(x) = 8x³ - 4x² - 2x + 1

(fⁿ)(x) = (f(x))ⁿ

So, we have

(fⁿ)(x) = (4x² - 1)ⁿ

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Answer:

0

Step-by-step explanation:

same numerator for that it is zero

Answer: A

Step-by-step explanation:

Answer:

120 miles

Step-by-step explanation:

Albert travels 40 miles for each hour he drives (units = mph = miles per hour)

If he drives 3 hours at 40 miles per hour...

3 hours x 40 miles / hour = 120 miles

40 miles will he have after 85 minutes of driving .

Given :

austin is driving to san francisco, suppose that the distance to his destination in miles is a linear function of total driving time. has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving .

slope = y2  - y1  / x2 - x1

m = 47.5 - 67 / 75 - 49

= -19.5 / 26

= -3/4

= -0.75

Use the point slope y - y1 = m(x - x1)

y - 67 = -.75 ( x - 49 )

y - 67 = -.75x + 36.75

y = -.75x + 36.75 + 67

y = -.75x + 103.75

x = 85

y = -.75(85) + 103.75

y = -63.75 + 103.75

y = 40 miles  

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Full question :

austin is driving to san francisco, suppose that the distance to his destnation in miles is a linear function of total driving time  has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving . How many miles will he have after 85 minutes of driving ?

Answer:

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

hope this helped:)

brainliest for the brains........................

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Here, we have,

The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.

Factors of 54: 1,2,3,6,9,18,27 and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.

To find the factors of a number, 54, we will use the factorization method.

To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.

54 ÷ 1 = 54

54 ÷ 2 = 27

54 ÷ 3 = 18

54 ÷ 6 = 9

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