20. A rectangle has a length of x + 2 meters and a width of 2x - 5. (A.APR.1)
A. Write an expression for the perimeter of the rectangle. Simplify your final answer.
B. Write an expression for the area of the rectangle. Simplify your final answer.
x + 2
2x - 5
A. Perimeter =
B. Area =
C. If x is 5, what is the perimeter? What is the area?
Rubric
2 pts - Two key elements are present
1 pt - One key element is present
O pts - No key elements are present

Answer:

D

Step-by-step explanation:

perimeter of square = 4 length of its sides

x represents the side lengths

y represents the perimeter of the a square

y = ax + b

a = slope = y2-y1 / x2 -x1

= 8-4 / 2-1 = 4

y = 4x + b

from any point (1,4 )

4 = 4 .(1) + b

b= 0

y = 4x

The value of x from the expression is 2.083

Given the equation expressed as:

Subtract 14,8 from both sides

32.3 - 14.8 = 14.8 - 14.8 + 8.4x

17.5 = 8.4x

x = 17.5/8.4

x = 2.083

Hence the value of x from the expression is 2.083

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Answer:

Solve.

32.3 = 14.8 + 8.4x

Enter your answer as a mixed number in simplest form in the box.

x = 2 1/12

Correct answers:

Step-by-step explanation:

(a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

The Continuous Compounding formula for the principal P , rate of interest r , and time t is

A = P×\(e^{rt}\)

In the question ,

it is given that

Part(a)  

the amount deposited (P) = $5200

rate percent (r) = 3.7% = 3.7/100 = 0.037

time = 9 years

Amount = 5200×\(e^{0.037\times9}\)

= 7254.76

the future value after 9 years is $7254.76   .

Part(b)

the effective rate is calculated using the formula

effective rate = \(e^{r}\) - 1

effective rate = \(e^{0.037}\) - 1

= 1.03769 - 1

= 0.03769

= 3.769%

Part(c)

the time to reach $10000 is calculated using the formula

10000 = 5200\(e^{0.037\times t}\)

\(e^{0.037\times t}\) = 10000/5200

\(e^{0.037\times t}\) = 100/52

taking ㏑both the sides , we get

0.037×t×㏑(e) = ㏑(100/52)

0.037t = 0.65392

t = 0.65392/0.037

t = 1.76735

t ≈ 1.77 years

Therefore , (a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

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Answer:

Rational.

Step-by-step explanation:

A rational number doesn't have a repeating decimal. -2 is a rational number.

Answer: irrational

Step-by-step explanation:

In other words, a rational number is negative, if its numerator and denominator are of the opposite signs. Each of the rational numbers -1/6, 2/-7, -30/11, 13/-19, -15/23 are negative rationals, but -11/-18, 2/5, -3/-5, 1/3 are not negative rationals. 1. ... Since both the numerator and denominator are of the same sign.

Using elimination method in the equation 2x+y=7 and 2x*3y=3, x is 3 and y is 1.

Two equations are given solving it by using rule of elimination,

2x+y=7....(1) and 2x*3y=3. (2)

Multiply equation (1) by three to get 6x+3y=21. (3)

Add equations (2) and (3) together to get

8x=24

x=24/8

x= 3

Replace this number in equation (1):

2(3)+y=7

6+y=7

y=7-6

y= 1

Consequently, the answer is x=3,y=1.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

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Answer:

-34/45

Step-by-step explanation:

first step you wanna do is Multiply the numbers -1/5- 1 (-2/3)- (5/6)= -1/5 and -5/9 then subtract those two fractions and you get -34/45 since both of the fractions were negative the answer results as a negative aswell

Number of dogs in the farm of Pisquet is approximately 21.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

If we have two ratio p : q and r : s and if these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given that,

On the planet Gespil, there are 5 dogs to every 12 cats.

Number of dogs for 12 cats = 5

Let Number of dogs for 50 cats = x

Using concept of proportion,

12 / 5 = 50 / x

Cross multiplying,

12x = 5 × 50

12x = 250

x = 20.83 ≈ 21

Hence there are approximately 21 dogs for 50 cats.

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The number of the significant digits in the expression 2.123 × 10¹² miles will be 3.

Significant digits are figures that show how precise measurements and computations have been made. Significant numbers shouldn't be tallied if they don't improve a reading's accuracy.

The expression is given below.

⇒ 2.123 × 10¹² miles

The rule of significant digits is given as:

Then the number of the significant digits in the expression 2.123 × 10¹² miles will be 3.

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Answer: 122

Step-by-step explanation:

▪︎ Perimeter = (width + length) * 2

374 = (width + 65) * 2

width + 65 = 374 / 2

width + 65 = 187

width = 187 - 65

width = 122

0.708 more of the deck did connor take than ethan.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

connor takes 7/8 of the cards from a deck,

ethan took 1/6 of the cards from the same deck.

i.e. difference of them = 7/8 - 1/6

                                      =0.708

Hence, 0.708 more of the deck did connor take than ethan.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer: the paper is 8 inches

Step-by-step explanation: I'm sure the answer is 8.

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

x=143

Step-by-step explanation:

scale factor (if that is the correct term) is 13. you find that by matching sides to side. this means that 91/7=13, therefore you know that 4*13 is 52 and 11*13 is 143

Answer:

4.8

...

....

....

....

....

.

.

....

(a) The required sample size is 1.96.

(b) Sample size = n = 89

(c) Sample size = n = 62

What is standard deviation?

The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

(a) Population standard deviation = σ = 3

Margin of error = E = 0.253

At 95% confidence level the z is,

α = 1 - 95%

α = 1 - 0.95 = 0.05

α/2 = 0.025

Zα/2 = 1.96

sample size = n = [Zα/2* σ / E]^2

n = [1.96 * 3 / 0.253]2

n = 540.14

Sample size = n = 541

b) Population standard deviation = σ = 24

Margin of error = E = 5

sample size = n = [Zα/2* σ/ E] 2

n = [1.96 * 24 / 5]2

n = 88.51

Sample size = n = 89

c) Population standard deviation = σ = 8

Margin of error = E = 2

sample size = n = [Zα/2* σ / E] 2

n = [1.96 * 8 / 2]2

n = 61.46

Sample size = n = 62

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Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

We conclude that the board's length is equal to 2564.0 millimeters.

Step-by-step explanation:

We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.

Let \(\mu\) = population mean length of the board.

So, Null Hypothesis, \(H_0\) : \(\mu\) = 2564.0 millimeters    {means that the board's length is equal to 2564.0 millimeters}

Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) 2564.0 millimeters      {means that the boards are either too long or too short}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =  \(\frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }\)  ~  \(t_n_-_1\)

where, \(\bar X\) = sample mean length of boards = 2559.5 millimeters

            s = sample standard deviation = 15.0 millimeters

             n = sample of boards = 26

So, the test statistics =  \(\frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }\)  ~   \(t_2_5\)

                                     =  -1.529    

The value of t-test statistics is -1.529.

Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the board's length is equal to 2564.0 millimeters.

Answer:

The answer is D

Step-by-step explanation:

Plug in the values and see which one is correct.

The quadratic equation that passes through points (1/2, 9/16) (1,9/2) (-1, 11/2) are 1/2 = 81 a/256 - 9b/16 + c  ,9/2= a + b + c  and 11/2 = -a - b + c    .

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.

Given:

The given points are

(1/2, 9/16) (1,9/2) (-1, 11/2)

According to given question we have

We know the basic quadratic equation are

\(y = ax^{2} + bx + c\)

We have 3 points we can plug in for (x, y) to create 3 simultaneous equations

The equation are at the points

1. (1/2, 9/16)

1/2 = 81 a/256 - 9b/16 + c  

The equation are at the points

2. (1,9/2)

9/2= a + b + c  

The equation are at the points

3.  (-1, 11/2)

11/2 = -a - b + c      

Therefore, the quadratic equation that passes through points (1/2, 9/16) (1,9/2) (-1, 11/2) are 1/2 = 81 a/256 - 9b/16 + c  ,9/2= a + b + c  and 11/2 = -a - b + c    .

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

a 1lb 13 oz

Step-by-step explanation:

1 lb= 16 oz. convert to oz. 68oz - 39oz = 29 oz. vconvert back to lbs.= 1 lb 13 oz.

Answer:

The upper confidence bound for population mean escape time is: 379.27

The upper prediction bound for the escape time of a single additional worker  is 413.64

Step-by-step explanation:

Given that :

sample size n = 26

sample mean \(\bar x\) =  371.08

standard deviation \(\sigma\) = 24.45

The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%

We need to determine the standard error of these given data first;

So,

Standard Error S.E = \(\dfrac{\sigma }{\sqrt{n}}\)

Standard Error S.E = \(\dfrac{24.45 }{\sqrt{26}}\)

Standard Error S.E = \(\dfrac{24.45 }{4.898979486}\)

Standard Error S.E = 4.7950

However;

Degree of freedom df= n - 1

Degree of freedom df= 26 - 1

Degree of freedom df= 25

At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

Similarly;

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 4.7950

The Margin of error = 8.18986

The upper confidence bound for population mean escape time is = Sample Mean + Margin   of  Error

The upper confidence bound for population mean escape time is =  371.08 +  8.18986

The upper confidence bound for population mean escape time is = 379.26986  \(\approx\) 379.27

The upper confidence bound for population mean escape time is: 379.27

b.  Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.

The standard error of the mean = \(\sigma \times \sqrt{1+ \dfrac{1}{n}}\)

The standard error of the mean = \(24.45 \times \sqrt{1+ \dfrac{1}{26}}\)

The standard error of the mean = \(24.45 \times \sqrt{1+0.03846153846}\)

The standard error of the mean = \(24.45 \times \sqrt{1.03846153846}\)

The standard error of the mean = \(24.45 \times 1.019049331\)

The standard error of the mean = 24.91575614

Recall that : At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

∴

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 24.91575614

The Margin of error = 42.55611149

The upper prediction bound for the escape time of a single additional worker  is calculate by the addition of

Sample Mean + Margin of Error

= 371.08 + 42.55611149

= 413.6361115

\(\approx\) 413.64

The upper prediction bound for the escape time of a single additional worker  is 413.64

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

Step-by-step explanation:

y - 3 = -2/3(x - 3)

y - 3 = -2/3x + 2

y = -2/3x + 5

Answer:

Step-by-step explanation:

Answer:

is it 20% I'm not really sure

Answer:

$71.74

Step-by-step explanation:

Given:

Old price of the jacket  = $ 80

Discount = 15 %

Therefore, discounted price =

Now, sales tax = 5.5 % on discounted price =

Therefore, the new price of the jacket after discount and paying sales tax is given as:

New price = Discounted price + Sales tax

New price = $ 68 + $ 3.74 = $ 71.74

So, the new price of the jacket is $ 71.74.

Answer:-3

Step-by-step explanation:

Answer:

Here,

a= 12

b = 6

Then,

a+b

= 12 + 6

= 18

.°. 18 is the solution

Answer:

\( \boxed{ \bold{ \boxed{ \sf{18}}}}\)

Step-by-step explanation:

If the values of variables of algebraic expressions are given, the value of the term or expression can easily obtained by replacing the variables with numbers.

Given, a = 12 and b = 6

\( \sf{a + b}\)

plug the values

⇒\( \sf{12 + 6}\)

Add the numbers

⇒\( \sf{18}\)

Hope I helped!

Best regards!!

The constant of proportionality of red beads to blue beads is 2/3

This refers to the Fixed ratio of Gabby's blue beads to red beads in the 5 bags. In order words, the constant of proportionality describes a ratio is which is does not change as it is fixed

Now, carefully follows my explanation below:

Then it goes further as thus:

Blue : Red = 32 : 48

= 32/48

= 4/6

= 2/3

Blue : Red = 48 : 72

= 48 : 72

= 2 / 3

Blue : Red = 60 : 90

= 2 / 3

So therefore, from the solution which I have provided above, it can be concluded that the constant of proportionality of the red beads to blue beads is 2/3.

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