The adjacent sides of the parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram.

Answer:

[tex]12(1 + x)[/tex]

Step-by-step explanation:

We will use order of operations to simplify this expression.

We will evaluate the brackets first.

3(5+7)-6(4-2x) =

[tex]3(12) - 6(4 - 2x) \\ = 36 - 6(4 - 2x) \\ = 36 - 24 + 12x \\ = 12 + 12x[/tex]

You can further simplify it by factorising it:

[tex]12 + 12x \\ = 12(1 + x)[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3(5 + 7) - 6(4 - 2x)}[/tex]

[tex]\mathsf{= 3(5) + 3(7) - 6(4) - 6(-2x)}[/tex]

[tex]\mathsf{= 15 + 21 - 24 + 12x}[/tex]

[tex]\mathsf{= 36 - 24 + 12x}[/tex]

[tex]\mathsf{= 12 + 12x}[/tex]
[tex]\mathsf{= 12x + 12}[/tex]

[tex]\huge\text{Therefore, your answer should be:\boxed{\mathsf{12x + 12}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 26.3 < 26.5

Step-by-step explanation:

On the number line, 26.3 lies to the left of 26.5, meaning that 26.3 is less than 26.5.

1(2x^9y^n) (4x²y^10)-8x^11 y^20

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Answer:

C: 10

Step-by-step explanation:

Edge 2022

1) The equation of the parallel line in Slope Intercept Form is; y = -x - 1

2) The equation of the perpendicular line in Slope Intercept Form is;

y = ³/₂x - 4

1) When two lines are parallel, it means their slopes are the same.

Formula for equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, slope of y = -x + 1 is m = -1.

Equation of parallel line is;

(y - (-5))/(x - 4) = -1

y + 5 = -x + 4

y = -x - 1

2) When two lines are perpendicular, it means their slopes are the negative inverse of each other. Thus;

Slope of line = -2/3 and so slope of perpendicular line = 3/2. Thus, equation of new line is;

(y + 1)/(x - 2) = 3/2

2y + 2 = 3x - 6

2y = 3x - 8

y = ³/₂x - 4

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Answer:

Second one i believe

Step-by-step explanation:

Well u know the sides arent given

Answer:

12

Step-by-step explanation:

The Surface Area of the cone 12π cm².

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given,  A cone with the height of 2√3 and the radius of base is 2 cm.

Since, Surface are of Cone = rlπ + B

Where l= slant height, and B = area of the base

In our case,

r = 2

B = π * r*r = π* 4

for slant height,

Slant makes a perfect right angle triangle with the center line thus,

from Pythagorean theorem,

l² = (2√3)² + 2²

l² = 12 + 4

l = 4 cm

Thus,

Surface area for the Cone = π * 2 *4 + π * 4

Surface area for the Cone = 12π

therefore, Surface Area of the cone 12π cm².

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Answer:

D. Opposite angles in a parallelogram are supplementary.

Answer:

[tex]y=7x-26[/tex]

Step-by-step explanation:

1) Write it in the slope-intercept form of [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.

[tex]y=7x +c[/tex]

2) Substitute the given coordinates into [tex]y=7x +b[/tex], and then solve for c.

[tex]9=7(5) +b\\9=35+b\\9-35=b\\b= -26[/tex]

3) Substitute c into [tex]y=7x +b[/tex]

[tex]y=7x-26[/tex]

Therefore, the answer is [tex]y=7x-26[/tex].

Answer:

X and Y intercept

Step-by-step explanation:

X and Y intercept is much easier as the equation is linear it is easy to find the intercepts

Answer:

Your answer is 2x³ + 7x²y + y²- x²

Step-by-step explanation:

(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² ) ​

= 2x³  + 4x²y  +  5xy² - 3y² - x² + 3x²y  - 5xy² + 2y²

= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² -  x²

= 2x³ + 7x²y + y²- x²  ans.

Hope its helpful!

Please mark me as brainlist.

Step-by-step explanation:

(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² ) ​

= 2x³  + 4x²y  +  5xy² - 3y² - x² + 3x²y  - 5xy² + 2y²

= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² -  x²

= 2x³ + 7x²y + y²- x²  ans.

Answer: b. f(x) is an even function for all even values of m.

Step-by-step explanation:

[tex]f(x)=(x^m +9)^2[/tex]

If m is even, then [tex](-x)^m=x^m[/tex].

This means that [tex]f(-x)=(x^m+9)^2 \implies f(-x)=f(x)[/tex]

Thus, b is the correct answer.

In the inequality models, the number of additional weeks is 1558+60x≥2158.

Given that the initial savings is $1558, the amount needed is $2158 and additional savings is $60 weekly.

Let the number of weeks be x.

So, she will save 60x in x weeks.

Total savings after x weeks is

Initial saving +60x       .......(1)

According to the question, she needs $1258 for repair.

So, that means the minimum requirement is 2158.

≥2158      ........(2)

Combine equations (1) and (2) and get

Initial savings +60x≥2158

As given that the initial savings is 1558.

Substitute this in above inequality and get

1558+60x≥2158

To find the number of weeks find value of x.

Subtract 1558 from either sides of the inequality.

1558+60x-1558≥2158-1558

60x≥600

Divide both sides with 60 as

60x÷60≥600÷60

x≥10

Hence, the inequality that models the number of additional weeks marie needs to continue saving to afford the home repairs is 1558+60x≥2158 and she needs to save $60 for at least 10 weeks.

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The supply equation of the company's total cost is 0.75x

The question implies that we determine the equation of the company production and categorize the equation as demand or supply

The given parameters are:

The total cost of production is calculated as:

Total Cost = Overalls * Cost price

To determine the equation, we set the number of overalls to x.

So, we have:

Total Cost = x * 0.75

Evaluate

Total Cost = 0.75x

Hence, the equation of the company's total cost is 0.75x

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The probability of getting a total less than 4 is 1/12

In a roll of two dice, we have

Outcomes = 36

Sum less than 4 = 3

The probability is then calculated as:

P  = Sum less than 4/Outcomes

This gives

P = 3/36

Simplify

P = 1/12

Hence, the probability of getting a total less than 4 is 1/12

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Answer:

Step-by-step explanation:

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation for table 3 is y=(5/2)x-4.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The slope for the tables,

Table 1.

m₁ = (3-1)/(5-2) = 2/3

m₂ = (43-31)/(20-17) = 12/3 = 4

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (13-10)/(2-1) = 3/1

m₂ = (34-29)/(7-6) = 5/1

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (6-1)/(4-2) = 5/2

m₂ = (31-26)/(14-12) = 5/2

Since the slope is the same the relationship is linear.

The equation for table 3 will,

y = (5/2)x + c

1 = (5/2)2 + c

1 = 5 + c

c = -4

Hence, the equation for table 3 is y=(5/2)x-4.

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The value of x, using the cosine ratio, is approximately: 11.47.

The cosine ratio is:

Cos ∅ = adjacent length/hypotenuse length.

Given the parameters:

∅ = 55°

Adjacent length = x

Hypotenuse length = 20

Apply the cosine ratio:

cos 55 = x/20

x = (cos 55)(20)

x ≈ 11.47

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For the given cost equation we have:

a) Fixed cost is $900.

b) For making 25 items the cost is $1150.

c) D: x ∈ [0, 150]

   R: c ∈ [900, 2400]

Here we know that the cost equation is:

c(x) = 10*x + 900.

First, we want to get the fixed cost, it is given by evaluating the function in x = 0.

c(0) = 10*0 + 900 = 900

The fixed cost is 900.

b) Now we want to get the cost for making 25 items, to get this, we just evaluate in x = 25.

c(25) = 10*25 + 900 = 250 + 900 = 1150

c) Now, if the maximum cost is 2400, then the maximum number of items that we can make is x₀, such that:

c( x₀) = 2400 = 10*x₀ + 900

Solving for x₀ we get:

x₀ = (2400 - 900)/10 = 150

Now we want to get the range and domain.

We know that we can make between 0 and 150 items, so the domain is:

D: x ∈ [0, 150]

For the range, we know that the fixed cost for 0 items is 900, and the maximum cost is 2400, then the range is:

R: c ∈ [900, 2400]

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Answer:

28%

Step-by-step explanation:

250÷ .28 = 180

.28 = 28%

Answer:

4/5

Step-by-step explanation:

one and one third times as much sugar as chocolate chips

=> S + 1/3(S) = C

one and two thirds cups of sugar is used

=> S + 2/3(S) = ?

now criss cross the two:

S + 1/3(S) = C

S + 2/3(S) = ?

C×(S+2/3(S)) = S + 1/3(S)....find C

C = (S + 1/3(S)) / (S + 2/3(S))

= (3S + S / 3) / (3S + 2S/ 3)

= 3S + S / 3S + 2S

= 4S / 5S

= 4/5.

Hello :

    3/8 = x/(15 + x)

⇔ 3(15 + x)/8 = x

⇔ (45 + 3x)/8 = x

⇔ 45 + 3x = 8x

⇔ 8x - 3x = 45

⇔ 5x = 45

⇔ x = 45/5

⇔ x = 9

Answer:

3200

Step-by-step explanation:

0.13x    + 0.04*(6100-x) = 532    dollars.

  0.13x + 0.04*6100 - 0.04x = 532

 (0.13 - 0.04)x = 532 - 0.04*6100

 x = 532 - 0.04 - 6100/0.13-0.04 = 3200

The couple invested:

to earn $477 as the total interest for the first year.

The interest over an investment is the additional amount that a person receives on investing his/her money in the cause.

In the question, we are informed that in investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477.

We are asked to find the amount invested in each rate.

We assume the amount invested in savings account to be $x.

Therefore, the amount invested in development plan is $(6150 - x).

Simple interest on a sum of money (P), at a rate (r) over a time period (t), is given as S.I. = (Prt)/100.

We calculate the interest earned in both investments:-

Investment in savings account:

Amount invested (P) = $x.

Rate of interest (r) = 6%.

Time for investment (t) = 1 year.

Therefore, interest received = (Prt)/100 = $(x*6*1)/100 = $ (6x)/100

Investment in development plan:

Amount invested (P) = $(6150 - x).

Rate of interest (r) = 9%.

Time for investment (t) = 1 year.

Therefore, interest received = (Prt)/100 = $((6150 - x)*9*1)/100 = $ {9(6150 - x)}/100.

We know that the total interest received is $477.

Thus on adding Interests from both the investments, we can write an equation:

(6x)/100 + {9(6150 - x)}/100 = 477

or, 6x + 55350 - 9x = 47700,

or, 55350 - 47700 = 3x,

or, 3x = 7650,

or x = 7650/3 = 2550.

Thus, the investments in:

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All the figures can be proven to be parallelograms by the markings

The properties of parallelogram are:

Based on the above properties, all the figures can be proven to be parallelograms

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From the given output the regression equation is

StopDist = ₋89.99 ₊5.7053(speed)

The slope of the regression equation is 5.7053

from the Excel output the 95% confidence interval for the slope of the regression line is (5.0809, 6.3296)

By the rejection rule ,reject the null hypothesis.

Given,

from the given output the regression equation is

StopDist = ₋89.99 ₊ 5.7053(speed)

Interpreting the slope of the regression line.

from the given output the regression equation the slope is 5.7053.

To find a 95% confidence interval for the slope of the regression line follow the excel procedure:

From the excel output the 95% confidence interval for the slope of the regression line is (50809, 6.3296).

State the hypothesis

Null hypothesis:

H₀ : β₁ ≠ 0

Alternative hypothesis:

Hₓ : β₁ ≠ 0

Reject rule:

If p value≤ α(=0.05), then reject the null hypothesis.

By the rejection rule, reject the null hypothesis (H₀)

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Answer:

s = 3 + (4d)

Step-by-step explanation:

s is the number of states, so we put a s and an equal sign. Then 3 is the number of days he started with, so we add that, and 4d is 4 states times the number of days.

If the company's average tax rate is 34 percent, Its net income after taxes is: $138,090.48.

Revenues of $880,300

General and administrative expenses ($353,300)

Leasing expenses ($108,195)

Earning before interest, taxes, depreciation and amortization $418,805

Depreciation expenses ($131,455)

Earning before interest and taxes $287,350

Interest expenses ($78,122)

Earning before taxes $209,228

Taxes 34%              $71,137.52

Net income/Loss $138,090.48

Therefore Its net income after taxes is: $138,090.48.

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The radioactive isotope of phosphorus P-32 is used as a tracer in the liver. If 3.5 mg is left in a sample after 288 hrs then the initial amount of P-32 administered was 7 mg.

A radioactive isotope is a form of an element that has an unstable nucleus and undergoes radioactive decay, emitting radiation in the form of particles and/or energy.

These isotopes can be used for various purposes in medicine, industry, and research.

We can use the radioactive decay formula to solve this problem:

N = N0 * (1/2)^(t/T)

where:

- N is the final amount of P-32 remaining after 288 hours (3.5 mg)

- N0 is the initial amount of P-32

- t is the time elapsed (288 hours)

- T is the half-life of P-32 (14.3 days converted to hours is approximately 343.2 hours)

Substituting the given values into the formula, we get:

3.5 mg = N0 * (1/2)^(288/343.2)

Simplifying and solving for N0:

N0 = 3.5 mg / (1/2)^(288/343.2) = 7 mg

Therefore, the initial amount of P-32 administered was 7 mg.

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Step-by-step explanation:

Area of sector = (θ/2) × r2

= (1.75/2) × 2×2

= (0.875) ×4

= 3.5 In2