Harris is building a deck around his pool. His contractor charges $525 for labor plus an additional $4.75 per square foot for materials. Formulate a function that can be used to determine the cost, in dollars, for a deck with an area of x square feet.

Answer:

Speed of Amy is 3.75 miles per hour.

Step-by-step explanation:

We have, speed of Amy = 110 yards per minute

This means, she covers 110 yards of distance in 1 minute.

Now, to convert the speed of Amy into miles per hour, we will first convert the distance from yards into miles and then convert time from minutes to hour.

We know that,

  1 yard = 3 feet

∴ 110 yards = 3 × 110 feet = 330 feet

Now, we also know that,

 5280 feet = 1 mile

∴ 1 feet = [tex]\frac{1}{5280}[/tex] miles

So, 330 feet = [tex]\frac{1}{5280}\times330[/tex] = [tex]\frac{1}{16}[/tex] miles

∴ 110 yards = 330 feet = [tex]\frac{1}{16}[/tex] miles

Now, 60 min = 1 hr

∴ 1 min = [tex]\frac{1}{60}[/tex] hrs

So, 110 yards = [tex]\frac{1}{16}[/tex] miles and 1 min = [tex]\frac{1}{60}[/tex] hr

So, we can say that, Amy covers a distance of [tex]\frac{1}{16}[/tex] miles in

[tex]\frac{1}{60}[/tex] hr.

We know that,

[tex]speed=\frac{distance}{time}[/tex]

[tex]speed=\frac{(\frac{1}{16}) miles}{(\frac{1}{60})hr}[/tex]

[tex]speed=\frac{60}{16} miles/hr = 3.75 miles/hr[/tex]

Therefore, the speed of Amy in miles/hr is 3.75 miles/hr.

Answer:

m∠CEB is 55°

Step-by-step explanation:

Since ∠ADE = 55°, and ∠ADE is half of ∠ADC because ED bisects ∠ADC. Bisect means to cut in half.

∠ADC = 110° because it is double of ∠ADE.

Since AB║CD and AD║BC, the two sets of parallel lines means this shape is a parallelogram. In parallelograms, opposite angles have equal measures.

∠ADC = ∠CBE = 110°

All quadrilaterals have a sum of angles 360°. Since ∠DCB = ∠BAD and we know two of these other angles are each 110°:

360° - 2(110°) = 2(∠DCB)

∠DCB = 140°/2

∠DCB = ∠BAD = 70°

∠DCB was bisected by EC, which makes each divided part half.

∠DCE = ∠BCE = (1/2)(∠DCB)

∠DCE = ∠BCE = (1/2)(70°)

∠DCE = ∠BCE = 35°

All triangles' angles sum to 180°.

In ΔBCE, ∠BCE = 35° and ∠CBE = 110°.

∠CEB = 180° - (∠BCE + ∠CBE)

∠CEB = 180° - (35° + 110°)

∠CEB = 55°

Therefore m∠CEB is 55°.

A. Part 1- The scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2- The length of side EF is 221/182

C. Part 3- The exact area of EFGH is 7213127/33124​  square inches.

Let's solve each part step by step:

A. Part 1:

To find the scale factor from BC to FG, we need to find the ratio of the lengths of the corresponding sides of the similar quadrilaterals.

Given:

Diagonal AC (in quadrilateral ABCD) has length 7.

Diagonal EG (in quadrilateral EFGH) has length 13.

Using the fact that the diagonals of similar quadrilaterals are proportional, we have:

BC/ FG​ = AC/ EG

Substituting the given values:

BC/ FG​ = 7/13

So, the scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2:

Given side AB has a length of 17/26 . To find the length of side EF, we use the scale factor found in Part 1.

If the scale factor from BC to FG is 7/13 , then the length of side EF can be found using the proportion:

EF/ AB​ = FG/ BC

Substituting the given values:

EF=7/13×17/ 26

Solving for EF:

EF= 13/ 7​ × 17/ 26 = 221/ 182

So, the length of side EF is 221/182

​C. Part 3:

If the area of quadrilateral ABCD is 147 square inches, and the scale factor is 7/13 , the area of quadrilateral EFGH can be found using the scale factor squared.

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

So,

( EF/AB )^2 =( 7/13 )^2

( 221/ 182)^2 =( 7/13 )^2

Solving for ( 221/ 182 )^2 :

( 221/182 )^2 = 48841/ 33124

Now, if the area of ABCD is 147 square inches, then the area of EFGH would be:

147× 48841/ 33124 = 7213127 /33124

So, the exact area of EFGH is 7213127/33124​  square inches.

Answer:

There are 7 copies of 2 and 1 copy of 11 in the product:

1408 = 2^7×11

Step-by-step explanation:

Factor the following integer:

1408

The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:

1408 = 2 704:

1408 = 2×704

The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:

704 = 2 352:

1408 = 2×2×352

The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:

352 = 2 176:

1408 = 2×2×2×176

The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:

176 = 2 88:

1408 = 2×2×2×2×88

The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:

88 = 2 44:

1408 = 2×2×2×2×2×44

The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:

44 = 2 22:

1408 = 2×2×2×2×2×2×22

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

1408 = 2×2×2×2×2×2×2×11

11 is not divisible by 2 since 11 is odd and 2 is even:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |  

- | | 7 |  

| | 4 | (remainder)

11 is not divisible by 7:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)

No primes less than 11 divide into it. Therefore 11 is prime:

1408 = 2×2×2×2×2×2×2×11

There are 7 copies of 2 and 1 copy of 11 in the product:

Answer: 1408 = 2^7×11

Final answer:

The prime factorization of 1408 is 2 raised to the power of 7 multiplied by 11, represented as 2^7 × 11. This is found by repeatedly dividing 1408 by 2 until we are left with the prime number 11, which cannot be divided further.

Explanation:

The prime factorization of 1408 involves breaking down the number into its prime factors until all the factors are prime numbers. To find the prime factors of 1408, we can use a factor tree or the method of division. We can start by dividing 1408 by the smallest prime number that divides it evenly, which is 2. If we keep dividing by 2, we get the following sequence of divisions:

1408 ÷ 2 = 704

704 ÷ 2 = 352

352 ÷ 2 = 176

176 ÷ 2 = 88

88 ÷ 2 = 44

44 ÷ 2 = 22

22 ÷ 2 = 11

Since 11 is a prime number, we cannot divide any further. Therefore, the prime factorization of 1408 is 27 × 11, since 2 was divided 7 times and 11 is the last prime factor found.

9514 1404 393

Answer:

  8 inches, 13 inches, 19 inches

Step-by-step explanation:

Let's identify the side lengths (shortest to longest) as a, b, c. Then we have ...

  a + b + c = 40 . . . . . . perimeter

  2c -a = 30

  2a +2b +c = 61

__

Subtracting the third equation from twice the first gives ...

  2(a +b +c) -(2a +2b +c) = 2(40) -(61)

  c = 19 . . . . .  simplify

Using this in the second equation, we have ...

  2(19) -a = 30

  38 -30 = a = 8 . . . . add a-30

Then the first equation reveals b:

  8 + b + 19 = 40

  b = 40 -27 = 13

The side lengths are 8 in, 13 in, and 19 in.

Answer:

25% or 1/4. I don't know how to type Vietnamese.

Step-by-step explanation: If you take a look at the right side of the equation, a 3 is being added to our variable x.

If you were going to solve this equation, you must subtract 3 from the right side and the left side to isolate our variable.

You would end up with 4 = x.

Answer:

x = 35°

Step-by-step explanation:

The question is as following

cos x = sin(20 + x)°  and  0° < x  < 90°  ,   find X?

==============================================

cos x = sin(20 + x)°

sin and cos are co-functions,

which means that: cos x = cos [90 - (20 + x)]

∴ x = 70 - x

∴ 2x = 70

∴ x = 35°

======================

Note: cos θ = sin ( 90 - θ )

Answer:

x = 35°

Step-by-step explanation:

The question is as following

cos x = sin(20 + x)°  and  0° < x  < 90°  ,   find X?

==============================================

cos x = sin(20 + x)°

sin and cos are co-functions,

which means that: cos x = cos [90 - (20 + x)]

∴ x = 70 - x

∴ 2x = 70

∴ x = 35°

======================

Note: cos θ = sin ( 90 - θ )

Answer:

$2.49 per visit

Step-by-step explanation:

Mean or Average Value

It's referred to as the center of a numerical data set. In some circumstances, a list of values needs to be expressed as a single number who best represents them.

The registration fee of the health club is $49. It also charges a $17.50 monthly fee. In one year, the total cost will be $49 + 12*$17.50 = $259. If Ed Parker visits the club 2 times a week for a year, it will make an approximate of 2*52=104 visits a year. The mean cost by visit will be:

$259/104= $2.49 per visit

Answer:

3.55

Step-by-step explanation:

Answer:

Part 1) The slope is [tex]m=25[/tex] (the cost of the gym is $25 per month)

Part 2) The y-intercept is the point (0,-100) see the explanation

Part 3) [tex]y=25x-100[/tex], After 14 months the cost is [tex]\$250[/tex]

Step-by-step explanation:

Part 1) What is the slope of the line

Let

x ---> the number of months

y ---> the total cost in dollars

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

From the graph take two points

(0,-100) and (4,0)

substitute the values in the formula

[tex]m=\frac{0+100}{4-0}[/tex]

[tex]m=\frac{100}{4}[/tex]

[tex]m=25[/tex]

Remember that the slope is equal to the unit rate of the linear equation

That means ----> the cost of the gym is $25 per month

Part 2) What is the y-intercept of the line

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the graph the y-intercept is the point (0,-100)

In context this problem, the y-intercept represent the rebate of $100 that the gym was offering for sign up for a full year      

Part 3) What is the linear equation for the line in this situation? What is the cost of the gym membership after 14 months

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept      

we have

[tex]m=25[/tex]

[tex]b=-100[/tex]

substitute the values

[tex]y=25x-100[/tex]

For x=14 months

substitute

[tex]y=25(14)-100[/tex]

[tex]y=350-100=\$250[/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

The complete question is

m ∠ A = 100 - x

m ∠ B = 80 + x

m ∠ C = 110 - 3x

m ∠ D = 75 + 2x

Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.

Options

A) x = 5

B) x = 7

C) x = 10

D) x = 15/2

we know that

In a parallelogram, opposite angles are parallel and consecutive angles are supplementary

so

m ∠ A=m ∠ C

m ∠ B=m ∠ D

m ∠ A+m ∠ B=180°

m ∠ B+m ∠ C=180°

step 1

Find the value of x

we know that

m ∠ A=m ∠ C

substitute the given values

[tex](100-x)^o=(110-3x)^o[/tex]

solve for x

Group terms

[tex]3x-x=110-100[/tex]

Combine like terms

[tex]2x=10[/tex]

[tex]x=5[/tex]

step 2

Verify the measure of the angles

[tex]m\angle A=100-5=95^o[/tex]

[tex]m\angle B=80+5=85^o[/tex]

[tex]m\angle C=110-3(5)=95^o[/tex]

[tex]m\angle D=75+2(5)=85^o[/tex]

therefore

[tex]m\angle A=m\angle C[/tex] ---> is ok

[tex]m\angle B=m\angle D[/tex] ---> is ok

[tex]m\angle A+m\angle B=180^o[/tex] ---> is ok

[tex]m\angle B+m\angle C=180^o[/tex] ---> is ok

A descending sort would list the data from tallest to shortest in the height field of a database about trees.

The kind of sort that would list the data from tallest to shortest in the height field of a database about trees is a descending sort. This sort arranges the data in reverse order, with the tallest tree at the top and the shortest tree at the bottom. To perform a descending sort in a database, you can use the ORDER BY clause with the DESC keyword in the SQL query.

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Answer:

in polynomial form

Step-by-step explanation:

if you have any question then reply me

The area of the rectangle can be found by multiplying its width by its height, which is a polynomial expression in this case.

To find the area of a rectangle, we multiply its width by its height. In this case, the width of the rectangle is y3+6y and the height is 2y3+5. So, the area of the rectangle is:

A = width × height

A = (y3+6y) × (2y3+5)

A = 2y^6 + 5y^3 + 12y^4 + 30y

This is the area of the entire rectangle, expressed as a polynomial in standard form.

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Answer:

b $80

Step-by-step explanation:

Interest = Principal x Interest Rate x Time

$40 = P x 0.1 x 5

$40 = 0.5 P

Dividing the equation by 0.5 we get;

P = $40 / 0.5

P = $80

Answer:

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

Step-by-step explanation:

Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.  

Which statement must be true?

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.

c) Gym A sold more gold membership than Gym A did.

d) If Gym B sold 50 membership, 25 would be gold memberships.

Given: Gym A have sold 40% gold membership of total membership.

Gym B have sold 25% gold membership of total membership.

Lets take option A first to find if it is true statement.

As per option A, There are total number of membership is 80.

∵ Gym A has sold 40% gold membership.

∴ Gym A gold membership= [tex]40\% \times 80[/tex]

⇒ Gym A gold membership= [tex]\frac{40}{100} \times 80= 32 member.[/tex]

∴ Gym A gold membership= 32.

Now, Gym B

∵ Gym B has sold 25% gold membership.

∴ Gym B gold membership= [tex]25\% \times 80[/tex]

⇒ Gym B gold membership= [tex]\frac{25}{100} \times 80=20 member.[/tex]

∴ Gym B gold membership= 20.

Next finding difference gold membership for Gym A and Gym B

[tex]32-20= 12 \ membership[/tex]

Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.

Answer:maybve

Step-by-step explanation:

no

Answer:1 2/3

Step-by-step explanation:

2/3+1/3+2/3=5/3=1 2/3

Answer:

Range [tex]\rightarrow[/tex] all real numbers less than or equal to 0 [tex]\rightarrow[/tex] ( - ∞ , 0 ]

Step-by-step explanation:

For visual understanding a graph of the  function is attached with the answer.

For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).

For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]

Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

Answer:

B

Step-by-step explanation:

all real numbers less than or equal to 0

Final answer:

The equation of a line perpendicular to y=2/3x-6 has a slope of -3/2. The general form of the equation is y = -3/2x + b, where b is the y-intercept.

Explanation:

The student has asked for an equation of a line that is perpendicular to the line given by y=2/3x-6. For two lines to be perpendicular, the product of their slopes must be -1. Since the slope (m₁) of the given line is 2/3, the slope of the line perpendicular to it (m₂) must satisfy the equation m₁×m₂ = -1. Therefore, m₂ must be -3/2 (since (2/3)×(-3/2) = -1).

An equation of a straight line can be represented by y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line perpendicular to y=2/3x-6, we can use the slope m₂ = -3/2. The general form of the equation of the line we are seeking would then be y = -3/2x + b, where b is the y-intercept that can be determined based on a specific point the line passes through.

Answer:

C

Step-by-step explanation:

note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 10x + 7 - (x² - 7x) ← distribute parenthesis by - 1

= 10x + 7 - x² + 7x ← collect like terms

= - x² + 17x + 7 → C

Final answer:

To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The answer is -x^2 + 17x + 7.

Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

Given f(x) = 10x + 7 and g(x) = x^2 - 7x, we substitute these values into (f - g)(x):

(f - g)(x) = f(x) - g(x) = (10x + 7) - (x^2 - 7x)

Expanding and simplifying, we get (f - g)(x) = -x^2 + 17x + 7.

Answer:

12x-183

Step-by-step explanation:

2(4x+3)+3(x-63)+x

8x+6+3x-189+x

12x+6-189

12x-183

Answer:

x > 5

Step-by-step explanation:

Given

9x - 2 > 43 ( add 2 to both sides )

9x > 45 ( divide both sides by 9 )

x > 5

The solution to the inequality (9x - 2 > 43) is (x > 5).

To solve the inequality (9x - 2 > 43), follow these steps:

1. Add 2 to both sides of the inequality to isolate the term with x on one side:

[tex]\[ 9x - 2 + 2 > 43 + 2 \] \[ 9x > 45 \][/tex]

2. Divide both sides of the inequality by 9 to solve for x:

[tex]\[ \frac{9x}{9} > \frac{45}{9} \] \[ x > 5 \][/tex]

This means that any value of x greater than 5 will satisfy the original inequality. The solution set is all real numbers greater than 5.

Answer:

0.6

Step-by-step explanation:

it is right

The proportion of laptop prices that are between 624 dollars and 768 dollars would be: 0.3907 or 39.07%.

To determine the proportion of laptop prices that are betwee the specified prices, we would ge the z scores in the following way:

624 dollars

Z1 = (624 - 750) / 60 = -2.1

768 dollars

Z2 = (768 - 750) / 60 = 0.3

Now, if we use the standard distribution table, we would arrive at;

P(-2.1 < Z < 0.3) ≈ 0.3907

Learn more about proportions ehre:

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Answer:

  $15.21

Step-by-step explanation:

The tax and tip percentages are both being figured on the original bill amount, so they can be added. The tax and tip together come to ...

  11.75% +15% = 26.75%

This is added to the original bill amount, so the final total will be ...

  $12 + $12×0.2675 = $12×1.2675 = $15.21

Vera's meal cost $15.21.

The calculated cost of spraying the rectangular field is $846

Calculating the cost of spraying the rectangular field

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

Dimension = 720 m by 500 m

Unit cost = $23.50 per hectare

The area of the field is calculated as

Area = 720 m * 500 m

So, we have

Area = 360000 square meters

Converted to hectares, we have

Area = 36 hectares

So, we have

Cost = $23.50 per hectare * 36 hectares

Evaluate

Cost = $846

Hence, the cost of spraying the rectangular field is $846

Answer:

B. When its angles are right angles.

Step-by-step explanation:

A rhombus is a quadrilateral with all 4 sides congruent. The sides can be slanted, which would keep it from being a square. If you make all the sides of a rhombus straight vertically and horizontally so you have 4 right angles, you have a square. A square is a quadrilateral with all 4 sides AND all 4 angles congruent.

Answer:

4x

Step-by-step explanation:

Answer:

(0-4)/(1-k)= -2

-4/(1-k)= -2

-2(1-k)= -4

-2 +2k = -4

2k = -2

k = -1

(-1, 4)

y - 4 = -2( x + 1)

y - 4 = -2x - 2

y = -2x + 2

Answer:

[tex]y = - \sqrt{x - 5} + 3[/tex]

Step-by-step explanation:

The function [tex]y = - \sqrt{x - 5} + 3[/tex] has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of [tex]- \sqrt{x - 5}[/tex] will be negative.

So, [tex]- \sqrt{x - 5} \leq  0[/tex]

⇒ [tex]- \sqrt{x - 5} + 3 \leq  3[/tex]

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)

Answer:

x intercepts at (-3,0), and (1,0)

there is a minimum at (-1,-4)

Step-by-step explanation:

Please see attached image for the requested graph of the function [tex]f(x) = x^2+2x-3[/tex], and observe that the crossings of the x-axis are at the points (-3,0), and (1,0) , marked in red in the image.

We can also see that there is no maximum, but a minimum value, and located at the point (-1,-4) [marked in green in the image]

Final answer:

In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB. The corresponding sides of RGK and MQB are RG = MQ, RK = MB, and GK = QB.

Explanation:

In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB.

In this case, RGK and MQB are both triangles, so we need to compare their corresponding sides. The corresponding sides of a triangle are the sides that are in the same position (opposite vertices) in the two triangles.

Therefore, the corresponding sides of RGK and MQB are:

RG = MQ

RK = MB

GK = QB