Mathematics High School

The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects, Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let a represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.​

Answers

Answer 1

Answer:

Statement 2, Statement 4, and Statement 5 all applies

Step-by-step explanation:

Statement 1:

The expression 50ℎ represents the total charge for Rock the House Digital Designs.

Rock the House Digital Designs:

Initial consultation charge of $500 + $50 for every additional hour of work for the house plans

500 + 50h

NOT TRUE

Statement 2:

The expression 75ℎ represents the total charge for Elegance Home Architects.

Elegance Home Architects:

$75 per hour for the house plans

75h

TRUE

Statement 3:

The cost for using Rock the House Digital Designs for an initial consultation only is $550.

The cost for using Rock the House Digital Designs for an initial consultation only is $500

NOT TRUE

Statement 4:

If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

Rock the House Digital Designs = 500 + 50h

500 + 50(15)

= 500 + 750

= $1,250

Elegance Home Architects = 75h

= 75(15)

= $1,125

TRUE

Statement 5:

If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

Rock the House Digital Designs = 500 + 50h

= 500 + 50(40)

= 500 + 2,000

= $2,500

Elegance Home Architects = 75h

= 75(40)

= $3,000

TRUE

Related Questions

Find the missing angles with reasons.

Answers

Answer:

C and D

Step-by-step explanation:

C) C = [360 - 148(2)] divide 2

= 32 degrees

Explanation: 148 and C is an opposite angle so the angles oppose to it has the same value

D) h = 76

Explanation: opposite angles

I = 76

Explanation: transverse angles

j = [360 - 76x2] divide 2

= 104 degrees

Explanation: same as C

Hope this helps!

help ASAP!!

i need help finding out the pattern of 3 and 4

Answers

Answer:

See below.

Step-by-step explanation:

For 3, we have:

1, 3, 6, ___, 15, 21, _____, 36, _______

Let's try to determine the pattern. From 1 to 3, we added 2.

From 3 to 6, we added 3.

So, it seems that the fourth term would be to add 4, and then add 5. Let's try it:

6+4=10

10+5=15.

So, it seems we're correct. So, we will add 6, then 7, and then 8, etc. Therefore, our correct sequence would be:

1 (+2), 3 (+3), 6 (+4), 10 (+5), 15 (+6), 21 (+7), 28 (+8), 36 (+9), 45

For 4, we have:

100, _____, 64, ______, 36, 25, _______

Notice that these all are perfect squares. 10 squared is 100, 8 squared is 64, etc. Thus, we can rewrite this as:

10², _____, 8², ______, 6², 5², ______

Therefore, our blanks would be:

10², 9², 8², 7², 6², 5², 4².

Evaluated, this woul be:

100, 81, 64, 49, 36, 25, 16.

And we're done!

Find patterns between 3 to 10 percent

Mara found the length of time of an investment. The principal of the investment was $4,300, the interest rate was 6.2 percent, and the interest was $2,666. Mara made an error in her work. I = p r t. 2666 = (4300) (0.062) t. 2666 = (266.6) t. StartFraction 266.6 over 2666 EndFraction = t. 0.1 = t. What was Mara’s error?

Answers

Answer: Maria did not divide correctly

Step-by-step explanation:

Answer:

Maria did not divide correctly

Step-by-step explanation:


Multiply (6 − 7i)(3 − 6i).

Answers

Answer:

-24 - 57i

Step-by-step explanation:

i'm assuming that this is a question about imaginary numbers and that i²= -1

we can expand the binomial by using the FOIL method (see attached)

(6 − 7i)(3 − 6i)

= (6)(3) + (6)(-6i) + (-7i)(3) + (-7i)(-6i)

=18 - 36i - 21i + 42i²   (recall that i²= -1)

= 18 - 57i + 42(-1)

= 18 - 57i - 42

= -24 - 57i

What is the image of (-12,-3) after a dilation by a scale factor of 1/3 centered at the origin?

Answers

Answer:

(-4, -1)

Step-by-step explanation:

Multiply both coordinates by 1/3 which is the same as dividing by 3.

Answer: (-4, -1)

Owen follows the rule "divide by 2" to write the pattern below . He will write two more numbers to complete the pattern. Which statement is true? 800,400,200,100,_____​

Answers

Answer:

50,25

Step-by-step explanation:

you continue to divide by 2 so 100/2 is 50 then 50/2 is 25

please help with the following maths question

Answers

Answer:

120 degrees

Step-by-step explanation:

Regular hexagon means all the sides are equal

(6-2)(180)=The sum of interior angles of hexagon

=>720 degree

Therefore each angle=720/number of sides

=720/6=120 degree

So let the marked angle in figure be 'x'

And the adjacent equal angles to x, y

So y+y+x=360 [Angle around point=360]

2y+x=360 [but y=120 degree proved]

240+x=360

x=120

Answer:

the answer is 120 degrees- i dont feel like typing everything out about how i got it but ik thats the answer.

Step-by-step explanation:

Does anyone know what the answer is

Answers

Answer:

cheating in entrance

Step-by-step explanation:

circumference: 14π

area: 49π

Answer:

nope

Step-by-step explanation:

Corinna has $72. She wants to buy a $281 plane ticket. She will save up her earnings from working at the museum where she earns $19 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $281? A. n ≥ 11 B. n ≤ 10 C. n ≥ 10 D. n ≤ 11

Answers

Answer:the correct answer is b

Step-by-step explanation:

6. Which units do we use when calculating the perimeter? (select all that
apply)
-millimetres
-kilogram
-metres
-centimetres
-kilometres

Answers

Answer:

The perimeter is a distance so all length units apply

● millimeters

● meters

● centimeters

help on absolute value!

Answers

Answer:

9

Step-by-step explanation:

we have

[tex]|\frac{27}{-3}|\\\\=|-9|[/tex]

and absolute value of -9 is 9

so answer is 9

A=1/2(B+C-D) SOLVE FOR B

Answers

Answer:

           B = 2A - C + D

Step-by-step explanation:

  A = ¹/₂(B + C - D)

  ×2      ×2

 2A = B + C - D

-C+D         -C+D

  2A - C + D = B

please help ! ALGEBRA 1

Answers

Answer:

Option B is the correct answer.

Step-by-step explanation:

[tex]0. \overline{79} + \pi[/tex]

Here [tex] 0.\overline{79}[/tex] is a rational number and [tex] \pi[/tex] is an irrational number whose sum gives irrational number.

Answer:

Te answer  would be to tenth of PIE so 0.79 would be ruled out

Step-by-step explanation:

I WILL GIVE YOU BRAINLIEST,5 STARS, AND THANKS.(P.S. AT LEAST TWO PEOPLE GIVE ANSWER SO I CAN GIVE BRAINLIEST)

Answers

Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

Which of the following numbers is a whole number?
O 03
02
0-8
3

Answers

The following number that is a whole number is 3 because there is no fractional part and no negatives . Therefore , 3 is the correct answer / whole number .
The correct answer is 3

What is the base in -5x2

Answers

Answer:

Step-by-step explanation:

10 lol

The answer to the problem is -10

Joe is making key chains with beads. He wants each key chain to have the same number of beads. He has 90 blue beads and 72 yellow beads. What is the highest amount of key chains he can make?

Answers

Answer:1.25

Step-by-step explanation:90/72

Joe can make 9 key chains to have the same number of beads with 90 blue beads and 72 yellow beads.

What are HCF and distributive property?

The HCF of two or more than two numbers is the highest number that divides the given two numbers completely.

Joe wants each key chain to have the same number of beads.

∴ HCF of 72 and 90 is 18

Now with those 18 beads 9 each type he can make (90 + 72)/18 key chains.

= 162/18.

= 9 key chains.

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if x=7+4√3,find the value of √x+¹/√x​

Answers

Answer:Answer:x = 7+4√3Answer:x = 7+4√3To find √x we proceed,Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form ofAnswer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√3Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we getAnswer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =1/√x = 2-√3Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =1/√x = 2-√3Hence √x +1/√x = 2+√3 +2 -√3 = 4

factorise 7a + 14b + ax + 2bx
​

Answers

Answer:

Step-by-step explanation:

7(a + 2b) + x(a + 2b)

(7 + x)(a + 2b)

Answer:

(7 + x)(a + 2b) This is most simplified it can be

If point A is translated 4 units left and 6 units down, what are the coordinates of A?
A)
(6, 1)
B)
(6, -1)
C)
(-2, 1)
D)
(-2,-1)

Answers

Answer:C (-2, 1)

Step-by-step explanation:

You have 20 gallons of roof coating to apply to the roof of a mobile home that is 16 feet wide. Twenty gallons covers 760 to 1000 square feet. Find the interval for the length of x that you will cover before you need to buy more roof coating.

Answers

Area = length x width.

Divide the two total areas by the width to find the lengths:

760/16 = 47.5

1000/16 = 62.5

The interval is:

47.5<= x <= 6.5

The interval for the length of x that you will cover before you need to buy more roof coating will be 47.5 ≤ x ≤ 6.5.

What is inequality?

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.The space occupied by any two-dimensional figure in a plane is called the area.

Given that you have 20 gallons of roof coating to apply to the roof of a mobile home that is 16 feet wide. Twenty gallons covers 760 to 1000 square feet.

The formula to calculate the area of the

Area = length x width.

Divide the two total areas by the width to find the lengths:

760/16 = 47.5

1000/16 = 62.5

The interval is:

47.5 ≤ x ≤ 6.5

Therefore, the interval will be 47.5 ≤ x ≤ 6.5.

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Tables of Ratios: Mastery Test
Drag each number to the correct location on the table. Not all numbers will be used.
The table gives ratios between distance and time. Complete the table to form equivalent ratios.
10
210
490
Distance (miles)
140
Time (hours)
2
4
5
280
350
420
560
6
8
12
700

Answers

Answer: Distance(Miles)

140,420,560

Time(Hours)

5,10

PLS HELP
what would be an appropriate level for the dependent variable on this graph?

Answers

Answer:

Y-axis = scoops sold

X-axis = month

What minus 5 equals 14

Answers

Answer:

19

Step-by-step explanation:

All you have to do is add 14 to 5 to find out x-5=14

PLEASE HELP, Find the slope of the following lines :D

Answers

number one is 2/6 number 2 is -10/4 and number three is 4.
you have to do rise over run and then divide if you need to. if it’s going to the right then it’s positive and if it’s going to the left then it’s negative.

1 gallon is around 3.8 liters. State this as a ratio of liters to gallons, in the form a:b. Give your answer in simplest form

Answers

So the answer is 3.4 um and ya

The ratio of liters to gallons in simplest form is 5 : 19.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, 1 gallon is around 3.8 liters.

So, The ratio of liters to gallons in a : b form is 1 : 3.8

Or, 10 : 38,

Or 5 : 19.

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Use the distributive property: (5x - 3y + 4)6

Answers

Answer:

30x - 18y + 24

Step-by-step explanation:

When the distributive property is in play, you multiply all the numbers in the parenthesis by the number that's right next to it. In this case, you're multiplying 6 to all of the numbers in the paranthesis (5x - 3y +4).


A jar contains 6 yellow marbles, 4 black marbles, and 2 purple marbles. Two marbles are picked at random, without replacement. What is the probability of
selecting both yellow?

Answers

Answer:

The probability of selecting both yellow is 5/22.

Step-by-step explanation:

Given the number of yellow marbles = 6

Black marbles = 4

Purple marble = 2

Now find the total number of marbles in the jar.

Thus total marbles = Yellow marbles + Black marbles  + Purples marble

Now insert the values in the above formula.

Total marbles = 6 + 4 + 2

Total marbles = 12

The probability of 2 yellow marble:

[tex]= \frac{6}{12} \times \frac{5}{11} \\= \frac{5}{22}[/tex]

Thus, the probability of selecting both yellow is 5/22.

-3(4x+2)=18 WHAT IS IT????

Answers

Answer:

x = -2

Step-by-step explanation:

-3(4x + 2) = 18

Divide by -3:

-3(4x + 2) / -3 = 18 / -3

4x + 2 = -6

Subtract 2:

4x + 2 - 2 = -6 - 2

4x = -8

Divide by 4:

4x / 4 = -8 / 4

x = -2

Which of the following is NOT a type of bank?
OA) savings and loans association
OB) credit union
OC) modern bank
OD) commercial bank

Answers

Answer:

OC) modern bank

Step-by-step explanation:

OC) modern bank

There is no such type of bank.

OC) modern bank, there is no such thing
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