An architect has a scale drawing of an addition that is to be added to a house with a scale of 1 inch : 2 feet. If the drawing is 6 inches by 10 inches, how big is the addition to the house going to be?
Answers
In order for us to solve this problem, we will be needing to form a ratio just like the ones the question provides to us. In case you don't quite understand how to do it, don't fret and watch me explain it. I will also be attaching an image with all the work shown in case you need extra help.
As we know, the scale of the house is 1 inch : 2 feet. First of all, let's balance the unit sizes by converting 2 feet into inches, thus making the problem much easier.
One foot is 12 inches, meaning that two feet should be two times more than 12 inches.
[tex]12(2)=24[/tex]
Great! We can now form the balanced ratio. It is going to be 1 inch : 24 inches. Now, let's form an actual ratio with plugged in unknown variable in order for us to solve for it.
[tex] \frac{1}{24} : \frac{6}{x} [/tex]
According to the ratio, our numerator on the right side is six time bigger than numerator on the left side, meaning that our denominator on the right side is six times bigger than denominator on the left side as well. Keeping this in mind, let's solve for it.
[tex]24(6)=144[/tex]
Awesome! One of the sides is 144 inches. We are left with only one side which is 10 inches on the scale. Let's form the same ratio and solve for it.
[tex] \frac{1}{24} : \frac{10}{x} [/tex]
Just like we did in our last step, let's multiply the left denominator with the right numerator.
[tex]24(10)=240[/tex]
We now know values of two sides, and we can set it as our answer.
Answer:144 by 240 inches is the size of the house.
Related Questions
You are a farmer and want to spend under $35,000 on farm equipment. You need a hay bailer that costs $6,250 and several plowing disks cost $2,500 each. Write an inequality that models how many plowing disks could be purchased within your budget. What is the maximum number of plowing disks you can buy?
Answers
Maximum plowing disks: 10 which would cost you $31, 250
Answer:
A) 2,500x + 6,250 < 35,000; 11 plowing disks
Step-by-step explanation:
The hypotenuse of a right triangle is 37 mm. One leg of the right triangle is 12 mm. What is the length of the other leg? 30 mm 35 mm 40 mm 47 mm
The legs of a right triangle are 10 cm and 24 cm. What is the length of the hypotenuse?
22 cm 26 cm 30 cm 34 cm
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What does the y-intercept have to do with the graph?
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Ex:(3, 6)
The y is the 6 the 6th number up the line.
A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 7 and the hole has a radius of x + 6, what is the area of the washer?
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[tex]A_c = \pi r^2[/tex]
Now, we need to find the radius of the entire metal circle which the hole was drilled on:
[tex]R_w = (x+7) - (x+6) = 1[/tex]
Plug it in to find the area of the metal plate:
[tex]A_p = \pi (1)^2 = \pi [/tex]
Now, you subtract the area of the hole from the area of the plate. The area of the hole will be:
[tex]A_h = \pi (x+6)^2[/tex]
[tex]A_h = \pi (x^2+12x+36) = [/tex]
Subtract the area of the hole from the metal plate to get:
[tex]A_w = \pi - (\pi x^2+12 \pi x+36 \pi) = \pi x^2+12 \pi x -35 \pi[/tex]
That's your answer, although it looks wrong because not much information was provided.
A square has an area of 49 square inches. Explain how to find the perimeter of the square.
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9. 10. 11. And need work or won’t get credit
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Answer:
9) 22 - 5(6v - 1) = -63
22 - 30v + 5 = -63
27 - 30v = -63
-30v = -90
v = 3
10) 18x - (8x - 7) = 67
18x - 8x + 7 = 67
10x = 60
x = 7
11) 8(-2x - 4) + 12 = -52
8(-2x - 4) = -64
-2x - 4 = -8
-2x = -4
x = 2
200 grams of fertilizer are used for each tree in an orchard containing 1200 trees. at $2.75 per kilogram of fertilizer, how much does it cost to fertilize the orchard ?
Answers
To fertilize an orchard of 1200 trees, with 200 grams of fertilizer per tree and the cost of fertilizer at $2.75 per kilogram, the total cost would be $660.
To calculate the cost to fertilize an orchard of 1200 trees, assuming 200 grams of fertilizer are used per tree, and the fertilizer costs $2.75 per kilogram, we need to follow these steps:
Convert the amount of fertilizer needed per tree into kilograms, as the cost is given per kilogram. Since there are 1000 grams in a kilogram, 200 grams is equal to 0.2 kilograms.
Multiply the amount of fertilizer needed per tree by the number of trees to find the total amount of fertilizer needed for the orchard. This is 0.2 kg/tree times 1200 trees = 240 kilograms.
Multiply the total kilograms of fertilizer by the cost per kilogram to find the total cost of fertilizing the orchard. This is 240 kg times $2.75/kg = $660.
Therefore, the total cost to fertilize the orchard is $660.
y=-x+7 , y=x-1 and show your work Help !
Answers
[tex]7=2x-1 \\ 8=2x \\ 4=x[/tex]
Then, substitute 4 into one of the original equations to find y.
[tex]y=(4)-1=3[/tex].
The solution is [tex](4,3)[/tex]. I have attached a graphical representation of the solution as well.
According to the Transitive Property of Congruence: If CD≅EF and EF≅GH, then _____
A. CD≅EF
B. EF≅EF
C. CD≅GH
D. EF≅GH
If you're reading this the answer is C
Answers
Answer:
The answer is the option C
CD≅GH
Step-by-step explanation:
we know that
The Transitive Property of Congruence states that
If [tex]a=b[/tex] and [tex]b=c[/tex]
then
[tex]a=c[/tex]
In this problem we have
CD≅EF and EF≅GH
therefore
CD≅GH -------> by Transitive Property of Congruence
simplify the expression
(3x^4y^-5)3
Answers
To simplify the expression (3x^4y^-5)^3, apply the power rule to each term, calculate the result, and combine them. The simplified form is 27x^12y^-15.
How to Simplify the Expression (3x^4y^-5)^3:
Let's simplify the given expression step by step:
Apply the power rule of exponents to the entire expression. This means raising each term inside the parentheses to the given power:(a^m * b^n)^p = a^(m*p) * b^(n*p)
So, (3x^4y^-5)^3 becomes:
(3^3) * (x^(4*3)) * (y^(-5*3))
Calculate each term separately:3^3 = 27x^(4*3) = x^12y^(-5*3) = y^-15Putting it all together, we get:
27x^12y^-15
Simplified Form:In conclusion, the simplified form of (3x^4y^-5)^3 is 27x^12.y^-15.
A triangle has a side lengths of (5.5x + 6.2y) centimeters, (4.3x+8.3z) centimeters and (1.6z -5.1y) cenrimeters which expression represents the perimeter,in centimeters of the triangle
Answers
Answer:
Perimeter of given triangle is ( 9.8x + 1.1y + 9.9z ) centimeters.
Step-by-step explanation:
Given : A triangle has a side lengths of (5.5x + 6.2y) centimeters, (4.3x+8.3z) centimeters and (1.6z -5.1y) centimeters
We have to find the expression that represents the perimeter (in centimeters)
of the triangle.
Perimeter of a figure is defined as the sum of all the sides.
Since given figure is triangle so perimeter of triangle is the sum of all the sides.
Given side lengths are
(5.5x + 6.2y) , (4.3x + 8.3z) and (1.6z -5.1y)
Thus, perimeter = (5.5x + 6.2y) + (4.3x + 8.3z) + (1.6z - 5.1y)
Perimeter = 5.5x + 6.2y + 4.3x + 8.3z + 1.6z - 5.1y
LIKE TERMS are term with same variables.
Rearrange, we get
Perimeter = 5.5x + 4.3x + 6.2y - 5.1y + 8.3z + 1.6z
Adding like terms, we get,
Perimeter = (5.5 + 4.3)x + (6.2 - 5.1)y + (8.3 + 1.6)z
Perimeter = (9.8)x + (1.1)y + (9.9)z
Thus, Perimeter of given triangle is 9.8x + 1.1y + 9.9z centimeters.
The sum of two numbers is -1. When twice the first number and four times the second number are added, it equals -10. What are the two numbers?
Answers
x+y=-1......i
2x+4y=-10.....ii
solving the simultaneous equation we have:
from equation i, making x the subject we get:
x=-1-y........iii
substituting iii in ii we get:
2(-1-y)+4y=-10
-2-2y+4y=-10
2y=-10+2
2y=-8
y=-8/2=-4
substituting the value of y in iii we get:
x=-1-(-4)
x=-1+4
x=3
therefore the first number is 3 and the second number is -4
What is the same as 98.52 divided by 10
Answers
Dividing 98.52 by 10 involves moving the decimal one place to the left, resulting in 9.852. This process is the same for all decimals when dividing by powers of 10, such as 10, 100, or 1000.
When we divide a number by powers of 10, we're effectively moving the decimal point to the left by as many places as there are zeros in the power of ten. For instance, dividing 1.9436 by 10 moves the decimal one place to the left, becoming 0.19436. Similarly, dividing 98.52 by 10 moves the decimal one place to the left as well, giving us the simplified answer of 9.852.
If we were to multiply a number by powers of 10, we would do the opposite, moving the decimal to the right. For example, to multiply 45.86 by 100, you would move the decimal two places to the right to get 4586.
In conclusion, 98.52 divided by 10 is 9.852. Even if the answer is rounded, the process remains the same; you simply adjust the decimal point accordingly based on the power of 10 you are dividing by.
Number 14
I need help with this
Answers
The puzzles measures 12 inches by 12 inches.what is the area of the puzzle.
Answers
PLEASE HELP ME!!!!!!!!!!! FAST PLEASE ITS URGENT!!!!!!!! WILL GIV BRAINLIEST!!!
The golf scores for the 32 members of the Belmont Country Club were 108, 89, 74, 115, 92, 86, 103, 107, 94, 89, 111, 78, 116, 82, 99, 107, 74, 78, 101, 93, 85, 98, 109, 82, 83, 105, 91, 106, 97, 84, 92, 96. Which histogram correctly shows the frequency distribution of the scores using ten-point intervals?
Answers
Histogram options for golf scores: (a) 3,9,8,9,2; (b) 5,7,10,7,4; (c) 4,8,9,8,3; (d) 5,8,9,8,5. Correct choice (d) accurately represents the frequency distribution of scores in ten-point intervals.
To create a histogram with ten-point intervals for the given golf scores, we need to organize the scores into ranges and determine the frequency of scores within each range. Let's examine each option:
a. 70-80: 3 scores, 80-90: 9 scores, 90-100: 8 scores, 100-110: 9 scores, 110-120: 2 scores.
b. 70-80: 5 scores, 80-90: 7 scores, 90-100: 10 scores, 100-110: 7 scores, 110-120: 4 scores.
c. 70-80: 4 scores, 80-90: 8 scores, 90-100: 9 scores, 100-110: 8 scores, 110-120: 3 scores.
d. 70-80: 5 scores, 80-90: 8 scores, 90-100: 9 scores, 100-110: 8 scores, 110-120: 5 scores.
The correct histogram is option (d) with scores in the 70-80, 80-90, 90-100, 100-110, and 110-120 ranges having frequencies of 5, 8, 9, 8, and 5, respectively. This accurately represents the distribution of golf scores in ten-point intervals among the members of the Belmont Country Club.
shannon uses 30 inches of ribbon to make one bow.how many feet are needed to make 10 bows?
Answers
hope this helps
PLEASE HELP!!!! THANK YOU!!!
The graph of the function y = x2 is shown. How will the graph change if the equation is changed to y = 2x2?
A) The parabola will become wider.
B) The parabola will become narrower.
C) The parabola will move up 2 units.
D) The parabola will move down 2 units.
Answers
The parabola will become narrower, the correct option is B.
How the graph will change?
For a function f(x), we define a vertical stretch of scale factor k as:
g(x) = k*f(x).
If k > 1, we have a stretch, if 0 < k < 1, we have a contraction.
In this case, we have:
f(x) = x^2g(x) = 2*x^2So we have a vertical stretch of scale factor 2, this means that we are stretching our function vertically, so it will become narrower, meaning that the correct option is B.
If you want to learn more about transformations, you can read:
https://brainly.com/question/4289712
for every pound a company spends on advertising it spends £0.64 on its websites. express the amount spent on advertising to the amount on its website it's website as a ratio it's in its simplest form
Answers
= 25:16
Solution:
we are given that
For every pound a company spends on advertising it spends £0.64 on its websites.
we have been asked to express the amount spent on advertising to the amount on its website it's website as a ratio it's in its simplest form.
We can find the required ratio as below
[tex]Ratio=\frac{1}{0.64} \\ \\ Ratio=\frac{100}{64} \\ \\ Ratio=\frac{25}{16} \\[/tex]
Hence the required ratio is 25:16.
Landons front lawn measures 20 feet by 8 feet he counts to find that there are 120 blades of grass per square inch how many blade do grass are in the entire lawn use proportions
Answers
1 foot = 12 inches
20feet = 20*12=240 inches
8feet = 8*12=96 inches
Now we can calculate total area:
A = height * width
A= 240 * 96
A=23040 inches²
We know the amount per one inch² and we need to find out total number of blades:
1 inch² 120 blades
23040 inches² x blades
Now we cross-multiply numbers:
1*x = 23040 * 120
x= 2764800
There are total of 2764800 blades in the entire lawn
Kade makes 5/6 cup salad dressing. He uses 2/3 cup dressing on a salad. How much salad dressing is left
Answers
[tex] \dfrac{5}{6} - \dfrac{4}{6} = \dfrac{5-4}{6} = \dfrac{1}{6} \ cups[/tex].
Kade has 1/6 cup of salad dressing left after using some on a salad. We found this by converting 2/3 cup to 4/6 cup and then subtracting it from the 5/6 cup he initially had.
To find out how much salad dressing Kade has left after using some on a salad, we need to subtract the amount used from the total amount he made. Kade made 5/6 cup of salad dressing and used 2/3 cup on a salad. To perform the subtraction, both fractions need a common denominator. The smallest common denominator for 6 and 3 is 6. The fraction 2/3 can be converted to 4/6 so that both fractions have the same denominator. Now we can subtract:
Convert 2/3 cup to 4/6 cup (Since 3*2 = 6, and 2*2 = 4).Subtract 4/6 cup from 5/6 cup: 5/6 - 4/6 = 1/6 cup.Hence, Kade has 1/6 cup of salad dressing left after using it on the salad.
A business owner purchases supplies for a laundromat and a car wash.
Part A
The owner purchases 6 cases of laundry soap, 8 cases of fabric softener, and 3 cases of bleach for the laundromat. Each case of laundry soap costs $68.45, eash case of fabric softener costs $39.71, and each case of bleach costs $52.25.
Which is the best estimate of the total cast, in dollars, of the laundry items?
Answers
The best estimate of the total cast, in dollars, of the laundry items is $885.
What is total?A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.
Given that, the owner purchases 6 cases of laundry soap, 8 cases of fabric softener, and 3 cases of bleach for the laundromat.
Each case of laundry soap costs $68.45
So, the cost of 6 cases of laundry soap
= 6×68.45
= $410.7
Each case of fabric softener costs $39.71
So, the cost of 8 cases of fabric softener
= 8×39.71
= $317.68
Each case of bleach costs $52.25
So, the cost of 3 cases of bleach for the laundromat
= 3×52.25
= $156.75
Total =410.7+317.68+156.75
= $885.13
≈ $885
Therefore, the best estimate of the total cast, in dollars, of the laundry items is $885.
Learn more about the total here:
https://brainly.com/question/15842940.
#SPJ3
Chris is making a poster for Bike Safety Week. The diameter of circle A is 14 in.
If the area of circle B is the area of circle A, what is the area of circle B? (Use 3.14 for .)
Answers
Answer:
30.772 in2.
Step-by-step explanation:
First, find the radius of circle A.
* in picture*
Next, use the formula and the radius of circle A to find the area of circle A.
*in picture*
Last, multiply the area of circle A by to find the area of circle B.
*in picture*
Therefore, the area of circle B is 30.772 in2.
Principle = $15,500 Interest Rate = 8.75% Time = ? Years Simple Interest = $5425.00
Solve for the Time in Years
Answers
I = P x i x t
I is the interest
P is the total principal
i is the rate of interest per year
t is the total time in years
In this example, when we plug our known values in, our formula looks like this:
t = [tex] \frac{I}{i*p} [/tex]
t = [tex] \frac{5425}{0.0875 * 15500} [/tex]
t = 4
So time (in years) would be 4 years.
Simplify the expression. 6k – 1 + 6k
Answers
6k + 6k - 1
12k - 1
graphing system y=2x-2 2y=4x- 4
Answers
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In the graph here, the graph of one equation is shown as a dotted line, not be cause those are the only points on the graph, but because I wanted you to see the other equation describes exactly the same line.
Answer:
These two equations describe the same line.
___
In the graph here, the graph of one equation is shown as a dotted line, not be cause those are the only points on the graph, but because I wanted you to see the other equation describes exactly the same line.
A ________ is a monomial or the sum or difference of two or more monomials. Base, polynomial, linear term,quadratic equation
Answers
"A polynomial is a monomial or the sum or difference of two or more monomials".
By definition, the terms of a Polynomial Function have the form ax^n, where "n" is a natural number.
To classify a polynomial, you must count the number of its terms. For example:
5x²-2x (This is a binomial, because it is formed by two terms).
x³-3x+1 (This is a trinomial, because it has three terms):
To identify the degree of a polynomial, you must see the term which has the highest exponent. For example, the degree of following polynomial is 2.
4x²-x+3
The degree of this polynomial is 3:
x³+2x²-x+10
A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
Answers
Answer:
Multiply [tex]2\frac{1}{2}[/tex] by [tex]3[/tex] and then add [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{(3/4)}{1}\frac{in}{week}=\frac{x}{3}\frac{in}{weeks} \\ \\x=3*(3/4)\\ \\x=9/4\ in[/tex]
Find the height of the plant in [tex]3[/tex] weeks
[tex]2\frac{1}{2} +\frac{9}{4}=\frac{5}{2} +\frac{9}{4}\\ \\=\frac{19}{4}\ in[/tex]
therefore
The incorrect method is
Multiply [tex]2\frac{1}{2}[/tex] by [tex]3[/tex] and then add [tex]\frac{3}{4}[/tex]
because
[tex]2\frac{1}{2}*3+\frac{3}{4}=\frac{15}{2}+\frac{3}{4}\\ \\=\frac{33}{4}\ in[/tex]
The table shows the change in the low temperature in Albany compared to the day before.
Wednesday : +3.5
Thursday: -4.1
Friday : 0
Saturday: -2.2
On which day did the low temperature change the most?
Answers
Answer: On Thursday the low temperature change the most.
Explanation :
From the given table we can conclude that change is the lowest in Thursday .
And there is no matter if it is positive or negative
Because change defines final - initial only i.e. difference between final and initial
So, we consider absolute value only.
According to which Thursday has the atmost change i.e 4.1 which is the lowest amongst the other .
So ,on Thursday the low temperature change the most.
The day with the most temperature change in Albany compared to the day before is Thursday.
The day with the most temperature change was Wednesday.
To determine the most significant change, we calculate the absolute difference for each day's temperature change:
Wednesday: |+3.5| = 3.5Thursday: |-4.1| = 4.1Friday: |0| = 0Saturday: |-2.2| = 2.2Therefore, Thursday had the most substantial temperature change.
Help me with this one question and think closely it is not 8 or 800 question 36
Answers
≈ 22.75 gal
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The conversion from liters to gallons is accurate to the digits shown, but is not exact.