Scale factor is the ratio of representation measurement of the figure to the original figures.
The actual dimensions of the kitchen is 12 ft by 14 ft.
What is scale factor?Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures.
Given information-
Dimensions of the balcony of the apartment is 4 ft by 7 ft or 48 in by 84 in (multiplying it by 12 to convert in inches).
Dimensions of the balcony of the apartment is 0.8 ft by 1.4 in on the scale of drawing.
Dimensions of the kitchen is 2.4 inches by 2.8 inches on the scale of drawing.
The scale factor of the width of the balcony is the ratio of scale dimension of width and the actual dimension of the width . Thus,
[tex]r=\dfrac{0.8}{48} \\r=\dfrac{1}{60}[/tex]
The scale factor of the length of the balcony is the ratio of scale dimension of length and the actual dimension of the length . Thus,
[tex]r=\dfrac{1.4}{84} \\r=\dfrac{1}{60}[/tex]
Thus the scale factor of the length and width of the scale is same which is 1/60.
As the scale is same for the balcony and the kitchen. Thus the scale factor would also be same.
The scale factor of the width of the kitchen is the ratio of scale dimension of width and the actual dimension of the width .
Let the width of the kitchen is x in.Thus
[tex]\dfrac{1}{60}=\dfrac{2.4}{x} \\x=144\rm in[/tex]
Thus the width of the kitchen is 144 in or 12 ft.
The scale factor of the length of the kitchen is the ratio of scale dimension of length and the actual dimension of the length .
Let the length of the kitchen is y in. Thus
[tex]\dfrac{1}{60}=\dfrac{2.8}{y} \\y=168\rm in[/tex]
Thus the length of the kitchen is 168 in or 14 ft.
Hence, the actual dimensions of the kitchen is 12 ft by 14 ft.
Learn more about the scale factor here;
https://brainly.com/question/10253650
How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies
To find total cookies sold add each kind of cookie together.
total = 320 + 270 = 590
answer: 590 total cookies
Answer:
590
Step-by-step explanation:
You must add the two numbers.
320 + 270 = 590
Hi, can someone help with this problem ASAP?
Answer:
the value of x is 68
Step-by-step explanation:
because the line does change on either of the sides so that makes x the same value as the other side which is 68. forgive me if im wrong.
Desk 4
Christopher had $125 in his savings account
to buy a used car. He used the equation
A = 50w + 125 to determine the amount in
his savings, A, after depositing the same
amount in his account every week, W.
• What is the slope of the line?
• What does the slope represent in the
context of the problem?
Answer:
50; every week he deposits $50
Step-by-step explanation:
the slope in this equation is 50
using the formula y = mx + b with m being the slope we can tell that 50 is where the m is
this means that every week he deposits $50
One restaurant sells a family meal for $22 plus $2 per drink.
.
Another restaurant sells a family meal for $25 plus $1.50 per
drink. How many drinks need to be purchased at each
restaurant so the the total cost for a meal and drinks is the
same?
Answer:
the 2$ resturant needs 11 and the $1.50 needs 16
Step-by-step explanation:
division
Which of the following expressions is equivalent to 22−10y+2(y−3)?
Select one:
28−8y
8(2−y)
14y−72
3(7+3y)
PLEASE HELP ME!
Answer:
B. 8(2-y)
Step-by-step explanation:
22-10y+2(y-3)
22-10y+2y-6
22-6-10y+2y
16-8y
Using factorisation method
8(2-y)
b) A factor of 30 is chosen at random.
What is the probability, as a decimal, that it is a 2-digit number?
Answer:
0.375
Step-by-step explanation:
Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30
three two digit numbers and 8 total so 3/8
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS
Answer:
∠C and ∠R
Step-by-step explanation:
1. ∠C and ∠T don't match
- One slanted, One Straight
2. ∠D and ∠T don't match
- One slanted, One Straight
3. ∠C and ∠R both match
- Both Straight
4. ∠D and ∠U don't match
- One slanted, One Straight
which of the following linear systems has a solution
(5,0)
SOMEONE PLS HELPPP
Answer:
D
Step-by-step explanation:
out of the choices
A) 2x-y=-2
3x+2y=-10
B) x+4y=3
2x+5y=3
C) 2x+3y=5
x-4y=-14
D) 3x+4y=15
x+y=5
only the system in D has a solution of x=5 and y=0
solve by substitution x+y=5 so x=5-y
plug into the other equation so 3(5-y)+4y=15
distribute 15-3y+4y=15 then minus 15 on both sides and combine like terms
so y=0 then put that value back into the other equation
so x+y=5 equals x+0=5 so x=5 this means the solution to the system of equations is the point (5,0)
Hope this helps! :)
which of the following is a type of special triangle
a) 45- 45-90
b ) 25-50-75
c) 60-60-60
d) all of above
Answer:
A) 45-45-90
Step-by-step explanation:
45-45-90 is a special right triangle.
Does this graph represent a function?
Answer:
The answer is B.
Step-by-step explanation:
some of the y values are paired with two x-values.
HELP ME PLZZZZZZZZZZZZZZZ
Step-by-step explanation:
g(f(x)) = f(x) substituted in g(x)'s function.
g(3x^2 - x - 8) = 3x^2 - x - 8 + 5 = 3x^2 - x - 3.
if 5 likes of milk weighs 3,5 kg how much does 2litres of milk weighs. the unit rate
What is 2s+3 > 15 it’s a two step inequalities?
Answer:
s > 6
Step-by-step explanation:
1st step: subtract 3 from each side of the inequality to get:
2s > 12
2nd step: divide each side by 2 to get:
s > 6
How to find an equation given the slope and y intercept.
Answer:
y = (slope) + (y-intercept)
Step-by-step explanation:
You put them both together.
Write and solve an inequality for situation.
1. Karin has $3 to spend in the arcade.
2.
The game she likes costs 50¢ per play.
What are the possible numbers of times
that she can play?
Answer:
6 times
Step-by-step explanation:
you divide 3.00 by 0.50
HELP ASAP!
Select the correct answer from each drop-down menu.
Consider polygon JKLMNO on the coordinate grid.
Drop-down options
First one 17.07, 12.5, 25
Second 50, 30, 20
Third one 61, 47, 68.5, 37
The area of the polygon JKLMNO is 68.5 square units
The area of triangle MNOThe coordinates of the triangle are:
M = (-1, -5)
N = (-8, -6)
O = (-5, -2)
Calculate the base and the height of the triangle using:
[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]
So, we have:
[tex]ON = \sqrt{(-5+ 8)^2 +(-2 + 6)^2[/tex]
ON = 5
[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]
OM = 5
The area is:
Area = 0.5 * ON * OM
This gives
Area = 0.5 * 5 * 5
Evaluate
Area = 12.5
Hence, the area of the triangle MNO is 12.5 square units
The perimeter of rectangle JLMOThe coordinates of the rectangle are:
J = (1, 6)
L = (5, 3)
M = (-1, -5)
O = (-5, -2)
Calculate the length and the width of the rectangle using:
[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]
So, we have:
[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]
OM = 5
[tex]ML = \sqrt{(-1 - 5)^2 + (-5 - 3)^2[/tex]
ML = 10
The perimeter is:
Perimeter = 2 * (OM + ML)
This gives
Perimeter = 2 * (5 + 10)
Evaluate
Perimeter = 30
Hence, the perimeter of the rectangle JLMO is 30 units
The area of the polygonIn (a), we have:
The area of the triangle MNO is 12.5 square units
The area of the rectangle JKMO is:
Area = OM * ML
This gives
Area = 5 * 10 = 50
The coordinates of triangle JKL are:
J = (1, 6)
K = (5, 6)
L = (5, 3)
Calculate the base and the height of the triangle using:
[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]
So, we have:
[tex]KL = \sqrt{(5- 5)^2 +(3 - 6)^2[/tex]
KL = 3
[tex]JK = \sqrt{(1- 5)^2 +(6 - 6)^2[/tex]
JK = 4
The area of JKL is
Area = 0.5 * KL * JK
This gives
Area = 0.5 * 3 * 4
Area = 6
Add the three areas
Total area = 6 + 12.5 + 50
Evaluate
Total area = 68.5
Hence, the area of the polygon JKLMNO is 68.5 square units
Read more about area and perimeter at:
https://brainly.com/question/11957651
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What is the slope of the line 3x - 13y=60
Answer:
3/13
Step-by-step explanation:
We put this equation into slope-intercept form by adding 13y to both sides. Then we divide both sides by 13. Lastly, the number we multiply x by equals our slope.
Determine if the following sequence is an Arithmetic Sequence. If it is, what would be the 31st term? NOTE: an=a1+(n-1)d
7, 11, 15....
A- 131
B- 127
C- 117
Answer:
The arithmetic sequence of 31st term is 127.
Step-by-step explanation:
Here's the required formula to find the arithmetic sequence :
[tex]\longrightarrow\pmb{\sf{a_n = a_1 + (n - 1)d}}[/tex]
[tex]\pink\star[/tex] aₙ = nᵗʰ term in the sequence[tex]\pink\star[/tex] a₁ = first term in sequence [tex]\pink\star[/tex] n = number of terms [tex]\pink\star[/tex] d = common differenceSubstituting all the given values in the formula to find the 31st term of arithmetic sequence :
[tex]\leadsto{\sf{ \: \: a_n = a_1 + (n - 1)d}}[/tex]
[tex]\leadsto{\sf{ \: \: a_{31} = 7+ (31- 1)4}}[/tex]
[tex]\leadsto{\sf{ \: \: a_{31} = 7+ (30)4}}[/tex]
[tex]\leadsto{\sf{ \: \: a_{31} = 7+ 30 \times 4}}[/tex]
[tex]\leadsto{\sf{ \: \: a_{31} = 7+ 120}}[/tex]
[tex]\leadsto{\sf{ \: \: a_{31} =127}}[/tex]
[tex] \star \: \: \pink{\underline{\boxed{\sf{\purple{a_{31} =127}}}}}[/tex]
Hence, the arithmetic sequence of 31st term is 127.
[tex]\rule{300}{2.5}[/tex]
write an algebraic expression
1. add 2 to k
2. Sam sells P rulers for Y dollars each
3. Difference between 10 and z
Answer:
1. k + 2 (or other way around, it doesn't matter)
2. PY or P×Y
3. 10 - z
Step-by-step explanation:
1. You are adding here, so you add the two terms together.
2. If we had the amount of rulers and how much they cost, we could multiply to find these. Since we don't, we just leave the two variables to be multiplied.
3. It is asking the difference between two numbers, meaning that you need to subtract. With these types of problems, you always use the first number that appears in the problem to start the expression. For instance, if it had listed z first, then you would have done z - 10.
Find the value of x fast pls
Answer:
Solution,
[tex]5x+12=6x-10\\12+10=6x-5x\\22=x\\x=22[/tex]
Step-by-step explanation: They are equal because they are vertically opposite angles.
Hope it will help you.
Ollie, a young man with insurance coverage, ends up in the hospital with a broken wrist suffered while playing football with a group of friends. After an X-ray, MRI, doctor visit, orthopedist visit, and cast, he leaves the hospital with a bill for $9,000. He has a $2,000 annual deductible, and this is his first visit to a doctor in this calendar year. He also has a 20% co-pay. The amount that he is responsible for paying is?
Answer choices ↓
nothing since he did not need to stay overnight in the hospital.
$3,400.
only the $2,000 annual deductible.
$1,800.
Answer: only the $2,000 annual deductible.
$1,800.
Step-by-step explanation:
How do I solve for the variables?
Answer: To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all the other variables and constants on the other side.
I don't know if this helps at all
Help please I need an answer for this fast
Answer:
B 9, -9
Step-by-step explanation:
x^2 - 81 = 0
Add 81 to each side
x^2 = 81
Take the square root of each side
sqrt(x^2) = sqrt(81)
x = ±9
Hi! Please help me, will mark brainliest!
Answer:
p(t) = 0 for t = 1
p(t) = 1 for t = 1/8 = 8^-1
Step-by-step explanation:
the graph you will have to do yourself.
just go there and type in
[tex] - log_{8}(x) [/tex]
well, don't type "log" in letters.
you start by typing the "-" sign, and then you need to look up the functions by clicking on the "funcs" button and look for the log functions .
pick the
[tex] log_{a}[/tex]
option. and then simply enter 8 as the first parameter in the {} brackets and x as the second in the () brackets.
and then you see.
any logarithm is 0 for x (or t) = 1.
because any a⁰ = 1.
and the logarithm gives you that exponent of the base number that leads to the given x value.
in other words : a logarithm is the inverse function of an exponential function.
the exponential function is
y = a^x
and the logarithm then determines
[tex]x = log_{a}(y) [/tex]
that is all.
and
[tex] - log_{8}(x) = 1[/tex]
means that the logarithm itself delivered -1.
and 8^-1 = 1/8
so, p(t) = 1 for t = 1/8
Brad's family traveled
2
7
of the distance to his uncle’s house on Saturday. They traveled
4
5
of the remaining distance on Sunday. What fraction of the total distance to his uncle’s house was traveled on Sunday?
Answer : 4/7
Here it's given that Brad's family travelled 2/7 of the total distance to his uncle's house on Saturday . So if we assume the total distance to be 1 , then the remaining distance will be ,
[tex]\sf\longrightarrow 1 - \dfrac{2}{7}=\dfrac{7-2}{7}=\boxed{\dfrac{5}{7}}[/tex]
Again it's given that they travelled 4/5 of the remaining distance on Sunday . So , the distance travelled would be ,
[tex]\sf\longrightarrow \dfrac{4}{5}\times \dfrac{5}{7}=\boxed{\sf \dfrac{4}{7}} [/tex]
Therefore Brad's family travelled 4/7 of the total distance on Sunday .
Hep helo heloe e dkdnd. E
Answer:
[tex]Solution,\\Diameter(d)=106yd\\Radius(r)=106yd/2=53yd\\Now,\\Area=\pi r^{2} \\Area=3.14*(53yd)^{2}\\ Area=3.14*2809yd^{2} \\Area=8820.26yd^{2}[/tex]
Step-by-step explanation:
Hope it will help you.
Look at the picture below <3 please help!
Answer:
9
Step-by-step explanation:
f(x)=5-4x/15. Find F-1(x)
Answer:
Substitute f(x)=0
0=5-4x over 15 multiply both sides
0=75-4x move the variable to the left
4x=75 divide both sides
solution x=75 over 4
alternate form is x=18 3 over 4, x=18.75
Step-by-step explanation:
Pls help! Solve the equation by using quadratic formula.
-2x’2 + 4x = 5
Answer:
[tex]x=\frac{2\pm i\sqrt{6}}{2}[/tex]
Step-by-step explanation:
[tex]-2x^2+4x=5\\\\-2x^2+4x-5=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-4\pm\sqrt{(4)^2-4(-2)(-5)}}{2(-2)}\\\\x=\frac{-4\pm\sqrt{16-40}}{-4}\\\\x=\frac{-4\pm\sqrt{-24}}{-4}\\ \\x=\frac{-4\pm2i\sqrt{6}}{-4}\\ \\x=\frac{2\pm i\sqrt{6}}{2}[/tex]
I total of 508 tickets are sold for the school play they were either adult tickets or student tickets there were 58 more student tickets sold than adult tickets how many adult tickets were sold?
Answer:
Adult tickets sold = 225
Student tickets sold = 283
Step-by-step explanation:
Let A = total adult tickets sold
Let S = total student tickets sold
If a total of 508 tickets were sold, then A + S = 508
If there were 58 more student tickets than adult tickets sold, then
S = A + 58
Substitute S = A + 58 into A + S = 508 to find S:
A + (A + 58) = 508
2A + 58 = 508
2A = 508 - 58 = 450
A = 450 ÷ 2 = 225
If A = 225, then using S = A + 58, find S:
S = 225 + 58 = 283
Adult tickets sold = 225
Student tickets sold = 283
