Step-by-step explanation:
a scale factor means that every dimension or line in the original object is multiplied with the exact same factor to create a transformed (larger or smaller) new object.
the area of an object (including a simple form like this rectangle) is always the product of 2 dimensions.
that means the scale factor is multiplied in twice creating a squared factor for the area of the new object.
so, yes, therefore the area grows or shrinks with the square of the scale factor.
FYI - following the same reason, the volume grows or shrinks with the power of 3 of the scale factor.
1. k=2
new area = k² × old area = 4 × 12 = 48 square units.
2. k=5
new area = k² × old area = 25 × 12 = 300 square units.
3. k=1
new area = k² × old area = 1 × 12 = 12 square units.
4. k=1/4
new area = k² × old area = 1/16 × 12 = 12/16 = 3/4 square units.
5. k=1.2
new area = k² × old area = (1.2)² × 12 = (12/10)² × 12 = (6/5)² × 12 = 36/25 × 12 or 1.44 × 12 = 432/25 = 17.28 square units.
What is the meaning of the statement ((30) =76?
Answer:
A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F
B) [tex]f(x)=-0.4x+88[/tex]
Step-by-step explanation:
A)
In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.
So we have:
x = minutes after the air conditioner started to cool the house
f(x) = temperature
Here we want to find what is the meaning of
[tex]f(30)=76[/tex]
Which implies that:
[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house
[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F
So, the interpretation of f(30) =76 is that:
"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"
B)
Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.
We know the following information:
- At time x = 0, the temperature inside the house is 88°F
- At time x = 30 min, the temperature inside the house is 76°F
We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:
[tex]f(x)=mx+q[/tex]
where
[tex]q[/tex] is the value of the temperature at x = 0, so q = 88
m is the rate of change of the temperature
The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:
[tex]m=\frac{76-88}{30-0} =-0.4[/tex]
which means that the temperature decreases by 0.4°F every minute. So, the function can be written as
[tex]f(x)=-0.4x+88[/tex]
help will give brainliest
Answer: the answer is line 2
Step-by-step explanation:
what is 39/17 as a decimal rounded to the nearest tenths?
The mean of 7 numbers is 15. When an 8 thnumber is added, the mean decreases to 12. What is the 8 thnumber?.
Answer:
-9?????????????????????????
Step-by-step explanation:
What is (-2) power 35?
Answer: − 34359738368
PLEASE TELL ME A STORY I WANT AN IDEA ON WHAT TO WRITE NOT JUST A SIMPLE ANSWER LIKE I GAVE A HOMELESS MAN MONEY Describe a time when you solved a problem. What actions did you take, and what impact did you make?
Answer:
Write about like something that happened at school that involved you and others.
Step-by-step explanation:
Hope this helps!
Are repeating decimals like 34.79 rational numbers?
Answer:
Yes. 34.79 is a rational number because it can be written as a fraction.
Step-by-step explanation:
Hoped this helped.
The sum of two numbers is x . If one of the numbers is 12, what is the other?
Answer:
x-12
Step-by-step explanation:
let us say that the other number is n. then we have n+12=x or n=12-x
helpppppppppppppppppppppppppppppppp
Answer:
x ≤ -14
Step-by-step explanation:
What is the solution for the inequality 4≤r/18+10?
[tex]4 \leq \dfrac{r}{18} +10\\\\\\\implies 4-10 \leq \dfrac{r}{18}\\\\\\\implies -6 \leq \dfrac r{18}\\\\\\\implies -6(18) \leq r\\\\\\\implies -108 \leq r\\\\\\\implies r \geq -108\\\\\\\text{Interval,}~ [-108 , \infty)[/tex]
If 2/15 is 40 then 1/15 is?
(Sorry I know this is a easy question but my brain isn't processing the question right now so I need help)
Answer:
20
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] = 40
[tex]\frac{2}{15}[/tex] ÷ [tex]\frac{2}{1}[/tex] = [tex]\frac{1}{15}[/tex]
40 ÷ [tex]\frac{2}{1}[/tex] = 20
If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.
Answer:
Where's the question?
Step-by-step explanation:
Find the total surface area of this triangular prism.
Answer:
look at the photo.....................The surface area of the given triangular prism = 920 square cm.
In the given triangular prism
S1 = 25 cm
S2 = 25 cm
S3 = 14 cm = base
Height = 24 cm
length = 10 cm
Perimeter = S1 + S2+ S3
= 25+25+14
= 64 cm
Area of base = length x base
= 10x14
= 140 square cm
Since we know that,
Surface area of triangular prism = (Perimeter × Length) + (2 × Base Area)
= (64x10) + 2x140
= 640 + 280
= 920 square cm
Hence,
The required surface area = 920 square cm.
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solve pls brainliest
Answer:
0.92 can be written as a fraction, because it is a terminating decimal. ( See the following. )
[tex] \frac{23}{25} [/tex]
0.777... can't be wrtten as a fraction, because it is a repeating decimal.
0.444... can't be written as a fraction, because it is a repeating fraction.
0.5813.. can't be written as a fraction, because
it is a decimal that neither terminates nor repeats.
For example : Root numbers don't terminates or repeats.
[tex] \sqrt{ 2} = 1.41421...[/tex]
I hope it helps.
0.125 ultiply by 1000
Answer:
125 is answer .........:)
(ASAP) i also need help with this plss
Answer:
The right answer is 32
Step-by-step explanation:
3/4 × 32 = 24
Answer:
18
Step-by-step explanation:
divide 24 by 4 which gives you 6. Multiply 6 by 3 which gives you 18 or (3÷4) × 24 = 18
Which table is not a proportional relationship
Answer:
B and D
Step-by-step explanation
Answer:
D
Step-by-step explanation:
sequence in the earnings is unproportional difference between 27 and 54 is not 9sale 90%Luca buys a swing set during the sale. If the original price was $270, how much does Luca pay?
Answer:
$243
Step-by-step explanation:
Juana buys a computer for $785.00. Her local sales tax is 6.85%. How much does Juana pay for the computer, including tax?
Answer:
838.7725
Step-by-step explanation:
make x the subject of the formula
y=a √x
Answer:
Y^2/a = x
Step-by-step explanation:
Y = a sqr X
Square both sides
Y^2 = a * x
Divide a
Y^2/a = x
Answer:
[tex] x = \dfrac{y^2}{a^2} [/tex]
Step-by-step explanation:
[tex] y = a\sqrt{x} [/tex]
Square both sides.
[tex] (y)^2 = (a\sqrt{x})^2 [/tex]
[tex] y^2 = a^2(\sqrt{x})^2 [/tex]
[tex] y^2 = a^2x [/tex]
Divide both sides by a².
[tex] \dfrac{y^2}{a^2} = x [/tex]
Switch sides.
[tex] x = \dfrac{y^2}{a^2} [/tex]
PLEASE ANSWER THIS RIGHT ASAP
Answer:
x=9
Step-by-step explanation:
23=7/9(6x-36)+9
Distribute 7/9.
23=14/3x-28+9
Add.
23=14/3x-19
Add 19 to both sides of the equation.
42=14/3x
Divide 14/3 from both sides of the equation.
X=9
Hope this helps :)
In a raffle, 100 tickets are sold and 10 of the tickets, selected at random, win a $5 prize. A participant buys one ticket. What is the standard deviation of the amount won?
order -9, -16, -13, 0 from least to greatest
Answer:
_16,-13,-9,0
Step-by-step explanation:
hope this helps u out!!
Conducting numerous, separate statistical analyses increases the chance that one or more of the results appear to be statistically significant, but are actually attributable to random variation or measurement error. The problem is referred to as:
A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.
In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.
Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.
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1\4-2\7 plese show your work
Answer:
-1/28
Step-by-step explanation:
You need to convert 2/7 and 1/4 into the same denominator. The GCD is 28. 2/7=8/28 and 1/4=7/28. 7/28-8/28=-1/28
Answer:
-1/28
Step-by-step explanation:
You have to find the least common multiple for 7 and 4, the denominators, to add the fractions. The LCM of 7 and 4 would be 28. You would have to multiply 7 by 4 and 4 by 7, meaning you have to multiply the numerators by the same number. 1x7/4x7-2x4/7x4= -1/28.
I need help this goes towards my grade so please be correct
Answer:
0 us the answer for this question
ASAP!! Use the slope formula to find the slope of the line passing through the points ( -66) and ( 3,3) . Use pencil and paper. Find two more points that the line passes through.
The slope of the line is
Answer: y = -66x + 201
Step-by-step explanation:
spilled $40 into the ratio of 3:7
Answer:
$12/$28
Step-by-step explanation:
Let x and y represent the two amounts of money adding up to $40.
Assume that x is the smaller amount. Then:
x 3
----- = ----- Remembering that x + y = $40, we get x = $40 - y
y 7
amd sp we have
$40 - y 3
-------------- = ------ which, after cross-multiplication, is $280 - $7y = 3y
y 7
Simplifying this, we get $280 = 10 y, so that y must be $28. If y = $28, x must be $40 - $28, or $12.
$12
Then $40, split in the ratio 3/7, is the ratio ----------------
$28
Check: Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.
1) The measures of the angles of a triangle are in the ratio of 1:3:6. What are the measures of the angles?
1:
3:
6:
Answer:Answered 2 years ago. The total of the sum of the measures of any triangle has been proven to be 180 degrees. If the ratio of angle measure is 1:3:6.
Step-by-step explanation:
Answer:
1: 18 3: 54 6: 108
Step-by-step explanation:
A triangle has 180 degrees.
You need to add up all the ratios 1+3+6
Then divide that by 180----> 180/10=18
Then multiply all the ratios by but answer(18)
1*18=18
3*18=54
6*18=108
Find the monomial if the expression is a cube of that monomial (find the cube root)
-27/64a^9b^6
-0.0001a^3n+3
I can't figure this out and need helppppppppp
Answer:
first one is -3/4a^3b^2
Step-by-step explanation:
i dont know the second one and i need help on that one too im sorry
The monomial of the functions are;
1. - 3/4 a³b²
2. - 0.1 aⁿ⁺¹
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
the expression are;
1. - 27/64 a⁹b⁶
2. - 0.001 a³n³ⁿ⁺³
Now,
Solve the expression as;
1. - 27/64 a⁹b⁶
Take cube root, we get;
∛- 27/64 a⁹b⁶ = ∛ - 3 × - 3 × - 3/4×4×4 a³a³a³ b²b²b²
= - 3/4 a³b²
And, - 0.001 a³n³ⁿ⁺³
∛ - 0.001 a³n³ⁿ⁺³ = ∛-0.1×0.1×0.1 aⁿ⁺¹ aⁿ⁺¹ aⁿ⁺¹
= - 0.1 aⁿ⁺¹
Thus, The monomial of the functions are;
1. - 3/4 a³b²
2. - 0.1 aⁿ⁺¹
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