Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]
[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]
[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]
Now, comparing areas:
[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]
[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25
The area of ΔABC is 2.25x greater than the area of ΔDEF.
The recommended number of flowers to plant in a garden is proportional to its area, as shown in the
table below. What is the recommended number of flowers for a garden of 24 square feet?
Garden Area
(square feet)
12
Number of
Flowers
16
20
15
24
30
40
(A) 24
(B) 29
(C) 30
(D) 32
Answer:
What’s is the answer o need heelpp
Step-by-step explanation:
Recommended number of flowers for a garden of 24 square feet is 32 so option (D) will be correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
Given data is forming a linear function.
Since the slope of a linear function is always constant
Slope = difference in y's coordinate / difference in x's coordinate
Lets say Garden area is x and the number of flowers is y
Then,
Slope = (y - 20)/(24-15) = (20-16)/(15-12)
(y - 20)/9 = 4/3
y = 12 + 20 = 32
Hence " Recommended number of flowers for a garden of 24 square feet is 32".
For more about the linear function,
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please help!!! if anyone knows
Answer:
The answer is 24in a am very sure
Step-by-step explanation:
Answer: The missing side is 24 inches
Step-by-step explanation:
Since it is a right angle that means that we can use the Pythagorean Theorem formula to solve for the B.
The formula says that a^2 + b^2 = c^2 Since we know a is 18 and c is 30 we will input the value into the formula to solve for b.
18^2 + b^2 = 30^2
324 + b^2 = 900
-324 -324
b^2 = 576
b = [tex]\sqrt{576}[/tex]
b = 24
If f(x)= (2x +5)and g(x) = (2x2−5x+3), find f(x) · g(x) (please help)
A. 4x3 − 31x + 154x3 − 31x + 15
B.4x3 − 20x2 +19x + 154x3 − 20x2 +19x + 15
C.4x3 − 19x + 154x3 − 19x + 15
D.4x3 + 20x2 − 19x +15
Answer: 4x³-19x+15
Step-by-step explanation:
We are given f(x) and g(x). Since we need to find f(x)·g(x), we multiply f(x) and g(x).
[tex](2x+5)(2x^2-5x+3)[/tex] [distribute by FOIL]
[tex]4x^3-10x^2+6x+10x^2-25x+15[/tex] [combine like terms]
[tex]4x^3-19x+15[/tex]
Now we know [tex]4x^3-19x+15[/tex] is the correct answer.
graph y=3/4x-4 pls helppppppp.......,,,,,,,,,,.,,,,,
Step-by-step explanation:
Plug in y=3/4x-4 into desmos :)
A bus leaves a station traveling north at 70 kilometers per hour. Half an hour later a
second bus leaves the same station traveling north at 80 kilometers per hour. How far
from the station will the buses meet?
Answer:
280 km
Step-by-step explanation:
Given that a bus, say [tex]b_1[/tex], leaves a station traveling north at speed of 70km/hour.
Half an hour later the second bus, say [tex]b_2[/tex], leaves a station traveling north at speed of 70km/hour.
As, distance = speed x time,
so, the distance traveled by bus [tex]b_1[/tex] in 0.5 hours = 70 x 0.5 = 35 km.
Note that, both the buses are traveling in the same direction and when the second bus leaves the station, the first bus already covered a distance of 35 km.
Let the second bus took [tex]t[/tex] hours to meet the first bus and both the buses meet at a distance of [tex]d[/tex] km from the station.
The distance traveled by the first bus from the station, [tex]d = 35 + 70t[/tex] km
[tex]\Rightarroe t= \frac {d-35}{70}\cdots(i)[/tex]
and the distance traveled by the second bus, [tex]d = 80t[/tex] km
[tex]\Rightarrow t=\frac {d}{80}\cdots(ii)[/tex]
Now, equation the equation (i) and (ii), we have
[tex]\frac {d-35}{70}=\frac {d}{80} \\\\\Rightarrow 8(d-35)=7d \\\\\Rightarrow 8d - 280 = 7d \\\\\Rightarrow 8d-7d=280 \\\\\Rightarrow d = 280 km[/tex]
Hence, both the bus will meet at a distance of 280 km from the station.
What is the inverse of the function f(x) = one-quarterx – 12?
Answer:
f^(-1)(x) = 4x + 48.
Step-by-step explanation:
Is suppose the function is f(x) = 1/4 x - 12
This is equivalent to the line y = 1/4 x - 12.
To get the inverse, change the x and y:
x = 1/4 y - 12
Now solve for y:
x + 12 = 1/4 y
y = 4x + 48
So the inverse f^(-1)(x) = 4x + 48.
Answer:
f-1(x) = 4x + 48.
Step-by-step explanation:
let f(x) = y = 1/4 x - 12
We solve for x:
y = 1/4 x - 12
1/4 x = y +12
Multiply through by 4:
x = 4y + 48
The inverse f-1(x) = 4x + 48.
What is the location of the second endpoint if the first endpoint is at (5,2) and
the midpoint is at (-5,5)?
HELP
Which BEST describes the system of equations graphed on the coordinate plane?
if i have 50 assignments to do and 4 days to do ot how many assignments do i need to do a dwy to get them done on time
Answer:
12.5assignments
Step-by-step explanation:
50 assignments over 4 days
50/4
=12.5 assignments
Answer: I just did a semesters worth of work in a day and a half. You can do this!!! I know it’s frustrating and hard and you’re probably burned out but keep pushing. It’s worth it :)
Step-by-step explanation:
Dilations map rays to segments true or falue
Answer:
true?
Step-by-step explanation:
What is the slope of the line that passes through the points (4, 5) and (12, 7)?
Answer:
1/4
Step-by-step explanation:
To find slope, we use the formula rise over run (y2-y1 over x2-x1)
So first, our y's: 7-5=2
And our x's: 12-4=8
2/8 simplifies to 1/4
what is the value of the expression of -9 x 2.2
Answer:
-19.8
Step-by-step explanation:
hope this helps!
Please, I need help ASAP!
Answer:
A
Step-by-step explanation:
You can eliminate B and D because it’s using [tex]\frac{g}{f}[/tex], but the question is asking [tex]\frac{f}{g}[/tex]. So it’s either A or C. They are both written correctly, but out of the two, A is correct because just that x ≠ [tex]\sqrt{7}[/tex] part of it is what makes it true.
The reason being is that the only thing that won’t make [tex]\frac{2x+1}{x^{2}-7 }[/tex] true is when the denominator equals 0, because anything divided by 0 is undefined. So, when you plug [tex]\sqrt{7}[/tex] for x in the denominator you get: [tex]\sqrt{7^{2} } -7[/tex]. The [tex]\sqrt{7^{2} }[/tex] part just turns into 7, and 7 - 7 is 0. So you don’t want x to equal [tex]\sqrt{7}[/tex].
So the answer is A: [tex]\frac{2x+1}{x^{2}-7}[/tex], [tex]x\neq[/tex] ± [tex]\sqrt{7}[/tex]
There you go my friend!
I hope you understand and that this helps with your question! :)
Hadley runs several times around the
track. One lap around the track is
equal to 0.15 miles. She then runs 0.4
miles home for a grand total of 1.75
miles. Determine the number of laps
Hadley ran around the track.
Select the correct answer.
What is the simplest form of the ratio 40:16?
ОА.
20:8
OB.
10:4
OC.
5:4
OD
5:2
OE.
10:8
Answer:
D: 5:2
Step-by-step explanation:
40:16 simplified is 5:2
The simplest form of the ratio 40:16 is 5:2.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
To find the simplest form of the ratio 40:16, we can divide both terms by their greatest common factor (GCF).
First, let's find the GCF of 40 and 16.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
The factors of 16 are 1, 2, 4, 8, and 16.
The largest number that appears in both lists is 8.
Therefore, the GCF of 40 and 16 is 8.
To simplify the ratio, we divide both terms by 8:
40 ÷ 8 = 5
16 ÷ 8 = 2
Thus,
The simplest form of the ratio 40:16 is 5:2.
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Tamika wants to predict the outcome of next Tuesday’s game, between the Nets and the Warriors.
She believes that the Warriors will score 19 points less than the Nets. Tamika also predicts that the total amount of points scored for both teams will be 207 points.
How many points does Tamika think that the Warriors will score? How many points will the Nets score?
Step-by-step explanation:
Let x be the Warriors' score. Then from Tamika's prediction, (x + 19) is the Nets' score.
Toal score = x + (x + 19) = 2x + 19 = 207.
Therefore 2x = 188 and x = 94.
Hence Tamika thinks that the Warriors will score 94 points and the Nets will score 94 + 19 = 113 points.
PLEAZE HELP MS OUT I DONT UNDERSTAND
Answer:
cant see the pic
Step-by-step explanation:
Answer:
C.) SAS
Step-by-step explanation:
When the marks on a triangle are the same as another, they have a congruent measure.
In the given triangles, the red line and arch on both mean they have a congruent side and angle.
Since they share a side, that side is congruent for both.
So now we have a congruent side, angle, and side. This is the SAS theorem,
If the relative frequencies are 0.48 and 0.52, which
conclusion is most likely supported by the data?
O There is likely an association between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are not similar in value.
O There is likely an association between the
categorical variables because the relative
frequencies are both close to 0.50.
Answer:The Last One
Step-by-step explanation:
Option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
What is relative frequency?The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted. The sum of all relative frequencies will be one.
For the given situation,
The relative frequencies are 0.48 and 0.52.
A two-way frequency table can be used to show, analyze, and examine the relationships that exists between two categorical variables.
The two relative frequencies have the values that are similar to (close to) each other. So, there will be no association between the categorical values.
Hence we can conclude that option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
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NEED HELP ASAP!!!!!!
Answer:
x=57
Step-by-step explanation:
63+60= 123
A triangle is 180 degrees
180-123= 57
x=57
Answer:
pretty sure x = 57
Step-by-step explanation:
60 + 63 = 123
180 - 123 = 57
4(1-x)+2x=-3x+-3 I need helpppo
Please help this is my last question'
And if you can show the steps that would be appreciated but if not, that's okay too! I just need the answer! Please
4/5√50
Answer:
all the questions we have to solve
Answer:
See below
Step-by-step explanation:
First question is not visible.
Second one is already answered
Third one is given below
[tex] \frac{4}{5} \sqrt{50} = \frac{4}{5} \times 5 \sqrt{2} = 4 \sqrt{2} \\ \\ [/tex]
what is the value of y for which a ll b
Answer:
110
Step-by-step explanation:
I’m really bad at geometry pls help! Thanks
The right hexagonal pyramid
has a hexagon base with equal-length sides. The lateral
faces of the pyramid are all triangles (that are exact copies of one another) with
heights of 18 ft. Find the surface area of the pyramid.
Answer:
Lateral area of the pyramid = 72 unit²
Step-by-step explanation:
Lateral surface means side part of pyramid. So we nee need to find area of 6 triangles with base 4 and height 6.
Lateral area of the pyramid = 6 x Area of 6 triangles with base 4 and height 6
Hope this helped...
1. Convert 0.28 to a fraction.
2. Convert 3/5 to a decimal.
3. Convert 185% to a fraction.
NEED THIS DONE ASAP DO TOMORROW
Answer:
0.28 as a fraction is 28/100 and if you need it simplified it is 7/25
3/5 as a decimal is 0.60
185% as a fraction is 185/1 or if you need that simplified it is 1 85/100
Step-by-step explanation:
Ask me if you need it simpler than that and I'll help.
The school store sells markers for $0.25 each and pencils for 0.50 each.Anthony spent $ 5.50 to buy a total of 16 markers and pencils. How many markers did Anthony buy?
Answer:
The answer to your question is Antony bought 5 pens
Step-by-step explanation:
pens = p = $0.35
pencils = n = $0.15
total amount = 12
total money spent = $2.80
Process
1.- Write equations
p + n = 12 -------------- (l)
0.35p + 0.15n = 2.80 --------------(ll)
2.- Solve the system of equations by elimination
Multiply equation l by - 0.35
- 0.35p - 0.35n = -4.2
0.35p + 0.15 n = 2.8
0 - 0.2n = -1.4
Solve for n
n = -1.4 / -0.2
n = 7 He bought 7 pencils
3.- Find the value of p
p + 7 = 12
p = 12 - 7
p = 5 He bought 5 pens
Question 13) Olivia has read 143 pages of a 220 page novel. What
percentage of the book does she still need to read? *
Answer:
77%
Step-by-step explanation:
Answer:
The answer to Question 13 is 35%.
Step-by-step explanation:
Subtract 143 from 220, which will give you 77. Then, you take that 77 and search, "77 out of 220" in Google. You should get 35 and just put the percentage symbol. Olivia still needs to read 35% of the 220 page book:).
ASAP!!!!!!!!!!!! I NEED HELP!!!!! I WILL MARK BRAINLIEST!!!!!!!
someone help!!??? pleaseee
Answer:
I'm not sir but I think it is ISOSCELES
please give me correct answer this is major
Answer:
d
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
What is the coefficient of the variable in the expression 6 − 4x − 8 + 2? (3 points)
Group of answer choices
A. 6
B. 2
C. −4
D. −8
Answer:
I thik the answer is B.
Step-by-step explanation:
hope this helps
Answer:
c -4
I did the math