Answer:
The ratio of the perimeters is 3
The ratio of the areas is 9
Step-by-step explanation:
Given:
Dilate a triangle with vertices (0, 0), (0, 2), and (2,0) using the scale factor k = 3.
To Find:
What is the value of the ratio (new to original) of the perimeters? the areas?
Solution:
What is the value of the ratio (new to original) of the perimeters?
Since, two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let the following be:
k ⇒ the scale factor
x ⇒ the perimeter of the new triangle
y ⇒ the perimeter of the original triangle
Knowing that:
k = x/y
Thus:
k = 3
Now Substitute:
x/y = 3
-------------------------------------------------------------------------------------------------------------
What is the value of the ratio (new to original) of the areas?
Since, two figures are similar, then the ratio of its areas is equal to the scale factor squared.
k ⇒ the scale factor
x ⇒ the area of the new triangle
y ⇒ the area of the original triangle
k ² = x/y
Since,
z = 3
Then,
x/y = 3 ²
3 ² means to 3 × 3
x/y = 9
-------------------------------------------------------------------------------------------------------------
Kavinsky
Multiply out and simplify (2x-3)(4-5x+x^2)
Step-by-step explanation:
reference attachment ..............
Shaniece was given a large box of 48 chocolates for her birthday. If she eats exactly 3 chocolates each day, how many chocolates would Shaniece have remaining 5 days after her birthday?
Answer:
33 chocolates
Step-by-step explanation:
3 chocolates times 5 days = 15 chocolates
48 chocolates minus 15 chocolates = 33 chocolates
factor the following expression
[tex]16x^{2} - 25[/tex]
[tex]16x^2-25\\\\=(4x)^2-5^2\\\\=(4x+5)(4x-5)[/tex]
PLEASE ANSWER QUICKLY Which of the following is the correct graph of the compound inequality 4p + 1 > -15 and 6p + 3 < 45?
o
7
-7 -6 -5
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
O
-7 -6 -5 -4
O
7
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9 10 11
- 7 -6 -5 -4 -3 -2 -1
0 1 2
3
4
5
6
7
8
9 10 11
Answer:
abce
Step-by-step explanation
correct
Complete part (a) and part(b) given the following system of equations. I really need help!!!
x-y=0
2x+3y=-5
a) Solve this system graphically.
b) Write your answer
Answer:
x=−1 and y=−1
Step-by-step explanation:
Solve by substitution
x−y=0;2x+3y=−5
Step: Solve x−y=0 for x:
x−y+y=0+y(Add y to both sides)
x=y
Step: Substitute yfor x in 2x+3y=−5:
2x+3y=−5
2y+3y=−5
5y=−5(Simplify both sides of the equation)
5y/5=−5/5 (Divide both sides by 5)
y=−1
Step: Substitute−1 for y in x=y:
x=y
x=−1
Answer:
x=−1 and y=−1
The solution to the system is x = -1.8 and y = -1.8.
What is a system of equations?A group of two or more equations that must be solved simultaneously make up a system of equations. There are many unknown variables in a system of equations, and each equation in the system depicts the relationship between those variables.
A set of variable values that satisfy every equation in a system of equations is the solution to the system of equations.
To solve this system of equations graphically, we can plot the two equations on a coordinate plane and find the point where they intersect, which represents the solution to the system.
a) To plot the equation x - y = 0, we can rearrange it to y = x and plot the line passing through the origin and the point (1, 1), as shown below:
Graph of the line y = x passing through the origin and the point (1, 1).
To plot the equation 2x + 3y = -5, we can rearrange it to y = (-2/3)x - 5/3 and plot the line passing through the points (-2, 1) and (1/3, -5/3), as shown below:
Graph of the line y = (-2/3)x - 5/3 passing through the points (-2, 1) and (1/3, -5/3).
b) The point where the two lines intersect is the solution to the system. From the graph, we can see that this point is approximately (-1.8, -1.8).
Therefore, the solution to the system is x = -1.8 and y = -1.8.
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Which set of coordinates represents the reflection of the following image over the y–axis?
A
(–6 , 2), (–4 , 8), (–2 , 2)
B
(6 , 2), (4 , 8), (2 , 2)
C
(–6 , –2), (–4 , –8), (–2 , –2)
D
(–2 , 2), (0 , 8), (2 , 2)
Answer:
B. (6,2), (4,8), (2,2)
Step-by-step explanation:
When it reflects over the y-axis (the vertical line) it is going to look the exact same just in the box on the top right. Instead of negatives in the coordinate points they are going to be positive. The only one that does this is B.
Ans: B. (6,2), (4,8), (2,2)
m∠A= 81∘; m∠B = 109∘ Are the two angles complementary, supplementary, or neither?
Answer:
neither
Step-by-step explanation:
complementary means the angles should add up to 90∘ but here in this case they add up to 190.
Supplementary means the angles add up to 180∘ but again in this case they don't.
which means the answer only has one choice.
At Ashley Furniture Store, there is a marble table that you want to
purchase for your mother. The length of the table is (-8x+2) and the width
of your rug is (3x-4). What is the total area of the table? Solve the
problem using the best method. Write the answer as a trinomial.
Step-by-step explanation:
in my opinion
total area = the width × the length
= (3x-4)(-8x+2)
= -24x²+6x+32x -8
= -24x² + 38x -8
Watch help video
Kaylee owns a small business selling clothing. She knows that in the
last week 3
customers paid cash, 21 customers used a debit card, and 46 customers used a credit
card.
Based on these results,
debit card as a
express the probability that the next customer will
pay with
The probability the next customer pays using a debit card based on the last three weeks is 30% or 0.3.
What is a probability?This is the chance or likelood for an event to occur. For example, if in a city it has snowed every year on December 25th, there is a high probability it will snow this year and in the next years.
How to calcuate the probability?Total of a specific outcome/ total of outcomes
Based on this, let's calculate the probability the next customer pays using the debit card:
Total that pay with debit card: 21 customersTotal of customers: 70 customers21/ 70 =0.3 or 30%Learn more about probability in: https://brainly.com/question/11234923
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Find the approximate volume of the cone.
o 1,017.4 cm
226.08 cm
o 324 cm
Answer:
~ 1017.4
Step-by-step explanation:
volume of a cone 1/3 pi r^2 h
1/3 pi * 9^2 * 12 = 1017.8
Solve for m. Please Help!
Answer:
m = 39°
Step-by-step explanation:
angles on the circumference of the circle subtended by the same arc are congruent.
∠ BDC = ∠ BAC = 33° ( both subtended by arc BC )
then ∠ ADC = 36° + 33° = 69°
Opposite angles of a cyclic quadrilateral sum to 180° , so
∠ ABC = 180° - 69° = 111°
then
m + 72° = 111° ( subtract 72° from both sides )
m = 39°
Carlos answered 122 questions correctly on his multiple choice science final and earned a grade of 61%. How many total questions were on the final exam?
In terms of π, what is the volume of the sphere?
[tex]v = \frac{4}{3} \pi \: {r}^{3} \\ [/tex]
[tex]v = \frac{4}{3} \times \pi \times ({ \frac{60}{2} })^{3} \\ [/tex]
[tex]v = \frac{4}{3} \times \pi \times {30}^{3} \\ [/tex]
[tex]v = \frac{27000 \times 4}{3} \pi \\ [/tex]
[tex]v = 900 \times 4\pi[/tex]
[tex]v = 3600\pi \: \: \: {ft}^{3} [/tex]
For f(x)= 2x + 1 and g(x) = x^2 - 7, find (f+g)(x).
Answer:
x^2+2x-6, or C
Step-by-step explanation:
We want to combine the values of both f(x) and g(x) into one equation.
We could write this as 2x+1+x^2-7
Simplified- x^2+2x-6, or C
Raina is mailing packages. Each small package costs her 2.30 to send. Each large package costs her 4.10 . How much will it cost her to send 7 small packages and 4 large packages?
Answer:
32.5
Step-by-step explanation:
Take the 2.30 and multiply it by 7. Then take 4.10 and multiply it by 4. From there you add the answers together.
slove for x 10(2x-4)=100x A.x=7 B.x=3 C.x=1/2 D.x=-1/2
Answer:
The answer is D. x=-1/2
Step-by-step explanation:
multiply the parantheses by 10 that'll give us 20x-40=100x2. move terms, that'll give us 20x-100x=403. subtract 100x from 20x, that'll give us -80x=404. divide both sides by -80, which is x=-1/2Answer:
D. x = -1/2Step-by-step explanation:
10(2x - 4) = 100x1. Divide both sides by 10.
10/10 (2x - 4) = 100x/102x - 4 = 10x2. Add 4 to both sides.
2x - 4 +4 = 10x + 42x = 10x + 43. Subtract 10x from both sides.
2x - 10x = 10x + 4 - 10x-8x = 44. Divide both sides by -8.
-8x/-8 = 4/-8x = -1/2The answer is D.
(t divide 3) + 1= 5 + 1
Answer:
t=15
Step-by-step explanation:
t/3 + 3/3 = 6
combine fractions w/ common denominator:
t+3/3 = 6
multiply both sides by denominator (3):
note: the two threes from 3 x t+3/3 cancel each other out
t+3=3x6
t+3=18
subtract 3 from both sides and you get 15
t=15
hope this helps :)
if x=15 degrees and the measure of Arc YZ is 3 centimeters, what is the circumference of the circle?
A- 24
B- 45
C- 60
D- 72
The circumference of the circle is 72cm.
Arc length formula[tex]Arc length = 2\pi r(\frac{x}{360} )[/tex]
where
r is the radius of the circle
x is the central angle of the arc
Circumference of the circleCircumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It is calculated as
circumference of the circle = 2πr
According to the given question we have
central angle of the arc, x = 15 degrees
Arc length = 3 cm
Let r be the radius of the given circle.
Then,
Arc length = 2πr[tex](\frac{15}{360} )[/tex]
⇒ 3 ×[tex]\frac{360}{15}[/tex] = circumference of the circle ( circumference or circle =2πr)
⇒ circumference of the circle = 72 cm
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Need help with 7 and 8
Answer:
see explanation
Step-by-step explanation:
The tangent segments are equal so you set them equal to each other and solve.
7) 3x-6 = x + 10 8) 4x + 2 = 2x + 8
Two shops sell the same brand of baked beans but in different sizes of tin.
Calculate the price of 1 kg of baked beans for each shop.
Give your answers in pence.
Write the shop which is better value in the comment box.
Shop A
Shop B
BAKED
BEANS
BAKED
BEANS
5kg for £5.75
2kg for £2.12
Answer:
Step-by-step explanation:
shop a=115p
shop b=106p
shop b better value as its cheaper
Question 6 of 10
What is the slope of the line shown below?
6.9)
O A
7
O B.
OB
O c. /
OD.
ON
5
15
7
5
0.-5)
Slope = change in y / change in x
slope = (9 - -5) / ( 6-0)
Slope = 14/6
Divide by 2
Slope = 7/3
Answer: B. 7/3
Find the equation of
the line that cuts through (0, 5) and (1, 2)?
a. y=-3x+5
C.
y =-57+3
b. y = 3x+5
d.
Y=--X+3
Please select the best answer from the choices provided
write 1 1/3 as a percent
Answer:
1.3
Step-by-step explanation:
⅓ put into to decimal form is a repeating decimal
Answer:
133.3333333%
Step-by-step explanation:
1 = 1.00 = 100%
1/3 = 0.3333333 = 33.33333333%
Note that the extra 3s are for repeating decimals.
Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine! Payton is overcome with emotion and needs your help to save her dog. You can repel down and successfully rescue Willow, but you must calculate how much rope is needed.
The ravine is 153 feet deep the repel line will be the diagonal distance from the top of the ravine to Willow The anchor and repel line form a 35 degree angle; this is angle A in the image below.
(a) Calculate the length of the repel line using one of the 3 trigonometry ratios taught (sin, cos, tan) Round your answer to the nearest whole number. Show all needed math for calculating this length.
The length of the repel line using one of the 3 trigonometry ratios will be 186.78 feet.
How to calculate the length?From the information given, Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine.
The length will be calculated thus:
Cos 35° = 153/AC.
AC = 153/cos 35°
AC = 153/0.819
AC = 186.78 feet.
Therefore, the length is 186.78 feet.
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will give brainliest, thanks in advance!!
Answer:
-3+15i
Step-by-step explanation:
Apply complex arithmetic rule: [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex]
[tex]\left(-3\cdot \:3-3\left(-2\right)\right)+\left(-3\left(-2\right)+3\cdot \:3\right)i[/tex]
-3 * 3 -3 (-2) = -3
[tex]-3+15i[/tex]
During which decade did an economic boom and bust occur in the united states? 1900s 1910s 1920s 1930s
An economic boom and bust occurred in the United States during the 1920s, which is also known as the Roaring Twenties.
When the economic boom in the united states took place?This period was marked by a significant increase in consumer spending, economic growth, and technological innovation, particularly in the areas of automobiles, radio, and electricity. However, the boom came to an abrupt end with the stock market crash of 1929, which triggered the Great Depression of the 1930s.
The economic boom of the 1920s in the United States was a period of rapid economic growth and expansion, characterized by a surge in consumer spending, increased industrial production, and the expansion of credit. This period was fueled by a number of factors, including technological innovation, such as the widespread adoption of the automobile and the growth of the aviation industry, as well as the widespread availability of electricity.
The 1920s also saw significant changes in the social and cultural landscape of the United States, with the rise of a new consumer culture that emphasized leisure and entertainment. The entertainment industry grew rapidly during this time, with the rise of radio broadcasting and the popularity of Hollywood films.
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Given that f(x) = 3x + 3 and g(x)=x2- 2x-5, find (g of)(4).
(gof)(4)=0
(Simplify your answer. )
Answer:
-5=0
Step-by-step explanation:
g(4)=8-8-5=-5 you substitute 4 into x
-5=0
-
(3/4)+1 7/8 divided by 1/2 =n
Answer:
n=1.3125/ if the (3/4) was negative the anwser would be -1.3125
Step-by-step explanation:
Answer:
n = [tex]5\frac{1}{4}[/tex]
----------------------------------------------------------------------------------------------------------
First, evaluate 3/4 + 1 7/8 without including whole numbers for now.[tex]3/4 + 7/8 =~?[/tex]
When dealing with unequal fraction denominators, find the greatest common factor of both numbers to make the denominators match.
[tex]GCF(3,4) = 2\\GCF(7, 8) = 1\\\\\frac{3 * 2}{4 * 2} = \frac{6}{8}\\\\\frac{7 * 1}{8 * 1} = \frac{7}{8}[/tex]
Next, add these two numbers together.
[tex]\frac{6}{8} + \frac{7}{8} = \frac{13}{8}[/tex]
Oh no! It looks like we have an improper fraction. To solve this, count each time the numerator passes the denominator and count that as a whole number. Like 9/8 is 1 1/8 because the numerator went over the denominator 1 time, counting the extra unit fraction.
[tex]\frac{13}{8} = 1\frac{5}{8}[/tex]
Now, add the whole numbers.
[tex]1 + 1 + \frac{5}{8} = 2\frac{5}{8}[/tex]
Last not not least, divide by one half. Since 2 5/8 is equal to 21/8, convert it to this fraction.
[tex]\frac{21}{8} / \frac{1}{2}[/tex]
Use the 2 in 1/2 and the 1 in 1/2, then multiply 2 by 21, and 8 by 1
[tex]\frac{21*2}{8*1} = \frac{42}{8}[/tex]
Finally, simplify 42/8
if 8 × 5 is 40 you can tell the number will be close to 40
[tex]\frac{42}{8} = 5\frac{1}{4}[/tex]
That said, the answer is [tex]\frac{42}{8}[/tex] and also [tex]5\frac{1}{4}[/tex]
What is the value of the expression
below when a
8, b = 16, and c = -4 ?
Answer:
35
Step-by-step explanation:
5*³√8-（-4）*√16+9=5*2+4*4+9=35
Determine the equation of the circle graphed below.
10
8
-10 -8
8
-6
-2
F
4
2
N
T
-6.
2
10
Answer:
[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]
Step-by-step explanation:
From the graph we can see that
Diameter = 6 units
=> Radius = 3 units and centre is at (-3,7)
=> Equation is Circle with centre (-3,7) and radius of 3 units will be
[tex] = > {(x + 3)}^{2} + {(y - 7)}^{2} = {3}^{2} [/tex]
[tex] = > ( {x}^{2} + 6x + 9) + ( {y}^{2} - 14y + 49) = 9[/tex]
[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]