Answers
Answer:
A'(-16,4), B'(16,-12), C'(8,12), D'(-4,16)
Step-by-step explanation:
The dilation with a center of dilation at (0,0) and scale factor of [tex]\frac{1}{4}[/tex] has the rule
[tex](x,y)\rightarrow \left(4x,4y\right)[/tex]
Quadrilateral ABCD has vertices at points A(-4,1), B(4,-3), C(2,3) and (-1,4).
Therefore, the image vertices are
[tex]A(-4,1)\rightarrow A'(-16,4);[/tex][tex]B(4,-3)\rightarrow B'(16,-12);[/tex][tex]C(2,3)\rightarrow C'(8,12);[/tex][tex]D(-1,4)\rightarrow D'(-4,16).[/tex]Related Questions
What is the inverse of the function h(x) = 5/2x + 4
Answers
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Step-by-step explanation:
Given function is:
[tex]h(x) = \frac{5}{2}x+4[/tex]
In order to find the inverse:
Replacing h(x) with y
[tex]y = \frac{5}{2}x+4[/tex]
Replacing x with y and y with x
[tex]x = \frac{5}{2}y+4[/tex]
Solving for y
[tex]x = \frac{5}{2}y+4\\x - 4 = \frac{5}{2}y+4-4\\x-4 = \frac{5}{2}y\\y = \frac{2}{5}(x-4)\\y = \frac{2x-8}{5}[/tex]
Replace y with h^(-1)(x)
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Hence,
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Keywords: Inverse, Functions
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Find the annual rate of interest. Principal = 4600 rupees, Period = 5 years, Total amount = 6440 rupees, Annual rate of interest = __%
Answers
The annual rate of interest per year is 8%
Solution:
Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees
First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest
Interest = Amount – Principal
Interest = 6440 – 4600 = 1840
Now using the formula of simple Interest and on putting values we get,
[tex]\text {Simple Interest }=\frac{P \times R \times T}{100}[/tex]
Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period
[tex]1840=\frac{4600 \times R \times 5}{100}[/tex]
[tex]\begin{aligned} \mathrm{R} &=\frac{1840 \times 100}{4600 \times 5} \\\\ \mathrm{R} &=\frac{1840}{230} \\\\ \mathrm{R} &=8 \% \end{aligned}[/tex]
Hence, the required rate of interest per year is 8%
Answer:
The annual rate of interest per year is 8%
Solution:
Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees
First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest
Interest = Amount – Principal
Interest = 6440 – 4600 = 1840
Now using the formula of simple Interest and on putting values we get,
Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period
Hence, the required rate of interest per year is 8%
Let me know if it is correct! Thank you. :)
Step-by-step explanation:
A small business owner wants to compare how much she spent with how much money she earned. The table shows her expenses and income.
If the expenses and income form a proportional relationship, what was the amount of income when she spent $300? pst the answer is d
A. $400
B. $600
C. $900
D. $1,200
Answers
Answer:?=x
100.800=200.400
200.x=300.800
200.x=240000
X=1200
Good luck!
Step-by-step explanation:
Answer:
D) $1,200
Step-by-step explanation:
300*4=1200
Given that sin=2/5 and cos<0. Find the rest of the trigonometric functions
Answers
Answer:
[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]
Step-by-step explanation:
Given
[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]
Use formula:
[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]
Since [tex]\cos x<0,[/tex] then
[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]
By definition,
[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]
write down in terms of n an expression for the nth term -7,-12,-17,-22,-27
Answers
The expression for the nth term of the given sequence -7, -12, -17, -22, -27 is -7 - 5(n-1).
Explanation:The given sequence is -7, -12, -17, -22, -27. In this sequence, each term is obtained by subtracting 5 from the previous term. So, we can write the expression for the nth term as:
-7 - 5(n-1)
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visa usa stated that over the last year, the number of friday and saturday sales transactions increased 16% to $38.8 million. what were the total sales transactions at this time lasy year?
Answers
Answer:
$33.45 million
Step-by-step explanation:
The transaction increased by 16% between last year and this year.This mean that [tex]S_1=S_0\times{(1+16\%)=S_0\times{1.16}[/tex] ([tex]S_0[/tex] are last year sales and [tex]S_1[/tex] are this year sales. This means that, today's sales are greater than last year sales by a 16%.Then, [tex]S_0=\frac{S_1}{1.16} =33.45[/tex].Answer:
Last year’s sales transaction was $33.448 million
Explanation:
Consider the last year’s total sales transaction be x
According to question,
Sales were increased by 16% to 38.8 million
Then, according to question,
x + 16% of x = 38.8 million
Solving for x,
[tex]x + (\frac{16}{100})x[/tex] = 38.8 million
[tex]\frac{116}{100}x[/tex]= 38.8 million
x = [tex]\frac{(38.8 million \times 100)}{116}[/tex]
x = 33.448 million
Therefore, last year’s sales transaction was $33.448 million
Clare wants to mail a package that weighs 4 1/2 ponds what could be its volume in liters
Answers
Answer:
The volume in liters is 2.041165665 liter.
Step-by-step explanation:
Given : Clare wants to mail a package that weighs [tex]4\frac{1}{2}[/tex] pounds.
To find : What could be its volume in liters ?
Solution :
We know that,
Pound (lb) is a unit of Weight used in Standard system.
Liter (l) is a unit of Volume used in Metric system.
To convert 1 pound into liter is
1 pound (lb) = 0.45359237 liter (l)
[tex]4\frac{1}{2}[/tex] pounds in simpler fraction is [tex]\frac{9}{2}[/tex]
Converting into liter,
[tex]\frac{9}{2}[/tex] pound (lb)=[tex]\frac{9}{2}\times 0.45359237[/tex] liter (l)
[tex]\frac{9}{2}[/tex] pound (lb) = 2.041165665 liter (l).
Therefore, the volume in liters is 2.041165665 liter.
Given: <SPT = <RQT, ST = RT Prove: PR = QS
Answers
Answer:
See explanation
Step-by-step explanation:
Consider triangles PTS and QTR. In these triangles,
[tex]ST=RT[/tex] - given;[tex]\angle SPT=\angle RQT[/tex] - given;[tex]\angle STP=\angle RTQ[/tex] - as vertical angles when lines PR and SQ intersect.Thus, [tex]\triangle PTS\cong \triangle QTR[/tex] by AAS postulate.
Congruent triangles have congruent corresponding sides, so
[tex]PT=QT[/tex]
Consider segments PR and QS:
[tex]PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}][/tex]
So,
[tex]PR=SQ\ [\text{Substitution property}][/tex]
Can someone help me answer this?
Given the function f(x)= x^2+7x+10 / x^2+9x+20
Describe where the function has a hole and how you found your answer.
We need to simplify the function by factoring the numerator and the denominator. Plug the excluded values into the simplified function to find the hole.
Answers
Answer:
The function f(x) has a hole at point x = - 5.
Step-by-step explanation:
We are given a function as
[tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
Now, we have to describe where the function has a hole.
Now, [tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
⇒ [tex]f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}[/tex]
Therefore, the common factor of the numerator and denominator is (x + 5).
Now, (x + 5) = 0
⇒ x = - 5
Therefore, the function f(x) has a hole at point x = - 5. (Answer)
By factoring and simplifying the function f(x)=(x^2+7x+10)/(x^2+9x+20), we find a hole at x=-5. This is because -5 was an excluded value in the original function, but does not cause the denominator to be zero in the simplified function.
Explanation:The given function is f(x) = (x^2+7x+10) / (x^2+9x+20). To find where the function has a hole, we need to factor both the numerator and the denominator. We also must exclude any values of x that would cause the denominator to be zero as these are undefined in the function.
The numerator factors into (x+2)(x+5), and the denominator into (x+4)(x+5). If we simplify, the x+5 term will cancel out, leaving us with f(x) = (x+2)/(x+4).
Originally, x could not be equal to -4 or -5, as these would make the denominator zero. In the simplified function, only x=-4 causes the denominator to be zero. But since x=-5 was an excluded value in the original function, that indicates there is a 'hole' at x=-5 on the function.
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The length of a rectangle is 3 cm greater than its width. the area of the rectangle is 180 cm². find the length and the width.
Answers
Answer:
L=15 W=12 15*12 = 180
Step-by-step explanation:
W*L = area
W*(W+3) = 180
Do the distributive
W^+3 W-180=0
Find 2 numbers that when multiplied ,the result is -180
and when added the result is 3
- 12* 15 = -180
-12 +15 = 3
3 pounds of bananas cost 1.5. what is the constant of proportionality that relates the cost in dollars ,y, to the number of pounds of bananas ASAP
Answers
Answer:
$0.5
Step-by-step explanation:
formula ; y = kx
where ; y = $1.5
x = 3 pounds of bananas
k = constant of proportionality
Step 1. Do the equation based on the data given
y = kx
$1.5 = k3
Step 2. Compute the mathematical equation. Divide both sides by the coefficient of 3.
$1.5 = k3
3 3
k = .5
Answer; $0.5 is the constant of proportionality cost in dollars per pound of banana.
Answer:
0.25
Step-by-step explanation:
Have a nice day <3
I need help!! Can you please make t the subject
Answers
Answer:
t=3
Step-by-step explanation:
[q(t + 3) + 4t = 2]
[qt + 3q + 4t = 2]
[qt + 4t = 2 - 3q]
[t(q + 4) = 2 - 3q]
[t = (2 - 3q)/(q + 4)]
Death Valley, located in California, is the lowest place in North America. It is 282 feet below sea level, or -282 feet. Mount McKinley in Colorado is the highest place in North America. Its elevation is approximately -71.76 times the elevation of Death Valley. What is the approximate elevation of the Mount McKinley?
-20,236.32 feet
20,236.32 feet
-3.93 feet
3.93 feet
Answers
Answer:
20,236.32
Step-by-step explanation:
because (-282) * (-71.76) = 20,236.32
Answer:
20236.32 feet
Step-by-step explanation:
-282*-71.76=20236.32
find the product of the following expression (x-15) (x-3)
Answers
Answer:
x²-18x+45
Step-by-step explanation:
(x-15)(x-3)
Product of the first terms is x² [x times x] F
Product of the outer term is -3x [x times -3] O
Product of the inner term is -15x [-15 times x] I
Product of the last term is 45 [-15 x -3] L
Combine like terms and you'll get x²-18x+45
Which of the following linear equations matches the graph?
y = 1/x
y = 1/3 x
y = 3x
y = -x
y = x
Answers
Answer:
y=x
Step-by-step explanation:
Answer:
y = x
because it's at 1y axsis, and 1x axsis
Erin loves to play sports! She has earned 333 tennis trophies, 444 basketball trophies, 777 soccer trophies, and 111 volleyball trophy.
What is the ratio of Erin's tennis trophies to soccer trophies?
Answers
1 : 2 1/3
The ratio of Erin's tennis trophies to soccer trophies is 3/7.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
She has earned 333 tennis trophies, 444 basketball trophies, 777 soccer trophies, and 111 volleyball trophies.
The ratio of tennis trophies to soccer = 333/777
3/7(111/111) = 3/7
Hence "The ratio of Erin's tennis trophies to soccer trophies is 3/7".
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Match each scientific notation with the appropriate number
Answers
Answer:
wheres the answer choices
What are the next two terms in the sequence?
2, 14, 26, 38, ...
Answers
Answer:
50, 62
The drawing will help
Answer:
50, 62Step-by-step explanation:
[tex]a(1)=2\\\\a(2)=a(1)+12=2+12=14\\\\a(3)=a(2)+12=14+12=26\\\\a(4)=a(3)+12=26+12=38\\\\a(5)=a(4)+12=38+12=50\\\\a(5)=a(5)+12=50+12=62[/tex]
If you want the formula.
It's an arithmetic sequence with the first term 2 and common difference 12.
The explicit formula of an arithmetic sequence:
[tex]a(n)=a(1)+(n-1)d[/tex]
d - common difference
Substitute:
[tex]a(n)=2+(n-1)(12)[/tex] use the distributive property
[tex]a(n)=2+12n-12[/tex]
[tex]a(n)=12n-10[/tex]
harvey the wonder hamster can run 3 1/6 km in 1/4 hour. harvey runs at a constant rate.
find his average speed in kilometers per hour.
___ kilometers per hour
please help lol.
Answers
Answer:
38/3 km per hour
Step-by-step explanation:
3 1/6=19/6
1/4=0.25
(19/6)*4=38/3
luisa orders a sandwich from a food truck, the piece of the sandwich before tax is $8. Luisa wants to know the total price including a 7% sales tax
Answers
Luisa needs to pay $8.56 including sales tax.
Step-by-step explanation:
Price of piece of sandwich = $8
Sales tax = 7%
Amount of sales tax = 7% of price of sandwich
Amount of sales tax = [tex]\frac{7}{100}*8[/tex]
Amount of sales tax = [tex]\frac{56}{100} = \$0.56[/tex]
Total price to pay = Price of piece of sandwich + amount of sales tax
Total price to pay = [tex]8+0.56 = \$8.56[/tex]
Luisa needs to pay $8.56 including sales tax.
Keywords: sales tax, percentage
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If you could marry, anyone in the world. Who would it be?
Answers
Answer:
I would marry Ino from Naruto
Step-by-step explanation:
Plz mark brainliest
Answer:
my bestfriend jaheim
Step-by-step explanation:
Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.3 pounds. This month, the puppy weighed 8.48 pounds. What is the percentage increase of the weight of the puppy?Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.3 pounds. This month, the puppy weighed 8.48 pounds. What is the percentage increase of the weight of the puppy?
A. 63%
B. 3%
C.60%
D. 37%
Answers
The puppy's weight increased by 60%.
Answer:
Step-by-step explanation:
60
Which fuction is positive for the entire interval [-3, -2 ]
Answers
Answer:
f(x) = |x| or f(x) = x² etc.
Step-by-step explanation:
There are several functions that gives positive value for entire interval [-3,-2].
Like the function, y = |x| , where if you put any negative value of x, the resulting output of the value of y is always positive. Therefore, for domain of [-3,-2] the range of the function will be [3,2]
Again, the function y = x², where if you put any negative number as a value of x, the corresponding value of y will be always positive.
Therefore, for domain of [-3,-2] the range of the function will be [9,4] (Answer)
Find the slope of the line that contains (3, -4) and (7, -2).
Answers
Answer:
The slope is 1/2.
Step-by-step explanation:
m=(-2-(-4))/(7-3)=(-2+4)/4=1/2
find last years salary if, after 6 percent raise, this years salary is $33,920
Answers
Last year's salary is $32000
Step-by-step explanation:
We will use the linear equations to solve the given problem
Let x be the last years salary
then
0.06x will be the raise in the salary
This year's salary is $33920
So,
[tex]x+0.06x=33920\\1.06x=33920[/tex]
Dividing both sides by 1.06
[tex]\frac{1.06x}{1.06}=\frac{33920}{1.06}\\=32000[/tex]
Hence,
Last year's salary is $32000
Keywords: Percentage, Linear equations
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Madison used a coordinate plane to map out an L-shaped
herb garden, shown at the right. Each unit on the grid
represents yard. To buy a fence for the garden, she nee
to know its perimeter. What is the perimeter of the garde
od coction of the
Answers
Answer:
The perimeter of the garden is 14 yard.
Step-by-step explanation:
Consider the figure:
Each unit on the grid represents [tex]\frac{1}{2}[/tex] yard.
From the figure we can find that:
The length of FA is 3.5 yard
The length of EF is 3.5 yard
The length of DX is 2 yard
The length of CD is 2 yard
The length of CB is 1.5 yard
The length of AB is 1.5 yard
To find the perimeter of the garden we need to add all the length as shown:
Perimeter = FA + EF + DX + CD + CB + AB
Perimeter = 3.5 + 3.5 + 2 + 2 + 1.5 +1.5
Perimeter = 14 yards
Hence, the perimeter of the garden is 14 yard.
Samantha deposit 300 in an account that earns an annual interest rate of 2.5 after nine months she computes the simple interest. What mistakes did Samantha make?
Answers
Answer:
She is doing a mistake of calculating interest after 9 months in place of after 12 months.
Step-by-step explanation:
Samantha deposit $300 in an account that earns an annual interest rate of 2.5%.
Now, Samantha after nine months of deposit computes the simple interest.
She is doing a mistake of calculating interest after 9 months in place of after 12 months.
The calculation of interest should be on a yearly basis (i.e. 12 months) as the interest rate is 2.5% per year. (Answer)
the difference between the measures of two supplementary is 42. Find both angles.
Answers
Answer:
111 deg and 69 deg
Step-by-step explanation:
let the angles be x and y
given:
x - y = 42 degrees -------> eq 1
also given that they are supplemantry,
i.e x + y = 180 degrees ----------> eq 2
by elimination,
eq 1 + eq 2
(x-y) + (x+ y) = 42 + 180
2x = 222
x = 111 degrees (substitute back into eq 2)
111 + y = 180
y = 180 - 111
y = 69 deg
(5 x 2) + (5 x 4) = 5 x (2 + 4)
Which picture represents this equation?
A) A
B) B
C) C
D) D
Answers
Answer:
Step-by-step explanation:
Wheres the picture?
The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) showcases the distributive property in mathematics where two different expressions yield the same result.
The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) is a demonstration of the distributive property in mathematics.
(5 x 2) + (5 x 4) can be simplified as 10 + 20 = 30.
5 x (2 + 4) can be simplified as 5 x 6 = 30.
Hence, both sides of the equation result in the same value, displaying the equality of the expression.
In a video game green gems are worth 5 points and blue gems are worth 10 points. Eric collects 25 gems and earned 160?points form his gems. Find how many green gems and how many blue gems Eric collected.
Answers
Eric collected 18 green gems and 7 blue gems.
Step-by-step explanation:
Let,
Green gems = x
Blue gems = y
One green gem = 5 points
One blue gem = 10 points
According to given statement;
x+y=25 Eqn 1
5x+10y=160 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=25)\\5x+5y=125\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2;
[tex](5x+10y)-(5x-5y)=160-125\\5x+10y-5x-5y=35\\5y=35[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{35}{5}\\y=7[/tex]
Putting y=7 in Eqn 1;
[tex]x+7=25\\x=25-7\\x=18[/tex]
Eric collected 18 green gems and 7 blue gems.
Keywords: linear equations, subtraction
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Eric collected 18 green gems and 7 blue gems. This conclusion is reached by forming and solving a system of linear equations based on the problem's conditions related to the total number of gems and their respective point values.
Explanation:This question deals with a system of equations, defined by the value of the gems and the total number of gems. Here, let's represent green gems as 'g' and blue gems as 'b'.
The two equations formed from the problem are as follows: g + b = 25 (since Eric collected 25 gems) and 5g + 10b = 160 (since green gems are worth 5 points each and blue ones 10, yielding a total score of 160).
To solve it, we need to isolate one of the variables: first, multiply the first equation by 5: 5g + 5b = 125. Then subtract this equation from the second equation, so we get 5b = 35, which simplifies to b = 7.
Substitute b = 7 into the first equation to get g = 25 - 7 = 18. Therefore, Eric collected 18 green gems and 7 blue gems.
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