When the triangle XYZ is dilated by a scale factor of 4/3, the resulting triangle would have a bigger side lengths
The algebraic rule is [tex](x,y) \to (\frac 43x,\frac 43y)[/tex]
How to determine the algebraic rule?From the question, we understand that:
The scale factor (k) of the dilation is:
k = 4/3
The dilation rule across the origin is represented as:
[tex](x,y) \to k(x,y)[/tex]
Substitute 4/3 for k
[tex](x,y) \to \frac 43(x,y)[/tex]
Expand
[tex](x,y) \to (\frac 43x,\frac 43y)[/tex]
Hence, the algebraic rule that represents how to find the coordinates of triangle X’Y’Z’ is [tex](x,y) \to (\frac 43x,\frac 43y)[/tex]
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Evaluate the given algebraic expression for x = 7 and y = 3.
Answer: = 2(7 + 3) ^2= 2 * 10^2= 200
Find the quotient of 2. 5 × 10-3 and 7. 1 × 106. What can be concluded about the solution? Check all that apply. The E indicates that the solution is given in scientific notation. The coefficient is 3. 5211. The exponent is 10. The solution can be written in scientific notation as 3. 5211 × 10-10. The solution is 35,211,000,000.
Scientific notation is the way through which a very small or a very large number can be written in shorthand. The quotient of 2.5×10⁻³ by 7.1×10⁷ is 3.5211×10⁻¹¹.
What are Scientific notations?Scientific notation is the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5e+12.
We know we need to divide 2.5×10⁻³ by 7.1×10⁷. Therefore, if we divide the two numbers the solution will be,
[tex]\dfrac{2.5 \times 10^{-3}}{7.1 \times 10^7}\\\\ = \dfrac{2.5}{7.1} \times 10^{-3-7}\\\\= 0.35211 \times 10^{-10}\\\\= 3.5211 \times 10^{-11}[/tex]
Hence, the quotient of 2.5×10⁻³ by 7.1×10⁷ is 3.5211×10⁻¹¹.
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Answer:
A. The E indicates that the solution is given in scientific notation.
B. The coefficient is 3.5211.
D. The solution can be written in scientific notation as 3.5211 × 10^-10
Step-by-step explanation:
Edge 2023
The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?
Answer: 0.27
Population density of the species in water:
Population density of a species in the water is given by the expression,
Density =Given in the question,
Number of goldfish in the tank = 12
Volume of the tank = 45 cubic feet
Substitute these values in the expression,
Density =
= 0.267
≈ 0.27 goldfish per cubic feet
Therefore, density of the tank will be 0.27 goldfish per cubic feet.
Diana is trying to choose a broker who will help her purchase a par value $1,000 corporate bond from deegan pharmaceuticals. broker p charges a commission of 4.4% of the market value of each bond purchased, and broker q charges a flat fee of $32.50 for each bond purchased. if bonds from deegan pharmaceuticals are selling at 104.682, which broker will give diana the better deal, and by how much? a. broker p’s commission will be $9.47 less than broker q’s. b. broker p’s commission will be $27.89 less than broker q’s. c. broker q’s commission will be $13.56 less than broker p’s. d. broker q’s commission will be $11.50 less than broker p’s.
Broker q’s commission with a charge of $32.50 will be $11.50 less than broker p’s commission of 4.4%
What is a bond?A bond is a fixed-income instrument that represents a loan made by an investor to a borrower.
Par value of bond = $1,000
Commission on this by broker p= 4.4% = 1000*(4.4)/100= $44
So, the total price spent to purchase this bond = $1044
Par value of bond = $1,000
Commission on this by broker q= $32.50
So, the total price spent to purchase this bond =1000+32.50 = $1032.50
Difference between both deals = 1044-1032.50 = $11.50
Therefore, broker q’s commission will be $11.50 less than broker p’s.
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Answer:
C. Broker Q's commission will be $13.56 less the Broker P's.
Step-by-step explanation:
I just took the test and got it right.
I would really like help with A & B
Check the picture below.
Make sure your calculator is in Degree mode.
A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym?
Answer:
dimensions are 51x91
Step-by-step explanation:
Assuming that the gym is rectangular in shape, then...
l*w=4641
and 2l+2w=284
We have two variables and two equations so to solve this we plug one equation into another.
Solve for one variable:
l*w=4641
w=4641/l
Plug into the other equation...
2l+2(4641/l)=284
Solve
l*(2l+9282/l)=284
2l^2+9282=284l
2l^2-284l+9282=0
Factor the trinomial:
2(l−51)(l−91)=0
l−51=0 or l−91=0(Set factors equal to 0)
l=51 or l=91
now, lets plug it into one of the equations to find w
51*w=4641
w=91, l=51
or...
91*w=4641
w=51, l=91
Answer:
91 ft × 51 ft
Step-by-step explanation:
while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).
and it assumes you can find the right factoring of the expression.
so, I will show you here how to generally solve this, even if you cannot find the right factorization :
l×w = 4,641 ft²
w = 4641/l
2l + 2w = 284
2l + 2(4641/l) = 284
2l + 9282/l = 284
2l² + 9282 = 284l
2l² - 284l + 9282 = 0
to make things easier let's divide everything by 2
l² - 142l + 4641 = 0
the general solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = l
a = 1
b = -142
c = 4641
l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =
= (142 ± sqrt(20,164 - 18,564))/2 =
= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20
l1 = 71 + 20 = 91
l2 = 71 - 20 = 51
w1 = 4641/91 = 51
w2 = 4641/51 = 91
so, they are interchangeable (it does not matter which we call length and which width).
the dimensions are 91 ft × 51 ft
I need help with this problem in math I don’t know how to find the y but I know how to get the slope can someone teach me
Answer:
Use the equation y=mx+b
Step-by-step explanation:
So you know how to get the slop, which is awesome
Now to get y all you have to do is use the equation:
y=mx+b
m being slop
b being y- intercept in this case being 2
so you have y=-2x+2
all you have to do is insert different x values and solve the equation for y and see if they match up together in any of the tables
When Sally decided to run for class treasurer, she predicted how many votes she would get. After the election, Sally found out she had received 150 votes. She had predicted she would get 20% fewer votes than that. How many votes did Sally predict she would get?
Answer:
3000
because you need to dived it
What is the volume of this figure? Enter your answer in the box. ft³
Answer:
75 ft³ for K12
Hong purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Hong paid.
Answer:
5n=c
Step-by-step explanation:
the equation 5n=c can represent the total cost Hong would have paid for the notebooks because given that each notebook costs $5, you would multiply 5 by the number of notebooks (n) that Hong would be purchasing, which would bring you to the cost (c) of the notebooks all together
sorry for the delay. hope this helps
Find the perimeter of the shape shown below.
perimeter = turn of the figure
P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36
the triangle has 2 équal sides => isosceles
and 1 angle is 60° so the triangle is equilateral
I bought a 4 pack of tissues for $8.80. What was the unit rate?
Answer: 2.2 and/or 2.20 the zero doesn't matter
Step-by-step explanation:
4 goes into 8, 2 times bring the 2 up (4x2=8)
8-8=0
Bring down the next 8
4 goes into 8, 2 times bring the 2 up (4x2=8)
8-8=0
4 goes into 0, 0 times
0-0=0 bring up the 0 or don't
you should get 2.2 and/or 2.20
Phillip is going to a college where tuition is $7,000 per year. He has a scholarship that pays 75% of tuition. He has a grant that pays $1,500 per year. How much will he need to borrow to pay tuition each year?
Marie is making her own website. She has 45 background colors, 130 fonts, and 20 themes to choose from. How many different designs can she create?
Answer:
20 designs
Step-by-step explanation:
Some websites have limited data and bytes to hold, so she might have to have one theme, 5 fonts, and 2 background colors to look nice. 1 × 5 × 2 = 10. Add all the other background colors and fonts and themes and divide them by 10.
Therefore, she can create about 20 designs
The graph of the function f(x) = x2 is shifted 2 units up and 1 unit to the right. Which of the following corresponds to the shifted graph?
Answer:
g(x) = (x - 1)^2 + 2.
Step-by-step explanation:
1 unit to the right x---> (x - 1)
2 units up ------ f(x) moves up ---> + 2
answer is (x - 1)^2 + 2
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. What is the height of the pole? Round to the nearest hundredth. 12. 00 feet 19. 60 feet 24. 17 feet 38. 40 feet.
The height of the pole from the ground is 19.60 feet round to the nearest hundredth.
How to find the length of longest side in right angle triangle?To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.
According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. Thus, the length of side of h by the Pythagoras theorem can be given as,
[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]
Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.
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Describe the relationship between pi and circles.
Answer:
The circumference (C) of a circle is found by the equation C = 2*[tex]\pi[/tex]*radius
There is a second relationship between [tex]\pi[/tex] and circles. That of the area (A) of the circle which is found by the formula A = [tex]\pi*radius^{2}[/tex]
Step-by-step explanation:
HELP!! Using the geometric sequence 2,2/3,2/9,. ,2/243, find the approximate sum of the geometric series. Round your answer to the nearest whole number.
Answer choices:
4
3
1
6
we can always get the common ratio of a geometric sequence by simply dividing the current term by the previous term, in this case for the sake of simplicity let's divide 2/3 by 2, so
[tex]\cfrac{2}{3}\div 2\implies \cfrac{2}{3}\div \cfrac{2}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{3}\impliedby \textit{common ratio}[/tex]
so the sequence more or less looks like [tex]2~~,~~\cfrac{2}{3}~~,~~\cfrac{2}{9}~~,~~\cfrac{2}{81}~~,~~\cfrac{2}{243}[/tex]
so we'd want the sum of the first 5 terms
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\\\ S_5=2\left( \cfrac{1~~ - ~~(\frac{1}{3})^5}{1~~ - ~~\frac{1}{3}} \right)\implies S_5=2\left( \cfrac{~~\frac{242}{243}~~}{\frac{2}{3}} \right)\implies S_5=\cfrac{242}{81}\implies S_5=2\frac{80}{81}[/tex]
PLEASE HELP!! 100 POINTS
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b)What is the scale factor? Explain and show your work.
The red figure is the original and the green the dilation. We know this because the dilated points are marked with '.
Therefore, we can see that the dilation is a reduction of the original figure. The figure got smaller in size after the dilation.
To find the scale factor, we'll need to look at a few of the points before and after the dilation.
A = (-4, 4)
A' = (-2, 2)
C = (0, 4)
C' = (0, 2)
---The scale factor will be the same on all the points, which is why I have selected only 2 sets of points to look at.
Now, we can figure out the scale factor by thinking about how -4 got to -2, how 4 got to 2. In this case, it is simply dividing by 2. The scale factor must be in multiplication, so we cannot use division in reporting the scale factor, it must be a fraction.
2 / 4 = 1 / 2
The scale factor, therefore, is 1/2.
Hope this helps!
Answer:
a) A reduction.
b) 0.5 or 1/2
Step-by-step explanation:
a) The new points are indicated by the ' next to the letters. By observing the graph, we can see that new points have lessened, and therefore shrank the dialtion, so it is a reduction.
b) On each point, it is reducted by 0.5.
Point A went down from 4 to 2, which is half of 4.
Point B went down from -2 to -1, which is half of -2.
Point C went down from 4 to 2, which is half of 4.
Point D went down from 8 to 4, which is half of 8.
hope this helps!
MIGHT GIVE BRAINLIEST.
Calculator What is the surface area of the square pyramid?
Answer:
I need to know the dimensions to solve
Will give brainliest <333
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 8 kg weighs 80 N. Calculate the mass of another object that weighs 100 N.
This isn't my work, though it's the answer to your question.
Answer:
The weight of an object when the mass is 10 kg will be 30 N.
Step-by-step explanation:
8/10 = 24/x
Cross multiply
8x = 24 × 10
8x = 240
x = 240/8
x = 30
Answer:
I’m just answering for him to get brainliest :)
Step-by-step explanation:
A store is having a clearance special and every item is 10% off. What is the sale price of a $310 suit?
Answer:
$279
Step-by-step explanation:
10% off $310 is $31
310-31 is 279
Answer: the sale price of the suit is $279 or $31 dollars off
Step-by-step explanation:
$310 x 0.10= $31
$310 - $31= $279
WHAT IS THE AVERAGE NUMBER OF POINTS THAT CHANGED HANDS
3/8x5/7=? please help
thank you
Answer:
15/56
Step-by-step explanation:
multiply the top fractions by making the equation the following
3x5
-------
8x7
_________________________
3x5 =15
8x7= 56
hope this helps :)
The solution to the product of fractions is 13/56
How to evaluate the product of fractionsFrom the question, we have the following parameters that can be used in our computation:
3/8 * 5/7
Evaluate the product of 3 and 5
So, we have
3/8 * 5/7 = 13/8 * 1/7
Evaluate the product of 8 and 7
So, we have
3/8 * 5/7 = 13/56
Hence, the solution is 13/56
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please help I am confused
Answer: -5
Step-by-step explanation:
Opposite sides of a parallelogram are parallel, and thus have equivalent slopes.
Juan has forty dollars in his jacket. Every day he spends half of the money that is in the jacket. On the first day (Monday), he spends $20 leaving him with twenty dollars. On what day will he start with less than $3.00 in his jacket?
A) Friday
B) Thursday
C) Tuesday
D) Saturday
Answer:
FridayStep-by-step explanation:
Monday he is left with 20,
Tuesday he will start with 20 and end with 10
Wednesday he will start with 10 and end with 5
Thursday he will Start with 5 and end with 2.5
Friday Start with 2.5
which is >3
MARK ME AS BRAINLISTAnswer:
D) Friday
Hope it helps...
PLS HELP :How is energy causing motion or creating a change in this image? (2 points)
(leaves of a plant in the sunlight)
1.Energy from fuel allows the plant to grow and make its own food.
2.Energy from the sun allows the plant to grow and make its own food.
3.Energy from the wind allows the plant to grow and make its own food.
4.Energy from the water allows the plant to grow and make its own food
Answer:
Not entirely sure but im sure its no. 2
Step-by-step explanation:
Answer:
I think it's 2
Step-by-step explanation:
What is 170.6% of 366?
Answer:
624.396
Step-by-step explanation:
I did the math myself XD
Evaluate the expression for m = -3.
-4|5 + m|
Type the correct answer in the box. Use numerals instead of words.
Answer:
The answer is -8
-4 l5 +(-3)l
-4 (2) = -8
Answer: Correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Edmentum Answer
Please help I don't get this
Answer:
5(t+6). I think this may helps you