Find the Greatest Common Factor (GCF)
GCF = 2xy
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2xy(8x^3y/2xy + -8x^2y/2xy + -30xy/2xy)
Simplify each term in parenthesis
2xy(4x^2 - 4x - 15)
Split the second term in 4x^2 - 4x - 15 into two terms
2xy(4x^2 + 6x - 10x - 15)
Factor out common terms in the first two terms, then in the last two terms;
2xy(2x(2x + 3) -5(2x + 3))
Factor out the common term 2x + 3
= 2xy(2x + 3)(2x - 5)
The table below shows two equations:
Equation 1 |4x − 3|− 5 = 4
Equation 2 |2x + 3| + 8 = 3
Which statement is true about the solution to the two equations?
* Equation 1 and equation 2 have no solutions.
* Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution. *
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.
Answer:
Option C is correct.
Step-by-step explanation:
Equation 1 |4x − 3|− 5 = 4
Adding +5 on both sides
|4x − 3|− 5 +5 = 4 +5
|4x − 3| = 9
Apply absolute rule:
IuI = a and a>0 then u = a and u = -a
so, 4x-3 = 9 and 4x-3 = -9
Solving
4x = 9+3 and 4x = -9+3
4x = 12 and 4x = -6
x = 12/4 and x = -6/4
x = 3 and x = -3/2 or -1.5
Equation 2 |2x + 3| + 8 = 3
Adding -8 on both sides
|2x + 3| + 8 -8 = 3 -8
|2x + 3| = -5
Apply absolute rule:
IuI = a and a>0 then u = a and u = -a
But we cannot apply absolute rule because in our case a < 0 i.e -5
So, Equation 2 has no solutions.
Hence Option C The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution is correct.
Which of the following shapes is convex?
D. Is a convex shape.
A convex shape will have no angles less than 180 degrees pointing inward. A, B, and C all have at least one of these angles. Whereas D, only has outward angles.
Only the shape D is convex structure.
What is convex?A form that curves outward is convex.
We know that the convex structure has no inward shape.
In the shape A,B and C;
all of the shape have inward structure.
Whereas shape D has only outward structure.
Therefore, Only shape D is convex.
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Clara's class is going on a trip to the local science museum. Twenty-five students, one teacher, and three parents are going on the trip. The museum charges $3.50 admission for each student and $5.00 for each adult. How much will it cost for all the students and the adults to enter the museum?
Question 2 options:
a $87.50
b $101.50
c $102.50
d $107.50
Answer:
$107.50
Step-by-step explanation:
$3.50 = 1 STUDENT
$5.00 = 1 ADULT
TWENTY FIVE STUDENTS = $3.50 × 25 = $87.50
FOUR ADULTS (ONE TEACHER AND THREE PARENTS) = $5.00 × 4 = $20.00
TOTAL COST = $87.50 + $20.00 = $107.50
What is the midpoint of AC
ANSWER
B) (m+p,n+r)
The coordinates are :
A(2m,2n)
B(2p,2r)
To find the x-coordinate of the midpoint of AB, we add the x-coordinates of the two points and divide by 2.
[tex]x = \frac{2m + 2p}{2} [/tex]
Factor
[tex]x = \frac{2(m + p)}{2} [/tex]
Simplify:
[tex]x = m + p[/tex]
Similarly, the y-coordinate is
[tex]y = \frac{2n + 2r}{2} [/tex]
[tex]y = \frac{2(n + r)}{2} [/tex]
[tex]y = (n + r)[/tex]
Hence the midpoint is
(m+p,n+r)
when an exponent of a power is an even number and the base is a negative number, the value is always:
A. positive
B. negative
C. 0
D. none of the choices
Answer:
The correct answer option is A. positive.
Step-by-step explanation:
When an exponent or a power is an even number and the base is a negative number, the value is always positive.
Suppose we have a negative base [tex] - 3 [/tex] and a power which is even, lets say, [tex] 6 [/tex] so what we get is a positive value.
[tex](-3)^6=729[/tex]
Therefore, a negative base with even power is always a positive value.
Answer: A. positive
Step-by-step explanation:
We know that powers are written in this form:
[tex]b^m[/tex]
Where "b" is the base and "m" is the exponent.
By definition, the exponent indicates how many times to base must be multiplied by itself. Then, if the base is negative and the exponent is an even number, you get:
[tex](-3)^4=(-3)(-3)(-3)(-3)=81\\\\\\(-2)^2=(-2)(-2)=2\\\\\\(-5)^6=(-5)(-5)(-5)(-5)(-5)(-5)=15,625[/tex]
Therefore, when an exponent of a power is an even number and the base is a negative number, the value is always positive.
What is the equation of a line that passes through the point (2, 4) and has a y-intercept at y = -10?
Answer:
The equation of the line is y = 7x - 10
Step-by-step explanation:
* Lets revise the form of the equation
- The form of the equation of a line is y = mx + c , where m is the slope
of the line and c is the y-intercept
- The y-intercept means the line intersect the y-axis at point (0 , c)
- The slope of the line which passes through points (x1 , y1) , (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The y-intercept is y = -10
∴ The line intersects the y-axis at point (0 , -10)
∵ The line passes through the points (2 , 4) and (0 , -10)
- Lets find the slope of the line using the rule of the slope above
∵ [tex]m=\frac{-10-4}{0-2}=\frac{-14}{-2}=7[/tex]
∴ The slope of the line is 7
∵ c is the y-intercept
∵ The y-intercept is y = -10
∴ c = -10
∵ y = mx + c
∴ y = 7x + -10
∴ y = 7x - 10
* The equation of the line is y = 7x - 10
Owen uses colored pencils on his homework assignment. His red pencil is 12.195 centimeters long. His blue pencil is 9.13 centimeters long.
What is the total length of these two pencils if he lines them up end to end
Enter your answer, as a decimal
Answer:
21.325 is the correct answer
please gimme brainliest :))!!Answer: 21.325
Explanation: 12.195+9.13
Which number line shows the solutions to n < -3?
Ples help
The number line for the inequality n < -3 would have an open circle at -3 and be shaded to the left, representing all numbers less than -3.
When considering the inequality n < -3, the number line that represents the solutions to this inequality would show all the numbers that are less than -3. This means that any point to the left of -3 on the number line would be shaded to indicate that it is part of the solution set. Additionally, the number -3 would typically be represented with an open circle, indicating that -3 is not included in the set of solutions because the inequality is strictly less than, not less than or equal to.
If you were to graph this inequality on a number line, you would start at the point -3 and shade everything to the left of -3 going towards negative infinity. This visualization shows that n can take any value that is less than -3. Therefore, the number line for the solutions of n < -3 would look like a horizontal line with an open circle at -3 and a shaded region extending to the left from -3.
What are the steps needed to solve the following problem:
(2x - 3)(x + 4) = -5?
Answer:
it is very simple -5 =(5)(-1)=(x+4)(2x-3).so compare( 5)=(x+4) and (x=1) it can be solved by mind.....(2x^2)+5x-7=0 then
These are the steps.
1. Write out the equation.
2. FInd any whole numbers and put them together and find any variables and put them together, both in parentheses.
3. Solve both equations in parentheses.
4. Divide -5 by 3 to find x. The answer is on step 5.
[tex]1. (2x - 3)(x + 4) = -5\\2. (-3 + 4)(2x + x) = -5\\3. (1)(3x) = -5\\4. 3x = -5\\5. x = -1.66[/tex]
Consider the data set on the number line. Determine the interquartile range.
A) 3
B) 6
C) 14
D) 17
Answer:
b
Step-by-step explanation:
todo lol que tienes que hacer es hacer la cosa ricola sexta
Simplify the number 8 ^2/3
Answer:
4
te ayudara en las ecuaciones
The value of [tex]8^(^2^/^3^)[/tex] is equal to 4 by exponent property
To simplify the number [tex]8^(^2^/^3^)[/tex]
we can apply the property of exponents which states that [tex](a^m)^n = a^(^m^\times^n^).[/tex]
Now [tex]8^(^2^/^3^)[/tex], which means we need to raise 8 to the power of 2/3.
Now, let's rewrite 8 as a power of a base that is a perfect cube:
8 = 2³
[tex](2^3)^(^2^/^3^)[/tex]
Applying the exponent property mentioned earlier, we multiply the exponents:
[tex]2^(^3 ^\times^2^/^3^)[/tex]
2²
we get four, 4
Therefore, [tex]8^(^2^/^3^)[/tex] is equal to 4.
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What is 15/7 as a mixed number
Answer:
Fraction can't be reduced (simplified). /7 = - 15/7 = - 2 1/7 = - 2.142857142857; Result written as a negative improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fraction reducing to lowest terms (simplifying), answer with explanations below.
Step-by-step explanation:
2 1/7 Is Your Answer.
First, divide the numerator (the 15) by the denominator (the 7). This will give
you 2, with a remainder of 1.
The mixed number can be created by using the 2 as the whole number, the 1 as the numerator
and the 7 as the denominator.
The distance around a circular park is 88 yards. What is the area of the park?
Answer:
A = 617 yd², to the nearest yard
That distance is called the "circumference," and its formula is C = 2πr.
We need r to find the area of the park. So we solve C = 2πr for r:
C
r = -------
2π
Substituting 88 yd for C, we get r = (88 yd) / (6.28) = 14.01 yd
The formula for the area of this circular park is A = πr².
Here, r = 14.01 yd, so the area of this park is:
A = π(14.01 yd)² = 3.14(196.36 yd²) = 617 yd², to the nearest yard.
The area of the park is [tex]A = 617 yd^2[/tex], to the nearest yard.
That distance is called the circumference and
We have to determine the area of the park
What is the formula for the circumference of the circle?The circumference of the circle is C = 2πr.
We need r to find the area of the park.
So we solve C = 2πr for r:
[tex]r=\frac{C}{2\pi}[/tex]
Substituting 88 yd for C,
We get r = (88 yd) / (6.28)
r= 14.01 yd
The formula for the area of this circular park is
A = πr².
Here, r = 14.01 yd, so the area of this park is,
[tex]A = \pi (14.01 yd)^2[/tex]
[tex]A = 3.14(196.36 yd^2)[/tex]
[tex]A = 617 yd^2[/tex], to the nearest yard.
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Which of the following are identities? Check all that apply.
Answer:
Options A and D.
Step-by-step explanation:
To check the identities we have to check each option given.
A. tan(x - π) = tanx
We take left hand side (L.H.S.) of the equation.
tan(π - x) = tanx [ since we know tan(π ± x) = tanx ]
So L.H.S. = R.H.S.
It's an identity.
B. sin(x + y) + sin(x - y) = 2cosx siny
We take L.H.S. first
sin(x + y) + sin(x - y)
= sinx coxy + siny cosx + sinx cosy - cosx siny
= 2sinx cosy ≠ R.H.S.
Option B is not an identity.
C. cos(x + y) - cos(x - y) = 2cosx cosy
We take L.H.S. of the equation.
cos(x + y) - cos(x - y) = cosx cosy - sinx siny - (cosx cosy + sinx siny)
= -2sinx siny ≠ R.H.S.
Therefore, option C is not an identity.
D. cos(x + y) + cos(x - y) = 2cosx cosy
We take L.H.S. of the equation.
cos(x + y) + cos(x - y) = cosx cosy - sinx siny + cosx cosy + sinx siny
= 2cosx cosy = R.H.S.
Therefore, option D is an identity.
Options A and D are the identities.
Match each cross section with its perimeter
64 inches
26 inches
48 inches
34 inches
Answer:
64 inches : cross-section, cube, 16 inches
26 inches : right rectangular prism, 10x 3 x 14 inches
48 inches : cube with 12-inches edges
34 inches : rectangular prism, 5x12x4 diagonal of 13 inches
Step-by-step explanation:
right rectangular prism, 10x 3 x 14 inches
The cross-section is parallel to the base, so it cuts the height, maintaining the length and width. So, we have:
P = 10 + 3 + 10 + 3 = 26 inches
cube with 12-inches edges
This time, the cross-section is done perpendicular to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.
P = 12 + 12+ 12 + 12 = 48 inches
rectangular prism, 5x12x4 diagonal of 13 inches
The cut is done perpendicular to the base, but along a diagonal of 13 inches, so the height is preserved, and the diagonal length becomes the new side other than height.
P = 13 + 4 + 13 + 4 = 34 inches
cross-section, cube, 16 inches
Again, the cross-section is done parallel to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.
P = 16 + 16 + 16 + 16 = 64 inches.
Answer:
points
Step-by-step explanation:
A library has 15,000 fiction books and 8,800 nonfiction books.
Currently, 3/5 of the fiction books are checked out.
Currently 1/4 of the nonfiction books are checked out.
3/10 of the books that are checked out are due back this week.
How many books are due this week?
Answer:3360
Step-by-step explanation:
a photograph of a full moon is enlarged so that the diameter is 8 times larger. how much larger is the circumfrence?
Answer:
25.13
Step-by-step explanation:
Since the Diameter is 8 the equation to find the Circumference is pi time D
3.14 x 8 equals 25.13274...
let's recall that the radius of a circle is half of the diameter, now, if the diameter say "d" got enlarged 8 times, to it became 8d, then the radius "r" got enlarged 8 times as well, namely 8r.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} r=8r \end{cases}\implies \stackrel{\textit{is 8 times larger than that of the original}}{C=2\pi (8r)\implies C=\stackrel{\downarrow }{8}[2\pi r]}[/tex]
Find the solution of the system of equations shown on the graph.
Answer:
no solution
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
The 2 lines shown here are parallel and never intersect
Hence the system has no solution
What is the reverse of “multiply by 6”
Answer:
Divide by 6
Step-by-step explanation:
The reverse or inverse of multiply by 6 is divide by 6.
Find the interest earned and the future value of an annuity with semiannual payments of $1,500 for 16 years into an account that pays 9% interest per year compounded semiannually.
Answer:
interest earned= 1853.98
the future value of an annuity= 2453.98
Step-by-step explanation:
Given Data:
Interest rate= 9%
time,t = 16 years
Semi-Annual payment, P= 600
n= 2 as Semi-Annual
At the end of 16 years, final investment A= ?
As per the interest formula for compounded interest
A= P(1+r/n)^nt
Putting the values in above equation
= 600(1+0.09/2)^32
= 2453.98
Interest earned = A-P
= 2453.98-600
= 1853.98 !
A machine assembly requires two pyramid-shaped parts. One of the pyramids has the dimensions shown in the figure. The other pyramid is a scaled version a
irst pyramid with a scale factor of 4. What is the volume of the larger pyramid?
A. 48 cubic units
B. 192 cubic units
C. 256 cubic units
D. 768 cubic units
Multiply the given dimensions by the scale factor of 4:
2 x 4 = 8
3 x 4 = 12
6 x 4 = 24
The volume of a pyramid is found by multiplying the Length x the width x the height and dividing by 3:
Volume = (8 x 12 x 24) / 3
Volume = 2304 / 3
Volume = 768 cubic units.
The answer is D.
The volume of the larger pyramid is 768 units³.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given that,
A machine assembly requires two pyramid-shaped parts.
Volume of the pyramid = 1/3 × base area × height
If the larger pyramid has a scale factor of 4, each dimension is 4 times this pyramid.3
Base area of the larger pyramid = (4 × 3) × (4 × 2)
= 96 units²
Volume of the larger pyramid = 1/3 × 96 × (6 × 4)
= 768 units³
Hence the required volume is 768 units³.
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Name a container that you see at home that when filled has a liquid volume of about 1 liter.
Answer: flower vase
Step-by-step explanation:
A container that has a liquid volume of about 1 liter at home is typically a soda bottle. A liter is a metric unit of capacity and is equivalent to 1,000 cubic centimeters or milliliters, making it a convenient measure for everyday use.
An example of a container that you might find at home which, when filled, has a liquid volume of about 1 liter is a soda bottle. Liters and milliliters are metric units for measuring capacity. A liter is a convenient measure for everyday liquid volumes and is commonly used for beverages and other liquids in the home. Since a liter is equal to 1,000 milliliters, and taking into account that a juice box holds about 25 centiliters, which is 250 milliliters, a soda bottle's capacity is approximately four times that of a typical juice box. It's interesting to note that the liter can also be connected to cubic meters, as 1 liter is the same as 1,000 cubic centimeters (1,000 cm³), making these units interchangeable.
Please help will give brainliest
Answer:
[tex]b = 17[/tex]
Step-by-step explanation:
For this triangle we have to
[tex]a=18.2\\B=62\°\\C=48\°[/tex]
We want to find the length of b
We know that the sum of the internal angles of a triangle is 180 °
So
[tex]A + 62 +48=180\\\\A=180-62-48\\\\A=70\°[/tex]
Now we use the sine theorem to find the length of b:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Then:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}\\\\b=\frac{sin(B)}{\frac{sin(A)}{a}}\\\\b=a*\frac{sin(B)}{sin(A)}\\\\b=(18.2)\frac{sin(62)}{sin(70)}\\\\b=17[/tex]
A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if:
b
Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 18 cm, m∠B = 30°. Find r.
Answer:
The radius = 18 cm
Step-by-step explanation:
* Lets take about the inscribed triangle in a circle
- If the three vertices of a triangle lie on the circumference of a circle,
then this triangle is inscribed in the circle
- The vertices of the triangle are inscribed angles in the circle
- The inscribed angle opposite to a circle's diameter is always a
right angle (its measure is 90°)
- Now lets solve the problem
∵ Δ ABC is a right triangle at C
∴ m∠C = 90°
∵ Δ ABC is inscribed in a circle
∴ A , B , C lie on the circumference of the circle
∴ ∠A , ∠B , ∠C are inscribed angles in the circle
∴ m∠C = 90°
∵ ∠C is opposite to the side AB
∴ AB is the diameter of the circle ⇒ from the bold note above
∵ m∠B = 30°
∵ AC = 18 cm
- Lets use the trigonometry function to find the length of AB
* In Δ ABC
∵ AC is opposite to angle B
∵ AB is the hypotenuse
∵ sin Ф = opposite/hypotenuse
∴ sin B = AC/AB
∴ sin (30)° = 18/AB ⇒ using cross multiplication
∴ AB sin (30)° = 18 ⇒ divide both sides by sin (30)°
∴ AB = 18/sin(30)°
∵ sin(30)° = 1/2
∴ AB = 18/(1/2) = 36 cm
∵ AB is the diameter of the circle
∵ The length of the radius of a circle = 1/2 the length of the diameter
∴ The radius = 1/2 × 36 = 18 cm
The initial count of a certain type of bacteria in a culture is 580. If the bacteria continually grow at the rate of 18% per hour, which function models the number of bacteria after t hours?
Answer:
[tex]P (t) = 580e ^ {0.18t}[/tex] or [tex]P (t) = 580 (1.18) ^ t[/tex]
Step-by-step explanation:
There are two models of exponential growth that you can use to predict the population of bacteria after t hours.
I) [tex]P (t) = pe ^ {rt}[/tex]
II) [tex]P (t) = p (1 + r) ^ t[/tex]
Where
p is the initial population of bacteria
r is the growth rate
t is the time in hours.
In this case we know that:
[tex]p = 580\\\\r = \frac{18}{100}\\\\r = 0.18[/tex]
Then the equations that can be used to predict the population of bacteria after t hours are:
I) [tex]P (t) = 580e ^ {0.18t}[/tex]
II)[tex]P (t) = 580 (1 + 0.18) ^ t[/tex]
The probability that a randomly selected American
household owns at least one dog is 43%. The probability that
the household owns at least one cat is 31%. The probability that
the household owns either a dog or cat is 57%. What is the
probability that the household own both a cat and a dog?
A 12%
B.17%
0.37%
D. 131%
Answer:
B. 17%.
Step-by-step explanation:
The General Probability Addition Rule is
P(A∪B) = P(A) + P(B) − P(A∩B) where P(A∪B) = P(A) or P(B) and P(A∩B) = P(A) and P(B).
So applying this to our problem we have:
0.57 = 0.43 + 0.31 - P( household has a cat and a dog)
so the answer is 0.43 + 0.31 - 0.57
= 0.17 or 17%.
The probability that the household own both a cat and a dog will be 17%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The General Probability Addition Rule is
P(A∪B) = P(A) + P(B) − P(A∩B) where P(A∪B) = P(A) or P(B) and P(A∩B) = P(A) and P(B).
So applying this to our problem we have:
0.57 = 0.43 + 0.31 - P( household has a cat and a dog)
so the answer is 0.43 + 0.31 - 0.57
= 0.17 or 17%.
Hence the probability that the household own both a cat and a dog will be 17%.
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Find the median of the following data:
8, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20
O A. 10
O B. 16
O c. 12
O D. 14
The correct answer is C. 12
If you were to line up all the numbers in chronological order, the order would be: 5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21. Twelve is the center of all the numbers. There's eight numbers on each side of 12. Hope this helps! Please mark brainliest! Thank you v much! :)
Answer:
C) 12
Step-by-step explanation:
Step 1: List the numbers in order from least to greatest. Take a look at the data and cross out numbers as you place them. There are 16 numbers. The order of these numbers are:
5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21
Step 2: Cross out numbers from each side to the furthest left and right. By the time you do this, the remaining numbers should be 12 and 12.
Step 3: Find the median. Because there are two numbers left, you do this by adding the two remaining numbers and divinding them by 2. However, because they are the same number, you can safely say that the median is 12.
Please answer quickly!!!
Answer:
1. 64cm² , 2. 240yd² , 3.≈220.5cm² , 4.≈193.4m² , 5. 38.6ft² , 6. ≈78.1yd² , 7. ≈120.7
Step-by-step explanation:
1. A=12x4.5+2x5 , 2. A=24x8+0.5x12x8 3. A=0.5x16x15+0.5x8²π ,4. A=7x15+0.5(15/2)² 12 ,5. A=3.6(16/2)+0.5x7x2.8 ,6. A=8(16/2)+0.5x9π ,7. A=(8/4)x5²xcot(180/8)
Let me know the answer plz
Answer:
The correct answer option is H. 4374.
Step-by-step explanation:
We are given the following geometric sequence and we are to find its 8th term:
[tex]\frac{2}{9}, \frac{2}{3}, 2,...[/tex]
Here [tex]a_1=\frac{2}{9}[/tex] and common ratio [tex](r) = \frac{\frac{2}{3} }{\frac{2}{9} } =3[/tex].
The formula we will use to find the 10th term is:
nth term = [tex]a_1 \times r^{(n-1)}[/tex]
Substituting the values in the formula to get:
10th term = [tex]\frac{2}{9} \times 3^{(10-1)}[/tex]
10th term = 4374
Triangle ABC was rotated 90° clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4. Triangle A'B'C' is the resulting image. Compare the perimeters of ΔABC and ΔA'B'C'. Explain your reasoning.
Answer:
it is 170 degrees
Step-by-step explanation:
Answer: The image will be the same shape by all the sides will be 4 times larger than the original triangle but all 3 angles will be the same as the original.
Step-by-step explanation: