Answer:
y = 2(x +3)² -1
Step-by-step explanation:
You want the vertex form of the equation y = 2x² +12x +17.
Vertex formThe vertex form of the equation is ...
y = a(x -h)² +k² . . . . . . where (h, k) is the vertex and 'a' is a scale factor
ConversionThe equation can be converted to vertex form by the following steps.
factor the leading coefficient from the variable terms:The equation you want is ...
y = 2(x +3)² -1
Answer:
Rewrite the equation in vertex form.
[tex]{y = 2(x+3)^{2}}-1[/tex]
Use the vertex from, [tex]{y = a(x-h)^{2} + k[/tex], to determine the values of [tex]{a, h, }[/tex] and [tex]k[/tex]
[tex]a = 2\\h = -3\\k = -1[/tex]
Find the vertex [tex](h, k).[/tex]
[tex](-3, -1)[/tex]
Mary weighed 7 1/2pounds when she was born. What number makes the statement true? 7 1/2 = ?/2
For a data set of weights (pounds) and highway fuel consumption amounts (mpg) of ten types of automobile, the linear correlation coefficient is found and the P-value is 0.013. Write a statement that interprets the P-value and includes a conclusion about linear correlation
The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.
Given that,
The complete statement is,
The p-value is given as:
[tex]p=0.013[/tex]
Express as percentage
[tex]p=1.3[/tex] %
This means that the probability that the linear correlation coefficient is at least as extreme is 1.3%.
From the z-table, we have:
[tex]z = 1.81[/tex], when the p-value is 0.013
This value of z-score is low, compared to the percentage of the scores have a z-score of between -1 and 1.
So, the p-value implies that it is likely that there is a linear correlation between the variables.
Hence, the texts that complete the three blanks are: "1.3%", "low" and "is"
Therefore,
The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.
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A stationary shop orders a batch of pens from a factory.
The factory could make the batch of pens in 20 days using 12 machines.
Due to a fault, only 3 machines were used for the first 8 days.
All 12 machines were used from day 9 onwards.
Work out the total number of days taken to make the batch of pens
Answer:
22
Step-by-step explanation:
(8 + 20) - ((8 * 9) ÷ 12)
Using PEMDAS, let us find the product to get;
(8 + 20) - (72/12)
Next operation is to divide what is in the bracket to get:
(8 + 20) - 6
Next operation is addition of the bracket content to get; 28 - 6
Next operation is to carry out subtraction to get: 22
Thus, the total number of days taken to make the batch of pens is 22.
Cooperative-Learning Activity Using the Quadratic Formula to Plan a Patio
Professionals, such as architects, engineers, contractors, and project managers, work collaboratively
to successfully complete quality projects. In this activity, you will need to help your group recommend
to a homeowner one of two patio options. Below is the information you will use to help with this
project.
A homeowner wants to build a patio around a 35-foot by 20-foot rectangular swimming pool.
The homeowner has two options and a budget of $40,200 (which all needs to be used) for the
patio.
Option 1 Surround the pool with a concrete band of equal width on all sides. The concrete
costs $50 per square foot.
Option 2 Surround the pool with a tile band of equal width on all sides. The tile costs $80 for
each square foot tile.
The homeowner should go with option 1 for his budget of $40,200 to use complete budget.
What is Quadratic equation?Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").
ax² + bx + c = 0
where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.
Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.
Given a rectangular pool of 35-foot by 20-foot
area of pool = 35 x 20 = 700 sq. foot
and to built a patio around pool of equal width,
budget of patio of $40,200 all amount to be used,
Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.
the area covered by amount is 40200/50 = 804
let width of patio be x
new length = 35 + x and new breadth = 20 + x
area covered by patio = new area including width - area of pool
new area including width = area covered by patio + area of pool
new area including width = 804 + 700 = 1504
1504 = (35 + x)(20 + x )
1504 = x² + 35x + 20x + 700
x² + 55x - 804 = 0
solving the equation by quadratic formula
x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/ 2a
where a = 1, b = 55, and c = -804
x = (-55 ± [tex]\sqrt{(55)^{2} - 4*1*(-804) }[/tex])/2
x = (-55 ± √(3025 + 3216))/2
x = (-55 ± 79)/2
taking positive values
x = (-55 + 79)/2 = 12
new length = 35 + 12 = 47 foot
new breadth = 20 + 12 = 32 foot
area covered by patio = (47x32) - (35x20)
area covered by patio = 804 sq. foot
and cost will be 804 x 50 = $40,200
for option 2: Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.
area for patio = 40200/80 = 502.5
since the area is in fraction the cost will come in approximation.
Hence the homeowner should go with option 1 for complete use of budget.
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A volunteer for a political campaign makes phone calls to raise funds for the candidate. The number of calls that she has left to make can be estimated with the equation C = 80-7h, where C is the number of calls left to make that day and h is the number of hours she has worked that day. How many calls does she have to make per day?
The number of calls she makes per day is 12
What is a function?A function can be defined as an expression, law or rule that describes the relationship between two variables.
These expressions are termed;
The dependent variableThe independent variableFrom the information given, we have that the function is;
C = 80-7h
Where;
C is the number of calls to make per dayh is the number of work hoursI day = 24 hours
Now, substitute the value into the formula
C = 180 - 7(24)
expand the bracket
C = 180 - 168
Subtract the values
C = 12
Hence, the value is 12
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If f(x) = x³ + 14x² + 61x + 84, which of the following is not a factor of f(x)?
What is the fourth root of 625
The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:
Step 1: Start with the number 625.
Step 2: Take the fourth root of 625.
Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.
Step 3: Determine the number that, when raised to the power of 4, equals 625.
To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..
Step 4: Solve the equation [tex]x^4 = 625[/tex].
To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]
The fourth root of 625 is (625)^(1/4).
Step 5: Simplify the expression.
We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:
[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]
Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
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is the following a qualitative or quantitative variable?: the type of flowers you plant in your garden
Qualitative variables include all observable qualities or characteristics of a group or population that can not be measured numerically.
What is Qualitative?
The goal of qualitative research is to collect and examine non-numerical data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality.
Quantitative Variable
Quantitative variables, as the name implies, are those that can be expressed by a numerical value.
1. Quantitative (Discrete)
2. Quantitative (Continuous)
3. Quantitative (Discrete)
4. Qualitative (nominal)
5. Qualitative (nominal)
6. Qualitative (nominal)
7. Qualitative (nominal)
8. 9. Quantitative (Continuous)
10. Qualitative (nominal)
11. Quantitative (Continuous)
12. Qualitative (ordinal)
13. Qualitative (nominal)
14. Quantitative (Discrete)
15. Qualitative (nominal)
Complete question: Which is the following a qualitative or quantitative variable?
1)ordinal
2)Continuous
3)nominal
4) All of these
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determine the present value p you must invest to have the future value a at simple interest rate r after time t.
The present p value which have to be invest in future is $7619.05 at simple interest rate r.
Simple Interest:
Simple interest (S.I) is a method of calculating the amount of interest on a specific amount of money.
The simple interest formula helps determine the amount of interest given a principal, interest rate, and term.
The formula for simple interest is:
SI = PTR/100
where SI = simple interest
P = principal
R = interest rate (percentage)
T = term (years)
For calculating total amount
Amount (A) = principal Book (P) + Interest (I)
where
Amount (A) is the total amount repaid at the end of the borrowed period.
The simple interest total amount formula can also be written as:
A = P(1 + RT)
where
A = Total amount after specified period
P = Principal or original loan amount
R = Interest rate (annual)
T = Time (annual )
According to the Question:
Simple interest: I = PTR ---------------------------- (1)
Future amount : A = p + I = p + PTR ------------------ (2)
Given that:
r = 10% = 0.1
t = 6 months = 0.5 year
A = future amount = 8000
Now,
8000 = p + p (. 1)(0.5)
⇒ 8000 = 1.05 p
⇒ p = 8000/1.05
⇒ p = $ 7,619.05
Now,
Putting the value of p in equation (2)
I = 7619.05 (0.1) (0.5 ) = 380.95
7619.05 + 380.90 = $8,000
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What is 4 + 4? ....................................
The value of 4 plus 4 will be 8.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case:
4 + 4
= 8
The value is 8.
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1) En la figura que se muestra, si las rectas que están cortadas por la transversal son paralelas, entonces podemos concluir que las medidas de los ángulos 1 y 4 son iguales por el A) Teorema de los ángulos consecutivos internos B) Teorema de los ángulos alternos internos C) Teorema de los ángulos alternos externos D) Teorema de los ángulos correspondientes
En la figura que se muestra, La respuesta correcta es la opción B: Teorema de los ángulos alternos internos.
Qué es líneas?Generalmente, Cuando dos rectas son paralelas y son cortadas por una transversal, los ángulos alternos internos (es decir, los ángulos que están en posiciones opuestas en relación a la transversal y están en el mismo lado de la transversal) son congruentes. En este caso, los ángulos 1 y 4 son ángulos alternos internos y, por lo tanto, tienen la misma medida.
El teorema de los ángulos consecutivos internos se refiere a ángulos que están en posiciones opuestas en relación a la transversal y están en lados opuestos de la transversal.
El teorema de los ángulos alternos externos se refiere a ángulos que están en posiciones opuestas en relación a la transversal y están en el mismo lado de la transversal, pero están en el exterior de los dos pares de paralelas. El teorema de los ángulos correspondientes se refiere a ángulos que están en la misma posición en relación a las dos pares de paralelas.
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Using the graph below, find f(-2)
Answer:
f(-2) =3
Step-by-step explanation:
f(-2) = value of the function when x = -2
Using the graph find the value of the function when x = -2
The value is 3
f(-2) =3
A stamp collection consists of 3c 12c and 15c stamps. The number of 3c stamps is five times the number of 12c stamps. The number of 15c stamps is four less than the number of 12c stamps. The total value of the stamps in the collection is $3.18. What is the number of 15c stamps in the collection?
What is the variable part of the term -6bx?
The variable part is x and b.
What is variable?A mathematical object is represented by a symbol known as a variable. A variable can be a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations using variables solve a variety of problems in a single operation. By substituting the numerical values of the equation's coefficients for the variables that represent them in the quadratic formula, the quadratic formula, for instance, can be used to solve any quadratic equation.
Given a equation -6bx
here -6 is constant because it cannot be changed;
a number that has a proper worth in a given circumstance or generally or that is normal for some substance or instrument.
and x, b are variables,
A variable is an amount that might change inside the setting of a numerical issue or examination.
Hence for the equation x and b are variables.
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a=6.33 inches b=9.06 inches
c=9.5 inches h=5.8 inches
Area:_________
Perimeter:________
Type:____________
Answer:
28.42, 24.89
Step-by-step explanation:
To solve the area of a triangle, the equation we use look like this:
a = c × h × 1/2
Now add the numbers in:
C = 9.8
H = 5.8
The equation will look like this:
a = 9.8 × 5.8 × 1/2
Doing the math, 9.8 × 5.8 = 56.84
56.84 × 1/2 = 28.42
The area = 28.42
Now to solve for the perimeter, we add up all 3 sides.
a + b + c = p
6.33 + 9.06 + 9.5 = 24.89
The perimeter is equal to 24.89
The type is right triangle.
Factor completely and find all the zero(s)
Answer:
Factors are (x-1) (4x²-1)
Zero(s) are x = 1, x = 1/2, x = -1/2
Step-by-step explanation:
Given function is
4x³ - 4x² - x + 1
= 4x³ - x - 4x² + 1
= x(4x² - 1) - 1(4x² - 1)
= (x - 1) (4x² - 1) (Factors of the equation)
To find the zero(s),
Either, Or,
x - 1 = 0 4x² - 1 = 0
or, x = 1 or, x² = 1/4
or, x = √(1/4)
or, x = +- 1/2
What is the correct set up to finding the slope of a line that passes through the points (6, −3) and (−2, 7)
- 5/4 is the slope of line .
What is slope simple explanation?
Slope, usually referred to as rise over run, is a line's perceived steepness.
Slope is calculated by dividing the difference between two points' changes in y values by changes in x values. For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
Slope = y₂ - y₁/x₂ - x₁
the points (6, −3) and (−2, 7)
= 7 - (-3)/-2 - 6
= 7 + 3/-8
= - 10/8
= - 5/4
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I’m a computer graphics design program, Mario created a segment with endpoints at ( 1, 5) and ( 7, 3). He then reflected the segment about a vertical line through the segment’s own midpoint. WHAT ARE THE COORDINATES OF THE ENDPOINTS OF THE NEW SEGMENTS?
A. (5, 1) and (3, 7)
B (7, 5) and (1, 3)
C. (7, 3) and (1, 5)
D. (5, 1) and (7, 3)
Answer:
B (7, 5) and (1, 3)
Step-by-step explanation:
the other answer is right about finding the midpoint :
((x1 + x2)/2, (y1 + y2)/2) = ((1+7)/2, (5+3)/2) =
= (8/2, 8/2) = (4, 4)
now, there is a vertical line through this point, and the original line segment is reflected across this vertical line.
reflections across vertical lines keep the y-values unchanged.
and the x distance of the original point to the midpoint is the same as the x distance of the reflected point to the midpoint.
after all, a reflection means a mirroring.
so, the mirror points are
(..., 5) and (..., 3)
about the x coordinates of distances:
1 to 4 = 3
4 to mirrored point = 3, 4 + 3 = 7.
7 to 4 = 3
4 to mirrored point = 3, 4 - 3 = 1.
so, the points are
(7, 5) and (1, 3)
Researchers have collected data on the hours of studying in a week and the exam grade of a student. You are given the data below. Hours of Studying 1 3 3 3 5 Exam Grade 55 75 80 85 100 (1) Develop the least squares regression equation. (6 points) (2) Estimate the exam grade of a student with 2 hours of studying. (3 points) (3) Compute the coefficient of determination. (6 points) (4) Perform a t test to test whether the exam grade is significantly related to the number of hours of studying with a = 0.01. What is your conclusion? (5 points) (5) Perform an Ftest to test whether the exam grade is significantly related to the
since to> t∝/ ₂₁n-2 we reject H₀ and conclude that the exam grade is significant related to the no of hours of studying
X = 1 3 3 3 5
Y= 55 75 80 85 100
What is hypothesis ?
A hypothesis is an unproven claim that is backed up by all the information that is now available and a lot of weaker results in mathematics.
n=5
∑x=15
∑x²=53
∑y=395
∑x²=32275
∑xy=1275
Sxx= ∑x²-1/n (∑x)² =8
Syy= ∑y²-1/n (∑y)² =1070
Sxy= ∑xy²-1/n (∑x)(∑y) =90
= Sxy/sxx =90/8 =11.25
x= 395/5 =11.25 (15/5)
=45.25
y=45.25 +11.25 x
if x=2, y=45.25 +11.25 (2) = 67.75
3. coefficient of determination
R² = SSR/SST = β₁ SXY/SYY
R₂ = 11.25 X 90/1070
=0.946
4. M = SYY -β₁ SXY/n-2
=1070-11.25(90)
=19.167
Hypothesis = H₀ :β₁ =0
H₀ :β₁ [tex]\neq[/tex]0
Test statistic = t = β₁/
t₀ =11.25/
t₀=7.27
critical value= t∝/₂₁n-2
= t0.005
=5.841
since to> t∝/ ₂₁n-2 we reject H₀ ( Hypothesis) and conclude that the exam grade is significant related to the no of hours of studying
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The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?
The length of a diagonal of the square in simplest radical form is; 2√7
What is the length of the diagonal of the square?We are given that;
Perimeter of square = 56
Now, the formula for perimeter of a square is;
P = 4s
where s is side length of square. Thus;
56 = 4s
s = 56/4
s = 14
Now, the diagonal of a square is given by the formula;
Diagonal = √(2s²)
Thus;
Diagonal = √(2 * 14²)
Diagonal = √(2 * 2 * 7)
Diagonal = 2√7
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The following coordinates are each a result of a single transformation. What type of transformation occurred for each image?
D (3,7)---> D' (-7,3) Select One
Answer:
This is a 90° counterclockwise rotation
Step-by-step explanation:
When you rotate a point 90 °counterclockwise the x x and y coordinate values interchange and the new x coordinate has a negative sign while the y-coordinate retains the original sign
Write the complex equation 8 + 3; in trigonometric form.
The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.
What is trigonometric form ?
Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
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Answer to this required:
Answer:
B
Step-by-step explanation:
the hypotenuse is z
For the Pythagorean theorem:
x² + y² = z²
What is answer in simplest form for 7×2/5=
Answer:
7/10- 2/5=3/10=0.3
Johanntakes a random sample of 101010 of his coworkers and asks them each howmany hours they worked in the past week. Assume that their hours workedare independent, and let HHH represent the average number of hours worked. Is HHH a binomial variable
The average number of hours worked is not a binomial variable as there is no success or failure in the scenario.
What is binomial variable?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.
A variable with two possible forms is said to have a binomial distribution. It could result in success or failure, heads or tail, and yes or no. If a coin is tossed, for instance, it could land on its head or its tail. It is a binomial variable as a result.
Here, there may be more than two values for the typical hours worked. It is not a binomial variable as a result.
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Segment KL has endpoints located at (0, 0) and (-4, 6) when graphed on the
coordinate plane. After a dilation about the origin, which scale factor, k, produces an
image with endpoints located at (0, 0) and (-12, 18) ?
A.k = 1/3
B.k = 3/2
C.k 3
D.k=8
Answer:
Step-by-step explanation:
1/3
When you start from a given set of rules and conditions and determine what must be true, you are using reasoning.
A. conjunctive
B. inductive
C. deductive
D. conductive
In deductive reasoning, you start from a given set of rules and conditions to determine must be true
In the process, we eliminated the one that do not met the rules and conditions. Which ever option left after the deduction, that must be the truth
hope this helps
Answer:
C. Deductive
Step-by-step explanation:
Hope this helps :)
Max found a car he wants to buy that costs $16,000. He can
afford to pay $250 a month for the car. His bank offers him a car
loan of 7.3%. How will the length of his loan be for this payment
amount?
Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.
First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.
Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.
Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.
Step-by-step explanation:
Determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 11
Note that Option A is pairwise and is relatively prime.
Option B is not relatively primeOption C is also a relatively primeOption D is also relatively prime.What does it mean for a list of integers to be pairwise relatively prime?If every pair of elements in a list of integers is relatively prime, the list is pairwise relatively prime. For example, the numbers 121, 122, and 123 are relatively prime pairwise (even though they are each composite).
You can tell if a set of numbers are relatively prime if they do not share a common factor other than ±
Looking at set a:
11, 15, 19
Writing their prime factorization
11 = 11
15 = 3 x 5
19 = 19, hence since any pair of these numbers does not have any common factor, hence they are relatively prime.
Looking at set b:
14, 15, 21
Writing their prime factorization, we have:
14 = 7 x 2
15 = 3 x5
21 = 3 x 7
15, and 21 share a common factor of 3 while
14 and 21 share a common factor of 7, therefore, they are NOT relatively prime.
Looking at set c)
12, 17, 31, 37
Writing their prime factorization,
12 = 3 x 2²
17 = 17
31 = 31
37 = 37
In this case, no pair of these numbers have any common factor. Hence they are relatively prime.
Looking at set d)
7,8,9, 11, spelling out their prime factorization
7=7
8=2³
9=3²
11=11
Thus, any pair of these numbers do not have a common factor, hence they are relatively prime.
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Help me please ASAP (ﾒ﹏ﾒ)
Answer:
A ' ( -21, 14 )
B ' ( 28, 14 )
C ' ( -7, -7 )
Step-by-step explanation:
The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.
For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.
The dilation rule can be written as (x,y)—-> (7x,7y)
As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.
Example: side AB = 7 units, side A'B' = 49 units
Hopes this helps!!
