Answer: B. Reciprocal
Step-by-step explanation:
This is a fact.
The parent function represented by f(x) = -1/x is the reciprocal function.
Therefore, the correct answer is option B.
Reciprocal functions, also known as rational functions, are defined by an algebraic expression where the dependent variable is in the denominator. In this case, the dependent variable is x, and it appears in the denominator as 1/x.
The negative sign in front of the fraction simply indicates that the function is reflected over the x-axis.
The general form of a reciprocal function is f(x) = a/x, where "a" is a constant. In the given function f(x) = -1/x, a is equal to -1.
In the case of f(x) = -1/x, the graph of the function is a hyperbola that opens downwards in the first and third quadrants. It approaches the x-axis as x moves towards positive or negative infinity, and it moves away from the x-axis as x approaches 0.
Therefore, the correct answer is option B, the reciprocal function.
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Write an equation that represents the line
Answer:
y=2/3x±3
Step-by-step explanation:
use the formula y=MX+b m being alive b being the y intercept
Hello,
f(x) = ax + b
We know f(0) = 3 = b
a = ∆y/∆x = 3/2
equation that represents the line → y = 3/2x + 3
Which shows the equation in point-slope form of the line passing through the given point with the given slope?
(0, 5), m=13
y−5=−13x
y=13x−5
y−5=13x
y=x+13
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find the point-slope equation of the line, with the info given
[tex]\Large\maltese\underline{\textsf{This problem has been solved}}[/tex]
Formula used, [tex]\bf y-y1=m(x-x1)[/tex]
[tex]\bf y-5=13(x-0)}[/tex] | result
[tex]\rule{300}{1.7}[/tex]
[tex]\boxed{\bf aesthetic\not101}}[/tex]
If
f(x) = 2x² - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [?]x² + [?]x + [?]
Answer:
f(g(x)) = 50x² + 140x + 93
Step-by-step explanation:
f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.
So,
f(g(x)) = 2 (5x+7)² -5
= 2 ( 25x²+ 70x + 49) - 5
= 50x² + 140x + 93
:)
translate the sentence into an equation rhoda's score decreased by 10 is 51 use r to represent rhoda's score
Answer: r - 10 = 51
Step-by-step explanation:
How can you tell if 3 given angles form a triangle?
Answer:
You can tell if the sum of the degrees of all the angles adds up to 180.
Suppose 20 cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 20 cars is
There are 6,840 different top 3 finishes.
In how many ways can the top 3 cars finish the race?We need to count the number of options for each position.
For the first position there are 20 possible options (20 cars).For the second position, there are 19 options (because one car is already on the first position).For the third position, there are 18 options.The number of different top 3 finishes is given by the product between the numbers of options, so we have:
20*19*18 = 6,840
There are 6,840 different top 3 finishes.
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Select the correct answer.
Consider the graph of function f below.
Y
-8 -4
8+
O
A
O
4
-4-
-8
The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?
4 8
O g(x)=f(x) + 4
g(x) = f(x-4)
g(x) = f(x) - 2
Og(x)=f(x + 2)
Answer:
742
Step-by-step explanation:
4x203
Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6
What is function ?A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input.
Here, we have,
Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).
Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).
The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).
Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).
=> f(x) = (x-h)² + k
The outcome of translating a unit to the right with b unit up is
=>f'(x) = (x-h-a)² + k + b
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To number the pages of a book, 2022 digits are used. How many pages are in the book?
Answer:
710
Step-by-step explanation:
Numeration of pages goes from 1.
9 pages with 1-digit numbers, from 1 to 9.
90 pages with 2-digit numbers, from 10 to 99.
So, 2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.
The rest of numbers are 3-digit.
[tex]\frac{(2022-189)}{3}[/tex] = 611 pages with 3-digit numbers.
Total pages = 9 + 90 + 611 = 710.
Simplify: √36x² if x is less than or equal to 0
Answer:
[tex]-6x[/tex]
Step-by-step explanation:
[tex]\sqrt{36x^2} = 6\times\sqrt{x^2}\\\\=6\times-x\\\\=-6x[/tex]
A beekeeper’s hives are making honey at a constant rate. The profit from honey can be represented by the equation
P(t) = -16t2 + 2050t + 150, where t is the time in days and P(t) is the profit the beekeeper receives. After how many days should she harvest her honey to maximize profit?
Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.The profit function is given as follows:
P(t) = -16t² + 2050t + 150.
The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:
[tex]t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64[/tex]
Hence she should harvest her honey after 64 days to maximize profit.
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Find the inverse of f.
f(x)=x/x+6
Answer:
xy+6xStep-by-step explanation:
given:f(x)=x/x+6
let, f(x)=y
y=x/x+6
interchanging the roles of x and y
or, x=y/y+6
or, xy+6x=y
therefore,inverse of f is xy+6x
How many positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1?
Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:
[tex]n_1 = 10, n_2 = n_3 = 1[/tex]
Hence, the number of integers is given by:
N = 10 x 1 x 1 = 10.
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Which property is does
3 + (( − 3) + 4) = (3 + ( − 3)) + 4 represent?
commutative
associative
distributive
identity
inverse
i dont know help help pls
The solution to the expression [tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x[/tex] is 27.03
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The expression is given as:
[tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x\\\\When \ x=1\frac{1}{10}=\frac{11}{10} \\\\=3(5-\frac{1}{6} *\frac{11}{10} )+\frac{1}{8}(32+6(\frac{11}{10} ))+7.3(\frac{11}{10} ) -5*0.05(\frac{11}{10} )\\\\=27.03[/tex]
The solution to the expression [tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x[/tex] is 27.03
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The numeric value of the expression for [tex]x = 1\frac{1}{10} = \frac{11}{10} = 1.1[/tex] is: 27.03.
How to find the numeric value of an expression?To find the numeric value of an expression, we replace all instances of x by the desired value.
In this problem, the expression is:
[tex]3\left(5 - \frac{x}{6}\right) + \frac{1}{8}(32 + 6x) + 7.3x - 5(0.05x)[/tex]
The value of x is:
[tex]1\frac{1}{10} = \frac{11}{10} = 1.1[/tex]
Hence the numeric value of the expression is:
[tex]3\left(5 - \frac{1.1}{6}\right) + \frac{1}{8}(32 + 6(1.1)) + 7.3(1.1) - 5(0.05(1.1)) = 27.03[/tex]
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Which equations have the same value of x as 5/6x + 2/4 = -9? Select three options.
6(5/6x + 2/3)= -9
6(5/6x + 2/3)= -9(6)
5x+4-54
5x4-9
5x=-13
5x=-58
Answer: Options 2, 3, 6
Step-by-step explanation:
Option 2: Correct because both sides are multiplied by 6.
Option 3: Correct because the distributive property is used on the left.
Option 6: Correct because 4 is subtracted from both sides.
need help with this question
The Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special of type of ellipse).
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the graph:
a) The domain: all values of x
The range: all values of y
Except: Values at asymptotes are excluded.
Domain = (-∞, -2) U (-2, 2) U (2, ∞)
Range = (-∞, -2) U [-1, ∞)
b)
x-intercept = (-1.5, 0), (1.5, 0)
y-intercept = (0, -1)
c) Horiznotal asymptotes: y = -2
d)Vetical asymptotes: x = -2, x = 2
e) Oblique asymptotes: There is no oblique asymptotes
Thus, the Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
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the eastern alberta DC transmission like is a project that began construction in 2012. It includes a 500km, 500kv power line from the brooks area to the edmonton area. (the V stands for volts, and SI unit for the electrical potential)
The number of the required towers based on the information given is 3334.
How to calculate the number?From the information given, it should be noted that the length of power line is 500km
The towers supporting the line are 1.5hm apart. It should be be noted that 1km = 10hm. Therefore, the require towers will be:
= (500 × 10)/1.5
= 3334
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Please solve this thank you!
Answer:
[tex]1024x^{40}[/tex]
Step-by-step explanation:
So the first step is to add like terms since you can simplify the numerator by adding the two values sine they have the same variable and degree.
Add like terms:
[tex][\frac{8x^9}{2x}]^5[/tex]
Divide by 2x (divide coefficient by 2, subtract coefficient degrees)
[tex][4x^8]^5[/tex]
Multiply exponents and raise 4 to the power of 5
[tex]1024x^{40}[/tex]
The reason you multiply exponents is because you can think about it like this:
(4 * x * x * x * x * x * x * x * x) (this has one 4 and 8 x's because x is raised to the power of 8. Now if you do that 5 times which is what the exponent is doing you're going to have 40 x's and 8 4's. So it's essentially
(4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x). If you group like terms you'll get (4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x). Which simplifies to 4^5 * x ^ (8 * 5) which further simplifies to the answer 1024x^40
Answer:
1024x^40
Step-by-step explanation:
Apply exponent rule: (a/b)^c = a^c / b^c = (5x^9 + 3x^9)^5 / (2x)^5
Simplify:
(5x^9 + 3x^9)^5: 32768x^45
= 32768x^45 / (2x)^5
Simplify:
(2x)^5: 32x^5
= 32768x^45 / 32x^5
Divide the numbers: 32768 / 32 = 1024
= 1024x^45 / x^5
Apply exponent rule: x^a / x^b = x^a - b
x^45 / x^5 = x^45 - 5
= 1024x^45 - 5
Subtract the numbers: 45 - 5 = 40
= 1024x^40
Solve the system of equations.
y+4z=0
4x+y-2z=2
-3x-3z=-9
Step-by-step explanation:
y+4z=0
4x+y-2z=2
-3x-3z=-9
Answer:
x = 7/3y = - 8/3z = 2/3Step-by-step explanation:
y + 4z = 0
4x + y - 2z = 2
____________ -
- 4x + 6z = - 2
- 4x + 6z = - 2 → times 3 → - 12x + 18z = - 6
- 3x - 3z = - 9 → times 4 → - 12x - 12z = - 36
- 12x + 18z = - 16
- 12x - 12z = - 36
______________ -
30z = 20
z = 20/30
z = 2/3
y + 4(2/3) = 0
y + 8/3 = 0
y = - 8/3
- 3x - 3z = - 9
- 3x - 3(2/3) = - 9
- 3x - 6/3 = - 9
- 3x - 2 = - 9
- 3x = - 9 + 2
- 3x = - 7
x = - 7/- 3
x = 7/3
modal mark of 1,2,3,4,5,6,7,8
Answer:
1
Step-by-step explanation:
the mode is the number that is repeated more often than any other numbers. the given numbers are 1,2,3,4,5,6,7,8 firstly, the numbers should be counted accordingly.
the number 1 is counted as 1.
the number 2 is counted as 1.
the number 3 is counted as 1.
the number 4 is counted as 1.
the number 5 is counted as 1.
the number 6 is counted as 1.
the number 7 is counted as 1.
the number 8 is counted as 1.
after counting the numbers, the maximum number counted (or) repeated most is 1 as 1 times.
the mode of the given values is 1.
Solve the system.
{3x+ 2y=8
{3x+3=y
Let's take this problem step-by-step:
Note:
'-- (1), -- (2), etc.' are equation markers used to show steps
First step, isolate all the variables to one side and constant to the other
[tex]3x + 2y = 8--(1)\\3x-y=-3--(2)[/tex]
Second step: (1) - (2)
[tex](1) - (2)\\3x + 2y-(3x-y)=8-(-3)\\2y + y=11\\3y = 11\\y = \frac{11}{3} --(3)[/tex]
Third step: Plug (3)'s value of y into (2)
[tex](3)_.into_.(2)\\3x -\frac{11}{3} = -3\\3x = \frac{11}{3}-3\\ 3x = \frac{11-9}{3} \\3x = \frac{2}{3} \\x=\frac{2}{9}[/tex]
Answer: x = 2/9, y = 11/3
Hope that helps!
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Answer:
3x+ 2y=8 ⇒ ( 1 )
3x+3=y ⇒ ( 2 )
First, let us take the equation (1).
We can replace y with ( 3x + 3 ).
Solving the below expression let us find the value of x.
[tex]3x + 2y = 8\\3x + 2 ( 3x + 3 ) = 8\\3x + 6x + 6 = 8\\9x + 6 = 8\\9x = 8 - 6\\9x = 2\\x = \frac{2}{9}[/tex]
And now let us take equation ( 2) to find the value of y.
For that let us replace x with 2/9.
Let us find it now.
[tex]3x+3=y\\\\3*\frac{2}{9} +3=y\\ \\\frac{6}{9} +3=y\\ \\\frac{6}{9} +\frac{3}{1} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{27}{9} =y\\\\\frac{33}{9} =y\\\\\frac{11}{3} = y[/tex]
What is the slope of the following linear equation y + 2x = 5 ?
Answer:
slope = -2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. Since the given equation is not in the exact slope-intercept form, we need to rearrange it to identify the slope.
y + 2x = 5 <----- Given equation
y = -2x + 5 <----- Subtract 2x from both sides
Now, we can see that in the "m" position, there is a value of -2. This makes the slope = -2.
Find the perimeter and the area of the regular polygon
The perimeter of the regular hexagon is 180 ft
(Simplify your answer. Round to the nearest tenth as needed.)
The area of the regular hexagon is
(Simplify your answer. Round to the nearest tenth as needed.)
30 ft
The perimeter of the hexagon is 180 ft.
The area of the hexagon is 2338.3 ft
How to find area and perimeter of a polygon?The perimeter of the polygon can be found as follows:
The polygon is a regular hexagon.
Therefore,
perimeter of the hexagon = 30 × 6 = 180 ft
Area of the hexagon = 3√3 / 2 × s²
where
s = side lengthTherefore,
Area of the hexagon = 3√3 / 2 × 30²
Area of the hexagon = 3√3 / 2 × 900
Area of the hexagon = 450 × 3√3
Area of the hexagon = 2338.26859022
Area of the hexagon = 2338.3 ft
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Determine the amount needed such that when it comes time for retirement, an individual can make semiannual
withdrawals in the amount of $15,265 for 35 years from an account paying 4.5% compounded semiannually. Round
your answer to the nearest cent.
$938,272.00
b. $941,790.00
$535,528.03
0
$547,577.41
Answer:
the correct answer is 0 54,577.41
Step-by-step explanation:
you needed to take the withdrawal amount divide it by 35 and divide that answer by the 4.5 percentage rate
Answer:
C. $535,528.03
Step-by-step explanation:
Trust me
A company received a shipment of 8 boxes of metal brackets.
. There are 20 metal brackets in each box.
The total weight of the shipment is 48 pounds.
What is the weight, in pounds, of each metal bracket?
Answer:
160 boxes = 384 pounds
Step-by-step explanation:
sgshshdhdjd
For the sequence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is quence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is
A function assigns the value of each element of one set to the other specific element of another set. The third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively
A function assigns the value of each element of one set to the other specific element of another set.
Given the nth term of the sequence is given by the formula,
[tex]a_n = a_{(n-1)}+a_{(n-2)}[/tex]
Also, the first term and the second term of the sequence are 2 and 3 respectively, therefore, the other terms of the sequence are,
[tex]a_3 = a_{(3-1)}+a_{(3-2)}\\\\a_3 = a_2 + a_1\\\\a_3 = 3 + 2\\\\a_3 = 5[/tex]
[tex]a_4 = a_{(4-1)}+a_{(4-2)}\\\\a_4 = a_3 + a_2\\\\a_4 = 5 + 3\\\\a_4 = 8[/tex]
[tex]a_5 = a_{(5-1)}+a_{(5-2)}\\\\a_5 = a_4 + a_3\\\\a_5 = 8 + 5\\\\a_5 = 13[/tex]
Hence, the third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively.
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A swimming pool is 3 meters deep, 50 meters long, and 25 meters wide. If it takes 0.25 pounds of chlorine for every 15 cubic meters of water to keep the pool clean and healthy, how many pounds of chlorine are needed?
a. 27.2 pounds
b. 35.7 pounds
c. 45.4 pounds
d. 62.5 pounds
The amount of pounds of chlorine needed is 62. 5 pounds. Option D
How to determine the amount
WE have the perimeter of a rectangle to be;
Volume = l × h × w
L = length = 50 meters
w = width = 25 meters
height = 3 meters
Substitute into the formula
Volume = [tex]50[/tex] × [tex]25[/tex] × [tex]3[/tex]
Volume = [tex]3750[/tex] cubic meters
If 0. 25 pounds of chlorine is in 15 cubic meters of water
x pounds would be 3750 cubic meters
Cross multiply
0. 25 × 3750 = 15x
937. 5 = 15x
x = [tex]\frac{937. 5}{15}[/tex]
x = 62. 5 pounds
Thus, the amount of pounds of chlorine needed is 62. 5 pounds. Option D
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riangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are
(–1, 0). What are the coordinates of B?
B(, )
The coordinates of B is (-2, 3).
What is Translation?In geometry, translation is the movement of a point or shape from one position to another.
Here, The translation from ΔABC to ΔA'B'C' is (x, y) → (x + a, y + b)
Now, given coordinate
A ≡ (5, 1) ⇒ A' ≡ (6, -2)
A' ≡ (1+5, 1 - 3)
On comparing this coordinate with translation coordinate
(x + a, y + b), we get
a = 1 and b = -3
Now translation coordinates is (x + 1, y - 3),
Now, Another coordinate;
B' ≡ (-1, 0) and the coordinate of B ≡ (x, y)
B' ≡ (-2+1, 3-3)
On comparing this coordinate with translation coordinate (x + 1, y - 3), we get
x = -2 and y = 3
Thus, the coordinates of B is (-2, 3).
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The product of a number and the sum of six and five is equal to the sum of the number and thirteen. What is the number?
The number is 13 / 10
How to solve words problem using equation?The product of a number and the sum of six and five is equal to the sum of the number and thirteen.
Therefore,
let the number = x
x(6 + 5) = x + 13
Hence,
x(6 + 5) = x + 13
11x = x + 13
11x - x = 13
10x = 13
x = 13 / 10
Therefore, the number is 13 / 10
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Which of the following expressions is equivalent to ab² + 6ab + 7a³-14a?
a. (b + 7)(b + 6)(a²-2)
b. b(b + 6)+7(a2-2)
c. a[b(b + 6)+7(a²-2)]
d. a[(b + 7)(b + 6)(a²-2)]
Answer:
c. a[b(b + 6)+7(a²-2)]
Step-by-step explanation:
look at the pic
The equivalent expression of the expression ab² + 6ab + 7a³ - 14a is
C. a [b (b + 6) + 7 (a² - 2)]
Option C is the correct answer.
We have,
To find the expression that is equivalent to ab² + 6ab + 7a³ - 14a, we can factor out common terms from the given expression.
The common terms in the expression are "a" and "(b + 7)".
Step 1:
Factor out "a" from the expression:
ab² + 6ab + 7a³ - 14a = a(b² + 6b + 7a² - 14)
Step 2:
Factor the quadratic expression inside the parenthesis:
b² + 6b can be factored as b(b + 6)
7a² - 14 can be factored as 7(a² - 2)
Step 3:
Putting it all together, the equivalent expression is:
a [b (b + 6) + 7 (a² - 2)]
Now let's check which option matches this expression:
a. (b + 7)(b + 6)(a² - 2) - Not equivalent
b. b(b + 6) + 7(a^2 - 2) - Not equivalent
c. a[b(b + 6) + 7(a² - 2)] - Equivalent
d. a[(b + 6)(b + 7a² - 14)] -Not equivalent
Thus,
The equivalent expression is
C. a [b (b + 6) + 7 (a² - 2)]
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