(a) This is the factored form of the equation.
(b) The x - intercepts are (√2, 0) and (-√2, 0).
(c) The value of f(-1) is -8.
What is x - intercept?
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.
(a) Consider, the given equation
f(x) = 8x^2 - 16
First to factor the equation.
Take 8 common from both the terms,
f(x) = 8(x^2 - 2)
This is the factored form of the equation.
(b) Now to find the x- intercept.
Let y = 8x^2 - 16
Set y = 0
So,
0 = 8x^2 - 16
8x^2 - 16 =0
x^2 - 2 = 0
x^2 = 2
x = ±√2
Hence, the x - intercepts are (√2, 0) and (-√2, 0).
(c) Now to find the value of f(-1)
plug x = -1 in the given equation.
f(-1) = 8(-1)^2 - 16
f(-1) = 8(1) - 16
f(-1) = 8 - 16
f(-1) = -8
Hence, the value of f(-1) is -8.
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What are the vertices of ΔA'B'C produced by T⟨−3, 6⟩ (ΔABC) = ΔA'B'C? The graph with X-coordinate marks -4, -2, 0, 2, 4 and Y-coordinate mark -4, -2, -1, 0, 2, 4. -The triangle ABC with coordinates A at (3, 0), B at (3, -2), C at (0, -3).
[tex]\end{aligned}$$[/tex]So the new coordinates will be ( 0,6 ) , ( 0,4 ) , ( -3 , 3 )
What are coordinates of triangle ?A special example of barycentric coordinates for a triangle is referred to as triangular coordinates, and it is also known as a ternary plot or areal coordinates. Triangular coordinates can also refer to any of at least three other related systems of coordinates in the Euclidean plane.
Given[tex]$\[/tex] triangle ABC[tex]$[/tex] has co-ordinates:
A=(3,0), [tex]\quad[/tex]B=(3,-2), C(0,-3)
Now transaction of [tex]$(-3,6)$[/tex] is applied on Co-ordinates of [tex]$\triangle A B C$[/tex]. Therefore, new Co-ordinates will become:
[tex]$$[/tex] A[tex]^{\prime}= ( 3-3 , 0 + 6 ) = (0,6) . \\[/tex]
B[tex]^{\prime}=(3-3,-2+6)=(0,4) . \\[/tex]
C[tex]^{\prime}=(0-3,-3+6)=(-3,3)[/tex]
[tex]\end{aligned}$$[/tex]So the new coordinates will be ( 0,6 ) , ( 0,4 ) , ( -3 , 3 )
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one method used to measure diversity in a given area is the simpson index. a. how is it calculated?
Method used to calculate the measure of diversity of species of a particular community is Simpson diversity index which is given by
d = ∑nₐ(nₐ - 1)/N(N - 1).
As given in the question,
Let us consider 'd' represents the diversity of the species in a particular community.
nₐ represents the number of organism belongs to a particular given species .
N represents the total number of organism present.
Then calculation of Simpson diversity index is given by :
d =∑nₐ(nₐ - 1)/N(N - 1)
The range of the diversity of Simpson diversity index is in between 0 to 1.
Therefore, the calculation Simpson diversity index is given by
d = ∑nₐ(nₐ - 1)/N(N - 1).
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What is 30% off $75?
Answer:
22.5
Step-by-step explanation:
Answer:
22.5
Step-by-step explanation:
= (0.3)(75) = 22.5
Hope this helps
12. CT has a point C at (-7,-9) and point T at (9,7).
What are the coordinates of the midpoint?
A) (-1,-1)
C) (-1, 1)
B) (1,-1)
D) (1, 1)
The midpoint of CT is located at (b) (1, -1)
How to determine the coordinates of the midpoint?From the question, we have the following parameters that can be used in our computation:
C = (-7, -9)
T = (9, 7)
The midpoint of the line CT can then be calculated as
Midpoint = 1/2 * (C + T)
So, we have the following representation
Midpoint = 1/2 * (-7 + 9, -9 + 7)
Evaluate
Midpoint = 1/2 * (2, -2)
So, we have
Midpoint = (1, -1)
Hence, the midpoint is (1, -1)
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What is the inequality shown? -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 23 4 5 6 7 8
Answer:
-4<x≤5
Step-by-step explanation:
first at negative 4 there is a white dot and it’s pointing right so x is greater then it
And at 5 it is a closed dot pointing left so x is less then and equal to 5
Hopes this helps
c) what is an expression for C in terms of b?
Answer:
[tex]c=5b[/tex]
Step-by-step explanation:
Since we're solving for c, it should be by itself (normally on the left). If you look at the table, c is just 5 times what it's corresponding b value is, so that's what you write as the equation.
please answer this inequality |3d-7|>28
Answer: d < −7 or d > 35/3
Step-by-step explanation:
Tyler’s cell phone has a $50 charge each month, but no initial fee. On the same coordinate plane, graph the cost of Tyler’s cell phone plan over a period of two years. Then describe how the two graphs are the same and how they are different
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3, −2, and 1, and passes through the point (2,8).
The third-degree polynomial function for the given circumstances will be 5y=2(x-1)(x+3)(x+2) with zeros of 3, 2, and 1 and passes through the point (2,8).
What is polynomial?Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Here,
y=a(x+3)(x+2)(x-1)
x=2 and y=8
8=a(2+3)(2+2)(2-1)
8=a*5*4
a=8/20
a=2/5
y=2/5(x+3)(x+2)(x-1)
5y=2(x+3)(x+2)(x-1)
The polynomial function for given conditions that is third-degree, with zeros of −3, −2, and 1, and passes through the point (2,8) will be 5y=2(x+3)(x+2)(x-1).
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Please help! Worth more points will mark as brainiest
Answer:
252 m^2
Step-by-step explanation:
The equation for surface area in a rectangular prism is SA = 2 (lh +wh + lw ).
So when we plug in the numbers inti the equation we do SA = 2(12×3 + 6×3 + 12×6)
FOLLOW P.E.M.D.A.S (parentheses, exponents, multiplication, division, addition, subtraction)
we get SA = 2(36 + 18 + 72)
then we multiply 2, by each of the numbers.
SA = (72 + 36 + 144)
Add them together and you get
SA = 252
Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water, in inches, t
minutes after Tyler began to fill the bathtub.
These statements describe how the water level in the tub was changing over time. Use the statements to sketch an
approximate graph of function.
B (0) = 0
. B (1) < B (7)
B (9) = 11
• B (10) = B (23)
.
.
.
.
• B (20) > B (40)
You may want to use the following graph as a starting point for your sketch. Then fill it in with the information listed above.
The statements are -
B(0) = 0 depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0
B(1) represents the function one minutes after filling began. The function gives depth of water in inches 7 minutes after filling began.
B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.
Solved using the concept of function.
What is function?A statement, rule, or law in mathematics specifies the connection between an independent variable and a dependent variable (the dependent variable).
A graph is considered to be a function if any vertical line formed may cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through it twice or more.
B(0)=0The statement B(0) = 0 means the depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0
B(1) < B(7)B(1) represents the function one minutes after filling began. The function gives depth of water in inches 7 minutes after filling began
B(9)=11B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.
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Kara downloaded 384 selfies from her cell phone to her laptop. These selfies took up 768 megabytes of space on her laptop. Each selfie took up the same amount of space. How many megabytes do 40 selfies take up?
Answer:
80 megabytes
Step-by-step explanation:
768/384= 2 megabytes per photo
40 x 2 = 80 megabytes
The graphs below have the same shape. What is the equation of the red graph?
The equation of the red graph is x² + 2
What is meant by Equation ?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Since the function in the graph is headed upward , we know the portion of x² is positive . And since the highest point of the red line on the y-axis is 2, we can conclude the function represented by the red line is
x² + 2
Therefore the equation of red graph is x² + 2
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Write an expression that represents the height of a tree that begins at 8.4 feet and increases by 3.8 feet per year. Let's describe the number of years.
Answer: 8.4 + 3.8y
Step-by-step explanation: The expression is 8.4 + 3.8y ( y represents the amount of years multiplies by 3.8 or the amount grown per year )
Unless there is a total of height or the amount of years there is no way to complete this problem because there is an infinite number of possibilities.
Dean Willis earns $315.75 per weck. The Social Security tax rate is 6.2% and Medicare tax is 1.45% of gross pay. How much is the deduction from his pay check for Social Security and Medicare?
The total deduction from Dean's paycheck for Social Security and Medicare is $24.11.
What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or a ratio, and is denoted by the symbol "%".
To find the deduction from Dean's paycheck for Social Security and Medicare, we need to calculate the total amount of tax that he owes based on his gross pay.
First, we can calculate the Social Security tax by multiplying Dean's gross pay by the tax rate:
Social Security tax = $315.75 x 6.2% = $19.54
Next, we can calculate the Medicare tax by multiplying Dean's gross pay by the tax rate:
Medicare tax = $315.75 x 1.45% = $4.57
To find the total deduction from Dean's paycheck, we can add the two amounts:
Total deduction = $19.54 + $4.57 = $24.11
Hence, the total deduction from Dean's paycheck for Social Security and Medicare is $24.11.
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Rebecca buys some scarves that cost $5 each and 2 purses that cost $12 each. Rebecca can spend AT MOST $39. Write an inequality that can be used to find the number of scarves she can buy.
Answer:
$39-($12x2)=$15
$15 ÷$5=3scarves
Step-by-step explanation:
A grocery store sign indicates that plums are 6 for $1.50, and a sign by the apples indicates that they are 5 for $3.00. Find the total cost of buying 2 plums and 2 apples.
*Determine how much per plum and apple before finding the total cost.
A grocery store sign indicates that plums are 6 for $1.50, and a sign by the apples indicates that they are 5 for $3.00. Find the total cost of buying 2 plums and 2 apples.
*Determine how much per plum and apple before finding the total cost.
An apple would cost $0.6 while a plum would cost $0.25.
The total cost of buying 2 plums and 2 apples will be $1.7
What is Cost?Cost is the value of money that has been used or exchanged up to produce something or deliver a service. Money is an input that is gone in order to acquire something.
If 6 plums sell for $1.50, then;
1 plum will be (1.50/6) = $0.25
Also, if 5 apples cost $3.00, then;
1 apple will be (3/5) = $0.6
Therefore 2 apples will cost: 2 x $0.6 = $1.2
and 2 plums will cost: 2 x $0.25 = $0.5
Total cost for 2 apples and 2 plums will be = $1.2 + $0.5
The total cost = $1.7
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Simplify the expression. 4x^10 y^-3 over 12x-2y
The expression 4x^10 y^-3 over 12x-2y is x^8 y^-2 / 3
How to solve the expression:Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
1. Eliminate terms from the denominator and numerator.
2. Combine terms that have been multiplied into a single fraction.
3. Add exponents together.
Here, (Given)
4x^10 y^-3 /12x-2y
solving the expression we get
4x^10 / 12x = x^8 / 3
y^-3 / 2y = y^-2
=> x^8 y^-2 / 3
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).
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Find Volume of a cone
Answer:
Your answer is 65.97 meters.
Hence, the volume of the cone is [tex]64.998m[/tex] meters.
What is the volume of cone?
The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex.
Here given that,
The radius of cone is [tex]3m[/tex] and a height of a cone is [tex]7m[/tex].
As we kow the volume of cone is [tex]\pi r^2\frac{h}{3}[/tex].
Now substitute the values in the general formula of cone then,
[tex]V=3.14(3)^2\frac{7}{3}\\\\V=3.14(9)(2.3)\\\\V=3.14(20.7)\\\\V=64.998m[/tex]
Hence, the volume of the cone is [tex]64.998m[/tex] meters.
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if you test for the for the mean of the differences in a paired t-test, there are how many degrees of freedom?
There is zero or no degree of freedom in the mean of the differences in a paired t-test.
For the paired t-test, we need two variables. One variable defines the pairs for the observations. The second variable is a measurement. Sometimes, we already have the paired differences for the measurement variable. Other times, we have separate variables for “before” and “after” measurements for each pair and need to calculate the differences.
We also have an idea, or hypothesis, that the differences between pairs is zero. It is also known as the dependent samples t-test, the paired-difference t-test, the matched pairs t-test and the repeated-samples t-test.
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It takes Andre 4 minutes to swim 5 laps. How many minutes per lap is that?
Answer: 0.8 minutes
Step-by-step explanation:
4 divided by 5 =0.8
Answer: 0.8 minutes per lap
Step-by-step explanation:
divide the number of minutes by the number of laps to get a minutes per lap
4/5=0.8
is 14 a linear expression
Answer: No
Step-by-step explanation:
Linear expression is y=mx + b
14 is just a number, it doesn't have a slope or y-intercept!
Stevensville has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following functions would evaluate this situation?
p(s)=114000.0.985³
p(s) =114000
p(s)=114000x+0.985
None of the choices are correct.
Answer:
none of the choices
Step-by-step explanation:
normally, the form for the answer would be p(s)=Ab^x, but I don't see that here in any of the answer choices. The answer would be p(s)=114,000(0.985)^x.
hope this helps, but downvote this answer if it is wrong :(
5x -4 =19 please help me it’s for my do NOW
........... i need help past due
Answer:
[tex]\frac{16}{35}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{2}{5} }{\frac{7}{8} }[/tex]
There is a couple of ways that you can do this. I am going to divide the top and bottom fractions by [tex]\frac{8}{7}[/tex]
[tex]\frac{\frac{2}{5} }{\frac{7}{8} }[/tex] x [tex]\frac{\frac{8}{7} }{\frac{8}{7} }[/tex] = [tex]\frac{\frac{16}{35} }{\frac{56}{56} }[/tex] = [tex]\frac{\frac{16}{35} }{1}[/tex] = [tex]\frac{16}{35}[/tex]
How would the graph of the linear equation y = 2x change if the y-intercept were changed to 3?
O The line would shift down three units.
O The line would shift up three units.
O The line would become more steep.
The line would not change.
The required answer choice for the linear equation is option 2 (the line would shift up three units).
What is a linear equation?
An equation is said to be linear if the maximum power of the variable is 1. Another name for it is a one-degree equation.
Given, y = 2x
For y-intercept, x = 0
And when the y-intercept is changed to 3. then, y = 3 at x=0
Based on this condition, the equation will be y = 2x + 3
So, the line would shift up three units.
Hence, the required answer choice for the linear equation is option 2.
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Answer:
The line would shift up three units.
helpp, does anyone know the answer?!?
Answer:
Wdym
Step-by-step explanation:
Find the 9th term
1/8 , 1/2 , 2…
solve the system by using substitution or elimination[tex]-3x+y=6\\6x-2y=25[/tex]
We can not solve the system of equation because the equations represent two parallel lines (they have no points in common).
Given that,
The system of equations are -3x+y=6 and 6x-2y=25
We must resolve the equation system.
We know that,
Take the system of equation
-3x+y=6 ------->equation(1)
6x-2y=25 ------>equation(2)
We multiply equation(1) by -2 and subtracting them
-2(-3x+y=6)
6x-2y=-12
6x-2y=25
--------------- (subtract)
-12=-25
So, we can not solve the system of equation.
Therefore, We can not solve the system of equation because the equations represent two parallel lines (they have no points in common).
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Given two functions:
f(x) = -8x^3 + 9x^2 - 7x + 8
g(x) = −4x^3+ 3x^2 - 4x - 6
Find (f+g)(x)
Sum of two function f(x) and g(x) is -12x³+12x²-11x+2
What is function?A mathematical expression that indicates a relationship between independent variable and dependent variable. If x is an independent variable function is denoted by f(x) or g(x).
How do we determine the sum of two function?we are given two functions f(x)= -8x³+9x²-7x+8
g(x)= -4x³+3x²-4x-6
now we need to add these two. f(x)+g(x)= -12x³+12x²-11x+2
hence, we obtain another function.
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