Answer:8 ,-8
Step-by-step explanation:the absolute value of a number is how far it is from 0 so 8 and -8 are both 8 spots from 0. Hope this helps!
Which of the following functions is graphed below?
Answer:
2nd choice B.
Step-by-step explanation:
You can use the options A-D to help you eliminate pretty quickly without actually graphing
So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer
Second choice Possible
Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual
Fourth choice: same reason as third choice
Answer is the 2nd
The sequence 3, 5, 7, 9, ... has the explicit rule f(n)= 2n +1.
What is the third term in the sequence?
Answer:7
Step-by-step explanation:since it has the rule f(n) =2n+1
Third term is when n=3
Therefore 2(3) +1=7
The x-intercept is
The equation of the graphed line is x + 2y = 5. What is the
x-intercept of the graph?
|-6-5-4-3-2-1,
1 2 3 4 5
What’s the x intercept
Answer:
[5, 0]
Step-by-step explanation:
x-intercept is where 0 = y. Just simply plug in 0 for y, then your x is given to you in your face.
8x+23/(x+3)(x+2) partial fraction decomposition
Answer:
1/(x+3)+7/(x+2)
Step-by-step explanation:
I'm assuming the full numerator is (8x+23)... and by making that assumption I'm assumed the fraction was (8x+23)/[(x+3)(x+2)].
(8x+23)/[(x+3)(x+2)]=A/(x+3)+B/(x+2)
8x+23=A(x+2)+B(x+3) I multiply both sides by (x+3)(x+2)
Set x to -2 that gives -16+23=B so this means B=7
Set x to -3 instead that gives -24+23=A(-1) so this means A=1
So (8x+23)/[(x+3)(x+2)]=1/(x+3)+7/(x+2)
a quadrilateral has 2 right angles. the measure of the third angle is 73, what is the measure of the forth angle?
Answer: 107 degrees.
Step-by-step explanation:
A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.
By definition the interior angles of a quadrilateral add up 360 degrees.
We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.
Let be "x" the measure of the fourth angle.
Then you can write this expression:
[tex]360\°=90\°+90\°+73\°+x[/tex]
And finally solve for "x":
[tex]360\°=253\°+x[/tex]
[tex]360\°-253\°=x[/tex]
[tex]x=107\°[/tex]
What is the value of y in this linear system?
The calculated value of y in this linear system is 18
How to determine the value of y in this linear system?
From the question, we have the following parameters that can be used in our computation:
x + y + z = 62
x - y = 12
2x + y + z = 92
Subtracting the equations 1 and 2, we have
2x - x = 92 - 62
x = 30
In equation (2), we have
x - y = 12
This gives
y = x - 12
Substitute the known values into the equation
y = 30 - 12
Evaluate
y = 18
Hence, the value of y is 18
Please help....Alinakincsem Ace
Answer:
The correct answer option is E. [83 + 2(79) + 4(88)] × 1/7.
Step-by-step explanation:
We are given the quiz average, test average and final average for Sabra's grades for a class.
Given that her test average counts twice as much as her quiz average and final exam counts twice as much as her test average for her overall average:
[tex](83+79+79+88+88+88+88)[/tex] ÷ [tex]7[/tex]
This can also be written as:
[83 + 2(79) + 4(88)] × 1/7
From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.
Answer:
The vertical distance from the ground to the bird's eyes is 47.67 m
Step-by-step explanation:
* Lets explain the situation of the problem
- There is a bird on the top of a tree
- The bird looks down on a field mouse at an angle of depression of 50°
- The field mouse is 40 meters from the base of the tree
* Consider that the vertical distance from the ground to the bird's eyes,
the distance from the field mouse to the base of the tree distance
from the bird eyes to the field mouse formed a right triangle
- The hypotenuse is the distance from the bird eyes to the field mouse
- The horizontal side is the distance from the field mouse to the base
of the tree
- The angle between the hypotenuse and the horizontal side is the
angle of depression which = 50°
- The opposite side to the angle of measure 50° is the vertical distance
from the ground to the bird's eyes
* Lets use trigonometry functions to find the vertical distance
∵ The length of the adjacent side to the angle of measure 50° is 40 m
∵ The length of the opposite side to the angle of measure 50° is h m
∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф
∵ Ф = 50°
∴ tan 50° = h/40 ⇒ by using cross multiplication
∴ 40 tan 50° = h
∴ h = 47.67 m
* The vertical distance from the ground to the bird's eyes is 47.67 m
14. What is the simplified form of (5x2 + 11x - 9) - (2x - 3x + 5)?
Answer:5x2+12x-14
Step-by-step explanation:
(5x2+11x-9)-(2x-3x+5)
5x2+11x-9-2x+3x-5
5x2+12x-14
[tex](5x^2 + 11x - 9) - (2x - 3x + 5)=5x^2+11x-9-2x+3x-5=5x^2+12x-14[/tex]
-------------------------------------------------
[tex](5x^2 + 11x - 9) - (2x^2 - 3x + 5)=5x^2+11x-9-2x^2+3x-5=3x^2+14x-14[/tex]
Which function has a range of {yly < 5}?
f(x) = (x - 4)^2 +5
f(x) = -(x-4)^2 + 5
f(x) = (x - 5)^2 + 4
f(x) = -(x – 5)^2 + 4
Answer:
f(x) = -(x-4)^2 + 5
Step-by-step explanation:
The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.
Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:
[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]
The function which has a range of {y | y < 5} is f(x) = -(x – 5)² + 4.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given a range of the function, {y | y < 5}.
We want to find the corresponding function.
The range of the function contains all the values less than 5.
For the first two functions, when we substitute x = 4,
The value of the function, f(x) = 5
So this is not possible.
For the third function also, when we substitute any integers other than 5, the value of function is greater than 5.
Hence the correct option is D.
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Write two word problems that can be solved using
the equation x + 15 = –18.
Word Problem #1:
You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.
x = original depth
15 = height you rise up
-18 = final depth
x+15 = final depth
x+15 = -18 is the equation we solve to find the value of x
=========================================================
Word Problem #2:
You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18
So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.
If f(x) = 5х + 40, what is f(x) when x=-5?
Answer:
15
Step-by-step explanation:
Substitute x = - 5 into f(x)
f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15
What is equivalent to log3(x+1)=2
Answer:
3^2=x+1 is the equivalent
Step-by-step explanation:
3^2=(x+1) is equivalent to log_3(x+1)=2
where x+1 is positive
If f(x) = 3х^2 and g(x) = 4х^3 + 1, what is the degree of (f•g)(x)?
[tex]\bf \begin{cases} f(x)=3x^2\\ g(x)=4x^3+1 \end{cases}\qquad (f\cdot g)(x)\implies f(x)\cdot g(x)\implies [3x^2]\cdot [4x^3+1] \\\\\\ 12x^2x^3+3x^2\implies 12x^{2+3}3x^2\implies \stackrel{\textit{5th degree}}{12x^{\stackrel{\downarrow }{5}}+3x^2}[/tex]
At a store, the probability that a customer buys socks is 0.15. The probability
that a customer buys socks given that the customer buys shoes is 0.20.
Which statement is true?
O
A. Buying socks and buying shoes are dependent events.
O
B. The probability that a customer buys socks and shoes is 0.05.
C. Every customer who buys shoes also buys socks.
D. Buying socks and buying shoes are independent events.
Answer:
A. Buying socks and buying shoes are dependent events.
Step-by-step explanation:
We are given that
The probability that a customer buys socks ,P(A)=0.15
The probability that a customer socks given that the customer buys shoes P(A\B)=0.20
The probability that a customer buys shoes,P(B)=1-0.15=0.85
By using formula P(E')=1-P(E)
Where P(E)= Probability of an event that is happened
P(E')=Probability of an event that is not happened
We have to find [tex]P(A\capB)[/tex] for two events
[tex]P(A)\cdot P(B)[/tex]
[tex]=0.85\times 0.15=0.1275[/tex]
We know that conditional probability of an event when given that the probability of an event B is given
[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]
[tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex]
[tex]P(A\cap B)=0.20\times 0.85=0.17[/tex]
[tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].
Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.
Therefore, option A is true.
Answer: A. Buying socks and buying shoes are dependent events.
Step-by-step explanation:
Where do I find the “solution” do a quadratic equation on a graph? How many possible real solutions are there when you solve a quadratic equation?
Answer:
Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)
Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c
there are 3 situations:
1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)
2. discriminant = 0 → 1 real solution(1 x-intercept/zero)
3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution
Hope it helped!
Step-by-step explanation:
Answer:
1) You find the solution by identifying the x-intercepts.
2) Possible real solutions:
- One real solution.
- Two distinct real solutions.
Step-by-step explanation:
1) The graph of a quadratic equation is a parabola.
By definition, the x-intercepts (Where [tex]y=0[/tex]) are the solutions of the quadratic equation .
2) Given a quadratic equation [tex]ax^2+bx+c=0[/tex], you can know the number of real solutions by using this formula to find the Discriminant :
[tex]D=b^2-4ac[/tex]
If [tex]D=0[/tex], then there is one real solution with multiplicity two.
If [tex]D>0[/tex], then there are two distinct real solutions.
On a graph:
-If the graph has two x-intercepts, then the quadratic equation has two real solutions.
-If the graph has one x-intercept , then the quadratic equation has one real solution.
What is the best name for the part of the figure identified by
the arrow?
line of reflection
O line of symmetry
plane of reflection
O axis of symmetry
The best name for the part of the figure identified by the arrow is line of symmetry.
The best name for the part of the figure identified by the arrow is line of symmetry. It refers to a line that divides a figure into two equal halves, which are mirror images of each other.
The line of symmetry can be identified by the arrow in the figure where the reflection occurs.
For example, in the letter 'A', the line through the middle vertically is the line of symmetry, as both sides of the letter are identical when folded along that line.
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if m^-3=64, then 8m=
Answer:
The value of 8m is 2
Step-by-step explanation:
step 1
Find the value of m
we know that
[tex]m^{-3} =64[/tex]
so
[tex]\frac{1}{m^{3}}=64\\ \\m^{3}=\frac{1}{64}\\ \\ m=\frac{1}{\sqrt[3]{64}}\\ \\m=\frac{1}{4}[/tex]
step 2
Find the value of 8m
[tex]8m=8(\frac{1}{4})=2[/tex]
What is the slope of the line that passes through the pair of points? (–6, 8), (2, 3)
Answer:
Step-by-step explanation:
Slope = y/x
y1-y2/x1-x2=slope of 2 points
8-3/-6-2 = 5/-8 which equals -5/8 or -.625.
The slope of line for the points is -5/8.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
given:
We have the Points (–6, 8), (2, 3).
So, the slope is
m = (3- 8)/ (2- (-6))
m = -5 / (2+6)
m = -5 / 8
Thus, the Slope is -5/8.
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Can someone please help me ..I can’t get anymore questions wrong or else I will fail I need help
Answer:
maybe number 2
Step-by-step explanation:
because if 2+k=18 then there is no other k there and where did the additional 2 come from ?and 2k=18 then value of k is 9 + there is balance.I may be wrong correct me but i think it is no.2
Answer:
2k = 18
k = 9
Step-by-step explanation:
First we have to look at each side of the hanger.
There are 2 k's, which can be represented as "2 times the value of k" or 2k.
On the other side, we have the value of 18. The question states that the two sides are balanced. Therefore, the correct equation that represents the image is:
2k = 18.
To find the value of k that makes the equation true, we must isolate the variable k. To do this, we divide 2 from each side of the equation.
2k ÷ 2 = 18 ÷ 2
k = 9.
The value of k that makes the equation true is 9.
The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?
ANSWER
[tex]k = 17[/tex]
EXPLANATION
The given function is
[tex]f(x) = 2x + 3[/tex]
The translation that shifts this function 10 units to the right is
[tex]f(x - 10)[/tex]
This implies that
[tex]f(x - 10) = 2(x - 10) + 3[/tex]
We expand the parenthesis to get:
[tex]f(x - 10) = 2x -20+ 3[/tex]
[tex]f(x - 10) = 2x - 17[/tex]
Comparing this equation with
[tex]f(x) = 2x - k[/tex]
we have
[tex]k = 17[/tex]
k=17
The new function would be f(x)=2x-17
In the previous function when u put x=0 you got 3.
Now when the function moves 10 units to the right you still have to get y=3 for x=10. So
2x-k=3 substitute 10 for x
20-k=3 solve for k
K=17.
know factors and roots? please help me!!!!\
Answer: b) (2m³ - 4p⁵)(2m³ + 4p⁵)
Step-by-step explanation:
Use the difference of a square formula: a² - b² = (a - b)(a + b)
[tex]4m^6 - 16p^{10}\\\bullet a) \sqrt{4m^6}=2m^3\\\bullet b)\sqrt{16p^{10}}=4p^5[/tex]
(2m³)² - (4p⁵)² = (2m³ - 4p⁵)(2m³ + 4p⁵)
what is the slope of the line shown below?
Answer:
it is 2
Step-by-step explanation:
Hello There!
The slope of this line would be 3.
The slope is gradually increasing so starting from the Y intercept value, its consistently going up 3 on the Y axis and going over 1 on the X axis
What is the measure of X in degrees
Answer:
C. 40°
Step-by-step explanation:
From the diagram, in triangle XYZ, XY=XZ=6 units. This means triangle XYZ is isosceles triangle with base YZ.
In isoscels triangle angles adjacent to the base are congruent, so
∠ZYX=∠YZX=70°
The sum of all interior angles in triangle is always 180°, so
∠ZYX+∠YZX+∠ZXY=180°
∠ZXY=180°-70°-70°
∠ZXY=40°
∠ZXY is ∠X, so ∠X=40°
HELLPP
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
Answer:
[tex]\large\boxed{V=\dfrac{32}{3}\pi\ cm^3}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{We have}\ D=4\ cm\to R=\dfrac{4}{2}\ cm=2\ cm\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(2)^3=\dfrac{4}{3}\pi(8)=\dfrac{32}{3}\pi\ cm^3[/tex]
Which is not a correct way to rewrite this expression using the distributive property?
The correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).
To use the distributive property, we need to distribute the first factor,
(2x^2 +4−7), over the two factors in the second set of parentheses, (x) and (x−2).
This means we multiply each term in the first factor by each term in the second set of parentheses, and then add the products together.
Here is the correct distribution:
(2x^2+4-7)(x) + (2x^2+4-7)(x-2)
= (2x^3+4x-7x) + (2x^3-4x+14x-14)
= 4x^3-3x+7 + 10x-14
= 4x^3+7x-7
Therefore, the correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).
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Solve the formula
V= 1/3•3.14•r^2h for h
A) 1/3r^2V
B) 3V/3.14r^2
C) 3 3.14r^2V
D) V/3 3.14r^2
Answer:
[tex]\large\boxed{B)\ \dfrac{3V}{3.14r^2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{3}\cdot3.14\cdot r^2h=V\\\\\dfrac{3.14}{3}r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{3.14}{3\!\!\!\!\diagup_1}r^2h=3V\\\\3.14r^2h=3V\qquad\text{divide both sides by}\ 3.14r^2\\\\h=\dfrac{3V}{3.14r^2}[/tex]
What is the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1)?
Answer:
The y-intercept is the point (0,5)
Step-by-step explanation:
step 1
Find the slope of the line perpendicular to the line y=(3/4)x+3
Remember that
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
we have
m1=3/4 -----> the slope of the line y=(3/4)x+3
Find m2
substitute
(3/4)*m2=-1
m2=-4/3
step 2
Find the equation of the line into point slope form
The equation is equal to
y-y1=m(x-x1)
we have
m=-4/3
(x1,y1)=(3,1)
substitute
y-1=-(4/3)(x-3) ----> equation of the line into point slope form
step 3
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the equation of the line and solve for y
y-1=-(4/3)(0-3)
y-1=4
y=4+1=5
The y-intercept is the point (0,5)
Final answer:
The y-intercept of the line perpendicular to y = 3/4x+3 that includes the point (3, 1) is 5.
Explanation:
To find the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1), we first need to determine the slope of the perpendicular line. Since the given line has a slope of 3/4, the slope of the perpendicular line will be the negative reciprocal, which is -4/3. We then use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.
Substituting the point (3, 1) and the slope -4/3 into the equation gives us y - 1 = -4/3(x - 3). Simplifying, we get y = -4/3x + 5. The y-intercept of this line is the y-value when x is zero, which in this case is 5.
Point G is on line segment FH. Given FH=4x+8,FG=x,and GH=5x, determine the numerical length for GH
Answer: 20
Step-by-step explanation:
Given: Point [tex]\text{G}[/tex] is on line segment [tex]\text{FH}[/tex]. Given [tex]\text{FH}[/tex] is [tex]4\text{x}+8[/tex] , [tex]\text{FG}[/tex]. is [tex]\text{x}[/tex], and [tex]\text{GH}[/tex] is [tex]5\text{x}[/tex].
To Find: the numerical length for [tex]\text{GH}[/tex].
Solution:
Point [tex]\text{G}[/tex] is on the line segment [tex]\text{FH}[/tex]
therefore,
[tex]\text{FH}=\text{FG}+\text{GH}[/tex]
putting the values
[tex]4\text{x}+8=\text{x}+5\text{x}[/tex]
[tex]4\text{x}+8=6\text{x}[/tex]
[tex]8=2\text{x}[/tex]
[tex]\text{x}=4[/tex]
Now,
[tex]\text{GH}=5\text{x}[/tex]
[tex]\text{GH}=5\times4[/tex]
[tex]\text{GH}=20[/tex]
Hence numerical length of line segment [tex]\text{GH}[/tex] is [tex]20[/tex]
The numerical length of GH is 20
If Point G is on the line segment FH, this means that:
FG + GH = FHGiven the following parameters:
FH=4x+8
FG=x
GH=5x
Substitute the given values into the formula as shown:
x + 5x = 4x + 8
6x = 4x + 8
6x - 4x = 8
2x = 8
Divide both sides by 2
2x/2 = 8/2
x = 4
Get the length of GH
GH = 5x
GH = 5(4)
GH = 20
Hence the numerical length of GH is 20
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The population of a small town is 2,200
and is increasing at a rate of 3% per year;
10 years. Round to the nearest whole
number.
Answer:
2957
Step-by-step explanation:
Instead of just giving you a formula.. I want to show you how to understand the formula
So 2200 is the initial population
After 1st year, we are going to have an increase of 3% so 1st yr gives us 2200(1.03)=2266
After 2nd year, we are going to have increase of 3% from previous year so we could do 2266(1.03) or realize this is the same as 2200(1.03)^2 .
so you are going to keep multiplying factors of 1.03 to that per year.
So at 10 years we have 2200(1.03)^10
The formula I mentioned was really this initial population times (1.03)^(number of yrs)
So answer is 2956.616
To the nearest whole number is 2957