The range of the function y=3/x+8 is all real numbers except 8, since the function approaches 8 but never reaches it due to the vertical asymptote at x=0.
The range of the function y=3/x+8 refers to all possible output values (y-values) that the function can produce. To find the range, it is essential to consider the values that x can take. Since x is in the denominator, x cannot be 0, as division by zero is undefined. Therefore, the function has a vertical asymptote at x=0.
As x approaches both positive and negative infinity, y approaches the constant 8, because the term 3/x approaches 0. Thus, the function can get close to, but never equal, the value of 8. Also, since 3/x can take any value except 0, the range of the function is all real numbers, excluding 8.
The final range of the function y=3/x+8 is therefore: {y | y ≠ 8}, meaning all real numbers that are not equal to 8.
Evaluate the function rule for the given value. y = 4 • 2^x for x = –6
Answer:
y = 1/16
Step-by-step explanation:
y = 4 • 2^x
Let x = -6
y = 4 • 2^(-6)
The negative exponent puts it in the denominator
y = 4 • 1/ 2^6
y = 4 * 1/64
y = 4/64
y = 1/16
Find the equationOf the line who slope is -3 and Y intercept is five
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
It tells us that the slope (m) is -3 and the y-intercept (b) is 5. Plug this into the formula given above:
y = -3x + 5
Hope this helped!
~Just a girl in love with Shawn Mendes
The formula for the circumference of a circle is C = 2tr,
where r is the radius and C is the circumference. The
equation solved for r is r= .
The correct formula to calculate the circumference of a circle is C = 2πr. To solve for r, the radius, we can rearrange the equation to r = C/(2π), which can be used to find the radius when the circumference is known.
Explanation:The formula for the circumference of a circle is given by C = 2πr, where 'C' represents the circumference and 'r' is the radius of the circle. The formula has been provided in an errorneous format, it should be 2πr not 2tr.
If we want to solve this equation for 'r', which represents the radius, we would need to isolate 'r' on one side of the equation. We can do this by dividing both sides of the equation by 2π. The resulting equation solved for r would be r = C/(2*π).
This equation can be utilized to find the radius if the circumference is known.
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Find the coordinates when the parallel lines AB and PQ are reflected over the x-axis. The points are A(1, 1), B(1,4), and
P(3, 1). Q(3, 4).
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
A(1, 1 ) →A'(1, - 1 )
B(1, 4 ) → B'(1, - 4 )
P(3, 1 ) → P'(3, - 1 )
Q(3, 4 ) → Q'(3, - 4 )
478,387 to the nearest ten thousand
ANSWER = 270,000
MARK BRAINLIST
Answer:
478,387.0000
Step-by-step explanation:
Evaluate the expression, given functions f,g, and h:
Answer:
-1
Step-by-step explanation:
So you are asked to find 3f(1)-4g(-2).
In order to find this you must first find f(1) and g(-2).
So f(1) means what is the value of the expression 3x-2 for when x=1.
f(1)=3(1)-2
f(1)=3-2
f(1)=1
And g(-2) mean what is the value of the expression 5-x^2 for when x=-2.
g(-2)=5-(-2)^2
g(-2)=5-(4)
g(-2)=5-4
g(-2)=1
So both of those function values were 1.
Our problem of 3f(1)-4g(-2) becomes 3(1)-4(1)=3-4=-1.
Identify the number that is NOT the same as the others when rounded to the nearest tenth.
a. 34.62 c. 34.49 b. 34.59 d. 34.56
Please select the best answer from the choices provided
A
B
C
D
Answer:
c. 34.49
Step-by-step explanation:
Note that the nearest tenth place value is directly next to the decimal point (located on the right). Round each number to the nearest tenth. Look at the number in the hundredth place value. If it is 5 or greater round up, if 4 and less, round down.
a. 34.62 rounded to the nearest tenth is 34.6
c. 34.49 rounded to the nearest tenth is 34.5
b. 34.59 rounded to the nearest tenth is 34.6
d. 34.56 rounded to the nearest tenth is 34.6
This makes it so that C. 34.49 is your answer.
~
According to the graph, what is the value of the constant in the equation
below?
Answer:
The value of the constant is 0.8Explanation:
The graph has the following properties:
Horizontal-axis (independent variable): widthVertical-axis (dependent variable): heightPoints on the curve:(0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)
The equation represented by the graph is an inverse variation:
Height = constant / width.From that equation, you can solve for the contstant:
constant = height × widthNow, you can take any ordered pair to find the constant:
(0.5, 1.6) ⇒ constant = 0.5 × 1.6 = 0.8(0.8, 1) ⇒constant = 0.8 × 1 = 0.8(1.6, 0.5) ⇒ constant = 1.6 × 0.5 = 0.8(2, 0.04) ⇒ constant = 2 × 0.4 = 0.8Thus, you have obtained that the constant is 0.8.
I Need The Answer Plz Geometry Is Hard!!!
Answer:
∠F = 106°
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, hence
∠F = ∠J = 106°
A(n)_______ (rational /irrational) number answer is desired.
Answer: rational number answer is desired
Step-by-step explanation:
What are the zeros of the function f(x)=x^2+x-6 divides by x^2-x-6?
Answer:
It is B.
Step-by-step explanation:
x^2+x-6 / x^2-x-6 = 0
The numerator equates to zero:
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
the zeroes are {-3, 2).
The zeroes of the function f(x) = (x² + x - 6)/(x² - x - 6) are -3, 2.
Hence, option B. is the right choice.
What are functions?A function (say f(x)) is defined over x, when an expression in x, gives only one value f(x) for all the x in its domain.
What are zeroes of function?A zero of a function (say f(x)) is the value x, where f(x) = 0.
How do we solve the given question?We are asked to find the zeroes of the function
f(x) = (x² + x - 6)/(x² - x - 6).
To find the zeroes, we put the value of f(x) = 0, in the above equation to get:
(x² + x - 6)/(x² - x - 6) = 0
or, (x² + 3x - 2x - 6)/(x² + 2x - 3x - 6) = 0
or, {x(x + 3) -2(x + 3)}/{x(x + 2) -3(x + 2)} = 0
or, {(x - 2)(x + 3)}/{(x - 3)(x + 2)} = 0
Zeroes are where the numerator = 0, as the denominator can not be 0.
∴ (x + 3)(x - 2) = 0
∴ Zeroes of the function x + 3 = 0 ⇒ x = -3, and x - 2 =0 ⇒ x = 2, that is
-3, 2. Hence, option B. is the right choice.
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The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1=1/4(x-12) what is the standard formula equation for this line?
Answer:
x - 4y = 8Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
============================================
We have the points (-4, -3) and (12, 1).
Substitute:
[tex]m=d\frac{1-(-3)}{12-(-4)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex]
The standard formula of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex] multiply both sides by 4
[tex]4y-4=x-12[/tex] add 4 to both sides
[tex]4y=x-8[/tex] subtract x from both sides
[tex]-x+4y=-8[/tex] change the signs
[tex]x-4y=8[/tex]
Charlene is wrapping the box below. How much wrapping paper will she need? 7in x 9in x 5in,?
Charlene will need 286 square inches of wrapping paper to cover all six sides of the box with dimensions of 7 inches by 9 inches by 5 inches. This is found by calculating the surface area of each side and then adding them together.
To determine how much wrapping paper Charlene will need to wrap a box with dimensions 7 inches by 9 inches by 5 inches, we calculate the surface area of the box. The box has 6 sides, with each side being a rectangle. The dimensions of the sides are 7x9 inches (two sides), 7x5 inches (two sides), and 9x5 inches (two sides).
To find the total surface area, we calculate the area of each of these rectangles and then sum them together:
Area for two 7x9 sides: 2 * (7in * 9in) = 2 * 63in2 = 126in²
Area for two 7x5 sides: 2 * (7in * 5in) = 2 * 35in2 = 70in²
Area for two 9x5 sides: 2 * (9in * 5in) = 2 * 45in2 = 90in²
Adding these together gives:
Total surface area = 126in² + 70in² + 90in² = 286in²
Charlene will need 286 square inches of wrapping paper to wrap the box.
What is the conjugated expression?
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.
Answer:
1. W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3. E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.O(10,1),P(6,7),Q(14,9) and R(16,7).
Step-by-step explanation:
We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)
We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM
1.a transformation 3 units down and 3 units left
By using transformation rule [tex](x,y)\rightarrow (x-3,y-3)[/tex]
The new vertices of quadrilateral is (5,1), (1,7),(9,9) and (11,7).
Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A sequence of reflection across x- axis and y-axis in order
Reflection across x- axis
The transformation rule [tex](x,y)\rightarrow (x,-y)[/tex]
By using this rule
The vertices of quadrilateral are (8,-4),(4,-10),(12,-12) and (14,-10).
After the reflection across y- axis
The transformations rule
[tex](x,y)\rightarrow (-x,y)[/tex]
By using this rule
We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).
Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3.a translation 3 unit left and 2 units up
The transformation rule [tex](x,y)\rightarrow (x-3,y+2)[/tex]
By using this rule
The new vertices are (5,6),(1,12),(9,14) and (11,12).
Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.a translation 2 units right and 3 units down
The transformation rule
[tex](x,y)\rightarrow (x+2,y-3)[/tex]
By using this rule
The new vertices are (10,1),(6,7),(14,9) and (16,7)
Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).
Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?
Step-by-step explanation:
[tex]4x^3+x^2-8x-2\qquad\text{distributive}\\\\=x^2(4x+1)-2(4x+1)\\\\=(4x+1)(x^2-2)[/tex]
If h(x) is the inverse of f(x), what is the value of h(f(x))?
оо
0 1
ООО
o f(x)
Answer:
x.
Step-by-step explanation:
If h(x) is the inverse of f(x) them h(f(x)) = x.
If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
What is a function?A relation is a function if it has only One y-value for each x-value.
The inverse function of a function f is a function that undoes the operation of f.
If h(x) is the inverse of f(x), then by definition we have:
h(f(x)) = x
This is because the composition of h and f is the identity function, which means that applying h to f(x) gives us back x.
Therefore, the value of h(f(x)) is x.
Hence, If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
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Consider the function f(x) = x2 + 2x - 15. What are the x-intercepts of the function?
Answer:
x = - 5, x = 3
Step-by-step explanation:
To find the x- intercepts equate f(x) to zero, that is
x² + 2x - 15 = 0 ← in standard form
Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( + 2)
The factors are + 5 and - 3, since
5 × - 3 = - 15 and 5 - 3 = + 2, hence
(x + 5)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 ) ← x- intercept
x - 3 = 0 ⇒ x = 3 ⇒ (3, 0 ) ← x- intercept
Answer:
left most x intercept : ( -5, 0 )
right most x intercept : ( 3, 0 )
Step-by-step explanation:
Just got it right esketit
Please help!!
A multiple-choice test consists of 28 questions with possible answers of a,b,c,d. Estimate the probability that with random guessing, the number of correct answers is at least 12.
Answer:
Approximately 0.0294.
Step-by-step explanation:
Assume that there's only one correct choice in each question.
The chance of getting a question correct by random guess is 1/4.The chance of getting a question wrong by random guess is 3/4.What's the probability that exactly 12 answers are correct?
12 out of the 28 answers need to be correct. [tex]\displaystyle \left(\frac{1}{4}\right)^{12}[/tex].The other 28 - 12 answers need to be incorrect. Multiply by [tex]\displaystyle \left(\frac{3}{4}\right)^{28 - 12}[/tex].There are more than one way of choosing 12 answers out of 28 without an order. Multiply by the combination "12-choose-28" [tex]\displaystyle \left(\begin{array}{c}12\\28\end{array}\right)[/tex].The probability of getting exactly 12 answers correct is:
[tex]\displaystyle \left(\frac{1}{4}\right)^{12} \times \left(\frac{3}{4}\right)^{28 - 12}\times \left(\begin{array}{c}28\\12\end{array}\right)\approx 0.0182[/tex].
With the same logic, the probability of getting [tex]x[/tex] ([tex]x\in \mathbb{Z}[/tex], [tex]12\le x\le 28[/tex]) correct out of the 28 random answers will be
[tex]\displaystyle \left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}28\\x\end{array}\right)[/tex].
The probability of getting at least 12 correct out of 28 random answers is the sum of
the probability of getting exactly 12 correct out of 28, plusthe probability of getting exactly 13 correct out of 28, plusthe probability of getting exactly 14 correct out of 28, plusthe probability of getting exactly 15 correct out of 28, plusthe probability of getting exactly 16 correct out of 28, plus... all the way to the probability of getting exactly 28 correct out of 28.The Sigma notation might help:
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]}[/tex].
Evaluate this sum (preferably with a calculator)
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]} \approx 0.0294[/tex].
A flare is shot straight up from a flare gun, from a height of 6 meters, and with a velocity of 60 m/s. How many seconds it takes for the flare to hit the ground? Use the formula below where v0 is the initial velocity and h0 is the initial height. Approximately how long will is take the object to hit the ground?
[tex]h(t) = -4.9t^2 + v_0t + h_0[/tex]
10.8 sec
11.4 sec
11.8 sec
12.3 sec
Answer:
Step-by-step explanation:
Answer: 12.3 seconds.
Step-by-step explanation: Hope It Helps :)
18 is what percent of 24?
The number 18 expressed as a percentage of 24 is; 75%
To determine what percentage of 24 is 18;
We must evaluate the percentage as follows;
(18/24) × 100%= 0.75 × 100%= 75%Read more;
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which graph represents a function with direct variatio?
Answer:
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
Step-by-step explanation:
If you want a better answer you can post the graphs.
I will tell you the trick, direct variations is another words for the relation is proportional.
The graph will have equation y=kx where k (k can't be zero) is the slope and your y-intercept is 0. The graph should be a diagonal line.
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.
f(x)=?
Can some help?
Answer:
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Step-by-step explanation:
we know that
2 is a zero of multiplicity 3 of the polynomial
so
we have that
x=2 is a solution of the polynomial
A factor of the polynomial is
[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3
and the other solution is x=-2
since the polynomial is fifth degree, x=-2 must have a multiplicity 2
so
the other factor of the polynomial is
[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2
therefore
The polynomial is equal to multiply the factors by the leading coefficient
so
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Examine the first two steps used to solve the equation.
3 4 (20y − 8) + 5 = 1 2 y + 1 4 (20y + 8)
15y − 6 + 5 = 1 2 y + 5y + 2
15y − 1 = 11 2 y + 2
Which would be a good third step to solve the equation?
A. Combine like terms 11/2 and 2
B. Distribute 15 to each term on the left side.
C. Subtract 11/2y from each side of the equation.
D. Divide each side of the equation by 2.
Answer:
C.
Step-by-step explanation:
Your fractions are missing there fraction bars:
3/4 (20y − 8) + 5 = 1/2 y + 1/4 (20y + 8)
15y − 6 + 5 = 1/2 y + 5y + 2
15y − 1 = 11/2 y + 2
A. 11/2y and 2 aren't like terms because one contains the variable y and the other contains no variable
B. The distribute property can't be used there because you don't have 15(y-1) you have 15y-1
C. Subtracting 11/2y sounds like a good step because there is a y term on the opposing side.
15y-1=11/2y+2
Subtracing 11/2y on both sides
9.5y-1=2
That looks pretty good because then you would add 1 on both sides giving:
9.5y =3
Last step would get the y by itself which is dividing both sides by 9.5 giving you 6/19.
D. You could actually do this but it doesn't help you get x by itself. The equation would look like this: 15/2 y-1/2=11/4 y+1
Answer:
C. Subtract 11/2y from each side of the equation.
Step-by-step explanation:
The perimeter of a rectangle is 215 feet. The short sides are each 24 feet long, but the lengths of the long sides are unknown. Which equation represents this situation?
24a=215
2(24)+2a=215
24+2a=215
2(24)a=215
Answer:
2 ( 24 ) + 2 a = 215
Step-by-step explanation:
Perimeter of the rectangle is 215 feet, the short sides are 24 feet long and we need to work out the long sides (we will call a long side 'a') so,
24 + 24 + a + a = 215
For this case we have to:
Let "a" be the variable that represents the length of the rectangle and let "b" be the variable that represents the width of the rectangle. Then the perimeter is given by:
[tex]P = 2a + 2b[/tex]
We have as data that:
[tex]P = 215 \ feet\\b = 24 \ feet[/tex]
Then, replacing:
[tex]215 = 2a + 2 (24)[/tex]
Answer:
Option B
What are the coordinates of the image of vertex F after a
reflection across the line y = -x?
(-1, -3)
(3,-1)
(1,3)
(-3, 1)
G(-2, -3)
F(1.-3
E-1.-5)
H(2-5)
The coordinate of the vertex F across y = -x will be (3, -1). Then the correct option is B.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the reflection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
Now, the rule for reflecting a point about the line y = -x is;
While reflecting on the line y = -x, we get the reflected points by multiplying '-1' with the swapped coordinates.
The coordinates of the image are given below.
G(-2, -3), F(1, -3), E(-1, -5), and H(2, -5)
The reflection across the line y = -x.
Then the coordinate of the vertex F across y = -x will be (3, -1).
Then the correct option is B.
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Point W is located on QR so that QW/QR = 3/4. What are the coordinates of point W?
Answer:
(9,9)
Step-by-step explanation:
I like to use similar triangles.
To take some confusion out of of this let's translate the line down 3 units and left 3 units.
Alright from the drawing we get:
a/8 = b/8 and a/8 = 3k/4k (or b/8=3k/4k )
We don't need the k's, they cancel.
a/8 = b/8 and a/8=3/4
So the first equation means a=b.
Now let's see what a and b are by solving a/8 = 3/4.
Cross multiply:
[tex]\frac{a}{8}=\frac{3}{4}[/tex]
[tex]a(4)=8(3)[/tex]
[tex]4a=24[/tex]
a=6
So if a=b and a=6, then b=6.
The ordered pair is (6,6).
Now let's move the line back.
We have to move it up 3 units and right 3 units which gives us the point (9,9).
A rectangle has a base length of 14 inches and an unknown height, h. The area of the rectangle is less than 56 square inches.
Which inequality represents the possible values of h, the height of the rectangle?
on-14> 56
14-h <56
14h> 56
14h <56
Answer:
14h <56
Step-by-step explanation:
The area of a rectangle is given by
A =bh
We know the area is less the 56
bh <56
The base length is 14
14h <56
Answer:
D
Step-by-step explanation:
i got this question right on edgeinuity
Find the zeros of y = x + 6x- 4 by completing the square.
Answer:
[tex]\large\boxed{x=-3\pm\sqrt{13}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+6x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2(x)(3)=4\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=4+9\\\\(x+3)^2=13\Rightarrow x+3=\pm\sqrt{13}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{13}[/tex]
To pass science, a student must earn at least a grade of 70. How many students failed this science class?
Answer:
7 students.
Step-by-step explanation:
To pass science, a student requires at least 70 grades so students who scored below 70 will be failed.
From the given bar chart we can calculate the number of students who scored below 70 grades
Students who earned 50 - 59 = 2
Students who earned 60 - 69 = 5
Therefore, number of students who failed were
2 + 5 = 7 students.
Answer:7 students
Step-by-step explanation: