Answers
Answer:
[tex]\frac{k+5}{k-2}[/tex]
Step-by-step explanation:
[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]
multiply numerator and denominator by k² to eliminate fractions
= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← factor numerator and denominator
------------------------------
k² - 25 ← is a difference of squares
= (k - 5)(k + 5)
k² - 7k + 10
= (k - 5)(k - 2)
------------------------------
= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator
= [tex]\frac{k+5}{k-2}[/tex]
Related Questions
Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
help please D:
Answers
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up. the correct option is C.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given;
Suppose that g(x) = f(x) + 6.
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up.
Hence, the correct option is C.
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The complete question is
"Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
D. The graph of g(x) is the graph of f(x) shifted 6 units to the right."
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the perimeter of a right angle triangle is 24 cm and its area is 24 cm square if the hypotenuse is 13 cm find the remaining sides
Answers
Answer:
let the remaining sides be X and Y
perimeter = X + Y + 13
24 = X + Y + 13
11 = X + Y ---(1).
Area = 1/2 * base * height
24 = 1/2 * X * Y
XY = 48.-----(2)
solving eq 1 and 2
X + Y = 11
XY = 48
Xy + y² = 11y
Xy = 48
y²= 11y - 48
y² -11y + 48 = 0
no real solution of this equation.
Answer:
Step-by-step explanation:
the triangle is NOT a 3–4–5 or multiple,
so it is not a right triangle or your data is wrong.
Write a quadratic equation, in factored form solution are 0,and 6
Answers
Answer: [tex]x(x-6)=0[/tex]
Question 9 of 10
If f(x)= (3 + x) over (x-3)
what is f(a + 2)?
A. 3+ f(a+2) over f(a)-1
B. (5+ a) over (a-1)
c. (3+a) +2
(a-3)
Answers
Answer:
[tex]\huge\boxed{\sf f(a+2)=\frac{5+a}{a-1}}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{3+x}{x-3}[/tex]
Put x = a + 2
[tex]\displaystyle f(a+2)=\frac{3+a+2}{a+2-3} \\\\f(a+2)=\frac{5+a}{a-1} \\\\\rule[225]{225}{2}[/tex]
Shapes A and B are similar.
a) Calculate the scale factor from shape A to
shape B.
b) Find the value of r.
Give each answer as an integer or as a fraction in
its simplest form.
5 cm
11 cm
A
20 cm
3 cm
rcm
B
12 cm
Not drawn accurately
Answers
The scale factor from A to B is 5/3 and the value of r is 33/5
The scale factor from A to BFrom the figure, we have the following corresponding sides
A : B = 5 : 3
Express as fraction
B/A = 3/5
This means that, the scale factor from A to B is 5/3
The value of rFrom the figure, we have the following corresponding sides
A : B = 11 : r
Express as fraction
B/A = r/11
Recall that:
B/A = 3/5
So, we have:
3/5 = r/11
Multiply by 11
r = 33/5
Hence, the value of r is 33/5
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any
ete the equivalent ratio table.
D
B
(Equivalent Ratio
21
35
20 50
27
70
12:13
17:5
23
S
9
11
2
18
22
Answers
Answer:
????????????????????????????????????????/
Step-by-step explanation:
PLS HELP ME I WIL MARK BRAINLEST
Answers
Answer: 2. X=-4
A company makes 130 bags.
28 of the bags have buttons but no zips.
33 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?
Please answer in fraction form
Answers
Answer:
33 bags or 33/110 (which can be expressed as about 30%)
Step-by-step explanation:
BUTTONS ZIPS
28 Y N
33 N Y
49 N N
The only bags with zips is the second group of 33 bags. There are 110 bags in total, so the fraction would be (33/110)
The table above shows some values of the linear function F. Which of the following defines F? A) f(n) = n-3 B) f(n) = 2n-4 C) f(n) = 3n-5 D) f(n) = 4n-6
Answers
Answer:
3n - 5
Step-by-step explanation:
f(n) = 3n - 5. Works for all of them
A candle on Pauline’s dresser is 4 inches tall and burns at a rate of 0.6 inches per hour. How many hours will it take for the candle to burn down to a height of 1.3 inches?
Answers
Answer:
4 1/2 hours
Step-by-step explanation:
first i subtracted 1.3 from 4 and got 2.7
Next i just multiplied 0.6 by random numbers ubtil i got something close to 2.7
i ended up with 2.4 when I multiplied 0.6 by 4
it still is .3 short
since it takes an hour for the candle to burn, then if you cut it in half, that means 30 minutes
therfore, 4.5 hours
Fred's garage has a leaky roof. There are 24 holes in the roof. If it costs $124 to fix each hole, how much will it cost to fix all of the holes?
A. Subtract 24 from 124
B. Multiply 24 by 124
C. Add 124 to 24
D. Divide 124 by 24
Answers
the answer would be about $5.16
Simplify The Following - c^5xc
Answers
if a + b is equal to 2 find the value of a cube plus b cube + 6ab
If geometry symbol represented as small triangle with three sides. abc a geometry symbol represented as small triangle with three sides. dec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
Answers
Answer:
D. X=1
Step-by-step explanation:
It's clear if you work through it just use substitution and you'll get the same answer yourself
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function? As x → -∞, f(x) → 9 ; as x → ∞, f(x) → 9. As x → -∞, f(x) → -9; as x → ∞, f(x) → -9. As x → -∞, f(x) → -4; as x → ∞, f(x) → -4. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
Answers
Using limits, it is found that the end behavior of the function is given as follows:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In this problem, the function is:
[tex]f(x) = \frac{8x - 1}{2x - 9}[/tex]
Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4[/tex].Hence the correct statement is:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
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Answer:
D
Step-by-step explanation:
The area of a rectangle, A = l • w is represented by the expression 24x^6y^15. Which could be the dimensions of the rectangle?
Answers
After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Calculation:The inquiry relates to the laws of indices
where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]
Provided the query, A= [tex]24x^{6}y^{15}[/tex]
[tex]2* 12[/tex] might be used to calculate the length and width of 24.
Hence,
[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]
& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]
So, it can be written as,
A=l * w
⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]
Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
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Four parallel lines are drawn in a rectangular sign. The sign is painted using two colors in an alternating pattern, as shown.
A rectangle is shown. 4 parallel lines are drawn diagonally from one side of the rectangle to the opposite side. The shapes formed by the parallel lines are colored in an alternating pattern.
Which statements must be true about the two congruent, shaded figures? Select two options.
The figures are rectangles because they are formed inside a rectangle.
The figures are rhombi because they are formed by four congruent line segments.
The figures are trapezoids because each has exactly one pair of parallel sides.
The figures are parallelograms because their opposite sides are parallel.
The figures are quadrilaterals because each has four sides.
Answers
Answer:
D & E
Step-by-step explanation:
The figures are parallelograms because their opposite sides are parallel
The figures are quadrilaterals because each had four sides
The two statements that must be true about the two congruent, shaded figures are:
The figures are parallelograms because their opposite sides are parallel.
The figures are rhombi because they are formed by four congruent line segments.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
The fact that the figures are formed inside a rectangle does not necessarily mean that they are rectangles themselves.
Similarly, the fact that each figure has one pair of parallel sides does not necessarily make them trapezoids, as trapezoids have only one pair of parallel sides.
Finally, the fact that each figure has four sides does not necessarily make them quadrilaterals, as any closed shape with four sides can be considered a quadrilateral.
The two statements that must be true about the two congruent, shaded figures are:
The figures are parallelograms because their opposite sides are parallel.
The figures are rhombi because they are formed by four congruent line segments.
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Given two terms in a geometric sequence find the first five terms.
6) a5 = -162 and a2=-6
Help please!!!
Answers
The first five terms of the geometric series is : -2, -6, -18, -54, -162.
To solve the given problem :Given : [tex]a_{5} = -162[/tex]
[tex]a_{2} = -6[/tex]
We know G.P. series always increases in the form [tex]a.r^{n-1}[/tex]
Similarly, [tex]a_{5} = a.r^{5-1} = a.r^{4} = -162[/tex]
[tex]a_{2} = a.r^{2-1} = a.r = -6[/tex]
Now, [tex]\frac{a_{5} }{a_{2} } = \frac{a.r^{4} }{a.r^{1} } = r^{4-1}[/tex]
[tex]r^{3} = \frac{-162}{-6} = 27[/tex]
[tex]r = \sqrt[3]{27} = 3[/tex]
Now,
[tex]a_{2} = a.r = -6\\a.(3) = -6\\a = -2[/tex]
The first 5 terms are : [tex]a, a.r, a.r^{2} , a.r^{3} , a.r^{4}[/tex]
[tex]-2 , (-2).3 , (-2).3^{2} , (-2).3^{3} , (-2).3^{4}[/tex]
Therefore, The first 5 terms are : -2, -6, -18, -54, -162.
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What is the range of the function on the graph?
Answers
Answer:
the answer is [1, infinity)
Graphs of tinear Relationships: Mastery Test
Select the correct answer from each drop-down menu.
The graphs below show the average temperature of a city, y, in "F, for the first 8 months of last year. Both graphs show the same information.
Change in Temperature
Change in Temperature
Y
60
40
20
2
Month
Graph A
Month
Graph B
Bejaron is preparing a report and wants to emphasize that the temperature increased greatly over the first 3 months
Complete the forowing sentences
To me the
should
crease in temperature, it would be best for Benjamin to usa
us this graph for his presentation because the temperature
Temperature (°F)
150
120
BO
Temperature ("F)
Answers
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
How to determine the appropriate graph?The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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18% Commission on a $500 couch
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
$90
Step-by-step explanation:
Rate of commission = 18%Amount = $500Commission = 18% 0f 500 = 0.18*500 =$90a woman bought some oranges and 30% of them were bad if there were 60 bad oranges how many oranges did she buy
Answers
Answer:
if 60 is 30%, then add up to 100%
60+60+60= 180
but we still have 10% left so divide 30% by 3 to get 10% then add
30% (or 60) /3 is 20
add 20 to 180
boom you get 200 she bought 200 oranges i wonder how shes gonna fit them in her car that's a lot of oranges
Answer:
200
Step-by-step explanation:
To calculate 30 percent of a number, we multiply the number by 30 and then divide by 100. Therefore, we can make the following function:
30 ∗ x÷100
= 60
To solve for x, we first multiply both sides by 100 and then divide both sides by 30 to get the x = 200. Therefore, the answer to 60 is 30 percent of what number? is:
200
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)² = 19
☐A. X=
14
B. X= -√19+5
□ C. x= -√19 +5
3
□ D. X = √19 +5
3
DEX=√14
OF X= √19+
Answers
Answer:
[tex]\sf x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
Step-by-step explanation:
(3x - 5)² = 19
To find the solution for the equation, take square root on both sides.
[tex]\sf 3x - 5 = \± \sqrt{19}\\\\ Add \ 5 \ to \ both \ sides \\\\ 3x = \±\sqrt{19} + 5\\\\ Divide \ both \sides \ by 3\\\\ x = \dfrac{\±\sqrt{19}+5}{3}\\\\x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
Answers
The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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Describe the
translation.
y = (x - 5)² +5 →
y = (x −0)² +0
A.T<5,-5>
OB.T<-5,-5>
OC.T<-5,5>
OD. T<5,5>
Answers
The translation of the parabola from y = (x – 5)² + 5 to y = (x − 0)² + 0 will be (-5, -5). Then the correct option is B.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The translation of the parabola is given below.
y = (x – 5)² + 5 → y = (x − 0)² + 0
Then the translation will be (-5, -5).
Then the correct option is B.
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what is 349,001 + 209, 499?
Answers
Answer:
558, 500
Step-by-step explanation:
round 349,001 to 349,000 subtracted 1
round 209, 499 to 209, 500 added 1
349,000 + 209, 500 = 558, 500
Now, the added and subtract 1 cancel out so that is the final answer
I hope it’s help u !
how do i Solve this equation
√x+5-2=0
Answers
Answer:
9
Step-by-step explanation:
√x+5-2=0
√x+3=0
√x= -3
x=9 [(-3)*(-3) = 9]
Step 2 - Minus 5 - √x = -3
Step 3 - Square - x = -9
HELPPPPP I NEED HELP ITS URGENT !
Answers
Answer:
-5=m
Step-by-step explanation:
-3/4m-1/2=2+1/4m
-2/4m-1/2=2
-2/4m=2 1/2
m=-5
The proportional relationship between two variables, y and z, is represented by y = 11/2z. What is the constant of proportionality from z to y?
Answers
Answer:
Step-by-step explanation:
Comment
The constant you want is just the reciprocal of the constant you have been given. You can show it this way
y = 11/2 z Multiply both sides by 2
2y = 11z Divide both sides by 11
Answer
2/11 y = z
which statement is true of the function f(x) = -3 squared root x
Answers
Using translation concepts, it is found that the function [tex]f(x) = -3\sqrt{x}[/tex] is the function [tex]g(x) = \sqrt{x}[/tex] reflected over the x-axis and vertically stretched by a factor of 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, from [tex]g(x) = \sqrt{3}[/tex] to [tex]f(x) = -3\sqrt{x}[/tex], g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.
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The slope-intercept form of the equation of a line that passes through point (-2,-13) is y=5x-3. What is the point-slope form of the equation for this line?
Answers
Answer:
y + 13 = 5(x + 2)
Step-by-step explanation:
Point - slope form of equation:[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
Slope intercept of the line : y =5x - 3
Comparing with y = mx +b , m =slope = 5
m = 5 and Point (-2 ,-13)
y - [-13] = 5(x - [-2])
y + 13 = 5(x + 2)
