Answer:
B and E
Step-by-step explanation:
Given the rational expression
[tex]\frac{x-7}{2x^2-32}[/tex] ← factorise the denominator
2x² - 32 ← take out a common factor of 2 from each term
= 2(x² - 16) ← (x² - 16) is a difference of squares
= 2(x - 4)(x + 4)
The expression can now be written as
[tex]\frac{x-7}{2(x-4)(x+4)}[/tex]
The denominator of the expression cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the values that x cannot be.
2(x - 4)(x + 4) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 4 = 0 ⇒ x = - 4
These are the values of x that make the expression undefined.
x = 4 → B
x = - 4 → E
Which expression is equivalent to x^2-10x+24
Answer:
(x-4)(x-6)
Step-by-step explanation:
By factorization, x^2-10x+24 can be written in the form (x-4)(x-6). Thus the roots of the quadratic equation are x= 4 and 6 respectively.
The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates. Eight of the candidates are members of the debate team.
(a) What is the probability that all of the offices are filled by members of the debate team?
(b) What is the probability that none of the offices are filled by members of the debate team?
Answer:
The probability that all of the offices are filled by members of the debate team is 0.0512 and the probability that none of the offices are filled by members of the debate team is 0.0256
Step-by-step explanation:
The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates.
So, Number of candidates required = 4
Total number of candidates = 15
Number of candidates which are members of the debate team. = 8
So, Number of candidates which are not the members of the debate team = 15-8 =7
The probability that all of the offices are filled by members of the debate team = [tex]\frac{^8C_4}{^{15}C_4}=\frac{\frac{8!}{4!\left(8-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0512[/tex]
The probability that none of the offices are filled by members of the debate team=[tex]\frac{^7C_4}{^{15}C_4}=\frac{\frac{7!}{4!\left(7-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0256[/tex]
Hence The probability that all of the offices are filled by members of the debate team is 0.0512 and the probability that none of the offices are filled by members of the debate team is 0.0256
Simplify the ratio 9/12 by dividing both the numerator and denominator by the greatest common factor of 3
A) 1/4
B) 1/2
C) 3/4
D) 4/3
Answer:
Option C
Step-by-step explanation:
9/3=3
12/3=4
so, the answer is 3/4
Option C
Answer:
Think of it as 9 / 3 = 3
12 / 3 = 4
so it is 3/4. The ratio is equal because 3/3 = 1 so you are dividing by 1
Hope this helps
Step-by-step explanation:
Classify the triangle by its angles and by its sides
Right isosceles
Acute scalene
Acute isosceles
Obtuse isosceles
Answer:
Acute isoceles
Step-by-step explanation:
Two base angles of the triangle are equal making it isosceles
The top angle is less than 90° making it an acute angle
What is the area of this triangle?
PLSSS I WILL GUVE YOU THE POINTS
Answer:
12
Step-by-step explanation:
11. The x-intercept of the line 2x + 3y – 36 = 0 is:
Answer:
(18,0)
Step-by-step explanation:
2x + 3y – 36 = 0
The x intercept is when y = 0
Solve for x
2x + 3*0 – 36 = 0
2x +0 -36 = 0
2x -36 =0
Add 36 to each side
2x-36+36 = 36
2x = 36
Divide each side by 2
2x/2 = 36/2
x = 18
A. 5pi/6
B. 8pi/6
C. 3pi/6
D. 13pi/6
Answer:
Step-by-step explanation:
Find the equation of the line passing through the point (1,−5) and perpendicular to
y= 1/8x +2
Answer:
y=-8x+13
Step-by-step explanation:
you flip the m value
then you plug in the point (1,-5) to find b (y-intercept)
then you get 13.
The equation of the line is y = -8x + 3 passing through the point (1,−5) and perpendicular to y= 1/8x +2.
What is slope of line?Slope of line is defined as the angle of line. It is denoted by m.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
Let the equation of line : y = mx + c
Given that, the line passing through the point (1,−5) and
The line perpendicular to y = 1/8x +2
To determine the slope of the perpendicular line,
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line that is perpendicular to the given line is
m×1/8 = -1
m = -8
Substitute the value of slope m in the first equation,
y = -8x + c
To determine the equation of the line, substitute the found slope (-8) and the point (1,−5) into the point-slope form of a linear equation:
5 = -8(1) + c
-5 = -8 + c
c = -5 + 8
c = 3
So, the required equation of line : y = -8x + 3
Hence, the equation of the line is y = -8x + 3 passing through the point (1,−5) and perpendicular to y= 1/8x +2.
Learn more about Slope of Line here:
brainly.com/question/14511992
#SPJ5
The sum of 3c2d3 + (-5c2d3) + 10c2d3 is
Answer:
8c to the pwr of 2 d to the pwr of 3
Step-by-step explanation:
i think
Answer: To find the SUM of this expression, you end up with 8c^2*d^3. (Vote me brainliest please)
(URGENT)Which summation formula represents the series below?
13 + 9 + 5 + 1
Σ-4n+1)
Σ-47-15)
Σ(n-4)
Σ(n-4)
Answer:
Σ-47-15)
Step-by-step explanation:
Option D is correct, the summation formula that represents the series is Σ(n-4) for n=1 to 4.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
A series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
The series can be written as:
13 + 9 + 5 + 1 = (4×3 + 1) + (4×2 + 1) + (4×1 + 1) + (4×0 + 1)
= (4×(3-1) + 1) + (4×(2-1) + 1) + (4×(1-1) + 1) + (4×(0-1) + 1)
= Σ(n-4) from n=1 to 4
Therefore, the summation formula that represents the series is Σ(n-4).
To learn more on Sequence click:
https://brainly.com/question/21961097
#SPJ7
Classify the triangle by its angles and by its sides.
Answer:
Acute and Scalene.
Step-by-step explanation:
By definition, an acute triangle is one that has three angles that are less than 90 degrees. This triangle falls under the category.
By definition, a scalene triangle is one that has three sides with different measurements. This triangle falls under the category.
Hope this helps!
95 points!
The scatter plot shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend with family each week.
What is the y-intercept of the line of best fit and what does it represent?
11.5 hours; the number of hours students spend with family in a week when they do not watch television
9.2 hours; the number of hours students watch television in a week when they do not spend time with family
9.2 hours; the number of hours students spend with family in a week when they do not watch television
11.5 hours; the number of hours students watch television in a week when they do not spend time with family
9.2 hours; the number of hours students watch television in a week when they do not spend time with family
Step-by-step explanation:
We are given,
The x-axis represents the time spent with family and the y-axis represents the time spent on watching television.
Now, y-intercept is the point where the scatter plot crosses y-axis.
From the scatter plot and and according to the options, the data point is located at x= 0 and y= 9.2.
That is, the y-intercept represents that students watched television for 9.2 hours when they do not spend time with their family.
4(2+a)=24 what is the answer
Given:
4(2 + a)= 24
Use Distributive Property:
8 + 4a = 24
Subtract 8 to both sides:
4a = 16
Divide 4 to both sides:
a = 4
Answer:
A = 4
Step-by-step explanation:
Assuming the question is asking what a is, then all you have to do is follow a few steps to get the right answer.
1) Use the distributive property to simplify the first part of the equation.
4(2+a) distribute the 4 to what is within the parenthesis, so multiply 4 to what is in the parenthesis. P.S: This also gets rid of the parenthesis.
(8 + 4a)
2) Now your equation looks like 8 + 4a = 24. Now, use inverse operations to isolate a. Inverse operations are basically using the opposite signs and processes to get some parts of an equation to another side.
2a. Subtract 8 from both sides of the equation:
8 + 4a - 8 = 24 - 8.
So now you have 4a = 16.
2b. Divide 4 from both sides of the equation.
4a/4 = 16/4
So now you have a = 4.
Final answer:
A = 4
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) =
O A. g(x) = (x+4)2 - 3
O B. g(x) = (x - 42 - 3
O C. g(x) = (x – 4)2 + 3
O D. g(x) = (x+4)2 + 3
Answer:
A
Step-by-step explanation:
Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Given f(x) then the graph of f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here f(x) has been shifted 4 units left and 3 units down, thus
g(x) = (x + 4)² - 3 → A
The graph of y= -2x + 10 is:
O A. a point that shows the y-intercept.
O'B. a point that shows one solution to the equation.
O c. a line that shows the set of all solutions to the equation.
O D. a line that shows only one solution to the equation.
SUBMIT
Helppp me plzzzz
Answer:
A. a point that shows the y-intercept
Step-by-step explanation:
Show and explain why 6 is not a solution to the inequality below.
2x - 9 ≥ 5
Answer:
x ≥ 7
Step-by-step explanation:
2x -9 ≥ 5
+9
x ≥ 14
14/2
=7
x ≥ 7
Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T. Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l? Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m. Use the compass to construct a circle centered at Q through point P. Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P. Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q. Use the compass to construct a circle centered at P through point Q.
Answer:
The answer is B on Edge
Step-by-step explanation:
Answer:( B)Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Step-by-step explanation:
What is the height of the pyramid??
I need help on #5 on my summer packet my teacher never taught me this and I need help.
Answer:
c
Step-by-step explanation:
it can only be 0-9 that is in standard form- one digit then a decimal point
can u pls mark as brainliest?
Answer:
c
Step-by-step explanation:
hope that helps
The coordinate of point B is -6 and the coordinate of point E is 2.
Find the length of segment BE.
Answer:
4
Step-by-step explanation:
just because i just took it
Joshua has a rectangular vegetable garden with the dimensions shown below. If he doubles the length and width of the garden, how will the area of the new garden compare to the area of the original garden?
Which function has zeros at x = 3 and x = 7?
Answer:
f(x)= (x-3)(x-7)
Step-by-step explanation:
What is the scale factor used to
enlarge an 8" by 10" original
photo to a 16" by 20" image?
A. 2
B. 2.5
C. 0.5
D. 1.6
Answer:
!!B!!
Step-by-step explanation:
What is the scale factor used to
enlarge an 8" by 10" original
photo to a 16" by 20" image?
A. 2
B. 2.5....is the answer
C. 0.5
D. 1.6
I hope it helps.Answer:
A
Step-by-step explanation:
8x2= 16 10x2=20
The value of x in 5(8+x)=20
Answer:
x = -4
Step-by-step explanation:
5(8+x)=20
Divide each side by 5
5/5(8+x)=20/5
8+x = 4
Subtract 8 from each side
8+x-8 = 4-8
x = -4
The right answer is -4.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
What are the next three numbers in this pattern?
11, 22, 12, 23,...
A 13, 24, 15
B 13, 24, 14
C 13, 23, 14
D 32, 43, 33
Answer:
B
Step-by-step explanation:
because first it is 11, 12, after it is 13, and 14
: for 22, 23 and after 24
Answer:
B
Step-by-step explanation:
A premier credit card has an initiation fee that provides you with the privilege to use it and a monthly fee after the first two months. The initiation fee is $62 and the monthly fee is $30 per month after the first two months. If C represents the cost and g represents the total number of months, which equation could represent this plan when you have this card for more than two months?
A. C = 30 + 62(g-2)
B. C = 30 + 62(2-g)
C. C = 62 + 30(g-2)
D. C = 62 + 30(2-g)
Answer:
The correct option is C.
Step-by-step explanation:
To have this credit card there is two fees, one that is fixed payed upfront and other that is payed after the second month. The fixed fee costs $62, and doesn't escalate with time, while the other one is $30 and starts to be charged after the second month. Therefore, the total cost of the card is the fixed fee plus the monthly fee multiplied by the number of months the user had the card subtracted by two, or as shown below:
[tex]C(g) = 62 + 30*(g-2)[/tex]
The correct option is C.
−7/8 −(−5/6) in simplest form
Answer:
-1/24
Step-by-step explanation:
-7/8 - (-5/6)
Subtracting a negative is like adding
-7/8 + 5/6
Get a common denominator
-7/8 * 6/6 + 5/6 *8/8
-42/48 + 40/46
-2/48
-1/24
25 pints= gallons? pints?
Answer:
3.125 gallons
Step-by-step explanation:
25 pints could be converted to about roughly 3.125 gallons.
What is the solution of 3square root x+8 = -4?
• x=-72
• x=-66
• x=58
• no solution
Answer:
No solution
Step-by-step explanation:
I'd suggest you try to solve this first: 3√(x + 8) = 4. First, square both sides; this results in 9(x + 8) = 16, or x + 72 = 16/9, or x = -632/9. We cannot let x = -632/9 in √(x + 8) because -632/9 is not in the domain of the square root function. No solution.
If we now write 3√(x + 8) = -4 (note the negative sign), similar efforts at solution result in 9(x + 8) = -4, or x + 8 = -4/9, or x = -8 - 4/9. If we now substitute this result for (x + 8) in 3√(x + 8) = -4 (above), we get 3√(-8 + 8 - 4/9), which has no solution; -4/9 is not in the domain of the square root function.
The solution for the given equation is 16.
The given equation is 3√x+8=-4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The solution for the given equation can be determined as follows:
Now, 3√x+8=-4
⇒ 3√x=-4-8
⇒ 3√x=-12
⇒ √x=-12/3
⇒ √x=-4
Squaring both the sides, we get
x=16
Therefore, the solution for the given equation is 16.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ6
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
The figure could be a square because the diagonals of a square bisect the right angles.
Answer:
the figure could be a rhombus because the 2 lines of symmetry bisect the angles
Step-by-step explanation:
Option C is correct. , if a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
Quadrilaterals are figures with four sides and angles. Examples of quadrilateral include:
RectangleSquarerhombusA line of symmetry is a line that divides a shape such that they become mirror images of each other.
Hence, if a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, from the options, the figure could be a rhombus because the 2 lines of symmetry bisect the angles (divides the angles equally).
Learn more here: https://brainly.com/question/19670823
