Answers
Answer:
(a) (2x +7), (x -4)
(b) (-7/2, 0), (4, 0)
Step-by-step explanation:
(a)When looking for integer factors of a quadratic of the for ax² +bx +c = 0, it is useful to start by looking for factor pairs whose product is a·c and whose sum is b.
Here, that means you're examining the factors of 2·(-28) = -56, and looking for a pair that have a sum of -1. We can start by examining the ways that -56 can be factored:
-56 = -56(1) = -28(2) = -14(4) = -8(7)
Sums of these factor pairs are -55, -26, -10, -1, so it is the last pair we're interested in.
At this point, you can rewrite the x-term using these factors and then factor the quadratic by pairs.
2x² -8x +7x -28 = 0 . . . . . . . use -x = -8x+7x
(2x² -8x) +(7x -28) = 0 . . . . group into pairs of terms
2x(x -4) +7(x -4) = 0 . . . . . . factor each pair of terms
(2x +7)(x -4) = 0 . . . . . . . . . the factored equation
The factors of this equation are (2x +7) and (x -4).
__
(b)The x-intercepts are the values of x that make the factors zero.
2x +7 = 0 . . . looking for x that makes the first factor zero
2x = -7 . . . . . subtract 7
x = -7/2 . . . . divide by the coefficient of x
__
x -4 = 0 . . . . looking for x that makes the second factor zero
x = 4 . . . . . . add 4
The x-intercepts are x = -7/2 and x = 4.
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{QUESTIONS:}[/tex]
3. Given this quadratic equation, 2x²-x-28= 0.
(a) List the factors of this equation.
(b) Determine the x-intercepts
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{ANSWER:}[/tex]
(a) (x-4) and (2x+7)
(b) x=4 and x=-7/2
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{SOLUTION:}[/tex]
2x²-x-28=02x²+7x-8x-28=02x²-8x+7-28=02x(x-4)+7(x-4)=0(x-4)(2x+7)=0x-4= 0 or 2x+7=0x=4 or 2x=-7x=4 or x= -7/2[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnlearning
Related Questions
Marcus has $15.00 to spend on fruit. He buys 3 mangoes and spends the rest of the money on grapes. The store charges $0.75 for each mango and $2.50 per pound for grapes. Which equation represents the number of pounds of grapes, x, Marcus bought and how many pounds of grapes did he buy?
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It equals to $13.25
Step-by-step explanation:
Need help on HS geometry
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Answer:
The triangle must be an isosceles triangle so as to only get one measurement
Step-by-step explanation:
The Pythagorean theorem states that the square of the hight and base is added then square rooted to get the hypotenuse
THE FORMULA: A square+b square=c square
Lena was playing a card game. She placed the cards in 2 rows of 26 cards each. In which other way can Lena place all of the cards?
Answers
Answer:
4 raws of 13 each
Step-by-step explanation:
The total number of cards =2×26=52we can divide 52 by 4 which is 13help pls!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Name:
Grade & Section:
Date Submitted: 12/14/2021
Advent: Use it
Christmas: Open gifts under the tree left by Santa
Ordinary Time:
Lent: Celebrate Jesus.
Paschal Triduum: The Proper day to Celebrate Jesus
Easter: It is a Holiday where you celebrate a bunny and get candy.
Step-by-step explanation:
So is what you do here is you enter your Name, Grade & Section, and Date which i've already given you. So your assignment is about how you will participate in the seasonal activity. So Advent looks like it would be a Advent Calendar.
Christmas You wanna open gifts
Now I left Ordinary Time blank because you need to put what time you would regularly open gifts or if you do not celebrate Christmas put what time you'd like to open gifts at.
Lent: is where you celebrate Jesus and what he did on his time being on Earth.
Paschal Triduum is basically the same as Lent but it is the proper day you celebrate Jesus Which starts April 13 & Ends Saturday, April 16
Easter: Is where you usually get candy but it is in a hunt form
Write an inequality to compare the ratios 2/4 and 5/6.
Answers
Answer:
5/6>2/4
Step-by-step explanation:
5/6 is greater than 2/4
Find the value of a and b in parallelogram QRST
Answers
Answer:
a=7
b=11
Step-by-step explanation:
4a=3a+7
-3a -3a
a=7
2b=b+11
-b -b
b=11
sides parallel from eachother in a parallelogram are equal to eachother.
Evaluate.
(−16+0.6(−13)+1)2
What is the value of the expression?
Enter your answer as a simplified fraction in the box.
Answers
x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
Answers
Answer:
(x+1)^2*(x+2)*(x+3)
Step-by-step explanation:
(x+1)(x+2)(x+3)x.(x+1)
(x+1)^2*(x+2)*(x+3)
(x+3)
(((x•(x+1))•(x+2))•—————)•(x+1)
x
(x + 1) • (x + 2) • (x + 3) • (x + 1)
Multiply (x+1) by (x+1)
One whale sang to communicate with another whale. The song's sound wave traveled 2,100meters at a steady speed in 1.4seconds. What was the sound wave's speed?
Answers
Answer:
1500 meters / second
Step-by-step explanation:
Speed = the magnitude of distance / time
Distance = 2,100 meters
Time = 1.4 seconds
Speed = 2,100 meters / 1.4 seconds = 1500 meters / second
If F(x) = x - 7 and G(x) = x^3, what is G(F(x))?
=
A. x^3+ x - 7
B. X^3-7
C. (x-7)^3
D. x^3(x - 7)
Answers
Answer:
C
Step-by-step explanation:
a force of magnitude 10n is applied in the directions 3i-4j to displacement point of action from A to B of position vectors 2i+j,5i-2j respectively. Find the work done.
Answers
An object at point A moving to point B is displaced in the direction of
r = (5i - 2j) m - (2i + j) m = (3i - 3j) m
(I assume distance is measured in meters)
If the force is F = (10 N) (3i - 4j), then the work performed by F in the direction of r is
F • r = (10 N) (3i - 4j) • (3i - 3j) m = (10 N) (9 + 12) m = 210 J
whats the remainder of 45 divied by 8
Answers
Answer:
5
Step-by-step explanation:
8*5=40
45-40=5
r would be 5
hope this helps
Y - 7 =- 4(x - 2)
convert it into y-intercept form
Answers
Answer: the y intercept form is y= 4x-1
Step-by-step explanation: let me know if you need to know how I got it
(7−2)3×(24−11)? cause im in 6th grade lol
Answers
Answer:
(7−2)(3)(24−11)
=(5)(3)(24−11)
=15(24−11)
=(15)(13)
=195
Step-by-step explanation:
What is the surface area of the rectangular prism below?
Answers
Answer:
is 736 units
Step-by-step explanation:
my explanation is that I got it wrong because of the answer above of me an the right answer was 736 not 706
The surface area of the rectangular prism below with height as 8 units, length as 19 units and breadth as 8 units is A) 736 square units.
The surface area of a rectangular prism is the total area of all the faces of the prism. The rectangular prism below has 6 faces, each of which is a rectangle.
The area of a rectangle is given by:
area = length * breadth
The surface area of the rectangular prism is then given by:
surface area = 2 * (length * breadth + breadth * height + height * length)
Plugging in the values for the length, breadth, and height, we get:
surface area = 2 * (19 * 8 + 8 * 8 + 19 * 8) = 2 * (152 + 64 + 152) = 2 * 368 = 736 square units
Therefore, the surface area of the rectangular prism is A) 736 square units.
Here is a breakdown of the surface area of each of the faces:
Front face: 19 * 8 = 152 square units
Back face: 19 * 8 = 152 square units
Top face: 8 * 8 = 64 square units
Bottom face: 8 * 8 = 64 square units
Left face: 19 * 8 = 152 square units
Right face: 19 * 8 = 152 square units
The total surface area is the sum of the areas of all 6 faces, which is 736 square units.
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$200 at 15.5% for 2 years
Answers
• The outside temperature changes -4.8°F in 4 hours. What is the average change in temperature each hour?
-19.2°F
-12.2°F
-1.8°F
-1.2°F
Answers
Answer:
-1.2°F
Step-by-step explanation:
-4.8F = 4 hours
Divide both sides by 4 to get one side to 1 hour
-4.8F/4 = 4 hours / 4
-1.2F = 1 hour
The average change in temperature each hour is -1.2°F
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that the outside temperature changes -4.8°F in 4 hours
We need to find the average change in temperature each hour
To find this we need to use division.
We need to divide -4.8 by 4
-4.8/4
Minus four point eight divided by 4
-1.2
Hence, the average change in temperature each hour is -1.2°F
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Who’s smart ,but it’s math
Answers
Answer:
The answer is c
Step-by-step explanation:
Which functions are invertible
Select each correct answer
Answers
Answer:
the top two
Step-by-step explanation:
For a function to be invertible, it must pass the "horizontal line test." That is, there can be no horizontal line that will intersect the graph in more than one place. The bottom two graphs fail this test, so do not represent invertible functions.
The two top graphs show invertible functions.
What is the answer please give i really help and no links
Answers
Answer:
[tex]9\frac{57}{63}[/tex]
Step-by-step explanation:
First, we need to turn them into improper fractions:
[tex]2\frac{4}{7}[/tex] + [tex]7\frac{3}{9}[/tex]
7 x 2 + 4
7 x 9 + 3
[tex]\frac{18}{7}[/tex] + [tex]\frac{66}{9}[/tex]
Next, we need to find a common multiple of both 7 and 9
7, 14, 21, 28, 35, 42, 49, 56, 63
9, 18, 27, 36, 45, 54, 63
So the denomonator turns into 63.
We've multiplied the denomonater 9 times for the first fraction and 7 times for the second fraction, we therefore have to do the same to the numerator.
18 x 9 = 162
66 x 7 = 462
[tex]\frac{162}{63}[/tex] + [tex]\frac{462}{63}[/tex] = [tex]\frac{624}{63}[/tex]
Next, we have to turn it back into a mixed number.
To work it out: 624 / 63 = 9 (1 s.f) <--- Mixed number.
9 x 63 = 567
624 - 567 = 57 (Working out the remainder.)
Combining them, the answer is therefore [tex]9\frac{57}{63}[/tex]
Hope this helps and have a good day!
Explain whether the pairing is a function
Answers
it would’ve been a function if it had many to one
Georgia is 2 years younger than 1/3 of her Aunt Mika's age. How old would Georgia be if her Aunt Mika is 27?
Answers
Answer:
7
Step-by-step explanation:
First, we have to find 1/3 of 27, which is the aunt's age.
27/3 is 9.
Now, since Georgia is 2 years younger, we have to subtract 2 from 9.
9-2=7
-hope it helps
5.37 + x =12.89 explanation please it’s two step equation
Answers
Answer:
7.52
Step-by-step explanation:
5.37 + x = 12.89
In order to solve this equation, we must isolate the variable, x.
1.) To do this, subtract 5.37 on both sides of the equation.
5.37 + x = 12.89
-5.37 -5.37
x = 7.52
Therefore, x = 7.52
Answer:
Answers of given questions are written below :
1) x = 7.522) x = 113) x = 2.5Step-by-step explanation:
[tex]\large{\tt{\underline{\underline{\purple{SOLUTION : - }}}}}[/tex]
5.37 + x = 12.89
[tex] \implies{\tt{5.37 + x = 12.89}}[/tex]
[tex] \implies{\tt{ x = 12.89 - 5.37}}[/tex]
[tex] \implies{\tt{ x = 7.52}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{ x = 7.52}}}}}[/tex]
Hence, the value of x is 7.52
[tex]\begin{gathered}\end{gathered}[/tex]
42 = 6x - 24
[tex] \longmapsto{\sf{42 = 6x - 24}}[/tex]
[tex] \longmapsto{\sf{ 6x = 42 + 24}}[/tex]
[tex] \longmapsto{\sf{ 6x = 66}}[/tex]
[tex] \longmapsto{\sf{x = \dfrac{66}{3}}}[/tex]
[tex] \longmapsto{\sf{x = 11}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{ x = 11}}}}}[/tex]
Hence, the value of x is 11.
[tex]\begin{gathered}\end{gathered}[/tex]
10x + 25 = 50
[tex]{\longrightarrow{\rm{10x + 25 = 50}}}[/tex]
[tex]{\longrightarrow{\rm{10x= 50 - 25}}}[/tex]
[tex]{\longrightarrow{\rm{10x= 25}}}[/tex]
[tex]{\longrightarrow{\rm{x= \dfrac{25}{10}}}}[/tex]
[tex]{\longrightarrow{\rm{x=2.5}}}[/tex]
Hence, the value of x is 2.5.
[tex]\rule{300}{2.5}[/tex]
Please help me thank you :)
Answers
We know the equation.
=> y = mx + bWe also know the y-intercept, which is -3.
=> b = -3.All we need to find is the slope. Once the slope is found, our equation is set.
=> Slope = Rise/Run=> -1/2 = SlopeConclusion:Since the slope has been found, the equation is y = -x/2 - 3.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
what is the correct solution to the system of equations below?
2x+y=13
y=x-5
Answers
Answer:
2x+y=13
2x + x-5 = 13
3x = 13 + 5
3x = 18
x =18/3
x= 6
now
y = x- 5
y = 6- 5 = 1
thanks marks me as brainliest
Drag steps of the solution into order to solve for x in the equation 6(x-5) = 54
A. 6x – 30 = 54
B. 6x = 84
C. 6x = 24
D. x = 14
I need to figure out what order to put these in to get the answer I can only use three!
Answers
The steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
A. 6x – 30 = 54 B. 6x = 84 D. x = 14Given the expression 6(x-5) = 54
Expand the expression in parenthesis using the distributive law;
6x - 6(5) = 54
6x - 30 = 54
Add 30 to both sides
6x - 30 + 30 = 54 + 30
6x = 84
Divide both sides by 6
6x/6 = 84/6
x = 14
Therefore the steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
A. 6x – 30 = 54 B. 6x = 84 D. x = 14Learn more on equations here; https://brainly.com/question/2972832
What is the estimate height of 129.3
Answers
Brian has DVDs and CDs. The number of CDs he has can be modelled with the formula C = 2D + 11, where C represents the number of CDs and D represents the number DVDs. If he has 41 CDs, how many DVDs does he have?
Answers
Answer: 15 DVDs
Step-by-step explanation:
C = 2D + 11
41 = 2D + 11
2D = 30
D = 15 DVDs
Claire has 38 yards of material to make costumes for the school play.
She needs 2 3/8 yards for each costume. How many costumes can she
make?
Answers
Answer:
16
Step-by-step explanation:
38 divided by 2 3/8 is 16 and 16 times 2 3/8 is 38