Answers
Answer:
C
Step-by-step explanation:
10×-28=-280
35-8=27
35×(-8)=-280
10x²+27x-28
=10x²+(35-8) x-28
=10x²+35x-8x-28
=5x(2x+7)-4(2x+7)
=(2x+7)(5x-4)
=========================================================
Explanation:
One way we can factor is through use the of the quadratic formula.
Let [tex]10x^2+27x-28 = 0[/tex]
For now, the goal is to find the two roots of that equation.
Plug a = 10, b = 27, c = -28 into the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(27)\pm\sqrt{(27)^2-4(10)(-28)}}{2(10)}\\\\x = \frac{-27\pm\sqrt{1849}}{20}\\\\x = \frac{-27\pm43}{20}\\\\x = \frac{-27+43}{20} \ \text{ or } \ x = \frac{-27-43}{20}\\\\x = \frac{16}{20} \ \text{ or } \ x = \frac{-70}{20}\\\\x = \frac{4}{5} \ \text{ or } \ x = -\frac{7}{2}\\\\[/tex]
The two roots are x = 4/5 and x = -7/2
For each root, rearrange the equation so we have 0 on the right hand side, and it's ideal to get rid of the fractions
x = 4/5
5x = 4
5x-4 = 0 gives us one factor
and
x = -7/2
2x = -7
2x+7 = 0 gives the other factor
The two factors are 5x-4 and 2x+7
Note how (5x-4)(2x+7) = 0 leads to the two separate equations of 5x-4 = 0 and 2x+7 = 0 due to the zero product property. Solving each individual equation leads to the two roots we found earlier.
Alternative methods to solve this problem are the AC factoring method (which leads to factor by grouping), using the box method, or you could use guess and check.
Related Questions
Can someone please help me I don’t know how to do this (Due today)
Answers
First go to the y intercept (or the b in y=mx+b) look for the slope and plot the points on the graph they're talking about e.g. #23 the y-intercept is 6 go to the 6 on the y axis, and then look at the slope (x), so it goes up and over to the right since it's positive by 1
can someone please please help me :/ I have to get this right. please help
Answers
Work Shown:
Solve for y. Then replace y with f(x).
[tex]680x + 10y - 1000 = 0\\\\10y - 1000 = -680x\\\\10y = -680x + 1000\\\\y = \frac{-680x + 1000}{10}\\\\y = \frac{-680x}{10} + \frac{1000}{10}\\\\y = -68x + 100\\\\y = 100 - 68x\\\\f(x) = 100 - 68x\\\\[/tex]
Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.
Answer:
choice B
Step-by-step explanation:
I did this problem like 6 months ago......
Which expression is equivalent to 5/2?
Answers
Answer:
B
Step-by-step explanation:
5 divided by 2 is 5/2
Answer:
B
Step-by-step explanation:
5/2 the (/) is the divide sign
multiply 2x^2-4x 6c^2-5x
Answers
Answer:
a
Step-by-step explanation:
2x^2-4x 6x^2-5x
2x^2 times 6x^2= 12x^4
2x^2 times -5x= -10x^3
-4x times 6x^2= -24x^3
-4x times -5x= 20x^2
12x^4-10x^3-24x^3+20x^2
12x^4-34x^3+20x^2
(Also Brainliest if this helps pls)
Factorise : x^2+x-72 Step by Step
Answers
Answer:
(x + 9)(x - 8)
Step-by-step explanation:
f(x) = x^2 + x - 72
= x^2 - 8x + 9x - 72
= (x^2 - 8x) + (9x - 72)
= x(x - 8) + 9(x - 8)
= (x + 9)(x - 8)
Answer:
x² + x - 72 = (x + 9)(x - 8)
Step-by-step explanation:
[tex]x^2+x-72\quad \implies\quad a=1\,,\quad b=1\,,\quad c=-72\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-72)}}{2\cdot1}=\dfrac{-1\pm\sqrt{1+288}}{2}=\dfrac{17\pm\sqrt{289}}{2}\\\\x_1=\dfrac{-1-17}{2}=-9\quad,\qquad x_2=\dfrac{-1+17}{2}=8\\\\\\x^2+x-72=(x-(-9))(x-8)=(x+9)(x-8)[/tex]
or:
x² + x - 72 =
= x² + 9x - 8x - 72 =
= x(x + 9) - 8(x + 9) =
= (x + 9)(x - 8)
Scouts of ABC school made to run around a regular hexagonal ground fig 9, of perimeter 270 m .If they started running from point X and covered two fifth (2/5th) of the total distance.Which side of the ground will they reach?
Answers
Answer:
Scouts are on the third side in the sense they are running
Step-by-step explanation:
A regular hexagonal shape of perimeter 270 has each side of 270/6 = 45
Let´s call d the run distance then
d = 2/5 * 270 d = 108 m
We don´t have fig 9 available therefore if X is a vertex in the hexagon or at the middle point of one side, scouts are 108 m from the starting point which means they had run 2,4 sides of the hexagon. If X is not either a vertex or a middle point of a side then, we have two solutions for the question depending on the sense the scouts took when began the run (clockwise or counterclockwise)
what is this supposed to be bro pls help
Answers
Answer: 1
Step-by-step explanation:
so i put the amount of flour to servings into ratios (fractions)
28:14
9:12
10:13
then I put them into the same denominators
2184:1092
819/1092
840/1092
the first one is the greatest
pls help me ASAP !!!!!!!!!
Answers
Identify the reflection rule in the given figure.
A. Reflection along the line y = –1
B. Reflection along x-axis
C. Reflection along y = 1
D. Reflection along y-axis
Answers
Answer: A) Reflection along the line y = -1
===========================================================
Explanation:
Point A is at (1,5). Point A' is at (1,-7).
Apply the midpoint formula to find the center of these two points.
You should get (1,-1) as that midpoint.
Follow these steps for B(-1,3) and B'(-1,-5) to get the midpoint (-1,-1)
Those midpoints we found are located on the mirror line. We only need two such points to plot it. Drawing a line through (1,-1) and (-1,-1) graphs the equation y = -1. This is the horizontal line through -1 on the y axis.
Which properties belong to all isosceles triangles? Check all that apply.
The base angles are congruent.
All three angles are congruent.
The two sides opposite the base angles are congruent.
All three sides are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Answers
=====================================================
Explanation:
Let's go through the answer choices to see which are true and which are false.
A) True. The base angles are the same measure, and they are opposite the congruent sides. Any isosceles triangle has exactly two congruent sides.B) False. This is describing an equilateral triangle (where all three angles are 60 degrees each).C) True. See choice A.D) False. This is describing an equilateral triangle where all sides are the same length. E) True. You can use the SAS (side angle side) congruence theorem to prove that the angle bisector is also the perpendicular bisector. Furthermore, this segment is also a median. This only applies to the vertex angle.Answer:
The base angles are congruent.
The two sides opposite the base angles are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Step-by-step explanation:
what is the answer to -3/7 x -1 2/3
Answers
Answer:
-9x-35/21
Step-by-step explanation:
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]\frac{-3}{7}* (-1\frac{2}{3})=\frac{-3}{7}*\frac{-5}{3}\\\\= \frac{5}{7}[/tex]
Please Help!!
Write an absolute value equation that has the solutions x = -10 and x = -5.
The equation is:_____
Answers
Answer:
x=-10
x=-5
-10+-5=15
Step-by-step explanation:
answer 15
arav spent 1 3/4 hours in studies and 2 1/2 hours in playing cricket. how much time did he spent at all ??
Answers
= 7/4 + 5/2
= (7+10)/4
= 17/4
= 4 1/4
Answer:
[tex] \boxed{4 \frac{1}{4} \: \: hours}[/tex]Step-by-step explanation:
Time spent in studies = [tex]1 \frac{3}{4} [/tex]
Time spent in playing cricket = [tex]2 \frac{1}{2} [/tex]
Now, let's find the hours that he spent at all:
[tex] \mathsf {1 \frac{3}{4} + 2 \frac{1}{2} }[/tex]
Convert mixed fraction into improper fraction
[tex] \mathsf{ = \frac{7}{4} + \frac{5}{2} }[/tex]
Take the LCM
[tex] \mathsf{ = \frac{7 + 5 \times 2}{4} }[/tex]
Multiply the numbers
[tex] \mathsf{ = \frac{7 + 10}{4} }[/tex]
Add the numbers
[tex] \mathsf{ = \frac{17}{4} }[/tex]
Convert the improper fraction into mixed fraction
[tex] \mathsf{ = 4 \frac{1}{4} }[/tex] hours
Hope I helped!
Best regards!
If 2 < 20x - 13 < 3. what is one possible value for x?
Answers
Answer:
one possible value for x is 31/40
Step-by-step explanation:
Let's isolate the 20x term. Add 13 to all three terms:
2 + 13 < 20x - 13 + 13 < 3 + 13
and this simplifies to:
15 < 20x < 16
Dividing all three terms by 20, we get:
15/20 < x < 16/20
A fraction halfway between 15/20 and 16/20 is (31/20)/2, so
one possible value for x is 31/40.
Check by substituting this into the original equation and checking whether that equation is now true:
2 <20(31/40) - 13 < 3
or
2 < 31/2 < 16, or 2 < 15.5 < 16 (this is true, so 31/40 is a solution)
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answers
Answer: 4. A base area of 16y^2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Using the distributive property; you can see that 16y^2(y^2+y+3)=
16y^4+16y^3+48y^2
Answer:
D. a base area of 16y2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Ed22
find the volume of each figure. Round to the nearest tenth if necessary.
Answers
Answer:
1385.4
Step-by-step explanation:
Volume=pi*r^2*h=pi*49*9=1385.4
A file that is 276 megabytes is being dowloaded . If the downloaded is 16.7% complete how many megabytes have been dowloaded? Round ur answer to the nearest tenth ( can ya please hurry and answer thank you)
Answers
276 x .167 = 46.092
Answer: 46.1 megabytes
Step-by-step explanation:
simplify : 2(3+a)+4=36
Answers
a = 13
Step-by-step explanation:
2(3 + a) + 4 = 36
Subtract 4 from both sides
2(3 + a) = 32
Multiply 2 by each number in “( )”
6 + 2a = 32
Subtract 6 from both sides
2a = 26
Divide 2 from both sides
a = 13
Therefore, a = 13
I'm under the water on this problem, please help me:
question: f(x)=10x−3
answer choices:
A. f(−5)
B. f(0)
C. f(7)
D. f(t^2+2)
E. f(12−x)
F. f(x+h)
Answers
Answer:
See below
Step-by-step explanation:
Okay so...I might be interpreting the question wrong-if I am please comment! I'll fix it to the best of my ability.
A) Plug in -5 to all x values
f(-5)=10(-5)-3
==50-3
f(-5)= -53
B) f(0)=10(0)-3
f(0)= -3
C) f(7)=10(7)-3
=70-3
f(7)=67
D) f(t^2+2)=10(t^2+2)-3
=10t^2+20-3
f(t^2+2)=10t^2+17
E) f(12-x)=10(12-x)-3
=120-10x-3
f(12-x)=117-10x
F) f(x+h)=10(x+h)-3
=10x+10h-3
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answers
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
Question 8 If f (2) = (1 + 3) and g (2) VO+ 7, find g (f (x)). 9(f()) = 1 + 10 O g(f ()) = VI + 3 +7 Og(f (x)) = v= + 10 Og(f (2)) = 2? + 10
Answers
Answer:
x+10
Step-by-step explanation:
f(x) = (x+3)^2 and g(x) = sqrt(x)+7
g(f(x)) =
Replace f(x) in for x in the function g(x)
= sqrt((x+3)^2)+7
= x+3 +7
= x+10
PLEASE HELP ASAP
I WILL MARK BRAINLIEST
Answers
Answer:
Estimated 120 students
Step-by-step explanation:
Hi there!
The survey established that 3 out of the 75 students did not have social media accounts.
[tex]\displaystyle \frac{3}{75}[/tex]
Let [tex]x[/tex] be equal to the number of students in the entire school who does not have social media accounts.
[tex]\displaystyle\frac{x}{3000}[/tex]
Create a proportion:
[tex]\displaystyle \frac{3}{75}=\displaystyle\frac{x}{3000}[/tex]
Multiply both sides by 3000 to isolate [tex]x[/tex]:
[tex]\displaystyle \frac{3}{75}*3000=\displaystyle\frac{x}{3000}*3000\\\\\frac{9000}{75}=x\\\\120=x[/tex]
Therefore, the number of students in the entire school who do not have social media accounts is estimated to be 120.
I hope this helps!
how many are 1 raised to 3 ???
Answers
Answer:
1
Step-by-step explanation:
1^3
This is 1 multiplied by itself 3 times
1*1*1
1
Point Q is located at (-4, 6). Point R is located at (8, 6).
What is the distance from point Q to point R?
Answers
Step-by-step explanation:
Hi there!
Given;
Point Q is located at (-4, 6). Point R is located at (8, 6).
Note: Use distance formula.
Now;
[tex](d) = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
Keep all values;
[tex](d) = \sqrt{ {(8 + 4)}^{2} + ( {6 - 6)}^{2} } [/tex]
Simplify;
[tex](d) = \sqrt{( {12)}^{2} } [/tex]
Therefore, the distance is 12 units.
Hope it helps!
What is – x4 + 2x3 + 6x2 – 10x – 4 divided by X – 2?
Answers
Answer:
-x^3 + 6x + 2
Step-by-step explanation:
is 1/5 a rational or irrational number (20 points pls help)
Answers
Answer:
rational
Step-by-step explanation:
Answer:
it's Rational Number
Step-by-step explanation:
since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number
plot the inequality on the number line
Answers
Answer:
Hope this helps!
Rochelle deposits $6,000 in an IRA. What will be the value (in dollars) of her investment in 15 years if the investment is earning 9% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)
Answers
Answer:
$ 23,145
Step-by-step explanation:
This is a compound interest question where the interest is compounded continuously. Hence, the formula for the value of total amount of investment is:
A = P×e^rt
Where:
A = Total value of investment after t years
P = Principal or Initial amount invested = $6,000
e = Exponential function
r = interest rate = 9% = 0.09
t = time in years = 15
So:
A = $6000 × e^15 × 0.09
A = $6000 × e^1.35
A = $23,144.553184
Approximately , A ≈$23,145
Therefore, the value (in dollars) to the nearest cent of Rochelle's investment in 15 years if the investment is earning 9% per year and is compounded continuously is $23,145.
Geometry, please answer question ASAP
Answers
Answer:
A,53.37°
360-306.63=53.37
Answer:
A
Step-by-step explanation:
a whole circle has 360 degrees (one time all around).
so, going from J over M to L is "using" already 306.63 degrees of that. going then from L to J just finishes the full trip of going one time around the whole circle.
so, LJ is just the missing "piece" to 360 degrees.
LJ = 360 - 306.63 = 53.37
for the function y= -2+5 sin [pi/12(x-2)], what is the maximum value
Answers
Answer:
The answer is 0. There is no minum or maxium vaule, it equals 0.
Step-by-step explanation: