add the term that makes the given expression into a perfect square write the result as the square of a bracketed expression a square + 8a
Answer:
see explanation
Step-by-step explanation:
a² + 8a
using the method of completing the square
add ( half the coefficient of the a- term)²
a² + 2(4)a + 16
= (a + 4)²
Solve for the value of x :-
5(x+4)+5(2-x)
Answer:
[tex]30[/tex]
Step-by-step explanation:
Given expression:
[tex]5(x + 4) + 5(2 - x)[/tex]
Note: The value of "x" is undefined because the given sum is not an equation. Thus, I will simplify the expression as much as possible.
Let us simplify all the distributive properties stated in the expression.
Apply the distributive property rule [a(b + c) = ab + ac]
[tex]\implies5(x) + 5(4) + 5(2) - 5(x)[/tex]
Since 5(x) is being subtracted from 5(x), we get:
[tex]\implies 5(x) + 5(4) + 5(2) - 5(x)[/tex]
[tex]\implies 5(4) + 5(2)[/tex]
Finally, let us simplify the sum of the product of (5 and 4) and (5 and 2).
[tex]\implies20 + 10[/tex]
[tex]\implies \boxed{30}[/tex]
Learn more about one-variable expressions: https://brainly.com/question/15139917
Part B
Find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit
you found in part A.
the equation in part A is x^3-4x^2+2 and when x=3 y=-7 so, (3,-7) is the point the equation for part B needs to pass through
The linear equation that has a slope of -7 and crosses the x-axis at (3, 0) is:
y = -7x + 21
How to find the linear equation?
A general linear equation is:
y = a*x +b
Where a is the slope and b is the y-intercept.
The slope must be equal to the limit found in part a, and you say that it is equal to -7, so the slope is -7. And for how is written the problem, I understand that it crosses the x-axis at x = 3.
Then we will have:
y = -7*x + b
Such that, when x = 3, y = 0, then:
0 = -7*3 + b
21 = b
Then the linear equation is y = -7x + 21
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Answer:
The line will pass through (3,-7) and has a slope of 3
Step-by-step explanation:
x=3 , f(x) = x^3 - 4x^2 + 2
f(3) = 3^3 -4(3)^2 + 2
f(3) = -7
Help me! I don't understand algebra.
Step-by-step explanation:
g) 6g=54
g=54/6
g=9
h) 7h=73-10
h=63/7
h=9
I) 8x-32=48
8x=48-32
x=16/8
x=2
j) 63=27+9j
63-27=9j
36/9=j
4=j
k) 101-61=4x
40/4=x
20=x
l)46=8+x-5
46=3+x
46-3=x
43=x
Hope this helps you
have a nice day
A whale is at the surface of the ocean tto breathe. What is the whale's elevation? Draw a numhber line
Answer:0
<—————|—————>
0
Step-by-step explanation:
part A: Write the measure of each exterior angle directly on the diagram.
part b:What is the sum of the exterior angles of this pentagon?
Answer:
360°
Step-by-step explanation:
Sum of exterior angle of any polygon = 360
Sum of exterior angle of pentagon = 360
Find mPQ in the circle to the right
What is the value of x that makes 4(2x + 22.2) = 4(x – 17.87) true?
x=4.33
X=-13.36
O
Ob
Ос
Od
X=-40.07
x=40.07
Answer:
try youre best to complete youre succsess
Completely factor the given polynomial: 2x^2 - 8x - 10
Answer:
2(x - 5)(x + 1)
Step-by-step explanation:
2x² - 8x - 10 ← factor out 2 from each term
= 2(x² - 4x - 5) ← factor the quadratic
consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)
the factors are - 5 and + 1 , since
- 5 × 1 = - 5 and - 5 + 1 = - 4 , then
x² - 4x - 5 = (x - 5)(x + 1)
then
2x² - 8x - 10 = 2(x - 5)(x + 1) ← in factored form
Answer: [tex]2(x-1)(x+5)[/tex]
Step-by-step explanation:
Factor [tex]2[/tex] out of [tex]2x^2[/tex] [tex]+~8x-10[/tex]
[tex]Factor[/tex] [tex]2 ~out~ of ~2x^2[/tex]:
[tex]2(x^2)+8x-10[/tex]
[tex]Factor ~2~ out ~of ~8x[/tex]:
[tex]2(x^2)+2(4x)-10[/tex]
[tex]Factor ~2~ out~ of ~-10[/tex]:
[tex]2x^2+2(4x)+2~x~-5[/tex]
[tex]Factor ~2~ out~ of ~2x^2+2(4x):[/tex]
[tex]2(x^2+4x)+2[/tex] × [tex]-5[/tex]
[tex]Factor ~2~out ~of ~2(x^2+4x)+2[/tex] × [tex]-5:[/tex]
[tex]2(x^2+4x-5)[/tex]
factor:
[tex]Factor ~x^2+4x-5~ using ~the ~AC~ method.[/tex]
Consider the form [tex]x^2+bx+c.[/tex] Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex]. In this case, whose product is [tex]-5[/tex] and whose sum is [tex]4.[/tex]
[tex]-1,5[/tex]
Write the factored form using these integers.
[tex]2((x-1)(x+5))[/tex]
Remove unnecessary parentheses.
[tex]=2(x-1)(x+5)[/tex] ← final answer
What are geometric sequences?
Solve for the value of x.
Answer:
x=4
Step-by-step explanation:
Given M is the midpoint
We know that midpoint of a line divides the line into two equal parts
Therefore on equating we get
[tex]4x + 1 = 8x - 15[/tex]
[tex]1 + 15 = 8x - 4x[/tex]
[tex]16 = 4x[/tex]
[tex]x = 4[/tex]
Steps:
[tex]4x+1= 8x-15[/tex]
=>subtract 4 on both sides with 8x
[tex]1=4x-15[/tex]
=>now do add 15 both sides
[tex]16=4x[/tex]
=>Now divide 4x both sides
[tex]\frac{16}{4} =\frac{4x}{4}[/tex]
[tex]4=x[/tex]
So 4 is the answer
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Let x be a real number satisfying the condition : √x²-9 · √x²-1 = 2x+3
Calculate the expression value : Q = √x²-1 · √x^2-4 - 3x
Answer:
x= 2
1 =0.5
x=0
Step-by-step explanation:
6 2+8×3=
btw the two is supposed to be above the 6 like if you said 6 to the second power
Answer:
60
Step-by-step explanation:
(* = multiplication symbol)
6^2+8*3
36+8*3
36+24
60
Answer:60
Step-by-step explanation:
Use bidmas
(Brackets Indices Division Multiplication Addition Subtraction)
so first do 6 squared =36
Then 8x3 =24
Then 36+24= 60
Which of the following risk factors should be considered when choosing a form of investment for your money? Select all that apply.
interest rate
rate of Return
risk
term of investment
The risk factors should be considered when choosing a form of investment for your money is: interest rate and risk
What is investment?
Investment or investing means that an asset is bought, or that money is put into a bank to get a future interest from it.
While making an investment the investment consider:
Rate of inflation, it affects the value of the return.Investment History, it indicates the level of risk. Interest rate, it will show the real profit to be made.level of risk because if it is high, the potential loss will be higher.
So, The risk factors should be considered when choosing a form of investment for your money is: interest rate and risk
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PLEASE HELP !!!! I WILL GIVE BRAINLISET ! Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14, for π and round your final answer to the nearest hundredth.
Step-by-step explanation:
Volume = 4πr³/3
= 4•7³•π/3
=1372π/3
= 1372•3.14/3
≈ 1436.03 units³
to the nearest hundredth.
Determine the equation of the elastic curve for the beam using the x1 coordinate for 0 ≤ x1 ≤ l/2
The elastic curve between 0 to L/2 is a cubic curve. And the elastic curve is shown in the given diagram.
What is an elastic curve?The flexible curve of a beam is the curve generated by the crossover of the horizontal member with the beam's side, with continuous stresses on the fibers considered to be within the elastic limit.
The slope at L/2 will be
[tex]\rm \theta _{L/2} = \dfrac{PL^2}{8EI}[/tex]
The deflection of the beam at L/2 will be
[tex]\rm y_{L/2} = \dfrac{P(L/2)^3}{3EI}\\\\\rm y_{L/2} = \dfrac{PL^3}{24EI}[/tex]
And the deflection of the beam at L will be
[tex]\rm y_{L} = \dfrac{PL^3}{24EI} + \dfrac{L}{2} \times \theta _{L/2} \\\\\rm y_{L} = \dfrac{PL^3}{24EI} + \dfrac{L}{2} \times \dfrac{PL^2}{8EI}\\\\\rm y_{L} = \dfrac{5PL^3}{48EI}[/tex]
Then the elastic curve will be shown in the diagram.
More about the elastic curve link is given below.
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Given C is the midpoint of line AB, D is the midpoint of line AC, and E is the midpoint of line DC. If AE=16, what is DB?
Answer:
DB = 32
Step-by-step explanation:
Given :
⇒ C is the midpoint of the line AB
⇒ E is the midpoint of the line DC
⇒ AE = 16
=============================================================
Understanding :
⇒ AC = BC = 1/2AB
⇒ AD = DC = 1/2AC = 1/4AB
⇒ DE = 1/2AD = 1/4AC = 1/8AB
=============================================================
Finding AB :
⇒ AE = AD + DE
⇒ 16 = 1/4AB + 1/8AB
⇒ 3/8AB = 16
⇒ AB = 16 x 8 / 3
⇒ AB = 128/3
=============================================================
Finding DB :
⇒ DB = DC + CB
⇒ DB = 1/4AB + 1/2AB
⇒ DB = 3/4AB
⇒ DB = 3/4 × 128/3
⇒ DB = 128/4
⇒ DB = 32
Tomic and Brooke make a game of shooting free throws. Each basket is worth 212 points. Each miss is worth −34 points. Out of 30 free throws, they make 16 baskets. What is the correct number of points that Tomic and Brooke scored?
Answerfdf:d
fd
dffdfsd
What is the area of this triangle?
WILL MARK AS BRAINIEST
14
43
Use a unit multiplier to convert 965 centimeters to meters.
a
Answer:
9.65 meters
Step-by-step explanation:
965 cm * 1 m / 100 cm = 9.65 m
Answer:
by multiplying the numbers
The length of the hypotenuse of a 30°–60°–90° triangle is 13. Find the perimeter.
Answer:
The hypotenuse is 12 so the other side lengths are 6 and 6sqrt(3). Therefore the perimeter is 18 + 6sqrt(3). i hope it helps if not im glad to help step by step
Step-by-step explanation:
SEE IMAGE PLEASE !!!
Answer:
A. 38
Step-by-step explanation:
Diagonals of a rhombus bisect 90° at the center. Taking O to be the center :
90° + x° + (x +14)° = 180° [Angle Sum Property]2x + 104 = 1802x = 76x = 38Option AWhat does x equal with this equation
x/6-33= -27
Answer:
The first thing that we have to do is add 33 to both sides to try to reduce the amount of variables on the left hand side.
[tex]\frac{x}{6} - 33 = -27[/tex]
[tex]\frac{x}{6} - 33 + 33 = -27 + 33[/tex]
[tex]\frac{x}{6} = 6[/tex]
Now that we have simplified the left hand side even more we only have one part left to get x by itself which is to multiply both sides by 6.
[tex]\frac{x}{6} = 6[/tex]
[tex]\frac{x}{6} * 6 = 6 * 6[/tex]
[tex]x = 36[/tex]
Therefore, our final answer for what the value of x equals is 36.
Hope this helps! Let me know if you have any questions
If a1= 3 and an= 2an-1 then find the value of 06.
Answer:
a₆ = 96
Step-by-step explanation:
assuming you mean find a₆
using the recursive rule and a₁ = 3 , then
a₂ 2a₁ = 2 × 3 = 6
a₃ = 2a₂ = 2 × 6 = 12
a₄ = 2a₃ = 2 × 12 = 24
a₅ = 2a₄ = 2 × 24 = 48
a₆ = 2a₅ = 2 × 48 = 96
Find the radius of the circle in which the central angle arc=3 intercepts an arc of length is =6ft.
Answer: 2
Step-by-step explanation:
A answer number 1 please
Answer:
Number one is not reasonable
Find the value of "x" in x² -2 = 47
Thanks :)
[tex]~~~~~x^2 -2 = 47\\\\\implies x^2 = 47 +2 \\\\\implies x^2 = 49\\\\\implies x = \pm\sqrt{49}\\\\\implies x = \pm 7\\\\\text{Hence, }~ x = 7,~~ x = -7[/tex]
The Cooper family drove 987.6 miles on their vacation. They drove the same number of miles each day. If the trip was 6 days, how many miles did they drive each day?
Answer:
164.6
Step-by-step explanation: i'm a human calculator
Answer:
164.6
Step-by-step explanation:
Divide 987.6 by 6 = 987.6/6= 164.6
I NEED HELP! ASAP, THIS IS SO HARD AND MY BRAIN HURTS, IF U HELP ME WITH OTHER QUESTIONS LIKE THIS ILL GIVE U 50+ POINTS
help me here plss Fast
1. and 2. thanks ^^
Step-by-step explanation:
here you go hope it helps