Answers
We are given the equation x² + 8x = 33, and we need to solve it from completing the square, for which we will be following the below steps
Step 1 :- First, notice, what's the coefficient of x², if it's 1, then proceed to step 2, if not then divide both sides by the coefficient of x²
[tex]{:\implies \quad \sf x^{2}+8x=33}[/tex]
Step 2 :- Here, we need to develop a whole square in both sides somehow, so we have the coefficient of x, so add the square of half of coefficient of x on both sides :
[tex]{:\implies \quad \sf x^{2}+8x+{\bigg(\dfrac82\bigg)}^{2}=33+{\bigg(\dfrac82\bigg)}^{2}}[/tex]
Simplify both sides now :
[tex]{:\implies \quad \sf x^{2}+8x+(4)^{2}=33+(4)^{2}}[/tex]
Step 3 :- So now, here LHS is in the form of a² + 2ab + b², so we can just replace it by (a + b)², and we will keep simplifying RHS
[tex]{:\implies \quad \sf (x+4)^{2}=33+16}[/tex]
[tex]{:\implies \quad \sf (x+4)^{2}=49}[/tex]
[tex]{:\implies \quad \sf (x+4)^{2}=(\pm 7)^{2}}[/tex]
Step 4 :- As, power on both sides is 2, so we can just equate the bases
[tex]{:\implies \quad \sf x+4=\pm 7}[/tex]
Step 5 :- Equating x + 4 to 7, will yield x = 3, and equating it to -7, will yield x = -11, so we are now left with
[tex]{:\implies \quad \boxed{\bf{x=-11,3}}}[/tex]
Related Questions
What number represents 8 times as many as 2
Answers
answer: 16
explanation: 8*2=16
The number that represents 8 times as many as 2 is 16.
The times in the question is nothing but multiplying a number with another number.
To find the number that represents 8 times as many as 2.
we need to multiply 2 by 8.
Two times eight is equal to sixteen.
2 × 8 = 16
Therefore, the number that represents 8 times as many as 2 is 16.
To learn more on Multiplication click:
https://brainly.com/question/5992872
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At Garcia's Bike Rentals, it costs 31 to rent a bike for 7 hours. How many hours of bike use does a customer get per dollar?
Answers
[tex]\tt \dfrac{7}{31}=0.226~hours/dollar[/tex]
You pick a card at random. Without putting the first card back, you pick a second card at random.
3
4
5
What is the probability of picking a 5 and then picking a 5?
Write your answer as a fraction or whole number.
Answers
Answer:1/169 i think
Step-by-step explanation:
Because you have to get a 5 twice in a row your first probability for one would be 4/52 or 1/13 but because you have to do it twice in a row you multiply the odds together 1/13*1/13=1/169
Kristen made a floor plan for her dog's kennel. The floor plan is shown below.
Note: Figure is not drawn to scale.
If a = 56 in, b = 22 in, c = 73 in, and d = 25 in, what is the perimeter of the floor plan?
A.
346 in
B.
240 in
C.
302 in
D.
256 in
Answers
Answer:
346in
Step-by-step explanation:
[tex]\hookrightarrow Here,\\\\\hookrightarrow a=56 in, b = 22 in, c = 73 in, and d = 25 in\\\\Now,\\\\\hookrightarrow Perimeter=Sum\:of\:all\:sides\\\\\hookrightarrow Perimeter=a+b+b+d+(c-2d)+b+d+b+a+c\\\\\hookrightarrow Perimeter=56+25+22+22+(73-25-25)+22+25+22+56+73\\\\\hookrightarrow Perimeter=346in[/tex]
PLEASE HELP ILL MARK BRAINLIEST PLEASEEEEE HELPPPPP
Answers
Answer:
m < 2 = 130°
m < 3 = 50°
m < 4 = 130°
m < 5 = 50°
m < 6 = 130°
m < 7 = 50°
m < 8 = 130°
Step-by-step explanation:
I hope this helps.
Identify the polynomial that is the difference of two squares.
A. 25m2 − 16n
B. 49m2 − 81n4
C. 36m2 − 8n8
D. 9m2 − 5n6
Answers
Answer:
Option B, [tex]49m^2 - 81n^4[/tex]
Step-by-step explanation:
Step 1: Determine the difference of two squares
According to online, "In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra." a^2 - b^2 gives us (a + b)(a - b)
The only one that would work is Option B so lets factor it out.
[tex]49m^2 - 81n^4[/tex]
[tex](7m + 9n^2)(7m - 9n^2)[/tex]
Answer: Option B, [tex]49m^2 - 81n^4[/tex]
Which point is a solution to the linear inequality y < -1/2
X + 2?
Answers
Answer:
This is the best answer I could find but it may be incorrect (3,-2)
(Five Stars & Thanks to whoever answers first)
Answers
Answer:
2/3
Step-by-step explanation:
They rolled an even number 40/60 times which simplifies to 2/3
Answer:
C
Step-by-step explanation:
Table
Dice Roll Number of times
1 4
2 11
3 6
4 17
5 10
6 12
Total 60
Total of the even numbers
11
17
12
40
P(even) = even / total
P(even) = 40/60
AnswerP(even) = 2/3
How to tell if an equation is a porabilula
Answers
Answer:
Parabolas have a plane-curve shape, like the one shown in the picture.
What is the most inexpensive way to measure heart rate during exercise?
A. Doing a rate of perceived exertion
B. Taking your pulse
C. Wearing a heart rate monitor
D. None apply
Answers
Answer:
C
Step-by-step explanation:
Taking your own heart rate is the most inexpensive, but it is also accurate if you can measure it correctly.
pls answer i need help
Answers
Step-by-step explanation:
xcos60 = 5root3/3
1/2x = 5root3/3
x = 10root3/3
Choice C
Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer. ( If you reshare another students answer from brainly or any other websites you'll be reported) Will Mark Brainliest if answered correctly and draw a diagram). Thank you.
Answers
We need theta first (angle
[tex]\\ \rm\rightarrowtail sin\theta=\dfrac{P}{H}[/tex]
[tex]\\ \rm\rightarrowtail sin\theta=\dfrac{11.8}{12}[/tex]
[tex]\\ \rm\rightarrowtail sin\theta=0.9834[/tex]
[tex]\\ \rm\rightarrowtail \theta=sin^{-1}(0.9834)[/tex]
[tex]\\ \rm\rightarrowtail \theta=79.54°[/tex]
On rounding it will go till 80°
So it's not safeHurrrryyyyy plllzzz. Determine the equation of the line that passes through the given points
(10,2) and (-3,2)
Answers
y = 2
Step-by-step explanation:To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.
Finding the Slope of the line:[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Substitute the coordinates of the given points:
[tex]\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10 }[/tex]
Simplify the equation to determine the slope:
[tex]\implies \text{Slope} = \dfrac{0}{-3 - 10 }[/tex]
∴ 0 divided by ANY number is ALWAYS 0.
[tex]\implies \text{Slope} =0[/tex]
Finding the equation of the line:Point slope form formula: y - y₁ = m(x - x₁)
x₁ and y₁ are the coordinates of any given point.m is the slopeSubstitute the values in the point slope form:
[tex]\implies \text{Equation of line:} \ y - y_{1} = m(x - x_{1} )[/tex]
[tex]\implies \text{Equation of line:} \ y - 2 = 0(x - 10)[/tex]
Simplify the equation to determine the equation of the line:
∴ Any number multiplied by 0 is 0.
[tex]\implies \text{Equation of line:} \ y - 2 = 0[/tex]
[tex]\implies \text{Equation of line:} \ y = 0 + 2[/tex]
[tex]\implies \text{Equation of line:} \ y = 2[/tex]
Thus, the equation of the line is y = 2.
Marta studied 20.75 hours total in April and May, she studied 13 hours total in May.
How many hours did Maria study in April?
Answers
Answer:
20.75-13=7.75
Maria studies 7.75 hours in April
Step-by-step explanation:
Brainliest would be appreciated
how many solutions does 2a-5a=-3a have
Answers
Answer:
Step-by-step explanation:
2a-5a = -3a, combine like terms
-3a = -3a , this is true all the time so ...
The equation 2a-5a = -3a has infinite many solution.
Genetics, stress and_________can also have an impact on the health of the cardiovascular system.
A. attitude
C. lifestyle
Answers
Answer:
C. lifestyle
Step-by-step explanation:
Hope this helps!
please i really need help right now 25 points
Answers
Answer:
C
Step-by-step explanation:
f(x) are 6; 2; -3; 4, finalle the answer C is correct.
Simplify: (-4ab^2)(-3b^2c) (5a)
Answers
Answer:
[tex]60a^{2} b^{4} c[/tex]
Step-by-step explanation:
just multiply first paranthesis with second one. They are each 1 unit as there are no addition or subtraction inside the parantehsis so DON'T distribute. It's more simple.
(12ab^4c)*(5a)
now multiply these 2 paranthesis, again just 2 units to multiple.
60a^2b^4c
What are the x- and y-intercepts of the graph of 5x – 4y = 20?
Answers
Answer:
The x-intercept is (4, 0)
The y-intercept is (0, -5)
Step-by-step explanation:
The x-intercept is always (x, 0)
Knowing this we can sub 0 for y in the equation so we can find the x-intercept
[tex]5x-4y=20\\5x-4(0)=20\\5x=20[/tex]
Now solve for x
[tex]5x=20\\\frac{5x}{5} =\frac{20}{5} \\x=4[/tex]
The x-intercept is (4,0)
The y-intercept is always (0, y)
Knowing this we can sub 0 for x in the equation so we can find the y-intercept
[tex]5x-4y=29\\5(0)-4y=20\\-4y=20[/tex]
Now solve for y
[tex]-4y=20\\\frac{-4y}{-4} =\frac{20}{-4} \\y=-5[/tex]
The y-intercept is (0, -5)
In the above figure, m∠A = 26° and m∠B = (2x + 16)°. If angles A and B are complementary angles, what are the value of x and the measure of angle B?
A. x = 24, m∠B = 64°
B. x = 50, m∠B = 64°
C. x = 69, m∠B = 154°
D. x = 24, m∠B = 48°
Answers
Answer:
A. x = 24, m∠B = 64°
Hope this helps!
What is the solution to n+25= -1
Answers
Answer:
n=-26
Step-by-step explanation:
Since n+25=-1, that means n must be less than -25 since if -25+25=0, so n=-26 since -1 is 0-1.
Select the correct answer.
Rewrite the following expression.
Answers
What are the solutions to the problem?
(A B C or D?)
Answers
Answer:
C
step by step equation:
add 3 to both side
than simplify
If you have 5 blue marbles, 8 yellow marbles, and 2 green marbles. What is the probability of pulling a yellow marble?
Answers
How many yellows? 8/15 = 0.533 ~~ 53%
Answer: 8/15
Step-by-step explanation: take all the color of marbles and add them together. There is where you get your denominator of 25. Next, since you are finding for yellow marbles, take the number of yellow marbles (8) and that will be your numerator.
What number is 35% of 675?
Answers
Answer:
236.25
Step-by-step explanation:
35/100x675=945/4 = 236.25
An athlete has aggressive outburst towards the opposing players is
A. extrovert/stable
B. introvertlunstable
C. introvert/stable
D. extrovert/unstable
Answers
Answer:
D. extrovert/unstable
Step-by-step explanation:
one more than nineteen
Answers
And in numerical form, 20
Answer:
20
Step-by-step explanation:
first yo get the number 19 then after that you can add 1 and your answer is 20 and aafter 20 (just incase you want to know) is 21
please help me find the formula of this table graph thingy
the topic Is graph and direct propotion
Answers
Find the ratio of the given one: 20/200 = 0.1
this means the sugar (y) is 0.1 amount of soda (x)
Multiply the amount of soda by 0.1:
Formula is y = 0.1x
Formula : y = kx or y = k/x
Thus since the formula is y = kx then we can substitute:
y = 20
k = ?
x = 200
20 = ? / 200
? = 10
Therefore for the rest of the blank
100/10 = 10
500/10 = 50
1000/10 = 100
So the chart now is:
| Drink (x ml) | 200 | 100 | 500| 1000|
| Sugar (y g) | 20 | 10 | 50 | 100 |
[RevyBreeze]
a blank is a transformation that changes the slope of a line
Answers
Answer:
I'm pretty sure its Stretches and Compressions.
Step-by-step explanation:
Find BC.
Round to the nearest tenth.