Which of the following are solutions to the equation below?
Check all that apply.
x2 + 10x + 25 = 8
Answers
Answer:
The correct options for the solution values are:
[tex]x=2\sqrt{2}-5[/tex][tex]x=-2\sqrt{2}-5[/tex]Step-by-step explanation:
Given the expression
[tex]x^2+10x+25=8[/tex]
Subtract 25 from both sides
[tex]x^2+10x+25-25=8-25[/tex]
Simplify
[tex]x^2+10x=-17[/tex]
Add 25 or 5² to both sides
[tex]x^2+10x+5^2=8[/tex]
as
[tex]x^2+10x+5^2=\left(x+5\right)^2[/tex]
so the expression becomes
[tex]\left(x+5\right)^2=8[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solve
[tex]x+5=\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5=2\sqrt{2}-5[/tex]
[tex]x=2\sqrt{2}-5[/tex]
solve
[tex]x+5=-\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5=-2\sqrt{2}-5[/tex]
[tex]x=-2\sqrt{2}-5[/tex]
Therefore, the solution to the equation
[tex]x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5[/tex]
Hence, the correct options for the solution values are:
[tex]x=2\sqrt{2}-5[/tex][tex]x=-2\sqrt{2}-5[/tex]Related Questions
the mean of a,b,c,and d is 9 and the mean of a,b,c,d,e and f is 12. find the mean of e and f
Answers
Answer:
mean of e + f = 18
Step-by-step explanation:
(a + b + c + d)/4 = 9 Multiply by 4
a + b + c + d = 9 * 4 = 36
(a + b + c + d + e + f ) / 6 = 12
but a + b + c + d = 36
(36 + e + f)/6 = 12 Multiply by 6
36 + e + f = 72 Subtract 36 from both sides
e + f = 36 Divide by 2 to find the mean.
(e + f)/2 = 36/2
mean of e + f = 18
If x and y are positive integers is x - y always positive explain
Answers
Note that x and y are nonzero integers. It means that x and y will always have same sign (both are either positive or negative, since they are nonzero). Hence, xy term is always positive.
Answer:
No, if y happens to be a larger integer than x, then the result will be negative.
Step-by-step explanation:
For example, lets say that x=4 and y=9, so x-y = 4-9 = -5.
But if we were to reverse it and make x=9 and y=4, then x-y = 9-4 = 5.
-x+3=4 plz solve and Explain
Answers
Answer:
x=-1
Step-by-step explanation:
-x+3=4
-3 -3
-x=1
multiply by negative one to get rid of negative in front of x
x=-1
Answer:
here we have to bring the +4 into first part then -x in second part then it will be 3-4=x
then solve now -1=x
write a function G whose graph represents the indicated transformation of the graph f
[tex]f(x) = \frac{2}{3} {x}^{2} + 2[/tex]
vertical stretch by a factor of 3
Answers
Answer:
[tex]G(x) = 2x^2+6[/tex].
Step-by-step explanation:
The given function is
[tex]f(x) = \frac 2 3 x^2 +2[/tex]
On vertical stretch by a factor of 3, the new function G(x) is
G(x) = 3 f(x)
So, [tex]G(x) = 3 \times ( \frac 2 3 x^2 +2)= 2x^2+6[/tex]
Hence, the required function is [tex]G(x) = 2x^2+6[/tex].
________ Is the largest industry In the world.
O Technology
O Travel and tourism
O Manufacturing
O Education
Answers
I believe it’s travel and tourism. Hope this helps!
Answer:
Manufacturing is the largest industry In the world.
If another equation is graphed so that the system has no solution, which equation could that be?
y=-2(x-1/2)
y=-1/2(4x+2)
y=-x+1
y=-1/2x+2
Answers
Answer:
y=-2(×-1/2)
Step-by-step explanation:
...........
Answer question in the picture for brainliest and 10 points.
Answers
Answer:
D
Step-by-step explanation:
I know because I am smart. Trust me, it is D.
Its D
Step-by-step explanation:
pwease ik
Gracie is sharing 75 marshminnows among 4 of her friends. If each of her friends gets the same number of marshminnows, and she gives them as many marshminnows as
possible, how many are left for Gracie?
none
3
18
19
Answers
Answer:
18
Step-by-step explanation:
If you want to give people something, you need to divide the number that she is sharing (75) and the number of how many people she is sharing with (4).
So 75/4 = 18
So 18 marshminnows are left for Gracie.
A cyclist travels 8 miles in 15 minutes.
What is her average speed in mph?
Answers
Answer:
0.53 mph
Step-by-step explanation:
A cyclist travels 8 miles in 15 minutes.
So the average speed is
=8/15 mph
=0.53 mph
Suppose that a new employee starts working at $7.72 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y=$7.72(1.04)t. Find the amount of time after which he will be earning $10.00 per hour.
Answers
Answer:
6.5978 years
Step-by-step explanation:
y=7.72(1.04)^t
10=7.72(1.04)^t
1.04^t=1.2953367875647668
log 1.04^t=log 1.2953367875647668
t log 1.04=log 1.2953367875647668
t=6.5978 years .............
Im confusion? Could someone help me out.
Answers
Answer:
20cm
Step-by-step explanation:
for the triangle:
Perimeter = 30cm
a + a + a = 30
3a = 30
hence a = 10cm
For the rectangle:
Perimeter = 30cm
a + a + b + b = 30
but a = 10cm
10 + 10 + b + b = 30
20 + 2b = 30
2b = 10
hence b = 5cm
Perimeter of square = b + b + b + b
= 5 + 5 + 5 + 5 = 20cm
The sum of three consecutive numbers is 72 what is the smallest of the numbers
Answers
Answer:
23
Step-by-step explanation:
Suppose,
the first number = x
the second number = x+1
the third number = x+1+1 = x+2
Question wise,
x+x+1+x+2 = 72
3x+3 = 72
3x = 72-3 = 69
x = 69/3 = 23
so the numbers are,
23,(23+1)=24 and (23+2)=25
4
5 6 7 8 9 10
11
12 13
The sum of three numbers is 56. If the second number is equal to the first diminished by 4, and the third number is 3
times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
x = 3x-4
56=4x4
56=3x-4
56-5x4
a
OX
e here to search
Answers
Answer:
56-5x4
Step-by-step explanation:
The reason you want to do it that way is because they will cansle eatch other out
Identify the initial amount and the growth rate of the following:
Y = 250 (1+0.2)
Answers
Answer:
y = 300
Step-by-step explanation:
y = 250 (1+0.2)
First add the 1 and 0.2
y=250(1.2)
multiply 250 with 1.2
y = 300
:)
What is the rate of change (slope) of the function?
X
y
-2
+1
-1
+2
+3
1
+4
2
+5
02
Answers
Answer:1
Step-by-step explanation:
what is the area of a shaded region in the quarter circle
radius 12
Answers
Answer:
I guess that the shaded area is a quarter of a circle of radius 12 units.
Is easy to know that the area, will be equal to the quotient between the area of a circle of radius 12, and 4
We know that the area of a circle of radius R is:
A = pi*R^2
in this case, R = 12
pi = 3.14
Then:
A = 3.14*12^2 = 452.16
And a fourth of that is:
A/4 = (452.16)/4 = 113.04
The area of the shaded region is 113.04 square units
Which statement describes the graph of function g?
f(x) = 2x
g(x) = 2x + 3
The graph of g is 3 units to the left of the graph of f.
The graph of g is 3 units below the graph of f.
The graph of g is 3 units above the graph of f.
The graph of g is 3 units to the right of the graph of f.
Answers
9514 1404 393
Answer:
The graph of g is 3 units above the graph of f.
Step-by-step explanation:
Adding 3 to each y-value shifts the graph up 3 units.
__
In the case of the straight line given here, it also has the appearance of shifting the graph left. The left-shift, however, is not 3 units. The amount of apparent horizontal shift will depend on the slope of the original line.
Answer:
The answer is above
Step-by-step explanation:
its above because the sign is positive
find the amount on #45,000 in 3 years at 10% per annum and also find the compound interest
Answers
Answer:
Amt. = 45000 ( 1+ 10/100 ) ^3
Interest = 45000 - Amt.
Step-by-step explanation:
Hope this helped have an amazing day!
The equation modeling the population growth of a small town is P(t)=30000(1.02)^t, where P represents the population, and t represents the years from now. What is the approximate population change that occurs between 2 years from now and 10 years from now.
Answers
Answer:
5358
Step-by-step explanation:
The equation modeling the population growth of a small town is given as:
P(t)=30000(1.02)^t
When t = 2
P(2) = 30000(1.02)^2
P(2) = 31212
When t = 10
P(10) = 30000(1.02)^10
P(10) = 36569.8326
The approximate population change that occurs between 2 years from now and 10 years from now is calculated as:
= P(10) - P(2)
= 36569.83259984272 − 31212
= 5357.8325998
Approximately ≈ 5358
What is the value of b? 10 ( 1 + 3b ) = -20
Answers
Answer:
b=-1
Step-by-step explanation:
10(1+3b)=-20
1+3b=-2
3b=-3
b=-1
For question b, how is the answer is ㏒ₐ2 + 4(n-1)㏒ₐ3?
Please help me.
Answers
Answer:
[tex]T_n=(4-n)\text{log}_a(3)+\text{log}_a(2)[/tex]
Step-by-step explanation:
nth term of an A.P. is given by the explicit formula,
[tex]T_n=a+(n-1)d[/tex]
Here, 'a' = First term
n = number of term
d = common difference
For an A.P. given as,
[tex]\text{log}_a(54),\text{log}_a(18),\text{log}_a(6),....[/tex]
First term 'a' of the given A.P. = [tex]\text{log}_a(54),[/tex]
Common difference 'd' = [tex]T_2-T_1[/tex]
= [tex]\text{log}_a(18)-\text{log}_a(54)[/tex]
= [tex]\text{log}_a(\frac{18}{54})[/tex]
= [tex]\text{log}_a(\frac{1}{3})[/tex]
= [tex]-\text{log}_a(3)[/tex]
[tex]T_n=\text{log}_a(54)+(n-1)[-\text{log}_a(3)][/tex]
[tex]=\text{log}_a(54)-(n-1)\text{log}_a(3)[/tex]
[tex]=\text{log}_a(3^3\times 2)-(n-1)\text{log}_a(3)[/tex]
[tex]=\text{log}_a(3^3)+\text{log}_a(2)-(n-1)\text{log}_a(3)[/tex]
[tex]=3\text{log}_a(3)+\text{log}_a(2)-(n-1)\text{log}_a(3)[/tex]
[tex]=3\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)+\text{log}_a(3)[/tex]
[tex]=4\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)[/tex]
[tex]=(4-n)\text{log}_a(3)+\text{log}_a(2)[/tex]
in order to receive a b on an essay, the grade must be no lower then 82% and no higher than an 89%.write a compound inequality to represent the range of scores to earn a B on the essay
Answers
Answer:
0.82 ≤ x ≤ 0.89
Step-by-step explanation:
hope this helps, pls mark brainliest :D
In some languages, every consonant must be followed by a vowel. How many seven-letter ‟words” can be made from the Hawaiian word MAKAALA if each consonant must be followed by a vowel?
Answers
Answer:
One. Kamala.
Step-by-step explanation:
please help will give brainliest
Answers
Answer:
a² = 144
b² = 25
c² = 169
c = 13
Step-by-step explanation:
• a² = 12×12
= 144
• b² = 5×5
= 25
• a² + b² = c²
= 144 + 25 = 169
• c = _/169
= 13
I
4)
73,693 I’m lookin to round the number
Answers
Answer:
Which place are you rounding with?
If your rounding with ones then the answer will be 73,690
If your rounding with tens then the answer will be 73,700
If your rounding with hundreds then the answer will be 73,600
If your rounding with thousands then the answer will be 74,000
There you go and your welcome!
PLssssss HELPPPPPPP will GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Mr. Mayhood had 4½ pounds of sand in a bucket. He put 2¾ pounds
of sand around his flower bed. How much sand did he have left in the
bucket?
Answers
Answer:
For addition 7 1/4. For subtraction 1 3/4. For multiplication 12 2/8. For division 1 7/11.
Step-by-step explanation:
Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 4 laps on a running trail and then runs 8 more miles. On Tuesday and Sunday, she runs 6 laps on the trail and then runs 4 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?
Lilliana runs ??? laps on Saturday.
Answers
Answer: 17 3/4
Step-by-step explanation: because yes
Answer:
Actualy 17 3/4 is incorrect ( she actualy ran 8 laps on saturday)
Step-by-step explanation:
I dont feel like typeing out my math but i am correct because I had this same question on my homework.
At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?
Answers
Answer:
37.5%
Step-by-step explanation:
OOF DIS COMPLICATED
I messed up big timeeeeeeeee
A lot of percent problem are very simple by just assuming values, especially in case the answer is also a percentage.
If there are 100 birds, 20% are tagged so 20 are tagged.
Out of the rest 80, 30 should be tagged so that a total of 50% are tagged.
30/80 = 37.5%
(The huge number given is unnecessary, just to make you waste your valuable time. Read the question again to realize that it is not needed.)
The percent of the untagged birds that must be tagged so that half of all birds in the refuge are tagged is 37.5%.
Untagged birds percentage:First step
Currently Tagged birds= 54210 ×20/100
Currently Tagged birds=10842
Second step
Untagged birds=54210 - 10842
Untagged birds=43368
Third step
Untagged birds percentage:
Untagged birds percentage=( 54210/2)-10842/43368
Untagged birds percentage=(27105-10842)/43368
Untagged birds percentage=16263/43368
Untagged birds percentage=0.375×100
Untagged birds percentage=37.5%
Inconclusion the percent of the untagged birds that must be tagged so that half of all birds in the refuge are tagged is 37.5%.
Learn more about percentage here:https://brainly.com/question/24304697
I WILL GIVE BRAINLIEST. HURRY PLEASE
Answers
Answer:
Concept: Linear Algebra
Let us pick -5 and -4 which are one unit apart.We will find the difference by finding the slope: -3-(-11)/-4-(-5)= 8 Next for 2 units apart we will choose 1 and 3We do the same thing: 53-37/3-1= 16/2=8 Next we will pick something 2 units apart. Let's pick 0 and 3 Hence we will do the same: 53-29/3-0= 24/3=8No matter what difference we pick, whether that be one, two or three units, the difference is the same and consistent.Rate brainlist and drop a followWhat is the value of u? 6.4u−5.1u=−3.25
Answers
Answer:
-2.5
Step-by-step explanation:
6.4u-5.1u=-3.25
1.3u=-3.25
u=-3.25/1.3
u=-2.5