Answers
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
[tex]\sqrt{x+6} =x-6\\[/tex]
square both sides:
[tex]\implies x+6=(x-6)^2[/tex]
Expand brackets:
[tex]\implies x+6=x^2-12x+36[/tex]
Collect and combine like terms:
[tex]\implies x^2-13x+30=0[/tex]
[tex]\implies (x-10)(x-3)=0[/tex]
[tex]\implies x=10, x=3[/tex]
Substitute values back into original equation:
[tex]x=10: \sqrt{10+6} =10-6 \implies 4 = 4 \ \ \checkmark[/tex]
[tex]x=3: \sqrt{3+6} =3-6 \implies 3 = -3 \ \ \textsf{incorrect!}[/tex]
Therefore, [tex]x=10[/tex] only
[tex]\\ \tt\rightarrowtail \sqrt{x+6}=x-6[/tex]
[tex]\\ \tt\rightarrowtail x+6=(x-6)^2[/tex]
[tex]\\ \tt\rightarrowtail x+6=x^2-12x+36[/tex]
[tex]\\ \tt\rightarrowtail x^2-13x+30=0[/tex]
[tex]\\ \tt\rightarrowtail x^2-10x-3x+30=0[/tex]
[tex]\\ \tt\rightarrowtail (x-3)(x-10)=0[/tex]
[tex]\\ \tt\rightarrowtail x=3,10[/tex]
Related Questions
WILL GIVE BRAINLIEST AND 15 POINTS!
Answers
Answer:
Rational
Step-by-step explanation:
[tex]\sqrt[3]{125}[/tex] is also equivalent to 5
The definition of a rational number is any whole number, fraction, or decimal that ends or repeats, while an irrational number is any number that cannot be turned into a fraction.
5 is a whole number, and therefore, is a rational number.
Answer:
rational
hope it helps you
HELPPPPPPPPPPPPHHHHHHH
Answers
Answer:
26.3
Step-by-step explanation:
Mackenzie is about to ride a straight water slide. The length of the water slide itself is 15
meters. The splash pool at the end of the slide is 12 meters away from the base of the tower
that leads up to the launching platform. How high is the launching platform?
meters
Answers
Answer:
9
Step-by-step explanation:
Use Pythagoras’ theorem;
the hypotenuse is 15:
one side that isn't hypotenuse is 12:
[tex]a^2 +12^2=15^2\\= a=225-144\\a=81\\\sqrt{81}=9[/tex]
Did you hear about the newspaper editor?
Answers
Answer:
Yes, I've heard about the newspaper editor
Today is saturday what day will it 21 day later
Answers
Answer:
thise day is
Tuesday
February 17 2022
Saturday
Find the area and the circumference of a circle with radius 3 cm.
Write your answers in terms of it, and be sure to include the correct units in your answers.
Answers
1. Observe problem
Solve for the area and Circumference of a circle who's radius is 3 cm
Area for circle formula:
pi*r^2=
9pi
I simplicity is needed, 9 pi is around
28.2743338823cm^2
Circumference for circle formula: 2*pi*r
which is
6pi
if simplicity is again needed, its around
18.8495559215cm
SOMEONE HELP RIGHT NOW!! 50pts!!! NEED CORRECT ANSWER AND WORK/PROOF!!!
(SAT Prep) Find the value of x
Answers
Answer:
x=70°
Step-by-step explanation:
y=350° (angle inside triangle equal to 35°)
x=180-y-(180-105)
x=70°
Hope it helps!
Solution:
We can see that two lines are parallel, intersecting a line. We can also see a triangle formed with the lines.
=> x + (180 - 105) + 35 = 180 [The '35' came from Alternate inner angles]=> x + 75 + 35 = 180=> x + 110 = 180=> x = 180 - 110=> x = 70The measure of x is 70°.
if x varies direcly as y and x=9 when y=3 find x when y=12
Answers
Answer:
36
Step-by-step explanation:
x = 9 and y = 3
3 times 3 equal 9 so if y is 12 then 12 x 3 = 36
Find the x - and y -intercepts of the graph of the linear equation -4x+8y=-16 .
The x -intercept is
.
The y -intercept is
.
Answers
Answer:
x -intercept is 4
y -intercept is -2
Step-by-step explanation:
SOLUTION:
(x -intercept)
-4x+8y= -16
-4x+8×0= -16
-4x+0= -16
-4x/-4 = -16/-4 (divide both sides by -4)
x=4
______________________
(y -intercept)
-4x+8y= -16
-4×0+8y= -16
0+8y= -16
8y/8 = -16/8 (divide both sides by 8)
y= -2
•| HOPE IT HELPS |•
Evaluate the following
2/3 + 11/3 – 1/3
Answers
Answer:
12/3 which is =4
Step-by-step explanation:
for adding fractions you keep the denominator the same and just add or subtract the numerators
2+11-1=12
How much is 2 quarters, 3 dimes, 3 nickels, and 5 pennies
Answers
Dimes = 30
Nickels = 15
Pennies = 5
Add them all together
50 + 30 + 15 + 5 = $1
I’ve dollar
2 quarters, 3 dimes, 3 nickels, and 5 pennies equals
What are Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object
1 dollar = 4 quarters
1 dollar = 10 dimes
1 dollar = 20 nickels
1 dollar = 100 pennies
We have to calculate the total dollar measurement of 2 quarters, 3 dimes, 3 nickels, and 5 pennies.
4 quarters = 1 dollar
2 quarters = 2/4 dollars
= 0.5 dollars
10 dimes = 1 dollar
3 dimes = 3/10 dollar
= 0.3 dollar
20 nickels = 1 dollar
3 nickels = 3/20 dollar
= 0.15 dollar
100 pennies = 1 dollar
5 pennies = 5/100 dollar
= 0.05 dollar
Total currency value = 0.5 dollars + 0.3 dollar + 0.15 dollar + 0.05 dollar
= 1 dollar
Hence the total worth of coins given is 1 dollar.
Learn more about Currency Units here :
https://brainly.com/question/28440750
#SPJ2
Which expression is equivalent to 3m + 2m + m?
Answers
Answer:
6m
Step-by-step explanation:
Combining like terms, we have
3m + 2m + m = (3 + 2 + 1)m = 6m.
why me lol? - whats 1+1
Answers
Answer:2
Step-by-step explanation:So the tides connection so therefore the magnetically magnetic magnitude yeah
What is the volume of this sphere?
Use a ~ 3.14 and round your answer to the nearest hundredth.
18 in
Answers
Answer:
3052. 08
Step-by-step explanation:
volume = 4/3πr^3
= 4/3π*(9)^3= 3052.08 in^3
Really confused as to what I need to do. I tried to solve for Y and got 69 but that didn't work. Am I supposed to use a^2 + b^2= c^2? How do I do that when there are multiply letters? I really feel like there's just something I'm not seeing. Help is really appreciated, and please explain your answer.
Answers
Answer:
t = [tex]\sqrt{63} \\[/tex] or 7.94
Step-by-step explanation:
Yes, you have to use the Pythagorean theorem
A^2+B^2=C^2
So, A=9, B=t, C=12
9^2+t^2=12^2
81+t^2=144
-81 -81
t^2 = 63
t = [tex]\sqrt{63} \\[/tex]
in decimal 7.94
Hope this helps :)
pls give brainliest
Male mosquitos have pretty short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 888 days and a standard deviation of 666 days. A biologist collects a random sample of 505050 of these male mosquitos and observes them to calculate the sample mean lifespan. We can assume that the mosquitos in each sample are independent.
What will be the shape of the sampling distribution of the sample mean lifespan?
Answers
Answer:
Approximately Normal
Step-by-step explanation:
The sample size is large (n50≥30n), so the sampling distribution of the sample mean will be approximately normal even though the population is skewed.
How do I find the product of (10−11i) and its conjugate?
Answers
Step-by-step explanation:
Given - 10 - 11i
1st requirement - conjugate
Z = X + Yi
Change the sign between x & yi to find the conjugate of a complex
number.
Z = 10 + 11i
Now multiply the conjugate & the 1st complex number
=10-11i × 10+11i
= (10 × 10)+ (10× 11i)+ (-11i × 10) + (-11i × 11i)
Recall that i = √-1
= 100 + 110i - 110i + (-(-(11 × 11))...since √-1 × √-1 = -1.
= 100 + 121
= 221.
I need to determine the figure is a parallelogram using the slope formula
Answers
Answer:
KL // MN & KN // LM
Step-by-step explanation:
One property of parallelogram is every two opposite sides are parallel to each other and if a two lines (sides) are parallel so they must have the same slope.
In the parallelogram KLMN:
using the slope formula = y2-y1/x2-x1
plug the numbers: KL // MN & KN // LM so KLMN is a parallelogram
If 600 people submitted the survey above, how many were in the 21-30 year old group? A) 112 B) 122 C) 132 D) 142
Answers
The survey is an illustration of expected value
132 people in the survey were in the 21 - 30 year old group
How to determine the number of people in the groupFrom the complete question, 22% of people are in the 21 - 30 year old group
Given that 600 people were surveyed.
The number of people in the 21 - 30 year old group would be:
n = 22% * 600
This gives
n = 132
Hence, 132 people in the survey were in the 21 - 30 year old group
Read more about expected values at:
https://brainly.com/question/15858152
need math help asap!
Answers
Answer:
B. 9Step-by-step explanation:
According to intersecting secants theorem we have:
3*(x + 3) = 4*(4 + 5)3(x + 3) = 36x + 3 = 12x = 9Correct choice is B
Answer:
the only thing that cause I understand that cause disinfect your day going so far today at saka embroidery hoop earrings for the day and shadingBrainliest if correct
Answers
9y-18 9y-18 9y-18
9y-18 9y-18 9y-18
Suzie is going to run for 32 minutes. She can run 1 mile in 5 minutes and she cools off for 7
minutes. How many miles can she run in her time limit?
Answers
Answer:
She can run 3 miles in her time limit.
Step-by-step explanation:
Suzie is going to run for 32 minutes. She run 1 mile in 5 minutes and she cools off for 7 minutes
5+7=12 minutes
she runs 1 mile needs 12 minutes total
32÷12=2⋯8
8-5=3 minutes
2+1=3 3×1=3 miles
She can run 3 miles in her time limit.
{Distance=Time × speed}
Dividends for common stock must be in cash
Answers
Answer:
Legally, corporations must have a credit balance in Retained Earnings in order to declare a dividend. Practically, a corporation must also have a cash balance large enough to pay the dividend and still meet upcoming needs, such as asset growth and payments on existing liabilities.
simplify (3x^2-y)^2. please
Answers
Hope it helped
The most likely sum that can occur when the two dice are rolled is
:: 4
:: 7
:: 10
:: 12
Answers
Answer:
7
Step-by-step explanation:
7 is the most common roll with two six-sided dice.
Incorrect
Question 5
0/1 pt
Perimeter of PQRS = 228. Solve for x and PS.
S
4x + 1
R
>
2x - 3
р
T 4
Q
X= 58/3
PS = 107/3
Answers
Answer:
x = 56/3
PS = 103/3
Step-by-step explanation:
Perimeter: (4x + 1) + 2(2x - 3) + (4 + 4 + 4x + 1) = 228
Collect and combine like terms: 12x + 4 = 228
Subtract 4 from both sides: 12x = 224
Divide both sides by 12: x = 56/3
PS = (2 x 56/3) - 3 = 103/3
A half-ton pickup truck has a curb weight (weight empty but ready-to-drive) of 5/2 ton. If curb weight is evenly divided among four truck tires, how much weight is each tire bearing?
NO LINKS!!!
Answers
Answer:
0.625 tons or 5/8 tons
Step-by-step explanation:
(5/2)/4
0.625 tons or 5/8
Answer:
5/8 ton
Step-by-step explanation:
1/4 of 5/2 ton is on each tire, so the weight it is bearing is ...
(1/4)(5/2 ton) = 5/8 ton
Each tire is bearing 5/8 ton.
_____
Additional comment
If that is a US short ton (2000 lb), then the weight on each tire is 1250 pounds. If the tires are inflated to 50 pounds per square inch, then the area of rubber on the road at each tire is 1250 lb/(50 lb/in^2) = 25 in^2. That's the size of a 5-inch square.
cassidy had 8 7/10 inches of string. she used 5 3/8 inches of string
Answers
Answer:
Cassidy has 4 in of string left.
Step-by-step explanation:
I hope it helps! Have a great day!
Lilac~
Answer:
Step-by-step explanation:
4 inches
PLZZZZZZZZZZZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
Your first step is to figure out which variable you want to cancel out.
Luckily, all these problems have x or y already set up to eliminate.
You can find these variables because they are opposite signs of each other, such as -x and x
Add the y's together and the #'s on the other side together, then solve to find the 2nd variable. Once you find one, you can plug that answer into the easier of the two equations and solve for the other variable.
2(x+5) = [ ]x + [ ] what is the answer
Answers
Answer:
2x + 10
Step-by-step explanation:
2(x+5)
(2)(x) + (2)(5)
2x + 10
Answer:
2x + 10
Step-by-step explanation:
2 × X= 2x
2×5=10
so it is 2x + 10