Answers
Answer:
x = 8, x = 10
Step-by-step explanation:
[tex]\sqrt{4x - 31}[/tex] = x - 7 ( square both sides )
4x - 31 = (x - 7)² ← expand using FOIL
4x - 31 = x² - 14x + 49 ( sub 4x - 31 from both sides )
0 = x² - 18x + 80 ← in standard form
0 = (x - 8)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 8
left side = [tex]\sqrt{4(8)-31 }[/tex] = [tex]\sqrt{32-31}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 8 - 7 = 1
Then x = 8 is a solution
x = 10
left side = [tex]\sqrt{4(10)-31}[/tex] = [tex]\sqrt{40-31}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 10 - 7 = 3
Then x = 10 is a solution
Related Questions
How many integers between 50 000 and 60 000 are squares of integers?
Answers
Perfect squares are the squares of integers
There are 990 integers between 50000 and 60000 that are squares of integers
There are 1000 perfect squares, and 100 perfect cubes between 1 and 1000000
This is because:
[tex]\mathbf{100000 = 1000^2 = 100^3}[/tex]
Rewrite as:
[tex]\mathbf{100000 = x^2 = y^3}[/tex]
Where x lies between 1 and 1000, and y lies between 1 and 100.
If y^3 is a perfect square, then y is a perfect square
List out the perfect squares from 1 to 1000
[tex]\mathbf{y = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}[/tex]
Take the cube of these numbers
[tex]\mathbf{y^3 = 1^3, 4^3, 9^3, 16^3, 25^3, 36^3, 49^3, 64^3, 81^3, 100^3}[/tex]
[tex]\mathbf{y^3 = 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000}[/tex]
So, the count of numbers that are perfect squares and perfect cubes between 1 and 1000000 is 10.
The count of integers between 50000 and 60000 that are squares of integers is:
[tex]\mathbf{n = x -10}[/tex]
Substitute 1000 for x
[tex]\mathbf{n = 1000 -10}[/tex]
[tex]\mathbf{n = 990}[/tex]
Hence, there are 990 integers between 50000 and 60000 that are squares of integers
Read more about perfect squares at:
https://brainly.com/question/13521012
I need help with number 5 please
Answers
Answer:
-4[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I hope this helps!
is 0.667 elastic or inelastic?
Answers
Answer:
inelastic is the answer
keep safe
whats the answer can someone answer please
Answers
Answer:
21. 2x + 28
22. 18a - 17b
23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.
24. 8.8888888888889 × 10^{0}
Step-by-step explanation:
PLEASE HELP WITH THIS ONE QUESTION
Answers
Answer:
g(x) = x(x-2)^2(x-3) -3
Step-by-step explanation:
the translation from f(x) to g(x) is right 1 down 3.
vertical translations are easier since you just add the amount to everything. so we have f(x) - 3 = (x-1)^2(x-2)(x+1) -3.
for the horizontal translation, we make every x into x-1, so now we have (x-1-1)^2 (x-1-2) (x-1+1) - 3 or (x-2)^2(x-3)x -3
looking at the answers it is g(x) = x(x-2)^2(x-3) -3
Riley would like to buy a house that is selling for $330,000. The loan requires a 20% down payment. He currently has $5,300 saved, how much more money does Riley need to save for the down payment?
Answers
Answer: 1060
Step-by-step explanation:
164 people need to ride the elevator to the top of a skyscraper. The elevator can hold 7 people at a time. How many people will be in the elevator on the last trip to the top?
Answers
Answer:
3
Step-by-step explanation:
we know that 23x7=161
so there will be 3 people on the last trip to the top
Here's Robert's spending diary for one week. It may not look like he's spending much. Use a calculator to add up Robert's total spending for the week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday Lunch $7.00 Shampoo $6.00 Lunch $7.00 Jacket $40.00 Lunch $7.00 Breakfast $4.50 Coffee $2.00 Bus $3.00 CD $14.00 Lunch $7.00 Lunch $7.00 Movie $12.00 Haircut $40.00 Total: $21.00 $13.00 $10.00 $47.00 $19.00 $44.50 $2.00 How much does Robert spend on lunch in a week, in a year? If Robert continues to buy his lunch every weekday, he will be spending /week. S weeks in a year = $ spent during the year.
Answers
If a shirt cost $60 is on sale for 50% off and you have another offer that gives you an additional 20% off the sale price does that mean you get a total of 70% off show your work to justify your answer
Answers
Answer:
No
Step-by-step explanation:
50 % off $60 =$30
20% off $30 =$6
But 70% =42
Therefore it's not the same as 70%
7433654 round to the nearest thousand
Answers
Answer:
Already rounded to the nearest thousandth.
7433654.000
There were 96 iPads at Fun Elementary. A company donated some iPads and the school purchased 300 more iPads. Now there are 865 iPads. How many iPads were donated to Fun Elementary?
Answers
Answer:
469 iPads were donated.
Step-by-step explanation:
The school purchased 396 iPads in total: 300+96
Now, you subtract how many the school purchased from the total amount of iPads to see how many iPads were donated: 865-396 = 469
Solve this problem and show the steps with check steps confirming answer is correct.
4x-7=2x+15
Answers
Answer: X=11
Step-by-step explanation:
Add 7 to both sides of the equation 4x-7=2x+15
4x-7+7=2x+15+7
Simplify
Add the numbers :4x -7 + 7 = 2 x + 15 + 7
Add the numbers:4 x = 2x + 15+7
down
4x=2x+22
Subtract
2 2 x 2 x from both sides of the equation
4 x = 2x +22 4x - 2x = 2x +22- 2x
Simplify
2x = 2x +22-2x
Divide both sides of the equation by the same term
2x = 22 2x/ = 22/2 x =22/2x =22/2 x=11
A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior citizens. Create a function f(x) which models the amount, in dollars, a senior citizen would pay for x pounds of bananas on a Wednesday.
Answers
Answer:
f(x)= 0.90(0.59x)
Step-by-step explanation:
The 10% discount will make it so the senior citizens will pay 90% of the price. 90%=0.90
Also we need to know that 0.59x means how much money per pound the bananas cost.
So when you put it together, you should get f(x)=0.90(0.59x)
2 1/4 x 3 1/5 i need help
Answers
Answer:
7 1/5
Step-by-step explanation:
2 1/4 * 3 1/5
Change to improper fractions
2 1/4 = (4*2+1)/4 = 9/4
3 1/5 = (5*3+1)/5 = 16/5
9/4 * 16/5
Rewriting
9/5 * 16/4
9/5 * 4/1
36/5
Change back to a mixed number
7 1/5
General Instructions: Solve the following problems. Write your answers on the space provided.
Find the area under the standard normal curve that lies between the following: (3 pts each)
z=0 and z=2 __________________________
z=0 and z=3 __________________________
z=-3 and z=3 __________________________
z=0 and z=1.70 __________________________
Find the AREA under the standard normal curve: (4 pts each)
to the left of z=-0.40 __________________________
for z<0.40 __________________________
to the right of z=1.65 __________________________
Given the graph below, find the following:
the degree of each vertex (11 points)
Is there an Euler Trail? If there is, give 1 example. (1 point)
Is there a Hamiltonian Path? If there is, give an example. (3 points)
Answers
Answer:
Step-by-step explanation:
HELP!! DUE IN 10 MINS!!!
Solve the following system using the elimination method.
x+y=12
x−y=12
Answers
Answer:
x = 12
y = 0
Step-by-step explanation:
Sum them:
2x = 24
so x = 12
12 - y = 12
so y = 0
if AB=12 cm and BC =13 cm then AC = 25 cm
Answers
Answer:
AB=12
Hope this helps!
Use the distributive property to write an expression equivalent to 7(48).
Drag and drop the appropriate number into each box.
Answers
Answer:
336
Step-by-step explanation:
7x48=
7(8)= 56
7(4)+5= 33
7(48) = 336
Answer:
336
Step-by-step explanation:
Which of the following correctly factors the expression −20x+4y−2?
A
4(−5x+4y+2)
B
2(−10x+2y−1)
C
−2(10x+2y+1)
D
−20(x−4y+2)
Answers
9514 1404 393
Answer:
B 2(−10x+2y−1)
Step-by-step explanation:
The greatest common factor is 2. Factoring that out gives the factorization shown in choice B.
2(-10x +2y -1)
__
You could factor out -2. Doing that would give ...
-2(10x -2y +1) . . . . . . . doesn't match choice C
Eduardo's teacher made the table shown here His teacher asked him to identify the missing value in the table Eduardo's answer was correct Which statement describes Eduardo's answer? A Eduardo s answer as 8. He added 6-2 Eduardo s answer was 12 He subtracted 2 from 14 Eduardo's answer was 10 He multiplied the number of cats by 2 Eduardo's answer was 15. He multiplied the number of cats by 3. USATestprep, LLC 2021, All Rights Reserved. Read Our Blog Privacy Policy PHONE 1 - 877 - 377- 9537 I FA
Answers
Answer:
Your Answer is C!
Step-by-step explanation:
2x2 = 4
3x2 = 6
5x2 = 10
7x2 = 14
In the figure, a || b || c. Find the value of m<1 + m<2 + m<3 + m<4 + m<5.
(A). 360°
(B). 180°
(C). 270°
(D). Cannot be determined
Answers
Answer:
The answer is D cannot be determined
Step-by-step explanation:
this is because you don't have enough information
© Write
[tex] \sqrt{8} [/tex]
power of 2
Answers
Answer:
2³
Step-by-step explanation:
2×2×2=8
so √8 = 2³
Hope this helps you
which of the following is a number where the digit 2 represents 1/10 the value of the digit 2 in the number 1,947.5286
Answers
Answer:
0.002
Step-by-step explanation:
the digit "2" in this equation represents 0.02 or also 2/100
1/10 of 2/100 would be like multiplying 1/10 and 2/100 and that would get us 2/1000
2/1000 is also 0.002
0.002 is the value of the digit 2 in the number 1,947.5286.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here we have,
the number 1,947.5286.
the digit "2" in this equation represents 0.02 or also 2/100
1/10 of 2/100 would be like multiplying 1/10 and 2/100
and that would get us 2/1000
i.e.
2/1000 is also 0.002
Hence, 0.002 is the value of the digit 2 in the number 1,947.5286.
To learn more on number click:
brainly.com/question/17429689
#SPJ2
Thanksgiving Meal Challenge
Considering the final price of the meal, would you rather have a $25 gift
card to apply toward to total price or a 35% off coupon? Show your work
and explain.
Answers
If the price of the meal is less than $71, then the $25 gift card would be better than the 35% off coupon.
Let y represent the price of the meal.
For a $25 gift card to be applied, the final price is:
Final price = y - 25
For a 35% off coupon, the final price is:
Final price = y - 0.35y = 0.65y
y - 25 < 0.65y
0.35y < 25
y < 71.42
If the price of the meal is less than $71, then the $25 gift card would be better than the 35% off coupon.
Find out more at: https://brainly.com/question/25285332
PLZZZZ HELP BRAINLYEST AND 100 POINTS
Identify the number of real and imaginary solutions for: f(x)=x4+3x3+2x−6
(Write answer as a number, not a word)
Imaginary=
real=
Answers
Answer:
2 imaginary; 2 real
You can factor it as ...
f(x) = (x^2 -16)(x^2 +1) . . . . . . . . . x^2-16 is the difference of squares
= (x -4)(x +4)(x^2 +1)
The two linear factors have real zeros; the quadratic factor has two imaginary zeros. There are 2 imaginary and 2 real zeros.
Step-by-step explanation:
Hope this helps:)
Suppose A and B are mutually exclusive events, and that P(B)=0.24 and P(A OR B)=0.27. Find P(A).
Answers
Step-by-step explanation:
(4 - x)(x - 4) = 16 - x2 help me please sir please help me please sir fasthelp me please sir please help mehelp me please sir please help mehelp me please sir please help mehelp me please sir please help me
Answer:
Step-by-step explanation:
this equals 0.03
What is the quotient of -9 Divided by 3 ?
Answers
-9 divided by 3
Is -3
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\large\text{\bf Guide to remember}\downarrow\\\large\textsf{2 negatives = positive}\\\large\textsf{1 negative \& 1 positive = negative}\\\large\textsf{2 positives = positve}\\\large\textsf{1 positive \& 1 negative = negative}[/tex]
[tex]\large\text{This means your answer will most likely be a \boxed{\text{negative}} because}\\\large\text{you have a negative number (-9) \& a positive number (3).}[/tex]
[tex]\large\boxed{\mathsf{-9 \div 3}}\\\large\boxed{\mathsf{= \dfrac{-9}{3}}}\\\large\boxed{\mathsf{= \dfrac{-9\div3}{3\div3}}}\\\large\boxed{\mathsf{= \dfrac{-3}{1}}}\\\large\boxed{\mathsf{= -3\div 1}}\\\large\boxed{\mathsf{= -3}}\\\\\\\\\\\huge\boxed{\text{Therefore. your answer is: \boxed{\textsf 3}}}\huge\checkmark[/tex]
[tex]\huge\text{\bf Good luck on your assignment \&}\\\huge\text{\bf enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]pls help fastttttttttttttttttttttttttt
Answers
Answer:
y = 5 x + 7
Step-by-step explanation:
work out the value of 35-3×9
you must remember to do the bidmas or bodmas in those type of question
First you must try to do multiplie this question 3×9 = 27
than subtract
35-27 =8
8 is final answer
Answers
Answer:
8
Step-by-step explanation:
35-3×9=35-27
=8
Hope this helps!!!
2 dived by 49 with a remainder
Answers
Answer:
The answer is 24 with remainder of 1
Step-by-step explanation:
First, solve the problem by seeing what number gives you 4 when multiplied by 2. That would be 2 (2x2=4)
you subtract 4 by 4 to get zero and bring down the nine
Then you see which number would get you close to nine without overlapping when multiplied by two. That would be 4 (2x4=8)
your answer would be 24 then you subtract 9 by 8 to get a remainder of 1