Find one value of x that is a solution to the equation:
(x^2– 8)^2 + x^2 – 8 = 20
x=
Answer:
x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
Step-by-step explanation:
Solve for x:
-8 + x^2 + (x^2 - 8)^2 = 20
Expand out terms of the left hand side:
x^4 - 15 x^2 + 56 = 20
Subtract 20 from both sides:
x^4 - 15 x^2 + 36 = 0
Substitute y = x^2:
y^2 - 15 y + 36 = 0
The left hand side factors into a product with two terms:
(y - 12) (y - 3) = 0
Split into two equations:
y - 12 = 0 or y - 3 = 0
Add 12 to both sides:
y = 12 or y - 3 = 0
Substitute back for y = x^2:
x^2 = 12 or y - 3 = 0
Take the square root of both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0
Add 3 to both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3
Substitute back for y = x^2:
x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3
Take the square root of both sides:
Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
The possible values of x that satisfy the equation are
x = ±√3 and x = ±2√3.
Here, we have,
To find a value of x that is a solution to the equation, we need to solve the equation for x.
Let's go through the steps:
Start with the given equation:
(x² - 8)² + x² - 8 = 20
Expand the squared term (x² - 8)²:
(x² - 8)(x² - 8) + x² - 8 = 20
Simplify:
(x⁴ - 16x² + 64) + x² - 8 = 20
Combine like terms:
x⁴ - 16x² + x² + 64 - 8 = 20
Simplify:
x⁴ - 15x² + 56 = 20
Rearrange the equation to bring all terms to one side:
x⁴ - 15x²+ 56 - 20 = 0
Simplify:
x⁴ - 15x² + 36 = 0
Now, we have a quadratic equation in terms of x².
Let's substitute y = x² to simplify further:
y² - 15y + 36 = 0
Solve the quadratic equation for y:
(y - 3)(y - 12) = 0
This gives us two possible values for y:
y - 3 = 0 --> y = 3
y - 12 = 0 --> y = 12
Substitute back y = x²:
For y = 3:
x² = 3 --> x = ±√3
For y = 12:
x² = 12 --> x = ±√12 = ±2√3
So, the possible values of x that satisfy the equation are x = ±√3 and x = ±2√3.
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10 points for this answer with an explanation (im in a timed test) What is the solution to the equation represented by the model below? 3 x tiles and 8 positive 1 tiles = 4 x tiles and 6 positive 1 tiles x = negative 14 x = negative 2 x = 2 x = 14
Answer:
2
Step-by-step explanation:
2
Answer:
Step-by-step explanation:
its c
Point P is located at (-5,-1) and point Q is located at (-1,-7).find the slope of line segment PQ.
Point A (x1,y2) = (-1, -7)
Point B (x2,y2) = (-5, -1)
Objective :
Find the slope of a line that passes through points A and B.
Formula :
Slope
[tex] m= \frac{y2-y1}{x2-x1} [/tex]
Solution:
Slope (m) = [tex] \frac{-1-(-7)}{5-(-1)} [/tex]
=6 - 4
m = -1.5
Which of the following describe a simple event?
Answer: B
Step-by-step explanation:
In Miami, the number of highway accidents increased by 20% over a four year period. How many accidents were there in 2013 if there were 5.120 in 2009?
Answer:
Step-by-step explanation:
20/100 * 5,120 = 1024
Number of cases in 2013 = 1024 + 5120 = 6,144 cases
I need help with this please ASAP!!!!
Answer:
c
can i have brainliest?
What is the slope of the line that passes through the points (4, 10) and (1, 10)?
Write your answer in simplest form
Answer:
The slope will be 0
Step-by-step explanation:
Once you do the slope formula which is y2 - y1 over x2-x1
You will get 0/3 in this case. So if the numerator is a 0 the slope will also be 0.
The slope of the a straight line is given by the ratio of the Rise to the Run
of the line. The rise between the given points is zero.
The slope of the line that passes through the points (4, 10) and (1, 10) is zero.
Reason:
The given points are; (4, 10) and (1, 10)
The slope of a line, m, is given by the following formula;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) = (4, 10) and (x₂. y₂) = (1, 10), we get;
[tex]Slope, \, m =\dfrac{10-10}{1-4} = 0[/tex]
The slope of the line that passes through the points (4, 10) and (1, 10) is 0.
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Find the area. Will mark brainliest.
Answer:
13.5 i think
Step-by-step explanation:
You multiply 1/2*base*height which is 1/2*4.5*6.That is equal to 13.5
hope this helps:)
Answer: home / math / area calculator
Area Calculator
Rectangle
Length (l)
Width (w)
Calculate
Triangle
Result
s =
a + b + c
2
=
4.5 + 6 + 7.5
2
= 9 yards
Area = √s(s-a)(s-b)(s-c)
= √9×(9 - 4.5)×(9 - 6)×(9 - 7.5)
= 13.5 yards2
Together Emily and Charlotte have a total of 60 strawberries Emily eats four times the amount that Charlotte eats how many strawberries does Charlotte eat?
Answer:
12
Step-by-step explanation:
If you were asking how many strawberries it would take to finish all 60, this is the answer, otherwise please rephrase the question.
If Charlotte ate 12 strawberries, you would have to do 12 x 4 which would be four times the amount of strawberries Charlotte ate, 12 x 4 = 48, Emily ate 48 strawberries, 48 + 12 = 60.
Charlotte eats 12 strawberries.
Let the amount of strawberries eaten by Charlotte be represented by x.
Since Emily eats four times the amount that Charlotte eats, then Emily will eat:
= (4 × x) = 4x.
Since Emily and Charlotte have a total of 60 strawberries, then this will be:
4x + x = 60
5x = 60
x = 60/5
x = 12
Therefore, Charlotte eats 12 strawberries.
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To calculate the sum ot two vectors using the parallelogram method, where should the blue line be placed?
a. at the vertex between the green and red vectors c. at the tail of ONLY the green vector
b. at the head of the red vector
d. at the head of the green vector
Please select the best answer from the choices provided
0
0
0
0
Answer:
A is the answer to your question.
Answer:
a.
at the vertex between the green and blue vectors
Step-by-step explanation:
priya finds (1.05) x (2.8) by calculating 105 x 28 then moving the decimal point three spaces to the left
Answer:
Yes, That is correct.
Step-by-step explanation:
Example: Multiply 0.05 by 1.1
start with:
0.05 × 1.1
multiply without decimal points:
5 × 11 = 55
0.05 has 2 decimal places,
and 1.1 has 1 decimal place,
so the answer has 3 decimal places:
0.055
Priya's method easy finds the product of decimals because multiplying whole numbers is easier than multiplying decimal numbers.
Given that, Priya finds (1.05) × (2.8) by calculating 105 × 28 and then moving the decimal point three spaces to the left.
We need to explain why Priya's method makes sense.
How to multiply two decimals?To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Now, 105 × 28 = 2,940
Moving the decimal point three spaces to the left, we get 2.940.
Also, (1.05) × (2.8) =2.940
Therefore, Priya's method easy finds the product of decimals, because multiplying whole numbers is easier than multiplying decimal numbers.
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Your question is incomplete, probably the complete question/missing part is:
Priya finds (1.05) × (2.8) by calculating 105 × 28 and then moving the decimal point three spaces to the left. Why does Priya's method make sense?
While shopping at a clearance sale, Samantha finds a $60.00 dress on sale for 25% off. Samantha also has a 50% off coupon
Which statement correctly summarizes her savings?
Samantha will save $45.00 because the two sales will combine for 75% off the original cost.
Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction
Samantha will save $22.50 because she must first find the 25% sale price before taking the extra 50% reduction
Samantha will save $15.00 because the two sales will combine for 75% off the original cost
PLEASE HELP!!!!
Answer:
Samantha will save 45 dollars because the two sales will combine for 75 percent off the orignial cost.
Step-by-step explanation:
50 + 15 equals 75
75 percent off of 60 equals 15 dollars
60-15 equals 45 dollars so she saved 45 dollars.
Answer:
Samantha will save 45 dollars because the two sales will combine for 75 percent off the orignial cost.
Step-by-step explanation:
50 + 15 equals 75
75 percent off of 60 equals 15 dollars
60-15 equals 45 dollars so she saved 45 dollars.
Step-by-step explanation:
14 is 12 1/2% of what number?
Answer:
112
Step-by-step explanation:
The price of a car is £15400 before it is reduced by 8%.
How much does it cost after the reduction?
Answer:
14168
Step-by-step explanation:
15400 / 100 x 8 = 1232
1232 = 8%
15400 - 1232 = 14168
Please answer ASAP!
The isosceles trapezoid is part of an isosceles triangle with a 34 degree vertex angle. What is the measure of an acute base angle of the trapezoid? What is the measure of an obtuse base angle?
Please show your work!
Answer:
A would assume each side is 73 degrees. (not 100% sure)
Step-by-step explanation:
The reason being all triangles angles equal up to 180 so 180-34/2 would each 73 degrees.
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.
P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction
0.211
0.244
0.756
0.944
Answer:
The answer is C.) 0.756
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
just did the test on edge 2020
PLS HELP
The expression
3(x-9) is equivalent to
1.3(x)+9.
2.3(x)+3(9).
3.3(x) – 9.
4.3(x) – 319).
Answer:
the answer is 3(x)- 3(9)
What is the value of (–3 + 3i) + (–2 + 3i)?
–5 – 6i
–5 + 6i
5 + 6i
5 – 6i
Answer:
-5+6i
Step-by-step explanation:
We have given two complex numbers (-3+3i) and (-2+3i)
We need to simplify the given expression
(-3+3i) + (-2+3i) for simplification we will firstly open the parenthesis we will have expression as -3+3i -2+3i it will gives us the value
-5+6i
In complex numbers we add real part with real part and imaginary part with imaginary part
We have general representation of complex number as a+ib where a is real and b is real part of imaginary.
Answer:
B is your answer.
Step-by-step explanation:
The area of a square is 25 square inches. What is the perimeter of the square?
Answer:
25 square root is 5 so the missing sides is 5.
5+5=10 x 2 = 20
perimeter is 20
Hope this helps
Step-by-step explanation:
The perimeter of the given square is 20 inches.
What is the perimeter of the square?The perimeter of a square is defined as the addition of the lengths of the square.
The perimeter of a square = 4a
Where a is the length of the side of the square
Given that the area of the square is 25 square inches.
Let a is the length of the side of the square
The area of the square = a² = 25
So a = 5
Since all sides of a square are equal, we can calculate the perimeter by multiplying the length of one side by 4:
The perimeter of a square = 4a
The perimeter of a square = 4(5)
The perimeter of a square = 20 inches
Therefore, the perimeter of the square is 20 inches.
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If cos 0 < 0, which quadrant(s) could the
terminal side of a lie?
Answer:
quadrants 2 & 3
Step-by-step explanation:
cos = adj/hyp
adj is negative in quadrants 2 & 3.
Jack has two jars of wax. One jar is 1/6 full. The other jar is 4/6 full. Write an equation to find the amount of wax Jack has.
Answer:
1/6 + 4/6 = 5/6
Step-by-step explanation:
I hope this helped
Can some one help me???
Answer:
You will break even with the cost of your supplies equals your income how many cups of your hot chocolate and less you sell to break even
Step-by-step explanation:
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
The fastest train on earth can travel 800 miles in 2.5 hours because it uses magnets to make it hover above the tracks rather than touching the tracks. What is its average speed?
Answer:
Whatever google said
Step-by-step explanation:
"The original bullet train, the Series 0, hit a speed of about 200 kilometers per hour, or about 125 mph. The speeds gradually increased through the years, reaching the current figure of 177 mph in 2015."
Sorry, I don't know it off of the top of my head, but heres a little dude!
(づ￣ ³￣)づ
Hope he can make up for it...
What is the volume of a rectangular prism that measures 45units long, 25 units wide, and 35 units high?
Answer:
39375
Step-by-step explanation:
All you have to do is just multiply the length x width x height.
Answer:
Find a rectangular prism in your house exactly the same as this one,them you'll know the answer
Lordyn installed a rectangular Koi fishpond on one of the sides of her rock garden. The pond has a length of 14.2 feet and a perimeter of 36.9 feet. The pond can hold 313.82 cubic feet of water.
Write and solve an equation that can be used to determine the depth of the Koi fishpond.
Answer:
262.72
Step-by-step explanation:
I hope this helps :) :P
I need helpI need helpI need helpI need helpI need helpI need helpI need helpI need help
Answer:
2
Step-by-step explanation:
Answer:
The last one
Step-by-step explanation:
2 negatives is a positive, so -(-1) is basically +1, therefor the equation is -4+1
What is true about the dilation?
It is a reduction with a scale factor between 0 and 1.
It is a reduction with a scale factor greater than 1.
It is an enlargement with a scale factor between 0 and 1.
It is an enlargement with a scale factor greater than 1.
Answer:
A
Step-by-step explanation: :) am sure
Answer: A. A reduction is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image. If the scale factor is between 0 and 1 the image is a reduction. If the scale factor is greater than 1, the image is an enlargement.
Step-by-step explanation:
I hope this helps:)
Roger likes to eat Crunchy Flakes cereal for breakfast every morning. Crunchy Flakes comes in a 20-ounce box that costs $4.20 and a 30-ounce box that costs $6.00. Which is the better buy? (HINT: Find which one is less per ounce)
A. 20-ounce box
B. 30-ounce box
C. they both are the same per ounce
Answer:
B
Step-by-step explanation:
Divide $4.20 by 20 ounces and $6 by 30 ounces. You would get 0.21 and 0.2. So, B is the cheaper and better buy.
