Answer:
The roots are {-3, -2, 2, 3}.
Step-by-step explanation:
The trick here is to represent y² by some other letter, such as x. If we do that, then y^4-13y^2+36=0 becomes x² - 13x + 36 = 0.
Recognize that the factors -4 and -9 of 36 sum up to 13. Thus,
x² - 13x + 36 = 0 is equivalent to (x - 4)(x - 9) = 0, and x = 4 or x = 9.
Recall that x = y².
When x = 4: y² = 4, and so y = ±2.
When x = 9, y² = 9, and so y = ±3.
The roots are {-3, -2, 2, 3}.
The roots of the bi-quadratic equation y⁴ - 13y² + 36 = 0 are,
- 2, 2, -3, 3.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, y⁴ - 13y² + 36 = 0.
This a bi-quadratic polynomial.
Let, x = y².
Therefore,
x² - 13x + 36 = 0.
x² - 4x - 9x + 36 = 0.
x(x - 4) - 9(x - 4) = 0.
(x - 4)(x - 9) = 0.
x = 4 Or x = 9.
Now,
For x = 4 ⇒ y² = 4 ⇒ y = ± 2.
For x = 9 ⇒ y² = 9 ⇒ y = ± 3.
So, The roots of the biquadratic equation are - 2, 2, -3, 3.
learn more about biquadratic equations here :
https://brainly.com/question/29015405
#SPj2
What number line represents the solution set for the inequality -1/2 greater
than or equal to 4
Answer:
[8, inifinity sign)
Step-by-step explanation:
(2)/1 x -1/2 (greater than or equal to sign) 4(2), You need to get rid of the fraction so times 2 on both sides.
So the fraction cancels out and your answer is x (greater than or equal to) 8
The open side of the sign always is facing the bigger number so like this > so x is positive.
Since i can't show the number line i'll try to explain it if it's a greater than sign its a closed dot on the 8 going right. The 8 is in a bracket and the infinity is with a parenthesis. like this [8, infinity sign)
My teacher may have taught me different but it should be about the same.
Hope my answer has helped you and if not i'm sorry.
A large rectangular movie screen in an IMAX theater has an area of 6,699 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide
Length =
Width =
Answer:
Length=87 ft
Width=77 ft
Step-by-step explanation:
Let
L ----> the length of rectangular movie screen
W ----> the width of rectangular movie screen
we know that
The area is equal to
[tex]A=LW[/tex]
[tex]A=6,699\ ft^{2}[/tex]
so
[tex]6,699=LW[/tex] ----> equation A
[tex]L=W+10[/tex] ----> equation B
substitute equation B in equation A
[tex]6,699=(W+10)W\\ \\W^{2} +10W-6,699=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]W=77\ ft[/tex]
see the attached figure
Find the value of L
[tex]L=77+10=87\ ft[/tex]
Use the diagram below to solve for x and y.
Answer:
Option A. x=30,y=42
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ZYX have three congruent interior angles
therefore
Triangles are similar
step 1
Find the value of x
[tex]\frac{ZY}{AB}=\frac{ZX}{AC}[/tex]
substitute the values
[tex]\frac{20}{x}=\frac{12}{18}[/tex]
[tex]x=20*18/12=30\ units[/tex]
step 2
Find the value of y
[tex]\frac{ZY}{AB}=\frac{XY}{CB}[/tex]
substitute the values
[tex]\frac{20}{30}=\frac{28}{y}[/tex]
[tex]y=30*28/20=42\ units[/tex]
Solve the inequality: x+7 < 4 or 7-x < 1 Please show all work!
Answer:
[tex]\large\boxed{x<-3\ or\ x>6}[/tex]
Step-by-step explanation:
[tex]x+7<4\qquad\text{subtract 7 from both sides}\\\\x+7-7<4-7\\\\x<-3\\\\7-x<1\qquad\text{subtract 7 from both sides}\\\\7-7-x<1-7\\\\-x<-6\qquad\text{change the signs}\\\\x>6[/tex]
Step-by-step explanation:
all work is pictured and shown
the length and width of a rectangle are consecutive even integers. the area of the rectangle is 8 square units. what are the length and width of the rectangle?
Answer: 4 feet and 2 feet
Step-by-step explanation: The only factor of 8 that is an even integer is 4 and 2. So the answer is 4 feet and 2 feet.
If 20% of a number is 12, what is 30% of the same number?
Answer:
The answer would be 18.
Step-by-step explanation
If 20% of a number is 12, then 30% of that same number would be 18. This means that the number would be 60 (6×2=12, 6×3=18). Hope this helps you to understand your math problem better!
jim works h hours in a week. to find his weekly pay he multiplies his hours by his pay of $10 per hour and adds $50 for his sales bonus. he's decided that he wanted to take one-tenth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?
Answer:
Step-by-step explanation:
Take home pay = 10*h + 50 I assume the 50 is a flat rate.
Savings = 1/10 of the take home pay.
Savings = (10*h + 50)/10
What is the area of a circle with a radius of 8 inches? Use = 3.14
Answer:
200.96 inch²
Step-by-step explanation:
formula for a circle: (pi) x r²
pi= 3.14
3.14 x 8²
=200.96 inch²
For this case we have by definition, that the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
A: It is the radius of the circle
They tell us as data that the radius is 8 inches.
Substituting we have:
[tex]A = \pi * (8) ^ 2\\A = \pi * 64\\A = (3.14) (64)\\A = 200.96[/tex]
Thus, the area of the circle is [tex]200.96 \ in ^ 2[/tex]
Answer:
[tex]200.96 \ in ^ 2[/tex]
if a school has w women and M men and you know that there are 100 more men than women write an algebraic equation relating W and M
Answer:
W+100=M
Explanation:
So the problem says there will always be 100 more men than woman. So that would mean you just have to add the amount of women and 100 to find the number of men. For example, if there are 3 women, there will be 103 men.
Hope this helps ;)
Certainly! To create an algebraic equation representing the given situation, we can use the information that there are 100 more men than women at the school.
Let's use the variables:
- \( W \) to represent the number of women
- \( M \) to represent the number of men
The key piece of information that we have is that the number of men is 100 more than the number of women. We can write this relationship with an equation:
\[ M = W + 100 \]
This equation states that if you take the number of women (\( W \)) and add 100 to it, you will get the number of men (\( M \)). It directly translates the information given into an algebraic equation, showing the relationship between the number of women and the number of men in the school.
Identify the vertex of the graph Tell whether it is a minimum or a maximum
Answer:
(1,2) maximum
Step-by-step explanation:
The vertex is the the point on the graph where the graph does a "u-turn".
this point can either represent the maximum value or the minimum value depending on which way the graph is facing.
In this case, the graph looks like an "n" (as opposed to a "u").
We can clearly see that the point where the graph makes a U-turn is (1, 2)
we can also see that no part of the graph extends above this point, hence this point represents the maximum value which y could possibly be.
Hence (1,2) is maximum
Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?
He is correct because both solutions satisfy the equation.
He is not correct because he made a sign error.
He is not correct because there are no solutions.
He is not correct because there is only one solution: x = 5.
Answer:
He is not correct because he made a sign error.
Step-by-step explanation:
-2 |8-x| - 6 = -12
-2 |8-x| = -12 + 6
-2 |8-x| = - 6
2 |8-x| = 6
|8-x| = 3
2 possible solutions:
8-x = 3 ----> x = 5
or
8-x = -3 ----> x = 11
Comparing the answer choices, we can see that Johan got the sign of x = 11 wrong.
Hence the correct answer is:
He is not correct because he made a sign error.
Answer: Just did it on ed, answer is "He is not correct because he made a sign error."
Step-by-step explanation:
there was a total of 750 and 2015 crickets in a pond, the population increased by 17% the next year. The year after that the population decreased by 10%. what is the percent of change of population from the 2015 to 2017?
Answer:
5.2% increase
Step-by-step explanation:
In 2015 the total population was 750.
In 2016 the total population was 17% more than in 2015, so 750 x 1.17 = 877.
In 2017 the total population was 10% less than in 2016, so 877 x 0.9 = 789.
Compared to 2015, the population in 2017 was 789/750 = 1.052 or 5.2% greater.
In one step:
((750 x 1.17) x 0.9) / 750 = 5.2%
In this question, we're going to need to find the population in 2017, while using the given information.
Answer: 5.3% increaseLets gather the information we should know from the question.
Key information:
2015 -- Population of 750
Increased by 17% in the next year
Decreased by 10% the next year
With the information above, we can solve the problem.
We know that our starting population for crickets is 750, and it increases by 17% for the next year (2016), so we would multiply 750 by 1.17
[tex]750*1.17=877.5[/tex]
Our population in 2016 is 877.5.
Now, we know that he population in 2016 decreased by 10% going into 2017. We would need to find how much of 877.5 is 10%, and then subtract.
[tex]877.5*.10=87.75\\\\877.5-87.75=789.75[/tex]
When you're done solving, you should get 789.75
This means that the population of crickets in 2017 is 789.75.
Now, we know that we started with 750 crickets, now we have 789.5 crickets.
We would divide 789.5 by 750.
[tex]789.5\div750=1.053[/tex]
We would move the decimal place two times to the right, giving us 5.3.
This means that the population increased by 5.3% from 2015 to 2017.
I hope this helps!Best regards, MasterInvestor.15 points
Line AB←→ passes through the points A(3,−1) and B(1,7).
Which lines are parallel to AB←→?
THIS IS MULTIPLE CHOICES
y=−4x
y=−4x+8
y=4x
y−1=2(x+2)
y+1=−4(x+1)
y=4x+7
y=2x−3
y−6=−4(x−3)
Lines that are parrellell presume to have the same slope.
So if we just calculate the slope of a function or a line we should be good.
[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now put in the data from the coordinates of the points [tex]A(3,-1)\wedge B(1,7)[/tex]
[tex]s=\dfrac{7-(-1)}{1-3}=\dfrac{8}{-2}=\underline{-4}[/tex]
The form of a function now looks like: [tex]
f(x)\vee y=-4x+n[/tex]
From here we are no longer required to calculate anything more. Leave n alone.
The solutions are the equations of the form above.
That would mean:
[tex]
y=-4x \\
y=-4x+8 \\
y+1=-4(x+1) \\
y-6=-4(x-3)
[/tex]
Hope this helps.
Write two fractions with different denominators whose LCD is 45
Answer:
2/5 and 8/9 (answers can vary)
Step-by-step explanation:
The lcm of 5 and 9 is 45 so that works for our denominators.
So 2/5 and 8/9 (the answers are many)
Answer:
1/45 and 8/90
Step-by-step explanation:
Between these two fractions, the lowest shared denominator is 45.
Which of the following is not a real number?
Answer:
D
Step-by-step explanation:
by definition, the square root of an negative number is known as an imaginary number. i.e Not a real number
[tex]\sqrt{-2}[/tex] = [tex]\sqrt{2}[/tex][tex]\sqrt{-1}[/tex] = [tex]\sqrt{2}[/tex]i (imaginary number)
The [tex]\sqrt{-2}[/tex] is not a real number.
The following information should be considered with respect to the real number:
The numbers should be found in the number line. It should be in fractions, whole, naturals, rational, irrational. But it can't be in imaginary numbers.Therefore, the first three options are considered to be the real number.
Thus we can conclude that the [tex]\sqrt{-2}[/tex] is not a real number.
Learn more: brainly.com/question/17429689
Using the diagram on the right, find the length of GT and TA.
Answer:
[tex]GT=10\ units[/tex] and [tex]TA=6\ units[/tex]
Step-by-step explanation:
we know that
In the diagram
Triangles GRT and GEA are similar by AA Similarity Postulate
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{GR}{GE}=\frac{GT}{GA}[/tex]
we have
[tex]GR=5\ units[/tex]
[tex]GE=5+3=8\ units[/tex]
[tex]GT=16-x\ units[/tex]
[tex]GA=16\ units[/tex]
substitute
[tex]\frac{5}{8}=\frac{16-x}{16}\\ \\5*16=8*(16-x)\\ \\80=128-8x\\ \\8x=128-80\\ \\x=48/8\\ \\x=6\ units[/tex]
therefore
[tex]GT=16-x=16-6=10\ units[/tex]
[tex]TA=x=6\ units[/tex]
Johnny has 19 bottles of dish soap and he gives Jeina 5. How much dish soaps will he have now?
Answer:
14 dish soaps
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
Answer:
14
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
A season pass to the local water park costs 84. If you go to the park ten times during the season, what is the unit rate of cost per visit?
Answer:
$8.40
Step-by-step explanation:
To find the unit rate, take the total cost and divide by the number of times that you went
84/10
8.4
The unit rate (or cost per visit) is $8.40
Find the value of x.
A. 4 root 2/ 2
B. 4
C. 4 root 2
D. 4 root 3
Answer:
C. 4 root 2
Step-by-step explanation:
Total amount of angles = 45° + 45° = 90°
sin90 * 4 root 2 = 5.656854
Answer:
4
Step-by-step explanation:
You will either use cos or sin solve this problem
1. set up the problem like this
x/sin 45 x 4 root 2/sin 90
2. cross multiply (it will be useful to use calculator or if you know unit circle then you're good)
sin 90 = 1 and sin 45 = .7071067812 (don't really need to know this)
1x = (sin 45 x 4 root 2)
3. Solve for x like normal
1x = 4
1x/1 = 4/1
x = 4
Which equation represent the line that is perpendicular to the line 5x-2y=-6 and passed through the point (5,-4)?
To find the equation of a line perpendicular to 5x - 2y = -6 and passing through (5, -4), first determine the slope of the given line and then find the negative reciprocal of that slope. Using point-slope form with the new slope and the given point, the equation is y = - (2/5)x - 2.
To find the equation of the line that is perpendicular to the given line 5x - 2y = -6 and passes through the point (5, -4), follow these steps:
Step 1: Find the slope of the given line
Rewrite the given line in slope-intercept form (y = mx + b):
5x - 2y = -6
-2y = -5x - 6
y = (5/2)x + 3
The slope (m) of the given line is 5/2.
Step 2: Find the slope of the perpendicular line
The slope of the line perpendicular to another is the negative reciprocal. Thus, the slope of the perpendicular line is -2/5.
Step 3: Use the point-slope form
Using the point (5, -4) and the slope -2/5 in the point-slope form (y - y1 = m(x - x1)):
y - (-4) = - (2/5)(x - 5)
y + 4 = - (2/5)x + 2
y = - (2/5)x - 2
Therefore, the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4) is y = - (2/5)x - 2.
A shirt originally cost $50.97, but it is on sale for $40.78. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.
Answer:
20% decrease.
Step-by-step explanation:
difference over original
50.97-40.78= 10.19
diff/orig=sales tax
10.19 / 50.97= 19.99..
19.99 is approximately 20.
A cylinder with a base diameter of x units has a volume of πx3 cubic units. Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units.
The radius of the cylinder is 2x units.
The area of the cylinder’s base is πx2 square units.
The area of the cylinder’s base is πx2 square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Answer:
The height of the cylinder is 4x units
Step-by-step explanation:
see the attached document
Answer:
The answer is 1,3, and 6 Hope this helps
Step-by-step explanation:
PLEASE HELP K12
WILL MARK BRAINLYIST
What is the Length of the line segment with endpoints (12, 6 ) and (12, -9 )
Answer:
15Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (12, 6) and (12, -9). Substitute:
[tex]d=\sqrt{(12-12)^2+(-9-6)^2}=\sqrt{0^2+(-15)^2}=\sqrt{225}=15[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The formula is:}\bf{\frac{y_2-y_1}{x_2-x_1}}[/tex] [tex]\text{ or you can say}\rightarrow[/tex] [tex]\frac{Rise}{Run}[/tex]
[tex]\text{y}_2=-9\\\\\text{y}_1=6\\\\\text{x}_2=12\\\\\text{x}_1=12[/tex]
[tex]\text{Now, that we know what our points are we could solve this equation}[/tex]
[tex]\frac{-9-6}{12-12}[/tex]
[tex]\text{-9 - 6 = -15}[/tex]
[tex]\text{12 - 12 = 0}[/tex]
[tex]\bf{= \ \frac{-15}{0}}[/tex]
[tex]\boxed{\boxed{\bf{Answer: \ \frac{-15}{0}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
56 coins = $9.80. how many are quarters how many are nickels
Answer:
So there are 35 quarters and 21 nickels.
Step-by-step explanation:
So I guess that is all we have is quarters and nickels.
Quarters are worth .25
Nickels are worth .05
Let x represent the number of quarters
Let y represent the number of nickels
x+y=56
.25x+.05y=9.8
We are going to solve this system.
I'm going to use substitution. I will solve the first equation for y and then plug that into the second equation.
y=56-x
.25x+.05(56-x)=9.8
.25x+2.8-.05x=9.8
.20x+2.8=9.8
.2x = 7
x=7/(.2) or 7*5=35
y=56-x
y=56-35=21
So there are 35 quarters and 21 nickels.
Answer:
A) n + q = 56
B) .05n + .25q = 9.80
We multiply A) by -.25
A) -.25n -.25q = -14 then add it to equation B)
B) .05n + .25q = 9.80
-.2n = -4.20
nickels = 4.20 / .20 = 21
quarters = 35
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities below? Y>-2x+2 Y<2x-1
Answer:
That would be B. Graph A.
Step-by-step explanation:
The graph y < 2x - 1 is a dotted line which rises to the right with a slope of 2 and passes through y = -1 and is shaded below the line. The graph y > -2 x + 2 rises to the left and passes through y = 2 and is shaded above the line.
What are the possible steps involved in solving the equation shown? Check all that apply.
3.5 + 1.2(6.3 – 7x) = 9.38
Add 3.5 and 1.2.
Distribute 1.2 to 6.3 and –7x .
Combine 6.3 and –7x .
Combine 3.5 and 7.56.
Subtract 11.06 from both sides.
Divide both sides by 9.38.
Answer:
B) Distribute 1.2 to 6.3 and –7x
D) Combine 3.5 and 7.56
E) Subtract 11.06 from both sides
Answer:
b, d, and e :)
Use the properties of exponents to rewrite the expression.
5e•5e•5e•5e
Answer:
(5e)^4
Step-by-step explanation:
Can (3,5 and square root 34) be sides on a right triangle?
Answer:
Yes, they are.
Step-by-step explanation:
Remember that a triangle is only a right triangle if its sides meet this mathematical requirement:
(leg)² + (leg)² = (hypotenuse)²
The hypotenuse of a right triangle is the longest side, while the legs are the two shorter sides. We can't say exactly where √34 is, but since √25 = 5 and √36 = 6, we know it must be at least bigger than 5, making it the triangle's longest side.
Using √34 as the "hypotenuse" and 3 and 5 as the "legs" of our triangle makes the equation 3² + 5² = (√34)², and simplifying gets us
9 + 25 = 34
34 = 34
The requirement's been met, so yes, this is a right triangle.
What is the simplest form of this expression?
2x(x2 – 3) – 6x2
Answer:
-6x - 6x² + 2x³
Step-by-step explanation:
Match each like-term to end up with the above answer.
I hope this helps.
PLEASE HELP ASAP.
Which graph has a correlation coefficient between the variables closest to 0?