Final answer:
The expression x⁴ + 8x² + 16 is a perfect square trinomial and it can be factored completely as (x² + 4)².
Explanation:
To factor completely the expression x⁴ + 8x² + 16, we should first recognize that this is a perfect square trinomial. A perfect square trinomial takes the form a² + 2ab + b², and can be factored into (a + b)².
Comparing our given expression to the perfect square trinomial, we see that x⁴ is the square of x² and 16 is the square of 4. Moreover, 8x² is twice the product of x² and 4, suggesting that the expression is indeed, a perfect square. Thus, we can factor it as:
(x² + 4)²
In conclusion, the expression x⁴ + 8x² + 16 can be factored completely as (x² + 4)².
Final answer:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial.
Explanation:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial of the form [tex]a^2 + 2ab + b^2[/tex]. The square root of the first term is [tex]x^2[/tex] the square root of the last term is 4, and twice the product of these square roots is [tex]8x^2[/tex], which matches the middle term of the given expression. Therefore, we can rewrite the expression as [tex](x^2 + 4)^2[/tex]. This is the completely factored form of the expression.[tex]a^2 + 2ab + b^2[/tex]
Perpendicular bisector of MU. Find the values of m.
What is the best first step in solving the equation 3 + = 5? Subtract 3 from both sides. Find the cube of . Cube both sides of the equation. Subtract 5 from both sides.
How many distinct triangles can be formed for which m∠X = 51°, x = 5, and y = 2? zero one two
Answer: B: One
Step-by-step explanation:
True or false the product of a complex number and its conjugate is a real number
It is true that the product of a complex number and its conjugate is a real number and this can be determined by using arithmetic operations.
Let the complex number be (a + bi). Therefore, its conjugate is given by (a - bi).
The following calculation can be used to determine the product of a complex number and its conjugate:
= (a + bi).(a - bi)
Multiply (a) by (a - bi) and then multiply (bi) by (a - bi) in the above expression.
[tex]\rm =a^2-abi+abi-b^2i^2[/tex]
Simplify the above expression.
[tex]\rm =a^2-b^2i^2[/tex]
Remember the value of ([tex]\rm i^2 = -1[/tex]). So substitute the value of [tex]\rm i^2[/tex] in the above expression.
[tex]\rm = a^2+b^2[/tex]
From the above calculation, it can be concluded that it is true that the product of a complex number and its conjugate is a real number.
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Suppose a random sample of 36 is selected from a population with a standard deviation of 12. if the sample mean is 98, the 95% confidence interval for the population mean is ______________.
Answer:
36%
Step-by-step explanation:
Philip has 2,000 and spends $23.75 on supplies.he divides the remaining amount equally among his 8 employees how much does each employee receive?
In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?
gallons per hour
You are paid $8.25/hour. You work 35 hours/week for 3 weeks. Your involuntary deductions are FICA (7.65%), federal withholding (13%), and state withholding (9%). How much is your realized income?
The answer is:
$609.39
In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC at point H and the angle bisector of ∠C meets AB at point K. Prove that BH = CK.
To prove that BH = CK in triangle ABC, we can use the angle bisector theorem. The theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments proportional to the other two sides. By applying this theorem and representing BH as x and CK as y, we can show that x = y, thus proving that BH = CK.
Explanation:In triangle ABC, to prove that BH = CK, we can use the angle bisector theorem. Since m∠B = m∠C, the angle bisector of ∠B will divide the side AC into two segments proportional to the other two sides. Let's denote BH as x and CK as y. According to the angle bisector theorem, we have:
AB / BC = AH / HCAC / BC = AK / BKSince AB = AC (isosceles triangle), we can rewrite the first equation as:
x / BC = AH / HC
And the second equation as:
AC / BC = AK / y
Since AB = AC, we can substitute AC with AB:
x / BC = AK / y
Now, we can cross-multiply and solve for x and y:
x * BC = AK * HC
y * BC = x * HK
Simplifying, we get:
x = AK * HC / BC
y = x * HK / BC
Since HK = HC, we have:
x = AK
y = x
Therefore, BH = x = CK = y.
What is the simplified form of each expression? (1 point)
1.) -(10)^-1
-1/10
-1/1^10
1/10
10
2.) 1/c^-5 (1 point)
c^5
5c
-c^5
-5/c
3.) What is the value of y^-5/x^-3 for x = 2 and y = -4? (1 point)
10/3
128
-1/128
-128
4.) Is the number written in scientific notation if not, explain. 5.1 x 10^8 (1 point)
Yes; the number is written in scientific notation.
No; the first factor is not a number between 1 and 10.
No; it is not written as a number times a power of 10.
5.) What is the number written in a standard notation? (1 point)
5.71 x 10^-3
-171.3
0.0571
0.000571
0.00571
6.) Suppose that the diameters of different types of hairs are 1.7 x 10^-4 cm, 1.4 x 10^-3 cm, 1.2 x 10^-5 cm, and 1.9 x 10^-4 cm? what is the order of the hairs from least to greatest diameter? (1 point)
Who ever is good at math please ''Try'' to help me out here?! :D And Thank you so much if ya do! :P
Answer:
a
b
a
d
a
a
Step-by-step explanation:
True or false if a function y = f(x) satisfies dy/dx = y, then y = e^x
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $504. What was the simple interest rate of the bonds? Do NOT round off a decimal answer.
If the typical balance on Lucy's credit card is $750 and the interest rate (APR) on her credit card is 16%, how much in interest would you expect Lucy to be charged in a typical month?
f(x)=24x+7 What is the domain of f
△ABC△ABC is similar to △XYZ△XYZ. Also, angle A measures 45° and angle C measures 60°.
What is the measure of angle Y?
Answer: The value of angle Y is 75 ° .
Step-by-step explanation:
Given Δ ABC ≈ Δ XYZ
∠ A = 45°
∠ C = 60°
To find =
∠Y =? in ΔXYZ
Solution:
In Δ ABC
∠ A = 45 °
∠ C = 60 °
∠ B = ?
∠ A + ∠ C +∠ B = 180 ° (angle sum property of triangle)
∠ B = 75 °
Since, given that Δ ABC ≈ Δ XYZ and in similar triangles ,angles of respective vertices are equal. As shown in the image attached
∠ A = 45 ° = ∠ X
∠ B = 75 ° = ∠ Y
∠ C = 60 ° = ∠ Z
So, the value of angle Y is 75 ° .
The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.
Find JL if JK = 17 - x, KL = 2x - 7, and K is the midpoint of JL
Final answer:
By setting up an equation where JK equals KL since K is the midpoint, solving for x, and substituting back to find the length of JL, we find that JL is 18 units long.
Explanation:
To find the length of JL when given that JK = 17 - x and KL = 2x - 7, and knowing that K is the midpoint of JL, we can form an equation recognizing that JL is the sum of JK and KL. Because K is the midpoint, we know that JK and KL are actually equal in length, so we can set them equal to each other and solve for x:
17 - x = 2x - 7
Combining like terms by adding x to both sides and adding 7 to both sides gives us:
24 = 3x
Dividing both sides by 3:
x = 8
Since JK and KL are equal and K is the midpoint, JL will be twice the length of either segment. Substituting x into either expression, JK or KL:
JL = 2 * JK = 2 * (17 - x) = 2 * (17 - 8) = 2 * 9 = 18
or
JL = 2 * KL = 2 * (2x - 7) = 2 * (2*8 - 7) = 2 * (16 - 7) = 2 * 9 = 18
Therefore, JL = 18.
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. include your work in your final answer. type your answer in the box provided or use the upload option to submit your solution.
Sawyer has triple the number of Hot Wheels cars as Fisher. If Fisher has x number of cars, how many does Sawyer have?
A) x + 3
B) 3x
C) 3/x
D) 2x
Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 .
an equation of the line passing through point P(0, 0) that is perpendicular to the given line is
[tex]y=\frac{1}{9} x[/tex]
Given :
the line passing through point P(0, 0) that is perpendicular to the line
y = −9x−1
The given equation is in the form of y=mx+b
where m is the slope and b is the y intercept
Find out slope from the given equation y=-9x-1
Slope of the given equation is -9
Slope of perpendicular lines are negative reciprocal of one another
slope of perpendicular line is negative reciprocal of -9 is [tex]\frac{1}{9}[/tex]
slope of perpendicular line m=[tex]\frac{1}{9}[/tex]
The line passes through the point (0,0) that means y intercept is 0
the value of b=0
[tex]m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x[/tex]
an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is
[tex]y=\frac{1}{9} x[/tex]
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The equation of the line passing through point P(0, 0) and perpendicular to the line y = -9x-1 is y = (1/9)x, with the slope of the line being the negative reciprocal of -9.
Explanation:To write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1, we first identify the slope of the given line. The slope of the line y = −9x−1 is −9, so the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular slope is 1/9.
Since the point P(0, 0) is also the y-intercept, we can directly write the equation of the perpendicular line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the line we are looking for is y = (1/9)x.
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David and his family went out to eat in the bill was $80 and he gave the waiter 30% how much was did he give the waiter
How do I find the value of the variable?
the three inside angels need to equal 180, so first find the missing inside angle:
86.5 + 41.4 = 127.9
180-127.9 = 52.1
now that angle and y need to equal 180 degrees
so 180 - 52.1 = 127.9
y = 127.9 degrees
Ana is driving from her home in Miami to her grandmothers house in New York. On the first day she will travel 240 miles to Orlando Florida to pick up her cousin. Then they will travel 350 miles each day write an equation for the total number of miles m that Ana has traveled after d days
The equation for the total number of miles m that Ana has traveled after d days is m = 240 + 350d.
What is an equation?
An equation is an equality relationship between two expressions written on both sides of the equal to sign.
Ana travels 240 miles on the first day.
Her cousin and she travel 350 miles everyday.
If d is the number of days, then to find the equation for the total number of miles covered m,
m = 240 + 350d miles in d days.
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Alan bowls one game, which consists of 10 frames. The number of pins he knocked down in each frame is 5, 6, 7, 5, 7, 9, 2, 4, 8, and 7. Which measure should Alan use to learn the difference of the greatest and the least number of pins he knocked down?
Answer:
Range.
Step-by-step explanation:
Alan must use the measure called Range, which indicates the dispersion between the extreme values of a variable. It is calculated as the difference between the highest and the lowest value of the variable. It is denoted as R. First the data is sorted, then it is calculated as:
R = x (n) - x (1) where,
x (n): It is the largest value of the variable.
x (1): It is the smallest value of the variable.
In the given case (5, 6, 7, 5, 7, 9, 2, 4, 8, and 7), we sort the data, and get,
2, 4, 5, 5, 6, 7, 7, 7, 8, 9
x (n) = 9
X (1) = 2
R = 9 - 2 = 7
Hope this helps!
The equation d = m/v can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V.
Answer:
The equivalent equation of [tex]d=\frac{m}{V}[/tex] is [tex]V=\frac{m}{d}[/tex].
Step-by-step explanation:
The given equation is
[tex]d=\frac{m}{V}[/tex]
Where d is density, m is mass and V is volume.
We have to solve this equation for V. To separate the variable V on one side multiply both sides by V.
[tex]d\times V=\frac{m}{V}\times V[/tex]
[tex]dV=m[/tex]
Diven both sides by d.
[tex]\frac{dV}{d}=\frac{m}{d}[/tex]
[tex]V=\frac{m}{d}[/tex]
Therefore the equivalent equation of the given equation is [tex]V=\frac{m}{d}[/tex].
Which of the following statements is true?
The interquartile range of weights of both apples is the same.
The upper quartiles of each group are within 2 grams of each other.
There were more Red Delicious apples weighed than Granny Smith apples.
The median weight of Granny Smith apples is less than the median weight of Red Delicious apples.
What is the midpoint of the line segment whose endpoints are (-8, 12) and (-13, -2)?
(-10.5, 5)
(-10.5, 7)
(-2.5, 7)
The midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
What is midpoint of a line segment?
Midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Formula for finding the midpoints of a line segment[tex](x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]
Where,
[tex](x, y)[/tex] is the midpoint of the line segment.
[tex](x_{1},y_{1}) and (x_{2} ,y_{2} )[/tex] are the endpoints of the line segment.
Let (x, y) be the midpoint of the line segment.
According to the given question
We have
(-8, 12) and (-13, -2) are the endpoints of the line segment.
Therefore, the midpoint of the line segment is given by
[tex](x,y)=(\frac{-8-13}{2} ,\frac{12-2}{2} )[/tex]
⇒[tex](x, y) = (\frac{-21}{2} ,\frac{10}{2})[/tex]
⇒[tex](x,y)=(\frac{-21}{2} ,5)[/tex]
Hence, the midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
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What is
Write
52 over 6
as a mixed number.
Give your answer in its simplest form.
Kelly reads x hours a week. tim reads two times more than kelly and jim reads five hours more than tim. which expression represents the amount of time jim reads?
Answer:
2x+ 5 expression represents the amount of time jim reads
Step-by-step explanation:
As per the statement:
Kelly reads x hours a week.
⇒Kelly read in a week = x hours
Also, tim reads two times more than kelly
⇒tim read in a week= 2x
It is also given that:
jim reads five hours more than tim.
⇒Jim = tim read + 5
⇒Jim read in a week = 2x +5
Therefore, expression represents the amount of time jim reads is, 2x+ 5
Complete the point-slope equation of the line through (1,3) and (5,1)
The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).
Explanation:To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.
Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.
The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).
Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).
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