The complete factorized form for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
Step-by-step explanation:
Step 1: Given expression:
[tex]81 x^{8}-1[/tex]
Step 2: Trying to factor as a Difference of Squares
Factoring [tex]81 x^{8}-1[/tex]
As we know the theory that the difference of two perfect squares, [tex]A^{2}-B^{2}[/tex] can be factored into (A+B) (A-B)
from this, when analysing, 81 is the square of 9, [tex]x^{8}[/tex] is the square of [tex]x^{4}[/tex]. Hence, we can write the given expression as,
[tex]\left(9 x^{4}\right)^{2}-1^{2}[/tex]
By using the theory, we get
[tex]\left(9 x^{4}+1\right)\left(9 x^{4}-1\right)[/tex]
Again, we can further factorise the term [tex]\left(9 x^{4}-1\right)[/tex]
[tex]9 x^{4}[/tex] is the square of [tex]3 x^{2}[/tex]. Therefore, it can be expressed as below
[tex]\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
Now, we can not factorise further the term [tex]\left(3 x^{2}-1\right)[/tex]. Because it will come as [tex]\sqrt{3} x[/tex] (3 is not a square term). Thereby concluding that the complete factorisation for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
12. What steps do you need to take to solve
the equation 2x + 6 - 187
A Add 6. Then multiply by 2.
B Subtract 6. Then divide by 2.
C Add 6. Then divide by 2.
D Subtract 6. Then multiply by 2.
Answer:
B is the right answer.
Solve write or draw to explain Saul and Luisa each scored 167 points on computer games How many points did they score together
Answer:167 + 167 = 334
Step-by-step explanation:
prove that sin^4x - cos^4x = 2sin^2x - 1
Step-by-step explanation:
Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation
Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)
LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²
= (sin²x - cos²x)(sin²x + cos²x)
= sin²x - (1 - sin²x) since sin²x + cos²x = 1
= 2 sin²x - 1
= RHS
Hence proved.
(1 point
4. A regression line has a correlation coefficient of r=-0.91. Which of the following statements
must be true?
The data are so varied that there is almost no discernible trend whatsoever.
O The data are very tightly clustered around the trend line.
The trend line has a very steep negative slope.
The trend line reliably represents only 91 percent of the data.
Answer:
A: The data are so varied that there is almost no discernible trend whatsoever.
Step-by-step explanation:
The other 3 don't make sense and are not true for the question
What is the solution 4x+6<18
Answer:
x < 3
Step-by-step explanation:
4x +6 < 18
add and subtract 6 from both sides
4x + 6 - 6 < 18 -6
4x < 12
x< 12/4
X < 3
Answer:
x < 3
Step-by-step explanation:
I took the test its, the right answer, trust me.
What is (8×^2+4×+6)(6×^2-5×+6)
Answer:
1
Step-by-step explanation:
I think it's 1 because I never did this question before.
Find the distance (D) Round your answer the nearest tenth.PLEASE HELP!!
The distance (D) is 10 cm.
Explanation:To find the distance (D), we can use the formula D = do + di, where do is the actual distance and di is the apparent image distance.
In the given information, it states that 2do must be less than 20 cm, so we can set do = 10 cm.
Therefore, the distance (D) is 10 cm.
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what is the a, b, and r for y=3.6(1.25)^x
Answer:
a=3.6, v=1.25 and r=25%
Step-by-step explanation:
The given exponential function is
[tex]y = 3.6 {(1.25)}^{x} [/tex]
We compare to the form:
[tex]y = a{(b)}^{x} [/tex]
We have a=3.6, b=1.25
The r is the percentage of increase or decrease.
We realized there is a 25% increase because
[tex]y = 3.6 {(1 + 25\%)}^{x} [/tex]
Hence
[tex]r = 25\%[/tex]
What does m equal?
3 3/4 m = 33 3/4
MAPS On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The on
ilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and
ove along Magnolia is 280 feet, what is the distance between the two streets along Kendall?
The distance between the two streets along Kendall is 347.9 feet.
Solution:
The image of the problem is attached below.
Distance between Wilmington to Ash Grove along Kendall = 820 feet
Distance between Wilmington to Ash Grove along Magnolia = 660 feet
Distance between Beech and Ash Grove along Magnolia = 280 feet
Distance between Wilmington to Beech along Magnolia
= 660 feet – 280 feet
= 380 feet
Let us x be the distance between Wilmington to Beech along Kendall and
820 – x be the distance between Beech and Ash Grove along Kendall.
The given streets are parallel.
By proportionality theorem, parallel lines cut by a transversal are in proportion.
[tex]$\Rightarrow\frac{380}{280} =\frac{x}{820-x}[/tex]
Do cross multiplication.
[tex]$\Rightarrow{380}({820-x}) =280x[/tex]
[tex]$\Rightarrow 311600-380x =280x[/tex]
[tex]$\Rightarrow 311600 =280x+380x[/tex]
[tex]$\Rightarrow 311600 =660x[/tex]
[tex]$\Rightarrow x=472.1[/tex]
Distance between Beech and Ash Grove along Kendall
= 820 – x
= 820 – 472.1
= 347.9
Hence the distance between the two streets along Kendall is 347.9 feet.
Final answer:
By analyzing the given distances along two parallel paths and using proportional reasoning, it is determined that the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
Explanation:
Since Wilmington Street, Beech Drive, and Ash Grove Lane are parallel, and given the distances along Kendall and Magnolia, we can deduce the relationships between these distances to find the desired measurement. Utilizing the ratio of distances along Magnolia, we can apply the same ratio to the distances along Kendall.
We know that the total distance along Magnolia (660 feet) minus the distance between Beech and Ash Grove (280 feet) gives the distance between Wilmington and Beech along Magnolia, which is 380 feet. Assuming the distance distribution is proportional along Kendall, the distance between Beech and Ash Grove along Kendall would be given by:
(280 feet / 660 feet) * 820 feet = (2/3) * 820 feet = 547.33 feet.
Therefore, the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
usually 1/1000 of the headphones cannot pass the tests . if they found 5 headphones failing, how many headphones did the workers test?
Answer: 5000
Step-by-step explanation: 5/5000
The workers tested 5000 headphones.
Explanation:To find out how many headphones the workers tested,
We can set up a proportion to solve the problem:
1/1000 = 5/x
Cross multiplying, we get:
x = 5 * 1000
x = 5000
Therefore, the workers tested 5000 headphones.
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9+3x=6(3-x) what is the answer
Answer:
x = 1
Step-by-step explanation:
9 + 3x = 18 - 6x
3x + 6x = 18 - 9
9x = 9
X = 1
Answer:
Step-by-step explanation:
9+3x =6(3-x)
9+3x =6 ×3 - 6x
9+3x =18 -6x
Collect like terms
9-18= -6x-3x
-9 =-9x
Divide both sides by -9
-9/-9 =-9x/-9
Minus cancels minus and 9 divided by 9 is 1 on both sides
1 =x
x =1
A miners' cage of mass 420 kg contains 3 miners of total mass 280 kg. The cage
is lowered from rest by a cable. For the first 10 seconds the cage accelerates
uniformly and descends a distance of 75 m. What is the force in the cable during
the first 10 seconds?
Answer:
5817 Newtons.
Step-by-step explanation:
Total mass of the cage + the miners = 700 Kg which is a downward force of 700g N.
The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.
We calculate the acceleration of the cage by using an equation of motion:
Distance = ut + 1/2 a t^2 where u = initial velocity , t = time and a = acceleration:
75 = 0(t) + 1/2 a (10^2)
50a = 75
a = 1.5 m s-2.
So using Newtons second law of motion
Force = mass * acceleration:
700*9.81 - T = 700 * 1.5
T = 700 * 9.81 - 700*1.5
= 5817 N.
The force in the cable during the first 10 seconds is 7930N. This was determined using the formulas s = ut + 1/2at² (to calculate acceleration) and F = ma + mg (to calculate the force).
Explanation:The subject of this question is Physics, specifically dealing with forces and acceleration. The total weight of the miners and the cage equals the sum of the miners' weight and the cage's weight, giving a total of 700kg, using the formula weight = mass x gravity (assumed to be 9.8m/s²). Therefore, the total weight is 700kg x 9.8m/s² = 6860N.
Then, we'd calculate the acceleration. The formula used is s = ut + 1/2at², where s is distance, u is initial velocity, a is acceleration, and t is time. Given that initial velocity is 0, the formula is simplified to s = 1/2at². After rearranging, we get acceleration (a) = 2s/t² = 2*75/10² = 1.5m/s².
Finally, we can determine the force on the cable using the formula F = ma + mg (F = force, m = mass, a = acceleration, g = gravity). Substituting, we get F = 700kg x 1.5m/s² + 700kg x 9.8m/s² = 7930N. Therefore, the force in the cable during the first 10 seconds is 7930N.
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3x + 6y= 6
9x - 12y = 18 elimination with multiplication
Answer: x = 4y/3+2
y = 0
Step-by-step explanation:
About 50 percent of the math questions are multiple choice and 50 percent are grid-in.
True. False
Answer:
True
Step-by-step explanation:
a new stadium will seat 83,820. There will be 132 different sections. If each section seats same number of people, how many people will each section seat?
Answer:
635
Step-by-step explanation:
83,820 / 132 = 635
If x varies inversely as y, and x = 3 when y= 8, find y when x=4
The value of y is 6 when x is 4
Step-by-step explanation:
If x varies inversely as y, then
x = [tex]\frac{k}{y}[/tex] , where k is the constant of variationxy = k, you can find k by using the initial values of x and y[tex]\frac{x_{1}}{x_{2}}=\frac{y_{2}}{y_{1}}[/tex]∵ x varies inversely as y
∴ x = [tex]\frac{k}{y}[/tex]
∵ When x = 3, y = 8
- Substitute these values in the equation to find k
∴ 3 = [tex]\frac{k}{8}[/tex]
- Multiply both sides by 8
∴ 24 = k
∴ The equation of variation is x = [tex]\frac{24}{y}[/tex]
∵ x = 4
- Substitute the value of x in the equation to find y
∴ 4 = [tex]\frac{24}{y}[/tex]
- Multiply both sides by y
∴ 4y = 24
- Divide both sides by 4
∴ y = 6
The value of y is 6 when x is 4
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two triangles are similar. The base of the first triangle is 10 cm and the height is 15 cm. The base of the second triangle is 12 cm. The height of the second triangle is?
Answer:
the height is 18cm
Explanation:
If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides. Are these ratios equal?
given that
Triangle 1 (first triangle)
base = 10cm
height = 15cm
Triangle 2 (second triangle)
base = 12cm
height = unknown
base 1 / base 2 = height 1 / height 2
10cm / 12cm = 15cm / xcm
xcm = 18cm
height = 18cm
2×1 1/2 -1 1/2×1 1/2
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
Whoever gives me the right answer gets extra points, please help me
Area of the carpet needed = 38 ft²
Solution:
The given image is splitted into two shapes.
One is trapezoid and the other is triangle.
Top base of the trapezoid = 8 ft
Bottom base of the trapezoid = 12 ft
Height of the trapezoid = 3 ft
Area of the trapezoid = [tex]\frac{1}{2} (a+b)\times h[/tex]
[tex]$=\frac{1}{2}(8+12)\times3[/tex]
[tex]$=10\times3[/tex]
= 30
Area of the trapezoid = 30 ft²
Base of the triangle = 12 ft – 8 ft = 4 ft
Height of the triangle = 4 ft
Area of the triangle = [tex]\frac{1}{2} b h[/tex]
[tex]$=\frac{1}{2} \times4\times4[/tex]
= 8
Area of the triangle = 8 ft²
Area of the carpet = Area of the trapezoid + Area of the triangle
= 30 ft² + 8 ft²
= 38 ft²
Area of the carpet = 38 ft²
Hence 38 square feet of outdoor carpet will need for this hole.
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Solve for r
-13 = r/9 + 8
r=
Answer:
r= -45
Step-by-step explanation:
trust on this one
Answer:
-189
Step-by-step explanation:
Josie's dog weighs 122 pounds. This is about 7 times as much as Len's dog weighs. About how much does Len's dog weigh? Select the numbers that correctly complete the sentence. Len's dog weighs between pounds.
Divide the weight of Josies dog by 7:
122 / 7 = 17.43
It weighs between 17 and 18 pounds.
Final answer:
Len's dog weighs about 17 pounds, calculated by dividing Josie's dog's weight (122 pounds) by 7 since her dog is approximately 7 times heavier than Len's.
Explanation:
Josie's dog weighs 122 pounds, which is about 7 times as much as Len's dog weighs. To find the weight of Len's dog, we need to divide the weight of Josie's dog by 7. Here's the calculation:
122 pounds by 7 = approximately 17.43 pounds
Therefore, Len's dog weighs about 17 pounds. This is a unit of weight that makes sense for the size of a dog. We choose pounds because ounces would be too small and tons would be too large to represent the weight of a large dog accurately. Thus, using pounds is appropriate to express the weight of a dog, such as Len's dog in this case.
How do you evaluate 2x3x5
Answer:
Step-by-step explanation:
Answer:I think it's 30
Step-by-step explanation:
Because 2x3=6 and 6x5= 30
Solve for x
X cubed =27/64
[tex]$x=\frac{3}{4}[/tex]
Solution:
Given expression is [tex]x^3=\frac{27}{64}[/tex].
To solve the expression and find the value of x.
[tex]$\Rightarrow x^3=\frac{27}{64}[/tex]
27 can be written as 3 × 3 × 3 = [tex]3^3[/tex]
64 can be written as 4 × 4 × 4 = [tex]4^3[/tex]
[tex]$\Rightarrow x^3=\frac{3^3}{4^3}[/tex]
Taking cube root on both sides of the function.
[tex]$\Rightarrow\sqrt[3]{x^3}=\sqrt[3]{\frac{3^3}{4^3}}[/tex]
Cube and cube roots are cancelled.
[tex]$\Rightarrow x=\frac{3}{4}[/tex]
Therefore, [tex]x=\frac{3}{4}[/tex].
For abc shown with vertices at A(-2,6),B(8,-2) and C(-8,-4), shown using coordinate geometry that the segment connecting the midpoint of sides Ac and BC is half the length of side AB.
Answer:
It is proved that AB = 2 × DE.
Step-by-step explanation:
The three vertices of triangle ABC are A(-2,6), B(8,-2) and C(-8,-4).
So, the mid point of AC (say D) has coordinates [tex](\frac{- 2 - 8}{2},\frac{6 - 4}{2}) = (-5,1)[/tex].
And the mid point of BC (say E) has coordinates [tex](\frac{8 - 8}{2}, \frac{- 2 - 4}{2}) = (0, - 3)[/tex].
Now, the length of DE will be [tex]\sqrt{(- 5 - 0)^{2} + (1 + 3)^{2}} = \sqrt{41}[/tex] units.
Again, the length of AB will be [tex]\sqrt{(- 2 - 8)^{2} + (6 + 2)^{2}} = 2\sqrt{41}[/tex] units.
So, it is proved that AB = 2 × DE. (Answer)
Find the equation of the line between (-7,4) and (5,9) in slope intercept form
Step-by-step explanation:
(9-4)/(5+7)= 5/12
y - 4 = 5/12(x + 7)
y - 48/12 = (5/12)x + 35/12
y = (5/12)x + 83/12
In the order of operations, what is the first operation that you should take care of?
Answer: Remember PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. But when trying to solve a problem with a variable, remember to go backwards.
Solve for X (simple)
Answer:
156°
Step-by-step explanation:
This is simply angle on a straight and this angle is 180°
X + 24 = 180
Collect like terms
X = 180 — 24
X = 156°
2 Points
Which equation represents the slope-intercept form of the line below?
y-intercept = (0,2)
slope =
O A. y= 2x-}
O B. y=-x-2
O C. y=-_x+2
O D. y= 2x+
Answer:
the answer is C
Step-by-step explanation:
In the y intercept formula which is y=Mx+b the b in the formula represents the y intercept
7.8 dividend by 0.03
Answer:
its 26
Step-by-step explanation:
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