Which expression is equivalent to 7x^2 square root of 2x^4 • 6 square root of 2x^12, if x does not equal 0?
Answers
For the given expression, the correct answer is C, 7x².√2x⁴.6√2x¹² = 84x¹⁰.
Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
A variable is a letter, like x, y, or z, that stands in for an arbitrary number. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.
Given,
the expression is 7x².√2x⁴.6√2x¹²,
Solving the under root,
⇒ 7x².√2x².6√2x⁶
⇒ 7x² . √2 x². 6. √2 . x⁶ [√2 × √2 = 2]
⇒ 7 × 6 × 2 × x¹⁰ = 84 x¹⁰
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Related Questions
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
Step-by-step explanation:
See attached graph.
The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
Answers
Please help with this geometry question!
Answers
Answer:[tex]\sqrt{303.51}[/tex]
Step-by-step explanation:
The difference in the radii of the two circles is [tex]4.3-1.8=2.5[/tex] inches.
Since the tangent has a length of 2.5 inches, by the Pythagorean theorem, the required distance is
Select the correct answer.
Which of the nets below will make a closed cube?
Mariatu Yakubu
Answers
The net that represents a cube is (b) net b
How to determine the net?A cube has 6 faces
This means that the net must have 6 faces
For a net to represent a cube, there must be four adjacent faces
And 2 two adjacent faces
Where
One of the two adjacent faces is at the end of the fourth faceThe other is at the 3rd positionBoth 2 faces do not face the same directionThe net that represents the above scenario is net (b)
Hence, the net that represents a cube is (b) net b
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what is the absolute value of -45/6. I need serious help
Answers
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
The absolute value of a number is just its distance from zero. In other words, if it's negative, the absolute value would make the number positive. This makes the absolute value [tex]\frac{45}{6}[/tex]. Now, reduce to get[tex]\frac{15}{2}[/tex].
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
Answers
[tex]x {}^{2} - 9 = 8x \\ x {}^{2} - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^{2} - 4(1)( - 9)} }{2( {1}^{}) } [/tex]
[tex]x = \frac{8 + \sqrt{64 + 36} }{2} = \frac{8 + \sqrt{100} }{2} = \frac{8 + 10}{2} = 9[/tex]
Answer: x = 9
Step-by-step explanation:
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
let x = a number
[tex]x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1[/tex]
taking only the positive solution, we get x = 9
Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.
a. How long is the belt?
b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground.
c. We need a ramp to the window. How long would it need to be?
Answers
From the given information,
a. The length of the belt is 180.28 ft
b. The height of the window from the ground is 100 ft
c. The length of the ramp needed is 141.42 ft
What is the Pythagorean theorem's formula?The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²
Calculation:It is given that,
The height of the silo is 150 feet
The distance from the belt to the silo is 100 feet
With the given measurements, a right-angled triangle is formed.
a. Finding the length of the belt:
From the diagram,
The height of the silo, sh = 150 ft
The base distance, sb = 100 ft
So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.
On applying the Pythagorean theorem,
bh² = sb² + sh²
⇒ bh² = (100)² + (150)²
⇒ bh² = 32500
⇒ bh = √32500 = 50√13
∴ bh = 180.28 ft
Thus, the length of the belt is 180.28 ft.
b. Finding the height of the window from the ground:
It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.
This creates a special right-angled triangle. I.e.,
The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)
So, the new triangle has angles of 90°- 45°- 45°
Thus, the new triangle is said to be an isosceles right angled triangle.
So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft
Therefore, the height of the window from the ground(sw) is 100 ft
c. Finding the length of the ramp(bw) to the window:
Since we have
sw = 100 ft and sb = 100 ft
On applying Pythagora's theorem,
bw² = sb² + sw²
⇒ bw² = (100)² + (100)²
⇒ bw = √20000 = 141.42 ft
Therefore, the length of the ramp to the window is 141.42 ft.
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Super confused need help
Answers
WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Answers
Answer:
20
Step-by-step explanation:
20+20=40
PLEASE HELP EDGE2022 Which inequality is represented by the graph?
y ≥ –2(x + 1)2 + 5
y ≤ –2(x + 1)2 + 5
x ≥ –2(y + 1)2 + 5
x ≤ –2(y + 1)2 + 5
Answers
The inequality graphed is the one in the first option.
Which inequality is represented by the graph?
On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).
And the shaded region is above the parabola.
Then the inequality is of the form:
y ≥ parabola.
By knowing where is the vertex, we know that:
parabola = -a*(x + 1)^2 + 5
Then the correct option is the first one.
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The following contingency table gives the results of a sample survey of Sowetan male and female respondents regarding their preferred mobile phone service provider.
What is the probability of selecting a respondent who does not prefer Cell C?
a.
0.2250
b.
0.50
c.
0.3750
d.
0.65
e.
0.7750
Answers
The probability of selecting a respondent who does not prefer Cell C is 0.775
How to determine the probability?The complete question is in the attached image
From the attachment, we have
Prefer cell C = 90
Total = 400
So, the number of respondents that do not prefer cell C is
Do not = 400 - 90
Do not = 310
The probability is then calculated as:
P = 310/400
Evaluate
P = 0.775
Hence, the probability of selecting a respondent who does not prefer Cell C is 0.775
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A = {1, 2, 6}
B = {x|x is an odd whole number less than 8}.
Find An B.
Answers
Answer:
A∩B = { 1 }
Step-by-step explanation:
Consider the sets :
A = {1, 2, 6}
B = {x ;where x is an odd whole number less than 8}
Suppose the numbers of B are natural numbers (not integers).
Then
B = {1 , 3 , 5 , 7}
We obtain :
A = {1, 2, 6} and B = {1 , 3 , 5 , 7}
The intersection of A and B or the set A∩B :
is the set of the common numbers of A and B.
Then
A∩B = { 1 }
The set A intersection B(or, A∩B) for the given set A and set B exists {1}.
What is A intersection B, (A∩B)?"The set A intersection B(or, A∩B) exists described as the set composed of all elements that belong to both A and B".
The intersection of a set A with a B exists the set of elements that exist in both sets A and B. The intersection exists represented as A∩B.
The intersection of two mathematical objects exists where they overlap. For geometric objects, the intersection exists as a point or group of points where the objects cross.
For numerical or non-numerical sets, the intersection exists every number or object the two sets contain in common.
Given: A = {1, 2, 6}
B = {x | x is an odd whole number less than 8}.
From the above information, we get
⇒ B = {1, 3, 5, 7}
If A = {1, 2, 6} and B = {1, 3, 5, 7}
then A∩B = {1, 2, 6} ∩ {1, 3, 5, 7}
A∩B = {1}
Therefore, the correct answer A∩B exists {1}.
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2. Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives one A in three-credit class, one D in three-credit class, three B in three-credit class and two C in one-credit class, what is the student’s grade point average?
Answers
Based on the student's grades, and the credit hours, their grade point average is 2.60.
What does the student get as their GPA?First, find the grade points earned:
= (4 x 3) + (1 x 3) + (3 x 3) + (2 x 1)
= 12 + 3 + 9 + 2
= 26
The GPA is:
=Grade points earned / total number of credits
= 26 / (3 + 3 + 3 + 1)
= 26 / 10
= 2.6
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What is the discount and sale price of a $300 item that has been discounted at 10%?
Answers
Answer:
Discount: $30 off
New Sale Price: $270
Step-by-step explanation:
$300*10% =
30
$300-30=
$270
or
$300*.1=
30
$300-30=
$270
Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Answers
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
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Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
Answers
[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]
[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]
As seen in the diagram below, Shandra is building a walkway with a width of feet
to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the
pool and the walkway will be 168 square feet, how wide should the walkway be?
Answers
The walkway should be about 2.57feet.
What is the total surface area?
The total surface area of the building is the sum of the total faces of an object contains.
The formula is expressed as:
TSA = 2(lw + wh + lh)
where,
l is the length ,w is the width , h is the height
Calculation
Given the following parameters
TSA = 168 square feet
length = 8 feet and Height = 6 feet
Required
Width of the walkway, Substitute the given values in the formula
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
4w = 84 - 48
14w = 36
w = 2.57feet
The walkway should be about 2.57feet.
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What is the domain and range of the quadratic function given by the equation /(x) = 2(x-4)] - 2
Answers
The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2
How to determine the domain and the range?The function is given as:
f(x) = 2(x -4)^2 - 2
A quadratic function can take any real number as its input.
So, the domain of the function is the set of all real numbers
The vertex of the above function is:
Vertex = (4, -2)
And the leading coefficient is:
a = 2
The y value of the vertex is;
y = -2
Because the value of a is positive, then the vertex is a minimum.
This means that the range of the function is the set of all values greater than -2
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Teacher increases spatial awareness for children as they use position words and provide experience through mapping and manipulating shapes.
a. True
b. False
Answers
It is true teachers can increase spatial awareness as they use position words or implement mapping and shape manipulation.
Whatis spatial awareness?This refers to the ability to understand the position of one's body in relation to space and other objects as well as understanding how location and movement work.
How can spatial awareness be increased in children?In children spatial awareness can be increased through:
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The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
Answers
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
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Ross Martin arrived at the following tax information gross salary 56,145 interest earnings 205 dividend income 65 standard deduction 12,000 itemized deductions 11,250 adjustments to income 1200 what amount with Ross report as taxable income income
Answers
The amount that Ross report as taxable income will be $31965.
What is a taxable income?Taxable income refers to the base upon which an income tax system imposes the tax.
In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.
From the information:
Gross salary = $56,145
Interest earnings = $205
Dividend income = $65
Standard deduction = $12,000
Itemized deductions = $11,250
Adjustments to income = $1,200
The taxable income is given by:
= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income
= 56145 + 205 + 65 - 12000 - 11250 - 1200
= $31965
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If two points on a line are A(10, −3) and B(12, 9), the rise is __________, and the run is __________, so the slope of the line is __________.
Answers
The rise is the difference in y-coordinates:
y₂ - y₁ = 9 - (-3) = 12The run is the difference in x-coordinates:
x₂ - x₁ = 12 - 10 = 2The slope is the quotient of rise over run:
m = 12/2 = 6========================
If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.
Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
Answers
It's 4 buns & 5 cakes
Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.
E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p
Please help!!! 24 points!!!
Answers
Answer:
-24
Step-by-step explanation:
-6 × f(3) - 6 × g(-1) = ?
to answer this we need to find the functional values of the functions at the specified points.
f(3) = -2
we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.
g(-1) = 6
we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.
and that's really it.
now we need to calculate it all in the main expression :
-6 × -2 - 6 × 6 = 12 - 36 = -24
you remember, that multiplications and divisions have to happen before any addition of subtraction ?
Is this Network a HAMILTONIAN Circuit? If so write the path.
Answers
The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.
What is a Hamiltonian Path?A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.
A traceable graph is one that contains a Hamiltonian path.
Hence, the path is given as;
A, E, B, C, D, F
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Dana believes that she needs to study for at least 14 hours to be prepared for her monthly accounting test. If she can study for 4 hours per day, what is the minimum number of days that she should allow to study for the test?
Answers
This is because 4x4 is 16, but it can’t be 3 since 4x3 is only 12.
7. (05.02 MC)
Luciana's laptop has 3,000 pictures. The size of the pictures is skewed to the right, with a mean of 3.7MB and a standard deviation of 0.78MB
Part A: Can you accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures? Explain.
Part B: If you take a random sample of 60 pictures instead of 20, explain how the Central Limit Theorem allows you to find the probability that the mean picture size is more than 3.8MB.
Answers
Considering the Central Limit Theorem, we have that:
a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.
b) The probability can be calculated, as the sample size is greater than 30.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.
In this problem, the underlying distribution is skewed right, that is, not normal, hence:
For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.For item b, the probability can be calculated, as the sample size is greater than 30.More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
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PLEASE IF ANYONE CAN HELP I HAVE 35 MINUTES LEFT 1-8 ANSWERS ONLY WILL DO THANK YOU
Answers
Answer:
1. x=2 2.
y=1
Step-by-step explanation:
Im sorry I TRIED :(
Imogen buys some sandwiches costing £3.50.
She has a 20% off coupon.
How much discount will Imogen receive?
K
4
Answers
Explanation:
3.50 x 0.2 = 0.7
A rectangle has a length of x-8 and a width of x-9. Which equation below describes the perimeter, P, of the rectangle in terms of x?
a. P=x² - 17x+72
b. P=x-17
c. P = 2x-17
d. P = 4x - 34
*show your work*
Answers
Answer:
d.
Step-by-step explanation:
Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].
Therefore the perimeter [tex]P[/tex] can be expressed as
[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]