which is equivalent to ( a^2/3 b ^1/3) ^1/2
Answer:
Answer E is correct
Step-by-step explanation:
We know that,
[tex](x^ay^b)^c=x^a^cy^b^c[/tex]
Let us use the above to find the answer to this question.
Let us solve it now.
[tex](a^\frac{2}3} b^\frac{1}{3})^\frac{1}{2}[/tex]
[tex]a^\frac{2}3}^*^ \frac{1}{2} *b^\frac{1}{3}^*^\frac{1}{2}[/tex]
[tex]a^\frac{2*1}{3*2} * b^\frac{1*1}{3*2}[/tex]
[tex]a^\frac{2}{6} * b^\frac{1}{6}[/tex]
Here, we can simplify the [tex]a^\frac{2}{6}[/tex] as [tex]a^\frac{1}{3}[/tex] by dividing the numerator and denominator by 2.
Therefore, the answer will be,
[tex]a^\frac{1}{3} b^\frac{1}{6}[/tex]
Select all the correct.
Which values are included in the solution set of this inequality?
2x2 1 > 6x
x = 3
x = -4
x = 1
x = 5
x = -2
Leg = 11 meters, Hypotenuse = 15 meters
Answer:
10.19
Step-by-step explanation:
Use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex]
Substitute the numbers given:
[tex]11^{2}+b^{2}=15^{2}[/tex]
[tex]121+b^{2}=225\\ b^{2}=225-121\\ b^{2}=104\\ \sqrt b^{2}= \sqrt{104} \\ b=10.19[/tex]
Select the correct answer.
The figure shows a vertical cross section of a sphere inscribed in a right cone.
A vertical cross section of a sphere inside a cone has a radius labeled lowercase r. The height of the cone is 12 centimeters. The half-length of the face of the cone is 5 centimeters.
Find the volume of the sphere in terms of π.
The volume of the sphere will be 49π cubic cm. Then the correct option is C.
What is the volume of the sphere?Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The figure shows a vertical cross-section of a sphere inscribed in a right cone.
A vertical cross-section of a sphere inside a cone has a radius labeled as r. The height of the cone is 12 centimeters. The half length of the face of the cone is 5 centimeters.
Then the volume of the sphere will be
In ΔADF, we have
tan a = 5 / 12
a = 22.61°
Then in triangle ΔABC, we have
sin 22.61° = r / (12 - r)
0.38 = r / (12 - r)
4.62 - 0.38r = r
1.38r = 4.62
r = 3.34 cm
Then the volume of the sphere will be
V = 4/3 π(3.34)³
V = 49π cubic cm
Then the correct option is C.
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Answer:
49cm
Step-by-step explanation:
49cm i got it right on edmentum
Find the value of x.
x = [?]
Answer: 8
Step-by-step explanation:
The triangles are congruent by SAS, so using CPCTC, the answer is 8
A water cooler holds 18 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters)
3 gallons
4 gallons
5 gallons
14 gallons
Answer:
5 gallons
Given:
• Liters in 1 gallon
• Cooler holds 18 liters
Step-by-step explanation:
[tex]\sf 18L \div 3.785 = 4.75G[/tex]
≈ [tex]\sf 5G[/tex]
Answer:
5 gallons
Step-by-step explanation:
Unit conversion (given) : 1 gallon = 3.785 liters
Here, we are given 18 liters.
Then, let the value in gallons be x. We can take the values in proportion.
⇒ [tex]\frac{x}{1} = \frac{18}{3.785}[/tex]
⇒ [tex]x = \frac{18}{3.785}[/tex]
⇒ [tex]x = 4.75561427[/tex]
⇒ x = approximately 5 gallons
4(a2 + 2b) - 2b when a = 2 and b = –2.
Answer:
4
Keys:
[tex]a \cdot (-b) = -a \cdot b[/tex][tex]-\left(-a\right)=+a[/tex]Step-by-step explanation:
[tex]4\left(\left(2\right)\cdot \:2+2\left(-2\right)\right)-2\left(-2\right)\\\left(2\right)\cdot \:2+2\left(-2\right)\\=4+2\left(-2\right)\\=4-4\\=0[/tex]
[tex]=4\cdot \:0-2\left(-2\right)\\4\cdot \:0\\=0\\=0-2\left(-2\right)[/tex]
[tex]2\left(-2\right)\\=-4\\=0-\left(-4\right)[/tex]
[tex]0-\left(-4\right)\\=0+4\\=4[/tex]
Classify the following triangle
Types of Triangles (Angles):
---Acute = all angles are less than 90 degrees
---Right = one angle is equal to 90 degrees
---Obtuse = one angle is greater than 90 degrees
Types of Triangles (Side Lengths):
---Equilateral = all sides are the same length
---Isosceles = two sides are the same length
---Scalene = all sides are different lengths
The following triangle is obtuse and scalene. It has one angle that is greater than 90 degrees and its sides are all different lengths.
Hope this helps!
B. Scalene
E. Obtuse
Step-by-step explanation:Triangles can be classified in 2 different ways. They can be classified based on their sides and angles.
Sides
There are 3 different categories for the sides: scalene, isosceles, and equilateral.
Scalene - these triangles have 3 sides that are all different lengths.Isosceles - Isosceles triangles have 2 congruent sides. This also means that they have 2 congruent angles.Equilateral - These triangles have all equal sides, which also means all the angles are also equal.Angles
Triangles can be classified as acute, obtuse, or right based on their angles.
Acute - Acute triangles only have acute angles. This means there is no angle over 89 degrees.Obtuse - Obtuse triangles have 1 obtuse angle. Obtuse angles are over 90 degrees.Right - Right triangles have 1 right angle. Remember that right angles are exactly 90 degrees.Scalene Obtuse Triangle
The triangle above has no equal sides, so it must be scalene. Additionally, because one of the angles is 132 degrees, it must be an obtuse triangle.
Can y’all help find the surface area please and thank you
To find the area of a complex shape:
⇒ must cut the whole shape into a simpler shape
square with side lengths of 4 in2 triangles with a base of 4 in. and a height of 8 in.2 triangles with a base of 4 in. and a height of 10 in.Let's calculate:
Area of 2 triangles with a base of 4 in. and a height of 8 in.[tex]Area = \frac{1}{2}*4*8 + \frac{1}{2}*4*8=16+16=32\\[/tex]
2 triangles with a base of 4 in. and a height of 10 in.[tex]Area = \frac{1}{2}*4*10 + \frac{1}{2}*4*10=20+20=40[/tex]
square with side lengths of 4 in[tex]Area = 4 * 4=16[/tex]
Total Area: 32 + 40 + 16 = 88 in²
Answer: 88 in²
Hope that helps!
Please Help!!!
Miguel is flying a kite, holding his hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 25^{\circ}
∘
. If the string from the kite to his hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answer:
63.5 m from the ground
answer is 66.9 ft
top is the step by step explanation, hope it helps <3
PLEASE SOLVE I WILL MARK BRAINLIEST HURRY PLEASE
Applying the Pythagorean theorem, the missing lengths in the right triangles are:
1. √19 ≈ 4.4
2. √96 ≈ 9.8
3. √60 ≈ 7.7
4. √231 ≈ 15.2
5. √21 ≈ 4.6
6. √24 ≈ 4.9
What is the Pythagorean Theorem?The Pythagorean theorem is a formula that can be used to find the leg of a right triangle, and is given as: c² = a² + b², where a and b are the smaller legs and c is the longest leg/hypotenuse.
1. missing leg = √(10² - 9²) = √19 ≈ 4.4
2. missing leg = √(11² - 5²) = √96 ≈ 9.8
3. missing leg = √(8² - 2²) = √60 ≈ 7.7
4. missing leg = √(16² - 5²) = √231 ≈ 15.2
5. missing leg = √(5² - 2²) = √21 ≈ 4.6
6. missing leg = √(7² - 5²) = √24 ≈ 4.9
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Nicole is deciding between two different movie streaming sites to subscribe to. Plan A costs $24 per month plus $1.50 per movie watched. Plan B costs $12 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Nicole watches xx per month, and let BB represent the monthly cost of Plan B if Nicole watches xx movies per month. Graph each function and determine the interval of movies watched, x,x, for which Plan A is cheaper than Plan B.
Answer:
Plan B
Step-by-step explanation:
If you multiply 21 by $2.50 you get $52.5 then add $5 you get 57.5 and that's you outcome for Plan A
but if you multiply 21 by $1.50 you get $31.5 then add $24 you get $55.5 so the best and cheapest plan would be Plan B
Zero is less than negative fifteen decreased by y, solve for y.
av <15
what is the answer?
The inequality equation will be 0 < -15 - y. Then the value of the variable y is less than negative 15.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Zero is less than negative fifteen decreased by y, can be written as mathematically
0 < -15 - y
Then solving for y, we have
y < -15
The value of the variable y is less than negative 15.
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Maddie's backyard is 25 meters by 25 meters. She wants to put a square cement patio in her backyard. She does not want the patio to be as
large as the yard. Let A be the area of the patio, in square meters.
Which inequality represents the possible length of the patio?
A. √A> 25
B. √A < 25
C. √A> 625
D. √A < 625
The inequality that represents the possible length of the patio is √A < 625.
How to represent an inequality?Maddie's backyard is 25 meters by 25 meters.
Therefore,
area of the backyard = 25 × 25 = 625 m²
Hence,
She wants to put a square cement patio in her backyard.
A = area of the patio, in square meters.
Hence,
area of the backyard = 625 m²
Therefore, the inequality that represents the possible length of the patio is √A < 625.
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Im trying to get everything on my overdue list done- but most of its math anyone help?
The total surface area of the given pyramid is:
A = 39ft²
How to get the surface area of the given figure?
The total surface area will be equal to the sum of the areas of the square and the 4 triangles.
Remember that for a square of side length S, the area is:
A = S².
In this case, S = 3ft, then:
A = (3ft)² = 9ft².
Now, the area of a triangle of base B and height H is:
A = B*H/2.
Here we can see that the triangles have a base of 3ft (the sides of the square) and a height of 5ft, then the area of each triangle is:
A = (3ft)*(5ft)/2 = 7.5 ft²
Then the total area of the figure is:
A = 4*(7.5 ft²) + 9ft² = 39ft²
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A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. how many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5
Answer:
16 red marbles
Step-by-step explanation:
8 red
9 yellow
7 green
total = 8 + 9 + 7
p(red) = 8/24 = 1/3
Add r number of red marbles to the total.
8 + r red
9 yellow
7 green
total = 8 + r + 9 + 7 = r + 24
p(red) = (8 + r)/(r + 24) = 3/5
Cross multiply.
40 + 5r = 72 + 3r
2r = 32
r = 16
Answer: 16 red marbles
Answer:
16
Step-by-step explanation:
bag red: 8 + x
yellow:9
green 7/24
3/5 = 8+ x/24+ x
5(8 + x) = 3 (24 + x)
40 + 5x
-40 -3x = 72 + 3x
-40 -3x -40 - 30
2x/2 = 32/2 so,x = 16
What is the relationship between the number of sides of the base of a prism and the number of lateral faces?
A . The number of sides of the base of a prism is less than the number of lateral faces. B. The number of sides of the base of a prism and the number of lateral faces is equal. C. The number of sides of the base of a prism is greater than the number of lateral faces.
C . There is no consistent relationship between the number of sides of the base of a prism and the number of lateral faces.
Answer: The number of sides of the base of a prism and the number of lateral faces is equal.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
edge exam
Which of the following is equal to 9•4
x - 4x² + 2x³
What is the degree of the polynomial?
Answer:
3
The degree of a polynomial is the highest power of any variable in the polynomial equation.
Here the highest power is 3 of the monomial with co-efficient of 2.
Mark the statements that are true. A. An angle that measures π/4 radians also measures 45°. B. An angle that measures 180° also measures π radians. C. An angle that measures 60° also measures π/3 radians. D. An angle that measures π/3 radians also measures 30°.
Answer:
TRUE: A, B, C
False: D
Step-by-step explanation:
A full circle of 360° has a radian measure of 2π radians. The relationship is proportional, so π radians is 180°.
__
A. An angle that measures π/4 radians also measures 45°. TRUE
45° × π/180° radians = π/4 radians
B. An angle that measures 180° also measures π radians. TRUE
180° × π/180° radians = π radians
C. An angle that measures 60° also measures π/3 radians. TRUE
60° × π/180° radians = π/3 radians
D. An angle that measures π/3 radians also measures 30°. FALSE
30° × π/180° radians = π/6 radians
Omar paid $8.64 for 5.4 pounds of grapes. what was the cost of 1 pound of grapes?
what is the x-intercept of 3y=2x-6 please also show steps this is due in a few minutes !!!!
An angle has a reference angle of 40° and its terminal side lies in Quadrant III. What are a possible positive measure and a negative measure for the angle?
The positive measure is 220° and the negative measure is -140°.
How to find the measures of the angle?First, we know that the reference angle is 40°, and it lies on the third quadrant.
So these 40° are measured from the negative x-axis (the axis where the quadrant starts).
This means that the angle measured in the standard way (from the positive x-axis) measures:
M = 40° + 90° + 90° = 220°.
To find the negative measure, we remember that any angle A is equivalent to:
B = A + n*360°.
Where n is an integer.
If we take n = -1 for our angle, we get:
M' = 220° + (-1)*360° = -140°.
So the positive measure is 220° and the negative measure is -140°.
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A TV has a listed price of $841.99 before tax. If the sales tax rate is 9.5%, find the total cost of the TV with sales tax included
Answer:
[tex]9.5 \div 100 \times 841.99 = 79.99 \\ \\ 841.99 + 79.99 \\ 921.98[/tex]
Answer:
$921.98905
Step-by-step explanation:
To find the sales tax amount we need to find 9.5% of 841.99
for this we can use 2 methods:
Method 1-
P%* X= Y
9.5%*841.99= Y
Convert 9.5% to a decimal by removing the percent sign and dividing by 100: 0.095
Substitute 0.095 for 9.5% in the equation: 9.5% * 841.99 = Y becomes 0.095 * 841.99 = Y
Do the math: 0.095 * 841.99 = 79.98905
OR
method 2-
9*841.99
=7998.905
÷100
=79.98905
Now that we know how much the the amount is all we have to do is add the amount with the original price of the tv
$841.99 + $79.97905= $921.98905
How to decompose 1 1/6
Answer:
7/6
Step-by-step explanation:
6*1=6
6+1=7
7/6
Hope this helped! :)
Abc is a right triangle. if ac=7 and bc=8 find ab
Name all of the obtuse angles that share a side with angle VON
A. Angles NOS, NOP, NOQ, VOS, VOQ, VOP
B. Angles NOS, NOT, NOV, VOR, VOU, VOP
C. Angles NOS, NOT, NOR, VOR, VOQ, VOP
D. Angles NOS, NOT, NOU, VOR, VOQ, VOP
The angles NOS, NOT, NOU, VOR, VOQ, VOP are obtuse angles
What is an Obtuse Angle ?An angle whose measure is more than 90 degree is called an obtuse angle.
In the given figure , the angles which have value more than 90 degree needs to be found.
The angles NOS, NOT, NOU, VOR, VOQ, VOP are obtuse angles as their measure is more than 90 degree.
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A student says that the x-intercept of the graph of × + 2y =5 is the point (0,5). Is the student correct or incorrect? Explain your answer and show your work.
Will give brainliest!!
The student is incorrect, the actual x-intercept is (5, 0).
Is the student correct or incorrect?
Here we have the equation:
x + 2y = 5
The student says that the x-intercept is the point (0, 5).
So if you look at the point you already can see that the student is incorrect, this is because the x-intercept always must have a y-value of 0. (the graph only intercepts the x-axis when y = 0).
So the point (0, 5) can't be an x-intercept.
For the given function:
x +2y = 5
The x-intercept is given by:
x + 2*0 = 5
x = 5
So it is (5 , 0).
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Grace buys a set of 14 notebooks. Each notebook has 85 pages. What is the total number of pages for all the notebooks?
Answer: 1190 pages
Step-by-step explanation:
The word problem states that Grace has a set of 14 notebooks, and each notebook has 85 pages. To find the total number of pages, we want to multiply the number of pages in each book by how many books there are.
14×85=1190 pages
A health food store makes trail mix using dried fruit and nuts. The cost of the dried fruit is $2.50 per pound, and the cost of the nuts is $2.00 per pound. The total cost to make the trail mix is $225. If the total cost can be represented by the equation 2.5x+2y=225, what does the term 2.5x represent?