Answers
[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]
Answer:
[tex]800\sqrt{5}[/tex]
Step-by-step explanation:
Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]
Properties of Exponents:
Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]
a number raised to a fraction, can be converted to a radical. the numerator becomes the exponent, and the denominator becomes the index of the radical.Product of Powers Property:
when multiplying powers with the same base, add the exponents.1. Convert into a radical:
[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]
2. Simplify the expression:
[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]
3. Evaluate the power:
[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]
4. Multiply:
[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]
Related Questions
A line, y mx + b, passes through the point (2, 3) and is parallel to y 2x + 5. What is the value of b?
Answers
Answer:
Step-by-step explanation:
If a line is parallel to another it must have the same slope
The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept
The line y = 2x + 5 has slope 2
So the slope of the line that passes through (2,3) must also have the slope 2
We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1
Hence the equation of the line is
y = 2x -1
Cross-check
Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent
Use f(x)=2x and f-1(x) = 2x to solve the problems.
f(2)=
f¹(1) =
f¹(f(2)) =
DONE
Intro
Answers
Answer:
1
2
2
Step-by-step explanation:
Which point lies on the line described by the equation below? y+ 4 = 4(x-3) O A. (3,-4) O B. (2,9) O C. (0,0) O D. (1,-11) E. (1,11) OF. (-2, 3) PREVIOUS SUBMIT 22949
Answers
The point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have an equation of a line:
y + 4 = 4(x - 3)
A (3,-4)
Plug the above points in the equation of the line.
-4 + 4 = 4(3 -3)
0 = 0 (true)
The point lies on the line
Similarly checking for others points we will find that points (2,9), (0,0) , (1,-11), (1,11), and (-2, 3) does not lie on the line y + 4 = 4(x - 3)
Thus, the point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
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What is the solurion to h/-24 < 18
Answers
Let's solve
h/-24<18Multiply- on both sides
h/24>-18Multiply 24 on boths sides
h>-18(24)h>-432Solution set
(-432,oo)Answer:
Step-by-step explanation:
Given inequality:
[tex]\sf \dfrac{h}{-24} < 18[/tex]
Eliminate the denominator of the fraction by multiplying both sides by -24, remembering to flip the relation (inequality symbol) as the factor is negative.
[tex]\implies \sf \dfrac{h}{-24} \cdot -24 > 18 \cdot -24[/tex]
[tex]\implies \sf h > -432[/tex]
Therefore, the solution is [tex]\sf h > -432[/tex]
hey can someone help me on this"in your own words describe when you should use area and when you should use volume in calculating the amount of space an object occupies.
Answers
Answer:
Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area
Find the volume of the figure. Use 3.14 for .
5 m
12 m
Answers
Answer:
1203.6 ---- the six is recurring ( .666666...)
Step-by-step explanation:
volume of hemisphere= [tex]\frac{2}{3}[/tex] x 3.14 x r^3
volume of cylinder= 3.14 x r^3 x h
1. Volume of hemisphere= 2/3 x 3.14 x 5^3 = 261.6 recurring
2. volume of cylinder = 3.14 x 5^2 x12 = 942
3. add the two together -----------> 1203.6
The table shows the number of cups of water required when cooking different amount of rice
Which statements apply to the ratio of rice and water? Choose two options.
A) The amount of rice is the dependent value.
B) the amount of the water is the dependent value.
C) the amount of rice is the independent value
D) the amount of water is the independent value.
E) the values cannot be labeled as dependent or independent without a given equation.
Answers
Explanation: the table shows the number of cups of water required when cooking different amounts of rice.
“cups of water required” shows that the water is the dependent variable.
“when cooking different amounts of rice” shows that the rice is the independent (changing) variable.
which formula represents this sequence
Answers
Answer:
pretty sure its b
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Solving Linear Equations: Variable on One Side
ssignment Active
Determining the Input Value That Produces the Same Output
Value for Two Functions
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x
for which f(x) = g(x) is true.
ty
X =
y = f(x)
y = g(x)
x
2 3
Done
-2
Intro
-1
4
3
2
1
1
Answers
answer 2/3
check the attachments for more info
hope it helps :)
The functions f(x) and g(x) are equal for the x = 2/3
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, are two functions, f(x) = -3x + 4 and g(x) = 2, we need to find the value of x for which both are equal,
So,
For f(x) = g(x) we should equate the two functions to get the value of x.
f(x) = g(x)
-3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
Dividing by -3 on both sides;
(-3x)/-3 = (-2)/-3
x = 2/3
Hence, the functions f(x) and g(x) are equal for the x = 2/3
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Describe van Hiele Level 1 (analysis), Level 2 (informal deduction) and Level 3 (deduction). Demonstrate the difference by using a scalene, isosceles and equilateral triangle as an example to explain learner thinking at the three different levels.
Answers
The van Hiele theory describes how young people in schools learn geometry.
How to explain the theory?
Van Hiele theory postulates five levels of geometric thinking which are visualization, analysis, abstraction, formal deduction, and rigor. The levels use their own language and symbols
Analysis: At this level, students start analyzing and naming the properties of geometric figures.
Informal deduction: At this level pupils or students perceive relationships between properties and figures.
Deduction: At this level, students can give deductive geometric proofs. They are able to differentiate between necessary and sufficient conditions.
An equilateral triangle has all sides equal. In an isosceles triangle, two sides are the same length. In a scalene triangle, none of the sides are the same length.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function .
Match each transformation of function f with a feature of the transformed function.
vertical asymptote of
function decreases as x increases
y-intercept at
x-intercept at
arrowRight
arrowRight
arrowRight
Answers
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
How to Interpret Graphs?We are given the function;
f(x) = In (x)
Now, from the given tiles and when we punch the respective values for the given functions, we can say that;
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
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this venn diagram shows sports played by 10 students what is p
Answers
P(A | B) is 2/10 = 0.2.
What is P(A | B) ?P(A | B) means the probability that a students pays both basketball and football. It is the intersection of both circles on the venn diagram.
P(A | B) = number of students that play both games / total number of students
2/10 = 0.2
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What is the solution to the equation |x − 4| = 17?
Answers
[tex]~~~~~~|x-4| = 17\\\\\implies x -4 = 17~~~~ \text{or}~~~~~ x -4 = -17\\\\\implies x = 17+4~~~~\text{or}~~~~~ x = -17+4\\\\\implies x = 21~~~~~~~~~\text{or}~~~~~x = -13[/tex]
Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
Ic. mode
The mode is.
Answers
Answer:
352
Step-by-step explanation:
it repeated more than once
help again...its for math offering 15 points
Answers
Answer:
[tex]\tan \dfrac{\theta}2 = \dfrac{1}2[/tex]
Step by step Explanation:
[tex]\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right][/tex]
[tex]=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2[/tex]
sjifisifnjsjemwjjfjwudjjsdjf
Answers
Answer:
No answer
Step-by-step explanation:
I'm just a smart guy
Which of the following correctly replaces the question mark in Aisha's proof?
OHL
O SSS
O SAS
O AAS
Answers
The option that correctly replaces the question mark in Aisha's proof is SAS (Option C). See it explained below.
Mathematical proofs are statements that are used to demonstrate that a mathematical expression or logic of true.
Since the portion of the question that shows the question mark is missing, we can rewrite the proof as follows:
Step 1
AB Dissects BC
AE ║ BD
Reason - It is given
Step 2
BC ≅ BE
Reason - Definition of Segment Bisector
Step 3
∠ABE ≅ ∠CBD
Step 4
∠BCD ≅ ∠BEA
Reason
Alternative Interior Angles
Step 5
ΔBCD ≅ ΔBEA
Reason
SAS Postulate
Step 6
QED
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Community Gardens
In 1977, in New York City, people noticed something surprising. It was there in a vacant lot. It wasn’t the heaps of garbage. It was the tomato plants that were growing wild. “If vegetable plants can grow there,” some of the people thought, “why can’t we plant vegetables ourselves?” So the people cleared away the garbage. They began growing vegetables, fruits, herbs, and even flowers. The Clinton Community Garden was started.
Community gardens are found in cities all around the country. People start community gardens in vacant lots and on apartment balconies. As unbelievable as it sounds, they even tend gardens on rooftops.
What exactly is a community garden? It’s a garden that different people in a neighborhood plant and tend. It does not belong to any one person. Community gardeners eat and sometimes share the food they grow. Some community gardeners donate their food to local food banks. They give it to people who cannot afford to buy food.
Some community gardens are one large plot of land. Everyone shares in the work. They all plant seeds, weed, water, and share in the rewards. In other community gardens, the larger piece of land is divided up. People tend to their plots.
Community gardens offer many benefits. For one thing, they bring people together. Community gardeners get to know each other. Older people work alongside kids. Another benefit is the low-cost food, of course. The vegetables and fruits are also fresher and more healthful. And people tending a garden are getting fresh air and exercise.
A community garden benefits the whole community. It makes the neighborhood more beautiful. There can be no disagreement about that. A community garden creates a green space among concrete streets and sidewalks. This helps reduce heat in the summer. The plants soak up sunlight. Concrete reflects the sun’s heat into the air. Community gardens indirectly help save fuel resources, too. Trucks don’t have to deliver as much food from long distances to grocery stores. People don’t have to drive as much to grocery stores, so less gas is used.
More community gardens should be started. With all the benefits they bring us, who could argue with that?
A family of three works in a community garden in the middle of a city with tall buildings.
Reread the sentence from the article.
There can be no disagreement about that.
What does the word disagreement most likely suggest?
A.
taking action
B.
getting along
C.
not taking action
D.
not getting along
Answers
Answer:
not taking action
Step-by-step explanation:
because it is talking about how beautiful the gardens are and it could be said like this, "It makes the neighborhood more beautiful. There can be not taking action about that."
Consider the following experiment:
A card is picked at random from a standard deck of 52 cards.
What is the sample space of the experiment? What is the probability of drawing a red card from the deck if 26 of the cards are
red?
a
26 possible outcomes; P(red card) =
26
25
52 possible outcomes: P(red card) = 52
52 possible outcomes: P(red card) = 2
26 possible outcomes; P(red card) = 13
11/13
b.
J
d.
Answers
The sample space is 52 while the probability of drawing a red card is 13/28.
What is probability?The term probability has to do with the probability that an event will occur or not. The probability must have values between 0 - 1.
The sample space refers to all possible outcomes and this is 52. The probability of drawing a red card = 26/52 = 13/28.
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Group the terms with variables on one side of the equal sign, and simplify. 39y = 4y + 11
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to solve the equation [tex]\large\pmb{39y=4y+11}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Isolate y.First, subtract 4 from both sides of the equal sign:
[tex]\pmb{39y-4y=11}[/tex]
Which gives us:
[tex]\pmb{35y=11}[/tex]
Divide both sides by 35:
[tex]\pmb{\cfrac{35}{11}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Work out (5*10^3)*(9*10^7).
Give your answer in standard form.
Work out (7*10^5) / (2*10^2).
Give your answer in standard form.
Answers
Answer:
(5*10^3)*(9*10^7) = 4.5*10^11
(7*10^5) / (2*10^2) = 3.5*10^3
Step-by-step explanation:
calculate 5 multiply by 9
5*9=45
the multiple of the power in the same base of number is calculated by using addition(+)
(10^3)*(10^7) = 10^(3+7)
= 10^10
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
45*(10^10)
= (4.5*10^1) * (10^10)
= 4.5*10^(1+10)
= 4.5*10^11
calculate 7 divide by 2
7/2=3.5
the dividing of the power in the same base of number is calculated by using subtraction(-)
(10^5)/(10^2)
= 10^(5-2)
= 10^3
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
3.5*10^3
Answer:
→ (5×10³)×(9×10⁷) = 4.5 × 10¹¹→ (7×10⁵) / (2×10²) = 3.5 × 10³Step-by-step explanation:
(5×10³)×(9×10⁷)
= 5×10³×9×10⁷
= 5×9×10³×10⁷ (commutative property)
= (5×9)×(10³×10⁷) (associative property)
= 45 × 10³⁺⁷
= 45 × 10¹⁰. (Exponent property)
= 4.5 × 10¹¹
…………………………………………
(7×10⁵) / (2×10²)
= (7/2) × (10⁵/10²)
= 3.5 × 10⁵⁻²
= 3.5 × 10³
HELPPP PLEASEEE i don’t know how to do this and i’m just trying to pass the test
Answers
(B) is the right answer
3-² how do i evaluate this
Answers
Answer:
This will be a negative exponent so get rid of that negative number,
Step-by-step explanation:
This is very useful
9, 16, 23, ...
Find the 46th term.
Answers
Answer:
324
Step-by-step explanation:
Formula: [tex]a_{n} =a_{1} +(n-1)d[/tex]
=> [tex]a_{46} =9_{1} +(n-1)7\\[/tex]
= [tex]9_{1} +(46-1)7\\[/tex]
= [tex]9+(45)7\\[/tex]
= [tex]9+315[/tex]
= [tex]324[/tex]
:D
On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of being correct on two questions.
Answers
All tick marks are equally spaced on each number line below. Find the unknown value (x) for
each. Be prepared to explain your reasoning.
Answers
By finding the value between consecutive tick marks, we will see that:
1) x = 20
2) x = 48
3) x = 9.5
How to find the values of X?
We know that each tick mark are equally spaced in the number lines below.
If you look at the first one (the already solved one). You can see that between the 4 and the 12 there are 4 ticks. If each tick has a value of T, we must have:
4 + 4*T = 12
4*T = 12 - 4 = 8
T = 8/4 = 2
Each tick values 2 units.
Between the 12 and the x there are 4 ticks, then:
x = 12 + 4*2 = 20
Now let's look at the second number line. There are 10 ticks between 25 and 140, then:
25 + 10*T = 140
10*T = 140 - 25 = 115
T = 115/10 = 11.5
And there are 2 ticks between 25 and the x, so:
x = 25 + 2*T = 25 + 2*11.5 = 48
x = 48.
Now the final number line. There are 8 ticks between 10 and 12, then:
10 + 8*T = 12
8*T = 12 - 10 = 2
T = 2/8 = 1/4 = 0.25
Now, the x is 2 ticks before the 10, then we have:
x = 10 - 2*T = 10 - 2*0.25 = 9.5
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Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
A cylindrical cup with a base diameter of 4 inches and a height of 12 inches is filled with orange juice that occupies 67% of the cup. What is the volume of the orange juice in the cup?
Answers
Volume
πr²hπ(2)²(12)48π150.7in³Volume of orange juice
67% of 150.70.67(150.7)100.969in³Answer:
101.0 in³ = 1.656 liters
Step-by-step explanation:
Formulas
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\textsf{Diameter of a circle}=2r \quad\textsf{(where r is the radius)}[/tex]
Given dimensions of cylinder:
diameter = 4 inheight = 12 inFirst, calculate the radius by halving the diameter:
[tex]\implies \textsf{Radius }(r)=4 \div 2=2\: \sf inches[/tex]
Substitute the given values into the formula to find the volume of the cup:
[tex]\begin{aligned}\textsf{Volume of a cylinder} & = \pi r^2h\\ \implies \textsf{Volume of the cup} & = \pi \cdot (2)^2 \cdot 12\\& = \pi \cdot 4 \cdot 12\\& = 48\pi \sf \:\:in^3 \end{aligned}[/tex]
The cup is filled with orange juice that occupies 67% of the cup. To find the volume of orange juice in the cup, multiply the found volume of the cup by 67%:
[tex]\begin{aligned}\implies\textsf{Volume of orange juice} & = 67\% \textsf{ of }48 \pi \\\\& = \dfrac{67}{100} \cdot 48 \pi \\\\& = \dfrac{3216}{100} \pi \\\\& = 101.0336197...\\\\& = 101.0\:\: \sf in^3\:(nearest\:tenth) \end{aligned}[/tex]
Liquid is usually measured in liters.
To convert cubic inches to liters, multiply by 0.016387064:
[tex]\implies \sf 101.0336197...in^3 \times 0.016387064 = 1.656 \: liters\:(3\:dp)[/tex]
Last year, the workers at Mark's lawn care business mowed 16,607 lawns. If the company charges $39 to mow each lawn, how much did Mark's business earn last year?
Answers
Answer:
$647,673
Step-by-step explanation:
Since each lawn is $39 to mow, you would multiply 16,607 by 39 and you would get $647,673.
Select the correct answer. Which expression is equivalent to this polynomial? 16x² +4
Answers
Answer:
(4x+2)(4x-2)
Step-by-step explanation:
Answer:
(4x+2)(4x-2)
Step-by-step explanation: