Answers
Answer:
Refer to below!
Step-by-step explanation (a):
[tex]\rightarrow \dfrac{10^{3} \times 10^{4} }{10^{5} } \\\\\\ \rightarrow \dfrac{10^{3 + 4} }{10^{5} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ] \\\\\\ \rightarrow \dfrac{10^{7} }{10^{5} } \\\\\\[/tex]
[tex]\rightarrow 10^{7 - 5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}] \\\\\rightarrow 10^{2}[/tex]
Step-by-step explanation (b):
[tex]\rightarrow \huge{\text{(}{10^{4} \times \dfrac{10^{12} }{10^{7} }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{12 - 7} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{5} }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}{10^{4 + 5} }\huge{\text{)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]
[tex]\rightarrow{10^{9} }[/tex]
Step-by-step explanation (c):
[tex]\rightarrow \huge{\text{(}\dfrac{10^{5} }{10^{3} } }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}10^{5 - 3} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow 10^{2} }[/tex]
Step-by-step explanation (d):
[tex]\rightarrow \dfrac{10^{4} \times 10^{5} \times 10^{6} }{10^{3} \times 10^{7} }[/tex]
[tex]\rightarrow \dfrac{10^{4 + 5 + 6} }{10^{3 + 7} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]
[tex]\rightarrow \dfrac{10^{15} }{10^{10} }[/tex]
[tex]\rightarrow 10^{15 - 10} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow 10^{5} }[/tex]
Step-by-step explanation (e):
[tex]\rightarrow \dfrac{(10^{5})^{2} }{(10^{2})^{3} }[/tex]
[tex]\rightarrow \dfrac{10^{5 \times 2} }{10^{2 \times 3} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^{2} )^{5} = a^{2 \times 5} = a^{10} ][/tex]
[tex]\rightarrow \dfrac{10^{10} }{10^{6} }[/tex]
[tex]\rightarrow {10^{10 - 6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow {10^{4}[/tex]
Related Questions
I need this done right now please i need help
Answers
Step-by-step explanation:
AB = x + 5 ...................
From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?
Answers
=============================================================
Reason:
There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.
If order mattered, then we'd have 20*19*18 = 6840 permutations.
However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.
Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = 1140 combinations.
-------------------------
Here's a more formulaic approach using the nCr combination formula.
Plug in n = 20 and r = 3
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]
If Madeline has one week to read 1293 pages of a book and if she wants to split her reading equally each day how many pages will she need to read each day in order to finish
Answers
Answer:
184 5/7 pages
Step-by-step explanation:
There are 7 days in a week. If Madeline wants to read equal portions of the book each day, each of those portions must be 1/7 of the book, or ...
1/7 × 1293 pages = 184 5/7 pages
Madeline will need to read 184 5/7 pages each day in order to finish.
6. The length of Garden B is 3 more than the length of Garden A. Write, and solve the equation
you can use to find the length of Garden A.
Answers
Answer:
B = A + 3
Step-by-step explanation:
Let B be the length of Garden B and A the length of Garden A.
We are told that B = A + 3
We can use this equation to find the length of Garden B.
Write an algebraic expression for the following word phrase.
The quotient of and x
Answers
The value of mathematical expression is,
⇒ 55 ÷ x
⇒ 55 / x
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The word phrase is,
''The quotient of 55 and x.''
Now, The value of mathematical expression is,
''The quotient of 55 and x.''
⇒ 55 ÷ x
⇒ 55 / x
Therefore, The value of mathematical expression is,
⇒ 55 ÷ x
⇒ 55 / x
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Mike spins a spinner and flips a coin. What
is the probability of getting E on the spinner
and the coin landing on heads?
Answers
Answer:
3/16
Step-by-step explanation:
The probability of spining an E is 3/8 and the probability of fliping heads on a coin is 1/2 so the probablility of both those things happening is 1/2*(3/8) or 3/16
A printer can print 14 pages in 28 sec.
The rate in lowest terms is____?
Answers
Answer:
1/2 or 0.5 :)
Step-by-step explanation:
We can divide to see lower forns :)
14/28 = 7/14 = 1/2
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
2 pages every 7 seconds, divide by the common denominator which is 7 to get the answer
A grain silo has a cylindrical shape. Its radius is 9 ft, and its height is 41 ft. What is the volume of the silo?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
As Per Provided Information
Radius of cylindrical shape silo 9 ft
Height of cylindrical shape silo 41 ft
We have been asked to determine the volume of cylindrical silo .
[tex] \boxed{\sf \: Volume_{(Cylindrical\:Silo)} = \pi {r}^{2}h}[/tex]
Substituting the given value in above formula and we obtain
[tex] \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times {9}^{2} \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 81 \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 3321 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10427.94 \: {ft}^{3} \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10428 \: {ft}^{3}[/tex]
Answer:
Volume is 10428 cubic ft.
Step-by-step explanation:
Given :-
Radius of grain silo is 9ft and height is 41ftTo find:-
Volume of grain siloSolution:-
Volume of cylindrical grain silo :- πr²hPutting the known values ,
Volume:- 3.14 × 9² × 41 cubic ft.
Volume :- 10427.94 cubic ft.
rounding off to nearest whole number ,
Volume :- 10428 cubic ft.
I don’t know what is the least common factor of 18 and 12.
Answers
Answer:
the common factors for both are 1,2,3,6
(3*8-3)/3
How do you solve this?
Answers
Answer:
7
Step-by-step explanation:
Equation: (3*8-3)/3
Step 1: (24-3)/3
Step 2: 21/3
Step 3: 7
Order of operations is used in this equation. You simplify the terms in the parentheses before the other terms in the equation. According to the order of operations (parentheses, exponents, multiplication, division, addition, and subtraction, you do the multiplication before the subtraction in the parentheses. Then you subtract your three from your multiplication result (twenty-four). This leaves you with 21. Finally, you divide twenty-one by three. This gets you seven.
Help picture below problem 15
Answers
Answer:
B. Pentagon
Step-by-step explanation:
A Pentagon is a polygon with 5 sides like this one.
Hope that helps!
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Answers
Answer:
I don’t get it
Step-by-step explanation:
I think it is 5
its 54 also for some reason my comment keeps getting deleted for saying 54??
Which of the following statements is true?
The meter is a unit of volume in the U.S. customary system.
The foot is a unit of length in the metric system.
The gram is a unit of mass in the metric system.
The liter is a unit of volume in the U. S. customary system.
Answers
Answer:
Step-by-step explanation: the meter is a unit of value in the US customary system
Answer: The gram is a unit of mass in the metric system
Select the correct answer.
The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?
A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6
Answers
Answer:
That would be week 2 and 4 (B). They are both at 12 students attending
PLEASE PLEWSE PLEASE HELP
Answers
Answer:
C) 63°
Step-by-step explanation:
Just add the numbers up together to get your solution
An inequality is shown.
Select all the values of that make the inequality true.
Answers
Answer:
2/5
1
3/2
Step-by-step explanation:
Note that:
> = Greater than
< = Less than
≤ = Less than or equal to
≥ = Greater than or equal to
Solution:
Since it given that 27/7n > 4/3
It means that
27/7n is greater than 4/3.
Now going through all answer chioces:
-----------------------------------------------------------------------------------------------------------
27/7(2/5) = 1 19/35
1 19/35 is greater than 4/3
Thus, 2/5 is true.
-----------------------------------------------------------------------------------------------------------
27/7(1/3) = 1 2/7
1 2/7 isn't greater than 4/3
Thus, 1/3 is false.
-----------------------------------------------------------------------------------------------------------
27/7(1) = 3 6/7
3 6/7 is greater than 4/3
Thus, 1 is true.
-----------------------------------------------------------------------------------------------------------
27/7(2/9) = 6/7
6/7 isn't greater than 4/3
Thus, 2/9 is false.
-----------------------------------------------------------------------------------------------------------
27/7(3/2)=5 11/14
5 11/14 is greater than 4/3
Thus, 3/2 is true.
-----------------------------------------------------------------------------------------------------------
[RevyBreeze]
Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. Write an algebraic equation to represent how much money he received
Answers
Answer:
x + 29 = 41
Step-by-step explanation:
Trevon received some money, but we don't know how much, so we will represent that with x.
The money he received will be add the amount he had last friday, $29.
The equation will equal his current amount, $41.
Find the perimeter of the parallelogram with these vertices.
(3.5), (-4. 2), (3.1), (-4. -2)
Give an exact answer (not a decimal approximation).
Simplify your answer as much as possible.
Answers
Check the picture below.
so we can say that two sides are "4" each in length, since opposite sides are equal, let's find how long the slanted sides are.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-4)]^2 + [5 - 2]^2}\implies d=\sqrt{(3+4)^2+3^2} \\\\\\ d=\sqrt{49+9}\implies d=\sqrt{58} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{4~~ + ~~4~~ + ~~\sqrt{58}~~ + ~~\sqrt{58}\implies 8+2\sqrt{58}}[/tex]
2. Find the probability of throwing a 10 with a pair of dice and choosing a red from a standard deck of cards.
Answers
Answer:
Step-by-step explanation:
You can get 10 with a pair of dice with:
4 + 6, 6 + 4, 5 + 5
out of a possibile 36 results
There are 52 cards in a standard deck of cards. Reds make up half of them (hearts and diamonds) , meaning theres a 50/50 chance of pulling red
10/36 * 1/2 = 5/36 chance of throwing 10 + pulling red
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 31 feet up. The ladder makes an angle of 78° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
a
necessary.
Answers
Answer:
50.41 feet
Step-by-step explanation:
Hypotenuse = length of ladder
31 = opposite side of angle
sin(angle) = (opposite)/(hypotenuse)
sin(78) = (36)/(hypotenuse)
hypotenuse = sin(78)/ (36)
hypotenuse = 50.41 feet
length of ladder = 50.41 feet
Please look at the attachments I posted. Anyone help me please
Answers
Answer:
This will be option D
Replace the k with -1/2 and f(x) with x^2
this will look like -1/2*x^2
plug this into a graphing website such as Desmos
help me out guys thank u
Answers
Answer:
[tex] \sf \: a5 = 769[/tex]
I’m confused can someone help?
Answers
Answer:
(a) check the first one, and the second one
(b) check the last one
Step-by-step explanation:
This is quite easy actually.
(A)3x+24 = 3 * x + 3 * 8
3(x+8) using distribute property.
3x + 24
You cannot simplify 3x+24 any further
And 3(8x+1) just doesn't work
since it's multiplying
The "*" is an X sign
(B)The first, second, and third are not correct
But the last one is.
help i dont know how to do this and i forgot the study guide
Answers
B is the right answer
I hope it will help you
Solve the simultaneous equations
4x + 5y = 4
2x - y = 9
Show clear algebraic working.
Answers
Answer:
[tex]x= \dfrac 72, ~~y= -2[/tex]
Step by step explanation:
[tex]4x+5y=4~~~...(i)\\\\2x-y=9~~~...(ii)\\\\\text{Multiply eq (ii) by 2 to isolate x:}\\\\4x-2y=18~~~.....(iii)\\\\(iii)-(i):\\\\4x-2y-4x-5y=18-4\\\\\implies -7y=14\\\\\implies y = -\dfrac{14}7 = -2\\\\\text{Substitute}~ y=-2~ \text{in equation (iii):}\\\\4x-2(-2) = 18\\\\\implies 4x +4 = 18\\\\\implies 4x = 18-4\\\\\implies 4x = 14\\\\\implies x = \dfrac{14}4 = \dfrac 72\\\\\text{Hence}~ (x,y) =\left(\dfrac 72 , -2 \right)[/tex]
Step-by-step explanation:
4x+5y=4 (equation 1)
2x-y=9 (equation2)
solving equation 1 and 2 and multiplying equation 2 by 2
4x+5y=4
4x-2y=18
- + -
________
7y= -14
y= -2
putting the value of y in equation 2
2x-y=9
2x+2=9
2x=7
x=3.5
Determine the zeros of x^2 + 19x = 6x - 30
Answers
Answer:
The number of Zeros (roots) is
-3 and -10
Step-by-step explanation:
x^2 + 19x = 6x - 30
A circular garden has a diameter of 10 feet. Approximately how much edging trim is needed to surround the garden by placing the trim all along the garden's circumference?
Answers
Answer:
31 feet
Step-by-step explanation:
circumference = pi × diameter
pi × diameter = 31.4 (10×3.14)
Answer: 31 ft
Step-by-step explanation:
circumference = pi × diameter
pi × diameter = 31.4 (10×3.14)
The horizontal lines (l and m) are parallel. They are crossed by two transversals (lines a and b).
Transversals a and b intersect to make a triangle. The m∠1 = 75°, and the m∠4 = 50°.
1. What is the m∠5? Explain how you know. (2 points)
2. What is the measure of the sum of the angles in a triangle? (2 points)
3. ∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3. (2 points)
4. What is the measure of a straight angle? (2 points)
5. ∠2 is in a straight line with ∠1 and ∠3. Write and solve an equation to find the m∠2. (2 points)
PLEASE ANSWER! WILL GIVE BRAINLIEST
Answers
1. m∠5 = 75° (corresponding angles theorem)
2. 180°
3. m∠3 = 55° (triangle sum theorem).
4. A straight angle = 180°
5. m∠2 = 50° (angles on a straight line)
What is the Triangle Sum Theorem?According to the triangle sum theorem, the sum of the angles in a triangle equals 180 degrees.
1. m∠5 = m∠1 = 75° (corresponding angles are congruent)
2. Measure of the sum of all angles in a triangle = 180°
3. To find ∠3, we would have the following equation:
m∠3 = 180 - m∠4 - m∠5 (triangle sum theorem).
Substitute and solve
m∠3 = 180 - 50 - 75
m∠3 = 55°
4. A straight angle = 180°
5. m∠2 = 180 - m∠3 - m∠1 (angles on a straight line)
Substitute and solve
m∠2 = 180 - 55 - 75
m∠2 = 50°
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Solve each of the quadratic equations.
PT. 1
3x = 0.5x2
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2
D. x = 1.5 x = 0 or x = 6
PT.2
0 = 5x2 - 2x + 6
A. x= 1±3i/2
B. x=1±√11/5
C. x=1±I√29/5
Answers
Answer:
the answer to pt 1 is D. x=1.5 x=0 or x=6
and the answer to part 2 is C. x=1±I√29/5
Step-by-step explanation:
1. The solution of this equation is x = 0 or x = 6 which is option D.
2. The solution of this equation is [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex] which is option C.
Use the concept of quadratic equation defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations.
The quadratic equation has the following generic form:
ax² + bx + c = 0
1. The given quadratic equation is,
3x = 0.5x²
Rearranging it,
0.5x² - 3x = 0
Common out x,
x(0.5x - 3) = o
Then we have,
x = 0 or,
0.5x - 3 = 0
Add 3 on both sides,
0.5x = 3
Divide both sides by 0.5,
x = 3/0.5
x = 6
Hence the solution of this quadratic equation is,
x = 0 and x = 6 which is option D.
2. The given quadratic equation is:
0 = 5x² - 2x + 6
It can be written as,
5x² - 2x + 6 = 0
Since we know the quadrature formula for ax² + bx + c = 0 is,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Here we have,
a = 5
b = -2
c = 6
Substitute values into the formula,
[tex]x = \dfrac{2 \pm \sqrt{4 - 120}}{10}\\\\x = \dfrac{1 \pm i\sqrt{29}}{5} \text{ }\text{ \text{ }} \text{\text{ }\ since } \sqrt{-1} = i[/tex]
Hence, option C is correct.
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The complete question is:
Solve each of the quadratic equations.
PT. 1
3x = 0.5x²
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2 or x = 1.5
D. x = 0 or x = 6
PT.2
0 = 5x² - 2x + 6
A. [tex]x = \dfrac{1 \pm 3i}{5}[/tex]
B. [tex]x = \dfrac{1 \pm i\sqrt{11}}{5}[/tex]
C. [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex]
A cylinder has a radius 3 inches and height 5 inches. A cone has the same radius and height. What is the volume of the cylinder
Answers
✰ Given Information :-
⠀
A cylinder with following dimensions :
Radius = 3 inchesHeight = 5 inches⠀
✰ To Find :-
⠀
The volume of the cylinder⠀
✰ Formula Used :-
⠀
[tex] \qquad \star \: \underline{ \boxed{ \purple{\sf Volume_{Cylinder} = \pi {r}^{2} h}}} \: \star[/tex]
⠀
Where,
r = radius h = height⠀
✰ Solution :-
⠀
Putting the values in the formula, we get,
⠀
[tex] \sf \longrightarrow Volume=3.14 \times {(3)}^{2} \times 5 \\ \\ \\ \sf \longrightarrow Volume=3.14 \times 45 \: cm \: \: \: \: \: \\ \\ \\ \sf \longrightarrow \underline{ \boxed{ \green{ \frak{Volume= {141 .3 \: cm}^{3} }}}} \: \star \: \: \: \: \: \\ [/tex]
⠀
Thus, the volume of the cylinder is 141.3 cm³.
⠀
[tex] \underline{ \rule{230pt}{2pt}} \\ \\ [/tex]
Step-by-step explanation:
As it is given that, a cylinder has radius 3 inches and height 5 inches and we are to find the volume of the cylinder, also a extra information is given that is a cone has the same radius and height.
[tex] \: [/tex]
We know,
[tex]{ \longrightarrow\qquad{\frak {\pmb{Volume_{(cylinder) } = \pi {r}^{2}h }}}} \\ \\[/tex]
Where,
r is the radius of the cylinder.h is the height of the cylinder.Here, we will take the value of π as 3.14 approximately .[tex] \: [/tex]
Now, we will substitute the given values in the formula :
[tex] \: [/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times ( {3})^{2} \times 5 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times 9 \times 5 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\sf {\pmb{Volume_{(cylinder) } = 3.14 \times 45 }}}} \\ \\[/tex]
[tex]{ \longrightarrow\qquad{\frak {\pmb{Volume_{(cylinder) } = 141.3 }}}} \\ \\[/tex]
Note :
Answer might be different if we take the value of π as 22/7 .