[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^{-4}}{a^{-6}}\implies a^{-4}\cdot a^6\implies a^{-4+6}\implies a^2[/tex]
Which choice is equivalent to the product below? Square root of 3/16 • Square root of 3/9
Answer:
3/12
Step-by-step explanation:
it was right on, you know, where its from
The product Square root of 3/16 • Square root of 3/9 = 3/12 = 1/4.
What is square root?The root is figuring out what number accelerated by way of itself is the same as the variety under the square root image. So: √9= 3, due to the fact 3² $ -3² = 9
square root, in mathematics, a component of a variety of that, while accelerated by way of itself, gives the authentic quantity. for example, each 3 and –3 are square roots of 9.
The square root of 3/16 • Square root of 3/9
⇒[tex]\sqrt{\frac{3}{16} }[/tex]×[tex]\sqrt{\frac{3}{9} }[/tex]
⇒3/4*3
⇒1/4.
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The absolute value of -5 and 5 are ?
Hey!
---------------------------
Absolute Value - the enormity of a number regarding its sign.
|-5| = 5
|5| = 5
---------------------------
Hope This Helped! Good Luck!
Mariano delivers newspapers. He always puts 3/4 of his weekly earnings in his savings account and then divides the rest equally into 3 piggy banks for spending at the snack shop, the arcade, and the subway.
a. What fraction of his earnings does Mariano put into each piggy bank?
b. If Mariano adds $2.40 to each piggy bank every week, how much does Mariano earn per week delivering papers?
Answer:
a. Fraction of earnings that Mariano put into each piggy bank is 1/12
b. Mariano earns $28.8
Step-by-step explanation:
Mariano divides his earning in a saving account and 3 piggy banks.
First , we have to know the fraction that we divide in the 3 piggy banks.
Piggy banks =Total earning-Saving account
Saving account 3/4,
Total earning is 1
to rest both term we have to get the same denominator , so we can say that the total earning is 4/4
Piggy banks =4/4-3/4=( 4-3)/4=1/4
Piggy banks =1/4
Each piggy bank will be 1/3 of that 1/4
1/3 x 1/4=
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1×1/3×4=1/12
This fraction cannot be reduced.
b. Mariano adds $2.40
1/12 is 2.40
total earning is ?
We use cross-multiplication
a/b=c/d replacing (1/12)/2.40 = 1/ ?
So, the total earning (?) is 1 x 2.40/ (1/12)
= 2.40 x 12=$28.8
Mariano puts 3/4 of his earnings in his savings account and divides the rest equally into 3 piggy banks. The fraction of his earnings that he puts into each piggy bank is (1/12)x dollars. Mariano earns 0 dollars per week delivering papers.
Explanation:To find the fraction of Mariano's earnings that he puts into each piggy bank, we need to calculate 3/4 of his earnings first. Let's assume he earns x dollars per week. Therefore, he puts 3/4 of x dollars into his savings account, which is (3/4)x dollars. The remaining (1/4)x dollars is divided equally into 3 piggy banks. So, each piggy bank gets (1/12)x dollars.
To find out how much Mariano earns per week delivering papers, we need to solve the equation (3/4)x + (1/12)x = x. Simplifying the equation, we get 9x/12 + x/12 = x. This is equivalent to (10/12)x = x. Multiplying both sides by 12, we get 10x = 12x. Subtracting 10x from both sides, we get 2x = 0. Therefore, x = 0.
Write three numbers that are between -3 and -4
Answer:
-3.3, -3.5, -3.7
Let P be the set of polynomials. Let a, b, c, and d be elements of P such that b and d are non-zero elements of P. Which of the following is
true regarding the sum below?
a/b+c/d
Answer:
A. The sum is a rational expression.
Step-by-step explanation:
The complete questions is:
Let P be the set of polynomials. Let a, b, c, and d be elements of P such that b and d are non-zero elements of P. Which of the following is true regarding the sum below?
a/b+c/d
A) The sum is a rational expression
B) The sum is an integer
C) The sum is a rational number
D) The sum is a polynomial
Solution:
We are given:
a/b + c/d
b and d are non-zero elements:
Therefore:
a/b is a rational number.
c/d is a rational number.
We see that there is an addition sign between the two terms:
So, sum of rational expression is also a rational expression
Thus, The correct option is:
A. The sum is a rational expression.
The sum of the given fractions a/b + c/d, where a, b, c, and d are polynomials, can be calculated by finding a common denominator, which is typically the product of polynomials b and d, and combining the adjusted numerators.
Explanation:The question deals with the operation of addition of fractions where the denominators are polynomials. Given the expression a/b + c/d, where a, b, c, and d are polynomials, and b and d are non-zero polynomials, we want to find their sum. It is important to note that adding or subtracting fractions requires a common denominator.
To combine a/b with c/d, we must first find a common denominator, which will be the product of b and d if they have no common factors. After that, we adjust the numerators accordingly and perform the addition. The resulting fraction will have a numerator that is the polynomial sum of ad and bc, and a denominator that is the polynomial product bd.
Given that y is directly proportional to x^2 and that y=2 when x=3 find the value of y when x=6
Answer:y=4/3
y is directly proportional to x^2 is written as
[tex]y \alpha {x}^{2} [/tex] introducing a constant,
y=kx^2
but from the question, when y=2 , x=3 . putting it in the formula to get the value of k
[tex]2 = {3}^{2} \times k[/tex]
2=9k . dividing through by 9 to get the value of k
[tex] \frac{2}{9} = \frac{9k}{9} [/tex]
[tex]k = \frac{2}{9} [/tex]
putting it in the general expression
[tex]y = \frac{2}{9} x[/tex]
the value of y when x=6
[tex]y = \frac{2}{9} \times 6[/tex]
[tex]y = \frac{4}{3} [/tex]
therefore the value of y when x=6 is
4/3
Solve -3 |2x+3| -4 = 1
Answer: x = 1.5
Step-by-step explanation:
First, we need to isolate the absolute value.
+ 3 to each side.
|2x + 3| - 4 = 4
Then, add 4 more to each side.
|2x + 3| = 8
Subtract 3 from each side.
|2x| = 5
Divide each side by 2
|x| = 1.5
Answer:
no solutions
Step-by-step explanation:
[tex]-3|2x+3|-4=1[/tex]
[tex]-3|2x+3|=1+4[/tex]
[tex]-3|2x+3|=5[/tex]
[tex]{\left|2x+3\right|}=\frac{5}{-3}[/tex]
The absolute value of a number is always positive or zero.
A rectangular prism measures 2 2/5 inches by 3 1/5 inches by 2 inches
How many cubes with edge length 1/5 inch fit in the prism?
Total 1920 cubes can fit in the given prism.
Given that:Dimensions of prism are: [tex]2\dfrac{2}{5} = \dfrac{12}{5}[/tex] , [tex]3\dfrac{1}{5} = \dfrac{16}{5}[/tex], and 2 inches respectively.
Size of a side of given cube = 1/5 inch
To find:Number of cubes that can fit in given prism.
Calculations and explanation:This problem is all about spaces. Only that number of cube will fit, which the prism will allow to. The given prism has got some space in it(The volume), and the cubes have some size (their volume).
Since prism is a cuboid(which is mistakenly written as rectangular in the question), thus we have:
Volume of prism = multiplication of lengths of its sides = [tex]\dfrac{12}{5} \times \dfrac{16}{5} \times 2 = \dfrac{384}{25}[/tex] cubic inches
Volume of the cube = cube of its one side's length = [tex](\dfrac{1}{5})^3 = \dfrac{1}{125}[/tex] cubic inches
We will divide the total space with space amount each cube take so as to find number of cubes allowed by prism to be fitted in it.
Thus:
[tex]\text{Number of cubes} = \dfrac{\dfrac{384}{25}}{\dfrac{1}{125}} = 1920 \: \rm cubes[/tex]
Thus, in total, there can be 1920 cubes fitted in the prism.
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The rectangular prism can hold 1920 cubes with edge lengths of [tex]\frac{1}{5}[/tex] inch. This is calculated by finding the volume of the prism and dividing it by the volume of one small cube.
To find how many cubes with an edge length of [tex]\frac{1}{5}[/tex] inch fit into a rectangular prism with dimensions [tex]2\frac{2}{5}[/tex] inches, [tex]3\frac{1}{5}[/tex] inches, and 2 inches, we follow these steps:
Convert the dimensions of the prism into improper fractions:
[tex]2\frac{2}{5}[/tex] inches = [tex]\frac{12}{5}[/tex] inches[tex]3\frac{1}{5}[/tex] inches = [tex]\frac{16}{5}[/tex] inches2 inches = [tex]\frac{10}{5}[/tex] inchesCalculate the volume of the prism:
Volume = [tex]\frac{12}{5} \times \frac{16}{5} \times \frac{10}{5} = \frac{1920}{125}[/tex] cubic inchesDetermine the volume of one small cube:
Edge length of a small cube = [tex]\frac{1}{5}[/tex] inch → Volume = [tex]\left(\frac{1}{5}\right)^3[/tex] = [tex]\frac{1}{125}[/tex] cubic inchesFind the number of small cubes by dividing the volume of the prism by the volume of one small cube:
Number of cubes = [tex]\frac{1920/125}{1/125} = 1920[/tex]Thus, 1920 cubes with an edge length of [tex]\frac{1}{5}[/tex] inch can fit into the given rectangular prism.
Corrected question:
A rectangular prism measures [tex]2\frac{2}{5}[/tex] inches by [tex]3\frac{1}{5}[/tex] inches by 2 inches
How many cubes with edge length [tex]\frac{1}{5}[/tex] inch fit in the prism?
Student-Facing Statement
A circle has radius 50 cm. Which of these is closest to its area?
Answer:
A = 7,850
Step-by-step explanation:
1. Area = 3.14(50)^2
2. A = 3.14(2500)
3. A = 7,850
The number of deer to
hunters is 17:3. Altogether
deer and hunters is 740.
How many deer and how
many hunters on the ranch?
The given ratio problem can be solved by converting the ratio to an algebraic equation and solving that equation. The total of deer and hunters on the ranch is 629 deer and 111 hunters.
Explanation:The given ratio is of deer to hunters is 17:3, and their total sum is given as 740. We solve such problems by converting ratio to equation i.e., 17x + 3x = 740, where 'x' is a constant multiplier.
Adding 17x and 3x gives us 20x = 740. By dividing both sides by 20, we calculate the value of 'x' which is 37.
Substitute the value of 'x' in 17x and 3x, we get the number of deer and hunters as 629 and 111 respectively.
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please help and find the missing side x
[tex]\text{Hello there!}\\\\\text{A simple way to find the value of x is to find the scale factor}\\\\\text{When you flip the shapes to make it look exactly the same,}\\\text{you would see that the numbers are divisible to it}\\\\\text{Side 21 is congruent to side 3}\\\\\text{Divide 21 by 3 and you'll get 7 (1/7 sine we're going to a smaller shape)}\\\\\text{The x side is congruent to the 91 side}\\\\\text{Divide 91 by 7}\\\\91\div7=13\\\\\large\boxed{x=13}[/tex]
Which of the following represents a combination? Select all that apply.
the PIN for a bank or credit card
a committee consisting of three members with the same role
a committee consisting of a president, vice president, and secretary
final standings in a professional sports league
m selecting two sandwiches from a menu of 10
Answer:
Combinations:
A committee consisting of three members with the same role
Selecting two sandwiches from a menu of 10
Step-by-step explanation:
A combination is a selection of items from a collection, such that the order of selection does not matter.
A permutation is a selection of items from a collection, such that the order of selection matters.
A. The PIN for a bank or credit card - order matters → permutation
B. A committee consisting of three members with the same role - order does not matter → combination
C. A committee consisting of a president, vice president, and secretary - order matters → permutation
D. Final standings in a professional sports league - order matters → permutation
E. Selecting two sandwiches from a menu of 10 - order does not matter → combination
Find the two roots of 4 49 A) 2 and 7 B) 2 7 and - 2 7 C) 2 and -7 D) -2 and -7
Answer:
the answer should be 2, -2, 7, -7
rewrite equation to solve for m 4n-6m=-2
Answer:
Step-by-step explanation:
4n - 6m = - 2 Subtract 4n from both sides.
4n-4n - 6m = -2-4n
-6m = - 2 - 4n Divide by - 6
-6m/-6= -2/-6 -4n/-6 Do the division
m = 1/3 + 2n/3
The signs change because each term has 2 minus signs. 2 minus signs make a plus. Or both minus signs cancel.
I need to know what this table is cause I need the answer
Answer:
f(- 2) = 1
Step-by-step explanation:
f(- 2) means what is the value of f(x) when x = - 2
From the table we can see that when x = - 2 f(x) = 1
Hence
f(- 2) = 1
Answer:
f(-2) = 1
Step-by-step explanation:
Actually, you need to know how to use this table to find the value of the function defined by the table when x = -2.
Look in the first column of the table for x = -2. When x = -2, f(x) = 1. This is the desired result ("What is f(-2)?")
Find the 15th term for the arithmetic sequence -3,3,9,...
Answer:
your adding 6 each time so just find the 15th term
Step-by-step explanation:
-3 + 6= 3 and 3+6 = 9
A go-kart travels 21 miles per hour. Convert this speed into feet per minute.
Answer: 1848 feet per minute
Step-by-step explanation:
[tex]\dfrac{21\ miles}{1\ hour}\times \dfrac{1\ hour}{60\ minutes}\times \dfrac{5280\ feet}{1\ mile}\quad =\dfrac{21\times 5280\ feet}{60\ minutes}\quad =\dfrac{110,880\ feet}{60\ minutes}\\\\\\=\large\boxed{1848\ feet\ per\ minute}[/tex]
Help ASAP please!
The figure shows three quadrilaterals on a coordinate grid:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled A is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled B is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled C is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1.
Which of the following statements is true about the three quadrilaterals? (5 points)
a
A and B are similar but not congruent.
b
A and C are similar but not congruent.
c
A and B are similar and also congruent.
d
B and C are similar and also congruent.
9514 1404 393
Answer:
(a) A and B are similar but not congruent
Step-by-step explanation:
All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.
A and B are similar, but not congruent.
Which is the most accurate measurement of 1 mile (Remember, there are 1760 yards in a mile
Answer: 1755 yards
Step-by-step explanation:
apex
This table shows the distance traveled by a car and the car’s average speed on different days. A three column table with six rows. The first column, Day, has the entries 3, 4, 5, 6, 7. The second column, Average Speed in miles per hour, has the entries, 55, 58, 63, 65, 68. The third column, Distance in miles, has the entries, 495, 660, 825, 990, 1,155. Given that the days are the independent variable, which dependent variable has a constant rate of change? What is the constant rate of change?
The Dependent variables are Average speed and Distance and the rate of change in distance is constant.
Day ____ Average Speed __ Distance
3 __________ 55 __________ 475
4 __________ 58 __________ 660
5 __________ 63 __________ 825
6 __________ 65 __________ 990
7 __________ 68 __________ 1155
The dependent variables are Average speed and Distance.
The rate of change is the change in the dependent variable per change in the independent variable.
Average speed :
The rate of change in speed for the different days is not constant.
Between Day 4 and 3 :
58 - 55 = 3
Between Day 5 and 4 :
63 - 58 = 5
Distance in miles :
Rate of change in distance for the different days is constant
Between Day 4 and 3 :
660 - 475 = 165
Between Day 5 and 4 :
825 - 660 = 165
Between Day 6 and 5 :
990 - 825= 165
Between Day 7 and 6 :
1155 - 990 = 165
Therefore, the rate of change in distance per day is 165 for days 3 to 7.
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Answer:
Distance and 165
Step-by-step explanation:
got it right
What the answer fast
To solve this problem, first let x=0.933333(repeating). Then, you want to multiply both sides by 10 to get 10x = 9.33333 (repeating). Next, take equation 2 and minus equation 1 from it giving you 9x = 8.4. Finally, multiply both sides by 10 and you will get 90x = 84. Divide both sides by 90 giving x=84/90. Answer is 84/90. 84/90 can reduce to 14/15.
Simplify 8 over negative 3 divided by negative 4 over 9. −8 −6 6
Answer:
6
Step-by-step explanation:
[tex] - \frac{8}{3} \div - \frac{4}{9} = - \frac{8}{3} \times -\frac{9}{4} = \frac{72}{12} = 6[/tex]
I am joyous to assist you anytime.
solve the equation 7-y-y=-1
Answer: y=4
Step-by-step explanation:
7-y-y=-1
Combine like terms
7-2y=-1
Subtract seven on both sides of the equation
7-7-2y=-1-7
-2y=-8
Divide both sides by -2
-2y/-2=-8/-2
y=4
Check the answer by plugging 4 back in the equation for y.
7-4-4=3-4=-1
The final answer is y=4
HELP PLZ!!!
In an equilateral triangle, all 3 sides are equal length, and the perimeter of an equilateral triangle is 3 times the length of one side. If one side measures 9 + 3x, and the measure of another side is 5x – 5, what is the perimeter of the equilateral triangle?
Check the picture below.
Answer:
The perimeter of the equilateral triangle is 90 units.
Step-by-step explanation:
Let the side of the triangle be = s
So, perimeter of equilateral triangle = [tex]s+s+s=3s[/tex]
One side measures 9+3x and the measure of another side is 5x-5.
Both are equal, so we get the sides as:
[tex]9+3x=5x-5[/tex]
[tex]3x-5x=-5-9[/tex]
[tex]-2x=-14[/tex]
x = 7
We get the sides as :
First side [tex]9+3(7)[/tex]
= 30
OR
Second side [tex]5(7)-5[/tex]
= 30
And the third side will also be 30 as it is equilateral triangle.
Hence, the perimeter is = [tex]30+30+30=90[/tex] units
Therefore, the perimeter of the equilateral triangle is 90 units.
When Spencer was 5, he was 28 inches tall. Today he is 5 feet 3 inches tall. What is the percent increase in Spencer’s height?
I appreciate any help! Thank you!
Answer:
The percentage increase in Spencer’s height is 125 %
Solution:
[tex]\begin{array}{l}{\text { Percentage increase }=\frac{\text { change in height }}{\text { initial height }} \times 100 \%} \\\\ {\text { percentage increase }=\frac{\text { increased height - initial height }}{\text { initial height }} \times 100 \%}\end{array}[/tex]
Initial height of spencer = 28 inches
Increased height of spencer = 5 feet 3 inches
= 5 feet + 3 inches
(5 feet = 5 ×12=60 inches)
= 60 + 3
[tex]\begin{array}{l}{\text { Increased height }=63 \text { inches }} \\ {\text { Percentage increase }=\frac{63-28}{28} \times 100 \%} \\\\ {=\frac{35}{28} \times 100 \%} \\\\ {=1.25 \times 100 \%} \\ {\text { percentage increase in height of spencer }=125 \%}\end{array}[/tex]
Hank started the month with $531.49 in his bank account. He deposited 2 paychecks during the month into his bank account. One for $240.42 and the other for $281.67. During the month he ended up spending $275.66 on food, $48.29 on gas, and $107.64 and on his phone. He then bought a new iPad which cost him $429.81. How much money was in Hank's account at the end of the month?
Answer:
$192.18
Step-by-step explanation:
$531.49+$240.42+281.67
$1053.58-$275.66-$48.29-$107.64-$429.81
=$192.18
The pass a quiz students need a score of at least 32 points out of a total of 40 points at least what percent do the students need to pass a quiz
Answer:
80%
Step-by-step explanation:
To find the percentage, we have to take 32 over 40 and multiply it by 100
32/40 * 100 = 80%
Therefore the students need 80% to pass a quiz :)PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL :)
Ms.Sinnott has 7/12 m of string and she cuts the string into eight pieces how long are the new piece of string
Answer:
7/96 m
Step-by-step explanation:
7/12 ÷ 8 = 7/96
Solve for b.
Give an exact answer in simplified form.
-67b + 6 < 9b + 43
it equals b 37 58 it welcome
Answer:
b≥− 37/76
Step-by-step explanation:
\begin{aligned}-67b+6 & \leq 9b + 43 \\\\ -67b&\leq 9b+37 &(\text{Subtract } 6 \text{ from both sides}) \\\\ -76b &\leq 37 &(\text{Subtract } 9b \text{ from both sides})\\\\ 76b&\geq -37&(\text{Multiply both sides by }-1)\\\\ b&\geq-\dfrac{37}{76}&(\text{Divide both sides by }76) \end{aligned}
−67b+6
−67b
−76b
76b
b
≤9b+43
≤9b+37
≤37
≥−37
≥−
76
37
(Subtract 6 from both sides)
(Subtract 9b from both sides)
(Multiply both sides by −1)
(Divide both sides by 76)
A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus 7 right-parenthesis.(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
y = y equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus StartFraction 5 Over 3 EndFraction.x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17
Answer:
A and D
Step-by-step explanation:
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