Answer:
Step-by-step explanation:
Prime factorize 12 , 28 , 21 and 16
12 = 2 * 2 * 3 = 2² * 3
28 = 2 * 2 * 7 = 2² *7
21 = 3 * 7
16 = 2 * 2 * 2 * 2 = 2⁴
[tex]\dfrac{12^{7}*28^{6}}{21^{7}*16^{6}}=\dfrac{(2^{2}*3)^{7}*(2^{2}*7)^{6}}{(3*7)^{7}*(2^{4})^{6}}\\\\\\\\=\dfrac{2^{2*7}*3^{7}*2^{2*6}*7^{6}}{3^{7}*7^{7}*2^{4*6}}\\\\\\=\dfrac{2^{14}*3^{7}*2^{12}*7^{6}}{3^{7}*7^{7}*2^{24}}\\\\\\=\dfrac{2^{14+12-24}*3^{7-7}}{7^{7-6}}\\\\\\=\dfrac{2^{2}*3^{0}}{7^{1}}\\\\\\=\dfrac{2^{2}}{7}[/tex]
Hint:
[tex]a^{m}*a^{n}=a^{m+n}\\\\\\(a^{m})^{n}=a^{m*n}\\\\\dfrac{a^{m}}{a^{n}}=a^{m-n} \ if \ m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}} \ if \ n>m[/tex]
If Mike has 3/4 a cup of butter and it is 2 pounds, how many pounds would a whole cup of butter be? Please add how you got the number. (Step by Step) Thanks!
Answer: 2.666... pounds
Step-by-step explanation:
Because 3/4 of a cup is 2 pounds, we can divide 2 by 3 to get how much 1/4 of a cup weighs.
2/3 = 0.666...
Multiply that by 4 to get 4/4 (1) and you get:
4 * 0.666...
= 2.666...
2.666... pounds
write the equation in general form
Step-by-step explanation:
here is your answer hope you will enjoy and mark me as brainlist
thank you
the sum of three consecutive no. is 7 and less than 700 .find the no.
Answer:
Sorry, the question isn't clear enough to answer.
Step-by-step explanation:
Sorry, the question isn't clear enough to answer.
Write an equation of the line that passes through (1, 2) and is perpendicular to the line y = -5x + 4
Answer:
y = -1/5 + 7
Step-by-step explanation:
Substitute the point (1,2) for the x and the y in the equation, set the 4 to b since we are solving for b.
2 = -5(1) + b now solve for b
2 = -5 + b
+5 +5
7 = b
we know that the slope must be the reciprocal for it to be perpendicular
y = -1/5 + 7 add b (7) to the equation and change the reciprocal
8th Grade Math
Janelle is saving $6 per week to buy a new bike. she has $85 on week five. How do you write this in slope intercept form?
Escribe 3 fracciones equivalentes a 20/24en donde el numerador sea menor que 20.
Answer:
[tex]\frac{20}{24} =\frac{15}{18} =\frac{10}{12} =\frac{5}{6}[/tex]
Step-by-step explanation:
I hope this help you
What was a social effect of Queen Hatshepsut’s economic policies?
Egypt experienced a decrease in status among other countries.
Religious reform became possible as peasants gained wealth.
The kingdom was peaceful and prosperous.
Workers became unhappy with the pharaoh.
Answer:
the answer is the kingdom was peaceful and prosperous
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
1. Given f(x) = 3x -4 and g(x)=-2x + 7. evaluate:
g(f(-2))
Answer:
[tex]f(x) = 3x - 4 \\ g(x) = - 2x + 7 \\ g(f(x)) = - 2(3x - 4) + 7 \\ g(f(x)) = - 6x + 8 + 7 \\ g(f(x)) = -6 x + 15 \\ g(f( - 2)) = - 6( - 2) + 15 \\ g(f( - 2)) = 12 + 15 \\ \boxed{g(f( - 2)) = 27}[/tex]
What percent of the bottle of apple juice is water?
percent of water is: 32/80*100= 40%
The perimeter of a rectangle is 78 units. The length is 5 units more than the width. Find the length.
Answer:
W = 8.5 units; L = 30.5 units
Step-by-step explanation:
The formula for the perimeter of a rectangle is P = 2L and 2W, where L and W represent the length and the width respectively. Here, L = 3W + 5. Adapting the formula P = 2L and 2W, we get: 78 = 2L + 2W = 2(3W + 5) + 2W, or 6W + 10 + 2W = 78, or 8W = 68, or W = 68/8 = 8.5 units If W = 8.5 units, then L = 3(8.5 units) + 5 units = 30.5 units
2. Erin earns $29.00 for 4 hours of babysitting. How much would she make babysitting for 10
hours?
Answer:
$72.5
Step-by-step explanation:
4 hours of babysitting = $29.00
Therefore $29.00 divided by 4 is 1 Hour of babysitting which is $7.25
To find 10 hours we multiply $7.25 by 10 = $72.5
So Erin would make $72.5 babysitting for 10 Hours.
Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Village revealed the following. 38% of students purchased a new pair of shorts (call this event H), 15% of students purchased a new pair of sunglasses (call this event G) and 6% of students purchased both a pair of short and a pair of sunglasses.
Where's your question?
i don’t understand someone please help me ! algebra 1
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
Please make sure the explain each step
Answer:
The axis of symmetry for f(x) is at x = 4 because it splits the function in half. I found it by looking at the vertex of the parabola and using the x-value as the axis of symmetry.
The axis of symmetry for h(x) is at x = -2 because it splits the function in half. I found it by looking at the vertex of the parabola and using the x-value as the axis of symmetry.
please make me Brainliest! : )
Can someone help? Show work
MATHEMATICAL CONNECTIONS Use the given information to write and solve a system of linear equations to find the values of $x$x and y$y$y . The text reads triangle L M N is congruent to triangle P Q R, the measure of angle L equals 40 degrees, the measure of angle M equals 90 degrees, the measure of angle P equals left parenthesis 17 x minus y right parenthesis degrees, the measure of angle R equals left parenthesis 2 x plus 4 y right parenthesis degrees. The equations are is equal to 40$=\ 40$= 40 and is equal to 50$=\ 50$= 50 . Question 2 $x\ =$x = and $y\ =$y =
The value of x and y is 2 and 11.5
The sum of the interior angle of a triangle is 180 degrees.
Since LMN and PQR are similar, hence:
m<L = m<P
m<M = m<Q
m<N = m<R
Given the following parameters
m< L = 40 degrees
m<M = 90 degrees
m<P = 17x - y
m<R = 2x + 4y
Get the measure of m<N
m<M + m<N + m<L = 180
90n+ m<N + 40 = 180
m<N = 180 - 130
m<N = 50degrees
Since m<P = m<L, hence;
17x - y = 40 ....... 1
Also m<R = m<N
2x + 4y = 50 .......... 2
Solve simultaneously
17x - y = 40 ....... 1 * 4
2x + 4y = 50 .......... 2 * 1
___________________________
68x - 4y = 160
2x + 4y = 50
Adding both equations
68x + 2x = 160 + 50
70x = 210
x = 2
Substitute x = 3 into the equation 2x + 4y = 50
2(2) + 4y = 50
4 + 4y = 50
4y = 50 - 4
4y = 46
y = 46/4
y = 11.5
Hence the value of x and y is 2 and 11.5
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The 4th grade class met their goal of reading of certain amount of hours during the fall. They earned their skiing trip this winter sponsored by the parent-Teacher organization. if each ski ticket costs $28 and there are 86 fourth grades, how much does PTO need to pay for the tickets?
Answer:
$2408.
Step-by-step explanation:
28 * 86
What is the sum of the 5th square number and the 3rd cube number?
Answer:
5²+3³= 25+27=52
Step-by-step explanation:
hope it helps you
As a puppy, Cricket weighed 2 1/4 pounds. At her 1-year check-up with the vet, Cricket weighed 9.5 pounds. How much weight did Cricket gain between the time she was a puppy and her 1-year check-up? Enter your answer as a decimal or simplified mixed number.
A. 6.25
B. 12.75
C. 11.75
D. 7.25
Answer:
D. 7.25
Step-by-step explanation:
9.50-2.25=x
9.50-2.25= 7.25
The weight gained by cricket in between the time she was a puppy and her 1-year checkup is 7.25 pounds. Hence, option D is correct.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the data provide by the question,
Initial weight of puppy = 9/4 = 2.25 pounds.
After 1-year, weight = 9.5 pounds.
Weight gained by the puppy = 9.5 - 2.25 = 7.25
Therefore, weight gained by the puppy is 7.25 Pounds.
To know more about arithmetic operations:
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Train A has a speed 35 miles per hour greater than that of train B. If train A travels 300 miles in the same times
train B travels 195 miles, what are the speeds of the two trains?
Step-by-step explanation:
That's the answer! hope it helped!
Taylor works for his father's landscaping business. He earns $50 a day and an additional $16 for each lawn he mows.
If he mows 5 lawns one day, how much will he earn?
Answer:
$130
Step-by-step explanation:
he makes the initial $50 dollars a day, and an extra $16 for each lawn he mows. he mows 5 lawns so you do 5*16 to get $80 which you then add to $50 and get $130
Answer:
$130
Step-by-step explanation:
$50 + $(16x5)
=> $130
6. Five more than eight times a number is greater than four less than
seven times the number. Write an inequality to represent this relationship.
Then solve the inequality. *
8x+5 > 7x -4
X+5> -4
X> -9
Answer:
8x + 5 > 7x - 4
x > -9
Step-by-step explanation:
Five more than eight times a number
8x + 5
is greater than
>
four less than seven times the number
7x - 4
All together:
8x + 5 > 7x - 4
-------------------------------
Solve:
Subtract 7x from both sides
x + 5 > -4
Subtract 5 from both sides
x > -9
48% of $650
19.6% of $170.65
Answer:
the answers are easy here is the answer if you don't know.
1. 312
2. 33.45
help!! show all steps!
Find SURFACE AREA
Answer:
132 cm²
Step-by-step explanation:
The area of the two triangular ends is ...
A = 2(1/2)(bh) = (4 cm)(3 cm) = 12 cm² . . . . . area of both triangles
The area of the three rectangular faces is ...
A = (b1)(h) +(b2)(h) +(b3)(h) = (b1 +b2 +b3)(h)
= (4 cm +3 cm +5 cm)(10 cm) = 120 cm²
Then the total surface area is ...
triangle area + rectangle area = (12 cm²) +(120 cm²) = 132 cm²
divide 96 into the ratio 1:7
Use the information given to enter an equation in standard form.
(27,31) and (37,45) are on the line.
WHATS THE ANSWER TO THIS??
Answer:
y - 1.4x = - 6.8
Step-by-step explanation:
To find the equation: find the slope, use point-slope form to calculate the equation, then convert the equation to standard form.
Slope: [tex]\frac{45-31}{37-27} = \frac{14}{10} = 1.4[/tex]
Use point slope form: y - y₁ = m(x - x₁)
Plug in x = 27, y = 31, and m = 1.4
y - 31 = 1.4(x - 27)
y - 31 = 1.4x - 37.8
y = 1.4x - 6.8
Convert this into standard form: ax + by = c
y - 1.4x = - 6.8
Each cube in the prism is one cubic unit.
What is the volume of this rectangular prism?
Enter your answer in the box.
Answer:
i got 120 because i think you gotta multiply the bottom front colom and right colum and the front row
Answer:
I think its 120
Step-by-step explanation:
you would do length x width x height
6 x 5 x 4
6 x 5 = 30
30 x 4 = 120
therefore the volume is 120 units squared
solve pls brainliest
Answer:
4/4, 12/3, -37
Step-by-step explanation:
an integer is a whole number thats not a fraction, but can be negative
Write the solution to the inequality.
f - 5 < -6
Step-by-step explanation:
add 5 to the -6 bc you have to isolate the variable so f = -1
GEOMETRY Find the the area of the polygon with the given vertices.
C(1,1) D(1,4)E(4,4)F(4,1)
pls give answer
worth 100
Answer:
sdd
Step-by-step explanation:
seds
