Question
Which expression is equivalent to [tex]\frac{4mn}{m^{-2}n^6}[/tex]. Assuming [tex]m \neq 0; n\neq 0[/tex]
Answer:
[tex]\frac{4m^3}{n^5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4mn}{m^{-2}n^6}[/tex]
Required:
Simplify
To simplify this, we start by splitting each individual function
[tex]\frac{4mn}{m^{-2}n^6} = \frac{4m}{m^{-2}} * \frac{n}{n^6}[/tex]
From laws of indices
[tex]\frac{a^x}{a^y} = a^{x-y}[/tex]
SO, the above expression can also be expressed the same way
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1-(-2)} * n^{1-6}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1+2)} * n^{1-6}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * n^{-5}[/tex]
From laws of indices,
[tex]a^{-x} = \frac{1}{a^x}[/tex]
So,
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * \frac{1}{n^5}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = \frac{4m^3}{n^5}[/tex]
Hence, [tex]\frac{4mn}{m^{-2}n^6}[/tex] is equivalent to [tex]\frac{4m^3}{n^5}[/tex]
Answer:
A
Step-by-step explanation:EDGE (not sure if im right let me know)
If the function f(x) = |x + 5| is transformed to g(x) = –|x + 5|, which type of transformation is seen in the graph?
Answer:
You would see the graph reflected over the x axis
Step-by-step explanation:
when there is a negative in front of the equation and not in the absolute value bars then it is a reflection over the x-axis...If there is a negative in front of the x in the absolute value bars then it is a reflection over the y-axis
Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
2(P +1) + 3(P + 2 ) > 2
Answer: [tex]-1\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2(P +1) + 3(P + 2 ) > 2[/tex]
Distribute 2 and 3
[tex]2P+2+3P+6>2[/tex]
Combine like terms;
[tex]5P+8>2[/tex]
Subtract 8
[tex]5P>2-8[/tex]
[tex]5P>-6[/tex]
Divide by 5
[tex]P>-\frac{6}{5}[/tex]
Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.
[tex]-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}[/tex]
When we do this, we can see that 5/5 = 1
[tex]-1-\frac{1}{5}=-1\frac{1}{5}[/tex]
is the function in the graph non-linear?
4
3
-32
2
5
O Yes, because it has a constant rate of change.
O Yes, because it does not have a constant rate of change.
No, because it has a constant rate of change.
No, because it does not have a constant rate of change.
Answer:
B. Yes, because it does not have a constant rate of change.
Step-by-step explanation:
For a function to be a function (or linear), the rate of change MUST be proportional. In this data set, the numbers do not seem proportional, which makes it non-linear.
63 as a product of prime factors
Answer:
3*3 *7
Step-by-step explanation:
63 = 9*7
7 is prime but 9 is not
Break 9 into its factors
= 3*3 *7
All of these are prime
Answer:3x3x7
Step-by-step explanation:
How long is the shorter leg of the triangle?
Answer:
6 is the answer
Factor 12x−54 using the GCF.
Answer:
6(2x-9)
Step-by-step explanation:
The two numbers in question are both even, so we can see that we can pull out 2, giving us:
2(6x -27)
Looking at this, we can see that we can no longer pull out 2, but we can pull out 3, giving us:
6(2x-9)
This can be simplified no further, so this gives us the final answer, where the GCF is 6.
32/20 fully reduced in prime numbers
Answer:
8/5
Step-by-step explanation:
EL NUMERADOR Y EL DENONINADOR SE DIVIDEN AL MISMO TIEMPO
ENTRE LOS NÚMEROS PRIMOS EN ORDEN HASTA QUE YA NO PUEDAN
DIVIDIRSE.
find the value of "y" log(4y+1)=log(y-7)-2log2
Answer:
y = -8/15
Step-by-step explanation:
log (4y + 1) = log (y - 7) - 2log2
log (4y + 1) = log (y - 7) - log2² (power law)
log (4y + 1) = log [(y - 7)/4]
4y + 1 = (y - 7)/4 (remove log)
4(4y + 1) = y - 7
16y - y = -8
15y = -8
y = -8/15
What is the slope? Help me please
Answer: Slope of 2.
Step-by-step explanation:
Start at where the line meets on the y-axis, -7. Then work your way upwards until you see the line align with a value of x, like (1,-5). Then you see a trend of it going up 2 units and over 1. 2/1 or 2 is your slope.
how to factor 5r^2+10r-240
Answer:
5 ( r+8) (r-6)
Step-by-step explanation:
5r^2+10r-240
First factor out the greatest common factor
5( r^2 +2r - 48)
Now factor what is inside the parentheses
What multiplies to -48 and adds to 2
8*-6 = -48
8-6 = 2
5 ( r+8) (r-6)
Solve for the value of x that would make line a parallel to line t?
Answer:
The value of [tex]x[/tex]:
[tex]x = 44[/tex]
Step-by-step explanation:
Find the value of [tex]x[/tex]:
[tex]2(x + 10) = 3(x-8)[/tex]
Use Distributive Property:
[tex]2(x + 10) = 3(x-8)[/tex]
[tex]2x +20 = 3x - 24[/tex]
-Subtract both sides by [tex]3x[/tex] and combine both [tex]2x[/tex] and [tex]-3x[/tex] together:
[tex]2x +20 - 3x = 3x - 3x - 24[/tex]
[tex]-x + 20 = -24[/tex]
-Subtract both sides by [tex]20[/tex]:
[tex]-x + 20 - 20 = - 24 - 20[/tex]
[tex]-x = -44[/tex]
Divide both sides by [tex]-1[/tex]:
[tex]\frac{-x}{-1} = \frac{-44}{-1}[/tex]
[tex]x = 44[/tex]
So, the final answer would be [tex]x = 44[/tex].
I need help with this please!!
Answer:
The answer is Point A is equal to (8,0) and Point B is (26,-20) and point C would be (16,-16) and point D would be (8,-30)
Step-by-step explanation:
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!
Answer:
n= -11/5+ 3/5m
Step-by-step explanation:
Answer:
g(n) = [tex]\frac{5n+11}{3}[/tex]
Step-by-step explanation:
Given
3m - 5n = 11
Rearrange making m the subject
Add 5n to both sides
3m = 5n + 11 ( divide both sides by 3 )
m = g(n) = [tex]\frac{5n+11}{3}[/tex]
Find the measure of arc FGH.
[tex]arc \: fgh = \: 238° \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Find the volume of the prism.
Answer:
792
Step-by-step explanation:
mark me brainliest!
12*11*6=792
v=l*w*h
*= times
Here are two squares, A and B. The length of the side of square A is 50% of the length of the side of square B
PLEASE HELP ME WITH MY MATHS HOMEWORK BELOW
if you answer it correctly i will rate you 5 stars and brainiest
Answer:
a) 52%
b) 7
Step-by-step explanation:
Total no of grids = 25
Shaded grids = 13
[tex]a) \\Percent \; of \: Shaded\: grids = \frac{13}{25} \times 100 = 13\times 4 = 52\%\\\\b)\\80\% \: of \: 25 =0.80\times 25 = 20\\No \; of \: squares\: more\: than \: 13 = 20 - 13 = 7[/tex]
The cost of a service call to fix a washing machine can be expressed by the linear function Y = 45x+35, where y represents th
total cost and x represents the number of hours it takes to fix the machine. What does the y-intercept represent?
Answer: brainliesss plsss
The cost of a service call to fix a washing machine can be expressed
Step-by-step explanation:
The cost of a service call to fix a washing machine can be expressed by the linear function y=45x+35 where y represents the total cost and x represents the number of hours it takes to fix the machine.
Answer:
whats the real answer?
Step-by-step explanation:
Consider the two triangles.
Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
How can the triangles be proven similar by the SSS similarity theorem?
Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent.
Show that the ratios StartFraction U V Over Z Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over X Y EndFraction are equivalent.
Show that the ratios StartFraction U V Over X Y EndFraction and StartFraction W V Over Z Y EndFraction are equivalent, and ∠V ≅ ∠Y.
Show that the ratios StartFraction U V Over Z Y EndFraction and StartFraction W U Over Z X EndFraction are equivalent, and ∠U ≅ ∠Z.
Answer:
(A)Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent.
[tex]\dfrac{UW}{XZ}=\dfrac{WV}{ZY}=\dfrac{UV}{XY}[/tex]
Step-by-step explanation:
In Triangles WUV and XZY:
[tex]\angle VUW$ and \angle YXZ$ are congruent. \\\angle U W V$ and \angle X Z Y$ are congruent.\\ \angle U V W$ and \angle Z Y X$ are congruent.[/tex]
Therefore:
[tex]\triangle UWV \cong \triangle XZY[/tex]
To show that the triangles are similar by the SSS similarity theorem, we have:
[tex]\dfrac{UW}{XZ}=\dfrac{WV}{ZY}=\dfrac{UV}{XY}[/tex]
As a check:
[tex]\dfrac{UW}{XZ}=\dfrac{40}{32}=1.25\\\\\dfrac{WV}{ZY}=\dfrac{60}{48}=1.25\\\\\dfrac{UV}{XY}=\dfrac{50}{40}=1.25[/tex]
The correct option is A.
Answer:
answer is a
Step-by-step explanation:
A cube fits perfectly in a sphere. If the cube has a side length of 10cm, what is the volume of the sphere? Round your answer to the nearest hundredth (2 decimal places) or leave your answer in Pi form
Answer:
Step-by-step explanation:
Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
d² = 10² + 10² = 200
d = √200 = 14.14cm
Formula for finding the volume of a sphere is expressed as
Volume = 4/3 × π × r³
Radius of sphere = diameter/2 = 14.14/2 = 7.07cm
Volume = 4/3 × π × 7.07³ = 471.19π cm³
if 11x+5y = 9
11x +3y=1
.
[tex]the \: value \: of \: x \: is \: - 1. \\ the \: value \: of \: y \: is \: 4 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Factor-2 out of -6x + 10
Answer:
3x - 5
Step-by-step explanation:
divide both numbers by -2
Solve for X.
X/3=5/8
4 4/5
17/8
8/15
Answer:
x = [tex]\frac{15}{8}[/tex]
OR
x = [tex]1 \frac{7}{8}[/tex]
Step-by-step explanation:
[tex]\frac{x}{3} = \frac{5}{8}[/tex]
Cross Multiplying
x × 8 = 5 × 3
8x = 15
Dividing both sides by 8
x = [tex]\frac{15}{8}[/tex]
OR
x = [tex]1 \frac{7}{8}[/tex]
i know it's a dumb question but please just answer it.
What is 2 x 1/6 =?
Answer:
answer is 0.33333333
Step-by-step explanation:
Answer:
0.33333333333
Step-by-step explanation:
My calculator gave me 1/3 but the real answer is 0.333 etc
different calculators give you different answers
Please I need help with this I’m stuck I need to get it right
Answer:
b
Step-by-step explanation:
What is the missing step in the proof? i need help
Direct Variation: If y = 12, when x = 4, find y when x = 20. a.40 b.48 c.12 d.60
Answer:
d
Step-by-step explanation:
Given the x and y are in direct variation then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 12 when x = 4, that is
12 = 4k ( divide both sides by 4 )
3 = k
y = 3k ← equation of variation
When x = 20 , then
y = 3 × 20 = 60 → d
Help me please show me how u got your answer PLZ and Thank You!!
Answer:
1/3 I think I am not sure tho.
btw I know st math I used to do that to! LOL!
Step-by-step explanation:
If I am please mark me BRAINLIEST!
Daily Brainliest #1 - Needs to be correct / First correct person to answer simple explanation gets today's brainliest
(2+5)×(8+5)
Answer:
91
Step-by-step explanation:
(2 + 5)(8 +5)
2 + 5 = 7
8 + 5 = 13
7 * 13 = 91
the sum of the present ages of A and B is 60 years.5 years hence their ages will be in the ratio 4:3.What were their ages 5 years ago? please show the working
Answer:
A= 30 years old
B= 20 years old
Step-by-step explanation:
Let the present age of A be x years old.
Since the sum of the present ages of A and B is 60 years,
present age of B= (60-x) years old
In 5 years
A= x +5
B= 60 -x +5= 65-x
Since the ratio of A:B= 4:3,
A would represent 4 units and B would represent 3 units.
Thus [tex]\frac{3}{4}[/tex]A=B
[tex]\frac{3}{4}[/tex](x+5)= 65 -x
[tex] \frac{3}{4} x + \frac{15}{4} = 65 - x \\ \frac{3}{4} x + x = 65 - \frac{15}{4} \\ \frac{7}{4} x = 61.25 \\ 7x = 61.25 \times 4 \\ 7x = 245 \\ x = 245 \div 7 \\ x = 35[/tex]
Thus, present age of A
= x
= 35 years old
present age of B
= 60 -x
= 60 -35
= 25 years old
5 years ago
A= 35 -5= 30 years old
B= 25 -5= 20 years old
* under the section in 5 years, [tex]\frac{3}{4} A=B[/tex] because both would be equal to 3 units each. Since B is 3 units and A is 4 units, in order to make both value the same, we divide the 4 units of A by 4 then multiply by 3 to get 3 units. Thus, [tex]\frac{3}{4}[/tex] of A is equal to B.
