Answers
Answer:
10
Step-by-step explanation:
There are several ways to solve this problem which I’ll demonstrate these ways and see which method is way easier to understand.
First Method
This method is to convert the fractional expression to a single exponent expression using a law of exponent.
[tex]\displaystyle \large{\frac{m^a}{m^b} = m^{a-b}}[/tex]
In words, it means if both divisor (denominator) and dividend (numerator) have same values or are same, we can subtract the exponent from dividend (numerator) with divisor (denominator).
The dividend (numerator) exponent is unknown, let’s say it’s got ‘x’ as an exponent and this ‘x’ is what we are going to find since we don’t know its value.
Now we have the equation:
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Apply the exponent rules above.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Solve an exponential equation - If both sides of equation have same base, we can solve the exponents.
Since LHS (Left-Handed Side) and RHS (Right-Handed Side) both have same base which is ‘m’ therefore, solve exponents.
[tex]\displaystyle \large{x-7=3}\\\displaystyle \large{x=7+3}\\\displaystyle \large{x=10}[/tex]
Therefore, the missing exponent is 10.
Additional Info
You can also use logarithm to solve an exponential equation.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Take a logarithm of base ‘m’ both sides so we can apply other properties.
[tex]\displaystyle \large{\log_m m^{x-7} = \log_m m^3}[/tex]
From the property [tex]\displaystyle \large{\log_a b^n = n \log_a b}[/tex]
[tex]\displaystyle \large{(x-7) \log_m m = 3 \log_m m}[/tex]
From the property [tex]\displaystyle \large{\log_a a = 1}[/tex]
[tex]\displaystyle \large{(x-7)1 = 3 \cdot 1}\\\displaystyle \large{x-7=3}\\\displaystyle \large{x=10}[/tex]
______________________________
Second Method
This method is to isolate the term with missing exponent.
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Transport m^7 to multiply with m^3 via transportation property.
[tex]\displaystyle \large{m^x = m^3 \cdot m^7}[/tex]
We also have to apply another law of exponent as well.
[tex]\displaystyle \large{m^a \cdot m^b = m^{a+b}}[/tex]
Similar to the one with division (fraction), this one, when same bases multiply each other, we have to add both exponents while the other one subtracts exponents.
[tex]\displaystyle \large{m^x = m^{3+7}}\\\displaystyle \large{m^x = m^{10}}[/tex]
In the first method, we know that when solving an exponential equation, if two bases from left and right sides are same, we solve the exponent.
Therefore, [tex]\displaystyle \large{m^x = m^{10} \to \boxed{x=10}}[/tex]
______________________________
Summary
Laws of Exponent
[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}\\\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}}\\[/tex]
For what I demonstrate in my explanation only.
Exponential Equation
When two bases from left side and right side are same, we can solve through exponents.
Examples:
[tex]\displaystyle \large{2^{x-3} = 2^{4}}\\\displaystyle \large{x-3=4}\\\displaystyle \large{x=4+3}\\\displaystyle \large{x=7}[/tex]
You can also substitute x-value in an equation to see if both sides are equal or not.
[tex]\displaystyle \large{2^{x-4} =2^3}[/tex]
Substitute x = 7 for check.
[tex]\displaystyle \large{2^{7-4} = 2^3}\\\displaystyle \large{2^3 = 2^3 \ \ \checkmark}[/tex]
Logarithm
This is not necessary used in this question. This is mostly used for converting to exponential and more advanced mathematics.
[tex]\displaystyle \large{\log_a b^n = n\log_a b}\\\displaystyle \large{\log_a a = 1}[/tex]
Only from what I demonstrate in my explanation.
______________________________
If you are still stuck or need clarification regarding my answer and explanation, you may ask in comment below.
Hope this helps! And wish you luck in your assignment.
Related Questions
They buy 400g with costs 2.56 how much would 350g cost
Answers
Answer:
2.24
Step-by-step explanation:
First I calculated the price for one g with the equation 2.56/400g.
I got .0064 per gram.
You can then multiply this by the 350g to get 2.24
Hope this helps
A row of 12 desks measures 27 feet. How many feet long is each desk? *
Answers
Step-by-step explanation:
To identify how long each desk is, divide 27 feet by the 12 desks. (Given values)
[tex]\frac{27}{12} = 2\frac{1}{4}[/tex] [tex]or[/tex] [tex]2.25[/tex]
Each desk is 2.25 ft long.
Check:
[tex]2.25 \times 12 = 27[/tex]
Correct.
Perimeter:
Area:
3.9 & 1.3
Answers
Answer:
1&0
Step-by-step explanation:
Enter a value for side 1 in metres with optional centimetres.
Enter a value for side 2 in metres with optional centimetres.
Click associated Get Results button.
Square metres (m2) and centimetres (cm2) remainder is shown.
Multiple calculations can be placed in the textbox below by pressing Move Results.
Multiple calculations total area is shown in the Grand Total Square Metres text box.
PLS HELP MEEEEEE Is Triangle M'S'V' a reduction or an enlargement of the original Triangle MSV?
In your answer, specify whether this dilation is a reduction or an enlargement and
explain how you know.
Answers
Answer:
reduction
Step-by-step explanation:
cause it is a smaller version
Answer:
its a reduction
Step-by-step explanation:
and because an enlargement scale factor is over 1 and a reduction scale factor is between 0 and 1 so the smaller trapezoid is a reduction because it isn't the original.
ok but like any middle schooler can one of u guys help me on this problem bc when i do it my teacher says its wrong so what percent of 15 is 60 ?
Answers
Answer:
9
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
15/60 = x/100
= 15 × 100 = 60x
= 1500 = 60x
= 1500/60 = x
= 25
Hope it helps ⚜
Is 9546 greater than, less than, or equal to 9.123 × 103 ?
Answers
Answer:
greater than
Step-by-step explanation:
9.123 * 103 = 939.669
9546 > 939.669
Which expression is equivalent to the expression below?
6r+3(3s+9r)
which one is it? SOS
Answers
Answer: 33r + 9s
Step-by-step explanation: First, we need to distribute
the 3 through both terms inside the set of parenthses.
Students will often multiply the 3 by the 3s but forget
to multiply the 3 by the 9r, beware of this mistake.
So we get 6r + 9s + 27r which simplifies to 33r + 9s.
The equivalent expression is 33r + 9s
How to determine the equivalent expression?The expression is given as:
6r + 3(3s + 9r)
Expand the expression
6r + 9s + 27r
Collect like terms
6r + 27r + 9s
Evaluate the like terms
33r + 9s
Hence, the equivalent expression is 33r + 9s
Read more about equivalent expressions at:
https://brainly.com/question/2972832
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 feet, what is the distance (x) from the plane (P) to the observer (O)? A right triangle is shown with angle O marked 55 degrees, hypotenuse marked x, and height marked 21,000 feet. 20,793 feet 25,636 feet 28,793 feet 36,585 feet.
Answers
Angle of elevation is angle measured from horizontal line to line of sight, The distance from the plane to the observer is 25,636 feet approx
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal line to the point where you stopped your head is called angle of elevation. See the figure where angle OPD is the angle when observer saw the plane. It is measured from the horizontal line OD.
Refer to the attached figure.
It is given that we have
Length of PD = |PD| = 21,000 feet
Angle ∠OPD = 55°
Assuming length of OP = |OP| = x feet, we get the sin ratio as
[tex]sin(55^\circ) = \dfrac{|PD|}{|OP|} = \dfrac{21000}{x}\\\\x = \dfrac{21000}{\sin(55^\circ)} \approx 25636.27 \approx 25636 \: \rm feet[/tex]
(tan 55° was calculated from online calculator)
Thus,
The distance from the plane to the observer is 25,636 feet approx.
Learn more about trigonometric ratios here:
https://brainly.com/question/22599614
Answer:
B. 25,636 ft.
Step-by-step explanation:
Cause I'm Asian, I make the rules here...
help with parallel lines please
Answers
Answer:
angle 2 = 38° { because they are corresponding angles ,so they are equal }
Answer:
Step-by-step explanation:
∠2 = 38 {corresponding angles}
A pair of angles on the same side of the transversal, one of which is and interior angle and the other one is an exterior angles, but do not form a linear pair, is known as corresponding angles
ight i knew this but forgot a lil so can u tell me the answer and explan it to me?
Answers
Answer:
30
Step-by-step explanation:
All straight line equations are in the form:
[tex]y=mx+c[/tex]
Where m is the gradient and c is the y-intercept
In this equation +30 is the y-intercept
Answer:
The y-intercept is 30 in this equation
Step-by-step explanation:
This equation is in slope-intercept form.
Slope intercept form includes two things, (you can probably already guess)
It includes the slope of the line and the y-intercept
In all slope-intercept form equations the 20x would be the slope and the 30 would be the y-intercept
So that should be enough to give you your answer! I hope this helps and please award brainliest if possible!
Use the Side-Splitter Theorem to determine the missing lengths.
Mark brainliest unless you show your work!
Answers
Hi there!
The answer is →[tex]15 \sqrt{3}[/tex]←
(Check the attached image for the explanation)
Expand & simplify
(x+3) (x+6)
Answers
Answer:
[tex]x^{2} +9x+18[/tex]
Explanation:
[tex]x(x+6)+3(x+6)\\x^{2} +6x+3(x+6)\\x^{2} +6x+3x+18\\x^{2}+9x+18[/tex]
Solve x2 = 121.
if you can help me it would be great
Answers
Answer:
The answer is X=11 and X=-11
Step-by-step explanation:
[tex] {x}^{2} = 121 \\ \sqrt{121} = 11 \\ therefore \: value \: of \: x \: is \: 11[/tex]
x^3+3x^2=24x+72 solve by factoring
Answers
Step-by-step explanation:
Irurjr8ri4b4 ririr 4 rikr r ririr r is the value of x in the equation 3 it is a good thing that you can use the rgb settings in the glorious model of your home and you will be able by the accounts department this is for the payable at on on Jan 1 2021 as I have not yet received the funds in the bank to pay the deposit for our deposit and the number y is greater than eight weeks notice and is a fat loss as brain is a fat loss for her outstanding amount but she will not be able to afford to pay for the correct answer and will not be able to make the payments to the base QR as I have not been paid for the last three months due to the formation of which substance of my
Help me fast, please!!!!!!!!!!!!
Answers
I believe these are the answers:
1. True.
2. False.
3. False.
4. True.
Let me know if those are right. :)
For each value of v, determine whether it is a solution to 6v-8>22.
Answers
[tex]6v - 8 > 22 \\ 6v > 22 + 8 \\ 6v > 30 \\ v > \frac{30}{6} \\ v > 5[/tex]
Simplify: ∛(2) × 2^(-1/13) × ¹²√(32)
[tex]simplify : \sqrt[3]{2} \times {2}^{ - \frac{1}{13} } \times \sqrt[12]{32} \\ [/tex]
Answers
Step-by-step explanation:
Given that:
∛(2) * 2^(-1/13) * ¹²√(32)
= ∛(2) * 2^(-1/13) * ¹²√(2⁵)
[since, ⁿ√(a) = a^(1/n)]
= 2^(1/3) * 2^(-1/13) * 2^{5 * (1/12)}
= 2^(1/3) * 2^(-1/13) * 2^{(5*1)/12}
= 2^(1/3) * 2^(-1/13) * 2^(5/12)
[since, a^m * a^n = a^(m+n)]
= 2^{(1/3) - (1/13) + (5/12)}
Take the LCM of 3, 13 and 12 is 156.
= 2^[{(1*52) - (1*12) + (5*13)}/156]
= 2^{(52 - 12 + 65)/156}
= 2^{(117 - 12)/156}
= 2^(105/156)
Now reduce the power fraction in simplest form by cancelling method.
= 2^(35/52) (or)= {2^(35)}^(1/52) (or)
= ⁵²√{2^(35)}
Answer: Hence, the simplified form of ∛(2) * 2^(-1/13) * ¹²√(32) = ⁵²√{2^(³⁵)}.
Please let me know if you have any other questions.
Applying the law of indices to the roots, we have that
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
So,
[tex]\sqrt[3]{2}[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]\sqrt[12]{32}[/tex] = [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]32^{\frac{1}{12} }[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex](2^{5} )^{\frac{1}{12} }[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]2^{\frac{5}{12} }[/tex]
Since we have the same base in all three numbers, we have that from the law of indices, [tex]a^{x}[/tex] × [tex]a^{y}[/tex] = [tex]a^{x + y}[/tex]
= [tex]2^{\frac{1}{3} }[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]2^{\frac{5}{12} }[/tex]
[tex]= 2^{\frac{1}{3} + (-\frac{1}{13}) + \frac{5}{12} } \\= 2^{\frac{1}{3} - \frac{1}{13} + \frac{5}{12} }[/tex]
Taking L..C.M of the denominators of the exponents, the L.C.M is 156.
So,
[tex]2^{\frac{1}{3} - \frac{1}{13} + \frac{5}{12} }\\= 2^{\frac{52 - 12 + 5 X 13}{156} } \\= 2^{\frac{52 - 12 + 65}{156} }\\= 2^{\frac{40 + 65}{156} }\\= 2^{\frac{105}{156} }[/tex]
Simplifying the exponent, we have
[tex]2^{\frac{105}{156} } \\= 2^{\frac{35}{52} }[/tex]
So, [tex]\sqrt[3]{2}[/tex] × [tex]2^{-\frac{1}{13} }[/tex] × [tex]\sqrt[12]{32}[/tex] = [tex]2^{\frac{35}{52} }[/tex]
Learn more about indices here:
https://brainly.com/question/10339517
A trucking company makes 50 deliveries in 5 days.
How long will it take for 400 deliveries?
8 days
or
10 days
or
20 days
or
40 days
Answers
Answer: 40 days
Step-by-step explanation: 50 divided by 5 equals 10 so 10 divided by 400= 40
Answer:
this is very hard, Good luck
whats the sqaure root of 1386
Answers
Answer: " [tex]3\sqrt{154}[/tex] " ;
or, write as: " 37.229 " .
__________
Step-by-step explanation:
The digits of "1386" ;
add up to: " (1 + 3 + 8 + 6) " ;
= " (1 + 3) + 8 + 6 " ;
= " (4) + 8 + 6 ;
= " (4 + 8 + 6) " ;
= " (4 + 8) + 6) " ;
= " (12) + 6 "
= "18 " ;
"18" is divisible ("evenly") ; by both: "2" : {" 18 ÷ 2 = 9 ".} ;
and by: "3" : {" 18 ÷ 3 = 6 ".}
Note: If a number is "evenly divisible by both: "2" and "3" ; then said number is divisible by "6" ;
_________
Other: If the sum of the digits of a number result in a number that is evenly divisible by "9" ; then said number is evenly divisible by "9" ;
_________
The sum of the digits of "1386" is: "18" ;
and: the sum of the digits of: "18" ; ⇒ " 1 + 8 = 9" .
{and: " 9 ÷ 9 = 1 ".}.
_________
Note: If number that ends with the last 2 (two) digits; in consecutive order; in which, taken as a "separate number" , is evenly divisible by "4" ; then, the entire said number is evenly divisible by "4".
Note: The number given: "1386 " ; ends with: "86" ;
and: " 86 ÷ 4 = 21.5" ; so we know that:
"1386" is not evenly divisible by "4".
_________
Note: If a number ends with the digit: "5" ; or "0" ; then the number is evenly divisible by: "5" . The number: "1386" ; does not meant either of these criteria.
_________
Note: If a number ends with the digit: "0" ; then the number is evenly divisible by: "10" . The number: "1386" ; does not meant this criterion.
_________
Note: If a number ends with the last 2 (two) digits; in consecutive order; in which, taken as a "separate number" , is evenly divisible by "7" ; then, the entire said number is evenly divisible by "7".
Note: The number given: "1386 " ; ends with: "86" ;
and: " 86 ÷ 7 = 12[tex]\frac{2}{7}[/tex] " ; so we know that:
"1386" is not evenly divisible by "7".
_________
Note: If a number ends with the last 2 (two) digits; in consecutive order; in which, taken as a "separate number" , is evenly divisible by "4" ; then, the entire said number is evenly divisible by "4".
Note: The number given: "1386 " ; ends with: "86" ;
and: " 86 ÷ 4 = 21.5" ; so we know that:
"1386" is not evenly divisible by "4".
_________
Note: If a number ends with the last 3 (three) digits; in consecutive order; in which, taken as a "separate number" , is evenly divisible by "8" ; then, the entire said number is evenly divisible by "8".
Note: The number given: "1386" ; ends with: "386" ;
and: " 386 ÷ 8 = 28[tex]\frac{1}{4}[/tex] " ; so we know that:
"1386" is not evenly divisible by "8" ;
_________
Since: we know that "1386" is evenly divisible by "9" ;
and "9" is a perfect square;
{since: " 3² = 3 * 3 = 36 " ; and since: " [tex]\sqrt[]{9} = 3[/tex] " }.
Let's see what the other factor of "1386" is when "9" is a factor:
" 1386 ÷ 9 = 154 " ;
_________
So: √(154) ;
= √9 * √(154) ;
= 3 * √(154) ;
Let's look at the factors of 154:
_________
⇒ 1 & 154; 2 and 77;
List this factors of "154" as: 1, 2, 77, 154;
→ none of which are "perfect squares" ;
→ So, the answer is: " [tex]3\sqrt{154}[/tex] " ;
or: further calculate with a calculator:
→ " [tex]3 * \sqrt{154} =[/tex][tex]37.2290209379725698[/tex] " ;
→ round to: " 37.229 ".
_________
Hope this is helpful. Best wishes!
_________
A new car is purchased for $23,700 the value of the car depreciates at 13. 5% per year what will the value the car be to the nearest cent after 10 years
Answers
Answer:
Compound interest
$5557.88
Step-by-step explanation:
Everything starts at 100% and since it depreciates you subtract 13.5 from 100 =86.5% now we want percentage as a decimal so we divide by 100=0.865 our multiplier
Now you have the original amount that you purchased for times by the multiplier to the power of number of years=10
23700 times 0.865 power of 10
=5557.88
help me pleaseeeeeeeeeeee
Answers
At which points are the equations y = x- + 3x + 2 and y = 2x + 3 approximately equal?
Answers
Select all the correct locations on the graph. At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal? 2.
Answer:
The equations are approximately equals at the points (0.618,4.236)(0.618,4.236) and (-1.618,-0.236)(−1.618,−0.236)
Mike and his friends will watch a concert this weekend. A concert ticket cost P 750.00 but for every 10 tickets you buy you will have a 15% discount. If they will buy 10 concert tickets, how much will they pay?
A. P 6 365
B. P 6 375
C. P 6 385
Answers
Answer:
B
Step-by-step explanation:
PLS HELP I'LL GIVE U BRAINLIEST
The temperature falls from 15 degrees to -10 degrees. What is the difference in those temperatures?
Answers
15-25=-10
-10+25=15
Answer:
the answer is 7 degrees /j
A(-6, 7)
B(6)-1)
C(-2,-5)
What is the midpoint of AC?
A( -2,1)
B (-4,1)
C (-4,6) D(0,3)
Answers
Answer:
-4,6
Step-by-step explanation:
6 horizontally and -4 vertically
What is the measure of the missing angle?
Answers
Answer: 60°
Step-by-step explanation:
triangles always equal 180°, in this case you’re looking at the entire triangle so
60°+35°+25° = 120
180-120 = 60°
the missing angle is 60°
hope this helps :)
The neighborhood swimming pool is 14 feet long, 11 feet wide, and 3 feet deep. Which formula below should be used to find how much water the pool can hold?
A.
2(14 feet) × 2(11 feet) × 2(3 feet)
B.
2(14 feet) + 2(11 feet) + 2(3 feet)
C.
14 feet + 11 feet + 3 feet
D.
14 feet × 11 feet × 3 feet
Answers
Answer:
D. 14 feet × 11 feet × 3 feet
Step-by-step explanation:
The volume of a rectangular prism is the product of its dimensions:
V = LWH
V = (14 ft)(11 ft)(3 ft) . . . . . matches choice D
What is the height of the triangular base? Show your work.
and What is the approximate amount of cardboard used to make the candy box?
Answers
Answer:
Hope it helps :)
Step-by-step explanation:
The volume of a triangular prism shaped box is 2,400 cubic centimeters.
Base of the triangle = 16cm
Sides of the triangle = 17cm
Length of the box = 20cm
Triangular prism
A triangular prism is a three-sided prism made of a triangular base and a corresponding side.
A. To find the height of the base = 3 x the volume divided by the base area = 15cm.
B. The approximate amount of card board used to make the candy box:
Using the lateral prism as the sides will be:
Lateral area = Perimeter of triangle X height of the prism
Lateral area = (16 + 17 + 17) X 20
Lateral area = 50 X 20
Lateral area = 1,000 cm2
Therefore, the answer is 1000cm2.
How do we do this please help.
Answers
Answer: he has 30 sweets
Step-by-step explanation:
3:2 - five parts all together
50 divide 5 = 10
10 x 3 because the 3 in 3:2
=30
To buy a car, Rachel
borrowed $3,000 at
946 interest per
year for 3 years
How much money
did she have to pay
back?
Answers
Answer: (3000)*(0.09)*(4) = $1,080.00
Step-by-step explanation:
When money is borrowed, interest is charged for the use of that money over a certain period of time. The amount of interest charged depends on the amount of money borrowed, the interest rate and the length of time for which the money is borrowed.
Principal is the amount of money borrowed. The interest rate is given as a percent. Time is the length of time in years for which the money was borrowed.
Interest = Principal * Rate * Time which is also written as I = P*R*T
Principal = $3,000, Interest rate = 0.09 and Time = 4
Raquel had to pay back $3,000 in principal plus $1,080 in interest for a total of $4,080.00
(3000)*(0.09)*(4) = $1,080.00