Solve for
-30 = 1/4 - 37
r =​

Answer:

(1)

Donna = Pounds 180

Kyra = Pounds 240

(2)

Kelly = Pounds 225

Nelly = Pounds 175

Step-by-step explanation:

(1)

Donna = x

Kyra = x + 60

If Donna spends 1/3 of her money she is left with 2/3 of her money;

2/3 x

Kyra now has twice as much money as Donna can be represented as;

X + 60 = 2 * 2/3 x

X + 60 = 4/3 x

(x + 60)3 = 4x

3x + 180 = 4x

180 = 4x – 3x

180 = x

Donna = 180

Kyra = 180 + 60 = 240

(2)

Kelly = x

Ned = y

Kelly spends 40% of her money. Therefore he is left with 60%;

60/100 x

Nelly spends Euros 40 of his money. Therefore he is left with;

y- 40

If they now have the same amount of money;

60/100 x = y – 40

3/5 x = y – 40

3x = 5y – 200

3x – 5y = -200

Remember Kelly & Ned has Euros 400 in total;

x + y = 400

Now we can solve the simultaneous equation by substitution;

x + y= 400

3x – 5y = -200

3x + 3y = 1200

-

3x – 5y = - 200

=

8y = 1400

Y = 175

X = 225

Kelly = 225

Nelly = 175

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Answer:

3. £60

4. Ned had £175

Step-by-step explanation:

3. 3 segments of Donna plus £60 is the money that Kyra has. Ater Donna spend 1/3 of her money, Kyra has twice as much money as Danna. This means that  2 segments of Donna are equal to 1 segment plus £60, so 1 segment is equal to £60. Donna spend 1 segment of her money, that is, £60.

4. Let's define x the money of Kelly, and y the money of Ned.

Kelly and Ned have £400 in total:

x + y = 400 (eq. 1)

Kelly spends 40% of her money (so she conserves the other 60%), Ned spends £40, They now have the same amount of money:

0.6*y = x - 40 (eq. 2)

From equation 1:

y = 400 - x

Replacing into equation 2:

0.6*(400 - x) = x - 40

240 - 0.6*x = x - 40

- 0.6*x - x = - 40 - 240

-1.6*x = -280

x = -280/-1.6

x = £175

Answer:

[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]

Step-by-step explanation:

Solving trigonometric equations.

We are given a condition and we must find all angles who meet it in the provided interval. Our equation is

[tex]cos5x=-\frac{1}{2}[/tex]

Solving for 5x:

[tex]5x=\frac{2\pi}{3}+2n\pi[/tex]

[tex]5x=\frac{4\pi}{3}+2n\pi[/tex]

The values for x will be

[tex]x=\frac{\frac{2\pi}{3}+2n\pi}{5}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+2n\pi}{5}[/tex]

To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval [tex](0,2\pi)[/tex]

For n=0

[tex]x=\frac{\frac{2\pi}{3}}{5}=\frac{2\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}}{5}=\frac{4\pi}{15}[/tex]

For n=1

[tex]x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+2\pi}{5}=\frac{2\pi}{3}[/tex]

For n=2

[tex]x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}[/tex]

For n=3

[tex]x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+6\pi}{5}=\frac{22\pi}{15}[/tex]

For n=4

[tex]x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+8\pi}{5}=\frac{28\pi}{15}[/tex]

For n=5 we would find values such as  

[tex]x=\frac{\frac{2\pi}{3}+10\pi}{5}=\frac{32\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}[/tex]

which don't lie in the interval [tex](0,2\pi)[/tex]

The whole set of results is

[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]

Answer:

[tex]K=-2J+28[/tex]

Step-by-step explanation:

For the given trend line, we need to find the y-intercept and slope of the line for determining its equation.

Equation of a line is of the form [tex]y=mx+b[/tex]

Where, 'm' is the slope and 'b' is the y-intercept.

Here, the variables are 'J' and 'K'.

The y-intercept is the point where the 'J' value is 0. From the graph, when 'J' is 0, then the 'K' value is 28. Therefore, the y-intercept is 28.

Slope is given as the ratio of change in 'K' and change in 'J'

The overall change in 'K' is 0 - 28 = -28.

The overall change in 'J' is 14 - 0 = 14

Therefore, the slope is given as:

[tex]m=\frac{\Delta K}{\Delta J}=\frac{-28}{14}=-2[/tex]

Therefore, the equation of trend line is given as:

[tex]K=-2J+28[/tex]

Answer:

Either x  = + i/2 or  x = i/2 is the solution for the given quadratic equation.

Step-by-step explanation:

Here, the given quadratic equation is:[tex]4x^2 + 1 = 0[/tex]

Now, comparing the given equation with standard Quadratic Form, [tex]ax^2 + bx + c = 0[/tex]

we get,a  = 4, b =0 and c = 1

Now, the Quadratic Formula is given as:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

So, here the solution for the given expression is:

[tex]x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies  x = \frac{0 \pm4i}{8}\\\implies x  =  \frac{0 + 4i}{8} = \frac{i}{2} \\or,  x  =  \frac{0 - 4i}{8} = \frac{-i}{2}[/tex]

Hence, either x  = + i/2 or  x = i/2 is the solution for the givenquadratic equation.

Answer:

3h-9/2

Step-by-step explanation:

3/4(4h-6)=3h-18/4

simplify

3h-9/2

Answer:

3(3h-3/2) in its simplified form.

Step-by-step explanation:

Given the equation 3/4(4h-6),

First we will open the bracket up by multiplying through by 3/4 to have;

3h - 9/2

Since 3 is common at both sides of the resulting equation, we will factor it out to have;

3(h-3/2).

Since we cannot simplify further, then the expression 3/4(4h-6) is also equivalent to 3(h-3/2).

Answer:

The number of math problems Annabelle solved = 5 problems

The number of pages Annabelle read=  20 pages

Step-by-step explanation:

Given:

Time taken for Annabelle to solve one problem =3 minutes

Time taken for Annabelle to read one page =2 minutes

Total time taken by Annabelle to complete her homework= 55 minutes

To find:

Total Number of problems solved by Annabelle=?

Total Number of pages read by Annabelle=?

Solution:

Let the number of problem solved be x

Let the number of pages read be y

It is given that the number pages read is 4 times the number of problem solved

So number of pages read y= 4x

Now time taken to solve x problems =  time taken to solve one problem X total number of problem

=>[tex]3\times x[/tex]

=>[tex]3x[/tex]

Similarly,

Time taken to read 4x pages= total number of pages read X  time taken to read one problem

=>[tex](4x)\times 2[/tex]

=>[tex]2(4x)[/tex]  

Now we know that

Time taken to solve x problems + Time taken to read 4x pages= 55  minutes

3x + (4x)2=55

3x+8x=55

11x=55 [tex]x=\frac{55}{11}[/tex]

x=5

So number of problem solved is x=5

Number of pages read  y=4(x)=4(5)=20

Answer:

Option B

Step-by-step explanation:

On the first row of the Punnett square, the offspring inherits IA from one parent and IB from another parent hence the resulting genotype is IAIB.

Answer:

0

Step-by-step explanation:

If the answer is between 0 to 0.49, the best estimate is 0.

If the answer is between 0.5-1.49, the best estimate is 1.

If the answer is 1.5 or greater, the best estimate is 2.

Without giving the fractions 1/10 and 1/12 a common denominator, we know the answer is between 2/12 and 2/10.

2/12 is less than 2/10. 2/10 is 0.2, which is less than 0.5.

Since the final answer is less than 0.5, the best estimate is 0.

Answer:

D: All of the above.

Step-by-step explanation:

A. All simple machines are useful in some way, weather that be making it easier to lift heavy objects, activating other machines, or something else.

B. Any simple machine must be, well, simple. i. e. have few moving parts.

Take the lever, for example. It has only one moving part, yet it is still very useful.  

C. They can be used to do work. Simple machines can be put together to make something that can do work.

Imagine a windmill that generates power, which then is taken by a motor attached to an Archimedes screw. All of these machines are simple, yet they are still used to do work.

Answer:

The answer is A.

Step-by-step explanation:

Just took the test. You are welcome.

Answer:

x=7 and x=(3/4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

5*m+t=4

Answer:

[tex]5(m+t)=4r[/tex]

Step-by-step explanation:

The given statement is

"Five times the sum of m and t is as much as four times r".

To find the equivalent expression to the given sentence, we just need to transform each part in mathematical expressions. Just remember, times is product, "as much as" indicates equality.

So, the part five times the sum of m and t, represents the product between the number five and the binomial expression, as follows

[tex]5(m+t)[/tex]

As much as four times r, expresses that the first part is equivalent to the product between 4 and r,

[tex]5(m+t)=4r[/tex]

Therefore, the expression is [tex]5(m+t)=4r[/tex]

Answer:

I believe the answer is A.

Step-by-step explanation:

Multiply each nunber by .10

Afterwards subtract what you get from the number (ex-20,000)

You get the next number after it.

Do the same for each number

The statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".

Consider the function:

y= a(1 ± r)ˣ

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

Given that An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.

Now, if the rate of decay and the initial price of the van can be found by substituting the value of x and y in the equation as shown below.

For the first column from the table, when the value of x and y is 0 and 20,000, respectively.

y= a(1 + r)ˣ

20,000 = a(1 + r)⁰

20,000 = a (1)

a = 20,000

For the second column from the table, when the value of x and y is 1 and 18,000, respectively. Also, the value of a=20,000.

y= a(1 + r)ˣ

18,000 = 20,000(1 + r)¹

18,000/ 20,000 = 1 + r

0.9 = 1 + r

0.9 - 1 = r

-0.1 = r

r = -0.1 = -10%

Hence, the statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".

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Answer:

-24*sqrt(35)

Step-by-step explanation:

Answer:

1. 79°

2. 54°

3. 107.5°

4. 44°, 35 cm

5. 76°, 3.5 cm

6. m∠U=36°, m∠M=m∠D=72°,  MD=8.6 cm

7. 78°, 93 cm

8. 81°, 75 cm

Step-by-step explanation:

1. The diagram shows an isosceles triangle because TH = OT. Angles adjacent to the base OH of isosceles triangle are congruent, so

[tex]m\angle H=m\angle O[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle H+m\angle O+m\angle T=180^{\circ}\\ \\2m\angle H+22^{\circ}=180^{\circ}\\ \\2m\angle H=180^{\circ}-22^{\circ}\\ \\2m\angle H=158^{\circ}\\ \\m\angle H=79^{\circ}[/tex]

2. The diagram shows an isosceles triangle DGO because DG = GO. Angles adjacent to the base DO of isosceles triangle are congruent, so

[tex]m\angle D=m\angle O=63^{\circ}[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle D+m\angle O+m\angle G=180^{\circ}\\ \\63^{\circ}+63^{\circ}+m\angle G=180^{\circ}\\ \\m\angle G=180^{\circ}-63^{\circ}-63^{\circ}\\ \\m\angle G=54^{\circ}[/tex]

3. The diagram shows an isosceles triangle SLO because LO = SO. Angles adjacent to the base SL of isosceles triangle are congruent, so

[tex]m\angle S=m\angle L[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle S+m\angle L+m\angle O=180^{\circ}\\ \\2m\angle L+35^{\circ}=180^{\circ}\\ \\2m\angle L=180^{\circ}-35^{\circ}\\ \\2m\angle L=145^{\circ}\\ \\m\angle L=72.5^{\circ}[/tex]

Angles OLE and L (SLO) are supplementary (add up to 180°), so

[tex]m\angle OLE=180^{\circ}-m\angle L\\ \\m\angle OLE=180^{\circ}-72.5^{\circ}\\ \\m\angle OLE=107.5^{\circ}[/tex]

4. The diagram shows an isosceles triangle AMR because [tex]m\angle A=m\angle M=68^{\circ}[/tex] (angles adjacent to the side AM are congruent, so triangle AMR is isoseceles).

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle A+m\angle M+m\angle R=180^{\circ}\\ \\m\angle R+2\cdot 68^{\circ}=180^{\circ}\\ \\m\angle R=180^{\circ}-2\cdot 68^{\circ}\\ \\m\angle R=44^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]RM=AR=35\ cm[/tex]

5. The diagram shows isosceles triangle RYD because YD = RD. Angles adjacent to the base RY are congruent, so

[tex]m\angle R=m\angle Y[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle R+m\angle Y+m\angle D=180^{\circ}\\ \\2m\angle Y+28^{\circ}=180^{\circ}\\ \\2m\angle Y=180^{\circ}-28^{\circ}\\ \\2m\angle Y=152^{\circ}\\ \\m\angle Y=76^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]YD=RD=3.5\ cm[/tex]

6. The diagram shows an isosceles triangle UMD because UM = UD. Angles adjacent to the base MD of isosceles triangle are congruent, so

[tex]m\angle D=m\angle M=72^{\circ}[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle D+m\angle M+m\angle U=180^{\circ}\\ \\72^{\circ}+72^{\circ}+m\angle U=180^{\circ}\\ \\m\angle U=180^{\circ}-72^{\circ}-72^{\circ}\\ \\m\angle U=36^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]UM=UD=14\ cm[/tex]

The perimeter of isosceles triangle MUD is 36.6 cm, so

[tex]UM+MD+UD=36.6\\ \\MD=36.6-14-14\\ \\MD=8.6\ cm[/tex]

7. The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle T+m\angle S+m\angle B=180^{\circ}\\ \\m\angle T+78^{\circ}+24^{\circ}=180^{\circ}\\ \\m\angle T=180^{\circ}-78^{\circ}-24^{\circ}\\ \\m\angle T=78^{\circ}[/tex]

Triangle STB is isosceles triangle because [tex]m\angle S=m\angle T=78^{\circ}[/tex] (angles adjacent to the side ST are congruent, so triangle STB is isoseceles).

To legs in isosceles triangle are always congruent, so

[tex]SB=TB\\ \\y+22.5=38.5\\ \\y=38.5-22.5\\ \\y=16[/tex]

Hence,

[tex]ST=16\ cm\\ \\TB=SB=38.5\ cm[/tex]

and the perimeter of triangle STB is

[tex]P_{STB}=16+38.5+38.5=93\ cm[/tex]

8. The diagram shows isosceles triangle CNB because CN = CB. Angles adjacent to the base RY are congruent, so

[tex]m\angle N=m\angle B[/tex]

The sum of the measures of all interior angles is always 180°, thus

[tex]m\angle N+m\angle B+m\angle C=180^{\circ}\\ \\2m\angle N+18^{\circ}=180^{\circ}\\ \\2m\angle N=180^{\circ}-18^{\circ}\\ \\2m\angle N=162^{\circ}\\ \\m\angle N=81^{\circ}[/tex]

To legs in isosceles triangle are always congruent, so

[tex]CB=CN=2x+90\ m[/tex]

The perimeter of the triangle CNB is

[tex]2x+90+2x+90+x=555\\ \\5x+180=555\\ \\x+36=111\\ \\x=111-36\\ \\x=75\ m[/tex]

So, [tex]NB=75 \ m[/tex]

Answer:

The Number is 8.

Step-by-step explanation:

Let the number be x.

Given:

1/2 is subtracted from four times the reciprocal of a number, the result is 0.

Hence the equation will become like;

[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]

Now Solving the equation we get.

[tex]\frac{4}{x} -\frac{1}{2}=0\\\\\frac{4}{x} = \frac{1}{2}\\\\x= 4\times 2\\x=8[/tex]

Now the we can see the number is 8, when 1/2 is subtracted from 4 times the reciprocal of number means 4/8 which becomes 1/2 and hence when 1/2 is subtracted from 1/2 it equals to 0.

Hence the number is 8.

Multiply the current price by 1 + percentage of increase.

3.50 x 1.11 = 3.89

The new price will be $3.89

Answer:

100 hours

Step-by-step explanation:

Monthly salary = monthly bonus + total wage based on hours worked

Monthly salary = monthly bonus + (dollars per hour x number of hours worked)

Given, monthly salary = $2000

MOnthly bonus = $400

dollars per hour = $16/hr

let h = number of hours worked

hence, equation becomes

2000 = 400 + (16 x h)

2000 = 400 + 16h   (subtract 400 from each side and rearrange)

16h = 2000 - 400

16h = 1600  (divide both sides by 16)

h = 1600 / 16 = 100 hours

Answer:

Yes

Step-by-step explanation:

2a+6=12

2a=12-6

2a=6

a=6/2

a=3

--------------

a+3=6

a=6-3

a=3

----------

Yes, the two equations are equivalent.

Answer:

√8 + √50

= 2√2 + 5√2

=√2(2+5)

= 7√2

Hope this helps!

Answer:

11i

Step-by-step explanation:

first you have to get a postive root.

[tex]\sqrt{-121} \\ \sqrt{-1}  \sqrt{121} \\[/tex]

then you solve the square roots from there, keeping in mind the imaginary number answer to the square root of -1, i.

[tex]\sqrt{-1} = i\\ \sqrt{121} =11\\ 11i[/tex]

You roll a 6-sided die. The probability of getting prime is 50%.

Solution:

Given, that we have rolled a 6 – sided die.

We have to find the P(prime) as percentage.

Now, It means that we have to find the probability of getting a prime number on the face.

On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6

Number of possible outcomes = 6

We have to get a prime number on rolling a die

The prime numbers in possible outcomes are 2, 3, 5

So number of favorable outcomes = 3

[tex]\text {Probability of an event as percentage }=\frac{\text { favourable number of outcomes }}{\text { total number of outcomes }} \times 100[/tex]

[tex]\text {Probability of getting prime number on face of die }=\frac{3}{6} \times 100[/tex]

[tex]\begin{array}{l}{\text { P(prime) }=\frac{1}{2} \times 100} \\\\ {\text { P(prime) }=50 \%}\end{array}[/tex]

Hence, probability of getting prime is 50%.

Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4

Given that

There are 3 feet in one yard  

And there are 12 feet in 4 yard  

Number of feet in one yard = 3 that is feet  : yard = 3 : 1  

Number of feet in 4 yards = 12 that is feet : yard = 12 : 4  

And 3 feet in 1 yard is equivalent to 12 feet in 4 yards means

[tex]\frac{3}{1}=\frac{12}{4}[/tex]

That is 3 : 1 : : 12 : 4

A proportion is statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a : b = c : d

Hence proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 :: 12 : 4

Answer: Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4

Step-by-step explanation: D

Answer:

The answer is C.

Step-by-step explanation:

Very easy question.

Answer:

its a or c

Step-by-step explanation:

Answer:

Equation:  2x + 10y = 98

y-intercept:  (0, 9.8)

Step-by-step explanation:

The easiest possible way to solve thios problem follows:

Keep the form of the given line 2x + 10y = 7, replacing the '7' with the constant 'c:'

2x + 10y = c

Now take the coordinates of the given point (4, 9) and substitute them into the above equation, to find c:

2(4) + 10(9) = c

Then 8 + 90 = c, and c = 98

Then the desired equation is 2x + 10y = 98

To find the y-intercept, let x = 0 and solve for y.  We get

10y = 98, so that y = 9.8.  The y-intercept is thus (0, 9.8).

The y-intercept of the line parallel to 2x + 10y = 7 and containing the point (4, 9) is 8.6.

The y-intercept of a parallel line can be found using the equation y = mx + b, where m is the slope and b is the y-intercept. Since the given line 2x + 10y = 7 is in the form Ax + By = C, we need to rearrange it to the slope-intercept form. Therefore, the equation becomes: 10y = -2x + 7 → y = (-2/10)x + 7/10. The slope of the given line is -2/10, which means any line parallel to it will also have a slope of -2/10. Now we can use the point-slope form to find the equation of the parallel line that passes through the point (4, 9):

y - y1 = m(x - x1) → y - 9 = (-2/10)(x - 4)

Expanding and simplifying the equation, we get:

y - 9 = (-2/10)x + 8/10 → y = (-2/10)x + 8/10 + 9 → y = (-2/10)x + 86/10

Therefore, the equation of the parallel line that contains the point (4, 9) is y = (-2/10)x + 86/10. The y-intercept of this line is 86/10 or 8.6.

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Correct Answer: A. Scatter plot A

Explanation: The line y=x slopes upward from the lower left corner of the graph to the upper right corner, at a 45-degree angle. The scatter plot whose points most closely match that trend is scatter plot A.

Answer:

Step-by-step explanation:

We need to find the scatter plot that is closest to y = x.

First of all, you must know the behaviour of y = x. That equation represents a straight line that passes through the origin of the coordinate system.

So, the right scatter plot must have the majority of points on this line that passes through the origin.

Notice that the Scatter plot A has this beahivour, if you draw a straight line through the origin and the points, you'll observe that the line best fits.

On the other hand, the other scatter plots are not following this linear behaviour.

Therefore, the right answer is A.

Answer:

62

Step-by-step explanation:

8 x n + m = ?

8 x 7 + 6

8 x 7 = 56

56 + 6 = 62

Answer: 62

Step-by-step explanation:

solution here m=6,n=7,and 8n+m=? now 8n+m =8×7+6 =56+6 =62

Answer:

21 feet

Step-by-step explanation:

multiple 13 by two which should give you 26 subtract 26 from 68 which them gives you 42.

then divide 42 by 2 which gives you 21 for your final answer.

Answer:

n = 36

Step-by-step explanation:

1. Let's find the value of n for the expression: (9^3)^12 =9^n

(9^3)^12 =9^n

(9³) ¹² = 9 ⁿ

Let's remember that the power rule tells us that to raise a power to a power, we multiply the exponents. Here you see that 9³ is raised to the 12th power is equal to 36 (3 * 12)

9 ³⁶ = 9 ⁿ

n = 36