Solve equation for a=

Answer:

[tex]log_n(m)= \frac{4}{3}[/tex]

Step-by-step explanation:

N^4/3=m

[tex]n^{4/3}=m[/tex]

We need to write the equation in logarithmic form

we take log on both sides

[tex]log(n^{4/3})=log(m)[/tex]

We apply log property to remove the exponent 4/3

As per log property we can move exponent before log

log(a^m) = m log (a)

So our equation becomes

[tex]\frac{4}{3}log(n)=log(m)[/tex]

Now we divide both sides by log(n)

[tex]\frac{4}{3} =\frac{log(m)}{log(n)}[/tex]

Now we apply change of base formula

log(a)/ log(b)= log_b(a)

[tex]\frac{4}{3} =log_n(m)[/tex]

So log form is

[tex]log_n(m)= \frac{4}{3}[/tex]

To convert [tex]N^{4/3}[/tex] = m to logarithmic form, identify the base (N), the exponent (4/3), and the result (m). The logarithmic form is [tex]log_N(m)[/tex] = 4/3.

To convert the given equation [tex]N^{4/3}[/tex] = m into logarithmic form, we'll follow these steps:

The general logarithmic form of the equation aᵇ = c is [tex]log_a(c)[/tex] = b.

Applying this to our equation:

Hence, the logarithmic form of the equation [tex]N^{4/3}[/tex] = m is:

Answer:

x + y = 1

Step-by-step explanation:

If the two equations are the same, then it can be shown by this:

6x + 8 = -4x - 2

We need to isolate the x values, so we need to move the -4x over to the other side making it a +4x:

6x + 4x + 8 = -2

Next, move the +8 over to the other side making it a -8:

6x + 4x = -2 - 8

10x = -10

x = -1

So now we can plug this value into the first equation:

6(-1) + 8 = y

-6 + 8 = y

y = 2

x + y = -1 + 2 = 1

So x + y = 1

Answer: 13

Step-by-step explanation:

f(x) = 4x + 1

f(3) = 4(3) + 1

     = 12 + 1

     = 13

Answer:

Multiply each equation by the coefficient of y in the other one.  

Step-by-step explanation:

(1)  6x + 5y = 2

(2) 4x + 2y = 8

Multiply each equation by the coefficient of y in the other one.

Multiply (1) by 2 and (2) by 5.

(3)   12x + 10y =   4

(4) 20 x + 10y = 40     Subtract (3) from (2)

                8x = 36      Solve for x

                  x = 9/2

Answer:

Subtract 5 times the first equation from 2 times the second equation

Step-by-step explanation:

2(6x + 5y = 2)

5(4x + 2y = 8)

12x + 10y = 4

20x + 10y = 40

Subtracting the second equation from first gives:

−8x = −36

x =  

−36

−8

x =  

9

2

Answer:

f(-3) = 27

Step-by-step explanation:

f(x) = (-x)^3

We want the value when x =-3

Substitute this in

f(-3) = (--3)^3

f(-3) = 3^3

f(-3) = 27

Answer:

RM  ≈ 6.08 ( to 2 dec. places )

Step-by-step explanation:

to calculate the distance use the distance formula

• d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = R(- 2, 3) and (x₂, y₂ ) = M(4, 2)

d = [tex]\sqrt{(4+2)^2+(2-3)^2}[/tex] = [tex]\sqrt{36+1}[/tex] = [tex]\sqrt{37}[/tex] ≈ 6.08

Answer:

[tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using [tex]\pi d[/tex] or [tex]2\pi r[/tex].

We write r: [tex]\pi d[/tex]  or r:[tex]2\pi r[/tex].

We can also write in fraction form:

[tex]\frac{r}{\pi d}[/tex] or [tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]

You can use the fact that ratio of one quantity to other is fraction involving one quantity over another quantity.

The specified ratio is given as

[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]

The ratio of a to b is  [tex]\dfrac{a}{b}[/tex]

It is sometimes written as [tex]a:b[/tex]

We can remove common factors of a and b to simplify them.

Thus, if

[tex]a = c \times x\\b = d \times x\\[/tex]
then

[tex]\dfrac{a}{b} = \dfrac{c \times x}{d \times x} = \dfrac{c}{d}[/tex]

The area of a circle with radius r units is

[tex]Area = \pi r^2[/tex]

The circumference of a circle with radius r units is

[tex]Circumference = 2 \pi r[/tex]

( Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex] )

Their ratio is

[tex]\dfrac{Area_r}{Circumference_r} = \dfrac{\pi r^2}{2\pi r} = \dfrac{r}{2}[/tex]

Thus,

The specified ratio is given as

[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]

Learn more about ratio here:

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Answer:

[tex]y=39\degree[/tex]

Step-by-step explanation:

The given triangle is a right angle triangle .

The known sides of the triangle that is opposite to angle y is 8 units while the side adjacent is 10 units.

The value of y can be calculated using the tangent ratio.

[tex] \tan(y)=\frac{8}{10}[/tex]

We solve for y to get,

[tex]y=arctan(\frac{4}{5})[/tex]

We evaluate to obtain,

[tex]y=38.66[/tex]

[tex]y=39\degree[/tex] to the nearest degree

Because AC lies opposite the angle of the smaller measure than the angle opposite FH. The sides at these angles have the same length.

Answer:

39 yards

hope it helps

Step-by-step explanation:

52 ÷ 4 = 13 per quarter of an hour  

we are gonna divide by four because there are 4 quarters in a hour and in 3 quarters there is 45 minutes  

13 x 3 = 39

The seamstress can sew 39 yards of material in 45 minutes.

To find out how many yards the seamstress can sew in 45 minutes, we need to convert 45 minutes into hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours.

Next, we can use the given information that the seamstress can sew 52 yards of material in one hour. Multiply the yards per hour by the fraction of an hour to find out how many yards can be sewn in 45 minutes:

Yards in 45 minutes = 52 yards/hour × 0.75 hours = 39 yards.

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Final answer:

(m-p)(x) represents the subtraction of function p(x) from m(x). Assuming p(x) is -4x + 2, (m-p)(x) simplifies to 7x - 4.

Explanation:

To calculate (m-p)(x), we need to subtract the function p(x) from the function m(x).

Given m(x) = 3x - 2 and noting there seems to be an error in p(x), as it should likely be a function of x, let's assume the student meant p(x) = -4x + 2 based on the pattern of the provided information.

The subtraction of these two functions is performed as follows:

m(x) - p(x) = (3x - 2) - (-4x + 2)

Simplify by distributing the negative sign through the second polynomial:

(3x - 2) + 4x - 2 = 3x + 4x - 2 - 2

Combine like terms:

7x - 4

So, (m-p)(x) = 7x - 4.

Answer:

B.$941.11

Hope this helped

Step-by-step explanation:

Answer:

The first year Sam invested $2,000. The third year sally invested $1,900.

Step-by-step explanation:

Let $x be the amount of money Sam invested the first year. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year, then the second year he invested

[tex]\$\left(\dfrac{5}{2}x-2,000\right).[/tex]

The third year, he invested $1,000 more than 1/5 of the amount he invested the first year, then the third year he invested

[tex]\$\left(\dfrac{1}{5}x+1,000\right).[/tex]

During three years Sam invested

[tex]\$\left(x+\dfrac{5}{2}x-2,000+\dfrac{1}{5}x+1,000\right)=\$\left(\dfrac{37}{10}x-1,000\right).[/tex]

The first year, Sally invested $1,000 less than 3/2 times the amount Sam invested the first year, then the first year she invested

[tex]\$\left(\dfrac{3}{2}x-1,000\right).[/tex]

The second year, she invested $1,500 less than 2 times the amount Sam invested the first year, then the second year she invested

[tex]\$(2x-1,500).[/tex]

The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year, then the third year she invested

[tex]\$\left(\dfrac{1}{4}x+1,400\right).[/tex]

During three years Sally invested

[tex]\$\left(\dfrac{3}{2}x-1,000+2x-1,500+\dfrac{1}{4}x+1,400\right)=\$\left(\dfrac{15}{4}x-1,100\right).[/tex]

If Sam and Sally invested the same total amount at the end of three years, then

[tex]\dfrac{37}{10}x-1,000=\dfrac{15}{4}x-1,100,\\ \\\dfrac{37}{10}x-\dfrac{15}{4}x=1,000-1,100,\\ \\-\dfrac{1}{20}x=-100,\\ \\x=\$2,000.[/tex]

Thus,

[tex]\$\left(\dfrac{1}{4}\cdot 2,000+1,400\right)=\$1,900.[/tex]

Answer:

A jagged curve

Step-by-step explanation:

Your always going to burn calories but the rate will always change and how many based on what you do will always change so it is never a constant slope.

Answer:

a jagged curve

Step-by-step explanation:

The number of calories you burn varies throughout the day, increasing and decreasing. A jagged curve represents increases and decreases over time.

Answer:

x=2, y=2

(2,2)

Step-by-step explanation:

To solve by elimination, we need to have on variable an its coefficient be the opposite of the other

I will multiply the second equation by 2 to make 2x  become 4x to eliminate the x variable

2(2x+4y) = 12*2

4x+8y = 24

Now add the first equation with the modified second equation

-4x - 2y = -12

4x   +8y =24

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

       6y   = 12

Divide each side by 6

6y/6 = 12/6

y =2

Now we need to find x

2x+4y = 12

Substitute in y=2

2*x + 4*2 = 12

2x+8 = 12

Subtract 8 from each side

2x +8-8 = 12-8

2x=4

Divide each side by 2

2x/2 =4/2

x=2

We must first open the parenthesis. We get 15*7+15y, or 105+15y. We can now add 12 to 105 which would be 117. Now we have -4-5y+117+15y. With this we can move the -4 to 117 which is 113 and the -5y to 15y which is 10y. So we got 113+10y as our answer.

Hope this helps. <3

Answer:

a(5) = 7

Step-by-step explanation:

Look at 5 on the n line, the horizontal line look up to the dot on that line.  Whats it value on the vertical line a(n)?  7 so a(5) = 7

Solution:

As given , g(x)= f(x) + k --------(1)

As also given : f(x) = [tex]\frac{1}{3}[/tex](x+2)

g(x) =  [tex]\frac{1}{3}[/tex](x+5)

Putting the value of f(x) and g(x) in equation (1).

→ [tex]\frac{1}{3}[/tex](x+5) = [tex]\frac{1}{3}[/tex](x+2) + k

→ [tex]\frac{1}{3}[x+5-x-2][/tex]= k

→ k = [tex]\frac{1}{3} \times 3=1[/tex]

So , the value of k is 1.

Answer:

K=5

Step-by-step explanation:

there you go

Answer:

52.94  miles per unit

Step-by-step explanation:

The unit rate is found by dividing miles per time

90 miles /1.7 unit

52.94117647  miles per unit

Answer:25%

Step-by-step explanation:

(10 x 100) - 800= 200

200/800 x 100

percantage profit= 25%

Answer:

80%

Step-by-step explanation:

800 ÷ 100 = 8$ → purchased each

8$ to 10$ = 80%

If PA = PB ,then P is located on perpendicular bisector of AB.

Look at the picture.

The solution to the basic vector problems are given as,
1)  (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

Here,
1)
initial point (5,3) and a terminal point (10,-8),
Vector = 10i -8j - 5i - 3j
Vector = 5i - 11j or [5, -11]

2)
Vector v with an initial point of (0,0) and a terminal point of (50, 120), is not equal to vector u with an initial point of (50, 120) and a terminal point of (0,0).

Thus, the solution to the basic vector problems are given as,
1)  (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.

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Final answer:

To find the component form for vector v, subtract the initial point from the terminal point. The answer is option C. The vectors in the second question have different initial points, so they are not equal.

Explanation:

To find the component form for vector v, we need to subtract the initial point from the terminal point. Subtracting the x-coordinates and y-coordinates separately, we get (10 - 5, -8 - 3), which simplifies to (5, -11). Therefore, the component form for vector v is option C, (5, -11).

For the second question, the vectors have the same initial points but different terminal points, so they cannot be equal. Therefore, the correct choice is option B, No, the two vectors have different initial points.

Answer:

The two angles are each 31 degrees.

Step-by-step explanation:

Find x

3x + 10

5x - 4

By setting 3x+10 equal to 5x-4, we find x=7. Substituting this value back into the expressions for both angles 1 and 2, we find that both angles measure 31 degrees, confirming that our solution is correct.

The question asks you to solve for the degree measure of both angles 1 and 2, which are represented by the expressions (3x+10)° and (5x-4)° respectively. Because these angles are vertical, we know that they are congruent, or equal in measure.

Therefore, we can form an equation by setting the two expressions equal to each other and then solving for x:

(3x+10) = (5x-4)

Subtracting 3x from both sides yields:

10 = 2x - 4

Then, adding 4 to both sides, we get 14 = 2x. Dividing both sides by 2, we find x = 7.

To check our work, we substitute x = 7 into the original equations for both angle 1 and angle 2:

Angle 1: 3(7) + 10 = 31°

Angle 2: 5(7) - 4 = 31°

As you can see, the degree measures are the same, which verifies that we solved for the variable correctly.

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Answer:

5/8=0.625

Step-by-step explanation:

Answer:

x=32, y=17

Step-by-step explanation:

Difference between two numbers is 15:

x-y=15

Greater number (x) is two less than twice the lesser number:

x=2y-2

-----

x-y=15,

x=2y-2.

x-y-x=15-2y+2

-y=15-2y+2

y=15+2

y=17

-----

x-y=15

x-17=15

x=17+15

x=32

To solve the word problem, we transcribe the information into algebraic equations. We then isolate one variable to solve for it first, and then substitute that variable's value into the second equation. The solution we find is that the two numbers are 17 and 32.

To solve the problem, we must translate the word problem into algebraic equations. We're trying to find two numbers based on the information that's given to us: their difference is 15, and the larger number is two less than twice the smaller number.

First, let's define the numbers as follows: x = smaller number and y = larger number. Now we can set up our two equations based on the problem:

Now we can substitute equation (2) into equation (1) which gives us: 2x -2 - x = 15. Simplify the equation, we get x = 17 and substitute x = 17 into equation (2), we get y = 32.

So, the two numbers are 17 and 32.

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11/20 + x = 9/10

x = 9/10 - 11/20

x = 18/20 - 11/20

x = 7/20

Answer:

x = 7/20

Step-by-step explanation:

11/20 +x= 9/10

Subtract 11/20 from each side

11/20-11/20 +x= 9/10-11/20

x = 9/10-11/20

We need a common denominator of 20

x = 9/10 *2/2 - 11/20

x =18/20 -11/20

x = 7/20

Answer:

12.5

Step-by-step explanation:

first you do the one in the 40-15 then you add 50 the you divide by 6

Answer: [tex]54\frac{1}{6}[/tex]

Step-by-step explanation:

Order of Operations (PEMDAS) states that we need to do the parenthesis first then division and then addition.

                    50 + (40 - 15) ÷ 6

parenthesis: 50 +     25      ÷ 6

division:        50 +           [tex]4\frac{1}{6}[/tex]

addition:           [tex]54\frac{1}{6}[/tex]

Answer:

the answer is $151.56

Step-by-step explanation:

our formula of interest is I = PxRxT

P (principal) = 421

R (rate) = 4%  (we have to turn it into a decimal which is 0.04)

T (time) = 9 years

so :

I = 421 x 0.04 x 9

I = 151.56

The total interest paid will be $151.56.

To find out how much interest you will pay on a loan of $421 over nine years at an annual interest rate of 4%, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Where the Principal amount is $421, the Rate is 4% (or 0.04 when converted to a decimal), and the Time is 9 years.