Express 16=2x as a logarithmic equation

Answer:

A

Step-by-step explanation:

The arc length is calculated as

arc = circumference × fraction of circle

     = 2π × 6 × [tex]\frac{135}{360}[/tex]

     = 12π × [tex]\frac{3}{8}[/tex]

     = [tex]\frac{36\pi }{8}[/tex] ≈ 14.1 in

Answer

14.1 in

Step-by-step explanation:

Length of the arc formula = circumference of the circle * central angle / 360

circumference of the circle formula = [tex]2\pi r[/tex]

where r is the radius of the circle

Radius = 6 in

central angle = 135 degrees

Length of the arc = [tex]2 \pi * radius* \frac{angle}{360}[/tex]

=[tex]2\pi*6* \frac{135}{360}[/tex]

= 14.137= 14.1 in

The answers are:

3. Addition property of equality

4. [tex]6x-7+7=12+7[/tex] - Simplification

7. [tex]x=\frac{19}{6}[/tex]

To solve the problem, we need to start with the result of the second step:

[tex]6x-7=12[/tex]

So,

For the step 3:

Then, for the 3rd step, we have to apply the addition property of equality.

The addition property of equality states that if we add a term to one side of the equality, we need to add it to the other side of the equality, in order to not alterate the equality.

Then, applying the property, we have:

[tex]6x-7=12[/tex]

Adding 7 to both sides, we have:

[tex]6x-7+7=12+7[/tex]

For the step 4:

Now, for the 4th step, we have to simplify the expression:

[tex]6x-7+7=12+7[/tex]

Then, simplifying, we have:

[tex]6x=19[/tex]

For the step 7:

Simplificating, we divide each side of the equality by 6:

[tex]\frac{6x}{6}=\frac{19}{6} \\\\x=\frac{19}{6}[/tex]

Have a nice day!

Answer: They cost the same amount.

Step-by-step explanation:

35(0.20)=7

35-7=28

40(0.30)=12

40-12=28

28=28

Answer:

median:36.5

mean:37

Step-by-step explanation:

to find medain put all of the numbers in order. then find the center number

for the mean add all of the numbers together ad divide it by the amount of data points there are

Answer:

median:                                  36.5

mean:                                       37

Step-by-step explanation:

Answer:

the mean is 73.4

Step-by-step explanation:

you add all the  numbers which equals to 367

then divide by 5

Answer: D

If there are 713 slices, and each pizza is divided into pieces, then you would divide.

713÷8=89.125. Round up and you get:

90.

Hope this helps and have a great day!!!

For this case we must indicate the number of whole pizzas needed for the company. For this we propose an equation.

Let "x" be the variable that represents the number of whole pizzas, then:

[tex]8x = 713[/tex]

We divide between 8 on both sides of the equation:

[tex]x = \frac {713} {8}\\x = 89,125[/tex]

90 pizzas are needed

ANswer:

Option D

Answer:

Vertex(3,-4) and y-int (0,5)

Zeroes are (1,0) and (5,0)

Step-by-step explanation:

Answer:

The solutions of the given graph are 1 and 5. The vertex of the graph is (3,-4) and the y-intercept of the graph is 5.

Step-by-step explanation:

From the given graph it is clear that it intersect the x-axis at (1,0) and (5,0).

Therefore the solutions of the given graph are 1 and 5.

Vertex of the parabola is the extreme point of the graph.

From the given graph it is clear that the the turning point or the extreme point of the graph is (3,-4).

Therefore the vertex of the graph is (3,-4).

The given graph intersect the y-axis at (0,5).

Therefore the y-intercept of the graph is 5.

Answer:

The surface area is approx. 1017.9 in^2.

Step-by-step explanation:

Total surface area of cone = πrl + πr^2. Since the radius is 12 in. and the slant height is 15 in, substitute 12 for r and 15 for l.

A = π(12)(15) + π(12)^2

    = 180π + 144π

    = 324π in^2

    ≈ 1017.9 in^2

Hope this helps!

Answer:

14 are red

Step-by-step explanation:

Let's identify the 2 types of transactions Juan machines do:

w : changes 1 white token into 4 red tokens (gain: 3 tokens overall)

r : changes 1 red token into 3 white tokens (gain: 2 tokens overall)

We know that Juan does 11 trades, so we can say:

w + r = 11

Overall, Juan started with 4 tokens and ends with 31... so, gain of 27 tokens.

We can model this as:

3w + 2r = 27

(3w because each w transaction, he gains 3 tokens, 2r because every r transaction, he gains 2 tokens).

From first equation we get r = 11 - w, which we place in the second equation:

3w + 2 (11 - w) = 27

3w + 22 - 2w = 27

w = 5, so r = 6 (from first equation).

Now, we know Juan did 5 w transactions and 6 r transactions.  But how many token of each color does he have?

Start: 4W (4 White chips)

He does 4 w transactions, he now has 16R tokens

He does 6 r transactions, he now has 10 (16-6) R tokens, plus 18 W tokens

He does another w transaction, he now has 14 R (10 + 4), plus 17 W(18-1) tokens

He did 11 transactions, and he has 31 tokens at the end, out of which 14 are red.

Answer:

0.125 m

Step-by-step explanation:

Answer:

0.125 meters

Step-by-step explanation:

There are 100 cm in a meter. 12.5/100= 0.125

Answer: 3,600,000 cm³

Step-by-step explanation: First you have to convert all the units into centimeters,

2 meters = 200 centimeters

1.5 meters = 150 centimeters

To find the volume of a rectangular prism you multiply all the sides.

120 * 200 * 150 = 3,600,000

The answer is 3,600,000 cubic centimeters.

The volume of a rectangular prism with the given dimensions is 3.6 cubic meters.

The dimensions of a rectangular prism are 120 centimetres(1.2 meters) by 2 meters by 1.5 meters.

The formula to find the volume of a rectangular prism is l×b×h.

Now, volume=1.2×2×1.5=3.6 cubic meters.

Therefore, the volume of a rectangular prism is 3.6 cubic meters.

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Answer:

57°

Step-by-step explanation:

ALL angles in a triangle add up to 180°

SO, if we know the sum of two angles which is 123° (why: 33+90=123), all we have to do is subtract this number from 180 to get the measure of the 3rd angle. Which in this case is 57°

The measure of angle B will be 57° for the given triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right angle triangle, equilateral triangle, and much more.

The sum of all three interior angles of any triangle is 180°.

So,

A + B + C = 180°

Given,

A = 33°  and C = 90°

33°  + B + 90°  = 180°

B = 180 - (90 + 33)

B = 180°  - 123°  

B = 57°

Hence, The measure of angle B will be 57° for the given triangle.

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Answer:

The equation is        y = - 1/2 x+7

Step-by-step explanation:

2 x  + 4y = 6  

4y = -2 x +6  

Divide both sides  by 4  

y = - 1/2 x + 3/2  

y=mx+b  

slope m = - 1/2  

The slope of a line parallel to another  line will be the same  

The slope of the required line will be - 1/2  

m= - 1/2 ,point ( 6 , 4 )

Plugging the values of m  and  the point in  

y=mx+b  

4 = -3 + b  

b= 7  

m= - 1/2  

Plug values   y = mx +b  

y = - 1/2 x+7

Answer:

jamie has 24 and kristen is 12

Step-by-step explanation:

jamie is twice  kristan which is 12+12

then 12 puls 24 is 36

For this case we have to:

Let x be the variable that represents the amount of money Jamie has.

Let y the variable that represents the amount of money that Kristen has

We have to:

[tex]x = 2y\\x + y = 36[/tex]

We substitute the first equation in the second:

[tex]2y + y = 36\\3y = 36\\y = \frac {36} {3}\\y = 12[/tex]

Looking for the value of x:

[tex]x = 2y\\x = 2 (12)\\x = 24[/tex]

Answer:

So, Jaime has $ 24 and Kristen has $ 12.

Answer:

C

Step-by-step explanation:

The oranges cost $4 per 2 lbs which is 4/2=$2 per lb. Option C has peaches at $6 for 3 lbs which is 6/3 =$2 per lb.

Answer:

C. Peaches at $6.00 Dollars for 3 pounds

Step-by-step explanation:

find the oranges $ per pound.

4 divided by 2 = 2

match it to each answer (example bellow, correct one)

6 divided by 3 = 2

Oranges per pound = $2.00

Peache per pound = $2.00

C.)

Hope this helped!

Lunar Rose Moon.

Answer:

option B

Step-by-step explanation:

Given in the question an equation y = (x+3)² + (x+4)²

Step 1

Expand this equation

y = (x+3)² + (x+4)²

y = (x²+9+6x) + (x²+16+8x)

y = 2x² + 14x + 25

Step 2

Find the minimum point of the parabola equation,  y = 2x² + 14x + 25

y = ax² + bx +c

x = -b/2a

  = -14/2(2)

  = -14/4

 = -7/2

Step 3

Find the vertex point by plugging value of x in the equation

y = 2(-7/2)² + 14(-7/2) + 25

  = 49/2 - 49 + 25

  = 1/2

vertex (h,k)

vertex (-7/2 , 1/2)

Step 4

vertex form

y = a(x - h)²+ k

y = 2(x + 7/2)² + 1/2

The would both be correct in it's own way depending on how the teacher is teaching.

Both Joel and Sara are correct. Their expressions represent the combined earnings accurately, considering hourly wage and bonus.

To determine who is correct, let's first break down the earnings for each person:

1. Joel:

  - Hourly wage: $9.75

  - Bonus: $18

  Joel's total earnings can be calculated using the formula provided: [tex]\(9.75j + 18\)[/tex], where [tex]\(j\)[/tex] represents the number of hours Joel worked.

2. Sara:

  - Hourly wage: $9.75

  Sara's total earnings can be calculated using the formula provided: [tex]\(9.75(j + S)\)[/tex], where [tex]\(S\)[/tex] represents the number of hours Sara worked.

Now, let's expand both expressions and see which one correctly represents the combined earnings of Joel and Sara.

Joel's expression: [tex]\(9.75j + 18 + 9.75S\)[/tex]

Sara's expression: [tex]\(9.75j + 9.75S + 18\)[/tex]

Comparing the two expressions, we see that both expressions have the same terms: [tex]\(9.75j\)[/tex], [tex]\(9.75S\)[/tex], and [tex]\(18\)[/tex]. The order of terms is different, but mathematically it doesn't matter since addition is commutative.

So, both Joel and Sara are correct. They just wrote their expressions in a different order, but the mathematical result is the same. They both correctly accounted for their hourly wage and the bonus.

Hi, hope this helps you. Have a good day. :)

Answer:

A = $5,417.42 (balance of the account)

I = $2,617.42

Answer:

The balance in the account after 12 years is $5417.42

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

 A = P e^rt

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the interest rate

• t = the time the money is invested for

- The formula gives you the future value of an investment,

  which is compound continuous interest plus the

  principal.

- If you want to calculate the compound interest only, you need

 to deduct the principal from the result.

- So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

∵ P = $ 2800

∵ r = 5.5/100 = 0.055

∵ t = 12

∴ A = 2800 e^(0.055 × 12) = $5417.42

* The balance in the account after 12 years is $5417.42

So, you want to calculate the interest on $300 at 5% interest per year after 7 years.

The formula we'll use for this problem is:

Where:

To find the simple interest, we multiply 300 x 0.05 x 7 to get that:

                                         The interest is: $105.00

Answer:

The correct answer is last option

$105.00

Step-by-step explanation:

Points to remember

Simple interest

I = PNR/100

Where P - Principle amount

N - Number of years and

R - Rate of interest

To find the simple interest

Here P = $300, R = 5% and N = 7 years

I = PNR/100

 = (300 * 5 * 7)/100

 = 3 * 5 * 7

 = 105

Therefore simple interest after 7 years = $105

The correct answer is last option

Answer:

3

Step-by-step explanation:

Wire is 4 1/2 feet, or 4.5 feet.

Each smaller wire needs to be 1 1/4 feet, or 1.25 feet.

How many whole 1.25 feet wire can we have from total of 4.5 feet wire?

Let's divide:

\[tex]\frac{4.5}{1.25}=3.6[/tex]

thus we can have 3 whole "1.25 feet long" wire and fractional amount.

Hence, maximum number of smaller pieces is 3

Answer:

it is the 2nd graph

Step-by-step explanation:

The graph of the linear equation is a right-angle triangle whose height is 2000 units and base is 200 units.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound.

To summarize the situation, the farmer writes the inequality

[tex]\rm 2 y + 20 x \leq 4,000\\\\y \leq 2000 - 10x[/tex]

where y be the number of pounds of fertilizer and x be the number of pounds of seeds.

Then the graph is shown below.

More about the linear system link is given below.

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Answer:

% decrease in the cost= 6114/23782⋅100=25.71%

Step-by-step explanation:

The decrease in the cost =$23782−$17668=$6114

Hence, % decrease in the cost=6114/23782⋅100=25.71%

the decrease is 23782 - 17668 = 6114.

if we take 23782 to be the 100%, what is 6114 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 23782&100\\ 6114&x \end{array}\implies \cfrac{23782}{6114}=\cfrac{100}{x}\implies 23782x=611400 \\\\\\ x=\cfrac{611400}{23782}\implies x\approx 25.71[/tex]

Answer:

1. LA = 92 sq. m.,  SA = 132 sq. m.

2. LA = 460 sq. in.,  SA = 700 sq. in.

3. LA = 118 sq. in.,  SA = 168 in. sq.

4. LA = 468 sq. cm.,  SA = 828 sq. cm.

Step-by-step explanation:

The lateral area is the area of the non-base faces. The surface area is the area of all the faces (so lateral area + area of base).

1.

Lateral area:

There are 2 same triangles each with height and base of 3 and 4, respectively. So

Area of triangle = 1/2 * base * height = 1/2 * 4 * 3 = 6

Since there are 2, so 6 * 2 = 12

Now, the slant height is gotten by using pythagorean theorem on the triangular face.

[tex]4^2+3^2=SlantHeight^2\\16+9=SlantHeight^2\\25=SlantHeight^2\\SlantHeight=5[/tex]

If you look at the side facing away, it is a rectangle with length 10 and width 5, so area of rectangle is length * width = 10 * 5  = 50

The side facing towards us is also a rectangle with dimensions 3 and 10. So area is 3 * 10 = 30

The lateral area is 30 + 12 + 50 = 92

Surface Area:

This is the lateral area we got before (92) + the area of the base.

The base is a rectangle with dimensions 4 and 10. So area = 4 * 10 = 40

The surface area is 92 + 40 = 132

2.

Lateral area:

all the faces are rectangles.

The dimensions of two side faces are 10 and 8. So area would be 2 * (10 * 8) = 2 * 80 = 160

The dimensions of back side and front side is 15 and 10. So area would be 2 * (15 * 10) = 2 * 150 = 300

The lateral area would be 160 + 300 = 460

Surface area:

the surface area is the lateral area (580) + the area of the bases (which is also a rectangle). The dimensions of the bottom and top are  15 and 8. So area of bottom and top  is  2(15 * 8) = 240

Thus, surface area = 460 + 240 = 700

3.

Lateral Area:

There are two rectangles (left and right) with dimensions 8 x 5 and 6 x 5. So area would be 8 * 5 = 40 and 6 * 5 = 30. Area = 40 + 30 = 70

There are two triangles (back and front) with base of 6 and height of 8. The area of both are:

(1/2 * 6 * 8 ) * 2 = 48

Lateral area is 70 + 48 = 118

Surface area:

The surface are would be lateral area (118) PLUS the base, which is a rectangle with dimensions 5 and 10. So area = 5 * 10 = 50.

Total surface area = 118 + 50 = 168

4.

lateral area:

there are 2 rectangles (left and right) with dimensions 10 x 12, and 9 x 12. So the total area would be:

(10*12) + (9*12) = 228

The front and back are trapezoids. The area of trapezoid is 1/2 (base1 + base2) * height.

The height is 8 and both the bases are 10 and 20. Plugging it into the formula, we get are of 2 of the trapezoids to be:

2 * (1/2(base1+base2)*height)

2 * (1/2(10+20)*8)

= 240

The lateral area = 228 + 240 = 468

surface area:

it will be 468 (lateral area) PLUS the area of the bases. The bottom base is a rectangle with dimensions 20 and 12. So the area of the base is 20 * 12 = 240

The top is a rectangle with dimensions 12 and 10. So area = 12 * 10 = 120

Surface area = 468 + 240 + 120  = 828

Answer:

[tex\large\boxed{\log2-\log4=\log\frac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\==========================\\\\\log2-\log4=\log\dfrac{2}{4}=\log\dfrac{1}{2}[/tex]

Answer:b

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

If you meant you want to find U,

1) Divide both side by 2. -> U = 4/9 divided by 2

2) You get U = 4/18, which you can further simplify by dividing 2 on top and bottom to get 2/9

Answer:

125 in³

Step-by-step explanation:

The net will form a cube.

Length of the cube = 5 in.

We will apply the formula for volume, volume = length³,  to find the volume of the cube.

Volume = 5 x 5 x 5 = 125 in³

Answer:

Step-by-step explanation:

The formula of an area of a circle:

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

r - radius

The formula of a circumference of a circle:

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

We have:

[tex]C=3\pi[/tex]

Substitute:

[tex]2\pi r=3\pi[/tex]            divide both sides by 2π

[tex]r=1.5[/tex]

Substitute:

[tex]A=\pi(1.5)^2=2.25\pi[/tex]

This answer is correct, I double checked it and got it right on the assignment in OW. :)

Answer:

it is 48 hope this helps

Step-by-step explanation:

The solution of expression is,

⇒ 48

We have to given that,

An expression to solve,

⇒ 12 × 4

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Hence, We get;

⇒ 12 × 4

⇒ 48

Thus, The solution of expression is,

⇒ 48

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20%

My equation:

15*100=1500

1500/75=20

The answer would be 20% off hope this helped!