what is the missing length.

Answer:

121

Step-by-step explanation:

2^3x - 4 = (2^x )^3 - 4 = 125 - 4 = 121

[tex]\implies\tt 2^x = 5 [/tex]

[tex]\implies\tt \Big( 2^x \Big)^3 - 4 [/tex]

[tex]\implies\tt 125 - 4 [/tex]

[tex]\huge\implies\tt 121 [/tex]

Answer:

$ 3051

Step-by-step explanation:

Original cost = $ 1000

Marked up Price = Original cost + 170% of 1000

                            = 1000 + 1.7 * 1000

                            = 1000 + 1700

                            = $ 2700

Sales tax = 13% of 2700

               = 0.13 * 2700

               = 351

Total cost paid by Bernie = 2700 + 351 = $ 3051

Step-by-step explanation:

Let the number to be found be x

68 is what percent of 80 is written as

[tex] \frac{x}{100} \times 80 = 68[/tex]

Multiply both sides by 100

We have

80x = 6800

Divide both sides by 80

we have the answer as

x = 85

Let the number be x

88.83 is 423% of what is written as

[tex] \frac{423}{100} x = 88.83[/tex]

Multiply through by 100

We have

423x = 8883

Divide both sides by 423

We have the answer as

x = 21

Let the number be x

36.8% of what number is 28.52 is written as

[tex] \frac{36.8}{100} x = 28.52[/tex]

Multiply through 100

We have

36.8x = 2852

Divide both sides by 36.8

We have the answer as

x = 77.5

What number is 95% of 40 is written as

[tex] \frac{95}{100} \times 40[/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

What's missing from the original condition.

1000

1001

1002

=====

3003

So the answer is y - 3003

Answer:

6

Step-by-step explanation:

12/2=6/1=6

Answer:

6

Step-by-step explanation:

Answer:

[tex]x = 10[/tex]. In other words, there number of girls is [tex]10[/tex].

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

[tex]\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}[/tex].

Rewrite to obtain:

[tex]\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}[/tex].

For this question:

[tex]\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}[/tex].

[tex]\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}[/tex].

On the other hand, there are [tex](15 + x)[/tex] boys and girls in total. Using the formula for average:

[tex]\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}[/tex].

From the question, this average should be equal to [tex]123[/tex]. In other words:

[tex]\displaystyle \frac{1875 + 120\, x}{15 + x} = 123[/tex].

Solve this equation for [tex]x[/tex] to obtain:

[tex]1875 + 120\, x= 123\, (15 + x)[/tex].

[tex](123 - 120)\, x = 1875 - 123 \times 15[/tex].

[tex]x = 10[/tex].

In other words, the number of girls here is [tex]10[/tex].

Answer:

7

Step-by-step explanation:

5×0.4 = 2

2 + 5 = 7

The number a would be 7 which is 40% more than five more than a number a.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given the number that is 40% more than five more than a number a.

We need to find the unknown number a.

So, 40 % = 0.4

Let find the first part that is; "the number that is 40% more than five"

5 × 0.4 = 2

Now, five more than a number a.

2 + 5 = a

a = 7

Therefore, the number a would be 7 which is 40% more than five more than a number a.

Learn more about the unitary method;

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Answer:

18 square units.

Step-by-step explanation:

Area of the triangle = ½*AB*CD

First of all, find the length of AB and CD using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

A(-6, 2) => (x1, y1)

B(3, 2) => (x2, y2)

[tex] AB = \sqrt{(3 -(-6))^2 + (2 - 2)^2} [/tex]

[tex] AB = \sqrt{(9)^2 + (0)^2} = \sqrt{81} = 9 [/tex]

[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

C(-2, 6) => (x1, y1)

D(-2, 2) => (x2, y2)

[tex] CD = \sqrt{(-2 -(-2))^2 + (2 - 6)^2} [/tex]

[tex] CD = \sqrt{(0)^2 + (-4)^2} = \sqrt{16} = 4 [/tex]

AB = 9

CD = 4

Area of rectangle = ½*AB*CD = ½*9*4 = 9*2 = 18 square units.

Answer:

18

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

13x-7+7x-13=180

Combine like terms

20x-20 = 180

Add 20 to each side

20x -20+20 = 180+20

20x=200

Divide by 20

20x/20 = 200/20

x = 10

Answer:x=10

Step-by-step explanation:

1.add the number

2.add the same term to bothe sides of the equation

3.simplify

4.divide bothe side of the equation by the same term

5.simplify

Answer:

Option R

Step-by-step explanation:

The point S is the end point of ray.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

According to the given information,

A ray's endpoint is a single point that denotes the conclusion of a line segment. In this instance, only one of the three lines that extend from point S contains a ray's terminus.

We must comprehend a ray's qualities in order to establish which location is the endpoint of a ray.

A ray originates at a single place and travels in one direction indefinitely. The beginning of the line segment is the endpoint of a ray.

We can see from the provided lines that the vertical line runs from point S via point R. Since it doesn't go on forever in one direction, this is not a ray example.

Similar to the vertical line,

The horizontal line also extends from point S through point T,

But it does not go on forever.

The third line is a ray because it is infinitely long in one direction and extends right and up from point S via point U.

Therefore, point S, the beginning of the line, is the endpoint of this ray.

Learn more about the equation of line visit:

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Answer: 4 or [tex]\sqrt{4 * 4}[/tex]

To find the square root of a number, remember that there will be two factors that are the same that will give you the product.

Lets start from 1:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

As you can see, 4 x 4 is 16. To make sure I'm correct, remember that a square roots consists two identical factors.

4 and 4 are the same numbers.

Therefore, [tex]\sqrt{16}[/tex] = 4

It can also be written as [tex]\sqrt{4 * 4}[/tex]

Answer:

the answer is 4

Step-by-step explanation:

I use a calulator but if you dont have one then the way to do square roots is find a number say 4 and put it to the 2 power and it equaks 16 (4^2)=16. I cant really explain much more

Answer:

4.625

Step-by-step explanation:

5/8 = 0.625

To find 5/8, simply divide it.

So 4 and 5/8

= 4.625

Answer:

the answer is /36

Step-by-step explanation:

3 goes into 36

4 goes into 36

9 goes into 36

Answer:

See below.

Step-by-step explanation:

1)

For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:

[tex]f(x)=2(3)^x[/tex]

The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.

2)

Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:

[tex]f(x)=10(2)^x[/tex]

The 10 represents the initial amount while the 2 represents the rate.

3)

I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.

4)

To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:

For Amber:

Day 3:

[tex]f(3)=3(4)^3=192[/tex]

Day 10:

[tex]f(10)=3(4)^{10}=3,145,728[/tex]

For Ben:

Day 3:

[tex]f(3)=2(3)^3=54[/tex]

Day 10:

[tex]f(10)=2(3)^{10}=118,098[/tex]

And for Carter:

Day 3:

[tex]f(3)=10(2)^3=80[/tex]

Day 10:

[tex]f(10)=10(2)^{10}=10,240[/tex]

5)

Amber's new graph of:

[tex]f(x)=3(4)^x+45[/tex]

will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.

6)

On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.

7)

If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.

Answer:

Here is the slope:

[tex]y = zy + dsince m = 0c = 9[/tex]

Hope this helps

Answer:  see proof below

Step-by-step explanation:

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity:     cos²A + sin²A = 1

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}[/tex]

[tex]\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}[/tex]

[tex]\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}[/tex]

[tex]\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}[/tex]

                               =  cos A

LHS = RHS:  cos A = cos A   [tex]\checkmark[/tex]

Answer:

0.19 = 19/100

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

0.19=0.191

Multiply to remove 2 decimal placesy 102 = 100

0.19/1 × 100/100 = 19100

Conclusion

0.19=19100

Answer:

3q + 5

Step-by-step explanation:

Three times a number q is 3q, and 5 more than that is 3q + 5.

Answer:

A) 2 miles

Step-by-step explanation:

2)   In the figure the solid path indicates the usual path of a taxi cab. Unfortunately, there was construction and the taxi cab had to take the dotted route. If each tick mark represents one mile, how much longer was the detour than the regular route?  

A) 2 miles  

B) 3 miles  

C) 5 miles  

D) 11 miles  

Answer:

[tex]\Huge \boxed{m=0}[/tex]

Step-by-step explanation:

[tex]m +5=-m-2-5m+7[/tex]

Adding m and 5m to both sides of the equation.

[tex]m +5+m+5m= -m-2-5m+7+m+5m[/tex]

Subtracting 5 from both sides of the equation.

[tex]m +5+m+5m-5=-2+7-5[/tex]

Combining like terms and simplifying.

[tex]7m=0[/tex]

Dividing both sides of the equation by 7.

[tex]m=0[/tex]

Answer:

m = 0

Step-by-step explanation:

m + 5 = - m - 2 -5m + 7

m + 5 = -m - 5m - 2 + 7

m + 5 = -6m + 5  (combine like terms)

m = 0

Answer: rs 4800, rs 3456

Step-by-step explanation:j

given data:

length of a sid = 48m

cost of ploughing the field = rs 25/m

cost of fencing the field = rs 18/m

solution:

we know a square has four equal sides. so total length of the field is

= m ( 48 + 48 +48 + 48 )

= 192m

cost of ploughing the field

= 192m * rs 25

= rs 4800

cos of fencing the field

= 192m * rs 18

= rs 3456

Answer:

156

Step-by-step explanation:

n times the constant of proportionality = a

so n will always 156 times greater

Answer:

y = 3x

Step-by-step explanation:

Use rise over run (y2 - y1) / (x2 - x1) to find the slope

(12 - 6) / (4 - 2)

6/2

= 3

The plant will be 0 cm at 0 weeks, since 3(0) = 0

So, the equation will be y = 3x

Answer:

f=2.93cm

Step-by-step explanation:

SOH CAH TOA [the length you are finding is adjacent to the angle and opposite to right angle is the hypotenuse, therefore use cosine]

cos(43°)=f/4

[times 4x on both sides it cancels on the left]

4cos(43°)=f

2.93=f

Answer:

answer is attached

Answer:

The answer is 1,000

Answer: 1

Step-by-step explanation:

You just simplify each number by the square and then you multiply all of them!!

Answer:

x(5)/(6)y(1)/(2)

Step-by-step explanation:

Hoped I helped

leave a like or rate.

Answer:

The reciprocal of n must be less than 10.

Step-by-step explanation:

It can be inferred from the question given that n is not a negative number.

But,

[tex](n)^{2}[/tex] < [tex]\frac{1}{100}[/tex]

Find the square root of both sides,

n < [tex]\sqrt{\frac{1}{100} }[/tex]

⇒ n < [tex]\frac{1}{10}[/tex]

n < 0.1

The reciprocal of n can be estimated as;

[tex](n)^{-1}[/tex] < [tex](\frac{1}{10}) ^{-1}[/tex]

[tex]\frac{1}{n}[/tex] < 10

The reciprocal of n is less than 10.

Answer:

15

Step-by-step explanation:

5bc = 5(-3)(-1) = -15(-1) = 15