Solve for x, using a
tangent and a secant line.
8 cm
2 cm
x

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer:

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

Answer:

Yes, w=5 is a solution for this inequality.

Step-by-step explanation:

w+11<22

If w=5, this is:

5+11<22

16<22, which is true. So w=5 works as a solution

Answer:

7/18

Step-by-step explanation:

²\(\frac{4}{7}\)=((2*7)+4)/7

2*7=14

14+4=18

18/7⇒7/18

The maximum height reached by the ball is 908.5 feet.

Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:

\(h(t) = -16t^2 + 152t + 6\)

This quadratic function models the height of the ball at any time t after it is thrown.

To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:

t = -b / 2a

where a = -16 and b = 152 are the coefficients of the quadratic function.

t = -152 / 2(-16) = 4.75

So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:

\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet

Therefore, the maximum height reached by the ball is 908.5 feet.

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Question

A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

See below for answers and explanations

Step-by-step explanation:

1) Substitute d=100 into the equation and solve for s:

s=sqrt(9.81d)

s=sqrt(9.81(100))

s=sqrt(981)

s≈31.32

Therefore, the speed of the wave will be about 31.3 m/s

2) Substitute d=1000 into the equation and solve for s:

s=sqrt(9.81d)

s=sqrt(9.81(1000))

s=sqrt(9810)

s≈99.05

Therefore, the speed of the wave will be about 99 m/s

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

x = 4/a

Step-by-step explanation:

8ax = 32

x = 4/a

Answer:

auxiliary lines

Step-by-step explanation:

Answer:

your answer is D

Step-by-step explanation:

Answer: Choice B

If you lower your rates by 6% you will increase the number of occupancies by 12%

========================================================

Explanation:

Price Elasticity of Demand is found by dividing the percent change of demand over the percent change in price

\(\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}\)

If the price drops 6% leads to a 12% increase in demand, then we get this elasticity

\(\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\% \text{ increase in demand}}{6\% \text{ drop in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\%}{-6\%}\\\\\text{Price Elasticity of Demand} = \frac{0.12}{-0.06}\\\\\text{Price Elasticity of Demand} = -2\\\\\)

The absolute value of that result is 2. We work backwards going from 2 to see the relationship between the 12% and 6%.

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

Side notes:

Answer:

103

Step-by-step explanation:

For any Triangle, The Sum of Interior Angles = 180°

So, For Triangle ABC ---> m∠A + m∠B + m∠C = 180°

By Substituting by the Givens m∠A =68 and m∠B=9

68 + 9 + m∠C = 180

77+ m∠C=180

Subtract 77 from both Sides

m∠C=180-77=103°

6a. The equation for the graph is y = 2√(x + 5).

6b. The equation for the graph is y = -|x + 1| + 5

In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;

y = a√(x - h) + k

Part 6a.

Next, we would determine value of a as follows;

4 = a√(-1 + 5) + 0

4 = a√4

4 = 2a

a = 2

Therefore, the required square root function is given by;

y = 2√(x + 5)

Part 6b.

Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:

y = a|x - h| + k

y = -|x + 1| + 5

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Frank will be 22 years old and Michelle will be 11

The amount you need to sell the job if you want to make 15% net margin, based on the costs, is $7, 857.26

First, find the total cost for the project:
= Equipment + cost of labor + overhead

Cost of labor and equipment:

= 4, 200 + ( 16 x 32 per man- hour)

= $ 4, 712

The total cost is then:
= 4, 712 x ( 1 + 45%)

= $6, 832.40

The amount to sell for is:
= Total cost x ( 1 + net margin)

= 6, 832.40 x ( 1 + 15%)

= $7, 857.26

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Answer: 144

Step-by-step explanation: it's so EZ just add all the sides.

Answer:

I think it is because if you take 1 from A and but it next to b it's going to be the same with B

Given function y = sin (x), y =0,  x = 2π , x = 3π . using same method in which volume of region about y axis . V = 2π \(5[x]\) = 10⊄ 2.

so required volume 'v' 2= 10⊄ 2 unit is the final answer.

V = ∫π\(rhdn\)            where r = radius

                                        h = height

                                      dn= thickness

    a = 2π ,  b = 3π

     r  = x ,    h(x) = sin (x)

volume    V  = \(\int\limits^3_2 {2\pi xsin (x)} \, dx\)

V = 2π \(\int\limits^3_2 {\pi xsin (x)} \, dx\)

using integeration by parts of ∫ \({\pi xsin (x)} \, dx\)

                          u = n v' = sin (x)              v =  ∫ sin(x) = -cos (x)

                      - ∫  \({\ xsin (x)} \,dx\) = n ( -cos (x))     ∫ \(\frac{d}{dx} x\)   x × ( -cos(x)) \(dx\)

                                  = - cos n + ∫ \(cos (x)dx\) = \(ncos x + sin x\)

                        V = 2π \([ - x cos (x) = sin (x) ]^{35} =25 [ =35 cos 35] + sin (35]\)

V = 2π \(5[x]\) = 10⊄ 2.

so required volume 'v' 2= 10⊄ 2 unit is the final answer.

How do you find the volume of a bounded region?

If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given V=∫abπ[f(x)]2dx.

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Answer:99cm.l

Step-by-step explanation:100-1

100-1=99

So then the answer is 99, because 99+1 is also equal to 100.

And if you subtract 1 from 100, you get 99.

Answer: 99cm

Step-by-step explanation:

1cm + x = 100cm

100cm - 1cm = x
Which means,

99cm is the correct answer.

The number we would use to show the error is 0.0064.

A decimal number is a number that uses the base-10 numbering system, which means it uses 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent values. The decimal system is also known as the Hindu-Arabic numeral system, and it is the most widely used numbering system in the world.

Decimal numbers can include a decimal point, which separates the whole number part from the fractional part. For example, 3.14 is a decimal number with a whole number part of 3 and a fractional part of 0.14.

To represent the error of 0.64%, we can write it as a decimal number by dividing it by 100. Therefore, the number we would use to show the error is 0.0064.

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Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

Answer:

9:25

Step-by-step explanation:

0.36 is 36% which is 36/100 or 36 to 100

36:100 is 9:25

Hope this helps!

Answer:

9 : 25

Step-by-step explanation:

We need to figure out what the ratio of 0.36 is.

First, we need to convert the decimal number to a fraction by making 0.36 the numerator and 1 the denominator.

1.  0.36  = \(\frac{0.36}{1}\)

Next, we need to multiply the numerator and denominator by 100 to eliminate the decimal point.

2.  \(\frac{0.36 * 100}{1 * 100}\) = \(\frac{36}{100}\)

After that, we need to simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 36 and 100. (The GCF of 36 and 100 is 4.)

3.  \(\frac{36 / 4}{100 / 4} = \frac{9}{25}\)

Finally, we need to convert the fraction in the previous step to a ratio by replacing the divider line with a colon.

4.  \(\frac{9}{25}\) = 9 : 25

So the ratio of 0.36 is 9 : 25.

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = \(\frac{1}{(x-2)(x+3)}\)

Answer:

35 is the answer i just did the lesson :)

Step-by-step explanation:

Answer:

b.

You have more debits than credits.

Step-by-step explanation

Being in the red means that you are in debt so im 90% sure its B

If you get this wrong then i am very sorry.This is my input :)

Answer:

B

Step-by-step explanation:

In accounting, if the debit balance is more than the credit balance on income statement, there is a loss.

If the credit balance is more than the debit balance on income statement, there is a profit.

Option C and D are both not correct because this does not relate to whether a Financial record is accurate or not.

1) Probability of drawing a spade is 14

2) Probability of drawing a seven is 1/13

3) Probability that a heart or spade is drawn = 1/2

4) Probability that blackjack is drawn = 1/26

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

1) There are 13 spades in total.

hence, the likelihood of drawing a spade is 13/52, or 14.

2) The sum of the seven is four. (4 suits are in the room)

Probability = 4/52 = 1/13

(3) A heart or spade is drawn.

Total hearts and spades: 13 + 13 = 26

Probability = 26/52 = 1/2

4) A blackjack is drawn, with a total of two blackjacks.

Probability = 2/52 = 1/26.

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Answer:

-50, -31.5, 44 I think

Step-by-step explanation:

The order from least to greatest is:

-50, -3, 1.5, 44

When the negative value increases ( from -1 to -2 ), the value in general decreases. Negative values have a lower value than non-negative numbers.

Answer:

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Step-by-step explanation:

Step(i):-

Given mean of the life time of a bulb = 510 hours

Standard deviation of the lifetime of a bulb = 25 hours

Let 'X' be the random variable in normal distribution

Let 'x' = 552

\(Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628\)

Step(ii):-

The  probability of a bulb lasting for at most 552 hours.

P(x>552) = P(Z>1.63)

               = 1- P( Z< 1.63)

               =  1 - ( 0.5 + A(1.63)

              =   1- 0.5 - A(1.63)

              =   0.5 -A(1.63)

              =   0.5 -0.4485

             =  0.0515

Conclusion:-

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515