Write the inductive hypothesis for this statement

The value of the expression when x = 4 is 12.

The value of the expression when x = -8 is 6.

We have,

To evaluate the expression 10 + x/2 for a given value of the variable x, we simply substitute the value of x into the expression and simplify.

For example:

If x = 4:

10 + x/2 = 10 + 4/2

= 10 + 2

= 12

So when x = 4, the value of the expression is 12.

If x = -8:

10 + x/2 = 10 + (-8)/2

= 10 - 4

= 6

So when x = -8, the value of the expression is 6.

Thus,

The value of the expression when x = 4 is 12.

The value of the expression when x = -8 is 6.

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Each of the graphs should be matched with the appropriate function as follows;

Graph 1: D. f(x) = (x - 2)² + 3

Graph 2: C. f(x) = -(x - 2)² - 3

Graph 3: B. f(x) = -(x - 3)² - 2

Graph 4: C. f(x) = (x - 3)² + 2

In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Mathematically, the vertex form of a quadratic function is modeled by this equation:

f(x) = a(x - h)² + k

Where:

In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.

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The value of length of AG is,

AG = 157.02

We have to given that;

AD = 31 cm

DC = 22 cm

Hence, We get;

AC = √31² + 22²

AC = √961 + 484

AC = √1445

AC = 38

Thus, We get;

cos 76° = AC / AG

0.242 = 38 / AG

AG = 38/0.242

AG = 157.02

Therefore, The value of length of AG is,

AG = 157.02

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∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.

option A.

Supplementary angles are the two angles that sum up to 180 degrees.

That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.

From the given diagram we can form the following equation;

∠ AFE + ∠ AFB = 180 (supplementary angles or sum of angles on a straight line )

∠ AFE = 180 - ∠ AFB

∠ AFE = 180 - 78

∠ AFE = 102⁰.

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Anna will make  $1602.71 in all over 10 weeks.

Here, the first week salary of Anna = $116

i.e., the initial salary a =  $116

She was guaranteed a raise of 7% each week.

so, her salary in the next week would be,

116 + 7% of 116

7 percent of 116 is:

116 × 7/100 = 8.12

so, her salary will be $124.12

So, the equation for the salary after 'm' weeks would be,

[tex]n = 116\times (1 + 0.07)^{m - 1}\\\\n = 116\times (1 .07)^{m - 1}[/tex]

Using this equation , the salary in the second week m = 2 would be,

n = 124.12

Salary in the third week m = 3 would be,

n = 116 × [tex](1.07)^{3-1}[/tex]

n = 132.81

Salary in the fourth week m = 4 would be,

n = 116 × [tex](1.07)^{4-1}[/tex]

n = 142.11

Salary in the fifth week m = 5 would be,

n = 116 × [tex](1.07)^{5-1}[/tex]

n = 152.05

Salary in the sixth week m = 6 would be,

n = 116 × (1.07)⁶⁻¹

n = 162.7

Salary in the seventh week m = 7 would be,

n = 116 × (1.07)⁷⁻¹

n = 174.08

Salary in the eighth week m = 8 would be,

n = 116 × (1.07)⁸⁻¹

n = 186.27

Salary in the nineth week m = 9 would be,

n = 116 × (1.07)⁹⁻¹

n = 199.31

And the salary after the tenth week m = 10 would be,

n = 116 × (1.07)¹⁰⁻¹

n = 213.26

The total money after 10 weeks would be,

T = 116 + 124.12 + 132.81+ 142.11 + 152.05 + 162.7 + 174.08 + 186.27 + 199.31 + 213.26

T = $1602.71

This is the required amount.

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Answer:

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

Given expression:

Group the expression as below and factorize:

Hence the factored form of the expression is (2x + 5)(x² + 3).

The factored form of the expression is,

⇒ (2x + 5)(x² + 3).

Given that;'

The expression is,

⇒ 2x³ + 5x² + 6x + 15

Now, Group the expression as below and factorize:

2x³ + 5x² + 6x + 15

(2x³ + 5x²) + (6x + 15)

x²(2x + 5) + 3(2x + 5)

(2x + 5)(x² + 3)

Hence, the factored form of the expression is (2x + 5)(x² + 3).

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Answer:

Step-by-step explanation:

[tex]\frac{x}{18} =cot~30\\x=18cot~30=18 \times \sqrt{3} =18\sqrt{3} \\base=36\sqrt{3} \\area~of~triangle=3\times \frac{1}{2} \times36\sqrt{3} \times 18=972\sqrt{3} \approx 1683.55~mm^2[/tex]

The measure of inverse of sinθ is c/√ (c² - a²)..

The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.

Mathematically, the trig identities are represented using the following method;

SOH CAN TOA

SOH is for sine θ

CAH is fof cos θ

TOA is for tan θ

From the diagram we need find the value of the opposite side;

b = √ (c² - a²)

Sin θ = b/c

The inverse of b/c = c/b

1/sinθ = c/b = c/√ (c² - a²).

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Answer:

the simplified expression is 4x - 4y

Step-by-step explanation:

1. Rewrite!

12x - 7y - 8x + 3y

2. Combine like terms:

12x - 8x - 7y + 3y

3. Solve both sides to simplify

12 x - 8x = 4x

and

-7y + 3y = -4y

So, 4x - 4y is your answer.

Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

The following equation denotes the correlation between the duration and output of an activity: A = kT

It should be noted that A represents the amount of production, T is the period of working on the task, and k consists of a constant ratio.

Therefore, it can be conclusively stated that the culminating yield is in direct correlation to the amount of effort contributed, as denoted by the factor of proportionality k, thus producing a linear relationship when displayed upon a graph.

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The three different types of visuals we use to organize all the possible outcomes in a sample space are:

For the second part of the question, select one of the three styles of graphical representation you listed in Part A to make a sample space for all probable results for putting the 3 books on a rack.

The table will show every feasible end result for setting up the 3 books on a rack.

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Answer: 1040

Step-by-step explanation: y=ab

The exponential equation is: y = 1040(1.3^x)

Calculate the value of y, which stands for the albums sold, and x represents the months passed from their release. For an exponential equation structured as y = a(b^x), identify the base b to solve it mathematically.

By analyzing the last month after launch, known as March, 1040 copies were made available for public consumption. One month further down the line, in April, the gross profit jumped up to 1352 units sold.

When we divide the copies traded throughout April by those resold in March, the value identifies the base:

b=1352/1040 ≈ 1.3

Thus, applying the coefficient a for the initial sales registered during March - totaling 1,040 copies - leads us to define the following form for our equations:

y = 1040(1.3^x)

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The difference between 13.56 and 10.02 is 3.54.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between 13.56 and 10.02 can be calculated by doing the subtraction. As,

(13 + 0.56) - (10 + 0.02)

= (13 - 10) + (0.56 - 0.02)

= 3 + 0.54

= 3.54

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The variance of the data-set in this problem is given as follows:

81 units squared.

The standard deviation for the data-set in this problem is given as follows:

9 units.

The relation between the standard deviation and the variance is that the standard deviation is the square root of the variance, hence the variance is the square of the standard deviation.

Hence the variance of the data-set in this problem is given as follows:

(9 units)² = 81 units².

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Answer:

92.5

Step-by-step explanation:

First, we need to put the data in order from smallest to largest:

$71, 81, 89, 92, 93, 94, 94, 99$

There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.

The middle two numbers are 92 and 93, so the median is:

$(92+93)/2 = 92.5$

Therefore, the median of the data is 92.5.

that would be 5 pieces of cardboard needed

By analyzing the end behavior of the function we can see that the correct options are A and D.

Here we have the exponential function:

[tex]F(x) = 2^x[/tex]

This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:

as x → ∞, f(x) → ∞

And when x is a really large negative number, the function tends to zero, then we have:

as x →-∞, f(x) → 0

Then the correct options are A and D.

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Answer:

289

Step-by-step explanation:

Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".

From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.

Using trigonometry, we can set up two equations:

tan(30.5°) = (d + 138) / h (1)

tan(23.5°) = d / h (2)

We can solve equation (2) for d:

d = h tan(23.5°)

Substituting this into equation (1), we get:

tan(30.5°) = (h tan(23.5°) + 138) / h

Simplifying:

tan(30.5°) = tan(23.5°) + 138/h

tan(30.5°) - tan(23.5°) = 138/h

h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet

Therefore, the height of the building is approximately 289.12 feet.

The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.

The cost price is the difference between the selling price and the profit or gain.

The difference is determined by subtraction.

Selling price of the article = Rs. 150

Loss if sold at Rs. 135 = 50% of the original gain

Original gain = Rs. 15 (Rs. 150 - Rs. 135)

50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)

Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)

Thus, the cost price is Rs. 127.50.

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Answer:

5.45

Step-by-step explanation:

literally do 10.9/2

The expressions that are equivalent to the expression 8x + 32y are:

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

Let's simply the options to see if they are equivalent to the expression 8x + 32y:

4(4 ⁢x + 8y) − 2⁢(4x)   = 16x + 32y - 8x

                               = 8x + 32y

8(x + 4y)  = 8x  + 32y

(2x + 12y) + (6x + 18y) = 2x + 6x + 12y + 18y

                                   = 8x + 30y

Therefore, only 4(4 ⁢x + 8y) − 2⁢(4x) and 8(x + 4y)  are equivalent to the expression below.

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Complete Question

Which of the following expressions are equivalent to the expression below?

8x + 32y

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

(2x + 12y) + (6x + 18y)

The correct graph is: a coordinate grid with the x-axis labeled rooms painted and the y-axis labeled amount of money earned and a line going from the point (0,100) through the point (4,200).

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

The painter pays $100 for supplies, which is a fixed cost, and charges $25 for each room painted, which is a variable cost.

Therefore, the relationship between the amount of money the painter earns and the number of rooms he paints can be represented by a linear equation in slope-intercept form:

Amount earned = (price per room) x (number of rooms painted) + (fixed cost)

In this case, the price per room is $25, the number of rooms painted is the x-value, and the fixed cost is $100. Thus, the equation is:

Amount earned = 25x + 100

To graph this equation, we can plot two points and draw a line through them. One point is when no rooms are painted, which gives the painter $100 for the fixed cost:

(0,100)

The other point is when four rooms are painted, which gives the painter:

Amount earned = 25(4) + 100 = 200

So the other point is:

(4, 200)

The correct option :

a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.

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Answer:

<4√97,-9√97>

Step-by-step explanation:

First, we need to find the values of A-C and B-D:

A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >

B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >

Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:

|A-C| = √((-4)^2 + 9^2) =√(97)

Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:

|A-C|(B-D) = √(97) * < 4, -9 >

= < 4√(97), -9√(97) >

So the final answer is < 4√(97), -9√(97) >.

A statement which is correct include the following: A. Roses cost $2.75 more than daisies.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of roses and cost of daisies, and then translate the word problem into a linear equation as follows:

Based on the information provided about the flowers purchased by Marla and Kelly. we have the following system of linear equations;

7x + 10y = 40.5

3x + 15y = 30.75

By solving the system of linear equations simultaneously, we have:

x = 4 and y = 1.25

Difference = 4 - 1.25

Difference = $2.75

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Answer: 16* 2

Step-by-step explanation:

Answer:

I Think 62°

Step-by-step explanation:

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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The ground distance of the plane is 170,138.5 ft.

The ground distance of the plane is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height attained by the plane is the opposite side, while the ground distance is the adjacent side

tan (10) = 30,000 ft/d

d = 30,000 ft/tan(10)

d = 170,138.5 ft

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Answer:

it can be simplify as follows: