Question 5, Please Answer and Explain

Answer:

[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]

Step-by-step explanation:

a basketball court is a rectangle, therefore its area is length x width.

the length given is (x+16)

the width given is (x-2)

substitute into the rectangular area equation:

length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32

specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].

therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].

i hope that helps :)

Answer:

therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].

Step-by-step explanation:

According to the information, Jonas realized that the four-digit sequence showing the distance traveled was the same sequence showing the time at 22h10min (question 25). Also, Lady Josephine removed 1/2 of impurities of the package of beans (question 26).

To calculate at what time Jonas realized the sequences of distance and time were the same we have to perform the following mathematics operation:

To calculate what fraction of the total amount of impurities was removed from package we have to perform the following mathematical operation:

According to the above, we can infer that 4% of impurities equals 50% or 1/2 of the total impurities in the package.

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Answer:

32

Step-by-step explanation:

Let's start with x to the third power. x=4 So that would be 4 to the third power. that would be 4x4=16.  16x4=64. So that would be 1/2*64. That equals 32

Answer:

8x² + 11x + 6

Step-by-step explanation:

6x + 7 + 8x² + 5x - 1 ← collect like terms

= 8x² + (6x + 5x) + (7 - 1)

= 8x² + 11x + 6

Answer:

The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.

The value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.

What is the triangle translation?

In mathematics, a triangle translation refers to the geometric transformation in which a triangle is moved to a new position without rotating or scaling it. The triangle is simply slid along a straight line in a certain direction, and the new position of the triangle will be parallel to the original one.

Given that ΔABC translates to ΔA'B'C', we can assume that the measures of the angles are the same in both triangles. Therefore, if we know the measure of an angle in one triangle, we can assume that the measure of the corresponding angle in the translated triangle is the same.

Given:

m∠A = y

m∠A' = 2x + 5

m∠C = 3x-y

m∠C' = 4

Since opposite angles in a rectangle are congruent, m∠A=m∠C' and m∠C = m∠A'

Therefore,

y = 4

3x-y = 2x + 5

Solving this equation gives us:

x = y + 5 = 4 + 5 = 9

y=4

m∠C = 3x - y = 3(9) - 4 = 25

m∠A' = 2x + 5 = 2(9) + 5 = 23

Hence, the value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.

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Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

The slope of the line through each pair of points (16,1), (17,7) is 6.

A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.

The slope of a line can be positive, negative, zero, or undefined.

In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.

To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula

m = (y2 - y1) ÷ (x2 - x1)

where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the slope of the line through the points (16,1) and (17,7) is:

m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6

So the slope of the line is 6.

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Answer:

[tex]S_{1000}=500500[/tex]

Step-by-step explanation:

[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]

The side lengths are;

tan x = e/f

cos x = e/d

sin x = f/d

We know that a right angled triangle is the kind of triangle that one of the sides of the triangle would be 90 degrees.

There are some ratios that are associated with the right angled triangle and we call them the trigonometric ratios. These include the sine the cosine and the tangent. All of these ratios does depend on the lengths of the sides of the right angled triangle.

The sides of the right angled triangle are the opposite, the adjacent and the hypotenuse and these can be obtained based on the relative position of the angle.

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Answer:

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

Given equation:

Its solutions are:

The product of the solutions is -15:

Answer: nine

Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9

Answer:

9

Step-by-step explanation:

1 first split  36 by 4 because  25% is 1/4

2 once when divided you should get 9 because 9x4 is 36  

Answer:

Step-by-step explanation: Total Cost: TC = $126.07

Base fee: B = $16.95

Rate per mile: r = $0.88/mile

Distance (miles) : d -->this is what we need to find

The general formula is:

TC = B + r*d

In this problem:

$126.07 = $16.95 + ($0.88/mile)*d

126.07 - 16.95 = 0.88d    (I dropped the units starting here)

d = (126.07 - 16.95)/0.88 = 124 miles  (notice the parentheses. subtraction has a lower precedence than division.  If you omitted them when using a graphing calculator you would get an incorrect answer)

So the answer is 124 miles.

On solving the question, 5 topping would pay the same amount for Pizza A and Pizza B,  the value of equation 0.50x=2.50=>   x=5

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x be the number of toppings,the total cost of a pizza is given by:

pizza cost+topping cost

for pizza a =10+1.50x

for pizza b=12.50+1.00x

we solve for when cost are same and for how many toppings

   10+1.50x=12.50+1.00x

   10+0.50x=12.50

   0.50x=2.50

        x=5

would pay the same amount for Pizza A and Pizza B. are 5 toppings,

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The result of the interpretation of the graph:

Spring side weakens the correlation shown in the scatter plot.

The correct option is D.

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given:

The mean test score is represented in the scatter plot as a function of the average class size.

This demonstrates that there is a negative link between the mean class size and the mean test score,

with the mean score decreasing as the mean class size increases.

The correct response is:

Spring-side decreases the association displayed in the scatter plot.

However, for Spring side, the mean test score is higher than most other schools with lower class sizes, which is a different outcome than predicted.

Therefore, spring-side weakens the correlation shown in the scatter plot.

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The complete question:

A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatter plot. One school in the report, Spring side Elementary, is labeled in the graph.

Which is a true statement regarding Spring side?

Spring side does not affect the correlation.

Spring side weakens the correlation shown in the scatter plot.

The spring side strengthens the correlation shown in the scatter plot.

Removing Spring side would increase the value of the correlation coefficient.

The scatter plot is attached in the image.

Answer:

x = 12 and y = 11

Step-by-step explanation:

4x+3y=-15 -----equation 1st

4x-y = -27 ____equation 2nd

then,

Multiple equation second by 3 and slove it with equation first

4X +3Y = -15

12X -3Y = -81 (Multiples it with 3)

-8x = -96 (subtracted)

x=-96/-8

therefore, x=12

again,

from equation first

4x+3y = -15

or 4 × 12 + 3y = -15

or 3y = -15+48

or 3y= 33

or y=33/3

therefore, y =11

I hope this helps. If you have any doubt feel free to ask!!

Answer:

x = -6,  y = 3

Step-by-step explanation:

1)  4x + 3y = -15

2)  4x - y =  -27

     0 + 4y = 12       subtract equation (2) from equation (1)

4y = 12

y = 12/4 = 3         substitute y = 3 into either equation 1 or 2 and solve for x

4x + 3(3) = -15

4x = -24

x = -6

Check your answers by plugging x = -6, y = 3 into the equations:

4(-6) + 3(3) = -15   correct!

4(-6) - 3 = -27        correct!

So basically what I do is find the formula for slope.

M= y2-y1/x2-x1

So I got

-5-(-6)/-9-(-6) = 1/3

answer = 1/3

:)

Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

The complete table of values of the function is

x    0    1    2    3

y     0   2   5   10

From the question, we have the following parameters that can be used in our computation:

The equation of the function is given as

y = x² + 1

The above function is a quadratic function

This is so because it has the following representation

y = ax² + bx + c

When this function is compared to the equation y = x² + 1, we have the following notations

a = 1

b = 0

c = 1

From the incomplete table of values, we have the x values to be

x = 1, 2, 3

Substitute x = 1, 2, 3 in the equation y = x² + 1

So, we have

When x = 1, y = (1)² + 1 = 2

When x = 2, y = (2)² + 1 = 5

When x = 3, y = (3)² + 1 = 10

When these values are represented on a table, we have

x    0    1    2    3

y     0   2   5   10

The above represents the complete table

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Complete question

Complete table with the Y-values for the equation y=ײ+1

x    0    1    2    3

y     0

Answer:

0.910

Step-by-step explanation:

since it'snot perfect it can't be one and since it a positive slope it is 0.9102.

The length of time to build the fence is 8 hours

From the question, we have the following parameters that can be used in our computation:

Length of the fence = 1 1/3 miles

Rate of building = 1/6 miles per hour

The length of time to build the fence is then calculated as

Length of time = Length of the fence/Rate of building

Substitute the known values in the above equation, so, we have the following representation

Length of time = (1 1/3 miles)/(1/6 miles per hour)

Evaluate the quotient

This gives

Length of time = 8 hours

Hence, the time taken is 8 hours

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Answer: x=3

Step-by-step explanation:

5x=7x-6

6+5x=7x

6=7x-5x

6=2x

solve for x which x=3

Answer:

x = 3

Step-by-step explanation:

Set the equations equal to each other:

5x = 7x - 6

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Division

Addition

Subtraction

~

Subtract 7x from both sides of the equation:

[tex]5x (-7x) = 7x (-7x) - 6\\5x -7x = -6\\-2x = -6[/tex]

Next, divide -2 from both sides of the equation:

[tex]\frac{-2x}{-2} = \frac{-6}{-2}\\ x = \frac{-6}{-2}[/tex]

*Remember that, when you divide two negative numbers, your answer will be positive:

[tex]x = \frac{-6}{-2} = 3[/tex]

3 is your answer for x.

x = 3.

~

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On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]

x = 0 , y = -1 so c = -1.

slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]

function f(x) = -5x - 1.

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Answer:

Step-by-step explanation:

1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10

(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:

3x + 1 = 7

3x = 6

x = 2

2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}

(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}

3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1

(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:

2x - 1 < -3

2x < -2

x < -1

so x can be any value less than -1

(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2

4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1

(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:

2x - 1 = 3(-2) + 1

2x - 1 = -5

2x = -6

x = -3

5. f(x) = px + q, given that f(2)= 4 and f(4) == 10

so

4 = 2p + q

10 = 4p + q

solving for p and q we get p = 3 and q = -2

6. (i) f(--3) = 3(-3)² - 5(-3) = -27

7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:

x-2 = (1/4)x² - 1

x-2 = x²/4 - 1

4x-8 = x²-4

x²-4x+4 = 0

x = 2, -2

(ii) To solve f(x) + g(x) = 0

x-2 + x²-1 = 0

x²-2x+1 = 0

(x-1)² = 0

x = 1

for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3

into the expression of f(x) = 3x² - 5x

3x² - 5x = -3

3x² - 5

The effect of subtracting 2 from the input on the graph of the function is a translation of 2 units to the right.

For any function f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

And what this does, is translate the graph N units horizontally.

if N > 0, then the translation is to the left.

if N < 0, then the translation is to the right.

Here we want to subtract 2 from the input, so we will get:

f(x - 2)

By using the definition above, we know that we will have a translation of 2 units to the right.

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Barren's net worth statement exists shown to the right.

Your total worth, including both financial and non-financial assets, equals your net worth less any outstanding obligations.

Using a net worth statement, you can view your financial situation at any given time. It is comparable to a "financial snapshot," showing the dollar amounts of your assets and liabilities (liabilities or debts).

Assets - Liabilities = Net Worth is the equation for calculating net worth.

The total of Lauren Juliana's debts will be subtracted from the total of her assets to determine her net worth (cash and jewelry).

= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)

simplifying the equation, we get

= $ 3,817

barren's net worth statement is shown to the right.

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The required total net worth of Lauren Juliana is $ 3,817.

Your all out worth, including both monetary and non-monetary resources, rises to your total assets less any remaining commitments.

Utilizing a total assets proclamation, you can see what is going on at some random time. It is equivalent to a "monetary preview," showing the dollar measures of your resources and liabilities (liabilities or obligations).

Resources - Liabilities = Total assets is the condition for working out total assets.

The complete of Lauren Juliana's obligations will be deducted from the absolute of her resources for decide her total assets (money and adornments).

= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)

working on the situation, we get

= $ 3,817

desolate's total assets articulation is displayed to one side.

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The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.

Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.

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The term below that refers to events that all have the same probability of occurring is; (2) equal probability events

By definition, we can say that the probability of occurrence of an event is defined as the number of trials in which a particular event happened divided by the total number of trials.

Probability = number of trials in which event happened/total number of trials.

Now, when we say that all items have the same probability of occurring, what we simply mean is they all have equal chance of occurrence or they all have equal outcomes. For example when we flip a coin, we have equal chance of getting a head or tail.

Thus, the term that best defines the above would be Option 2.

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Answer:

12 bananas

9 apples

18 pears

Step-by-step explanation:

You are tripling the recipe.

10 x 3 = 3

4 x 3 = 12

3 x 3 = 9

6 x 3 = 18