1. A trapezoid is pictured on the right. Its bottom base a is not changing while its top base b is increasing at the rate of 3 inches per second while its height h is decreasing at the rate of 0.5 inches per second. How fast is the area of the trapezoid changing, measured in square inches per second, at this moment?
A) -2.5
B) -.75
C) 1
D) 2
(Please explain)

The function operation ( f + g )( x ) in the functions f( x ) = x² + 2x and g( x ) = 4x² - 3 is 5x² + 2x  - 3.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, replace the function designators in f + g with actual functions.

( f + g )( x ) = ( f )(x) + ( g )( x )

( f + g )( x ) = ( x² + 2x ) + ( 4x² - 3 )

Remove the parenthesis

( f + g )( x ) = x² + 2x + 4x² - 3

Collect and add like terms

( f + g )( x ) = x² + 4x² + 2x  - 3

( f + g )( x ) = 5x² + 2x  - 3

Therefore, the function operation ( f + g )( x ) is 5x² + 2x  - 3.

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The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours (f − g)x = 5x - 25.

A function can be defined as the set of inputs that results in output.

Given, Cynthia earns 20 dollars per hour working as a camp counselor plus an additional 25 dollars as a bonus which is f(x) = 20x + 25, and as a lifeguard 15dollars per hour and an additional 50 dollars bonus which is g(x) = 15x = 50.

We know (f - g)x = f(x) - g(x).

∴  The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours is f(x) - g(x).

=  (20x + 25) - (15x + 50).

= 20x - 15x + 25 - 50.

= 5x - 25.

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Answer:

74 inches

Step-by-step explanation:

6 feet= 72 inches plus 2 inches equals this amazing height

Answer:

Hope the picture will help you.......

Answer:

a3 is your simplified answer.

Step-by-step explanation:

a5 divided by a2 is a3/1 which is a3.

Answer:

Step-by-step explanation:

a^3

Answer:

probability of getting 2 = 1/6

probability of getting an odd number=3/6=1/2

probability of getting number less than 5  = 4/6=2/3

multiply probabilities:

1/6x1/2x2/3

=2/36

=1/18

a)

If the triangles are similar, the corresponding sides vary on the same proportion, so the ratios between the corresponding sides are equal.

For

To solve for x you have to multiply both sides of the expression by 20

b)

Following the same logic, the ratio between x and 20 is the same as the ratio between 6 and 8

6/8 can be simplifies as 3/4. Then multiply both sides by 20 to determine the value of x.

As mentioned above, when two triangles are similar, the corresponding sides are always in the same ratio, that is why the results in a and b are the same.

The measure of x is found as 22 for the given vertically opposite angles.

For the given question;

5x + 4 = 114 (As both lines intersecting and vertical angles are formed).

Solving the equation;

5x = 114 - 4

5x = 110

x = 22

Thus, the measure of x is found as 22.

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The figure below has an area equivalent to 88 square units.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.

The opposing or confronting sides and the opposing angles in a parallelogram are of equal length.

Area = length * breadth is the formula for computing the area of a parallelogram.

Substituting the given values

Area = x * h

Area of the parallelogram = 8 * 11

Area of the parallelogram = 88 square units.

Consequently, the parallelogram above has an area of 88 square units.

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Sulfhuric acid, boric acid and vinegar have 7 atoms present in them

To find the compounds with equal number of atoms, we must take each individual atoms and find how many atoms are present in them.

In the first compound, we have sulfuric acid.

[tex]H_2SO_4 = 7 atoms\\[/tex]

Second compound, we have phosphoric acid

[tex]H_3PO_4 = 8 atoms[/tex]

Third compound, we have vinegar

[tex]C_2H_3O_2 = 7 atoms[/tex]

Fourth compound, we have boric acid

[tex]H_3BO_3 = 7 atoms[/tex]

From the above, only sulfuric acid, vinegar and boric acid have equal number of atoms present in them.

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I f Bill wants to maximize his utility while spending $31 on apple. Bill van buy 10 whole pounds of Apples

given data

Apples cost $3 per pound

Bananas cost $5 per pound

amount Bill has to spend $31

The number of whole apple Bill can buy

Using $31 the number of whole apples this can buy is gotten  dividing the  the total amount by the price of apple per pound.

= amount Bill has to spend $31 / Apples cost $3 per pound

= 31 / 3

= 10.33

Since we are solving for whole pounds of apple Bill can buy 10 whole pounds of apples

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Answer:

Step-by-step explanation:

Here in all these questions we need to follow the rules of BODMAS which tells us the steps to solve and mathematical operation.

B-Bracket

O-Of

D- Division

M-Multiplication

A-Addition

S-Subtraction

now,

A. 19+(8-25)

we need to solve what's inside the bracket first

so, 8-25= -17

=19+(-17)

=2

B. (-15+6)-(23-18)

=(-9)-5

= -14

C. (154-6)+3-(-9+7)

= 148+3-(-2)

=148+3+2

= 153

D. -13+(5+8)- (-4+8)

= -13+13-4

= -4

E. (-5)-(17+(-13))-((-8) -(+2))

= -5 -(4)-(-10)

= -5-4+10

= 1

F. (12-(-3))-(12-(-3))

= 15-15

=0

G. 15 -(-3-((+12)-16))

= 15-(-3-(-4))

= 15- 1

= 14

That's how we do it try the last one by your self!

Answer:

v=-0.5

Step-by-step explanation:

v=2+(-5×0.5)

v=2-2.5

v=-0.5

f is the given profit function whose input is number of cones and output is profit, f(50)=80 tells that $80 profit is made by selling 50 cones of ice cream.

A function is a relation that assigns each element of a set a unique element of another set.

f(x) denotes that function f works on the input values x and give output f(x).

If f is a function and f(x) = x+2, then if we have to check x= 1 , then

f(1) = 1+2 = 3 is the value of the function f at x=1

A La Mode Ice Cream Parlor uses a function f as profit function

The input x is the number of cones it sells and output is profit

f(50) = 85

⇒x = 50 and f(50) = 85

It means that when the parlor sells x = 50 cones , it makes  profit $ f(50) = 85

or On selling 50 cones the profit made is $80

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4π/ 5 radians = ?

Then if

π radians= 180°

(4/5)•π radians = 180• 4/5

. = 144

Answer is

4pi/5 radians = 144 degrees

Step-by-step explanation:

I don't see any statements either.

anyway, the only thing that can be said about the 2 lines is that they are crossing each other at one point.

the lines are not parallel, they are not perpendicular (90° to each other), they are not identical.

nothing can be said about a specific point on the line of intercepts with the x- and y-axis.

they are also not parallel and not perpendicular to any of the x- or y-axis.

Answer:

X = 12

Explanation:

3x/6 + 1= 7

/2 + 1 = 7

x/2 + 1 = 7

x/2 + 2/2 = 7

X+2/2 = 7

X = 12

hope this helps you :)

The general slope intercept form equation of a line is as stated below;

where m is the slope and b is the intercept.

If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.

The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;

So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);

Remember, the point slope form equation of a line is given as;

Substituting the above values, we'll have

Let's open up the parenthesis first, we'll have;

Let's isolate y by adding 7 to both sides of the equation;

The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).

A graph of the linear function (y = 2x - 3) which matches the answer is shown in the image attached below.

A graph refers a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis decreases or increases, the values on the y-axis decreases or increases simultaneously as shown in the image attached below.

In conclusion, a graph representing the given linear function shows a proportional relationship between the value of x and y.

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The meaning of each statement is shown below.

Step-by-step explanation:

Assume that the given statements are

(a) c(0)=0

(b) c(3)=c(8)

(c) c(n)=29

(d) c(13)<c(12)

Let c(t) be the number of customers in a restaurant t hours after 8 A.M.

We need to find the meaning of each given statement.

(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.

(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).

(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.

(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)

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The vertex and the range of the absolute value function are given as follows:

(−2, −3); −3 ≤ y < ∞.

The absolute value function in the context of this problem is defined according to the following rule:

y = |x + 2| − 3.

For the general equation, with vertex (h,k), the definition is given as follows:

y = |x - h| + k.

Hence, in the context of this problem, the coefficients of the vertex are given as follows:

h = -2, k = -3.

Hence the vertex is:

(-2,-3).

The range of a function is the set containing all the output values assumed by the function. For the absolute value function, it is given by the following interval:

k ≤ y < ∞

Hence, for the function defined in this problem, the interval is given by:

-3. ≤ y < ∞

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Answer:

The first questions unknown equals

[tex] \frac{3025}{49} [/tex]

The second question is unclear. I assume it is to simplify if that is the case the answer will be.

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

First Question I made ?=x for simplicity.

[tex]7 \sqrt{x} = 55[/tex]

then I divide both sides by 7

[tex] \sqrt{x} = \frac{55}{7} [/tex]

then I square both sides

[tex]x = \frac{3025}{49} [/tex]

Question 2

I simplified by dividing both the denominator and the numerator by their HCF (highest common factor) which is 5

[tex] \frac{5 \div 5}{10 \div 5} [/tex]

which equals

[tex] \frac{1}{2} [/tex]

Answer:

[tex]\textsf{1.} \quad 7\sqrt{\dfrac{3025}{49}}=55[/tex]

[tex]\textsf{2.} \quad \dfrac{5}{10}=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Let x be the unknown number:

[tex]\implies 7\sqrt{x}=55[/tex]

Divide both sides of the equation by 7:

[tex]\implies \dfrac{7 \sqrt{x}}{7}=\dfrac{55}{7}[/tex]

[tex]\implies \sqrt{x}=\dfrac{55}{7}[/tex]

Square both sides of the equation:

[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{55}{7}\right)^2[/tex]

[tex]\implies x=\dfrac{55^2}{7^2}[/tex]

[tex]\implies x=\dfrac{3025}{49}[/tex]

Divide the numerator and the denominator by the highest common factor:

[tex]\implies \dfrac{5 \div 5}{10 \div 5}=\dfrac{1}{2}[/tex]

The expression √-20 has an equivalent of 2√-5

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

√-20

Express 20 as the product of 4 and -5

So, we have the following equation

√-20 = √4 * -5

Expand the equation

So, we have the following equation

√-20 = √4 * √-5

Evaluate the exponent

√-20 = 2√-5

Hence, the equivalent expression of √-20 is 2√-5

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The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.

Number of model are represented on y axis and the hours are represent on x axis.

As we can observe,

One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)

The slope m between any two points (a,b) and (c,d) can be calculated as,

m = (d-b)/(c-a)

The two points we have are (4,6) and (2,3), so the slope M between them is,

M = (3-6)/(2-4)

M = -3/-2

M = 3/2.

And the slope M' between other two point (6,9) and (0,0) is,

M' = (9-0)/(6-0)

M' = 9/6

M' = 3/2.

As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.

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Answer: See explanation

Step-by-step explanation:

For questions 1 - 4, it's asking you to plug in numbers into the original functions.

1. f(-2): You would plug -2 into f(x) = 2x^2 - 3x, getting

2(-2)^2 - 3(-2)

2(4) - (-6)

8 + 6 = 14

f(-2) = 14

2. f(x) - g(x): You're basically just subtracting the two functions

(2x^2 - 3x) - (2 - 5x)

2x^2 - 3x - 2 + 5x

Combine like terms

2x^2 + 2x - 2

3. You're multiplying them so (2x^2 - 3x)(2 - 5x)

4. f(g(x)): It's like f(-2), but instead of -2, you plug in the function of g(x)

So in 2x^2 - 3x, x would equal 2 - 5x:

2(2 - 5x)^2 - 3(2 - 5x)

And then simplify that.

For questions 5 - 6, it's asking for shifting from the parent function. Parent function is always f(x) or g(x) or whatever variable it is.

5. f(x - 8) + 9: The 9 is the y value shift, meaning the parent function is shifted up 9 units. For -8, think of what x needs to be for (x - 8) to be 0. If that number is positive, function shifts right; if negative, shift left. In this case, x needs to be 8 in order for (x - 8) to be 0. Therefore, f(x) is shifted right 8 units.

6. -3f(x) - 2: From the previous question, we now know that -2 means f(x) is shifted down 2 units. When you have 3f(x), you're multiplying the entire function by 3, so it's called a vertical stretch of 3. The negative means it's reflected over the x-axis since the y value is the opposite of what it used to be.

Answer:

-8 < x < 5

Step-by-step explanation:

-3 < x + 5 < 10

=> Minus 5 in all sides

=> -8 < x < 5