For each expression, circle any like terms and list any variables.

The areas of the given triangle and rectangle are 60 cm² and 120 cm² respectively.

What are a triangle and rectangle?

A triangle is a three-sided polygon which has 3 angles formed when two sides join to form a vertex.

A rectangle is a four-sided polygon whose opposite sides have the same lengths and all sides are perpendicular to each other.

The given triangle is a right-angled triangle.

The area of a right-angled triangle is 1/2*b*h

where,

    b= base of the triangle

   h = height of the triangle

From the figure, b = 10 cm and h = 12 cm

     Area of triangle = 1/2*10*12 = 60 cm²

The given rectangles have a length of 12 cm and a breadth of 10cm.

The area of the rectangle is given by the product of breadth and length.

Area of rectangle = 12 * 10 = 120 cm²

Therefore the areas of the given triangle and rectangle are 60 cm² and 120 cm² respectively.

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Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output. In the case of the function f(x) = -x + 15, the function will take any real number as input and produce a corresponding output.

Therefore, the domain of the function f(x) = -x + 15 is all real numbers. This can be represented as (-∞, ∞) or simply as "all x".

Option O is correct: x are all real numbers

Option O x ≤ 30, O x > -2, O x >0 are incorrect

Step-by-step explanation:

Answer:  X= - 2

Step-by-step explanation:

Answer:

Step-by-step explanation:I  D   K

The property descibed by the statement "whatever is done on one side of the equation must also be done on the other side of the equation” is (d) Property of Equality

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

“whatever is done on one side of the equation must also be done on the other side of the equation”

This means that if x is added to the first side, it must be done on the other side

The property described above is (d)

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The probability of obtaining heads on fourth trial is 1/2

In a random experiment of tossing a penny, let H be the event of obtaining head and T be the event of obtaining tail

As it is a fair penny, the probability of obtaining head=1/2

The outcomes of the trials are independent when a coin is tossed multiple times.

Probability of getting three heads ,

P(3H)=P(H∩H∩H)

=P(H)xP(H)xP(H)

=1/2x1/2x1/2

=1/8

We will use conditional probability to find the probability of obtaining head in the fourth trial, given that three heads are already obtained in three trials

P(H|3H)=P(H∩3H)/P(3H)=(1/8x1/2)/(1/8)=1/2

Thus, the required probability is 1/2

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The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1 And y = 5 ounces of almonds in the last bag.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Isabel has 8 ounces of almonds to divide equally into 2 bags

In the last bag, she adds an ounce of almonds.

The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1

y = 4 + 1

y = 5 ounces of almonds in the last bag

Therefore,  5 ounces of almonds in the last bag

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The complete question:

Isabel has 8 ounces of almonds to divide equally into 2 bags. In the last bag, she adds an additional ounces of almonds. The equation shown can be used to find, the total number of ounces of almonds in the last bag. How many ounces of almonds are in the last bag?

Answer:

C & D

Step-by-step explanation:

The key formula will be y = mx + b

y = the function

m = slope

b = y - intercept

Another term for slope is rate of change

They asked for negative rare of change, so negative slope, which takes it to

y = -mx + b

The only two that work are C & D because C shows -4x and D shows -2x, both negative.

A & B are 7x and 2/3x, both positive.

All the given statements for the function g(x) is true.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

For the function g(x) -

When the value of x = 1, then the value of y = 22.

When the value of x = 3, then the value of y = -5.

When the value of x = 5, then the value of y = 6.

When 1 is an input, 22 is an output.

The point (-5, 3) lies on the graph of the function.

The solution to g(x) = -5 is x = 3.

When 6 is an input, 5 is an output.

The point (-5, 3) lies on the graph of the function.

The point, (5, 6) lies on the graph of the function.

Therefore, all the statements are true.

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a) Does not give an equivalent ratio

b) Does not give an equivalent ratio

c) Does not give  an equivalent ratio

d) Gives an equivalent ratio

An equivalent ratio is a ratio that is equal in value to a given ratio, but may have a different form. Two ratios are equivalent if they have the same relationship between the terms, even if the numbers are different.

In this case, we have the ratio 8/20. The process of addition or subtraction can not be able to give us the equivalent ratio that we are looking for but the multiplication  would do that. Recall that the original fraction is 8/20 so;

a) 10/22 = 5/11

b) 6/18 = 3/9

c) 4/10 = 2/5

d) 16/40 = 8/20

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Answer: 21.3

Step-by-step explanation: Let us split the figure into two triangles. If the total bottom length is 22, than the triangle's base is 22/2=11

We can use the Pythagorean theorem to get: 11^2+x^2=24^2  or      121+x^2=576

576-121=455

sqrt 455=21.33................

rounds to 21.3

The dosage for Devon's body weight is 5.25 ounces.

Note that 50 pounds of body weight require 1.5 ounces of medication,

Here by dividing the given amount of medication by 50 find the amount of medication for 1 pound of body  

Now multiply the result by the present body weight of the Devons.  

Here we have

The dosage of the medication is 1.5 ounces for every 50 pounds

Weight of Devon = 190 pounds    

If he loses 15 pounds, present Devon's weight = 190 - 15 = 175

Dosage for Devon's body = [tex]\frac{1.5}{50} \times 175[/tex]  

= [tex]0.03 \times 175[/tex]  

= 5.25

Therefore,

The dosage for Devon's body weight is 5.25 ounces.    

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There are 22 purple notebooks in the bin.

There are 37 pink socks in the bin.

In order to determine the number of purple notebooks that are in the bin, we would develop an expression to multiply the total number of notebooks (T) by the percentage of the number of purple notebooks placed in the note bin as follows;

Total number of purple notebooks (P) = 25/100 × 88

Total number of purple notebooks (P) = 0.25 × 88

Total number of purple notebooks (P) = 22 notebooks.

Total number of socks (S) = 50/100 × 74

Total number of socks (s) = 0.50 × 74

Total number of socks (s) = 37 socks.

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As per the combination method,

(a) at least one of each letter is 36

(b) at least two of each letter is 15

(c) at least one A, two Bs, and three Cs is 15

(d)  any number of each letter is 120

(e)  at least one A and at least two Bs is 36

In math the term combination method is known as  the number of possible combinations that can be obtained by taking a sample of items from a larger set.

Here we have given that the value of n is 10 and the value of r is 3.

Then the resulting values are calculated as,

Here for the letters with at least one of each letter then the length is 10 with a 3 elements to choose from the given set.

Here we know that 3 of the 10 slots will be taken up by A,B, and C. With 7 remaining, any letter could take up those spots it will be calculated as,

=> (7+3-1 choose 3-1)

=> (9 choose 2).

=> 36

Where as the other one is with at least two of each letter

Then here we have the letter with two of each letter 6 letters will take up 10 slots no matter what is calculated as,

=> 10-6 = 4

Now then we have 3 to choose from so (4 + 3 - 1 choose 3-1).

=> (6 choose 2)

=> 15

And the another option is to have at least one A, two Bs, and three Cs

=> 1A + 2B + 3C will take up 6 spots.

=> (4+ 3-1 choose 3-1)

=>  (6 choose 2).

=> 15

Where as the count is any number of each letter

=> 10 choose 3.

=> 120

Finally if we take at least one A and at least two Bs

Then at least 1 A and two Bs taking up a total of 3 slots is calculated as,

=> 10 - 3 = 7.

=>  (7 + 3 - 1 choose 3 - 1)

=> (9 choose 2) = 36

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For the 5 GB and x GB over use of the data plan per month the total cost paid by Penelope is $160 and $(35 + 25x ).

Let 'x' represents the extra GB used by Penelope in his smart phone data plan.

Cost to used fixed 9 GB of data in a month is equal to $35

Extra charge per GB over the included amount for fixed 9 GB is $25

Equation represents the data plan relation is:

35 + 25x

When Penelope used 5 GB extra over the 9 GB data plan then ,

x = 5GB

Amount to be paid for extra 5 GB is

= 35 + 25( 5 )

= 35 + 125

= $ 160

Amount to be paid for extra 'x' GB is $(35 + 25x).

Therefore, the total cost for extra use of data plan per month is:

a. For 5 GB it is $160.

b. For x GB it is $(35 + 25x).

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True. Testing other points in addition to the vertices is necessary

True. When trying to optimize (find the max or min) of a function, it is not enough to test only the vertices. The function may have a maximum or minimum value at a point that is not a vertex, such as an inflection point, or a point on the edge of the domain.

Thus, testing other points in addition to the vertices is necessary in order to ensure that the maximum or minimum value of the function has been found.

Linear programming is a powerful tool that can be used to model and solve a wide range of real-world problems in fields such as finance, manufacturing, transportation, and resource allocation.

For example, it can help to determine the optimal number of products to produce, the best way to use resources (e.g. labor, materials) and the best scheduling to minimize costs and maximize profits.

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The building is 39.06 yards tall.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse (ramp)= 60 yards

Angle of Elevation = 41°

Using Trigonometry

sin 41= P/H

0.651 = P/60

P= 39.06 yard.

Hence, the height is 39.06 yard.

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An equation to represent the relationship is y=15x.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given ,

The table represents a proportional relationship.

So we have to write an equation to represent the relationship

Given,

Time that is

x = {5,8,12 }

Distance that is

y = {75,120,180}

so here from the given table,

75 = 15*5

120 = 8*15

180 = 12*15

hence , it is in the form of y = 15x.

Therefore, An equation to represent the relationship is y=15x.

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The average number of burgers per person is 96

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here; The function f(d) =200d³+542d²+179d+1605

The number of visitors is given by g(d)=100d+321

Thus in 7 days, The total number of burgers sold are given by

f(7)=200×7³+542×7²+179×7+1605

    =68600+26558+1253+1605

    =98016

And the number of visitors is given by g(7)=100×7+321

                                                                      =1021

Thus, The average number of burgers per person is given by

Avg= 98016/1021

      =96

Hence, The average number of burgers per person is 96

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The word description "3 to the power of a + 4" should be written as 3^{a + 4}.

In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

By applying the property of exponents based on the law of indices for powers, we have the following:

Expression = 3^{a + 4}.

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Complete Question:

What is 3 to the power of a+4?

Answer:

5

Step-by-step explanation:

1.5+5x

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax n is nax n−1

5x1−1

Subtract 1 from 1.

5x 0

For any term t except 0, t 0 =1.

5×1

For any term t, t×1=t and 1t=t.

5

This is how i would solve it :))

All the correct expressions are,

Slope of BC = - 2/5

Slope of CD = 5/2

Slope of DE = - 3/5

Slope of EB = 3

Length of BC = √ 29

Length of CD = √ 29

Length of DE = √34

Length of EB = √40

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Coordinate of B = (- 9, 1)

Coordinate of C = (- 4, - 1)

Coordinate of D = (- 2, 4)

Coordinate of E = (- 7, 7)

Now, We know that;

The slope of line passing through the points (x₁ , y₁) and (x₂, y₂) is,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Thus, Slope of BC is,

⇒ m = (- 1 - 1) / (- 4 - (-9))

⇒ m = - 2/5

Slope of CD is,

⇒ m = (4 - (-1)) / (- 2 - (-4))

⇒ m = 5/2

Slope of DE is,

⇒ m = (7 - 4) / (- 7 - (-2))

⇒ m = 3/- 5

⇒ m = - 3/5

Slope of EB is,

⇒ m = (1 - 7) / (- 9 - (-7))

⇒ m = - 6/-2

⇒ m = 3

Length of CD is,

⇒ CD = √ (- 2 - (-4))² + (4 - (- 1))²

         = √4 + 25

        = √ 29

Length of BC is,

⇒ BC = √ (- 4 - (-9))² + (- 1 - 1)²

         = √25 + 4

        = √ 29

Length of DE is,

⇒ DE = √ (- 2 - (-7))² + (4 - 7)²

         = √25 + 9

        = √ 34

Length of EB is,

⇒ EB = √ (- 7 - (-9))² + (7 - 1)²

         = √4 + 36

        = √ 40

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In the given situation the given values can be correctly modeled by a (B) linear function.

What is a linear function?
A linear function has a straight line as its graph. A linear function has the form shown below. a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable.

The independent and dependent variables are X and Y, respectively.

In mathematics, the terms "linear function" refers to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

Therefore, in the given situation the given values can be correctly modeled by a (B) linear function.

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The equation of the new function is  f'(x) = -1/2x³

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

F(x) = x³

The transformations are given as

The rule of the above transformations is

f'(x) = -1/2f(x)

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

f'(x) = -1/2x³

hence, the equation is f'(x) = -1/2x³

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The slope of the line is 1/2 and the y-intercept is 4. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If you have a different linear equation such as y = (1/2) x + 4. Then the slope and y-intercept of the line are given as,

m = 1/2

y = 4

The slope of the line is 1/2 and the y-intercept is 4. Then the correct option is D.

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If a city's population doubles every 6 years, the city's population, 12 years from now, will be 2,152,000.

Every six months, the population increases by two times the current number.

Using multiplication by 2 or 4, we can determine the population in 12 years.

The current population of the city in Year 0 = 538,000

Doubling time = every 6 years

The estimated time = 12 years

In the first six years, the population will be 1,076,000 (538,000 x 2)

In the second six years, the number of people in the city will be 2,152,000 (1,076,000 x 2) or (538,000 x 4)

Thus, in 12 years, the city's population will become 2,152,000 people.

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Answer:

2,152,000

Step-by-step explanation:

Answer:

a. 1750; b. 900; c. sean 50%, Adrian = 850/3500= 24.3%, James =25.7%

Step-by-step explanation:

Sean got half = 3500/2 =1750

Adrian = 850

James = 3500-1750-850 =900

The monthly payment on a loan of $4,500 at 12% interest for a period of 48 months is: $128.34.

The monthly payment for a $4,500 loan at 12% interest for 48 months can be calculated using the formula:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:

M = the monthly payment

P = the principal (the amount of the loan)

r = the monthly interest rate (12% divided by 12 months)

n = the number of payments (48 months)

So the calculation is:

M = 4,500 * (0.01(1 + 0.01)^48) / ((1 + 0.01)^48 - 1)

This comes out to be $128.34.

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The probability of getting a green wrinkled pea from a yyrr x yyrr cross is 1/4.

A cross was made between a pure round yellow seeded pea plant (RRYY) with wrinkled green seeded pea plant (rryy). The yellow colour is dominant over green and round seed shape is dominant over wrinkled seed shape.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

All of the children were yellow because yellow has a dominant gene over green. The green phenotype was no longer present. To see how the second generation would appear, let the yellow pea plants self-fertilize.

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The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units is 401.13 and if it increase from 1 thousand units to 5 thousand units is 201.13

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

The expression, p(x) = 0.2 x^2 + 1.13x+5.2

where x is given in units of a thousand .

The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units.

p(x) = 0.2x^2 + 1.13x+5.2

p(2000 ) = 0.2 (2000*2000) + 1.13 (2000) + 5.2

= 800000 + 2260 + 5.2

= 802265.2

p(4000 ) = 0.2 (4000*4000 ) + 1.13 (4000) + 5.2

= 1600000 + 4520 + 5.2

= 1604525.2

p(2000) - p (4000) / 2000-4000  = 802265.2 - 1604525.2 /  -2000

= -8,02,260 / -2000

= 401.13

p (1000) = 0.2 (1000*1000) + 1.13 (1000) + 5.2

= 200000 + 1130 + 5.2

= 201135.2

p (5000 ) = 0.2 (5000*5000) + 1.13(5000) + 5.2

= 1000000 + 5650 + 5.2

= 1005655.2

p (1000) - p (5000) / 1000 - 5000  = 201135.2 - 1005655.2  / -4000

= 804520 / 4000

= 201.13

Hence, The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units is 401.13 and if it increase from 1 thousand units to 5 thousand units is 201.13.

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