Is -9(k-5+2k-8) and -27k+117 equivalent expressions

Triangle rst is congruent to triangle wxy. If the area of triangle wxy is 20 square inches, then the area of triangle rst is 20 square inches.

When two triangles are congruent, it means that they are exactly the same in every aspect, including their size and shape. This means that their corresponding sides and angles are equal in length and measure, respectively.

In terms of area, if two triangles have the same shape and size, then they will have the same area. This is because the area of a triangle is determined by the length of its sides and the angles between them, and if two triangles are congruent, then their sides and angles are equal.

Therefore, if the area of triangle WXY is 20 square inches, then the area of triangle RST must also be 20 square inches. This is because triangle RST has the same size and shape as triangle WXY, and therefore must have the same area.

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Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let, 'x' be the number of quarters,

Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.

So, x + 2x + 8x + 4x = 780.

15x = 780.

x = 52, The number of quarters.

2×52 = 104, The number of Dimes.

8×52 = 416 Nickels.

3×52 = 162 Pennies.

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The inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5

An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

Given that a finction f(x) = -5x-3, we need to find the inverse of the function,

We can write,

y = -5x-3,

Interplace, x and y,

x = -5y-3

-5y = x+3

y = -(x+3)/5

y = -x/5-3/5

f⁻¹(x) = -x/5-3/5

Hence, the inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5

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Answer:

2:1

2:5

4:3

Step-by-step explanation:

In these examples the comparison words "per", "to", "for every" is the colon.

Then just put the numbers in the same order they are in in the problem

1. Two cookies per student. __:__

Means 2 cookies per 1 student

We're writing the ratio

cookies:students

2:1

2. The odds of the horse winning the race are 2 to 5. __:__

The "to" is the colon

2:5

3. Colorado State University, there are 4 female students for every 3 male students. __:__

We are comparing

female:male

4:3

Answer :

x = -2

-8 + -4 + 12 = 3(-6 + 6)

Im not sure

Answer: Let's represent the cost of one roll of plain wrapping paper as x, and the cost of one roll of holiday wrapping paper as y. We can write two equations based on the information given:

2x + 11y = 208

11x + 9y = 320

We can use these equations to find the values of x and y. Solving the first equation for y:

y = (208 - 2x) / 11

We can substitute this expression for y into the second equation to eliminate y:

11x + 9((208 - 2x) / 11) = 320

11x + 208 - 18x / 11 = 320

11x - 18x / 11 = 320 - 208

-7x / 11 = 112 / 11

-7x = 112

x = -16

So one roll of plain wrapping paper costs -16 dollars, which is not possible. This means there is no solution for this system of equations, and therefore the problem has no solution.

Step-by-step explanation:

The probability of getting: A. a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% and B. a "four of a kind" is 0.00024, or 0.02401%.

A. The probability of getting a five-card hand that has three Jacks and two Queens can be calculated by using the formula:
P(3 Jacks and 2 Queens) = C(4,3) x C(4,2) / C(52,5)
Where C(n,k) is the combination of n items taken k at a time.

= (4 x 6) / 2598960
= 24 / 2598960
= 0.00000923

Therefore, the probability of getting a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% when rounded to six decimal places.

B. The probability of getting a "four of a kind" can be calculated by using the formula:
P(four of a kind) = (C(13,1) x C(4,4) x C(12,1) x C(4,1)) / C(52,5)

= (13 x 1 x 12 x 4) / 2598960

= 624 / 2598960
= 0.00024010

Therefore, the probability of getting a "four of a kind" is 0.00024, or 0.02401% when rounded to five decimal places.

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The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

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

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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The amount in the account after 15 years after round of to the nearest hundredth is $6,671.67, the correct option is B.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We are given that;

The amount earned is A equal to P quantity 1 plus 0.054 over 2 end quantity all raised to the power of 2 times t

Rate of compound interest= 5.4%

Investment= $3000

Time= 15years

Now,

A = 3000(1+0.054/2)^2*15

A = 3000(1+0.054/2)^30

A = $6,671.67

So, amount = principal + interest

Principal = $3,000.00

Interest = $3,671.67

=$6,671.67

Therefore, the compound interest will be $6,671.67

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To find the missing dimension of a cone when the height is 4.2 and the volume is 3.6 cubed is to equate the general formula with the given information.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

To obtain the missing dimension of a cone we must equate the general formula for the volume of a cone to the given information.

Therefore, (1/3)πr²×4.2 = 3.6

(1/3)πr² = 0.86.

r² = 0.86/1.05.

r² = 0.82.

r = 0.9

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The surface area of the rectangular prism is 130ft^2.

The surface area of a rectangular prism can be calculated by finding the area of each of the six faces and then adding them together.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

In this case, the length is 10ft, the width is 1ft, and the height is 5ft. Plugging these values into the formula, we get:

Surface area = 2(10ft)(1ft) + 2(10ft)(5ft) + 2(1ft)(5ft)

Surface area = 20ft^2 + 100ft^2 + 10ft^2

Surface area = 130ft^2

Therefore, the surface area of the rectangular prism is 130ft^2.

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The value of the variable r  when t = 5h and d = 240m is 48m/h

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

They are also made up of mathematical operations like subtraction. division, addition, multiplication, floor division, etc

From the information given, we have the equation;

d = rt

Make 'r' the subject of formula

r = d/t

Now, substitute the values into the equation, we get

r = 240/5

Divide the values

r = 48m/h

Hence, the value is 48m/h

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Answer:

The diameter is 8.3cm.

Step-by-step explanation:

The circumference is the distance all the way around a circle. To find circumference, multiply pi times diameter:

C = pi • d

Fill in given circumference.

26 = pi • d

Divide both sides by pi (you should use a calculator) in this question it doesn't happen to matter if you use a pi button or 3.14 for pi.

26/3.14 = d

8.276057 = d if you use the pi button.

or,

8.28025 = d if you use 3.14

Both of these round to 8.3, since the question asked for one decimal place (1dp)

The diameter is 8.3cm.

The amount of each deposit that Abbie made was $8

The amount of each deposit that Abbie made can be found by dividing the total amount she put into her savings account by the number of deposits she made.

In this case, we can use the formula: Amount of each deposit =

Total amount / Number of deposits

Substituting the given values into the formula, we get:

Amount of each deposit = $40 / 5

Amount of each deposit = $8

Therefore, the amount of each deposit that Abbie made was $8. In conclusion, if Abbie has put $40 into her savings account and has made 5 deposits of the same amount, then the amount of each deposit is $8.

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Answer:

v = 9

Step-by-step explanation:

4v - 18 = 6(v - 6)

1.) Distribute 6 into the parenthesis

4v-18 = 6v - 36

2.) Move 6v to the other side by subtracting from both sides

4v - 6v -18 = -36

3.) Move 18 to the other side by adding 18 on both sides

4v - 6v = 18 + -36

4.) Combine like terms

-2v = -18

5.) Divide -2 on both sides to get v by itself

v = 9

Answer:

the answer is 9

Step-by-step explanation:

4v-18=6(v-6)

4v-18=6v-36

4v-6v= -36+18

-2v= -18

divide both sides by -2

v=9

Answer:

Step-by-step explanation:

x/y=(5/6)/(3/4) = 5/6*4/3 = 10/9

x/y=10/9

y/x=9/10

y=9/10 * x

Second option

Answer:

y=5/8x

Step-by-step explanation:

The 40th customer who gets the t-shirt and water bottle.

If the sporting goods store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.

In finding the LCM, we also use prime factorization, namely multiplying all the factor numbers and if there are the same, take the largest value, if both are the same, then take one of them.

For example, determine the LCM of 30 and 48

30 = 2 x 3 x 5

48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

The LCM of 30 and 48 is 2⁴ x 3 x 5 = 240

The above Question can be solved with the concept of LCM

where the 8th customer gets a T-shirt and the 10th customer gets a water bottle. To find out which customer gets the two gifts, then look for LCM from 8 and 10

LCM(8, 10) =2×2×2×5=40

LCM of 8 and 10 is 40.

So the 40th customer who gets the t-shirt and water bottle.

If the store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.

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The function that models the growth of the Bacillus Megaterium over each generation is B. P (n) = 12 + 2n.

the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given a graph,

The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in set X has exactly one output in set Y. Note: All functions are relations but all relations are not functions.

thus the given graph is a relation but not a function.

Given relation is continuous in the domain.

since the domain of the relation is The set which contains all the first elements of all the ordered pairs of relation R.

the given relation and has x values from -4 to 4 thus, the domain of the relations -4> x> 4.

Therefore, the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.

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The product of the rational expression shown above include the following: B. x² - 36/(x² - 9).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = (x + 6)(x - 6)

Product of numerator = x² + 6x - 6x - 36

Product of numerator = x² - 36

For the denominator, we have the following:

Product of denominator = (x + 3) × (x - 3)

Product of denominator = x² - 3x + 3x - 9

Product of denominator = x² - 9

Therefor, the product of the rational expression is given by x² - 36/(x² - 9).

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The measure of side RS is 7.6 units .

A quadrilateral's interior angles add up to 360 degrees. Two quadrilaterals are said to be identical when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).

The corresponding angles of similar quadrilaterals should be equal in accordance with the similarity of quadrilaterals. Since we know that every angle in a square is 90 degrees, every matching angle in any two squares will be the same.

In the given question ,

Quadrilateral MNOP is similar to quadrilateral QRST .

[tex]\frac{ON}{NM} =\frac{RS}{RQ} \\\\\frac{2}{4} = \frac{RS}{15.2} \\\\\frac{1}{2} =\frac{RS}{15.2} \\\\RS=\frac{15.2}{2} \\\\RS=7.6units[/tex]

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The side lengths form a proportional relationship, and the ratios are as follows:

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

They must have Congruent angle measures.

They have Proportional side lengths.

Here, the triangles are similar, as they have the same angle measures.

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Thus, the side lengths form a proportional relationship, as the equivalent side have a ratio of 1.5.

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The required distance across the lake (LM) is 205 m.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,

As from the figure,

Triangle KLM is similar to triangle KNO so,
KL/KN = LM/NO
180+70/180 = LM/147.6
LM = 205 m

Thus, the required distance across the lake (LM) is 205 m.

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Answer:

Q1. The larger number is 54 and the smaller number is 37.

Q2. The number is 4.

Q3. The three numbers are 7, 8 and 9.

Step-by-step explanation:

Q1.

Let the larger number be x and the smaller number be y.

x+y= 91   (1)

x-y= 17   (2)

From (2) :

x= y+17   (3)

sub (3) into (1) :

y+17+y= 91

2y= 74

y= 37   (4)

sub (4) into (3) :

x= 37+17

 = 54

Q2.

Let the unknown number be x.

2x+16= 24

2x= 8

x= 4

Q3.

Let the smallest number be x.

2nd no. : x+1

3rd no. : x+2

x+(x+2)= (x+1)+8

2x+2= x+9

x= 7

x+1= 8

x+2= 9