Decide if each statement about the expressions is true or false for each statement.
a. 6(-b+8) and 2(-3b + 4) are equivalent
expressions.
b. -8h-3.5 and -0.5(16h - 7) are equivalent
expressions.
c. -9(k-5+ 2k - 8) and -27k + 117 are
equivalent expressions.
d. (36m +12) and 12m + 4 are equivalent
expressions.
True False
O
Il cholves bold hitems

The number of 2/3 parts in the number 4 will be 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number of 2/3 parts in the number 4. Then the expression is given as,

⇒ 4 ÷ (2/3)

⇒ 4 x (3/2)

⇒ 2 x 3

⇒ 6

The number of 2/3 parts in the number 4 will be 6.

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The gray squirrel population t years after introduction is P(t) = [tex]340 x 2^(t/9).[/tex]

The formula for the gray squirrel population, p, t years after the introduction of the population is [tex]P(t) = P0 x 2^(t/9)[/tex], where P0 is the initial population. We can use this formula to answer both (a) and (b). For (a), we can substitute t = 0 and P(t) = 680, to solve for P0. This gives us that the initial population of gray squirrels was 340. For (b), we can substitute t = 27 (the number of years since introduction) and P(t) = 680, to solve for P(27). This gives us that the expected population of gray squirrels t years after introduction is 1360. Therefore, the formula for the gray squirrel population t years after introduction is [tex]P(t) = 340 x 2^(t/9)[/tex].

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The cost per square inch is $0.16 per square inches ( nearest hundredth)

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

The area of a circular pie = πr²

= 3.14 × (10/2)² since r = d/2

= 3.14 × 5²

= 78.5 square inches

apple pies are sold for a cost of $12.85

Therefore the cost per square inches

= 12.85/78.5

= $0.16(nearest hundredth) per square inches

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The given polygons WXYZ and PQRS are similar.

Similar figures are those figures which are having the same shape, but the sizes are different.

Since the shape of similar figures are same, the corresponding angles of the figures will be equal.

And the corresponding sides will be proportional.

From the polygons WXYZ and PQRS, given,

∠X = ∠Q

∠W = ∠P

∠Y = ∠R

∠Z = ∠S

So the figures are similar.

WX / PQ = XY / QR = YZ / RS = WZ / PS

Hence the given figures are similar.

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Miguel finish an 800-meter race first.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Miguel ran 80 meters in 20 seconds while Trina ran 40 meters in 15 seconds.

Hence, The speed of Miguel is,

⇒ Speed = Distance / Time

⇒ Speed = 80 / 20

⇒ Speed = 4 m/s

And, The speed of Trina is,

⇒ Speed = Distance / Time

⇒ Speed = 40/15

⇒ Speed = 2.67 m/s

Cleary, The speed of Miguel is faster than Trina.

Hence, Miguel finish an 800-meter race first.

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The equation of the graphed line is y = 1/2 x + 6

The general formula for the equation of a graphed line is expressed with the formula;

y = mx + c

Where the parameters are;

From the diagram shown, the values are;

(0, 6) and (2. 7)

The intercept is 6

The slope is expressed as; y₂ - y₁/x₂ - x₁

Substitute the values

Slope, m = 7 - 6/2 - 0

Slope, m = 1/2

Then, the equation is

y = 1/2 x + 6

Hence, the equation is y = 1/2x + 6

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The graph of the linear function y = -1/3x + 8 is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is defined as follows:

y = -x/3 + 8.

Meaning that:

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Answer:

Kendall must have 5 dimes in her pocket.

Step-by-step explanation:

First, let's write down all the information that is given to us:

q = number of quarters   ["q, the number quarters"]

d = number of dimes     ["d, the number of dimes"]

q = 4     ["Kendall has 4 quarters in her pocket"]

25q + 10d = 150

Since the value of q is given to us, our equation now has one unknown variable, d, and we can solve for it.

25q + 10d =      150 [Plug in q]

25(4) + 10d =      150 [Simplify]

100 + 10d =      150 [Subtract 100 from both sides]

10d = 50     [Divide both sides by 10]

d = 5

So, since d=5, Kendall must have 5 dimes in her pocket.

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Answer:B

Step-by-step explanation:

If you simplify 3/6 you will get 1/2

Answer:

(3.369, 4.071)

Step-by-step explanation:

The solution is Option B.

The pressure at the ocean's surface is given by the equation A = 14.7 pounds per square inches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

P = 14.7 + ( f/22.5 )   be equation (1)

where P is the total pressure in pounds per inch²

And , f is the height in feet below the ocean's surface

Now , pressure at the ocean's surface is when f = 0

Substitute the value of f = 0 in equation (1) , we get

P = 14.7 + ( 0/22.5 )

On simplifying the equation , we get

P = 14.7 pounds/inch²

Hence , the equation is P = 14.7 pounds/inch²

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The amount of money Gabriela paid for the pair of glasses after the discount is $50.4

Regular price of the pair of glasses= $72

Percentage discount= 30%

Amount Gabriela actually paid= Regular price of the pair of glasses - (Percentage discount of Regular price of the pair of glasses)

= 72 - (30% × 72)

= 72 - (0.3 × 72)

= 72 - 21.6

= $50.4

Therefore, Gabriela paid $50.4 for the pair of glasses after deducting discount.

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Answer:

  a.  one solution (x = -8)

Step-by-step explanation:

You want to know how many solutions there are for the equation 2x -48 = 8x.

This is a 2-step linear equation.

Step 1: subtract 2x from both sides.

  -48 = 6x

Step 2: divide by the coefficient of x.

  -48/6 = -8 = x

There is one solution: x = -8.

__

Additional comment

When x terms are on both sides of the equal sign, there will be one solution if their coefficients are different.

If the coefficients are the same, the number of solutions may be 0 or infinite, depending on the constant value(s).

The solution is, Their rate of change is respectively 0.5.

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The slope-intercept form of the equation of a straight line is:

y=mx+c

where, m= rate of change.

From the given equations, the two that have the same rate of change are:

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

Their rate of change is respectively 0.5.

The correct choices are A and D.

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The probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

The probability of selecting exactly one defective calculator out of the 6 sent to the local high school can be calculated using the binomial probability formula. The binomial probability formula is [tex]P(x) = nCx * p^x * q^(n-x)[/tex]. For this problem, n = 6 (the number of calculators sent to the local high school), x = 1 (the number of defective calculators selected), p = 4/12 (the probability of selecting a defective calculator from the shipment of 12 calculators), and q = 8/12 (the probability of selecting a non-defective calculator from the shipment of 12 calculators). Plugging these values into the formula gives [tex]P(x) = 6C1 * 4/12^1 * 8/12^5[/tex], which simplifies to 0.29166. This means that the probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

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Answer:

y=1 x=5

Step-by-step explanation:

from the second equation

x=5y

then,when we substitute the equation

4(5y)+3y=23

20y+3y=23

23y=23

y=1

if and only if,x=5y and y=1

then x=5

Answer:

the answer is in the picture.. if you have any questions feel free to ask

Based on the provided lines and angles;

Let's discuss each problem we have:

Problem 2: Parallel lines m and n are cut by transversal l

Statement A: ∠1 = ∠5 is correct because both are corresponding angles and congruent.

Statement B: ∠2 = ∠4 is correct because both are vertical angles and congruent

Statement C: ∠2 = ∠7 is incorrect because ∠7 is the corresponding angle of ∠3 which is the supplementary angle of ∠2

Statement D: ∠3 and ∠6 form a linear pair is correct because both are consecutive interior angles and supplementary

Statement E: ∠4 and ∠5 are supplementary is correct because both are consecutive interior angles.

Problem 3: Parallel lines a and b are cut by transversal c and d

∠1 = 115°

∠8 = 105°

∠5 is adjacent and the supplementary angle of ∠8, then:

∠5 + ∠8 = 180°

∠5 + 105° = 180°

∠5 = 75°

∠11 is the alternate exterior angle of ∠5 and both are congruent, then:

∠11 = ∠5 = 75°

∠16 is the corresponding angle of ∠4 and congruent. ∠4 is the adjacent and supplementary of ∠1, then:

∠16 = ∠4

∠4 + ∠1 = 180°

∠16 + ∠1 = 180°

∠16 + 115° = 180°

∠16 = 65°

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The values of the probabilities are 4/7, 2/7 and 5/7

p(the trip will take 25 minutes)

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

25 minutes = 8

Total = 14

So, we have

P(25 minutes) = 8/14 = 4/7

p(the trip will take 20 minutes)

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

20 minutes = 4

Total = 14

So, we have

P(20 minutes) = 4/14 = 2/7

p(the trip will take atleast 25 minutes)

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

At least 25 minutes = 8 + 2 = 10

Total = 14

So, we have

P(At least 25 minutes) = 10/14 = 5/7

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1 Let's call the two numbers x and y. According to the ratio, x:y = 8:9, so y = (9/8)x. And since their sum is 136, x + y = 136, so we can substitute y = (9/8)x into this equation:

x + (9/8)x = 136

(17/8)x = 136

x = 64

So the two numbers are 64 and 72.

2 Let's call the three numbers x, y, and z. According to the ratio, x:y:z = 3:2:7, so y = (2/3)x and z = (7/3)x. And since their sum is 108, x + y + z = 108, so we can substitute y = (2/3)x and z = (7/3)x into this equation:

x + (2/3)x + (7/3)x = 108

(12/3)x = 108

x = 36

So the three numbers are 36, 24, and 84.

3 Let's call the four numbers a, b, c, and d. According to the ratio, a:b:c:d = 5:6:7:8, so b = (6/5)a, c = (7/5)a, and d = (8/5)a. And since the greatest of these is 24, d = 24, so we can substitute c = (7/5)a and d = (8/5)a into this equation:

a + (6/5)a + (7/5)a + (8/5)a = 24

(27/5)a = 24

a = 24 * 5/27 = 8

So the four numbers are 8, 9.6, 10.4, and 24. And the sum of these numbers is 8 + 9.6 + 10.4 + 24 = 52

4 Let's call the three heirs' land area x, y, and z. Since the eldest heir received three times as much as the youngest child, who received two times as much as the middle child, we can write the equation:

x = 3y and y = 2z

So we can substitute y = 2z into x = 3y to get:

x = 3 * 2z = 6z

And since the middle child received 12 ha of land, we can substitute z = 12 into x = 6z to get:

x = 6 * 12 = 72

So the total area of land they inherited is x + y + z = 72 + 2 * 12 = 96 ha.

5 Let's call the two numbers x and y. According to the ratio, x:y = 4:5, so y = (5/4)x. And since their sum is 108, x + y = 108, so we can substitute y = (5/4)x into this equation:

x + (5/4)x = 108

(9/4)x = 108

x = 36

So the two numbers are 36 and 45.

6 Let's call the three numbers x, y, and z. Then, we have:

x:y:z = 6:7:8

x + y + z = 63

To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:

x = 6t

y = 7t

z = 8t

We can use the second equation to solve for t:

6t + 7t + 8t = 63

21t = 63

t = 3

So, the three numbers are:

x = 6t = 6 * 3 = 18

y = 7t = 7 * 3 = 21

z = 8t = 8 * 3 = 24

7 Let's call the three numbers a, b, and c. Then, we have:

a:b:c = 2:3:5

a = 48 (the least of these)

To find the values of b and c, we can use the first ratio to write b and c as multiples of a:

b = 3a = 3 * 48 = 144

c = 5a = 5 * 48 = 240

8 Let's call the three numbers p, q, and r. Then, we have:

p:q:r = 3:5:7

r = 75 (the greatest of these)

To find the values of p and q, we can use the first ratio to write p and q as multiples of r:

p = 3r/5 = 3 * 75/5 = 45

q = 5r/7 = 5 * 75/7 = 50

9 Let's call the number of male students m and the number of female students f. Then, we have:

m:f = 2:3

m + f = 50

To find the values of m and f, we can use the first ratio to write m and f as multiples of the same number. Let's call that number t:

m = 2t

f = 3t

We can use the second equation to solve for t:

2t + 3t = 50

5t = 50

t = 10

So, the number of male students is:

m = 2t = 2 * 10 = 20

And the number of female students is:

f = 3t = 3 * 10 = 30

10 Let's call the number of stamps that Cherie has x, the number of stamps that Mona has y, and the number of stamps that Kate has z. Then, we have:

x:y:z = 3:4:5

x + y + z = 360

To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:

x = 3t

y = 4t

z = 5t

We can use the second equation to solve for t:

3t + 4t + 5t = 360

12t = 360

t = 30

So, Cherie has:

x = 3t = 3 * 30 = 90 stamps

Mona has:

y = 4t = 4 * 30 = 120 stamps

Kate has:

z = 5t = 5 * 30 = 150 stamps

11 The marbles are divided in the ratio 1:2:2:3, so there are 2 x 2 = 4 times as many yellow and blue marbles as there are red marbles. Therefore, there are 2 + 2 = 4 red marbles. Hence, there are 4 x 2 = 8 yellow and blue marbles. Furthermore, there are 3 times as many green marbles as there are red marbles, meaning there are 3 x 4 = 12 green marbles. Therefore, the total number of yellow and green marbles is 8 + 12 = 20.

12 According to the ratio, there are 6:5:2:3 of fiction to nonfiction to general reference to children's books. So the number of each category can be calculated as follows:

Fiction: 6/16 x 80 = 30 books

Nonfiction: 5/16 x 80 = 25 books

General reference: 2/16 x 80 = 10 books

Children's books: 3/16 x 80 = 15 books

So, there are 15 - 10 = 5 more children's books than general reference books.

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Answer:

Step-by-step explanation:

the total perimeter is 33 so all of the sides are equal to it.

33=3x+13+12

then combine like terms

33=3x+25

subtract from each side

(33)-25=(3x+25)-25

8=3x

divide by 3

x=2  2/3

Answer:

Timmy has been working at Monster Burger longer than Susie, which explains why he earns more money. Monster Burger employees are given a 50 cent raise each year, so Susie's salary will likely increase over time as she continues to work there.

Step-by-step explanation:

It is possible to determine how long Susie has been working at Monster Burger by using the information given. Since Timmy makes 720 dollars working 40 hours and Susie makes 600 dollars working the same hours, we can calculate their hourly wages:

Timmy's hourly wage: 720 / 40 = 18 dollars

Susie's hourly wage: 600 / 40 = 15 dollars

Since Monster Burger employees are given a 50 cent raise a year, this means that Susie's hourly wage has increased by 50 cents * x years, where x is the number of years Susie has been working there. Thus, we have:

15 + (0.50 * x) = 18

Solving for x, we get:

x = (18 - 15) / 0.50 = 6 years

Therefore, Susie has been working at Monster Burger for 6 years.

Answer: 101/20, 5 1/11, 5.57, 5.576

Step-by-step explanation:

I hope this is correct :D

Step-by-step explanation:

a)

-sin(2x) = cos(2x)

sin(2x) = cos(2x)

2sin(x)cos(x) = cos(2x)

2sin(x)cos(x) = 1 or -1

sin(x) = +/-√(1/2) or sin(x) = 0

x = (2n+1)π/4 or x = nπ

b)

3 tan(x) = 2 sin(2x)

tan(x) = 2/3 sin(2x)

sin(2x) = 3 tan(x)/2

cos^2(x) = (1 - sin^2(x)) = (1 - (3 tan(x)/2)^2)/4

x = nπ/2 + arctan(2√(2)/3) or x = nπ/2 + arctan(-2√(2)/3)

c)

sec(x) cos(3x) = 0

cos(x) = 0 or cos(3x) = 0

x = nπ/2 or x = (3n+1)π/6

d)

1 - cos(x) = 2 - 2sin^2(x)

cos(x) = 2sin^2(x) - 1

2sin^2(x) = cos(x) + 1

sin^2(x) = (cos(x) + 1)/2

sin(x) = +/- √((cos(x) + 1)/2)

e)

4cos^4(x) - 5cos^2(x) + 1 = 0

cos^2(x) = (1 ± √(5))/2

x = arccos(±√((1 + √(5))/2)) or x = arccos(±√((1 - √(5))/2))

Note: n is any integer in the given domain.

Step-by-step explanation:

false.

3x + 6x is equivalent to 9x

but not 3x + 6. 6 is a constant added term. not a multiplication factor. so, it cannot be combined with a multiplication factor.

but 3x + 6 = 9x

has one solution, one value of x for which this equation is true :

3x + 6 = 9x

6 = 6x

x = 1

so, for x = 1 (and only for x = 1) this is true. for any other value of x this is false.

therefore, the general equivalent statement is false.