Solve each of these equations. Explain or show your reasoning. Reduce all fractions in the lowest terms. Do not convert fractions into decimals.

You'll need to show ALL of your work to receive points.

1. 3b + 9 -5b + 3 = -14 + 6b - 8



2. 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x

Answer:

  27√2 -2√7 ≈ 32.8923

Step-by-step explanation:

Apparently, you want to simplify the expression √(14)*(3 √(7) + √(32) - √(28) + 2 √(2)).

  (√a)(√b) = √(ab)

  √(a²b) = a√b

  [tex]\sqrt{14}\cdot3\sqrt{7}+\sqrt{32}-\sqrt{28}+2\sqrt{2}\\\\=3\sqrt{14\cdot7}+\sqrt{4^2\cdot2}-\sqrt{2^2\cdot7}+2\sqrt{2}\\\\=3\sqrt{7^2\cdot2}+4\sqrt{2}-2\sqrt{7}+2\sqrt{2}=(3\cdot7+4+2)\sqrt{2}-2\sqrt{7}\\\\=\boxed{27\sqrt{2}-2\sqrt{7}}[/tex]

Question:

4 unit squares each have 5/7 of their area shaded. What is the total area that is shaded?

The total area that is shaded=20/7  unit squares

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

The total area= 4*(5/7)=20/7

This cannot be simplified any more than it is

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x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6 or in interval notation [-9,6]

To find out what are the steps in solving the below inequality:

Given equation is 2x - 3 > 15

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

−15≤2x-3≤15

First, subtract 3  from each segment of the system of equations to isolate the x term while keeping the system balanced:

−15−3≤2x-3−3≤15−3

−18≤2x-6≤12

−18≤2x-6≤12

Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:

[tex]-\frac{18}{2}\leq \frac{2x}{2} \leq \frac{12}{2}[/tex]

-9 [tex]\leq[/tex] x [tex]\leq[/tex] 6

or

x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6

or in interval notation [-9,6]

on the horizontal axis.

The lines will be a solid line because the inequality operators contain "or equal to" clauses.

We will shade between the lines to show the interval:

Hence the steps to solve an inequality has been show

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Answer: 9 hours

Step-by-step explanation:

Amount of money/ amount of hours worked
154/11 = 14

$14 made per hour, so $126 divide by 14 would equal to how many hours worked to have a same rate of $14 per hour.

126/14 = 9

Answer:

D 1/15 or 2/30

Step-by-step explanation:

Just make sure your subtracting and making sure that the answer choices don't throw you off, reduce all of the answers

Answer:

2/30

Step-by-step explanation:

4/6-3/5

We have to find common denominator

30 is a common factor so we change both fractions to have a denominator of 30

4x5/6x5-3x6/5x6

20/30-18/30

Now we subtract numerators and keep denominators the same

2/30

Hopes this helps please mark brainliest

Step-by-step explanation:

X = 51. Parallel line angle rules, alternate angle is equal.

Straight angle is 180

Right angle is 90

Y = 180 - 51 - 90 = 39

Z = Y = 39. Parallel line angle rules, alternate angle is equal.

Answer:

<3, < 6, <7 are all 102,

<1, <4, <5 and <8 are all 78

Step-by-step explanation:

If you slide angles 1, 102, 3 qnd 4 down along p, they will fit perfectly over 5,6,7 and 8.  So if you find the top four angles, you have found the bottom 4 angles.

<3 is a vertical angle to 102 and vertical angles always have the same measurement.

Angles 1 and 4 are supplemental to 102.  That means that the two angles will add to 180.  180 - 102 = 78

Answer

the one on the bottom left

Step-by-step explanation:

The equation of the line in point slope form is (c) y - 6 = -2(x + 2)

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (2, -2) and (-2, 6)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2, -2) and (-2, 6)

Substitute the known values in the above equation

So, we have the following equation

m = (6 + 2)/(-2 - 2)

Evaluate

m = -2

The equation of a line can be represented as

y  - Y = m(x - X)

Where

Slope = m = -2

(X, Y) = (-2, 6)

So, we have

y - 6 = -2(x + 2)

Hence, the line has an equation of y - 6 = -2(x + 2)

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The goal of a confidence interval is to provide a range of values that are reasonable for the parameter of interest. So the correct option is (A).

The goal of a confidence interval is to provide a range of values that is reasonable for the parameter of interest. The confidence interval is based on the sample data and the level of confidence. The level of confidence is the probability that the confidence interval contains the true value of the parameter.

The confidence interval is calculated using the sample mean, the sample standard deviation, and the level of confidence. The confidence interval is calculated by adding and subtracting the margin of error from the sample mean. The margin of error is the product of the critical value and the standard error. The critical value is based on the level of confidence. The standard error is the standard deviation of the sampling distribution.

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Answer:

C. five samples.

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

It intercepts the y at 2 and x at -3

Answer:

W.

Step-by-step explanation:

The y-intercept of 2 can be found on the vertical line ( up and down ) and the x-intercept of -3 can be found on the horizontal line ( left to right )

Therefore the answer would be graph W.

Answer:

A

Step-by-step explanation:

Answer:1=translation, 2= translation, 3=rotation, 4= reflection

Step-by-step explanation:

Answer: [tex]4\frac{2}{3} in;[/tex]  [tex]5\frac{2}{3} in;[/tex]  [tex]6\frac{2}{3} in[/tex]

1. The measure of angle H is 79 degrees

2. The measure of angle G is 54 degrees

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

1. Given is isosceles triangle

∠H=∠O = x

sum of all interior angles of a triangle= 180 degrees

22+x+x=180

2x+22=180

2x=158

x=158/2=79

So, ∠H=79

2. Given is isosceles triangle

∠D=∠O = 63

Let ∠G=x

sum of all interior angles of a triangle= 180 degrees

63+63+x=180

x+126=180

x=180-126=54

So, ∠G=54

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Answer:

no se Perdóname

Answer:

since 1 mile charge is $2.40

Then 12.45 miles is

2.40×12.45

=$29.88

Based on the calculation below, the number of years the person must leave the money in the bank until it reaches 6500 dollars is 4.3 years.

This can be calculated using the formula for calculating the future value (FV) as follows:

FV = PV(1 + r)^n ......................... (1)

Where:

FV = future value or the amount in the bank after certain years = 6500

PV = present value or the amount invested = 5000

r = quarterly interest rate = 6.25% / 4 = 0.0625 / 4 = 0.015625

n = number of quarters

Substituting relevant values into equation (1) and solve for n, we have:

6500 = 5000(1 + 0.015625)^n

6500 / 5000 = 1.015625^n

1.3 = 1.015625^n

Log linearize both sides, we have:

log1.3 = n * log1.015625

0.1139 = n0.0067

n = 0.1139 / 0.0067

n = 17 quarters

Number of years the money must be in the bank = n / number of quarters in a year = 17 / 4 = 4.25 years

To the nearest tenth of a year, we have:

Number of years the money must be in the bank = 4.3 years

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Answer:

Its actually 4.2

Step-by-step explanation:

saw it on delta

I can help you!

Answer:

1) b = 17/4

2) x = -3/5

Step-by-step explanation (question one):

Step 1: Simplify both sides of the equation.

3b +9 + −5b + 3 = −14 +6b +−8

(3b +−5b) +(9 +3)=(6b) +(−14 + −8) (Combine Like Terms)

−2b +12 = 6b −22

Step 2: Subtract 6b from both sides.

−2b +12 −6b = 6b −22 −6b

−8b +12 = −22

Step 3: Subtract 12 from both sides.

−8b +12 −12 = −22 −12

−8b = −34

Step 4: Divide both sides by -8.

(-8b/-8) = (-34/-8)

Step 5: Get your Answer

b = 17/4

Step-by-step explanation (question two):

Step 1: Simplify both sides of the equation.

2x +5 + −4x +8 = (5)(5) +(5)(6x) + −12x (Distribute)

2x +5 + −4x +8 = 25 +30x + −12x

(2x+−4x) + (5+8) = (30x +−12x) +(25) (Combine Like Terms)

−2x +13 = 18x +25

Step 2: Subtract 18x from both sides.

−2x +13 −18x= 18x +25 −18x

−20x +13 = 25

Step 3: Subtract 13 from both sides.

−20x +13 −13 = 25 −13

−20x=12

Step 4: Divide both sides by -20.

(-20x/-20) = (12/-20)

Step 5: Get your Answer

x = -3/5

Hope this helped you, good luck with your homework!

The angles formed between the parallel lines a and b and their common transversal are; on line a; 1,2,3,4. On line b; 5,6,7,8,

A two column table can be used to prove m∠1 = m∠5 with the correct options underlined as follows;

Statements                         [tex]{}[/tex]                                 Reasons

1. a ║ b                                 [tex]{}[/tex]              1. Given

2. m∠1 + m∠3 = 180°               [tex]{}[/tex]          2. (Linear pair Theorem)

3. m∠5 + m∠6 = 180°               [tex]{}[/tex]         3. (Linear pair Theorem)

4. m∠1 + m∠3 = m∠5 + m∠6             [tex]{}[/tex]4. (Substitution property of equality)

5. m∠3 = m∠6             [tex]{}[/tex]                       5. (Alternate interior angles)

6. m∠1 = m∠5             [tex]{}[/tex]                        6. (Subtraction Property of Equality)

Parallel lines are lines on the same plane that do not intersect or have a common point as they extend indefinitely in both directions.

The theorems and properties used to prove that the angles m∠1 = m∠5 are as follows

Linear pair theorem;

The linear pair theorem states that two angles that together form a linear pair are supplementary angles (Add up to 180°)

Substitution property of equality;

The substitution property of equality states that if two variables have the same value, then one variable can replace the other variable in equations and expressions without changing their value.

Subtraction property of equality

The subtraction property of equality states that when the same quantity is subtracted from two equal expressions, the values of the new expressions will also remain equivalent

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Answer:

Step-by-step explanation:

first of all the graph is shifted up by 1 then we should add 1 to the function we have.

after that its obvious that the function is sine because if we remove the 1 we add it then it will be 0 when the angle is 0.

the function we have now is y = 1 + sin(ax).

to know the value of a we choose an angle we already know its sine for example:

2 = 1 + sin(a * 1/8)

1 = sin(a * 1/8)

sin-1(1) = PI/2 = a*1/8 => PI = 180

a = 4 * PI

at the end we will have => y = 1 + sin(4PI * x).

Answer:

yes, by x=-1, y=0

Step-by-step explanation:

y=-4x-4

y=2x+2

-4x-4=2x+2

6x=-6

x=-1

y=0

Answer:

Bottom left option is correct.

Step-by-step explanation:

Now we have to find,

→ the table represents y as function of x.

Then the table will be,

→ | x || y |

| -1 || -1 |

| 0 || -1 |

| 2 || 0 |

| 3 || 2 |

(Because the values of x is not repeated)

Hence, bottom left option is correct.

Table number three represents y as a function of x.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

The data in table number 3,

x     y

-1     -1

0     -1

2     0

3     2

The above table has different values of input and the other tables have different values of output at the same value as the input which is not possible.

Therefore, table number three represents y as a function of x.

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the perimeter of the composite figure is 20cm and its area is 37cm².

what is perimeter  ?

Perimeter is the total length of the boundary of a two-dimensional shape or figure. In other words, it is the distance around the outside of a shape. To find the perimeter of a shape, you simply add up the lengths of all its sides.

In the given question,

To find the perimeter of the composite figure, we need to add up the lengths of all the sides.

Starting from the left side of the figure, we have a vertical line segment of length 6cm, followed by a horizontal line segment of length 5cm, then another vertical line segment of length 2cm, followed by a slanted line segment of length 3cm, then another horizontal line segment of length 2cm, and finally, a vertical line segment of length 2cm.

So the perimeter of the composite figure is:

Perimeter = 6cm + 5cm + 2cm + 3cm + 2cm + 2cm

Perimeter = 20cm

To find the area of the composite figure, we can break it down into simpler shapes and add up their areas.

The composite figure can be split into two rectangles, one with dimensions 6cm x 5cm and the other with dimensions 2cm x 2cm, and a right triangle with base 3cm and height 2cm.

The area of the first rectangle is:

Area = length x width

Area = 6cm x 5cm

Area = 30cm²

The area of the second rectangle is:

Area = length x width

Area = 2cm x 2cm

Area = 4cm²

The area of the right triangle is:

Area = (base x height) / 2

Area = (3cm x 2cm) / 2

Area = 3cm²

Therefore, the total area of the composite figure is:

Area = 30cm² + 4cm² + 3cm²

Area = 37cm²

So the perimeter of the composite figure is 20cm and its area is 37cm².

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Answer:

6 deliveries in 1 hour

Step-by-step explanation:

18 / 3 = 6

The line is dashed with a y-intercept at (0,-2) and slope of -3/2 which is a correct option(C)

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

-3x - 2y <6

Let's consider an equation of a line,

-3x-2y = 6

-2y = 3x + 6

y = -3/2x - 3

So, slope = -3/2

Substitute y =0 in the equation of a line

So, y-intercept at (0,-2)

Due to Inequality, the graphical representation of the line is a dashed line.

Hence, the line is dashed with a y-intercept at (0,-2) and a slope of -3/2

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The events that have probability of exactly three-fourths are

(a) not picking a square  ,

(d) picking shape that has only straight edges ,

(e) not picking a circle   .

In the question ,

it is given that ,

there are 2 circles , 4 triangles , 2 squares .

(a) probability of not picking a square = ( circles + triangles )/total

= 6/8 = 3/4

(b) probability of picking a square = number of square / total figure

= 2/8 = 1/4

(c) probability of picking up a triangle = 4/8 = 1/2

(d) probability of picking up shape with straight edge = ( triangle + square) / total

= 6/8 = 3/4

(e) probability of not picking a circle = ( triangle + square) / total

= 6/8 = 3/4 .

Therefore , The events that have probability of exactly three-fourths are

(a) not picking a square  ,

(d) picking the shape that has only straight edges ,

(e) not picking a circle   .

The given question is incomplete , the complete question is

A shape is picked at random from the group of 2 circles, 4 triangles, and 2 squares .

Which event has a theoretical probability of exactly Three-fourths? Select three options.

(a) not picking a square

(b) picking a square

(c) picking a triangle

(d) picking shape that has only straight edges

(e) not picking a circle

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Using cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.

The given equation is -

[tex]\frac{z}{-12}=-5[/tex]

We have to solve this equation.

Now,

[tex]\frac{z}{-12}=-5\\[/tex]

We have to use cross multiplication method to solve the given equation.

[tex]\frac{z}{-12}=-5\\\\= > z= (-5) (-12)\\= > z = 60[/tex]

Thus, by solving through cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.

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