a rectangle is drawn so the width is 49 inches longer than the height. if the rectangle's diagonal measurement is 61 inches, find the height.

The length of the rectangle is 7y - 3

What is a Rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. The area of  a rectangle A = L×W

Where,

A = Area of the rectangle which is 7y^2 - 3y

L = Length  which is unknown

W = Width of the rectangle which is y

Substituting,

7y^2 - 3y = L × y

divide through by y

(7y^2 - 3y)/y = L

L = 7y - 3

Therefore the length of the rectangle is 7y - 3

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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 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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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:

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

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The rate of change between (1,5) and (-5,1) is 0.

What is the rate of change?

The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).

Let (x,y)=(1,5), (m,n)=(-5,1)

Rate of change=(n-y)/(m-x)=(-5-(5))/(1-1)=0.

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Answer:

C. five samples.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

-1/5 j + 3/4 - 5/2 j - 7/8 =

= (-2-25)/10 j + (6-7)/8 =

= -27/10 j - 1/8

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

For the given graph, the gradient of the given blue line in the graph is equal to 2.

As given in the question,

For the given graph,

Consider two pairs of coordinates on the blue line of the given graph,

( x₁ , y₁ ) = ( 2, 2 )

( x₂ , y₂ ) = ( 3, 4 )

Gradient is nothing but slope of the line

Formula to calculate the gradient of the given blue line of the graph is given by:

Gradient = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Gradient = ( 4 - 2 ) / ( 3 - 2 )

              = 2 / 1

              = 2

Therefore, for the given graph, the gradient of the given blue line in the graph is equal to 2.

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"95% confidence interval" means that there is a 95% chance that the true fraction falls within the computed confidence interval.

Confidence Intervals: Confidence intervals are the range of estimates for unknown parameters.

Confidence intervals are more than just a range of estimated values. It also tells you how stable the estimates are. A stable estimate is an estimate that has approximately the same value if the study is repeated. An unstable estimate is one that would vary from one sample to another.

The confidence interval determines the range that one can be certain that contains the true mean of the population.

This means that, The 95% confidence means, there is a 95% chance that the true proportion will be in the calculated confidence interval or 95 percent confidence interval, you have a 5 percent chance of being wrong.

Hence, the true statement that represents "95% confidence interval" is chance of true fraction of sucess.

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Answer: $3.75

Step-by-step explanation:

Answer:

The cost of 6 cans of soup is 3.75

Step-by-step explanation:

12 = 7.50

1 can = x

12x = 7.50

We need to find the cost of 1 can. So we divide 7.50 by 12.

x = 0.625

Then multiply by 6.

0.625 x 6 = 3.75

As a result the cost of 6 cans of sup is $3.75

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

Step-by-step explanation:

Answer:

6 deliveries in 1 hour

Step-by-step explanation:

18 / 3 = 6

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).

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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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

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:

no se Perdóname

Answer:

since 1 mile charge is $2.40

Then 12.45 miles is

2.40×12.45

=$29.88

By solving a linear equation, we will see that the value of the greater integer is 12.

Let's define x as the smaller integer, then the greater integer is:

x + 2

(is +2 because is the next consecutive even integer)

We know the sum of an integer and 4 times the next consecutive even integer is 58.

So we can write the linear equation:

x + 4*(x + 2) = 58

x + 4x + 8 = 58

5x = 58 - 8

5x = 50

x = 50/5

x = 10

Then the greater integer is x + 2 = 10 + 2 = 12

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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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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:

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 number of unit cubes it would take to completely fill the prism with no gaps between unit cubes is 72

From the question, we are to determine how many unit cubes it would take to completely fill the prism with no gaps between unit cubes.

To do this, we will calculate the volume of rectangular prism

Assuming each cube is 1 cubic unit

Then,

From the top view,

The length of the rectangular prism = 9 units

The width of the rectangular prism = 2 units

From the Right-side view,

The height of the rectangular prism = 4 units

Thus,

The volume of the rectangular prism = 9 × 2 × 4

Volume of the rectangular prism = 72 cubic units

Now,

Number of cubes required to fill the rectangular prism = Volume of the prism / Volume of the cubes

Number of cubes required to fill the rectangular prims = 72 / 1

Number of cubes required to fill the rectangular prims = 72

Hence, the number of unit cubes it would take is 72

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Answer

the one on the bottom left

Step-by-step explanation:

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:

  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]