Jacob is playing miniature golf. He states that he cannot hit the ball from the start, bounce it off the back wall once, and reach the hole in one shot. Is Jacob correct? Label the diagram to support your answer.

Answer:

Find the Slope from a Graph

Identify rise and run from a graph

Distinguish between graphs of lines with negative and positive slopes

Find the Slope from Two Points

Use the formula for slope to define the slope of a line through two points

Find the Slope of Horizontal and Vertical Lines

Find the slope of the lines

x

=

a

and

y

=

b

Recognize that horizontal lines have slope = 0

Recognize that vertical lines have slopes that are undefined

Identify slopes of parallel and perpendicular lines

Given a line, identify the slope of another line that is parallel to it

Given a line, identify the slope of another line that is perpendicular to it

Interpret slope in equations and graphs

Verify the slope of a linear equation given a dataset

Interpret the slope of a linear equation as it applies to a real situation

Identify slope from a graph

The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:

You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Let’s look at an example.

EXAMPLE

Use the graph to find the slope of the line.

A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.

Show Solution

This line will have a slope of

1

2

no matter which two points you pick on the line. Try measuring the slope from the origin,

(

0

,

0

)

, to the point

(

6

,

3

)

. You will find that the

rise

=

3

and the

run

=

6

. The slope is

rise

run

=

3

6

=

1

2

. It is the same!

Let’s look at another example.

EXAMPLE

Use the graph to find the slope of the two lines.

A graph showing two lines with their rise and run. The first line is drawn through the points (-2,1) and (-1,5). The rise goes up from the point (-2,1) to join with the run line that goes right to the point (-1,5). The second line is drawn through the points (-1,-2) and (3,-1). The rise goes up from the point (-1,-2) to join with the run to go right to the point (3,-1).

Show Solution

When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line,

1

4

. The greater the slope, the steeper the li

Step-by-step explanation:

The angle of ∠FEG is 58 degrees

The angle DEF is a right angle.

Therefore,

∠DEF = 90°

Hence,

∠FEG + ∠GED = ∠DEF

∠FEG  = 5x - 22

∠GED = 2x

∠DEF = 5x - 22 + 2x

90 = 5x + 2x - 22

90  = 7x - 22

90 + 22 = 7x

112 = 7x

divide both sides by 7

x = 112 / 7

x = 16

∠FEG  = 5x - 22

∠FEG  = 5(16) - 22

∠FEG  = 80 - 22

∠FEG  = 58°

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The simplified expression of  -6√150 is -150√6

The expression is given as

-6√150

Express 150 as 25 * 6

So, we have

-6√150 =  -6√(150 * 6)

Take the square root of 25

So, we have

-6√150 =  -6 * 25√6

Evaluate the product

-6√150 =  -150√6

Hence, the simplified expression of  -6√150 is -150√6

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The given expression can be solved by determining the product of irrational numbers.  

Irrational number is a real number that cannot be expressed as the quotient of two integers. If a square root of a number is not a perfect square root, then it is an irrational number.  

In the given expression, there are two rational numbers 7 and 3 while two irrational numbers √7 and √7.

The integer 7 and 3 can be multiplied. Hence,

7√7*3√7=7*3*√7*√7=21*√7*√7

When multiplying terms in square root, √a*√b=√ab. Hence,

21*√7*√7=21√7*7

As square root of a number is the number multiplying itself i.e., √a*a=a

21√7*7= 21*7=147

The product of the expression 7√7.3√7 is 147

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No Extraneous solution

The given equation is

  ( 7x + 6 ) ^ 1/2 - (9 + 4x ) ^ 1/2 = 0

We have to find the value of x

[tex]\sqrt{7x + 6}[/tex] = [tex]\sqrt{9 + 4x}[/tex]

Squaring both sides of the equation

[tex](\sqrt{ 7x + 6} )^{2}[/tex] = [tex](\sqrt{9 + 4x})^{2}[/tex]

7x + 6 = 9 +4x

3x = 3

x = 1

To know whether the value of x is the extraneous solution or not, put the value of x in the equation

[tex]\sqrt{7 * 1 + 6}[/tex] -[tex]\sqrt{ 9 + 4 * 1}[/tex] = 0

[tex]\sqrt{13}[/tex] - [tex]\sqrt{13}[/tex] =0

0 = 0

Therefore there is no extraneous solution to the equation as x = 0 is the solution of the equation.

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Answer: 10 answers correct and 10 answers incorrect

Step-by-step explanation:

60 is the highest total assuming every one was correct

20 is the lowest total assuming every one was incorrect

40 is the middle meaning he got half write half wrong

Half of 20 is (10) (10 x 3 = 30 ) + ( 10 x 1 = 10 ) 30 + 10 = 40

Answer: 13.3 repeating is what I got see if it make sense according to my work

Step-by-step explanation: 20x3=60, and one mark per wrong answer, so 60-40=20 wrong. So, 40 divided by 3=13.3 repeating

Answer:

Distributive property is the answer

Answer:

kevin ate 1/6 more than Kathy or un simplified, 2/12

Step-by-step explanation:

least common denominator

Answer: 2979 Zeroes

Step-by-step explanation:

1. Figure out what 10^2985 is. (It's one followed by 2985 zeroes).

2. Using that knowledge, make 7.185629 a whole number. To do that, you need to multiply it by a number that has the same number of zeroes as it does to move the decimal place one by one to the right. In this case, it is 1,000,000, because it has 6 zeroes and you need to move the decimal point past 6 numbers (after 7 in 7.185629).

3. Subtract 2985 by 6, because you used 6 zeroes.

4. This gives you the answer 2979 zeroes because 2985 zeroes - 6 zeroes= 2979 zeroes.

The surface area of the triangular prism is 136 cm square.

The surface area of a triangular prism can be found as follows;

Therefore,

surface area of a triangular prism = (perimeter of the triangle × height of prism) + (2 × base area)

Hence,

perimeter of the triangle = 5 + 5 + 6

perimeter of the triangle = 16 cm

height of prism = 7 cm

base area = 1 / 2 bh

base area =  1 / 2 × 4 × 6

base area = 24 / 2

base area = 12 cm²

Therefore,

surface area of a triangular prism = (16 × 7) + (2 × 12)

surface area of a triangular prism = 112 + 24

surface area of a triangular prism = 136 cm²

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Answer: 59 eggs

Step-by-step explanation: Dividing 3 will get you 19 eggs with 2 left over.  Dividing 59 by 5 will get you 11 eggs and 4 left over

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: the answer is no solution

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.

If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.

See image.

Answer:

-3x^{4}+2x^{3}+4x^{2}

Step-by-step explanation:

Re-order terms so constants are on the left

-x^{2}\left( 3x^{2}-2x-4\right)

-x^{2}\left( 3x^{2}-2x-4\right)

2

Distribute

-\textcolor{#C58AF9}{x^{2}\left( 3x^{2}-2x-4\right) }

-\left( \textcolor{#C58AF9}{3x^{4}-2x^{3}-4x^{2}}\right)

3

Distribute

-\left( 3x^{4}-2x^{3}-4x^{2}\right)

-3x^{4}+2x^{3}+4x^{2}

Answer:

10.083333...ft

Step-by-step explanation:

length = 12ft

area = 121sqft

area = length * width

121sqft = 12ft * width

width = 121sqft / 12ft

[tex]width = 10\frac{1}{12}\mathrm{ft}[/tex]

width = 10.08(3)ft

Answer: I think the answer is never but I'm not sure

Step-by-step explanation:

1) Rounding up 4328 to 1 significant figure will give us; 4000

2) Rounding up 25446 to 1 significant figure will give us 30000.

3) Rounding up 38562.7  to 1 significant figure will give us; 40000

4) Rounding up 87600.2 to 1 significant figure will give us; 90000

When talking about significant figures with whole numbers, we mean all non - zero whole numbers. They include;

1) Rounding up 4328 to 1 significant figure will give us; 4000

2) Rounding up 25446 to 1 significant figure will give us 30000.

3) Rounding up 38562.7  to 1 significant figure will give us; 40000

4) Rounding up 87600.2 to 1 significant figure will give us; 90000

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Answer:

P [tex]\leq[/tex] 6

Step-by-step explanation:

Set up Equation:

17.50 + 36.25(p) [tex]\leq[/tex] 235

Simplify Expression to Solve for how many people can go the park, using inverse operations.

36.25(p) [tex]\leq[/tex] 235 - (17.50)

36.25(p) [tex]\leq[/tex] 217.5

p [tex]\leq[/tex] 217.5/36.25

p [tex]\leq[/tex] 6

Therefore, no more than six people can attend the amusement park.

You can let the sides be a and b. You can then use the Law of Sines to create an equation relating the two sides and the angles opposite them, and finally isolate a/b.

Answer:

B

Step-by-step explanation:

6x - 8x - 4 = - 2x - 2 , that is

- 2x - 4 = - 2x - 2 ( add 4 to both sides )

- 2x = - 2x + 2 ( add 2x to both sides )

0 = 2 ← not possible

this indicates the equation has no solution

Answer:

6x-8x-4=-2x-2 (group the like terms)

6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)

answer= 0=2

,therefore: it has no solution

Step-by-step explanation:

the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.

The nature of the roots in the given quadratic equation (x - 3)² + (x - 4)² = 0 is; A: two rational roots

We are given the quadratic equation;

(x - 3)² + (x - 4)² = 0

Now, some of the rules in naming the roots are;

If b² – 4ac > 0, then the roots are real and unequal

If b² – 4ac = 0, then the roots are real and equal

If b² – 4ac < 0 then the roots are unequal and Imaginary

If b² – 4ac > 0 (is a perfect square), then the roots are real, rational and unequal

If b² – 4ac > 0 (is not a perfect square), then the roots are real, irrational and unequal

From the above rules and comparing to our given equations, it is clear that we have two rational roots which are x = 3 and x = 4.

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Answer:

the answer is b

Step-by-step explanation:

thnx

Answer:

1)3√5

2)5√5

3)3√5

-7 = extraneous solution

The equation is

[tex]\sqrt{-3x - 5}[/tex] = x + 3

To find the value of x we need to square both sides of the equation

[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]

- 3x -5 = [tex]x^{2}[/tex] + 6x + 9

[tex]x^{2}[/tex] + 9x + 14 = 0

[tex]x^{2}[/tex] + 7x + 2x + 14 =0

x( x + 7) + 2( x + 7) = 0

(x + 7) (x + 2 ) = 0

x = -2, -7

To find the extraneous solution we have to put both the value of x in the equation.

x=-2

[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3

[tex]\sqrt{1}[/tex] = 1

1 = 1

x = -7

[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3

[tex]\sqrt{16}[/tex] = -4

4 = -4

The extraneous solution of the equation is -7 and -2 is the solution of the equation

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Answer:

Step-by-step explanation:

Answer:

This is more than Juan

Step-by-step explanation:

We need to know about natural exponential function to solve the problem. The given function is a natural base exponential function.

An exponential function is a function in which x is an exponent. An exponential function has an exponential graph that keeps growing. A natural base exponential function is one where the base of the function is e which is a mathematical constant and is approximately equal to 2.71828. The inverse of a natural exponential function is a logarithmic function. An exponential function is of the form y=[tex]b^{x}[/tex] where b is the base, in a natural base exponential function, the b is replaced by e which means y=[tex]e^{x}[/tex]. In the given question y=[tex]e^{x+7}[/tex] is a natural base exponential function since the base is the natural base.

Therefore we found that the given function is a natural base exponential function.

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