Then where dose the two lines intersect needs to be (x,y) pair

the original purchase price was:

original purchase= 210,000- 0.4(210,000)=210,000-84,000=126,000

So the final answer will be that she paid $126,000, 10 years ago for her house.

we can check that our answer is correct by adding 126,000+84,000=210,000

First figure

we have that the triangles

ABC is congruent with triangle DCB by HL (hypotenuse leg)

Second figure

The triangles are congruent by Angle-Side- Angle

Third figure

The triangles are congruent by Side-angle -side

Function:

A function is a relation in which each input (x) has only one output (y).

If any one input (x) has more than one output (y) then it is not a function.

As you can see from the given table, the value of (a) must be anything other than (2)

So we can set a value of 4 for (a)

Now if you notice, each input will have exactly one output value so the criteria of a function is satisfied.

So, the answer is 4

The two given algebraic expressions x²-1/2+8x-x²-6x and 2x²-2x are not equivalent as on simplification the first expression is linear but the second expression is quadratic.

the first expression is :

x²-1/2+8x-x²-6x

now we simplify by grouping all the like terms

or, x² - x² + 8x - 6x - 1/2

or, 2x - 1/2 (this is linear as the highest power of the variable x is 1)

Now the second expression is :

2x²-2x (this is quadratic as the highest power of the variable x is 2)

Hence these two expressions are not equivalent.

In mathematics, statements comprising variables, numbers, or both, and at least two terms connected by an operator are referred to as expressions.

Numerical expressions, which just contain numbers, and algebraic expressions, which also contain variables, are the two types of expressions used in mathematics.

A variable is a symbol having an unknowable value. One constant, one variable, or a combination of variables and constants multiplied or divided can all be used to create a term. A coefficient in an equation is a number that has been further multiplied by a variable.

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Original expresion

Let's use the following relationship to determine the answer

Now in the original expression

The answer would be A = 6

⇒They simply want you to make F the subject for the equation, since there are multiple variables in one equation we cannot solve for the exact values

[tex]c=\frac{(5f-32)}{9} \\c(9)=5f-32\\9c=5f-32\\5f-32=9c\\5f=9c+32\\\frac{5f}{5} =\frac{9c+32}{5} \\f=\frac{9c+32}{5}[/tex]

The function f(x)=(x-7.2)(x+7) is already in its factored form

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

f(x) = (x - 7.2)(x + 7)

When an equation has the form of

f(x) = (x - a)(x - b).....(x -n),

Then, the equation is already in its factored form

This means that the equation can not be further simplified, as the current form is its factored form

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translation 2x + 6 = -14

2x = -14 - 6

2x = -20

x = -20/2

x = -10

The percent discount of the item in the grocery store if the item is priced at $27, before discount and tax and $25.38 after discount and before tax is 6%.

Percent discount = (Price of item before discount and tax - Price of item after discount before tax ) / Price of item before discount and tax × 100

= (27 - 25.38) / 27 × 100

= 1.62 / 27 × 100

= 0.06 × 100

= 6%

In conclusion, the percent discount of the item is given as 6%

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Answer:

slope = 0

eq of line: y = -1

Step-by-step explanation:

A line parallel to the x-axis is a horizontal line. The equation of a horizontal line is " y = anumber". Horizontal lines have 0 slope. The point given is (2,-1). In the point (2,-1) the y is -1. The equation of the horizontal line thru (2,-1) is

y = -1

The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Out of 40 understudies, 14 are taking English organization, and 29 are taking chemistry. Assuming 5 understudies are in both classes the number of understudies that are in neither class.

The number of students in neither class will be given as,

⇒ 40 - (29 + 14 - 5)

⇒ 40 - 38

⇒ 2

The probability that a randomly chosen student from this group is taking only a chemistry class will be

P = (29 - 5) / 40

P = 24 / 40

P = 0.60

The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.

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Elizabeth's speed increased during the 0 to 5 minute interval

This interval shown on the graph is indicated by the rising line on the vertical axis (y-axis).

The x-axis shows the time intervals graded in 5-minute intervals. the other options shows a flat line (no change in speed) and a downward line (reduction in speed).

The 0 to 5 minute period of her run however is a rising line which means incresing speed.

Answer

y = ½x + 5

If y is the total amount Juanita makes for x inches of finished lanyard,

Base fee = y-intercept = 5

Cost per inch = Slope = 0.5 = ½

Explanation

To write the expression for this, we need to write the equation for the line representing the whole function

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

From the gaph, we can easily see that

b = y-intercept = point where the line crosses the y-axis = 5

For the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For this question,

(x₁, y₁) and (x₂, y₂) are (2, 6) and (6, 8)

Recall,

y = mx + b

m = slope = 0.5 = ½

b = y-intercept = 5

y = ½x + 5

If y is the total amount Juanita makes for x inches of finished lanyard,

Base fee = y-intercept = 5

Cost per inch = Slope = 0.5 = ½

Hope this Helps!!!

Answer:

$4.05

Step-by-step explanation:

8.64÷3.2=2.7

1.5×2.7=4.05

(not very sure)

curve: Y=x^3

The equation of the tangent line is:

y =

The height, h of the airplane to the nearest foot is 536 feet (option D).

The diagram shown is a right angled triangle. The take off point and the height of the plane form a right angled triangle.

Trigonometry would be used to solve of the height of the airplane. We are to determine the opposite side given the adjacent side and the angle of elevation.

Tan = opposite / adjacent side

Tan 15 = h / 2000

0.2679 = h / 2000

h = 2000 x 0.2679

h = 536 feet

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Answer:

b

Step-by-step explanation:

We can draw the flight as:

We can use the trigonometric ratio that relates the sine of an angle with the opposite side and the hypotenuse:

Answer: the distance can be expressed as 40 / sin(26 deg)

Answer:

Step-by-step explanation:

The cost of making the smaller circle a rational number.

A number is rational if it has a terminating or repeating decimal; for example, 1/2 = 0.5. It is irrational if a number has a non-terminating and non-repeating decimal.

A rational number is one that can be written as P/Q, where P and Q are integers and Q = 0. However, an irrational number cannot be written in simple fractions. A rational number is 2/3, whereas an irrational number is ✓2.

It should be noted that in this situation, the cost of making the larger circle can be 4.0. The cost of making the small one will be:

= 3/4 × $4.0

= $3.0

This illustrates a rational number.

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Answer:

35/1000

Step-by-step explanation:

the 5 is in the thousandths place therefore it is over 1000

Answer:

you would make it a 7 for the top and 200 for the bottom

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

a - b = 2       so   a = 2+b

a^2 - b^2 = 48      <===== substitute the value for 'a' underlined above

(2+b)^2   - b^2   = 48          expand L side

b^2 + 4b +4       - b^2    = 48      simplify

4b+4 = 48

4b = 44

b = 11      then  a = 2+b = 13

According to the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.

It is given to us that -

Hypotenuse length = 10

Leg of length = 5

We have to find out the number of distinct right triangles that have the given hypotenuse length and leg of length.

For a right triangle, the Pythagorean theorem states that -

[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (1)

where, a and b = Legs of the right triangle

and, h = hypotenuse of the right triangle

Substituting the given values of hypotenuse length and one leg of length in equation (1), we have

[tex]a^{2} +b^{2} =h^{2}\\= > 5^{2} +b^{2} =10^{2}\\= > b^{2} = 100-25\\= > b^{2} = 75\\= > b = 8.65[/tex]------ (2)

From equation (2), we see that another leg's length of the right triangle is equal to 8.65 which is not possible it is not a real number.

Therefore, applying the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.

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Answer:

Expressions: Student 1 and 4

Equations: Student 2 and 3

Step-by-step explanation:

Equations have an = sign. Expressions do not.

Range of the function f(x) = 3x² +18x is [-27,∞).

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Here, we have f(x) = 3x² +18x.

Let f(x) = y

⇒ y = 3x² +18x

⇒ y = 3(x²+6x)

⇒ y/3 = x²+6x

⇒ y/3 = x²+ 6x + 9 - 9

⇒ y/3 = (x+3)² - 9

⇒ y/3 + 9 = (x+3)²

⇒ (y+27)/3 = (x+3)²

Taking square root on both sides, we get

⇒ [tex]\sqrt{(y+27)/3}[/tex] = x+ 3

⇒ [tex]\sqrt{(y+27)/3} - 3[/tex]  = x

Now since f(x) = y ⇒ x = f⁻¹(y)

⇒ f⁻¹(y) = [tex]\sqrt{(y+27)/3} - 3[/tex]

⇒ range = [-27,∞).

Therefore, range of the function f(x) = 3x² +18x was found to be [-27,∞).

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Answer:

LM = √34

Step-by-step explanation:

L is at (-7, 4), and M is at (-2, 1).

LM

[tex] \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } [/tex]

[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]

SOLUTION

Let us make a graph of the function

This is shown below

(a) The domain is usually determined from the x-axis. From the graph, the domain is all real numbers, that is, it is infinite for both positive and negative values for x, as you can see that if the graph is extended, there is no limit for x-values that it can contain. So the domain is (-infinity, infinity)

Hence the answer, Domain is

(-inf, inf)

(b)

In

Hence, the answer is -2

(c)

In

Hence, the answer is 1

(d)

In

Hence, the answer is -1

(e)

In

Hence, the answer is -3

Given:

a) To find the vertex:

Here, a=-1, b=-2, and c=3

We know that the formula to find the x- coordinate of the vertex is given by,

Substitute x=-1 in the given equation we get,

Hence, the vertex of the graph is (-1, 4).

b) To find the range of the graph:

Let us find the y-intercept.

Put x=0, we get

From the figure, we observe that

The range of the graph is

c) To find the domain of the graph:

Let us find the x-intercept.

Put y=0, we get

From the figure, we observe that,

The domain of the graph is,

Answer:

312

Step-by-step explanation:

42 43 312

tan T = 8/8 = 1

tan ^-1 T = 45°

angle T = 45°

2) angle J = tan J = 2/4

tan J = 1/2

tan^-1 J = 26.57

rounded J = 26.6