8. Lori bought a shirt and a hat at a half-off sale.
If she spent a total of $21 on the two items,
what was the original price of the hat?

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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translation 2x + 6 = -14

2x = -14 - 6

2x = -20

x = -20/2

x = -10

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

a) We can write the cost function (in function of the units made) as the sum of the fixed cost (2000) and the variable cost (25*x):

b) The revenue R(x) is:

To find the value of x that maximizes R(x) we derive R(x) and equal it to 0:

We can now calculate the maximum revenue as R(3000):

c) The profit function P(x) can be calculated as the difference between the revenue and the cost:

In the same way as we did in b), we can calculate the number of units x that maximize the profit by deriving P(x) and making it equal to 0:

The maximum profit can be then calculated as P(1750):

We can graph R(x) and P(x) as:

Answer:

a) C(x) = 2000 + 25x

b) x = 3000 units

R(3000) = $90000

c) x = 1750 units

P(1750) = $28625

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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⇒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 maximum number of guests Gianna can serve will be 16.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers

From the information, Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream

The maximum number of guests Gianna can serve will be:

= 5 1/2 ÷ 1/3

= 11/2 ÷ 1/3

= 11/2 × 3

= 33/2

= 16.5

The maximum number will be 16.

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Complete question

Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream, what is the maximum number of guests Gianna can serve?

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:

$4.05

Step-by-step explanation:

8.64÷3.2=2.7

1.5×2.7=4.05

(not very sure)

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

Original expresion

Let's use the following relationship to determine the answer

Now in the original expression

The answer would be A = 6

find the slope of 4x + 3y equals to​

I will assume a value of a

so

4x+3y=a

Isolate the variable y

3y=-4x+a

y=-(4/3)x+a/3

therefore

Note: the value of the slope not depend of the value of a

slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.

If two lines are parallel, that means the slope of both equations are equal.

L2: y = 3x - 7, m = 3

So, m for L1 is m = 3.

Now we just need to find y - intercept, as follows:

L1 passes through (0,4), then:

4 = 3(0) + b

4 = 0 + b

b = 4

The equation for the line is y = 3x + 4

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]

Background:

• Even ,functions are symmetric with respect to the ,y-axis,.

• Odd ,functions are symmetric with respect to the origin.

• Neither ,has no symmetry with respect to the origin or ,y-axis,.

Answer: Even

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

Answer:

312

Step-by-step explanation:

42 43 312

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.

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

Answer:

1. Given (angle PQR and angle XYZ are complimentary)

2. Definition of complimentary angles (Complimentary means they are added to 90 degrees)

3. Definition of Complimentary angles (Complimentary angles only include two angles)

4. Subtraction postulate (90 degrees - 10 degrees= 80 degrees which proves they are complimentary)

5. Complimentary angles theorem (angle XYZ is 80 degrees)

Sorry if that's too vague, but I really hope this helps you! I bet someone elses answer would clear it up better, so more research or finding a different answer would probably help, just to confirm. I tried to explain as much as I could, I'm not good at teaching what I know.

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

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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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:

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

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!!!

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 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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Answer:

the answer is D: $10547.20