The bill for dinner was $61.66. You left $10.34 for the tip. What percentage of the original bill was the tip? Round your a
to the nearest whole percent.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y = x² +6x -16[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.

So, the values of x, when y = 0 are the roots of the given quadratic function.

that is : x = -8 and x = 2

And it can be represented as :

[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]

[ h1 and h2 represents roots of the quadratic function ]

[tex]\qquad \tt \rightarrow \: (x -2)(x + 8) = 0[/tex]

It can be further simplified as :

[tex]\qquad \tt \rightarrow \: {x}^{2} -2x +8x -16 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x {}^{2} +6x -16 = 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.

2) After 8 years of straight-line depreciation, the car's value will be $19,080.

Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.

Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.

Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.

Price of an automobile in 2003 = $30,600

Annual depreciation = $1,440

The car's value after t years = $19,080.

Value after t years = 30,600 - 1,440t

If 19,080 = 30,600 - 1,440t

1,440t = 30,600 - 19,080

1,440t = 11,520

t = 8 (11,520/1,440)

t = 8

= 8 years

Check:

x = 30,600 - 1,440t

x = 30,600 - 1,440(8)

x = 30,600 - 11,520

x = 19,080

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Based on the attached graph, the y-intercept is 3

The y-intercept of the function is the point or points where the graph of the function crosses the y-axis i.e. the point where the value of x equals 0

The graph that completes the question is added as an attachment

Using the definition above, we understand that

The y-intercept for the graph of the exponential function is the point where x = 0

On the attached graph, we have

y = 3, when x = 0

This means that the y-intercept for the graph of the exponential function is 3

This is so because the graph of the function crosses the y-axis  at y = 3 when x = 0

Hence, the y-intercept of the exponential function is 3

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When in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10)  degrees, then the ∠A, ∠B  and ∠C  are 109 degrees, 27 degrees and 44 degrees respectively  

The ∠A = (x-10) degrees

Angle B is one-quarter of angle A

∠B = (1/4)×(x-10)

= (1/4)x - (5/2)

= 0.25x-2.5

The angle C is two fifth of angle A

∠C = (2/5)(x-10)

= (2/5)x - 4

= 0.4x-4

We know sum of the angles in a triangle is 180 degrees

Then,

∠A + ∠B + ∠C = 180

Substitute the values in the equation

(x-10) + 0.25x-2.5 +0.4x-4 = 180

1.65x-16.5 = 180

1.65x = 196.5

x ≈ 119

∠A = (x-10)

= 119-10

= 109 degrees

∠B = 0.25x-2.5

= 0.25×119-2.5

≈ 27 degrees

∠C = 0.4x-4

= 0.4×119-4

≈ 44 degrees

Hence, when in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10)  degrees, then the ∠A, ∠B  and ∠C  are 109 degrees, 27 degrees and 44 degrees respectively  

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The net image of a figure is a visual representation of the original figure.

From the given net image, the solid that has the net image can be said to be a traingular

The correct answer is:  
     [A]:  " ∡2 is supplementary to ∡3 " .

___________________

The other answer choices given—which are correct statements—only prove that " a || b " {that is:  "Line A" is parallel to "Line B".}

___________________

olution

e have the following statement:

If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:

A) supplementary angles

How many pounds of Virginia peanuts does Sergio use?

Assume he is making 10 lb of the $3.40 mixture

Let x = no. of pounds of the Virginia ($3.50) peanuts

Then (10-x) = no. of pounds of the Spanish ($3) peanuts

The Equation:

3.5x + 3(10-x) = 3.4(10)

3.5x + 30 - 3x = 34

.5x = 34 - 30

x = 4/.5

x = 8 pounds of Virginia peanuts

:

(b)How many pounds Spanish peanuts does Sergio use?

Spanish peanuts must be 2 pounds since the total is 10 pounds

:

Check:

3.5(8) + 3(2) = 3.4(10)

28 + 6 = 34

29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i

33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i

37) – 4 i =  4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 4 i =   0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] =  4[tex]e^{\frac{3\pi}{2}i}[/tex]

41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]

49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex]  = [tex]\sqrt{26}e^{-0.197i}[/tex]

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the probability of winning a lottery game out of all the games played is 0.16.

We are given that:

In a lottery game, the chances of win are = 4 in 25

So, this means that:

if a person plays 25 games of lottery, then he will probably win 4 games out of them.

So, we get that:

Total games = 25

Win games = 4

Probability = win games / total games

Substituting the values, we get that:

Probability = 4 / 25

P = 0.16

Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.

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he standard form of a quadratic efunctionis:

Since the y-intercept is (0, -1.4), it follows that:

Substitute c = -1.4 into the equation:

Since the x-intercept is (0.905, 0), it follows that:

Since the graph passes through the third point (2, 0.6), it follows that:

Substitute equation (2) into equation (1):

Substitute a = -0.5 into equation (2), therefore,

Therfore the function is given by:

The equation of the parabola is y = -0.5x² + 2x - 1.4

.

The distance travelled by the unicycle is 226.08 inches.

The first step is to determine the circumference of  the wheel of the unicycle. A circle is a bounded figure which points from its center to its circumference is equidistant. The circumference of a circle is the distance round the circle.

Circumference of a circle = 2πr

Where:

3.14 x 2 x 12 = 75.36 inches

The next step is to multiply the circumference of the unicycle by the number of revolutions the tire made.

Distance travelled = 3 x  75.36 inches = 226.08 inches

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The set T can be rewritten by listing its elements as T = {-4}.

         Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.

Given:

Set T is equal to  {x | x is an integer and -5 < x < -3}.

By examining the interval in the set, the set can also be written as something else. 

It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.

As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.

Hence, the set can be rewritten as

T = {-4}

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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.

T = {x | x is an integer and -5 < x < -3}."

It is important the order we write the vertices of a triangle in a congruent statement as

B. The order tells us what sides are congruent.

D. The order tells us what angles are congruent.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.

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The function g(x) when x= - 2, 0 , 5 is -6 , 0 and 15 respectively.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given: g(x) = 3x

To evaluate : The function x= - 2, 0, 5.

g(-2) = 3× -2 = -6

g(0) = 3×0 = 0

g(5)= 3×5 = 15

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The x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .

X intercept of a function is defined as the point where the graph crosses the x axis ,

and the y intercept of the function  is defined as the point where the graph crosses the y axis .

In the question ,

it is given that

the function is y= (2/3)x-1

to find the x intercept we substitute y as 0 in the equation

On substituting  y as 0  , in the equation , we get

0 = (2/3)x-1

1=(2/3)x

x=1*(3/2)

x=3/2

the x intercept is 3/2.

to find the y intercept we substitute x as 0 in the equation

On substituting  x as 0  , in the equation , we get

y=(2/3)*0-1

y=0-1

y= -1

so, the y intercept is -1 .

Therefore , the x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .

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The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.

A function is simply a relationship that maps one input to one output.

Each x-values must have one y-value to qualify as a function.

Given the data in the question;

First, set up the function operation

( f + g )(x) = f(x) + g(x)

Replace the function designators f(x) and g(x) with the actual functions.

( f + g )(x) = f(x) + g(x)

( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )

Collect and add like terms

( f + g )(x) = 4x + 1 + x² - 5

( f + g )(x) = 4x + x² - 5 + 1

( f + g )(x) = 4x + x² - 4

Reorder the function

( f + g )(x) = x² + 4x - 4

Therefore, the function operation ( f + g )(x) is  x² + 4x - 4.

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The average consumption of the fruit juice would be 7.6 gallons for the year 2006.

Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.

Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).

Total consumption of the fruit juice in 2006=2.28x109 gallons.

Total population of the country in year 2006=3x108

Average Consumption=(2.28x109)/(3x108)

                = 7.6 gallons    

Hence the average consumption would be 7.6 gallons per person.

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Given:

TR = 11 Ft

∠RTS = 16°

Let's determine the length of Arc PS,

Step 1: Let's first determine the angle of Arc PS.

∠RTS = 16°

∠PTQ = 16° ; Vertical angle pair of ∠RTS

Since ∠QTR = ∠PTS under the rule of vertical angles, we can now determine the measure of ∠PTS or Arc PS.

We get,

Step 2: Let's determine the perimeter of the circle.

Step 3: Let's determine the length of Arc PS.

Therefore, the length of Arc PS is 31.47 ft.

Solution:

The cube is numbered from 1 to 6

The probability that any of the numbers from 1 to 6 will show will be

The expected value will be calculated below as

A.

This is not a correct choice

--------------------------

B.

This is a correct choice

---------------------------

C.

This is not a correct choice

------------------------------------------------

D.

This is a correct choice

-------------------------------------------

E.

This is a correct choice

The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is  

(-9x²+3xy-4y²).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Numbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

= (-3x²-xy-3y²) - (6x²-4xy+y²)

=  -3x²-xy-3y² - 6x²+4xy-y²

= (-9x²+3xy-4y²)

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The height of the building is 118. 89 feet

Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.

The different  types of trigonometric identities includes;

The trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

From the information given;

cos 43 = x/170

cross multiply

x = cos 43(170)

expand the bracket

x = 124.33 feet

To determine the height of the building is the opposite side

sin 73 = x/ 124.33

cross multiply

x = sin 73(124.33)

expand the bracket

x = 118. 89 feet

Hence, the value is 118. 89 feet

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6 possible values of squares that she can move.

What is possibility or probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.

Hence she has 6 different possible numbers of squares she can move.

The possibilities are:

-8 squares (if she rolls a 1)

-9 squares (if she rolls a 2)

-10 squares (if she rolls a 3)

-11 squares (if she rolls a 4)

-12 squares (if she rolls a 5)

-13 squares (if she rolls a 6)

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The value of x such that f(x) and g(x) have equal values is 3

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have

f(x) = -2x + 4

g(x) = 2x - 8

The question implies that the functions have equal values

This means that

f(x) = g(x)

Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms

2x + 2x = 8 + 4

Evaluate the like terms

4x = 12

Divide both sides of the equation by 4

x = 3

Hence, the value of x such that the equations are equal is 3

See attachment for the graph of the functions

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Answer:

24

Step-by-step explanation:

divide the sides added together by the middle

Solution

Step 1:

Write the rational expression:

Step 2:

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).

Step 3

Step 4:

\ertical} Asymptote is =-8,\ =3,