This graph represents a quadratic function. An upward parabola on a coordinate plane vertex at (minus 2, 2) and passes through (minus 3, 5) and (minus 1, 5). What is the value of a in the function’s equation? A. 3 B. 2 C. -3 D. -2

The height of the water depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.

According to the two cases described in the statement, we have clear example of sinusoidal model for the height as a function of time. In this case, we can make use of the following equation:

h = a + A · sin (2π · t/T + B)     (1)

Where:

Now we proceed to derive the equations for each case:

Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):

A = (20 m - 8 m)/2

A = 6 m

a = 14 m

Phase

20 = 14 + 6 · sin B

6 = 6 · sin B

sin B = 1

B = π/2

h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.

Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):

A = (40 m - 2 m)/2

A = 19 m

a = 21 m

Phase

2 = 21 + 19 · sin B

- 19 = 19 · sin B

sin B = - 1

B = - π/2

h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.

Lastly, we proceed to graph each case in the figures attached below.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

According to the graph

Maximum value is 1

So

Range is

Option C

Answer:

11/20

Step-by-step explanation:

1/4= 10/40

3/5=24/40

3/10=12/40

10/40+24/40= 34/40

34/40 - 12/40= 22/40

simplifies to 11/20

Answer:

x = 4

Step-by-step explanation:

Since M is the midpoint of segment KL, then segments KM and LM are congruent. They have the same length.

4x + 1 = 8x - 15

4x = -16

x = 4

Using the given information, the height of the tree is 48 ft

From the question, we are to determine the height of the tree

In the given diagram, the height of the tree is (x + 5) feet

First, we will determine the value of x

tan 47° = x / 40

x = 40 × tan47°

x = 42.89 ft

∴ The height of the tree = (42.89 + 5) ft

Height of the tree = 47.89 ft

Height of the tree ≈ 48 ft

Hence, the height of the tree is 48 ft.

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Answer:

8, 10, 14

Step-by-step explanation:

1. 8² + 10² = 164 and 14² = 196, so this works.

2. 9² + 12² = 15² = 225, so this is a right triangle.

3. 10² + 14² = 296 and 17² = 289, so this is an acute triangle.

4. 12² + 15² = 369 and 19² = 361, so this is an acute triangle.

Answer:

a

Step-by-step explanation:

The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.

let

n + q = 84

0.05n + 0.25q = 17.80

From equation (1)

n = 84 - q

Substitute into (2)

0.05n + 0.25q = 17.80

0.05(84 - q) + 0.25q = 17.80

4.2 - 0.05q + 0.25q = 17.80

- 0.05q + 0.25q = 17.80 - 4.2

0.20q = 13.60

q = 13.60 / 0.20

q = 68

Substitute q = 68 into

n + q = 84

n + 68 = 84

n = 84 - 68

n = 16

Therefore, the number of quarters and nickels are 68 and 16 respectively.

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First, you need to understand the vocabulary.
Saying x less than y means that you are subtracting from y. Your x here is 0.04, and your y is 1.38

y-x = 1.38-0.04 = 1.34

The values of x and y from the figure is 9 and 5 respectively

Two triangles are similar if the ratio of the similar sides is equal to a constant. From the given diagrams;

x/(8+4) = 6/8

x/12 =6/8

8x = 6 * 12

8x = 72

Divide both sides by8 to have:

8x/8 = 72/8

x = 9

Similarly;

10+y/x = 10/6

10+y/9 = 10/6

10+y/9 = 5/3

Cross multiply

3(10+y) = 5(9)

30 + 3y = 45

3y = 45-30

3y = 15

y = 5

Hence the values of x and y from the figure is 9 and 5 respectively

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Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage. In the given question, the percentage error is option b.  0.0772

Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage.

This can be expressed as;

percentage error = [tex]\frac{actual value - expected value}{actual value}[/tex] x 100%

Where the actual value is the accurate value, and the expected value is derived from the actual value.

Thus in the given question, it can be deduced that,

actual value = 625.483

expected value = 625.000

The difference between the two values = (625.483 - 625.000)

                                                  = 0.483

So that,

percentage error = [tex]\frac{0.483}{625.483}[/tex] x 100%

                   = 0.07722

percentage error = 0.0772

Therefore, the required percentage error is 0.0772 i.e option b.

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The child tickets were sold that day is 82.

Given the cost of child admission $6.30 and the cost of adult admission $9.80 and on Wednesday 144 tickets were sold for a total sales of $1124.20.

Let the child tickets are x and adult tickets are y.

On Monday, 144 tickets were sold for a total sales.

x+y=144              ........(1)

Total sales = $1124.20

Need to find the child tickets sold on Wednesday.

Total sales = 6.30x+9.80y

Total sales = $1124.20

So,6.30x+9.80y=1124.20                        .......(2)

Find the value of y from equation (1), we get

x+y-x=144-x

y=144-x

Now, we will substitute the value of y in equation (2) to find the value of x, we get

6.30x+9.80(144-x)=1124.20

Apply the distributive property that is a(b+c)=ab+ac, we get

6.30x+9.80×144-9.80x=1124.20

6.30x+1411.2-9.80x=1124.20

Combine the variable terms on left side, we get

1411.2-3.5x=1124.20

subtract 1411.2 from both sides, we get

1411.2-3.5x-1411.2=1124.20-1411.2

-3.5x=-287

Divide both sides with -3.5x, we get

-3.5x/(-3.5)=-287/(-3.5)

x=82

Therefore, 82 child tickets were sold on Wednesday when cost of child admission $6.30 and the cost of adult admission $9.80.

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If mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

Given that mean is 98,standard deviation is 20.41,n=81 and significance level be 10%.

We are required to find the value of sample mean.

Because the value of n is greater than 30 so we will use z statistics in the problem.

We know that,

Z=(X-μ)/σ  in which μ is population mean, σ is standard deviation.

Confidence level=1-0.01=0.09 means 90%.

Z value for 90% confidence level be 1.645.

we have to put the value of Z=1.645 , μ=98,σ=20.41 to get the value of X.

1.645=(X-98)/20.41

1.645*20.41=X-98

33.57445=X-98

X=98+33.57445

X=131.57445

Hence if mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

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The number which produces a rational number when multiplied by 1/3 is; Choice A; 2.

It follows from the definition of rational number that they can be represented as the quotient a/b of two integers such that b ≠ 0.

On this note, it follows that when 1/3 is multiplied by 2; the result is 2/3 which is a rational number.

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Answer: C

Step-by-step explanation:

Each term is half the previous term.

Answer:

D. The slope is -2. The y-intercept is (0,3)

Step-by-step explanation:

You can use any two points.

Let's use the first two points: (0, 3), (2, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - 3)/(2 - 0)

slope = -4/2

slope = -2

The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).

Answer: D. The slope is -2. The y-intercept is (0,3)

Usando proporciones, hay que la pangea tardra aproximademente 20,116,750 años para fragmentar-se.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

La deriva continental es del orden de 4 cm al año. La distancia actual entre Sudamérica y África es de 5000 millas. En cm, esta distancia es la seguiente:

5000 millas = 5000 x 160934 cm = 80,467,000 cm.

Asi, el tiempo que levará para la pangea fragmentar-se es:

t = 80,467,000/4 = 20,116,750 años

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By the inclusion/exclusion principle,

[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]

[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]

[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]

[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]

Answer: A=187.5,2

Step-by-step explanation:

Answer:

x = 1/3 or x = -2/3

Step-by-step explanation:

Let's solve your equation step-by-step.

9x2+3x−2=0

For this equation: a=9, b=3, c=-2

9x2+3x+−2=0

Step 1: Use quadratic formula with a=9, b=3, c=-2.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(9)(-2)} }{2(9)}[/tex]

[tex]x=\frac{-3\pm\sqrt{81} }{18}[/tex]

x = 1/3 or x = -2/3

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the quadratic formula?}[/tex]

[tex]\rm{x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\textsf{Or even}[/tex]

[tex]\rm{ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we looking for?}[/tex]

[tex]\rm{9x^2 + 3x - 2 = 0}[/tex]

[tex]\huge\textbf{What are the labels in the equation?}[/tex]

[tex]\mathsf{a \rightarrow 9}\\\\\mathsf{b\rightarrow 3}\\\\\mathsf{c \rightarrow -2}[/tex]

[tex]\huge\textbf{Solving for your equation:}[/tex]

[tex]\rm{x = \dfrac{-(3)\pm \sqrt{3^2 - 4(9)(-2)}}{2a}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{-3\pm \sqrt{81}}{18}}[/tex]

[tex]\rm{x = \dfrac{1}{3}\ or\ x = - \dfrac{2}{3}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf{x} = \dfrac{1}{3}\ or\ \mathsf{x} = - \dfrac{2}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

x = 5, y = sqrt6, z = 3

Step-by-step explanation:

[tex]\frac{10}{\sqrt{6} } \\\\\frac{(10)(\sqrt{6} )}{(\sqrt{6} )(\sqrt{6}) } \\\\\frac{10\sqrt{6} }{6} \\\\or\\\\\frac{5\sqrt{6} }{3}[/tex]

❄ Hi there,

let us revise the way we rationalize the denominator before we get down to the actual process.

__________

Suppose you had a problem, and you did all the steps, and you arrived at the following answer: [tex]\sf{\dfrac{10}{\sqrt6}}[/tex].

Well, this answer is not in its simplest form, because it has an irrational number in its denominator.

So what we do is we get rid of that irrational number in the denominator  by multiplying the fraction's top & bottom by [tex]\sqrt6[/tex]:

[tex]\sf{\dfrac{10\sqrt6}{\sqrt6\times \sqrt6}}[/tex]

Now we simplify

[tex]\sf{\dfrac{10\sqrt6}{6}}[/tex]

Reduce

[tex]\sf{\dfrac{5\sqrt6}{3}}[/tex]

- - - - -  - - -

Answer:

It's attached you may see it!!

Answer:

see attachments

Step-by-step explanation:

Given equations:

[tex]\begin{cases}5x + 7y = 50\\7x + 5y = 46\end{cases}[/tex]

To plot the graphs of the given equations:

Equation 1

[tex]\implies 5x + 7y = 50[/tex]

[tex]\implies 7y = -5x + 50[/tex]

[tex]\implies y = -\dfrac{5}{7}x+\dfrac{50}{7}[/tex]

[tex]x=-4 \implies y = -\dfrac{5}{7}(-4)+\dfrac{50}{7}=10 \implies (-4,10)[/tex]

[tex]x=3 \implies y = -\dfrac{5}{7}(3)+\dfrac{50}{7}=5 \implies (3,5)[/tex]

Plot the points (-4, 10) and (3, 5) then draw a straight line through them (see attachment 1).

Equation 2

[tex]\implies 7x+5y=46[/tex]

[tex]\implies 5y=-7x+46[/tex]

[tex]\implies y=-\dfrac{7}{5}x+\dfrac{46}{5}[/tex]

[tex]x=3 \implies y=-\dfrac{7}{5}(3)+\dfrac{46}{5}=5 \implies (3,5)[/tex]

[tex]x=8 \implies y=-\dfrac{7}{5}(8)+\dfrac{46}{5}=-2 \implies (8,-2)[/tex]

Plot the points (3, 5) and (8, -2) then draw a straight line through them (see attachment 2).

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Proportionately, the total jelly beans in the world will be 115,703,826.

A proportion refers to a fraction of a whole.

A proportion is a ratio or a number relationship between two or more values or variables.

The proportion of a whole value can be represented as a fraction, decimal, or percent.

Red jelly beans in the world = 1/3

And 1/3 = 38,567,942

1/1 = 115,703,826 (38,567,942/1/3)

Thus, if 1/3 of the jelly beans in the world is 38,567,942, then the whole jelly beans will be 115,703,826.

Thus, proportionately, the total jelly beans in the world will be 115,703,826 because 1/3 of 115,703,826 is 38,567,942.

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The value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

x/4 ÷ 2/3 = 1/5

x/4 × 3/2 = 1/5

(x × 3) / (4 × 2) = 1/5

3x / 8 = 1/5

3x × 5 = 8 × 1

15x = 8

x = 8/15

Therefore, value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

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Applying the angle of intersecting secants theorem, the measure of angle B is: 35°.

The measure of the angle formed outside a circle by two intersecting secants is equal to half the positive difference of the measures of the arcs they intercept based on the angle of intersecting secants theorem.

Applying the angle of intersecting secants theorem, we have the following:

Let the missing measure of the arc for angle A be x. Therefore:

6 = 1/2(x - 17)

2(6) = x - 17

12 = x - 17

12 + 17 = x

x = 29°

m∠B = 1/2(99 - x)

Plug in the value of x

m∠B = 1/2(99 - 29)

m∠B = 35°

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The area of the triangle is 4 units²

The area of a triangle is the half the base multiplied with the height of that triangle

Area = 1/ 2 × b × h

From the figure given,

base = 7 - 3 = 4 units

height = 4 - 2 = 2 units

Area = 1/ 2 × 4 × 2

Area = 1/ 2 × 8

Area = 4 units²

Thus, the area of the triangle is 4 units²

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