What are the exact values of a and b?
Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.

The graph of the absolute value function can be seen below.

Here we have the absolute value function:

[tex]f(x) = |x^2 - x -2|[/tex]

Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.

Then the graph of the function is the one you can see below:

If you want to learn more about absolute value functions:

https://brainly.com/question/3381225

#SPJ1

The time taken to the closest minutes for the pie to cool to 80∘F is 123 minutes

T(t) = 68e^−0.0174t + 72

80 = 68e^−0.0174t + 72

80 - 72 = 68e^−0.0174t

8 = 68e^−0.0174t

e^−0.0174t = 8/68

e^−0.0174t = 0.11764705882352

ln e (−0.0174t) = ln (0.11764705882352)

1 × −0.0174t = -2.1400661634962708

-0.0174t = -2.1400661634962708

t = -2.1400661634962708 / -0.0174

t = 122.9923

Approximately,

t = 123 minutes

Learn more about temperature:

https://brainly.com/question/12124788

#SPJ1

Answer:

51

Step-by-step explanation:

Let c be the number of child tickets sold.

Let a be the number of adult tickets sold.

From the information given from the question, we can deduce:

6.10c + 9.70a = 1074.20 - Equation 1

c + a = 146 - Equation 2

From here, we can use the substitution method in solving simultaneous equations to find a and c. We will use Equation 2 as the base.

c = 146 - a - Equation 2A

We will then substitute equation 2A into Equation 1 to find a.

6.10(146-a) + 9.70a = 1074.20

890.6 - 6.10a + 9.70a = 1074.20

890.6 + 3.6a = 1074.20

3.6a = 1074.20 - 890.6

3.6a = 183.6

a = [tex]\frac{183.6}{3.6}[/tex]

a = 51

Therefore we know that 51  adult tickets were sold that day.

After that you can substitute a into equation 2 to find c.

The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

Read more about exponential functions at:

https://brainly.com/question/11464095

#SPJ1

The equation of the given Absolute Value Function is; y = |-2x + 4|

We can see that the given graph is a Linear graph but since it is V-shaped, we can say that it is a graph of an absolute value function.

Now, from the graph we see that;

At x = 0, y = 4

At x = 1, y = 2

At x = 2, y = 0

At x = 3, y = -2

At x = 4, y = 0

At x = 5, y = 2

We can see that the y-intercept is at y = 4.

Slope between two consecutive points is;

(2 - 4)/(1 - 0) = -2

Equation is; y = -2x + 4

Now, this is an absolute value function and as such we will write it as;

y = |-2x + 4|

Read more about Linear Graphs at; https://brainly.com/question/4025726

#SPJ1

The critical values are 0.622, 0.707, 0.789 and 0.834

The sample size is given as:

n = 8

Calculate the degrees of freedom using

df = n - 2

So, we have:

df = 8 - 2

df = 6

Using the table of values of critical values, we have:

Critical values = 0.622, 0.707, 0.789 and 0.834

By comparing the critical values and the linear correlation coefficient, we can conclude that there is no significant linear correlation.

Read more about linear correlation at:

https://brainly.com/question/17237825

#SPJ1

[tex]\begin{array}{c|c|c|c} p & q & \neg q & p \land \neg q \\ T & T & F & F \\ T & F & T & T \\ F & T & F & F \\ F & F & T & F \end{array}[/tex]

[tex]\begin{array}{c|c|c|c} t & s & \neg t & \neg t \implies s \\ T & T & F & T \\ T & F & F & T \\ F & T & T & T \\ F & F & T & F \end{array}[/tex]

[tex]\begin{array}{c|c|c}p\land \neg q & \neg t \implies s & (p \land \neg q) \implies (\neg t \implies s) \\T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array}[/tex]

The given logical statement is false when [tex]p\land\neg q[/tex] and [tex]\neg t\implies s[/tex] are true and false, respectively.

The value of x has a z-score of three is 20

The given parameters are:

Mean = 2

Standard deviation = 6

z = 3

The z-score is calculated as:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]3 = \frac{x -2}{6}[/tex]

Multiply through by 6

18 = x - 2

Add 2 to both sides

x = 20

Hence, the value of x has a z-score of three is 20

Read more about z-score at:

https://brainly.com/question/15016913

#SPJ1

The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.

The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.

Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text

describing why the information provided matters to readers.

Read more on passages;

https://brainly.com/question/25849033

#SPJ1

The error is that

[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]

Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.

The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

To know more about Direct Variation, refer to:

brainly.com/question/14254277

#SPJ9

Answer:

1/5 :D

Step-by-step explanation:

Lets pick 2 point on the graph :)

We need this to find the slope!

Lets use (-5,1) and (0,2) :)

First we subtract the y coordinates! :)

2 - 1 = 1

Then we subtract the x coordinates!

0 - (-5) = 5

Now we divide!

1/5

Our answer is 1/5!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

first choice : 1/5

Step-by-step explanation:

need 2 points

one point is (0,2)

another is (5,3)

slope formula is

y2 - y1 / x2 - x1

3 - 2 / 5 - 0

1/5

This is a simple harmonic motion exercise. The proof that the resultant force on the particle, at time t, is -225 Newtons is indicated below.

Note that we have been given the following:

Mass = 9kg,

Y = 45 N

ζ = 0.4 m

Then, Y/ζ  = 45N/0.4m

= 112.5 N/m

Hence, the spring constant =

K = 112. 5N/m

From this point we can resolve the Amplitude (A):
Amplitude is given as:

A = CB - PB

= 0.6 - 0.5

A = 0.1m

I) So because one spring is elongated by x and the other is compressed by x, Hence, the spring force is:

F[tex]_{net}[/tex] = - Kₓ - Kₓ

= - 2Kₓ
= -2 x 112.5 x* X

F[tex]_{net}[/tex] = -225x Newton ..........Lets call this expression 1

From equation 1 above, we know that

Ma = -225x

a = (-225/m) x

⇒ a ∝ - x,

Hence, the motion is is simple harmonic in nature.

The time period, T = 2 π√m/K[tex]_{eq}[/tex]

Where, K[tex]_{eq}[/tex] = 2K

= 2π√(9/225)

= 2π * 3/15

= 2(22/7) * (3/15)

= 1.25714285714; thus

T ≈ 1.26 secs...............lets call this expression 2

Note that Angular Frequency is = 2π/T

= 2π/1.26

= 4.9866550057

ω = 4.99 rad/s

Since the velocity at any point x from the mean position is given by

V = ω √ (A² - x²); hence

V = 4.99 √[(0.1)² - (0.05)²

V = 4.99 x 0.0866
V = 0.432134

V ≈ 0.432..........Lets call this expression 3

Along the x-axis, A simple harmonic motion can be depicted as:

x = A sin (ωt + Ф) ..........lets call this expression 4

where, Ф = Phase constant

At t = 0; x = A

A = A sinФ

⇒ SinФ = 1

⇒ Ф = π/2

Expression 4 becomes:

x = A sin (ωt + π/2)

Inserting the values of ω and A, we have

x = 0.1 sin (4.99t + π/2).........Lets call this expression 5a

or  x  = 0.1 cos (4.99t).......Lets call this expression 5b

Hence,

Sin(π/2  + Ф) = CosФ

Learn more about simple harmonic motion at;
https://brainly.com/question/17315536
#SPJ1

The insurance cost for the second year from the information given will be $476.

The insurance cost for the second year will be:

= $14000 × 0.034

= $476

Therefore, the insurance cost for the second year will be $476

Learn more about insurance on:

https://brainly.com/question/25855858

#SPJ1

The insurance cost for the second year from the information given will be $476.

How to calculate the insurance cost?

The insurance cost for the second year will be:

= $14000 × 0.034

= $476

Therefore, the insurance cost for the second year will be $476

Learn more about insurance on:

brainly.com/question/25855858

#SPJ1

Using the z-distribution, the critical value for a confidence level of 90% is of Z = 1.65.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.65.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Okay, it's very simple, to solve this triangle you need to understand what the other angles are. We know that angle A is 90º, as it is represented as a square.

We now need to solve for angle B. angle B can be solved for by

Sin (x) = Opposite / Hypotenuse = 3 / 3√5 = 2.24ish
sin(x) = 2.24

x = [tex]sin^{-1}[/tex](2.24)

Use sin.

Answer:

Step-by-step explanation:

what's the answer

Answer:

Step-by-step explanation:

3 things of triangle are given.

2 sides + 1 angle

so, possible triangles = 1 ans

The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

An exponential function is represented as:

[tex]y = b^x[/tex]

The base is 3.

So, we have:

[tex]y = 3^x[/tex]

It is stretched vertically by 2/3.

So, we have:

[tex]y = \frac23(3)^x[/tex]

When reflected over the y-axis, we have:

[tex]y = \frac23(3)^{-x}[/tex]

An asymptote of y = 2, makes the function becomes

[tex]y = \frac23(3)^{-x} + 2[/tex]

Lastly, it passes through the point (0, 3.5).

So, we have:

[tex]y = \frac23(3)^{-x+h} + 2[/tex]

This gives

[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]

[tex]3.5 = \frac23(3)^{h} + 2[/tex]

Subtract 2 from both sides

[tex]1.5 = \frac23(3)^{h}[/tex]

Multiply by 3/2

[tex]2.25 = (3)^{h}[/tex]

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]

[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Read more about exponential equation at

https://brainly.com/question/23729449

#SPJ1

Answer:

x = 14

Step-by-step explanation:

PMN forms a triangle and the sum of interior angles in a triangle is equal to 180 therefore we can use the following equation to find the value of x

32 + 64 + 6x = 180 add like terms

96 + 6x = 180 subtract 96 from both sides

6x = 84 divide both sides by 6

x = 14

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:

(0.36x) + (y * 0.36) = 1(0.36)   (1)

Also:

0.28x + 0.64y = 1(0.55)    (2)

From both equations:

x = 0.25, y = 0.75

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Area left for flowers = Area of flower garden - Area of bird bath.

Area of flower garden [ rectangle ] :

[tex]\qquad❖ \: \sf \:length \times width[/tex]

[tex]\qquad❖ \: \sf \:3 \times 2[/tex]

[tex]\qquad❖ \: \sf \: 6\: \: {m}^{2} [/tex]

Area of bird bath [ Circle ] :

[tex]\qquad❖ \: \sf \: \pi{r}^{2} [/tex]

[tex]\qquad❖ \: \sf \:3.14 \times ( \frac{1}{2} ) {}^{2} [/tex]

[tex]\qquad❖ \: \sf \:3.14 \times \frac{1}{4} [/tex]

[tex]\qquad❖ \: \sf \:0.785 \: \: m {}^{2} [/tex]

Area left for flowers :

[tex]\qquad❖ \: \sf \:6 - 0.785[/tex]

[tex]\qquad❖ \: \sf \:5.215 \: \: m {}^{2} [/tex]

[tex]\qquad❖ \: \sf \: \approx5.22 \: \: m {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The simplified expression of the given equation is  [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]

There are three basic steps for addition or subtraction of two fractions

The given expression :- [tex]\frac{x+6}{x+4} +\frac{x-3}{3}[/tex]

Taking LCM or making the denominators same we get,

= {3(x+6) + (x-3)(x+4)}/3(x+4)

= {3x + 18 + x² +x -12}/3(x+4)

={x² + 4x + 6}/3x + 12

= [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]

Learn more about Fractions here :

https://brainly.com/question/1519053

#SPJ1

Answer:

i believe its B

Step-by-step explanation:

The total bill after tax is $38.44.

The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14

Now, determine the total cost after delivery fee has been added : $3 +  $32.14 =  $35.14

Now determine the total cost after tax : (1.094) x $35.14 = $38.44

To learn more about taxes, please check: https://brainly.com/question/25311567

#SPJ1

The total bill after tax of 9.4% is $38.44.

It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price

total cost of 4 pizzas= $6.79 *4

total cost of 4 pizzas=$27.16

total cost of 2 orders of breadsticks=$2.49*2

total cost of 2 orders of breadsticks=$4.98

total cost of purchase prior to adding delivery cost=$27.16+$4.98

total cost of purchase prior to adding delivery cost=$32.14

total cost of purchase after  delivery cost=$32.14+$3

total cost of purchase after  delivery cost=$35.14

total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)

total cost inclusive of 9.4% sales tax=$35.14*1.094

total cost inclusive of 9.4% sales tax=$38.44

Find detailed guidance on sales tax in the link found below:

https://brainly.com/question/9437038

#SPJ1

The coordinates of A exist (11, 0).

Let, the point A (-5, -2) exists reflected over the line y = -1, and then stand reflected over the line x = 3.

The distance between the y value exists -1 - (-2)= 1

We move 1 unit beyond the line y = -1

After reflection over the line y = -1 the coordinates of A becomes (-5, 1-1) is (-5, 0)

It exists reflected over the line x = 3

The distance between -5 and 3 exists 3 - (-5) = 8

We move 8 units out from the line x = 3

The Point (-5, 0) becomes (3 + 8, 0) exists (11, 0).

Therefore, the coordinates of A exist (11, 0).

To learn more about reflected over the line refer to:

https://brainly.com/question/1894106

#SPJ9

The complete question:

The point A (-5, -2) is reflected over the line y = -1, and then is reflected over the line x = 3. What are the coordinates of A.

Answer:

iTS 6 2/3 OPTION 2.

Step-by-step explanation:

Because Area = L*B

SO L = A/b

L= 65/3 * 4/13(reciprocal and multiply)

L=20/3 = 6 2/3

Answer:

So answer is 6 2/3

because Look carefully

Area =length× width

length=Area÷ width

so

[tex]21 \frac{2}{3} \div 3 \frac{1}{4} = 6 \frac{2}{3} [/tex]