Question 1
Elena, Lin, and Noah all found the area of Triangle Q to be 14 square units but
reasoned about it differently, as shown in the diagrams. Explain at least one student's
way of thinking and why his or her answer is correct.
Q
Lin
Elena
Q
Noah

Answer:

[tex]y=(x-3)^{2} -25[/tex]

Step-by-step explanation:

The standard form of a quadratic equation is [tex]y=ax^{2} +bx+c[/tex]

The vertex form of a quadratic equation is [tex]y=a(x-h)^{2} +k[/tex]

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

[tex]h=\frac{-b}{2a}[/tex]

In this case, our quadratic equation is [tex]y=x^{2} -6x-16[/tex]. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

[tex]h=\frac{-b}{2a}[/tex] ⇒ [tex]h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3[/tex]

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is [tex]y=x^{2} -6x-16[/tex]

[tex]y=x^{2} -6x-16[/tex] ⇒ [tex]y=(3)^{2} -6(3)-16[/tex] ⇒ [tex]y=9-18-16[/tex] ⇒ [tex]y=-25[/tex]

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: [tex]y=a(x-h)^{2} +k[/tex]

a: 1

h: 3

k: -25

[tex]y=(x-3)^{2} -25[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Since X and Y are supplementary angles it means that the sum of their angles add up to 180°

To find Y , add X and Y and equate it to 180° and solve

That's

X + Y = 180

Y = 180 - X

X = 72°

Y = 180 - 72

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

f(g(-3)

g(-3) = 3(-3) = -9 - 5 = -14

f(-14)= -4(-14) - 6 = 56 - 6 = 50

Answer:

f(3)=2

Step-by-step explanation:

To find f(3), we simply need to find the ordered pair at x=3.

From the graph, we can see that the ordered pair at x=3 is (3,2).

Thus, f(3)=2.

And we're done!

The general form of a conditional statement is written as "if p, then q" in which p is the hypothesis and q is the conclusion.

Answer:

B) 1

Step-by-step explanation:

All I did was simplify the equation

1509/1600

(Decimal: 0.943125)

HOPE THIS HELPS!!!! :)

<333333333333

Answer:

(5,6)

Step-by-step explanation:

move the dot 8 spaces to the right because that is the across the y axis.

Answer:

probability of randomly selecting an employee who is female and under the age of 25= 0.15

In percentage= 15%

Step-by-step explanation:

There are 300 female employees. There are 80 employees who are under the age of 25

Probabilty of choosing a female employees= 300/400

Probabilty of choosing a female employees= 0.75

Probabilty of choosing an employees under the age of 25

= 80/400

Probabilty of choosing an employees under the age of 25

= 0.2

probability of randomly selecting an employee who is female and under the age of 25= 0.2*0.75

probability of randomly selecting an employee who is female and under the age of 25= 0.15

In percentage= 0.15*100

In percentage= 15%

Answer:

48

Step-by-step explanation:

48 is greater then 6×4.2

It's even

It's a multiple of 3

the difference is 4

Answer: 11.18

Step-by-step explanation: To find one side of a square, you need to square root it’s area. The square root of 125 is 11.18.

Answer:

The scale factor is 2.2

Step-by-step explanation:

To find the scale factor, you look at the length of any two sides that correspond to each other. For example, in the diagram we can see that the side with the length of 4 on the smaller pentagon corresponds to the side with the length of 8.8 on the larger pentagon.

To find the scale factor, you divide the length of the side of the larger pentagon, by the length of the side of the smaller pentagon.

[tex]\frac{8.8}{4} = 2.2[/tex]

The scale factor is 2.2

Hope this helps!

Answer:

The answer is below

Step-by-step explanation:

The relative frequency is the proportion of a class or interval within a category. It is represented by the formula:

Relative frequency = frequency / total frequency

The percent frequency is the relative frequency expressed in percentage, it is given by the formula:

Percent frequency = Relative frequency × 100%

Using the formulas above, the table is filled:

The total frequency = 39

Class           Frequency     Relative frequency         Percent frequency

12 - 14                  2                  2/39 = 0.0513              0.0513 × 100% = 5.13%

15 - 17                  8                  8/39 = 0.2051              0.2051 × 100% = 20.51%

18 - 20                 11                 11/39 = 0.2821              0.2821 × 100% = 28.21%

21 - 23                  9                 9/39 = 0.2308             0.2308 × 100% =23.08%

24 - 26                 9                 9/39 = 0.2308             0.2308 × 100% =23.08%

Class           Frequency     Relative frequency         Percent frequency

12 - 14                  2                  0.0513                          5.13%

15 - 17                  8                  0.2051                          20.51%

18 - 20                 11                 0.2821                          28.21%

21 - 23                  9                 0.2308                          23.08%

24 - 26                 9                 0.2308                          23.08%

Answer:

x =-15

Step-by-step explanation:

[tex]8x-9x = \frac{150}{10} \\\\\mathrm{Add\:similar\:elements:}\:8x-9x=-x\\-x=\frac{150}{10}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{150}{10}=15\\-x=15\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{15}{-1}\\\\Simplify\\x=-15[/tex]

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius

From the question

r = 8 yd

π = 3.14

Substitute the values into the above formula and solve

Circumference = 2(8)(3.14)

We have the final answer as

Hope this helps you

Answer:

Option (3). EF

Step-by-step explanation:

From the figure attached,

Plane defined by EAB can be represented by the face EABF of the square prism also.

Similarly, plane EFG can be represented by the face EFGH of the prism.

Now these sides EABF and EFGH are joining each other at the edge EF of the cuboid.

Therefore, intersection of the given planes is EF.

Option (3) will be the answer.

Answer:

7 Sec

Step-by-step explanation:

Answer:

7.0 sec

Step-by-step explanation:

Answer:

Reliability= 149.94

Step-by-step explanation:

Field data have indicated that Unit A has a failure rate of 0.0004 failure per hour.

Reliability per hour=1- failure rate

Reliability per hour= 1-0.0004

Reliability per hour= 0.9996

Reliability= rate if reliability * number of hours

Rate of reliability= 0.9996 per hour

Number of hours= 150 hours

Reliability= 0.9996*150

Reliability= 149.94

Answer:

78 Words per minute

Step-by-step explanation:

A unit rate is simply comparable to an average.  Given this, we can say the following:

Unit_Rate = 3666 Words / 47 minutes

Unit_Rate = 78 Words per minute

Cheers.

Answer:

f(-2) = g(-2)

Step-by-step explanation:

The lines intersect at the point (-2, 4). That means that the solution of the system of equations is (-2, 4). When x = -2, the two functions, f(x) and g(x), have the same value, 4.

That means that f(-2) and g(-2) are equal and are both equal to 4.

Answer: f(-2) = g(-2)

Answer:

v = -5

Step-by-step explanation:

Step 1: Write out equation

-8 + 5v = -33

Step 2: Add 8 on both sides

-8 + 8 + 5v = -33 + 8

5v = -25

Step 3: Divide both sides by 5

5v/5 = -25/5

v = -5

Answer:

Solve

-8 +5v=-33

So 5v=-33+8

(-8 became 8 because we brought it back to the other side to have the v 《5v》 alone and the numbers alone )

5v= -25

So v=-25/5

We simplify -25/5

v=-5

Answer:

  x = (a +b)/c

Step-by-step explanation:

Perhaps you want to solve for x.

Multiply by x:

  a + b = cx

  x = (a +b)/c . . . . . divide by c

Answer:

b=22

Step-by-step explanation:

1 Remove parentheses.

b-11-29=-18b−11−29=−18

2 Simplify b-11-29b−11−29 to b-40b−40.

b-40=-18b−40=−18

3 Add 4040 to both sides.

b=-18+40b=−18+40

4 Simplify -18+40−18+40 to 2222.

b=22b=22

Answer:

[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx[/tex]

Step 2: Integrate Pt. 1

Set variables for u-substitution.

Step 3: Integrate Pt. 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integration

Answer:

[tex]\sec^2(\theta)=\frac{25}{16}[/tex]

Step-by-step explanation:

Recall what the relationship between cosine and secant:

[tex]\sec(\theta)=\frac{1}{\cos(\theta)}[/tex]

In other words, secant is the reciprocal of cosine.

So, if we know cosine, we only need to find its reciprocal to find secant.

We are given that cosine is:

[tex]\cos(\theta)=\frac{4}{5}[/tex]

Then secant must be:

[tex]\sec(\theta)=\frac{5}{4}[/tex]

So:

[tex]\sec^2(\theta)=(\frac{5}{4})^2[/tex]

Square:

[tex]\sec^2(\theta)=\frac{25}{16}[/tex]

And we're done!

The average ocean depth is 3.7 × 103 m, and the area of the oceans is 3.6 × 1014 m2. What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters. Round your answer to one decimal place.)