Write a similarity statement relating the three triangles in the diagram

Answer:

[tex]\sum_{i=1}^{12}(3i-1) = 222[/tex]

Step-by-step explanation:

The given series is

[tex]\sum_{i=1}^{12}(3i-1)[/tex]

The first term is

[tex]f(1) = 3 \times 1 - 1 = 2[/tex]

The last term is

[tex]f(12) = 3 \times 12 - 1 = 35[/tex]

To find the number of terms in the sequence, solve,

[tex]3i - 1 = 35[/tex]

[tex]3i = 36 \\ i = 12[/tex]

The sum of the first i-terms of an arithmetic sequence is:

[tex]S_i = \frac{i}{2} (f(1) + f(2))[/tex]

We substitute the values to get;

[tex]S_ {12}= \frac{12}{2} (2+ 35)[/tex]

[tex]S_ {12}=6(37)[/tex]

[tex]S_ {12}= 222[/tex]

Answer:

Step-by-step explanation:

B is correct.  This choice accurately describes the sample.

If they had six bags of cookies and each bag has thirteen cookies, then in total they have a total of seventy-eight cookies. If they've eaten twenty-nine cookies, then they now have forty-nine cookies because 78-29=49.

Answer:

[tex]\displaystyle y'' = \frac{-75}{16y^7}[/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:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y^4 + 5x = 21[/tex]

Step 2: Find 1st Derivative

Step 3: Find 2nd Derivative

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

Unit: Differentiation

Answer: x=0, x²=0

Step-by-step explanation:

Answer:

x=3 and x=5/2

Step-by-step explanation:

10

Step-by-step explanation:

first what is 10 take away 2 is 8 then 10 take away 2 is 8 + 2 equals 10 8 + 2 equals 10 so that's how I got the answer 10

Answer:

5ft

Step-by-step explanation:

1.1j=5.5ft

Divide both sides by 5.5

So: j=5ft.  This is the previous jump

Answer:

48

Step-by-step explanation:

Answer:

b)48

Step-by-step explanation:

Answer: 10cm^3 equals density please give briainliest

Step-by-step explanation: formula D=M/V

so D=20/2

D=10cm^3

Answer: Period: 4. Amplitude: 3

Step-by-step explanation: The period is how long it takes for one cycle of the function (one up and down). In this graph, one cycle ends at 4.

The amplitude is how far away the extremes of the graph are from the midline. This graph is a total of 6 units tall, making the amplitude 3. (I usually find total graph height and divide by 2.)

39>38

16=16

11<315

5>4

Hope this helps you mate

~♥~♪☆＼(^０^＼) ♪(／^-^)／☆♪☆＼(^０^＼) ♪(／^-^)／☆♪＼(*＾▽＾*)／＼(*＾▽＾*)／♪☆＼(^０^＼) ♪(／^-^)／☆♪ ♬ ヾ(´︶`♡)ﾉ ♬ ♪

Answer:

$34.70 rounded to $35, $278.22 rounded to $278, $45.89 rounded to $46, $8.38 rounded to $8.

Step-by-step explanation:

The inequality to represent the number of hours when Kent has ridden more than 30 miles is y = 6x for x > 5, where x is the number of hours ridden and y is the distance in miles.

Step-by-step explanation:

Step 1:

First, we need to plot the coordinates of the line on the graph.

We plot the points that fall exactly on an x axis value and also on a y axis value.

There are three such points on the given graph; (5, 30), (10, 60) and (15, 90). These points fall exactly on the values of the x axis and the y axis.

Step 2:

Now, we establish a relationship between the values of x (the number of hours ridden) and y (distance in miles).

Here y is the dependent value and x is the independent value i.e. the value of y values according to the values of x.

In 5 hours, Kent rode 30 miles. In 10 hours, he rode 60 miles and in 15 hours he rode 90 miles.

Step 3;

So for every 5 hours, Kent rides another 30 miles.

So y = 6x for x>5 is the

When x = 10, y = 6 × 10 = 60 miles,

When x = 15, y = 6 × 15 = 90 miles.

Answer:

Reflect across the line y = x (x, y) -> (y, x)

Step-by-step explanation:

The simplest way is just one step, a reflection across the line y=x.  when doing this the rule is (x, y) -> (y, x).

There are a number of ways to do it otherwise, such as a reflection across the x axis then the y axis, or the other way around, or a translaton then reflection.  Like I said though, the reflection across y=x is the fastest.  Let me know if you have any further questions.  

Answer:

All functions have a dependent variable.

All functions have an independent variable.

A horizontal line is an example of a functional relationship.

Step-by-step explanation:

i did it n got it right yayyyyyyyy

Answer:

Step-by-step explanation:

When dividing fractions, I use a method called Keep Change Flip. Let's use the example 1/2 divided by 3/4 as an example. First, you have to keep the first fraction the same. This is what you currently have: 1/2 / 3/4. Next, you have to change the divison sign into a multiplication symbol. Now, this is what it should look like: 1/2 x 3/4. Then, you have to flip the fraction 3/4 into 4/3. Now, you have 1/2 x 4/3. Multiply the fraction. If you don't know how to, multiply numerator by numerator, denominator by denominator. You should get 4/6. However, this isn't your final answer. You can simplify this by dividing by 2 to get 2/3. So, your answer is 2/3. Hope this helped you and let me know if you need more help! :D

Final answer:

There are 216 calories in 1 cup of yogurt.

Explanation:

To find out how many calories are in 1 cup of yogurt, we can use the given information that there are 162 calories in 3/4 cup of yogurt. We can set up a proportion to solve for the number of calories in 1 cup:

(3/4 cup) / (162 calories) = (1 cup) / (x calories)

By cross-multiplying, we get:

3/4 * x = 162 * 1

Simplifying the expression:

3x/4 = 162

Multiplying both sides of the equation by 4/3:

x = (162 * 4) / 3 = 216 calories

Therefore, there are 216 calories in 1 cup of yogurt.

Answer:

3/4, 75% chance

Step-by-step explanation:

you have four in total, three of which are not c, so you have a three out of four chance of NOT picking c. 3/4 as a percentage is 75%

Answer:

25%

Step-by-step explanation:

On MobyMax its 25%

The answer will be 150.8

Answer: AL≈150.8

Step-by-step explanation:

AL=2πrh

AL=2π3(8)

AL=2π24

AL=150.8 Rounded up

Answer:

24+8 square root 3

Step-by-step explanation:

The ratio is x : x radical 3 : 2x

hypotenuse= 2x= 16

x =8

x square root 3 = 8 square root 3

16+8=24

Answer:

180x cubic feet

Step-by-step explanation:

Multiply 15, 12 and x together.

Answer:

180x

Step-by-step explanation:

you multiply 12 and 15 and x.

Answer:

I will guess 21

Step-by-step explanation:

9+10=21 boi

Answer:

for Usatestprep it is 21

Step-by-step explanation:

i swear 100%

Answer:

x = -2 , y = 1

Step-by-step explanation:

Solve the following system:

{-2 x - y = 3 | (equation 1)

-9 x - y = 17 | (equation 2)

Swap equation 1 with equation 2:

{-(9 x) - y = 17 | (equation 1)

-(2 x) - y = 3 | (equation 2)

Subtract 2/9 × (equation 1) from equation 2:

{-(9 x) - y = 17 | (equation 1)

0 x - (7 y)/9 = -7/9 | (equation 2)

Multiply equation 2 by -9/7:

{-(9 x) - y = 17 | (equation 1)

0 x+y = 1 | (equation 2)

Add equation 2 to equation 1:

{-(9 x)+0 y = 18 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by -9:

{x+0 y = -2 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = -2 , y = 1

Answer:

C) (−2, 1)

Step-by-step explanation:

The -1 inside the parenthesis is an x value and the blank is a y value.

f(x) = y

Replace x in the equation with -1 to solve for y:

-2(-1) + 3 = 2+ 3 = 5

The answer is 5

Part a: The value of x is 33°

Part b: The measure of each base angle is 69°

Explanation:

It is given that the vertex angle of an isosceles triangle measures 42°.

The base angle in the triangle has a measure of [tex](2x+3)^{\circ}[/tex]

Part a: To determine the value of x

Since, in an isosceles triangle the base angles are always equal.

Thus, the three angles in an isosceles triangle add up to 180°

Hence, we have,

[tex]42+2x+3+2x+3=180[/tex]

              [tex]42+4x+6=180[/tex]

                     [tex]4x+48=180[/tex]

                             [tex]4x=132[/tex]

                               [tex]x=33^{\circ}[/tex]

Thus, the value of x is 33°

Part b: To find the measure of each base angle.

Base angle = [tex](2 x+3)^{\circ}[/tex]

Substituting [tex]x=33^{\circ}[/tex] , we get,

[tex]Base \ angle = (2(33)+3)^{\circ}[/tex]

                  [tex]=(66+3)^{\circ}[/tex]

                  [tex]=69^{\circ}[/tex]

Thus, the measure of each base angle is 69°

Answer:

33 and 69 lol funny number

Step-by-step explanation:

Answer:

No answer choices are correct; y=-9/6x-3

Step-by-step explanation:

Slope=Rise/Run=(3-(-6))/(-4-2)=9/-6=-9/6

y=-9/6x+b

3=-9/6(-4)+b

3=36/6+b

3=6+b

-3=b

So the equation is y=-9/6x-3, so none of your answer choices are correct

Step-by-step explanation:

The question above is answered below.

Consecutive numbers are set of numbers that follow one another in ascending or descending order, e.g. 1, 2, 3, 4, 5....

The sum of three consecutive numbers = 72

Let the unknown consecutive numbers be represented by x+1, x+2 and x+3 such that:

[tex](x + 1) + (x + 2) + (x + 3) = 72[/tex]

Remove the brackets

[tex]x + 1 + x + 2 + x + 3 = 72[/tex]

Collect like terms and simplify

[tex] x + x + x + 1 + 2 + 3 = 72[/tex]

[tex]3x + 6 = 72[/tex]

Make 3x subject of formula by subtracting 6 from both sides

[tex]3x + 6 - 6 = 72 - 6[/tex]

[tex]3x = 66[/tex]

To obtain the value of x, divide through by the coefficient of x, which is 3. Hence;

[tex] \frac{3x}{3} = \frac{66}{3} [/tex]

[tex]x = 22[/tex]

Since x = 22,

[tex]x + 1 = 22 + 1 = 23[/tex]

[tex]x + 2 = 22 + 2 = 24[/tex]

[tex]x + 3 = 22 + 3 = 25[/tex]

The smallest of these numbers is 23.

Check,

23 + 24 + 25 = 72

Answer:

the volume of the triangular prism is 1,185.6  in³

Step-by-step explanation:

To find the volume of these triangular prism, we will, first, find the area of the triangle then multiply by the length

Area of triangle = [tex]\frac{1}{2}[/tex] × b×h

From the diagram ,the height of the triangle  is given to be 10.4 in and the base is given to be 12 in.

We will now proceed to insert the values into the formula;

                 Area of triangle  = [tex]\frac{1}{2}[/tex] × b×h

                                              = [tex]\frac{1}{2}[/tex] × 12×10.4

                                                = [tex]\frac{1}{2}[/tex] × 124.8

                                                 =62.4

Area of triangle is 62.4 in²

From the diagram is given to be 19 in

Volume of triangular prism = area of triangular prism × l

                                              =62.4 in²   ×    19 in

                                              =1,185.6  in³

Therefore the volume of the triangular prism is 1,185.6  in³

Answer:

B is the answer I Know it is wright

Step-by-step explanation:

so you add 25 and 19 and then divide 44 and 2 and get 22

Answer:

The correct answer is B. 1 in 12.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Percentage of the U.S. population that catches the flu each season = 8%

8% = 8/100

2. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?

Let's review together each of the possible answers given:

A. 1 in 8  = 1/2 = 0.125 = 12.5%, this is not the percentage given.

B. 1 in 12  = 1/12 = 0.083 = 8.3%, if we round to 8%, this is the percentage given.

C. 1 in 18  = 1/18 = 0.056 = 5.6%, this is not the percentage given.

D. 1 in 80 = 1/80 = 0.0125 = 1.25%, this is not the percentage given.

The correct answer is B. 1 in 12.