Given: CD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: a2=b2+c2−2bccosAFigure shows triangle A B C. Segment A B is the base and contains point D. Segment C D is shown forming a right angle. Segment C D is labeled h. Segment A B is labeled c. Segment B C is labeled a. Segment A C is labeled b. Segment A D is labeled x. Segment D B is labeled c minus x. Select from the drop-down menus to correctly complete the proof.Statement ReasonCD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ACD and △BCD are right triangles. Definition of right trianglea2=(c−x)2+h2a2=c2−2cx+x2+h2Square the binomial.b2=x2+h2cosA=xbbcosA=xMultiplication Property of Equalitya2=c2−2c(bcosA)+b2a2=b2+c2−2bccosA Commutative Properties of Addition and Multiplication

Surface area of a rectangular prism:

Substitute 1.2 for all of the variables in the formula:

Using a calculator, you should get an answer of:

The answer is that the surface area of this shape is 8.64 yards.

The given fractions are,

The LCD of fractions is the least common multiple of the denominators.

So, the LCD of the above fractions is,

Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.

So, the first fraction can be expressed in terms of the LCD as,

The second fraction can be expressed in terms of the LCD as,

traveledGiven:

The total number of students is N = 142.

The number of students riding in a car is n(C) = 50.

The total number of buses is b = 4.

The objective is to find the number of students traveling on each bus.

Explanation:

Consider the number of students travelled in each bus as s.

Then, the total number of students traveling in 4 buses will be 4s.

The algebraic expression for the total number of students N can be represented as,

On plugging the given values in equation (1),

On further solving the above equation,

Hence, the number of students traveling on each bus is 23.

By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get

Now, lets multiply by 2 the second equation

With this two equations, lets subtract the second equation from the first equation

We get

If we divide y by 19 we get

Now, using this value in the second equation we get

If we subtract 6 on both sides, we get

Finally, we divide by 5 on both sides and we get

For a shape to be considered a parallelogram it has to meet the following conditions:

0. The opposite sides must be equal

1. The opposite sides are equal

2. Adjacent sides are supplementary

3. The diagonals bisect each other

4. The opposite sides are parallel

For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:

MN=QP and MQ=NP

MN || QP and MQ || NP

The diagonals MP and NQ bisect each other.

∠M=∠P and ∠N=∠Q

From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram

You have the following product:

27 x 8

To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.

Then, you have:

25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25

25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50

25 x 8 = 100 + 100 each pair of 50's add up 100

25 x 8 = 200

Hence, an estimation of the given product is 200, by considering 27 rounded to 25.

The distance on the map is 14 cm

Parameters:

Map scale: 5 cm = 2 km

Given actual distance = 5.6km

Let x be the distance on map, then

x = 5.6 km

2x = 5 * 5.6

2x = 28

x = 28/2

= 14 cm

ANSWER

P(x) = 2700(1.052)^t

P(4) = 3307. (Rounded to nearest student)

EXPLANATION

Given:

1. The current student population to be 2700

2. The growth rate = 5.2% = 0.052

Desired Outcome

1. The exponential growth model

2. Population of the students in 4 years

The Exponential Growth Model

Population in 4 years

Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)

Okay, in this case the statement talks about the sum, according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.

So, in this case the correct option is A. b+9 because it says sum

we have two points (0, 6) and (4, 3)

this can be represented as (x, y)

the equation of a straight line is

y = mx + c

slope = m = y2 - y1/ x2 - x1

x1 = 0, y1 = 6, x2 = 4 and y2 = 3

slope = 3 - 6 / 4 - 0

slope = -3/4

slope = -3/4

from the equation of a straight line

(y - y1) = m(x - x1)

y1 = 6 and x1 = 0

y - 6= -3/4(x - 0)

y - 6 = -3/4x + 0

y = -3/4x + 6

the error he made was that he used - 6 instead of +6 in the final answer

11 n+ 12

In this expression, to simplify means to reduce it to the simpler expression. Hence:

1) Grouping similar terms

4n + 12 + 7n =

2) Adding them up:

4n+7n+12=

11n +12

we know that

f(4) is the value of the function f(x) when the value of x is equal to 4

so

For x=4

Look at the graph

The value of the function f(x) is equal to 3

therefore

We must divide the 5 pound bag in 6 different containers, therefore:

Each container will hold 0.83 pet food

To find the average rate of change over an interval we need to calculate how much the function has changed over that interval by subtracting the final value by the initial one and dividing by the lenght of the interval. With this in mind we have:

The average rate of change for this interval is 1.5

First of all, simplify the given fractions

solution

For this case the tangent line to the circle and the point should be:

The reason is because the tangent line and the point needs to touch the circle just one time

In order to determine the surface area of the cube, use the following formula:

where a is the length of the side of a cube a = 11 m.

Replace the value of a into the formula for S:

Hence, the surface area of the given cube is 726m^2

ANSWER:

C.

STEP-BY-STEP EXPLANATION:

We have the following function:

Using the substitution method, we can calculate the value of x, like this:

The slope intercept form equation is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The formula for determining slope is expressed as

slope, m = (y2 - y1)/(x2 - x1)

From the information given,

y2 = 6, y1 = 2

x2 = 0, x1 = 4

Slope, m = (6 - 2)/(0 - 4) = 4/- 4

m = - 1

We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes

6 = - 1 * 0 + c

6 = c

c = 6

The equation would be

y = - x + 6

Answer:

Step-by-step explanation:

Since y and x are inversely proportional, we'll have that:

For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:

This way, our formula would be:

Plugging in x = 7,

Let u make the first box x and the second box y.

If there is a proportional relationship between the number of bananas and their weights, it means that:

We can take the first pair and solve for x as follows:

We can solve for y in the same manner:

Therefore, the boxes are filled as shown below:

We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.

The number 23:77 is a ratio and is it equivalent to:

To get the probability of the event not-E, we can proceed as follows:

So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).

Solution

Given

We want to determine if it's a Polynomial

A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Hence 4 - 8x + x^2 is a Polynomial

The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,

The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,

The age of Mary is 15 years old.

To solve this, we have three expressions:

Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry

Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:

Now we can replace T in the second equation:

Finally, we can replace J in the first equation to get the age of Mary:

Thus, the age of Mary is 15 years old.

Volume of a rectangular prism = base length x width x heigth

Where;

Volume = 600 cm3

base length = 15

width = x

height = 8

Replacing:

600 = (15) (x) (8)

Isolate x

600/ (15)(8) = x

x = 600/ (8)(15)

option C

And x is divisible by 6 . The natural number of x will be

To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:

Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):

therefore, the origin is not a point of the solution set.

As given by the question

There are given that the series

Now,

For step 1:

Put n=1

Then LHS =1

And

So,

P(n) is true for n=1.

Now,

Step 2:

Assume that P(n) istrue for n=k

Then,

Adding 2k+1 on both sides

So, we get:

P(n) is true for n=k+1

By the principle of mathematical induction P(n) is true for all natural numbers n.

Hence,

For all n.

Hence proved.

We will draw a sketch to see the position of the cable

From the figure, we can use the tangent ratio to find the height

By using the cross-multiplication

a) The height of the pole is 24.3 feet to the nearest tenth

To find the length of the cable we will use the cosine ratio

Switch L and cos(29.6)

b) The length of the cable is 49.1 feet to the nearest tenth