Given: triangle ABC is an equilateral triangle. L, M, and N are the midpoints of AC, CB, and AB respectively. Prove: LMNB is a rhombus

Answer

393.55

Explanation

The amount that results after an amount P is invested at compound interest at rate r% and time period t is given as

A = P (1 + r)ᵗ

For this question,

A = 800

r = 3% = 0.03

t = 2 (12) = 24 (Since the interest is compounded monthly, over 2 years)

P = ?

800 = P (1 + 0.03)²⁴

800 = P (1.03)²⁴

800 = P (2.0328)

2.0328P = 800

Divide both sides by 2.0328

(2.0328P/2.0328) = (800/2.0328)

P = 393.55

Hope this Helps!!!

Luke opened a savings account 3 years ago. the account earns 6%interest compounded quarterly if the current balance is 300.00 how much did he deposit initially

Answer

This is similar to the first one too.

A = P (1 + r)ᵗ

For this question,

A = 300

r = 6% = 0.06

t = 3 (4) = 12 (Since the interest is compounded quarterly, over 3 years; there are 4 quarters per year)

300 = P (1 + 0.06)¹²

300 = P (1.06)¹²

300 = P (2.0122)

2.0122P = 300

Divide both sides by 2.0122

(2.0122P/2.0122) = (300/2.0122)

P = 149.09

Hope this Helps!!!

find a slope of the line that passes through (6,8) and (95,86)​

Applying the formula to calculate the slope

we ahve

m=(86-8)/(95-6)

m=78/89

therefore

The U.S national debt on 2015 was 1.815 * 10^13

The U.S national debt on 2005 was 4.974 * 10^12

So, the amount of increase =

1.815 * 10^13 - 4.974 * 10^12 =

18.15 * 10^12 - 4.974 * 10^12 =

(18.15 - 4.974) * 10^12 = 13.176 * 10^12

= 1.3176 * 10 * 10^12 = 1.3176 * 10^13

STEP 1: Identify and Set Up

We are given a question that requires us to find mass when given volume and density.

It is common knowledge that these parameters are related by the formulae:

We use this relation to find mass

STEP 2: Execute

Density = 1.02 g/cc

Volume = 80ml = 80 cc

Mass is therefore:

Mass = 81.6g

Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:

As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.

1.a

We can rewrite the given information in an algebraic expression as follows:

where x represents the number of 3/8-inch thick books. Solving for x:

We can rearrange the operation:

Then, we need 16 3/8-inch books to make a stack 6 inches tall.

1.b

To solve this exercise, we can use the same procedure as in 1.a.

0. Writing the information in an algebraic expression.

where x represents the groups of 1/2 pound.

We can convert the mixed number into an improper fraction:

2. Rewriting the operation:

We have 5.5 groups of 1/2 pounds in 2 (3/4) pounds.

Answer:

• 1.a 16

• 2.b 5.5

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a^2

Here, a = 5 inches

The answer would be 150 in^2

Given the expression:

To simplify the expression, we will use the following rule of the exponents:

The answer will be:

you will write the answer as 3^6

Answer

Sale Price = $22

Explanation

Mark down percentage is given as

For this question,

Markdown percentage = 12%

Original Price = $25

Sale Price = ?

25 - (Sale Price) = 3

Sale Price = 25 - 3

Sale Price = $22

Hope this Helps!!!

The expression: 6E7, is a way of writing a number in scientific notation and it is equivalent to:

Since 10^7=10,000,000, then:

We have symbols that represent a letter and a number.

With the equations or relations in the left we have to find the numeric value for each picture, and then use the letter to complete the hidden message.

First equation is:

So, the value of a spyder web is 8 and the letter for that is i.

The second equation is:

The value of candy is 17 and the letter is T.

The Third equation is:

The value of cat is 3 and the letter is S.

The fourth equation is:

The value of ballons is 33 and the letter is E.

The fifth equation is:

The value of bat is 7, but there is some mistake, it must be 6 and the letter C.

The sixth equation is:

The value of pumpkin is 7 and the letter is O.

The seventh equation is:

The value of spyder is 24 and the letter is B.

The last equation is:

The only value for ghost is zero and the letter L and the value of tree is zero too and the letter is O.

The hidden message is:

BOIL IS IOOOCEOT

The general equation of line with the slope "m" and passing points (a,b) is :

y - b = m (x -a)

In the given question:

Slope m = -2, passing points (a,b) = (4,-4)

Substitute the value of a = 4, b = -4 in the general equation of line

The equation with the slope -2 and passing points (4,-4) is 2x + y = 4

Answer : 2x + y = 4

Solution

(1). Domain

Since the graph is a polynomial, thus

The domain is all the elements of the set of Real Number

(2) . Range

Notice that the graph is on the x - axis and above the x - axis throughout

The range will be

(3). x - intercept

We check where the graph touch the x - axis ( we have two)

That is at

(4). y - intercept

We also check where the graph touch the y - axis

That is at

(5). End Behaviour

First from the graph

Second from the graph

Options C and D.

The median age of the Sea turtles is 55 while the median age of the sharks is 30, thus validating OPTION C

We can get the ranges of the two distributions to be:

Sea Turtles: 65 - 45 = 20

Sharks: 55 - 10 = 45

Sharks have a larger range, validating OPTION D

In parallelogram ABCD, which angle is congruent to ?

Let us draw the parallelogram to better understand the problem.

As you can see from the above figure,

∠ABC and ∠CDA are congruent. (drawn in black color)

Also, ∠BCD and ∠DAB are congurent. (drawn in red color)

This means that the opposite angles are congruent in a parallelogram.

Therefore, the correct answer is option C

∠ABC and ∠CDA are congruent.

Solving Matrix Equation.

Thus, the correct answer is;

x = 3/7 and y = -2/7

ANSWER

p ≤ -3

EXPLANATION

To solve this inequality first we have to subtract 5 from both sides:

That's the solution, but we can flip it to see it more clearly:

To graph this, we have to draw a line from -3 to the left. Usually we have to draw a filled circle on -3, to indicate that that value is included in the solution.

The measure of angle m∠A will be 70°,for the parallelogram ABCD

Parallelogram and its Properties:

                      Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.

Properties:

                     1. Opposite sides are parallel to each other.

                     2. Length of opposite sides are equal.

                     3.Diagonally opposite angles are equal.

                     4. Diagonals bisects each other.

                     5. Sum of any two adjacent angle is 180°

From figure,

                     ABCD is a parallelogram

                      m∠A = 2x + 50

                      m∠ C = 3x + 40

In a parallelogram ABCD we know opposite angles are equal to each other,

                          m∠A = m∠C

                   2x + 50 = 3x + 40

                    3x - 2x = 50 - 40

                       x = 10

Hence,

               m∠A  = 2x + 50

                              put the value of x we get,

               m∠A  = 2 * 10 + 50

                          = 20 + 50

                         = 70°

                       m∠A  = 70°

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[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-34})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-34)}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-7)}) \implies y +34= 5 (x +7) \\\\\\ y+34=5x+35\implies {\Large \begin{array}{llll} y=5x+1 \end{array}}[/tex]

we have

2*2=2+2=4

5*5=5+5+5+5+.5=25

5 times 5

example

2*3

its 2 times 3

3+3=6

4*3

4 times 3

3+3+3+3=12

Answer:

2 x 2 = 4.

two multiplied by two equals four.

Answer:

The domain would be all real numbers.

Step-by-step explanation:

For Interval notation, it would be written as (-∝, ∝)

(I don't know what signs those are, but they are supposed to be infinity signs)

Domain is what x can or can't be. In the function that is in the image, the function is y=a constant. So, no matter what x is, y will always be the constant. So, x can be all real numbers.

Hope this helps!

C(r)=0.5r+1.5.

The domain of a function is the set of all input variables of the function. In this case "r"

The domain r is the number of tea refills.

The interval notation uses the form (x1,x2) and it depends on whether the interval includes or does not includes the limits. if the interval includes the limit then we use the notation [x1,x2].

a. Since neither of the endpoints is included in the inequality the interval notation should be

c. The inequality includes all numbers that are less to 4 but does not include number -4, the interval notation should be

d. The solution for the inequality includes two solutions, then we write both separately and unite them together. The interval notation should be

f. The numbers should be all less than pi, but it does not include pi

g. all numbers greater or equal to 3

h. All numbers less or equal to -2

i. All numbers greater than 0, but it does not include 0

j. all numbers less than e but it does not include e

Solution:

Given:

From the probability, it can be deduced that as the number of trials increases, the observed frequency will get closer to the expected frequency.

Therefore, if the number of trials increases significantly, then the observed frequency of landing heads up gets closer to the expected frequency based on the probability of the coin landing heads up.

Answer: 38.76

Step-by-step explanation:

All you have to do is move both decimals to the right and multiply, example, 10.2 = 102. & 3.80 = 380., then you multiply both numbers. In this case, 102 x 380 is 38760. After you multiply both numbers, you move the decimal to the left, so 38760. = 38.760 or 38.76.

To simplify this expression we need to follow this procedure:

It means that the correct answer is:

Starting with the expression:

Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:

Next, solve for multiplications. In this case, solve 23 times 4:

Finally, solve additions and substractions from left to right:

Therefore:

Given:

Derivative and sope of tangent

Required:

We want to define relation

Explanation:

The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example

and the slope of that tangent is the derivative of function at point P

Now to find equation of a tangent line

1) Find the first derivative of f(x).

2) Plug x value of the indicated point into f '(x) to find the slope at x.

3) Plug x value into f(x) to find the y coordinate of the tangent point.

4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

Given the table:

x f(x)

2 6

7 3

9 5

To determine the coordinate given in the table, we have the following:

f(2) = 6

f(7) = 3

f(9) = 5

From the answer choices, the only coordinate given is:

f(5) = 9

ANSWER:

f(9) = 5