Consider the diagram and the derivation below. Given: In △ABC, AD ⊥ BC Derive a formula for the area of △ABC using angle C. It is given that in △ABC, AD ⊥ BC. Using the definition of sine with angle C in △ACD results in sin(C) = . Using the multiplication property of equality to isolate h, the equation becomes bsin(C) = h. Knowing that the formula for the area of a triangle is A = bh is and using the side lengths as shown in the diagram, which expression represents the area of △ABC? bsin(C) absin(C) cbsin(C) hbsin(C) Mark this and return

A fact family is a group of math facts using the same numbers.

Example:

Using the numbers: 5, and 2,

5 ∙ 2 = 10

2 ∙ 5 = 10

10 ÷ 2 = 5

10 ÷ 5 = 2

A fact family is a set of related math facts using the same numbers to show the relationship between addition and subtraction or multiplication and division.

Definition of a Fact Family

A fact family in mathematics consists of a group of related math facts that use the same set of numbers. Specifically, in the context of addition and subtraction or multiplication and division, fact families demonstrate the relationship between these operations. For example, with the numbers 2, 4, and 6, a fact family would include the following equations: 2 + 4 = 6, 4 + 2 = 6, 6 - 2 = 4, and 6 - 4 = 2. Each pair of arithmetical operations, being related by inverse functions, create the concept of a fact family, illustrating how numbers and operations are interconnected.

Answer:

0 - 0.23 - 1.02 - 3/2 - 1.89 - 1.98 - 13/5

Step-by-step explanation:

We have to put the number in an increasin order:

0 - 0.23 - 1.02 - 3/2 - 1.89 - 1.98 - 13/5 or

0 - 0.23 - 1.02 - 1.5 - 1.89 - 1.98 - 2.6

Answer:

The constant of proportionality is 3/2

B is correct.

Step-by-step explanation:

We are given a table of Time (x) and Number of pages (y)

In x minutes printer prints y number of pages.

As we know the it would be direct proportion because if time increase number of printing page increase.

Thus, y=kx

x is time ( independent variable)

y is number of pages (dependent variable)

k is constant of proportionality.

From table we will take the value of x and y and to solve for k

x=2, y=3

3=2k

[tex]k=\dfrac{3}{2}[/tex]

Hence, The constant of proportionality is 3/2

Answer:

Option B) [tex]\frac{3}{2}[/tex]      

Step-by-step explanation:

We are given the following information in the question:

A table showing the number of pages printed(y) in time(x).

x:       2       6       8       18

y:       3        9      12       27

We have to find the constant of variation.

Constant of variation

Constant of variation =

[tex]\displaystyle\frac{y_2-y_2}{x_2-x_1}\\\\(x_1.y_1), (x_2,y_2)\text{ are the points belonging to the given table.}[/tex]

Putting the values, we get:

[tex]\text{Constant of variaion} = \displaystyle\frac{9-3}{6-2} = \frac{12-9}{8-6} = \frac{27-12}{18-8} = \frac{3}{2}[/tex]

Hence, the constant of variation is [tex]\frac{3}{2}[/tex]

Answer:

Option C.  [tex]6.3[/tex]

Step-by-step explanation:

we know that

To find the modulus of a complex number, apply the Pythagoras theorem

Let

c-----> the modulus

[tex]c=\sqrt{(-2)^{2}+(-6)^{2}}[/tex]

[tex]c=\sqrt{4+36}[/tex]

[tex]c=\sqrt{40}=6.3[/tex]

Answer:

The last ONE!!!

Step-by-step explanation:

In the attachment!

Answer:

 y > -3.

5y ≥ -4x -10.

Step-by-step explanation:

Given : Graph.

To find : Which system of linear inequalities is graphed.

Solution: We have given graph with two line one is dotted and other is solid.

Both the line are shaded up.

For dotted line :

We show the line by y = mx + b

Where, m = slope of line and b = y intercept .

The dotted line represent by the greater sign , slope of dotted line is zero and y intercept is -3.

So, equation would be y > 0x - 3.

y > -3.

For solid line : It represented by the greater than equal to sign for solid and shaded up. y intercept of solid line is -2.

Then equation would be 5y ≥ -4x -10.

Therefore, Equation would be  y > -3.

5y ≥ -4x -10.

x + 4x = 5x

90/5 = 18

x = 18

4x = 72

i believe the formula you need is; SA= n(3/10 ib) + 9b

Plug in each number in the set of x for x to get the set for y

y = x + 5

When x = 0, y = 5

5 = 0 + 5

When x = 1, y = 6

6 = 1 + 5

When x = 2, y = 7

7 = 2 + 5

When x = 3, y = 8

8 = 3 + 5

When x = 4, y = 9

9 = 4 + 5

y = 5, 6, 7, 8, 9

~Rise Above the Ordinary

Where are the images?

Answer:

18 Tala.

Step-by-step explanation:

1. You have that Ming learned that the exchange rate is 6 Tala for $2. Therefore, if she exchanged $6, she would get:

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

2. Now, you must solve for [tex]x[/tex], which is sthe amount of Tala:

[tex]x=\frac{(6)(6)}{2}\\x=\frac{36}{2}\\x =18[/tex]

3. Therefore, she would get 18 Tala.

Answer:

The fare in 1979 was $1.88.

Step-by-step explanation:

In 1999, bus fare in Atlanta was $4.70.

In 1979, the fare was 2/5 the fare in 1999.

This means the fare in 1979 was 2/5 of $4.70.

This means [tex]\frac{2}{5}\times4.70= 1.88[/tex] dollars

Hence, the fare in 1979 was $1.88.

To find the unknown number, one must solve the equation (10 + x) / 4 = 17, which simplifies to x = 58.

The student has asked to find a number such that when 10 is added to this number and the sum is divided by four, the result is 17. This can be written as an equation: (10 + x) / 4 = 17, where x represents the unknown number. To solve for x, we first multiply both sides of the equation by 4 to get rid of the denominator, resulting in 10 + x = 68. Then, we subtract 10 from both sides to isolate the variable, yielding x = 68 - 10. Therefore, x equals 58.

x^2-25 would be your answer

use the FOIL method: First, Outer, Inner, Last.

first: x*x = x^2

outer: x*-5 = -5x

inner: 5*x = 5x

last: 5*-5 = -25

put together: x^2 - 5x + 5x - 25

simplify: x^2 - 25

Let us first describe how partial product and regrouping are alike:

Partial Products and Regrouping are alike because both methods are multiplied by one number and if the product of the number has 2 digits it can be carried.

Now let us discuss how they are different:

Partial Products and Regrouping are different because Partial Products are doing multiplication step by step and regrouping is regular multiplication.

Hope it helps.

In the Quadratic Formula, the expression underneath the radical symbol determines the number and type of solutions the formula will reveal. This expression, b2 – 4ac, is called the discriminant of the equation ax2 + bx + c = 0.

if you mean this, then  [tex]ax^{2} + bx + cx = 0[/tex]

if you mean this, then  [tex]x = \frac{-b±\sqrt{b^{2} - 4 (a) (c) } }{2(a)}[/tex] *ignore the a thingy in between the -b and ±

hope this helps! ❤ from peachimin

That would be 236. Quotient means divide the numbers from one another.

Hope I could help! :)

Answer,

1,180/5 = 235

Hope this helps :-)

X<17, if i got it correct

Answer:

3 is less than or equal to x-9 is less than or equal to.

3<= x-9<=8

<= these mean less than or equal to.

hope I helped you!

Answer:

1,728 × 10 to power twelve

Step-by-step explanation:

(5.4 × 100000000)(3.2×1000000)

(540,000,000)(3,200,000)

1,728,000,000,000,000

1,728 × 10 to power twelve

Rational although it does repeat it is considered rational numbers that are 0 and are fractions are not considered rational such as square roots too.

Here is some helpful information: Also any decimal number that is repeating can be written in the form a/b with b not equal to zero so it is a rational number.

With out any functions to choose from...this is difficult.  But look for the equation that has a a decimal raised to a power (.07)^2

Answer:

f(x)=2(2/3)x

Step-by-step explanation:

compared to all of the other answers, 2/3 is the only one between 0-1 for the exponential decay.

Answer:

Mr. Aroxa is correct.

Step-by-step explanation:

Since we know that polynomials are closed under addition, subtraction and multiplication as when we will add, subtract or multiply two polynomials we will get a polynomial.

Polynomials are not closed under division because division of two polynomials is not necessarily a polynomial.

We can see it by dividing a binomial by a trinomial. This division will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.

Therefore, Mr. Aroxa is correct.

Find out how much money one woman would pay a year by multiplying $140 and 12 months together like this.

140×12=1680

Next, find out how much she'd be paying for 20 years by multiplying the product by the years like this.

1680×20=33600

Now, to find out how much money all 1000 women are paying for the 20 years, multiply the previous product with the number of women.

33600×1000=3600000

Therefore, all 1000 women would be paying $3,600,000 total during the 20 year time period.

HOPE THIS HELPS!

-1 plz mark brainliest

Find 4 on the x-line (the horizontal line).

Find where the red line crosses through that is where the 4 is at.

Once you find it, trace the line in which the 4 is x, and find the y.

The line gives (4, -1)

Find the slope of the line.

(4, -1) = (x₁ , y₁)

(0, 2) = (x₂ , y₂)

slope = (y₂ - y₁)/(x₂ - x₁) = (2 - (-1)/(0 - 4) = 3/-4

y = (-3/4)x + b

Plug in a point, for example (0, 2)

2 = (-3/4)0 + b

Simplify

2 = 0 + b

b = 2

Plug in 2 for b

---------------------------------------------------------------------------------------------------------------------------

f(x) = (-3/4)x + 2 is your equation.

Now, plug in 4 for x (as you are solving for x.

f(x) = (-3/4)(4) + 2

Simplify

f(x) = -3 + 2

f(x) = -1

-1 is your function when x = 4

hope this helps

CF + FE = CE.  Since F is the midpoint, then CF = FE, So, CF + CF = CE ⇒ 2CF = CE

Now, set up the proportion:

[tex]\frac{BF}{CF} = \frac{AE}{CE}[/tex]

[tex]\frac{23}{CF} = \frac{5x - 4}{2CF}[/tex]    substituted known values

23(2CF) = CF(5x - 4)   cross multiplied

23(2) = 5x - 4      divided both sides by CF

46 = 5x - 4    simplified

50 = 5x         added 4 to both sides

10 = x           divided both sides by 5

Answer: 10

here! y-intercept at -3.6 and x-intercept at 4.5

-30 feet

below meaning negative.

the answer would be -30 because its below the sea level if it was positive

it would say above sea level and that would be positive 30

but in this case its -30

question answered by

(jacemorris04)

the answer is 763 because 763 - 763 = 0

I don't want to sound rude here or anything but common sense would tell you it's 763. If you read and understand the problem it would be easy. Also if you add 763 to 0 you would get itself. Its just asking you to subtract 763 from itself. hope this helps!! :)

Remark

All you need do is subtract the beginning amount from the ending amount

Givens

Ending Amount (E) = 3.56

Beginning Amt (B) = 2.95

Amt Added (A) =         ?

Solution

A = E - B                 Substitute values

A = 3.56 - 2.95      Combine Like terms on the left

A = 0.61 mL           Answer