Cara is 14 years old . This is twice as old as her brother . How old is her brother

Answer:

When Sum of square of two Sides is equal to square of third side of triangle.

Step-by-step explanation:

Given:

Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.

First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.

Hence the two side would according be a and b and third side will become c.

For example if length of triangle  is given as 6 cm, 8 cm and 10 cm.

We will first take square of all

[tex]6^2=36\\8^2=64\\10^2=100[/tex]

Now we can see that

[tex]36+64=100\\6^2+8^2=10^2[/tex]

Now by Pythagoras theorem.

[tex]a^2+b^2=c^2[/tex]

Hence we can say a = 6 cm, b = 8 cm, c= 10 cm  

The Pythagorean Theorem is specifically applicable to right-angled triangles and states that:

[tex]\[a^2 + b^2 = c^2\][/tex]

Theorem, follow these steps:

1. Identify the longest side: The hypotenuse  c is always the longest side in a right-angled triangle.

2. Assign the longest side to c : Among the three given side lengths, the one with the greatest value should be assigned to c .

Example

Suppose you are given three side lengths: 5, 12, and 13. To determine which lengths correspond to  a ,  b , and c :

1. Identify the longest side: Among 5, 12, and 13, the longest side is 13.

2. Assign the longest side to c : So, c = 13 .

3. Assign the remaining sides to  a  and  b: Thus,  a and  b can be 5 and 12, respectively (or vice versa).

Verify using the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

[tex]5^2 + 12^2 = 13^2[/tex]

25 + 144 = 169

169 = 169

Since the equation holds true, the side lengths 5, 12, and 13 do indeed form a right-angled triangle, with 13 being the hypotenuse.

General Case

When given any three side lengths x ,  y , and z :

1. Determine the longest side and assign it to c .

2. The remaining two sides are a  and b

3. Check if [tex]\( a^2 + b^2 = c^2 \)[/tex] to verify if the triangle is a right-angled triangle.

By following this process, you can correctly identify the sides to substitute into the Pythagorean Theorem.

Answer:

24(x+2)

Step-by-step explanation:

24 can be pulled from both 24 and 48

Answer:

33 Students

Step-by-step explanation:

4+7=11 so the number of students in the class must be a multiple of 11. The only multiple of 11 between 24 and 40 is 33.

Answer:

33

Step-by-step explanation:

Let's take the constant of proportionality to be X

4x+7x=between 24 to 40

11x= 24 to 40

X should be a natural number therefore the number of students should be multiple of 11

Only multiple of 11 between 24 and 40 is 33

The correct equation for the booster club aiming to earn $200 per match from student and adult tickets priced at $4 and $8, respectively, is 4x + 8y = 200. This represents the sum of $4 per student ticket (x) and $8 per adult ticket (y) sold to reach the goal.

To solve the problem presented by the high school soccer booster club, we need to formulate a linear equation that represents their goal for ticket sales revenue from students and adults. The tickets are priced at $4 for students and $8 for adults. If we let x represent the number of student tickets sold and y the number of adult tickets sold, the total revenue T would be expressed as the sum of $4 per student ticket and $8 per adult ticket.

The booster club aims to earn $200 per match, which gives us the equation for their goal: 4x + 8y = 200. Here, the 4 and 8 are the prices of the tickets for students and adults, respectively, and x and y are the numbers of tickets sold. This clearly aligns with option b from the choices you've provided.

To illustrate with an example similar to your situation, a tutoring school equation of y = 3000x + 500  combines a one-time enrollment fee of $500 with a tuition of $3000 per year. In this case, y represents the total cost of attendance and x the number of years a student is enrolled.

Answer:

560mph

Step-by-step explanation:

11,760÷21=560

label- 560mph

Answer:

560 MILES

Step-by-step explanation:

11760/21=560

Answer:

[tex]-\frac{1}{3} < x < 2[/tex] and -3 < x < 3

Step-by-step explanation:

The inequality equation is  

3x² - 5x - 2 < 0

⇒ 3x² - 6x + x - 2 < 0

⇒ (x - 2)(3x + 1) < 0

Therefore, either (x - 2) > 0 and (3x + 1) < 0

⇒ x > 2 and [tex]x < -\frac{1}{3}[/tex] which is not possible for any particular value of x.

or, (x - 2) < 0 and (3x + 1) > 0

⇒ x < 2 and [tex]x > -\frac{1}{3}[/tex] which is valid.

So, the solution is [tex]-\frac{1}{3} < x < 2[/tex] (Answer)

Now, another inequality is  

x² - 9 < 0

⇒ x² < 9

Therefore, -3 < x < 3 is the solution. (Answer)

Answer:   (x-7)/(x-5)

The (x+1) terms divide and cancel out due to the rule that x/x = 1, when x is nonzero. In that rule, we can replace 'x' with any algebraic expression we want.

Answer:

4

Step-by-step explanation:

36 / 9 = 4

4 x 9 = 36

Answer:

k = -5

Step-by-step explanation:

2(7k + 1) - 5(3k + 3) = 1 - 2k + 6 + 5k

At first, we will break the parenthesis by multiplying by the adjacent number. As we know, (+) x (-) = (-) and (-) x (-) = (+) [Algebraic operation]

or, (2*7k) + (2*1) - (5*3k) - (5*3) = (1 + 6) + 5k - 2k

or, 14k + 2 - 15k - 15 = 7 + 3k

Interchanging the values, we can get,

or, 14k - 15k - 3k = 7 + 15 - 2

or, 14k - 18k = 22 - 2

or, -4k = 20

or, k = 20/(-4)

or, k = -5

Therefore, the answer is -5

The expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Given that, we have to use the numbers 4.3 , - 1.07 and – 2.971 such that the value of the expression with the given numbers and the either addition or subtraction operation between them to be negative value.

So, now take the numbers.

If we add the negative numbers and subtract the positive number from it, we will always get a negative number  

So, expression will be ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )  

- 1.07 – 2.971 – 4.3  

- 8.341

Here the result is negative value.

Hence, the expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Answer:

A

Step-by-step explanation:

An ordered pair is a point on a coordinate graph that represents data. The x represents an independent variable and the y a dependent. Your y is your vertical axis. Each square on this graph represents 50 feet. The line on your graph hits the intersection between 2 minutes and 100 feet. Therefore (2,100) Is an ordered pair

Answer:

6 lunch tables

Step-by-step explanation:

Since one lunch table can hold 10 students and 60 students are needed to hold,

60 ÷ 10 = 6 lunch tables

Answer:

6

Step-by-step explanation:

1 table is 10

60 divided by 10= 6

Answer:

Initial value (y-intercept) of each function.

Rate of change (slope) of each function.

Initial value to compare starting points.

Slope to compare rise or fall. (Answer)

Step-by-step explanation:

Sample Response: Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

Therefore, I included in the response  

Initial value (y-intercept) of each function.

Rate of change (slope) of each function.

Initial value to compare starting points.

Slope to compare rise or fall. (Answer)

Answer:

D. 158/6

Step-by-step explanation:

If you divide 158/6 you get 26.3333333333 which is a repeating decimal, and makes it a rational number.

Answer: c) 1 unit

Step-by-step explanation: Because if u take the scale factor and multiply it by 3

Answer:

C:  1 unit

Step-by-step explanation:

(3 units) times scale factor (1/3) comes out to (1/3)(3 units), or 1 unit.

The correct answer is C:  1 unit.

Nope!

They cannot be equal if they have the same numerator but different denominators. they need to be able to reduce into the same number

No, two fractions with the same numerator and different denominators can not be equal.

The numerator simply means the number that's on top of a fraction. The denominator simply means the number that's under the fraction.

Two fractions with the same numerator and different denominators can not be equal. An example is 1/4 and 1/6 aren't equal.

Read related link on:

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Answer:

draw a square

Step-by-step explanation:

draw a square then write 32mm on all sides

draw a triangle  with a wide bottom a small side a medium side

Answer:

Step-by-step explanation:

[tex]9c-7=7c-11\qquad\text{add 7 to both sides}\\\\9c-7+7=7c-11+7\\\\9c=7c-4\qquad\text{subtract}\ 7c\ \text{from both sides}\\\\9c-7c=7c-7c-4\\\\2c=-4\qquad\text{divide both sides by 2}\\\\\dfrac{2c}{2}=\dfrac{-4}{2}\\\\c=-2[/tex]

Answer:

2

Step-by-step explanation:

Simplifying

9c + -7 = 7c + -11

Reorder the terms:

-7 + 9c = 7c + -11

Reorder the terms:

-7 + 9c = -11 + 7c

Solving

-7 + 9c = -11 + 7c

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-7c' to each side of the equation.

-7 + 9c + -7c = -11 + 7c + -7c

Combine like terms: 9c + -7c = 2c

-7 + 2c = -11 + 7c + -7c

Combine like terms: 7c + -7c = 0

-7 + 2c = -11 + 0

-7 + 2c = -11

Add '7' to each side of the equation.

-7 + 7 + 2c = -11 + 7

Combine like terms: -7 + 7 = 0

0 + 2c = -11 + 7

2c = -11 + 7

Combine like terms: -11 + 7 = -4

2c = -4

Divide each side by '2'.

c = -2

Simplifying

c = -2

Answer:

20 cups

Step-by-step explanation:

16 ounces = 1 pound

8 ounces = 1 cup

16 ounces = 2 cups

1 pound = 2 cups

10 pounds = 20 cups

Answer:

20 cups

Step-by-step explanation:

Think

1 pound is 16 oz

So each cup has 8 oz

This you have to convert the 10 pound into ounces

Which then equals 160 ounces

Now divide 160 ounces by 8 and you get..

You get 20

So, 10 pounds of apples fit into 20 cups

Answer:

D. All answers are correct

Step-by-step explanation:

The film The Birth of a Nation promoted the KKK.

There was pseudo-scientific racism also going on.

From these two facts, we know that the answer definitely is D. Also, generally when there is "All of the above" as an answer, "All of the above" is correct.

Answer:

193 packets

Step-by-step explanation:

Each morning they order with a shipping fee of $10 daily.

Considering they order all 7 days of the week, so the total shipping fee for the week would be:

7 * $10 = $70

Their budget for the week is $554, out of which $70 is for shipping for the week, so remaining balance would be:

554 - 70 = $484

This 484 dollars are for coffee packets that cost $2.50 each, so the number of packets would be:

484/2.50 = 193.6

You can't order fractional packets so 193 packets is the max in this budget

Answer:

3.98/16= 0.24875 round up to make 0.25

5.98/32= 0.186875 round up to make 0.19

34.99/128= 0.273359375 = 0.27

Step-by-step explanation:

3.98/16= 0.24875 round up to make 0.25

5.98/32= 0.186875 round up to make 0.19

34.99/128= 0.273359375

Answer:

The quantity of large frames is 7

The quantity of small frames is 13

Step-by-step explanation:

Given as :

The price of each large frames = $ 10

The price of each small frames = $ 5

The total number of both frames bought = 20

The price for both the frames = $ 135

Now,

Let the quantity of large frames = L

And The quantity of small frames = S

So , According to question

The total number of both frames bought = 20

Or, The quantity of large frames + the quantity of small frame = 135

Or, L + S = 20         ......A

And $ 10 L + $ 5 S = $ 135                         ................B

Or, $ 10× ( L + S ) = $ 10× 20

Or, $ 10 L + $ 10 S = $ 200

(  $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135

Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65

Or, 0 + 5 S = 65

∴  S = [tex]\frac{65}{5}[/tex]

I.e S = 13

So, The quantity of small frames = S = 13

Put the Value of S in eq A

So , L + S = 20

Or, L = 20 - S

Or, L = 20 - 13

∴   L = 7

So, The quantity of large frames = L = 7

Hence The quantity of large frames is 7

And   The quantity of small frames is 13   Answer

Answer:

a. $18.36 for 3 pizzas  :  k  = 6.12

b. $4.17 for 3 pounds of bananas .   k  = 1.39

c. $16.48 for 4 pounds of potatoes .  k  = 4.12

d. 2 cups of flour to make 24 cookie .  k  = 12

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k is called the PROPORTIONALITY CONSTANT.

⇒  [tex]x\propto y \implies  k = \frac{x}{y}[/tex]

Now, for the given quantities:

a.  $18.36 for 3 pizzas [box]    

Here, [tex]k = \frac{18.36}{3}  = 6.12[/tex]

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here, [tex]k = \frac{4.17}{3}  = 1.39[/tex]

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here, [tex]k = \frac{16.48}{4}  = 4.12[/tex]

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here,  [tex]k = \frac{24}{2}  = 12[/tex]

So, the proportionality constant is 12

Answer:

x= 10

Step-by-step explanation:

45-15=30

30/3=10

Answer:

Step-by-step explanation:

Yeah it right thank sweetheart

The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.

Finding Original Dimensions of a Rectangle

Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.

The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:

w(w + 10) - (w - 2)(w + 8) = 48

Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:

[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48

w2 + 10w - w2 - 6w + 16 = 48

4w + 16 = 48

4w = 32

w = 8 cm.

Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).

Answer:

$8950.37

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.

Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:

$11,000 = P(1 + 0.07/2)^(2*3), or

$11,000 = P (1.035)^6

                                           $11,000        $11,000

Solving for P, we get P = ---------------- = ------------- = $8950.37

                                            1.035^6          1.229

Depositing $8950.37 with terms as follows will result in an accumulation of $11,000 after 3 years.

To determine how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $11,000 in three years, one needs to apply the formula for compounded interest and solve for the principle amount.

The subject in question pertains to compounded interest under the domain of financial mathematics. In this context, the student wants to determine how much money needs to be deposited today to accumulate a given amount, in this case, $11,000, in an account that earns 7% compounded semiannually in three years. It's important to note that when interest is compounded, it's added to the principal, and future interest calculations are based on this adjusted amount.

Applying the formula for compounded interest: A = P(1 + r/n)^(nt)

Where:

our aim is to find P (the principal amount or the amount to be deposited today), which can be mathematically rearranged from the formula above as follows:

**P = A / [(1 + r/n)^(nt)]**

Substituting A = $11,000, r = 7% (or 0.07 in decimal form), n = 2 (since the interest is compounded semiannually), and t = 3, we calculate P (the amount to be deposited today).

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Answer: 1/6

Step-by-step explanation: To multiply fractions, first multiply across the numerators, then multiply across the denominators.

So here, we have 1 × 2 which is 2 and 4 × 3 which is 12. So now we have the fraction 2/12.

Notice however that 2/12 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 2 and 12 which is 2.

So if we divide the numerator and the denominator by 2, we get 1/6.

Therefore, 1/4 × 2/3 = 1/6.

Answer:

1/6

Step-by-step explanation:

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1 x 2           2

-------    = --------

4 x 3          12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 2 and 12. GCF(2,12) = 2

2 divided by 2           1

------------------------   =  ----  

12 divided by 2         6

So...

1/4 x 2/3 = 1/6