What is the linear function equation represented by the graph?

Answer:

$30,2400

Step-by-step explanation:

First, we need to find how much interest he earns in a month

8.4% of $12,000 = $1,008

Next, we multiply the amount of interest per month by the number of months in 25 years

25 years = 300 months

Now we can multiply the two values to get our final answer

1,008 x 300 = $30,2400

Step-by-step explanation:

Pythagoras, Pythagoras, Pythagoras.

c² = a² + b²

for c being the Hypotenuse (the side opposite of the 90 degree angle).

that is something you should really burn into your brain for life. you will need that many times.

1.

89² = 80² + side²

side² = 89² - 80² = 1521

side = sqrt(1521) = 39 ft

2.

D

because here the x value of 2 has to different assigned result (y) values. but for a function it had to be exactly 1 value.

3.

the longer of the 2 given sides must be the Hypotenuse, because otherwise we would get a negative length.

97² - 72² = side² = 4225

sqrt(4225) = side = 65 cm

4.

the distance between 2 point is the Hypotenuse of a right-angled triangle, with its legs being the differences in x and y coordinates.

F = (-1, 6)

G = (3, 4)

FG² = (-1 - 3)² + (6 - 4)² = 16 + 4 = 20

FG = sqrt(20) = 4.472135955... ≈ 4.5

so, A is the right answer.

5.

that creates a right-angled triangle, with the flag pole and the distance on the floor to the flag pole as the legs, and the rope as Hypotenuse.

rope² = 53² + 28² = 3593

rope = sqrt(3593) ≈ 60 ft

6.

A

85² = 36² + 77²

7225 = 1296 + 5929 = 7225

correct. this is a right-angled triangle.

B

101² = 99² + 20²

10201 = 9801 + 400 = 10201

correct. this is a right-angled triangle.

C

123² = 120² + 27²

15129 = 14400 + 729 = 15129

correct. this is a right-angled triangle.

D

42² = 33² + 24²

1764 = 1089 + 576 = 1665

incorrect.

1764 - 567 = 1089 ?

1197 = 1089

also incorrect.

as is 1764 - 1089 = 567 and 1089 - 567 = 1764

so, this is not a right-angled triangle.

7.

the sum of all angles in a triangle (also in general triangles) is always 180 degrees.

since the right angle is already 90 degrees, it leave only 90 degrees for the other 2 angles.

A is the only correct option. 25 + 65 = 90.

8.

BC = 13

AC = 3

AB² = AC² + BC² = 3² + 13² = 9 + 169 = 178

AB = sqrt(178) = 13.34166406... meter

the tree was then originally

3 + 13.34166406... = 16.34166406... meter high

12.1.1

35² = 21² + side²

side² = 35² - 21² = 1225 - 441 = 784

side = sqrt(784) = 28 m

12.1.2

side² = 16² + 30² = 256 + 900 = 1156

side = sqrt(1156) = 34 ft

12.2.3

61² = 60² + 11²

3721 = 3600 + 121 = 3721

correct. this is a right-angled triangle.

12.2.4

40² = 37² + 9²

1600 = 1369 + 81 = 1450

incorrect. this is not a right-angled triangle.

neither is 1600 - 1369 = 81 nor 1600 - 81 = 1369 nor 1368 - 89 = 1600

12.2.5

38² = 35² + 15²

1444 = 1225 + 225 = 1450

incorrect. this is not a right-angled triangle.

neither is 1444-1225=225 nor 1444-225=1225 nor 1225-225 = 1444

12.2.6

53² = 45² + 28²

2809 = 2025 + 784 = 2809

correct. this is a right-angled triangle.

12.3.8

the x and y coordinate differences between A and B are 6 and 3.

AB² = 6² + 3² = 36 + 9 = 45

AB = sqrt(45) = 6.7

12.3.9

the x and y coordinate differences between B and C are 1 and 7.

BC² = 1² + 7² = 1 + 49 = 50

BC = sqrt(50) = 7.1

12.3.10

the x and y coordinate differences between A and C are 5 and 4.

AC² = 5² + 4² = 25 + 16 = 41

AC = sqrt(41) = 6.4

final question : you need that in many distance calculations, side lengths, diagonals, heights,... for rooms, yards, acres, buildings, mountains, ...

Answer:

Youngest child: $2

oldest child: $6

Second oldest: $2.50

Step-by-step explanation:

Youngest child= x

oldest child= 3x

Second oldest: .50+x

x+3x+.50+x=10.5

5x+.50=10.5

    - .50= - .50

5x=10

divided both numbers by 5 and x is equal to 2. So, the youngest child is $2 and you add .50, which is $2.50, and thats for the second child. Last, you do 2 times 3 equals $6 which is the oldest child.

The youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

Three children each contributing to their mother's birthday present. The eldest gave three times more than the youngest, while the second oldest contributed 50 cents more. If the gift costs $10.50 which is given in the question.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Let the youngest sibling contribute the amount of x dollars

As per the given information,

3x + 0.50 x + x + x = 10.50

Apply the addition operation,

4.50x = 10.50

x = 10.50 / 6.50

Apply the division operation to get

x = 1.90

So the youngest sibling contributed = $1.90

The oldest contributed 1.90 × 3 = $5.27

And the second oldest contributed (1.50)1.90= $2.85

Therefore, the youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

Learn more about Arithmetic operations here:

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[tex]\huge\textbf{Hey there!}[/tex]

[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]

[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]

[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]

[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]

[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

the answer is 5.9 since both sides are the same and on the other side its 5.9

Hope This Helps!!!

Answer:

110 squares

Step-by-step explanation:

= 10 x 11

= 110 small squares.

From the question,

Step one : • • = 1(2) small squares

Step two : • • • = 3 squares in two layers = 2(3) = 6 small squares

• • •

Step three : • • • • = 4 squares in 3 layers = 3(4) = 12 small squares

• • • •

• • • •

Answer:

4

Step-by-step explanation:

Well 3 x 4 equals 12, 12 x 4 equals 48, and so on.

hope this helps!

Answer:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Answer: What does I stand for? If you meant 1, 1 to the power of 5 is 1.

Answer:

i

Step-by-step explanation:

i^5=(i)(i)(i)(i)(i)

Since i^2=(i)(j)=-1,

it follows that i^4=(i^2)(i^2)=(-1)(-1)=1.

Thus i^4*i=i^5=1*i=i.

Therefore, i^5=i.

Answer:

k = 10

Step-by-step explanation:

the sum of any two interior angles is equal to the exterior angle of the unknown interior angle

4k+5 + 6k+10 = 115

10k + 15 = 115

10k = 100

k = 10

Answer:

3 (x - 4)

Step-by-step explanation:

Answer:

x = - 1.5

Step-by-step explanation:

2 - 3(2x - 2) = 17 ← distribute parenthesis

2 - 6x + 6 = 17 , simplify

8 - 6x = 17 ( subtract 8 from both sides )

- 6x = 9 ( divide both sides by - 6 )

x = [tex]\frac{9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5

Step-by-step explanation:

the scenario creates 2 similar triangles :

one main triangle with the house height the double floor distance and the double line of sight from the left point on the floor to the top of the house.

and the other triangle is the height of the tree, the single floor (from the left point to the tree) distance, and the single line of sight from the left point on the floor to the top of the tree.

similar triangles means : all angles are the same. and the side lengths of one triangle correlate to the corresponding side lengths in the other triangle by the same multiplication factor.

and that means that the floor distances of small and large triangle have the same ratio, as the view of line distance AND the height sizes.

we see : large triangle side / small triangle side = 2/1 = 2

and therefore, the same factor (2) applies to the heights.

so,

height of house / height of tree = 2

therefore,

height of tree = height of house / 2 = 150/2 = 75 ft

Percent Change = (new quantity - old quantity) / old quantity

#2:

(64 - 52) / 52

12 / 52

0.2308

23%

#4:

(12 - 18) / 18

-6 / 18

-0.33

33% decrease

#5:

(10 - 16) / 16

-6 / 16

-0.375

38% decrease

Hope this helps! :)

Answer:

Subtraction property of equality

Step-by-step explanation:

You subtracted c from both sides of the equation to preserve equality

The step 1 is explained by subtraction property of equality.

The correct option is A.

The standard form of Quadratic Equation is

ax² + bx + c = 0

Also, we must remove c from the right side and move it to the left side in order to derive the quadratic formula from the quadratic equation.

And to do that, we must subtract c from both sides, which is

-c = ax² + bx

Then, we have used subtraction property here.

Learn more about Subtraction here:

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Answer:

(3,1)

Step-by-step explanation:

(x,y) (-4,2)

so -4 +2 = - 2 ; -2 +5 = 3

and for y: 2 - 5 = - 3 ; - 3 + 4 = 1

(3,1)

Answer:

x < 6

Step-by-step explanation:

1) -5x > -30

2) divide both sides by -5

3) flip the sign as we divided inequality by a negative

4) x < 6

Answer:

4096

Step-by-step explanation:

Explanation:

The rule we use is (a^b)^c = a^(b*c). It says to multiply the exponents when we raise one exponential expression to another exponent. The base stays the same.

So, (2^4)^3 = 2^(4*3) = 2^12

You could take the slightly longer path to say the following

(2^4)^3 = (2^4)*(2^4)*(2^4) = 2^(4+4+4) = 2^12

Answer:

Part A:

The equation describing the relationship between speed and time is:

s = 32t

Ordered pairs of the form (speed, time) are:

(32, 1)

(64, 2)

(96, 3)

(128, 4)

Part B:

s = 32t

s = 32 * 5 = 160 feet per second

Step-by-step explanation:

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

Height of the cliff = 500 feet

Speed after one second = 32 feet per second

Speed after four seconds = 128 feet per second

2. Assume the relationship between time, t, and speed, s, is linear and write an equation describing the relationship. Use ordered pairs of the form (speed, time)

The equation describing the relationship between speed and time is:

s = 32t

Ordered pairs of the form (speed, time) are:

(32, 1)

(64, 2)

(96, 3)

(128, 4)

3.  Use the equation to determine the speed of the rock 5 seconds after is dropped.

s = 32t

s = 32 * 5 = 160 feet per second

Answer:

5.125, 5.14, ¹⁰³/₂₀, 5²/₉

Step-by-step explanation:

When you convert 103/20 to decimal you get 5.15 which is greater than 5.125 and 5.14.

When you convert 5²/₉ to fraction you get ⁴⁷/₉ which when converted to decimal is 5.222 which is greater than 5.125, 5.14 and 5.15.

Answer:

0.56

it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%

Answer:

(6 + n) - 8

Hope this helps.

Pls mark brainliest. :D

Answer:x < 2

Step-by-step explanation: 6+x < 8

x < (8-6)

x < 2

Answer:add 126 and 21 and 1.19

Step-by-step explanation:

126+21+1.19=

hope this helped

Answer:

7.14

Step-by-step explanation:

126 miles divided by 21 miles is 6 miles

So 6 gallons for 126 miles

1.19 times 6 is 7.14

Step-by-step explanation:

60 cookies with 4 cups

that means 60 per 4 = 60/4 = 15

and that means that he can make 15 cookies with 1 cup.

that is clear : from 60/4 we immediately know 15/1.

and now, as we know how many cookies can be made with 1 cup, it is easy to say how many cookies can be made with 3 cups. right, 3 times a much.

so, yes, we multiply 15 by 3 and get 45 cookies as answer.

Step-by-step explanation:

4⁵ × 4^-7 / 4^-2

it is important to understand that a negative exponent means 1/...

a^-n = 1/(a^n)

in that sense we have therefore

4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)

4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1

so, "1" is the fully simplified expression equal to the original expression.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

A standard die has 6 numbers, so the probability it will be greater than 4 is 6-4, or 2. Therefore the answer is [tex]\frac{2}{6}[/tex], but this can be simplified to [tex]\frac{1}{3}[/tex].