In March, Isaiah and Freddie had the same amount of money in their savings accounts. In April, Isaiah deposited $210 into his account. Freddie increased the money in his account by 15%. When they compared their balances, they found that they were still equal.

The values of the following functions are:-

f(-4) = 20

f(2) = -1

f(6) = 11

f(0) = -5

Given that ,

          -3x + 8, -6 ≤ x ≤ -3

f(x) =   [tex]x^2-5[/tex],  -2 ≤ x ≤ 3

          (1/2)x + 8 , 5  ≤ x  ≤10

We have to find the values of f(-4) , f(2),  f(6) and, f(0).

As, -6 < 4 < -3

So, we will write,

f(-4) = -3(-4) + 8 = 12 + 8= 20

As, -2 < 2 < 3

So, we will write,

f(2) = [tex](2)^2-5[/tex] = 4 - 5 = -1

As, 5 < 6 < 10

So, we will write,

f(6) = (1/2)(6) + 8 = 3 + 8 = 11

As, -2 < 0 < 3

So, we will write,

f(0) = [tex](0)^2-5[/tex] = 0 - 5 = -5

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Answer: y = 4x-1

Step-by-step explanation:

1) Choose two points for the later equation.

For this example, I will use (-1,-5) and (2,7)

2) Place it in a rise/run equation. (y/x)

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{7-(-5)}{2-(-1)} \\\\\frac{12}{3} \\\\4[/tex]

The Slope is 4.

3) Find the y-intercept

So, we can place a given point and slope into a y=mx+b function.

[tex]y=4x+b[/tex]

Next, we can substitute the point and slope.

[tex]7 = 4(2)+b\\7=8+b\\-1=b[/tex]

4) Finally, place it all in slope intercept form

y = 4x-1

Simplified expression for [tex] \frac{1}{( {5n⁴})^{- 3} } [/tex] is 1/125n¹².

As per the rule of exponents, the powers will be multiplied. Representing the mentioned rule in the form of example -

[tex]( {{a}^{m} })^{n} = {{a}^{m} }^{ \times n} [/tex]

Another rule of exponent to be used in the question is : [tex] {a}^{ - x} = \frac{1}{ {a}^{x} } [/tex]

Now, simplifying the expression mentioned in question as per the above written rule.

Rewriting the equation according to second rule.

Value = [tex] \frac{1}{( {5n⁴})^{ 3} } [/tex]

Now, solving the equation by taking cube according to first rule

Value = 1/125n¹²

Thus, the simplified expression is 1/125n¹².

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The Supplement postulate can be used to prove that the angles ∠CAB and ∠CAD are supplementary.

According to the Supplement Postulate, two angles are supplementary if they create a linear pair.

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Using the given information, the fraction is 3/8

From the question, we are to determine the fraction

Let the numerator of the fraction be x and the denominator be y

From the given information,

"if the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2, the result is 2"

That is,

4x/(y -2) = 2

and

" If the numerator of the fraction is increased by 15 and 2 is subtracted from the double of the denominator, the result is 9/7"

That is,

(x + 15)/(2y - 2) = 9/7

From the first equation,

4x/(y -2) = 2

4x = 2(y-2)

4x = 2y - 4

4x + 4 = 2y

y = 2x + 2 ----------- (3)

From the second equation,

(x + 15)/(2y - 2) = 9/7

7(x + 15) = 9(2y - 2)

7x + 105 = 18y - 18

Substitute equation (3)

7x + 105 = 18(2x + 2) - 18

7x + 105 = 36x + 36 - 18

105 - 36 + 18 = 36x - 7x

87 = 29x

x = 87/29

x = 3

Substitute the value of x into equation (3)

y = 2x + 2

y = 2(3) + 2

y = 6 + 2

y = 8

Thus, the number is 3/8

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Answer:

$2.39, hope this helps,

Step-by-step explanation:

1.50+0.89=2.39

Answer: $2.39

Step-by-step explanation: 0.89 + 1.50

0.8 + 1.5 = 2.3

89 + 50 = 139

2.39

Based on the price of the cell phone in November and December, the price of the cell phone in March was $39

To find the price of the cell phone in March, you need to first find the price of the cell phone in November.

The price of the cell phone in November was $25 more than the price in December:

= 25 + 53

= $78

The price in November was double the price in March so the price in March was:

= 78 / 2

= $39

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The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.

Felipe has a limited time period to use the 40 percent off coupon on a single item. First, we suppose he avail the 40 percent coupon in the given mean time which is 47:17 then that single item would have cost the Felipe

According to the question, the item have cost if he had not used the coupon, so let the value of the single item is x

x × 40 % = $ 16.42

x × [tex]\frac{40}{100}[/tex] = $ 16.42

40 × x = 16.42 × 100

x =    [tex]\frac{16.42 * 100}{40}[/tex]

x = $ 41.05

The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.

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Answer:

A = (1, 1)

B = (3, 2)

C = (2, 4)

Step-by-step explanation:

Vertices of the triangle:

Mapping rule for a 90° clockwise rotation about the origin:

(x, y) → (y, -x)

Therefore:

Mapping rule for a reflection in the x-axis:

(x, y) → (x, -y)

Therefore:

Therefore, the coordinates of the new triangle are:

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

expand the bracket

Volume, v = 4/ 3 (392.5)

Volume, v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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Answer:

x=21

Step-by-step explanation:

6-1/3x=-1

-6        -6

-1/3x=-7

__     __

-1/3    -1/3

x=21

Hello!

Let's solve:

 [tex]\text{Copy down the equation}\\6-\dfrac{x}{3}=-1 \\\\\text{Move 'x/3' to the right side and '-1 to the other side}\\6+1=\dfrac{x}{3}\\ 7=\dfrac{x}{3} \\\\\text{Multiply 3 to both sides}\\7*3=3*\frac{x}{3} \\x = 21[/tex]

Answer: x = 21

Hope that helps!

The associative property can be applied to addition and multiplication.

When more than two numbers are added together or multiplied, the outcome is always the same, regardless of how the numbers are arranged. This is known as the associative property.

For example,

2 × (7 × 6) = (2 × 7) × 6

2 + (7 + 6) = (2 + 7) + 6

Associative Addition Property

The associative feature of addition states that the total sum of the numbers will not change no matter how they are arranged. This may be stated as follows:

(x + y) + (z + y) = x

Associative Multiplication Property

The idea behind the associative property for multiplication is that no matter how the numbers are arranged, the result will always be the same. This may be stated as follows:

P = (q)/(r) = (q)/(r)

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Answer:

-21/2

Step-by-step explanation:

-5-2= - 7

7-4=3(+, - = -)

-7×3/2= - 21/2

Given expression:

[tex]7p+\frac{q}{3}[/tex]  , given that p = 6 and q = 12.

Here, we need to substitute the values of p and q in the given expression to  obtain the value of the expression.

On substitution, the expression becomes,

[tex]7X6+\frac{12}{3}[/tex]  ,

Here we use BODMAS rule ( Brackets, Orders, Division, Multiplication, Addition, Subtraction) , hence initially we do the division operation, then the multiplication operation and at last the addition operation,

= 7x6 + 4 =  42 + 4 = 46.

Hence, option D) 46 is the correct option.

These type of expressions can be solved by simply substituting the given values of the variables such as p, q and so on.

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1 2/3 divided by 4/5

= 5/3 ÷ 4/5

make common denominators:

[tex]\frac{25}{15} /\frac{12}{15}[/tex]

invert one and multiply across:

[tex]\frac{25}{15} * \frac{15}{12}[/tex]

= 375/180

reduce:

25/12 or 2 1/12

A. P( 2∪3∪6 ) = 1/2

B. P( 1∪2∪3∪4∪5 ) = 9/16

The probability of an occurrence e can be written as P (e), and its equation is as follows:

P (e) = Number of favorable outcomes / Total number of outcomes

This can only be used with a straightforward event.

The probability will also be influenced by other factors, whether they are imposed or a result of the event's inherent characteristics.

Using a six-sided die,

A) First, in order to gather as much information as possible from the question, we concentrate on the probabilities provided P(1∪4∪5)=1/2 and P(2∪3∪5)=1/2 and we need to use P(5)=7/16.

It's crucial to remember that while using a dice, receiving two values on the same roll is impossible. Due to this and the likelihood of certain circumstances:

P(1∪4∪5) = P(1) + P(4) + P(5) - P(1∩4)(= 0) - P(4∩5)(= 0) - P(1∩5)(= 0) + P(1∩4∩5)(= 0)

P(1∪4∪5)=P(1) + P(4) + P(5)

1/2 = P(1) + P(4) + 7/16

P(1)+P(4)=1/16

If we do the same with P(2∪3∪5), we get:

P(2) + P(3) = 1/16

Now that we have this new knowledge, we can determine P(6):

P(6) = 1 - P(1∪2∪3∪4∪5)

P(6) = 1 - [P(1) + P(2) + P(3) + P(4) + P(5)] -- (There is no chance that two of these will occur simultaneously.)

P(6) = 1 - (1/16 + 1/16 + 7/16)

P(6) = 1 - 9/16

P(6) = 7/16

And with it, we can find P(2∪3∪6):

P(2∪3∪6) = P(2) + P(3) + P(6)

P(2∪3∪6) = 1/16 + 7/16

P(2∪3∪6) = 8/16 = 1/2

B) Keep in mind that the probability you need to know if you wish to roll anything other than a 6 is P(1∪2∪3∪4∪5)" but we found that in part A

P(1∪2∪3∪4∪5) = 9/16

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ok

MPG = 66.8

Uniform line movement.

The uniform rectilinear movement is the movement that maintains a variation of the distance with respect to time always constant, since the acceleration is zero.

If we know that Wilson travels 53.7 miles in 1.6 hours, we determine the average speed from the following equation:

Speed = distance / time

Speed = 53.7 miles / 1.6 hours

Speed = 33.5625 miles/hour

V = 33.6 miles/hour

The average speed that Wilson travels is: V = 33.6 miles/hour.

The graph for given values is below -

The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.

For the graph,

the value of y for x = 1,

y = -6.3 or 13/2

(1,-6.5)

For x= 2,

y = -7

(2,-7)

For x = 4,

y = -8

(4, -8)

With respect to the given line which is y = -1/2x - 6

the coordinates are following -

(1,-6.5), (2,-7), (4, -8)

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Answer:

52% of them are girls

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3=1/3^27

Step-by-step explanation:

3 is the answer , you can do it with a calculator

Answer:

One, Buff Billy's, has a joining cost of $80 and charges $25 a month. The other, Shredded Eddie's, has no joining cost but charges $35 a ...

Step-by-step explanation:

Answer:

672 sq km

Step-by-step explanation:

Area of a regular polygon
[tex]A = \dfrac{P}{2} \times a[/tex]

P = perimeter of the polygon

a = apotherm which is defined as
The distance from the center of a regular polygon to the midpoint of a side.

The given polygon has 8 sides and each side is 12 km
So the perimeter P = 12 x 8 = 96 km

The apotherm is given as 14 km

So area
[tex]A = \dfrac{96}{2} \times 14 = 672 \text { sq km}[/tex]

At time 1.75 seconds the ball is in the 51 feet high.

What is substitution method?

Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The height of the football could be describe by the model,

h = - 16t² + 56t + 2   ..... (i)

Where, h describes the height of the ball in feet.

and t is the time in seconds after the ball was kicked.

Now,

At height 51 feet, the time is calculated as;

Substitute h = 51 in equation (i), we get;

h = - 16t² + 56t + 2  

51 = - 16t² + 56t + 2  

16t² - 56t - 2 + 51 = 0

16t² - 56t + 49 = 0

Solve for t by using quadratic formula;

t = - (-56) ± √(-56)² - 4 × 16 × 49 / 2 × 16

t = 56 ± √3,136 - 3,136 / 32

t = 56 ± 0 / 32

t = 56 / 32

t = 1.75 seconds

Thus, At time 1.75 seconds the ball is in the 51 feet high.

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The output value of f( 38 ) in the function f( x ) = x/2 is 19.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the output value of f( 38 ), replace all the occurrence of x with 38 in the function and simplify.

f( x ) = x/2

f( 38 ) = 38/2

Divide 38 by 2

f( 38 ) = 38/2

f( 38 ) = 19

Therefore, the output value is 19, this forms an ordered pair of ( 38,19 ).

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When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative

What is the explanation?

U(2, 7) → U'(-7, 2)

V(10, 7) → V'(-7, 10)

W(2, 3) → W'(-3, 2)

Step-by-step explanation:

From the picture attached,

Coordinates of the vertices of the given triangle,

U → (2, 7)

V → (10. 7)

W → (2, 3)

Since rule for the coordinates of a point P(x, y) after a rotation of 90° counterclockwise about the origin is,

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Answer:

Your missing number is -87.5.

Step-by-step explanation:

You want to follow reverse order of operations to isolate your variable x

First, you plug in y= 700 to get::

700 = (24x)/7 +1000

Then subtract 1000 from both sides to get:

-300 = (24x)/7

Then multiply both sides by 7 to get:

-2100 = 24x

Then, divide by 24 to get:

-87.5 = x

Thus, your answer x= -87.5

The interest for the first payment is $30.00

Interest is how much is paid for the use of money.

Therefore, you  take a $4,500 loan to pay for trip to the Amazon rainforest to photograph wild animals.

The  loan's interest rate is 8% for 1 year.

Therefore, the interest for the first payment can be calculated as follows:

Interest for the first payment = 8% of 4500 × 1 / 12

Interest for the first payment = 8 / 100 × 4500 × 1 / 12

Interest for the first payment = 8 × 45 × 1 / 12

Interest for the first payment = 360 / 12

Interest for the first payment = $30

Therefore,

interest = $30

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