A coin box contains $26.50 in dimes and quarters. There are 157 coins altogether. How many of each
type of coin are in the box?

(x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.

The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0

Here,

f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex]

substitute a = 2

[tex]f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2[/tex]

      = 48-24-36+10-2

      = 32-36

f(2)  = -4

f(2) [tex]\neq 0[/tex]

Hence, (x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

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The correct option is option B that is the function f(x) = 3 (4)ˣ.

A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. We need to find the function for the given graph. We have two points on the graph so we will satisfy the points in the options given options. The points are (0, 3) and (1, 12).

The first option is

f(x) = 3 (12)ˣ, after putting point (1, 12)

12 ≠ 3 (12), so it is not required function.

The second option is

f(x) = 3 (4)ˣ, after putting points (0, 3) and (1, 12)

3 = 3 and 12 = 12, so it is the required function.

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Answer:

130 m

Step-by-step explanation:

See the attached, pleasantly presented, worksheet.

The range of the function, f(x), that gives the total cost of the cleats of given that each cleat costs $15 and the number of cleats, x, is 5 ≤ x ≤ 9 is RANGE: [75, 135]

The range of a function is the set containing the output values that are obtainable with the function.

The given parameters are;

The number of players, n, in the sports team is; 5 ≤ n ≤ 9

The given cost of one cleat = $14

The function that represents the total cost of the cleats for the team is f(x) = 15•x

Given that each team member is given one cleat, we have;

Number of cleats is 5 ≤ x ≤ 9

The range of values for the total cost of the cleats is therefore;

15 × 5 ≤ f(x) ≤ 15 × 9

75 ≤ f(x) ≤ 135, which using interval notation gives;

RANGE: [75, 135]

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The expressions which is equivalent to 2x + 3 would be 4x + 6.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions. To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expressions which is equivalent to 2x + 3

Thus, we will Use the Distribute Property of Multiplication by multiplying the number outside the parenthesis with the numbers inside.

Let the expression be multiplying by 2 then;

2(2x + 3)

4x + 6

Hence, we can say that the expressions which is equivalent to 2x + 3 would be 4x + 6.

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Let's begin by identifying key information given to us:

Numbers of apples = 35

Number of oranges = 30

Total number of fruits = 65

The ratio of apples to oranges is given by:

Answer:

AS shown in the purse

Step-by-step explanation:

A. The school attendance happens in the sixth week

B. A(13) ≈ 42$

meaning : In the Thirdteenth week. The student attendance rate is 425

C. A(x)=400 =) x = 10

in the tenth week.The student attendance rate is 400

D.in the fourth week the least attendance nce.

E. It has 450 students

The number of attendance increased to 450.

And the area was flat

Answer:

n = 10

Step-by-step explanation:

(10 * 3) + 7 = 37

Answer: 6

Step-by-step explanation:

With these type of problems, it is best to work backwards.

1. Because of the seven more, you subtract 7 from 25. This gives you 18.

2. Then it says three times, this means to divide by 3. 18/3 is 6

3. Your final answer is 6

Proving the answer is 6:

1.   3 [tex]*\\[/tex] 6 = 18

2. 18 + 7 = 25

The solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

What is inequality?

In mathematics, the term 'inequality' is defined as a statement or equation with an ordered relationship like greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

-5 < 9- 6x

Adding 5 both the side we get,

5 - 5 < 9 - 6x + 5

⇒ 0 < 14 - 6x

⇒ 14 - 6x > 0

Dividing both the side by 6 we get,

⇒ 14 < 6x

⇒ x > 14/6 = 7/3

or, x ≤ 7/3

this is the required solution of the given inequality.

Thus, the solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

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Considering the equation of selling habitat between Niayla and Hamilton, the number of habitats that Niayla and Hamilton must sell to make an equal amount of money is 15

information gotten from the question include

Hamilton gets paid a flat fee of 350 dollars plus 50 dollars for each habitat he sells

Niayla gets paid a flat fee of 500 dollars 40 dollars for each habitat she sells

The equation as described is a linear function and is represented by the form. y = mx + c

where:

y = total amount made

x = number of habitat sold

m = cost per habitat

c =flat fee

some interpretation on the information from the question include

for Hamilton

y = 50x + 350

for Niayla

y' = 40x + 500

To make equal amounts y = y'

50x + 350 = 40x + 500

500 - 350 = 50x - 40x

150 = 10x

x = 150 / 10

x = 15

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The pair of vertical angles are

There are four angles made by the intersection of two lines. Those are ∠1, ∠2, ∠3 and ∠4

Vertical angles are the each of opposite angles formed when two lines meet each other at a point. So whenever two lines intersect each other four angles are formed and each set of opposite angles are called vertical angles

Here, two lines intersect each other and ∠1, ∠2, ∠3 and ∠4 are formed.

∠1,∠3 and ∠2,∠4 are the opposite angles

So the vertical angles are ∠1,∠3 and ∠2,∠4

Hence, the pair of vertical angles are

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Answer:

y=-5x+7

Step-by-step explanation:

15x+3y=21

(15x+3y)/3=21/3

5x+y=7

5x+y-5x=7-5x

y=-5x+7
yeah
i'm probably wrong but its my best

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 5x + 7[/tex]

____________________________________

The given equation is :

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 15x + 3y = 21[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3y = 21 - 15x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{21}{3} - \frac{15}{3} x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 5x + 7[/tex]

That's the required equation in slope intercept form, with slope (m) = -5, and y - intercept = 7

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

45g = 40.5°

45g = 40° 30′ 0″

The coordinates of  Point O that is on MN and divides it such that MO:NO is 2:1 is; (10, 10)

We are given a line segment as MN with its' endpoint coordinates as;

M(4,14) and N(13,8)

Now, point O divides MN such that MO:NO is 2:1.

Now, the formula for the coordinate of the point that divides a line segment in the ratio a:b is;

(x, y) = (ax₂ + bx₁)/(a + b), (ay₂ + by₁)/(a + b)

Since point O is the point that divides the line segment in the ratio 2:1, we have;

O(x, y) = (2*13 + 1*4)/(2 + 1), (2*8 + 1*14)/(2 + 1)

O(x, y) = (30/3), (30/3)

O(x, y) = (10, 10)

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Jummai and Tunde will each have 9 and 6 bananas respectively.

For the given ratio case we use the sharing ratio criterion to solve the problem.

Jummai is 12 years old.

Tunde is 8 years old.

Their ages are in ratio of;

                             A = 12 : 8

                             A =  3 : 2

The ratio's sum is 5.

15 bananas total are available for sharing.

Jummai will have [tex]x\\[/tex] bananas  [tex]x[/tex] = (15 x 3/5) = 9

Tunde will have [tex]y[/tex] bananas  [tex]y[/tex] = (15 x 2/5) = 6

Jummai and Tunde will each have 9 and 6 bananas with them.

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Answer:

3.5 * 10^2

Step-by-step explanation:

So you start with 350.

What you do is take the decimal from the beginning of 350 and move it to the left.

350.0 -> 35.0-> 3.5

And you move the decimal until you get only one number in front of the decimal.

Then you take the number of times you moved the decimal and put it with ten so in this case it would be. 10^2.

Making the final answer: 3.5 * 10^2

∠UXS    = 135°  is the value on transversal line.

What is a transversal angle?

∠RXU = 45°

∠UXS = ?

As we know that a line make 180 degree angle on it.

So, ∠UXS + ∠RXU = 180°

     ∠UXS =  180° -  ∠RXU

         ∠UXS =  180° - 45°

                     = 135°

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The rate of change of the function shown in the graph is $0.5 per minute.

What is rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta (Δ) is usually come in use to represent the ROC.

As shown in the graph,

The x-axis represents the minute and y-axis represents the cost.

and the cost is function of time.

For each 10 minute the cost increased $5

So, the cost is changing at a rate of $5 per 10 minute

$5 = 10 minutes

diving both side with 10

$0.5 = 1 minute

Therefore, the rate of change of the function shown in the graph is $0.5 per minute.

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Answer:

Two is subtracted by a number:

n - 2

And then the difference is divided by 3:

(n - 2) / 3

The result is 30:

(n - 2) / 3 = 30

(n -  2 ) / 3 = 30

(n - 2) = 30 • 3

n - 2 = 90

n = 90 + 2

n = 92

The number is 92

Answer:

sama sma tayi

Step-by-step explanation:

3×3()56(7)

Answer: v = 2

Step-by-step explanation:

1. Distribute the 5 to the items within the parenthesis.

-3v + 5v - 10 = -6

2. Combine V terms and Isolate V from other terms.

2v = 4

3. Divide both sides by 2.

v = 2

Answer:

solve the following system of equations by using gauss elimination method

Answer:

(-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,-5)

Step-by-step explanation:

see picture

The Inequality notation of the given equation 10+3x>-16 is x > -2

What is Inequality notation?

A mathematical statement known as an inequality expresses the relationship between two quantities while indicating that they are not completely equal. The four symbols used to represent inequality are. ≥, >,<, and ≤.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare the two values in inequality. Less than (or less than and equal to), greater than (and greater than or equal to), and also not equal to signs are used in place of the equal sign.

Consider the above equation.

-10 +3x > -16

Add 10 on both sides.

= -10+3x+10> -16+10

= 3x> -6

Divide by 3 to equation into both sides.

= [tex]\frac{3x}{3} > \frac{-6}{3}[/tex]

=  x > -2

Inequality notation is x > -2

Interval Notation: [−2,∞)

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just find it from the graph its not that hard

goodluck :)

Check the picture below.

Answer:

-5 2

Step-by-step explanation:

Using the vertical angle image we get the following answers:

Given the equations are:

42 = 4x-4 and 24 = x+50.

According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.

we know that,

∠2 = 4x-4 and ∠4 = x+50

a)To Find the value of x:

4x - 4 = x + 50

4x - x = 50 + 4

3x = 54

x = 54/3

x = 18

b) To Find the measure of ∠2:

∠2 = 4×18 - 4 = 72 - 4

= 68

c)  Angles 2 and 3 are supplementary so their sum is 180°.

∠2 + ∠3 = 180

68 + ∠3 = 180

∠3 = 180 - 68

∠3 = 112°

Hence we get the required angles.

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Your question is incomplete. Please find the missing content here:

Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.

A. What is the value of x?

B. What is the measure of ∠2?

C. Find the measure of ∠3.

Answer: 13 and 5= coeeficients, x and y = variables,  -2 and 3 =constants

Step-by-step explanation: