Write an equation of a quadratic function that has been reflected in the x-axis, shifted horizontally to the right 2 units and stretched by a factor of 3.

Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.

Answer:

A) Kevin has been saving money for 19 weeks.

B) Kevin still needs $515.

Step-by-step explanation:

A) 277=600-17x /-600

-17=-323 /÷(-17)

x=19

B) x=600-17×5

x=600-85

x= 515

The inductive hypothesis is P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + {6(a +1) +1} = (a + 1) {3(a + 1) + 4} is true for all (a+1) = n for the statement Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)

The statement is given as,

Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)

For n =1 we get,

P₁ : 6(1) + 1 =7

and,  1{3(1) + 4} = 7

Hence, 6n+ 1 = n(3n + 4) is true for n= 1.

Therefore assume that Pₐ is true for some a = n, we get,

Pₐ : 7 + 13 +19 +... + (6a +1 ) = a(3a + 4)

Let,  n =a+1 , we get,

P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + (6a +1) + {6(a +1) +1}

= Pₐ +   (6a+ 7)

= a(3a + 4) + 6a + 7

=  3a² + 4a + 6a + 7

=  3a² +10a + 7

= 3a² + 7a + 3a + 7

= a( 3a + 7) + 1(3a + 7)

= (a + 1) ( 3a + 7)

= (a + 1) {3(a + 1) + 4}

Hence, (a +1) is true for all (a+1) = n by mathematical induction principle. Thus, the inductive hypothesis is true.

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The exponential function represented by the given graph is:

y = 2(.5^x)

Here we have an exponential decay, the general form of these functions is:

y = A*(b)^x

Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.

Now let's look at the y-intercept, we can see that it is y = 2, then:

2 = A*(b)^0

2 = A

The function is of the form:

y = 2*(b)^x   with 0 < b < 1.

The option that meets these conditions is the first one: y = 2(.5^x)

So that is the correct option.

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Answer:

b

Step-by-step explanation: makes sense

The area of the semicircle is 157. 00 cm

To determine the area of the semi-circle, we need to consider the formua.

the formula for calculating the area of a semi-circle is expressed with the equation;

A = 1/2π²

Such that the parameters of the formula are;

It is important to note that

Formula for diameter is expressed as

Diameter = 2radius

Radius = 10cm

Substitute the values

Area = 1/2× 3.14 × 100

Multiply the values

Area = 157 cm²

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The value of p in the equation 7p - 4 = 8 is p = 12/7

From the question, we have the following parameters that can be used in our computation:

7p - 4 = 8

Add 4 to both sides

So, we have

7p = 12

Divide both sides by 7

So, we have

p = 12/7

Hence, the solution is p = 12/7

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The width of the worktable is 32 inches, and the length of the worktable is 82 inches.

Let's assume that the width of the worktable is "w" inches.

We are given that the length is 18 inches more than twice the width, which can be expressed as:

Length = 2w + 18

The perimeter of the worktable is the sum of the lengths of all four sides.

We know that the perimeter of the worktable is 228 inches, so we can write an equation:

Perimeter = 2 × (Length + Width)

228 = 2 × (2w + 18 + w)

228 = 2 × (3w + 18)

Dividing both sides by 2:

114 = 3w + 18

Subtracting 18 from both sides:

96 = 3w

Dividing both sides by 3:

w = 32

So, the width of the worktable is 32 inches.

Now we can use this value to find the length:

Length = 2w + 18

Length = 2 × 32 + 18

Length = 82

So, the length of the worktable is 82 inches.

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The total cost that Ellie would pay with 4 snacks is $59.

The total cost that Ellie would pay with x snacks is $29 + $5x.

The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.

The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.

Total cost = total cost of the tickets + total cost of the snacks

= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)

= (13 x 3) + ($5 x 4)

$39 + $20 = $59

Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39  + $5x

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The percentage of the total that women represent, would be 60% of the total.

Given that 60 % of men is equal to 40 % of women, we have :

0. 6 M = 0. 4 W

Solving for women in terms of Men gives:

W = ( 0.6 x M) / 0.4

= 1.5 x M

We can then find the percentage of women to be:

= (W / Total ) x 100

= ((1.5 x M) / (2.5 x M)) x 100

= (1.5 / 2.5) x 100

= 0.6 x 100

= 60%

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The radius of the circular mouse is 3.7 inches.

The area of the circular mouse pad 45 square inches. Therefore, the radius of the circle can be found as follows:

area of the circle = πr²

where

Therefore,

area of the circular mouse = 3.14 × r²

45 = 3.14r²

divide both sides by 3.14

r² = 45 / 3.14

r² = 14.3312101911

square root both sides

r = √14.331210911

r = 3.78565714243

r = 3.7 inches

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Answer: 12.6

Step-by-step explanation:

150/360*2*pi*r=10.

divide to get r alone

The maximum value of z = 28.  I occurs at (x, y) = 4

To solve thhis linear programming problem, we can use the graphical method..

Graph the feasible region defined   by the constraints.....

x >= 0 and y >= 0 represent the non-negative quadrants.

x + y < = 8   represents the area below the line passing through ( 8, 0) and (0, 8).

x + y >= 2 represents the area above the line passing through (  2 , 0) and (0 , 2).

Identify the corner points of the feasible region  .....

(0,  2)

 (  2, 0)

(   4, 4)

( 8, 0 )

Calculate tthe objective function at each corner point....

z(0,   2  ) = 3(0) + 4(2) = 8

z (2, 0  ) = 3(2) + 4(0) = 6

z(4, 4  ) = 3(4) + 4(4) = 28

z (  8, 0) = 3(8) + 4(0) = 24

Determine the    maximum value of the objective function and the values of x and y that give this maximum value

The maximum value of z is 28, which occurs at the corner point (4, 4).

So we c can be stated as follows --

Maximum value of z = 28

x = 4

y = 4

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Answer:

an = 36 + -4(n - 1)

Step-by-step explanation:

Explicit formula:

[tex]a_n=a_1+(n-1)d[/tex]

Where:

Here, we are given the following:

The first term is 36

To get to the next term, 4 is subtracted from the previous term so the common difference is -4.

So we have:

By plugging this into [tex]a_n=a_1+(n-1)d[/tex]

We acquire : [tex]a_n=36+(n-1)(-4)[/tex]

Answer:

  499,237 ft²

Step-by-step explanation:

You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.

To find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:

  A = 1/2bh

There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:

  4A = 4(1/2bh) = 2bh

The slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)

  h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet

  lateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²

The surface area of the glass is about 499237 square feet.

The length of u to the nearest centimeter is about 30 cm.

We are given that;'

s = 730 cm, t = 270 cm and U=125°.

Now,

The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:

c2=a2+b2−2abcosC

To find c = u. Plugging in the values, we get:

u2=7302+2702−2×730×270×cos125°

Using a calculator, we get:

u2≈912.9

Taking the square root of both sides, we get:

u≈30.21

Rounding to the nearest centimeter, we get:

u≈30cm

Therefore, by the law of cosine the answer will be 30 cm.

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The linear equation outlining the entire volume of water (y) which has coursed through the hourglass following x days. is

The volume of water passed each which is the slope is

To ascertain the amount of water that is passing through the hourglass daily:

where:

Total water capacity: 2000 pounds

Time: 365 days

Water transpiring every day = Total water capacity / Time

Water pervading each day ≈ 200 / 365

Water pervading each day ≈ 5.48 pounds/day

the linear function of the water traveling through the hourglass.

Making x the number of days and y being the total quantity of water which has crossed through the hourglass after x days--as the fluid fluxes at a constant velocity--thus a linear relationship between x and y can be determined.

Every single day (x), the hourglass moves 5.48 pounds of water. This reveals the linear representation of:

y = 5.48x

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The value of Q₃ of the data represented by the box plot is,

⇒ Q₃ = 30

Given that;

A box plot is shown in figure.

Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.

Since, we know that the upper or 3rd quartile is represented by the last line of the box.

We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.  

And, The middle line is at 25, so median for our given box plot is 25.

The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.

Therefore, the third quartile, is 30 for our given box-plot.

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Answer:

Step-by-step explanation:

The function f(x) = a * b^x represents exponential growth or decay. The value of a represents the starting value or y-intercept, while the value of b represents the growth or decay factor. If b is greater than 1, the function represents exponential growth, while if b is between 0 and 1, the function represents exponential decay.

To determine the values of a and b from a graph, we need to look for specific features. The y-intercept represents the value of a, so we can read it directly from the graph. The growth or decay factor b can be found by examining the slope of the graph. If the graph is increasing, then b is greater than 1, and if it is decreasing, then b is between 0 and 1.

There are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.

It is required to find the number of permutations when 4 things are selected from a total of 9 with replacement.

Use the formula for permutations with replacement, which is:

= [tex]^np_r[/tex]

Here n is the total number of items and r is the number of selections.

As per the question, n = 9 and r = 4.

So, the number of permutations is:

= ⁹p₄

= 9!/5!

= 9 x 8 x 7 x 6

= 3024

Thus, there are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.

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The ratio of the shaded area to the total unshaded area can be found to be 5 : 9.

The three shapes are similar to each other which means that their areas must be similar as well.

The only shape that is shaded is the second largest shape and it has the value of 5 in the ratio. This means that the other two shapes are not shaded and their ratio values are 1 and 8.

This then means that the ratio of shaded area to unshaded area can be written as :

Shaded area : Unshaded area

5 x width : ( 1 x width)  + ( 8 x width )

5 : 1 + 8

5 : 9

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Answer:

z = 12.52 in.

Step-by-step explanation:

Because this is a right triangle, we can solve for z using on the trigonometric ratios.

If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.

Thus, we can use the cosine ratio which is

[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]

Now, we can plug everything into the formula and solve for z, the hypotenuse:

[tex]cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52[/tex]

The percentage of pennies in the roll is A = 30 %

Given data ,

Let the percentage of pennies in the roll made before 1985 be A

Now , the total number of pennies be = 50 pennies

And , the number of pennies made before 1985 is = 15 pennies

So , the percentage is A = ( 15 / 50 ) x 100

On simplifying the equation , we get

A = 3/10 x 100

A = 30 %

Hence , the percentage is 30 %

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Answer:

c,,e,b,f

Step-by-step explanation:

Answer:

Put your calculator in degree mode.

sin(13°) = 500/x

x sin(13°) = 500

x = 500/sin(13°) = 2,222.7 miles

Using a trigonometric relation we can see that x =  2,222.7 ft

We can see a right triangle, there we can see that one of the angles has a measure of 13°.

The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.

Then we can use the relation:

sin(a) = (opp cathetus)/hypotenuse

Replacing what we know, we will get:

sin(13°) = 500/x

Solving that for x:

x = 500/sin(13°) = 2,222.7 ft

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The value of a polynomial function with the given zeros would be,

⇒ f (x) = x (x + 7) (x + 6)³

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Functions have zeroes 0, - 6, - 7 with multiplicity 1, 3, 1

Hence, We can formulate;

The value of a polynomial function with the given zeros would be,

⇒ f (x) = (x - 0)¹ (x - (- 6))³ (x - (- 7))¹

⇒ f (x) = x (x + 6)³ (x + 7)

⇒ f (x) = x (x + 7) (x + 6)³

Thus, The value of a polynomial function with the given zeros would be,

⇒ f (x) = x (x + 7) (x + 6)³

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