Find the length of the third side. If necessary, round to the nearest tenth.
17

25

Answer:

  A  (see attached)

Step-by-step explanation:

There are a couple of things you can look for to see if a table represents a quadratic function:

In the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.

In the remaining tables, the f(x) values are always increasing.

The f(x) values in table 1 have differences of ...

  -3, -1, 1, 3

These values have differences of ...

  2, 2, 2

The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...

  f(x) = x² +2

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

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The length of x in the sector is 7.08 cm.

area of a sector = ∅ / 360 × πr²

where

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

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The value of x from the given figure is 11

The sum of two complementary angles is 90 degrees.

The angles shown in the diagram are complementary such that;

20 + 5x + 15 = 90

5x + 35 = 90

5x = 90- 35

5x = 55

x = 55/5

x = 11

Hence the value of x from the given figure is 11

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The solution to the given inequality is x < -6

For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.

Given the inequality expression as shown

6x + 6 < -30

Subtract 6 from both sides

6x < -30 - 6

6x < -36

Divide through by 6

x < -36/6

x < -6

For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.

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Based on the given polynomial, the degree of the polynomial can be calculated to be 1.

the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.

from the above, we see that the highest power is 1 from 8x¹.

the degree of the polynomial is therefore 1.

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The median will change; the mode will stay the same.

The median is the number that is at the center of a data set when the data are arranged either in ascending or descending order.

Median = 23

When 68 and 75 are added, the median would change.

Mode refers to a value that appears most frequently in a data set.

The mode = 75

So, when 75 is added, the mode does not change.

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Using an exponential function, it is found that the decay rate is of 6.24% a year.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]0.5A(0) = A(0)(1 - r)^{10.75}[/tex]

[tex](1 - r)^{10.75} = 0.5[/tex]

[tex]\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}[/tex]

[tex]1 - r = (0.5)^{\frac{1}{10.75}}[/tex]

1 - r = 0.9376.

r = 1 - 0.9376.

r = 0.0624.

The decay rate is of 6.24% a year.

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Answer: Not similar

Step-by-step explanation:

The polygons are not similar because the ratio of the corresponding sides is not equal (30/18 is not equal to 18/8)

By using the triple integral, the wedge's volume is 4/15.

A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.

The wedge's volume, which the parabolic cylinder encloses, must be determined.

Consequently, as a result of the z=y form,

In addition to the specified boundary, the plane y=0 x = 0, z = 0.

For all of this, we are therefore in the first octant. additionally, the plane

x + y = 1 is a constraint.

Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.

The following would be written as a triple integral:

∫x=0 ∫y=0

∫z=0 dy dz dx

Once the values have been entered and the problem has been solved, we obtain the

[−4/15(1−x)^5/2] at x=0

The answer will then change to 4/15.

As a result, using the triple integral, the wedge's volume comes out to 4/15.

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Answer:

Angle A= 30

Step-by-step explanation:

Angle A and B are same side interior

So A + B = 180

x = 8

6(8)-18=30

Answer:23

Step-by-step explanation:

jaja

Answer:

The maximum amount of people that can go to the amusement park is 15.

Step-by-step explanation:

First you create an equation to represent the question

8.75+25.75x≤420

You put the less than or equal to sign because 420 is the maximum amount of money.

Now you just solve the equation.

25.75x≤420-8.75

25.75x≤411.25

x≤411.25/25.75

x≤15.9708738

Then you have to round down because you cant have .9 of a person.

So x≤15

Then, Check your solution

8.75+(25.75 x 15)≤420

8.75+386.25≤420

395≤420

That is true. But to make sure that is the maximum add another 25.75

395+25.75≤420

420.75≤420

This is equation is false so, our answer is correct.

The maximum amount of people that can go to the amusement park is 15.

The circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.

The formula for circumference of a circle is given as;

Circumference = 2 π r

We have diameter = 8. 6 inches

Radius = diameter/ 2

Radius = 8.6/2 = 4. 3 inches

Circumference = 2 × 3. 14 × 4. 3 = 27. 0 Inches

The formula for area of a circle = π r ^2

Area = 3. 14 × 4. 3 × 4. 3

Area = 58. 0 Inches square

Thus, the circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.

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Answer: C

Step-by-step explanation:

There is a vertical asymptote at x=3, so the denominator should have a factor of (x-3).

This eliminates everything except for C.

Answer: $37.50

Step-by-step explanation:

The table so fined below based on the information given about the function.

The table based on the function given will be:

Plan A. Plan B

Monday. 10. 30

Tuesday. 20. 40

Wednesday. 40. 50

Thursday. 80. 60

Friday. 160. 70

A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.

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Answer:

x-intercept is 6 [(6, 0) is the point]

y-intercept is 4 [(0, 4) is the point]

Step-by-step explanation:

To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:

[tex]2x+3(0)=12\\2x=12\\x=6[/tex]

So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0

To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:

[tex]2(0)+3y=12\\3y=12\\y=4[/tex]

So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0

Distributive property states that A × (B + C) = AB + AC. are always equal.

According to the statement

we have to explain the distributive property over multiplication.

Distributive property is the multiplication property.

According to this property, it generalizes the Distributive Law and it tells us that the an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

It means that From distributive property

A × (B + C) = AB + AC.

These are always equal with each other.

Now we will explain with an example,

Let A = 2, B = 3 and C = 4

Then

2 × (3 + 4) = 2(3) + 2(4).

2 × (7) = 2(3) + 2(4).

14 = 6 + 8.

14 = 14.

It proves that the A × (B + C) = AB + AC.

So, Distributive property states that A × (B + C) = AB + AC. are always equal.

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The volume of the composite solid shown in the diagram is: 80 ft.³.

Volume of the composite solid = volume of triangular prism + volume of triangular pyramid.

Volume = 0.5 × base of triangle × height of triangle × length of prism + 1/3 × Base area × Height = 0.5 × 8 × 5 × 3 + 1/3 × 0.5 × 8 × 5 × 3

Volume = 60 + 20

Volume of the composite solid = 80 ft.³.

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Answer: 18

Step-by-step explanation:

There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.

I hope this helps!

Answer:

3x - 4/2

Step-by-step explanation:

2 result(s) for "f(x) = 4x³ - 10 g(x)

Answer:

-12

Step-by-step explanation:

First, solve in parentheses.

2(-2-4)

=

2(-6)

Next, multiply 2 by -6.

Which equals -12.

So therefore using the distributive property shown above, the answer would be -12.

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

[tex]\huge\textbf{What is the distributive formula?}[/tex]

[tex]\mathsf{a(b + c)}[/tex]

[tex]\mathsf{= a(b) + a(c)}[/tex]

[tex]\mathsf{= ab + ac}[/tex]

[tex]\huge\textbf{What is the equation?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\huge\textbf{What are we simplifying?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]

[tex]\mathsf{= -4 - 8}[/tex]

[tex]\mathsf{= -12}[/tex]

[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\mathsf{= 2(-6)}[/tex]

[tex]\mathsf{= -12}[/tex]

[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]

[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]

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

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

r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.

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Answer:

D

Step-by-step explanation:

The solution to the equation using the completing the square are 2 and -3

These are equation that has a leading degree of 2. Given the equation below

-x^2 +x+6=0

This can also be written as

x^2-x-6 = 0

Complete the square

x^2-x = 6

x^2-x+ (1/2)^2 = 6 + (1/2)^2

(x-1/2)^2 = 6 + 1/4

(x+1/2)^2 = 25/4

x+1/2 = ±√25/4

x = 5/2 -1/2  or -5/2-1/2

x = 4/2  or -6/2

x = 2 and -3

Hence the solution to the equation using the completing the square are 2 and -3

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Answer:

S₁₂ = - 654

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 5 and d = - 9 , then

S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]

     = 6(- 10 - 99 )

    = 6 × - 109

    = - 654

Answer:

Step-by-step explanation:

The graph is widest when the coefficient of [tex]x^2[/tex] has the smallest absolute value.

The graph is narrowest when the coefficient of [tex]x^2[/tex] has the largest absolute value.

By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.

The graph is widest when the coefficient of [tex]x^{2}[/tex] has the smallest absolute value.

The graph is narrowest when the coefficient of [tex]x^{2}[/tex] has the largest absolute value.

The answer lies in the coefficient for the [tex]x^{2}[/tex] term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).

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Answer:

(A) 36°

Step-by-step explanation:

Find intercepted arc (RT):

360° - 288° = 72

*A circle is 360°*

Find angle RST:

An inscribed angle = 1/2 intercepted arc

angle RST = 1/2(72)

Angle RST = 36°

The expressions based on the information given are illustrated below

3/4 ÷ 1/2 = 1.5 = quotient is grater than 1

1/2 ÷ 3/4 = 2/3 = quotient is less than 1

2/9 ÷ 1/27 = 6 = quotient is grater than 1

5/3 ÷ 20/6 = 1/2 = quotient is less than 1

4/3 ÷ 3/5 = 20/9 = quotient is grater than 1

19/8 ÷ 2 3/8 = 1 = quotient is equal to 1.

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The volume of the composite figure is of 425 m³.

The volume of a prism is given by the base area multiplied by the height.

In this problem:

Hence the volume in m³ is:

V = 5² x 13 + 5² x 4 = 25 x 17 = 425 m³.

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Answer:

I and II only

The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

Firstly, we're given that the centre is (8,6).

Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]

We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.

Therefore, the radius is 6 units. Plug this into the general equation too:

[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]

[tex](x-8)^2+(y-6)^2=36[/tex]