4. Find the volume of the cylinder. Leave youranswer in terms of π.

The equation of the form [tex]f(x)=ax^2+bx+c[/tex] that must solve algebraically and f(1)=4, f(2)=13 and, f(4)=46 is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].

Putting x = 1 in the given equation, we get

[tex]f(1)=a(1)^2+b(1)+c[/tex]

f(1) = a + b + c = 4 ...(1)

Putting x = 2 in the given equation, we get

[tex]f(2)=a(2)^2+b(2)+c[/tex]

f(2) = 4a + 2b + c = 13 ...(2)

Putting x = 4 in the given equation, we get

[tex]f(4)=a(4)^2+b(4)+c[/tex]

f(4) = 16a + 4b + c = 46 ...(3)

Using elimination method to solve the set of linear equations, we get

(2) - (1), we get

3a + b = 9  ...(4)

(3) - (2), we get

12a + 2b = 33  ...(5)

Multiplying (4) by 2, we get

6a + 2b = 18 ...(6)

(5) - (6), we get

6a = 15

a = 15/6 = 5/2

Putting a = 5/2 in (4), we get

3(5/2) + b = 9

15/2 + b = 18/2

b = 3/2

Putting the values of a and b in (1), we get

5/2 + 3/2 + c = 9

4 + c = 9

c = 9 - 4

c = 5

Hence, the equation is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].

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The linear equation of given point (1, -7) and slope -1 is y = -x - 6.

Given:

Point(x₁ , y₁) = (1, -7)

Slope = -1

By using the Point-slope form of the linear equations, we get

y - y₁ = m(x - x₁)

⇒ y - (-7) = -1(x - 1)

⇒ y + 7 = -x + 1

⇒ y = -x + 1 - 7

⇒ y = -x - 6

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Check the picture below.

so is more or less the figure of a rectangular prism with a right-cylinder underneath that has a radius of 1, since it has a diameter of 2.

now, if we just get the volume of the prism, and then the volume of half of the cylinder, because only half-cylinder is really inside the prism, and then subtract that half-cylinder volume from that of the prism, what's leftover is the volume of the figure only.

[tex]\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\hspace{5em}\stackrel{\textit{volume of half a cylinder}}{V=\cfrac{1}{2}\pi r^2 h} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volumes}}{\stackrel{prism}{(4)(4)(8)}~~ - ~~\stackrel{half~cylinder}{\cfrac{1}{2}\pi (\underset{r}{1})^2(\underset{h}{8})}}\implies 128~~ - ~~4\pi ~~ \approx ~~\text{\LARGE 115.43}~cm^3[/tex]

DOMAIN X CAN BE ALL REAL NUMBERS.

RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.

Answer:

use keywords together. So I think all you have to do is multiply or add them both together. Try multiplying or adding but I know that those are part of the answer.

Step-by-step explanation:

The measure of angle PSR is 105°.

An arc's angle at the center of the circle is twice as large as its angle at any other point on the circumference.

Given:

The centre of the circle is O.

P, R, and S are points on a circle.

∠POR = 150°

Let Q be a point on the circumference of the circle with centre O.

By half angle property,

∠POR = 2∠PQR

∠PQR = [tex]\frac{1}{2} * 150[/tex] = 75°

In the figure, the points on the circle PQRS form a cyclic quadrilateral.

A cyclic quadrilateral has opposite angles that measure a total of 180 degrees.

∠PQR + ∠PSR = 180°

∠PSR = 180° - 75°

∠PSR = 105°

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P (-5), replace x by (-5).

Solve the parentheses:

Combine like terms:

243.83

Step-by-step explanation:

Multiple: 38/

3

* 77/

4

= 38 · 77/

3 · 4

= 2926/

12

= 1463 · 2/

6 · 2

= 1463/

6

Answer:

[tex]243 \frac{5}{6}[/tex]

Step-by-step explanation:

Given multiplication:

[tex]12 \frac{2}{3} \times 19 \frac{1}{4}[/tex]

Convert the mixed numbers to improper fractions:

[tex]\implies \dfrac{12 \times 3+2}{3} \times \dfrac{19 \times 4+1}{4}[/tex]

[tex]\implies \dfrac{36+2}{3} \times \dfrac{76+1}{4}[/tex]

[tex]\implies \dfrac{38}{3} \times \dfrac{77}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]

[tex]\implies \dfrac{38\times77}{3\times4}[/tex]

[tex]\implies \dfrac{2926}{12}[/tex]

Divide the numerator and denominator by 2:

[tex]\implies \dfrac{2926 \div 2}{12 \div 2}[/tex]

[tex]\implies \dfrac{1463}{6}[/tex]

Convert to a mixed number:

[tex]\implies 243 \frac{5}{6}[/tex]

If there are three blue marbles, five red marbles, and four green marbles, the probability of selecting a red marble is

Remember that the probability is the ratio between the number of events and the total number of all the events. In this case, the number of events is 5 because there are 5 red marbles, and the total number of all events is the sum of all the marbles.

Therefore, the probability of selecting red marbles is 5/12.

Notice that we have three different ratios, that is because each time we select a red marble it represents a different situation since we won't place back the red marble into the bag, that's why each event decreases by one and each denominator too.

Therefore, the probability of selecting three red marbles without replacement is 15/33.

As we said before, in Part B, we had to multiply each probability for each time we select a red marble. It's important to notice that the numerators decreased by 1 (5,4,3) because each time we select a marble we won't place it back, that's the reason why the denominator also decreased by 1.

Answer:

Danladi is correct

Step-by-step explanation:

Danladi is correct because 2^3×4^2 equals 128

8 to the 6th is 262144 and to the 5th is 32768

In order to find the solution of this compound inequation, let's first divide it in two inequations:

Solving the first inequation, we have:

Now, for the second inequation, we have:

Putting both solutions together:

So the correct option is C.

average change in price of silver per hour is $ 4  .

With the unitary method, you can solve issues by first calculating the value of a single unit, then multiplying that value by the quantity of units required.

$14 price dropped in 3 and half hours i.e. in 3.5hrs

so in 1 hour price dropped will be = 14 / 3.5

                                                        = $ 4 per hour

therefore average drop rate of price of silver per hour is $ 4  .

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0.5 hours

Step-by-step explanation:

60 mph for 7 hours = 60×7= 420 miles

540-420=120 miles left

60mph÷120miles= 0.5 hours

The measure of largest exterior angles is 150 degrees

Exterior angles are defined as angles of a polygon formed or created by two the sides of that polygon and sharing a common endpoint.

It is important to note that the exterior angle of a triangle is congruent to the sum of the two non-adjacent interior angles that are opposite to each other.

They are also known to be angles formed by a transversal line as it cuts through one of two lines and it is located on the outside part of the line.

Given the angles as;

Note that the sum of exterior angles are 360degrees

5x° + 9x° + 10x° = 360°

collect like terms

24x = 360

Make 'x' the subject of formula by dividing both sides by 24

x = 360/24

x = 15

But the largest angle is 10x = 10(15) = 150°

Hence, the value is 150°

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Let x be the number of game he can finish in 1 hour

1/4 = 1/3 hour

x = 1 hour

cross-multiply

1/3 x = 1/4

Multiply both-side of the equation by 3

x = 3/4 of his level game

He can finish 3/4 of his level game in an hour

The appropriate choice of ratio will be given by

Jonas got 30 oranges

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let Mary got 3x oranges and Rejoice got 2x oranges

By the Problem,

                           [tex]2x = 24[/tex]

                             [tex]x = \frac{24}{2}[/tex]

                             [tex]x = 12[/tex]

Number of oranges Mary got = [tex]12 \times 3[/tex]

                                                 = [tex]36[/tex]

Number of oranges shared between Mary and Rejoice = [tex]24 + 36[/tex]

                                                                                            = [tex]60[/tex]

Fraction of oranges shared between Mary and Rejoice = [tex]1 - \frac{1}{3}[/tex]

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

                                                                                            = [tex]\frac{2}{3}[/tex]

Total number of oranges = [tex]\frac{60}{\frac{2}{3} }[/tex]

                                          = [tex]60 \times \frac{3}{2}[/tex]

                                          = [tex]90[/tex]

Number of oranges Jonas got = [tex]90 \times \frac{1}{3}[/tex]

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Answer:

155

Step-by-step explanation:

4(-5)^2-11x

-5 squared is 25, times 4 =100, -11times-5 is 55 (positive) so 100+55=155

Answer:

HI

Step-by-step explanation:

HOW ARE

Step-by-step explanation:

The circumference of circle is [tex]\pi[/tex]d

What is a circle ?

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.

Given that : the circle with area =[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]

area of circle is =[tex]\pi r^{2}[/tex]

[tex]\pi r^{2}[/tex]=[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]

on comparing we get

r = [tex]\frac{d}{2}[/tex]

circumference of circle is 2[tex]\pi r[/tex]

= 2×[tex]\pi[/tex]×[tex]\frac{d}{2}[/tex]

=[tex]\pi[/tex]d

The circumference of circle is [tex]\pi[/tex]d

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Answer:

V= 30m/s u=0 A=1.5, time t=? distance S=?

Step-by-step explanation:

to find time:

A=v-u/t

t=v-u/a

t =30-0/1.5

t = 20 secs

to find distance S

S= UT +½at²

S= 0×20+ 1.5×20²/2

s= 300m

Line C has the constant of proportionality between y and x of 2/3.

For the given question;

Constant of proportionality = change in y / change in x

Check for each line;

Line A; select any coordinate from the graph.

(7, 3); Put in the formula

Constant of proportionality = 7/3

Thus, Line A has Constant of proportionality between y and x of 7/3.

Line B; select any coordinate from the graph.

(4, 3); Put in the formula

Constant of proportionality = 4/3

Thus, Line B has Constant of proportionality between y and x of 4/3.

Line C; select any coordinate from the graph.

(2, 3); Put in the formula

Constant of proportionality = 2/3

Thus, Line C has Constant of proportionality between y and x of 2/3.

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Simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

As given,

Simplification of the given problems without absolute value sign:

1. |5-x|-|x+8|, if x>5

 = x - 5-(x+8)

 = x-5 -x-8

 = -13

2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8

= x -2+ 8 -x+2

=8

3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5

 = x-5-(x-2)+(x+1)

=x-5-x+2+x+1

=x-2

4. |7 − x| + |4 − 2x| − |x − 8, if x < 2

= 7-x +4-2x-8 +x

=3-2x

Therefore, simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

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The constant of proportionality on the equation is 5.

What is constant of proportionality?

Constant of proportionality is defined as the ratio that relates two given value. When two values are directly or indirectly proportional to one another, there relation is expressed as y = kx.

We compare the general direct proportionality relation with the equation given.

The equation given : y = 5x

The direct relationship between y and x is :

y α x

y = kx - - - (1)

Where, y and x are variables and k is the constant of proportionality.

Comparing equation (1) with the equation given :

y = kx

y = 5x

We can observe that, k in the equation (1) equals to 5 in the given equation.

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a. Yes, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

A cell phone plan costs $30 for each line.

Now, Let the number of lines be x and total cost be y.

So, We can evaluate;

y = 30x

Thus, This equation represent Linear function.

So, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

Since, You can have a maximum of four lines on a plan.

So, The possible values are;

x = 0, 1, 2, 3, 4

After substitute all the value of x in equation y = 30x we get;

For x = 0

y = 30 × 0 = 0

For x = 1

y = 30 × 1 = 30

For x = 2

y = 30 × 2 = 60

For x = 3

y = 30 × 3 = 90

For x = 4

y = 30 × 4 = 120

Thus, The range of the function will be 0 ≤ x ≤ 4.

And, The domain of the function will be 0 ≤ y ≤ 120.

Therefore,

a. Yes, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.

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Answer:

5 times the length of the short piece = 75 inches

The length of the short piece =75 / 5 = 15 inches

Length of the long piece = 4 times the length of the short piece = 60 inches

Check: 15 + 60 = 75 inches

yay

The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.

Let l be the length l the rectangle and w be the width of the rectangle.

The area of a rectangular living room is 450 square feet.

⇒ A = l × w

⇒ 450 = l × w                     ................(1)

The length of the room is 15 feet less than three times the width.

So we get an expression,

l = 3w - 15

Substitute above vale of l in equation (1)

450 = (3w - 15) × w        

450 = 3w² - 15w

3w² - 15w - 450 = 0

w² - 5w - 150 = 0

(w - 15)(w + 10) = 0  

w - 15 = 0  or w + 10 = 0

w = 15    or    w = -10

But width of the rectangle cannot be -10

So, w = 15 feet

and l = 3(15) - 15

l = 30 feet

Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.

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The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

The dollar amount the club would contain if they reached half of their goal T + 50.

The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.

The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.

The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.

The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.

The complete question is:

To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?

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Ratio in three ways are given below.

The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply. A ratio's two numbers can only be compared if they share the same unit. Ratios are used to compare two objects. a connection between two values that is typically expressed as the quotient of one value divided by the other. For instance, the ratio of red to blue marbles is 6:4, or six red to four blue marbles, in the case of a box containing six red and four blue marbles. A decimal or percentage can also be used to indicate a ratio.

Given Data

An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees.

a) Rows of Gala apple trees to Granny apple smith trees:

Ratio

First way = 15 to 12

Second way = 15:12

Third way = [tex]\frac{15}{12}[/tex]

b) Rows of Fuji apple trees to total number of apple trees

Total number = 12 + 10 + 15 + 2 +2

Total number = 41

Rows of Fuji apple trees = 10

First way = 10 to 41

Second way = 10: 41

Third way = [tex]\frac{10}{41}[/tex]

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