The lateral surface area of a cylinder is given by the formula S = 2pirh . Solve the equation for r.

Answer:

Is this correct??

if yes then reply

Answer/Step-by-step explanation:

I don't know whether to distribute -6 or multiply 4x - 6 by 3x + 4. So I'll do both.

1. Multiply

(4x - 6)(3x + 4)

4x (3x + 4) - 6 (3x + 4)

12x² + 16x - 18x - 24

12x² - 2x - 24

2. Distribution

4x - 6(3x + 4)

4x - 18x - 24

-14x - 24

I hope either of my answers helps!

The greatest common factor for the given expression is 5z.

What is GCF?
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF). The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.

Given, the first expression is: y₁ = 70x³z = 5z.14x³ -(i)
Also, the second expression is: y₂ = 45y4z² = 5z.36yz -(ii)
Comparing (i) and (ii), the greatest common factor for y₁ and y₂ is 5z.
Thus, the greatest common factor for the given expression is 5z.

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Answer:

The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway

Step-by-step explanation:

if a car uses 3 1/8 gollon per one hour

Multiply the gallon usage of the car by the hours the car will travel on the road

3 1/8(gallons) x 3(hours on the road)

9 3/8 or if you change it to simple form it will be equal to 9.375

Answer:

180 Degrees for both

they are symmetrical therefore 180 degrees

Answer:

I believe it should be 5/6

Step-by-step explanation:

Here's why, the probability of getting a B, or an even number is 3/6 since there are 3 even numbers on a dice. The probability of getting a multiple of 3 is 2/6 since the only multiples of 3 are 1 and 3. Add the 2 together to get 5/6. Hope this helps.

Answer:

[tex]\text{P}(B \text{ or }C)=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Mutually Exclusive Events

For two events, A and B, where A and B are mutually exclusive:

[tex]\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}[/tex]

Probability distribution table:

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}[/tex]

where X is the score on a fair, six-sided dice.

P(B or C) means "the probability of rolling an even number or a multiple of 3".

As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.

Calculate the probabilities for events B and C.

Event B

Rolling an even number.

[tex]\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}[/tex]

Event C

Rolling a multiple of 3.

[tex]\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}[/tex]

Solution

[tex]\begin{aligned}\implies \text{P}(B \text{ or }C)&=\text{P}(B)+\text{P}(C)\\\\& = \dfrac{3}{6}+\dfrac{2}{6}\\\\& = \dfrac{5}{6}\end{aligned}[/tex]

Answer: 7/12 =x

Step-by-step explanation:

Answer:

FALSE.

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the above formula, we have

h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2

So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2

h'(3) = (12-36)/4

h'(3) = -24/4 = -6

So, h'(3) = -6 and not -12.

So, the given value is FALSE.

Answer:

98 + (-24)

Step-by-step explanation:

A difference between two values indicates whether one is smaller, larger, or simply not equal to other. From the set {12, 22, 25}, value of x makes the inequality true 3x < 66 is 12.

Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. a week ago.

A difference between two values indicates whether one is smaller, larger, or simply not equal to other.

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The value of a is 9 and b is 4.5

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that can be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

[tex]sin(60)=\frac{opposite}{hypotenuse} \\\frac{\sqrt{3} }{2}=\frac{\frac{9\sqrt{3} }{2} }{a}\\ a =9\\ tan(60)=\frac{opposite}{adjacent}\\ \sqrt{3}=\frac{\frac{9\sqrt{3} }{2} }{b} \\b=4.5[/tex]

The value of a is 9 and b is 4.5

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The number of tiles measuring 20cm by 50cm  that are needed to completely cover a wall 4m by 8m is :320.

First step is to convert the Meters to Centimeters

4m = 400cm

8m = 800 cm

Hence,

4m by 8m = 400 cm × 800 cm

4m by 8m = 320,000 cm²

Second step is to determine the how many tiles are needed

Number of needed tiles =  320,000 cm² / ( 20 cm × 50 cm)

Number of needed tiles =  320,000 cm² /1,000 cm²

Number of needed tiles =  320

Therefore 320 tiles are needed.

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22.44% probability that the marbles are red, 77.55% probability that they are blue

Answer:

105

Step-by-step explanation:

5 minutes=75 pages

1 minute=15 pages

7 minutes=15*7

7 minutes=105pages

Answer: 105

Step-by-step explanation:

75pg —-> 5mins

X ——> 7 mins

•

•

x= (75 x 7)/5 = 105pages

We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

So, the wood we need to make 120 pins:

Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

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Bunting has been hung in a straight line between a wall and a house, then the height, P, of the house P = 6.61 m.

Third angle in a triangle = 180 - (90+36)

= 180-126

= 54°

So,

Third angle in a triangle = 54°

We can use Sin rule,

Then, we get,

[tex]\frac{Sin A}{BC} =\frac{Sin B}{AC} =\frac{Sin C}{AB}[/tex]

Based on the given condition,

We can write,

Sin A = 54°

Sin B = 36°

BC = 5.47

Then,

Sin 54°/5.47 = Sin 36°/AB

Hence, Sin 54° = 0.8090

Sin 36° = 0.5877

[tex]\frac{0.8090}{5.47} =\frac{0.5877}{AB}[/tex]

AB = [tex]\frac{0.5877 * 5.47}{0.8090}[/tex]

AB = [tex]\frac{3.2147}{0.8090}[/tex]

AB = 3.97 m

So,

Height , P = 2.64 + 3.97

P = 6.61 m.

Therefore,

We can use triangle formula, then the height, P, of the house P = 6.61 m.

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[tex] = 16 - ( - 2) \\ = 16 + 2 \\ = 18[/tex]

The positive difference is 18.

Answer:

Step-by-step explanation:

Note: In solving our problems below, we will use the value of the coins in dollars which are listed under the third column in the table above. As you can see, the penny has a value of 0.01, the nickel has a value of 0.05, the dime has a value of 0.10, and the quarter has a value of 0.25

The coefficient of the variable term in the equation 6s - 3/4 is 6. The variable term is s while the constant term is -3/4

given data

6s-3/4

The coefficient of the variable term is the number multiplying the variable term. The variable term in the equation is "s"

The number in the given equation is 6

The equation could be written as

6 * s - 3/4

from the rewritten equation we can see that 6 is multiplying the variable and hence the coefficient.

The other term in the equation is constant term and this is - 3/4

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Variable x as the subject of the equation given is expressed as: x = p(m - n).

To make a variable the subject of a formula implies that we express the equation in terms of the variable. Thus, to make a variable the subject of the formula, we have to make the variable stand alone on one side of the equation.

Given the equation, m = n + x/p, make x the subject as explained below:

m = n + x/p [given]

Subtract n from both sides

m - n= n + x/p - n (subtraction property of equality)

m - n = x/p

Multiply both sides by p

p(m - n) = x/p(p) (multiplication property)

p(m - n) = x

x = p(m - n)

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I WILL USE CROSS MULTIPLICATION

[tex]t(1.3) = 6.5(1.2) \\ 1.3t = 7.8 \\ \frac{1.3t}{1.3} = \frac{7.8}{1.3} \\ t = 6 [/tex]

ATTACHED IS THE SOLUTION

Answer:

206

Step-by-step explanation:

Let x=4.

[tex]f(4)=-3.334(4)^4+35.607(3)^3-97.645(4)^2+41.268(4)+177.537 \approx 206[/tex]

Answer:8

Step-by-step explanation:if it is 4/5 per hour then you mulitply 4/5 x 10

and 4/5=.8

     .8 x 10=8

The output value of f( -4 ) in the function f(x) = -x² - 4x + 42 is 42

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

Given the data in the question;

To find the output value of f( -4 ), replace all the occurrence of x with -4 in the function and simplify.

f( x ) = -x² - 4x + 42

f( -4 ) = -(-4)² - 4(-4) + 42

f( -4 ) = -( 16 ) + 16 + 42

f( -4 ) = -16 + 16 + 42

f( -4 ) =  42

Therefore, the output value of f( -4 ) is 42, this forms an ordered pair of (-4, 42).

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All the values that we can put in the given box so that A is a polynomial,

[tex]A=(2x^{2} +5-7)\\A =2(x^{2} -1)\\A=2(x+1) (x-1)[/tex]

[tex]x[/tex] can take any value except ±1.

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Answer: 7 games

Explanation:

1. take the information and put it into a equation (being y=3.25x+3 or f(x)=3.25+3)

2. replace the x with a whole number because you can't bowl half a game.

Ex: f(3)=12.75 or f(6)=22.50

3. The highest you can go without going over your money is 7 games ($25.75) leaving you with a total of 2.25.

Hope this helps :)

Answer: B) 90º counterclockwise

Step-by-step explanation:

           First, let us look at clockwise vs counterclockwise. Clockwise is in the direction of a clock, spinning around to the right. Counterclockwise is the opposite, spinning to the left.

     A) 90º clockwise

➜ This is 90 degrees to the right.

     B) 90º counterclockwise

➜ This is 90 degrees to the left

     C) 180º

➜ This is directly flipped.

     D) 270º clockwise

➜ This is 270 degrees to the right.

     E) 270º counterclockwise

➜ This is 270 degrees to the left.

           We will look at the answer options and decide which makes the most sense. This looks to be option B, 90º counterclockwise as shown in the image attached.

In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.

An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.

Both Ang and Julia have savings balances of x and y dollars, respectively.

Ang = x dollars

Julia = y dollars

Ang offers Julia a third of his savings, which she then transfers to her own savings account.

Amount in Julia's account = (1/3)x + y

Julia then spends a quarter of the total into her savings account.

Amount of money Julia spent = 1/4 × [(1/3)x + y]

                                                 = (1/12)x + (1/4)y

                                                 = y/4 + x/12

Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.

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