x2 + y2 + 12x + 2y – 1 = 0

Option D: [tex]1176 \pi \ {m}^{3}[/tex] is the volume of the cylinder

Explanation:

Given that the cylinder has a radius of 14 m and a height of 6 m

We need to find the exact volume of the cylinder.

The formula to determine the volume of the cylinder is given by

[tex]Volume=\pi r^{2} h[/tex]

Let us substitute [tex]r=14[/tex] and [tex]h=6[/tex] in the above formula, we have,

[tex]Volume=\pi (14)^{2} (6)[/tex]

Squaring the terms, we get,

[tex]Volume=\pi (196)(6)[/tex]

Multiplying we have,

[tex]Volume=1176\pi \ m^3[/tex]

Thus, the volume of the cylinder is [tex]1176 \pi \ {m}^{3}[/tex]

Therefore, Option D is the correct answer.

Answer:

[tex]5 {y}^{2} - 80[/tex]

Step-by-step explanation:

The given polynomials are:

[tex]5 {y}^{2} - 80[/tex]

and

[tex]y + 4[/tex]

Let us factor the first polynomial to get:

[tex]5 {y}^{2} - 80 = 5( {y}^{2} - 16)[/tex]

We need to rewrite as difference of two squares:

[tex]5 {y}^{2} - 80 = 5( {y}^{2} - {4}^{2} )[/tex]

We can now factor to get:

[tex]5 {y}^{2} - 80 = 5( {y} - 4)(y + 4)[/tex]

So the least common multiple of

[tex]5( {y} + 4)(y - 4) \: and \: (y + 4) \: is \: 5( {y} + 4)(y - 4) = 5 {y}^{2} - 16[/tex]

l

Answer:

[tex]\leq[/tex]11

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

The other number is 375.

Step-by-step explanation:

The given information are,

The one number out of the two numbers is 300.

Let, the another number be assumed as 'x'.

The first number = 300 and the second number = x.

To find the number x :

The HCF × LCM = product of two Numbers  is a logic to used to find the unknown number.

We know the values of HCF = 75 , LCM = 1500 and one number = 300 and the second number is x.

Therefore, substituting those values in the above formula, we get

⇒ 75 × 1500 = 300 × x

⇒ 1125 / 3 = x

⇒ 375 = x

Therefore, the second number is 375.

Answer:

675 ft (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

A. 4r=v

Step-by-step explanation:

It says that she ate 4 times as many as Reagen and r represents the number that Reagen at so it would be 4r. While v represents how many Olivia ate which is 4r so 4r = v.

Answer:

A.4r = v

Step-by-step explanation:

Because is really asking for a ratio so the comparison of two objects

so if Olivia ate  four times as much as Reagan then first start off by finding the variables which is  R and V .R is how much Reagan ate well we know she at 4 times more than Olivia so 4R and now you gotta figure V how much Olivia ate so 4R = V

if you need any more help let me know ...

A scale drawing is a drawing made with proportionate scaling. It helps represent objects or spaces accurately and proportionally.

A scale drawing is a drawing that is done with a scale so that specific small units of measure represent larger units of measure. Scale drawings are used to represent objects or spaces proportionally, aiding in visualizing and understanding relationships between different elements.

The equivalent value of the expression is A = ( 10x² - 4 ) - ( 7x² + 3 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 3x² - 7   be equation (1)

On simplifying , we get

Let the second expression be represented as B

where B = ( 10x² - 4 ) - ( 7x² + 3 )

On simplifying , we get

B = 10x² - 4 - 7x² - 3

B = ( 10x² - 7x² ) - ( 4 + 3 )

B = 3x² - 7

Therefore , the value of B = A

Hence , the expression is B = ( 10x² - 4 ) - ( 7x² + 3 )

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Answer:

97+70+89+99+100+78+79+77+72=85

Answer:

B. 1/10 i think c:

Step-by-step explanation:

Answer: 0.65   I think 1/10

Step-by-step explanation: You find 25% of 1,  (.25), then add 2/5

Answer:

Step-by-step explanation:

does it have to be right?

Answer: volume is 26.9

Step-by-step explanation:

Volume of a cone is calculated by V=πr^2h/3

Where π is a constant, with value of 3.14

h is height, given as 8.4

r is radius, radius = diameter ÷ 2

Since Diameter is given as 3.5, radius = 3.5/2 = 1.75

Slot the values into the formula

V= 3.14 x 1.75^2 × 8.4/3

= 3.14 x 3.06 x 2.8

=26.9

I hope this helps.

Answer:

0.416

Step-by-step explanation:

Answer:

[tex]\huge\boxed{x=1\ \vee\ x=2}[/tex]

Step-by-step explanation:

[tex]3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}[/tex]

[tex]\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}[/tex]

Final answer:

To solve the given equation involving exponents, convert 3^(x+1) and solve as a quadratic equation.

Explanation:

The equation is: 3^(2x) - 4*3^(x+1) + 27 = 0. To solve this, we can use the rules of exponents to change 3^(x+1) into 3*3^x.

Step-by-step solution:

Substitute 3^(x+1) with 3*3^x in the equation.

Now, you have a quadratic equation in terms of 3^x, solve it to find the value of 3^x.

Once you find the value of 3^x, proceed to find the value of x.

Answer: I dont know

Step-by-step explanation:

He is almost dead and wants the pp

Answer:

NF = 16 units

Step-by-step explanation:

∵ N is the in-center of ΔABC

∴ N is equidistant from the sides AB, BC and CA

- That means the perpendicular segments from N to AB, BC

   and AC are equal

∴ ND = NE = NF

∵ ND = 6x - 2

∵ NE = 3x + 7

- Equate them to find x

∴ 6x - 2 = 3x + 7

- Subtract 3x from both sides

∴ 3x - 2 = 7

- Add 2 to both sides

∴ 3x = 9

- Divide both sides by 3

∴ x = 3

- Substitute the value of x in ND to find its length

∵ ND = 6(3) - 2 = 18 - 2

∴ ND = 16 units

∵ ND = NE = NF

∴ NF = 16 units

Answer:

y=1/4x+400

Step-by-step explanation:

Slope=Rise/Run=(300-200)/(-400-(-800))=100/400=1/4

Now we have the slope, making our equation:

y=1/4x+b

We need b, the y-intercept, which we can use any ordered pair to plug in:

200=1/4(-800)+b

200=-200+b

400=b

So the equation that passes through the points (-800, 200) and (-400, 300) is: y=1/4x+400

The equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.

The general equation of straight line is -

y = mx + c

Given is a line that passes through the points P(-800, 200) and

Q(-400, 300).

First we will find the slope of the line -

m = (y₂ - y₁)/(x₂ - x₁)

m = (300 - 200)/(-400 + 800)

m = 100/400

m = 1/4

Now, the line passes through the point Q(-400, 300). Therefore -

300 = (1/4) x (- 400) + c

300 = - 100 + c

c = 400

The final equation of the line will be -

y = x/4 + 400

Therefore, the equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.

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Answer:

175.93cm²

Step-by-step explanation:

Answer: 175.929 yd^2

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

just mutiply  120 by 1,2,3,4,5,6,7,8

The radius of a circle is half the length of the diameter, and the circumference is the perimeter of the circle. However, the circumference is not triple the radius, and the diameter is not triple the length of the radius.

In the context of Mathematics, particularly geometry, the following statements are indeed true about the components of a circle:

However, the statements that the circumference is triple the radius, to find the circumference multiply it by the diameter, and the diameter is triple the length of the radius, are incorrect. The circumference of a circle is calculated as 2πr (two times the radius times Pi), and the diameter is twice the length of the radius, not triple.

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Answer:

mean: 7

median: 6

mode: no mode

Step-by-step explanation:

To find the mean, add all numbers together and subtract by how many numbers there are:

4 + 6 + 12 + 5 + 8 = 35

35/5 = 7

To find the median, you put the numbers in order from smallest to largest and find the very center number:

4, 5, 6, 8, 12

The very center number is 6

To find the mode, you choose the number that appears most often. Since every number in this set only appears once, there is no mode.

Answer:

median=6, mean=5, mode=none

Step-by-step explanation:

median= number in the middle, mean= add up all numbers then divide by how many numbers there are, mode= most common number

Answer:

A. Strong negative

General Formulas and Concepts:

Statistics

Step-by-step explanation:

According to the graph and the data set, we can see that we do indeed have a negative correlation trend. Therefore, options B and D can be eliminated.

Looking at the graph, we can see that we can definitely tell that it is a negative slope and it would be pretty steep. Therefore, the best answer choice would be A. Strong negative.

Answer:

$3150

Step-by-step explanation:

I = P • R • T

Intrest Equals Principal Amout times Rate of Intrest times Amount of Time

P is our Principal amount of $3,000

R is our Rate of 7%

T is the time span of  years

Now if we plug in the values and solve the equation we get $3150 dollars in intrest.

Final answer:

Roxanne will earn $3,150 in interest after 15 years.

Explanation:

To calculate the interest Roxanne will earn, we can use the formula:

Interest = Principal x Rate x Time

Where Principal is the initial amount invested, Rate is the interest rate, and Time is the number of years.

Plugging in the given values, we get:

Interest = $3,000 x 0.07 x 15

Interest = $3,150

Therefore, Roxanne will earn $3,150 in interest after 15 years. This implies that Roxanne will accumulate $3,150 in interest after 15 years, illustrating the straightforward application of the interest formula to quantify the financial growth derived from the initial investment over the specified period.

Answer:

True

Step-by-step explanation:

The nature of roots of a quadratic equation are determined by

[tex] {b}^{2} - 4ac[/tex]

where a, b, and c are the coefficients of the quadratic equation

[tex]a {x}^{2} + bx + c = 0[/tex]

Therefore it is true that, the roots of a quadratic equation depend on the values of the coefficients.

The value of x is approximately 5.4 when x^3 -10x = 100

The equation is given as:

x^3 -10x = 100

Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100

After several attempts, we have:

x = 5.4 (approximately)

Substitute 5.4 for x in x^3 -10x = 100

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100

This means that x is approximately 5.4 when x^3 -10x = 100

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A solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).

let's use the trial and improvement method to find a solution for the equation

x^3 −10x=100.

Start with a reasonable guess for x. In this case, it's often helpful to start with small integers.

Substitute the guess into the equation and see if it satisfies the equation.

Let's try

5^3 −10×5=125−50=75

The result is not equal to 100. Since the result is less than 100, we need to increase our guess.

Let's try

6^3 −10×6=216−60=156

The result is still not equal to 100. Since the result is now greater than 100, we need to decrease our guess.

Let's try

5.5^3 −10×5.5=166.375−55=111.375

This result is still greater than 100, so we need to try a smaller value.

5.2^3 −10×5.2=140.608−52=88.608

Now, this result is closer to 100. We can continue to refine our guess.

Let's try

5.3^3 −10×5.3=150.097−53=97.097

This result is getting closer to 100. We can keep refining our guess, but for the sake of brevity, let's stop here.

So, a solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).

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Answer:

9802.9

Step-by-step explanation:

find 17.4% of 8350 and then add that to the original price

Answer:

16%

Step-by-step explanation:

Percentage of the tip is the tip divided by the original bill and the result multiplied by 100%

That’s

$11.43/$73.57 x 100%

0.1554 x 100%

15.54

16%

The tip was 16% of the original bill

The tip was about 16% of the total bill. This was calculated by dividing the tip amount by the total bill, multiplying by 100 to get a percentage, and then rounding to the nearest whole percent.

To find out what percentage the tip was of the original bill, you would divide the amount of the tip by the total bill before the tip, and then multiply that number by 100 to get a percentage. Here's how you would calculate it in this case:

So, the tip was about 16% of the total bill.

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[tex]m\angle B= 41^{\circ},[/tex] [tex]m\angle F= 70^{\circ},[/tex] [tex]m\angle H = 61^{\circ},[/tex] [tex]m\angle K= 56^{\circ}.[/tex]

Step-by-step explanation:

Step 1:

The total of the angles in any triangle is 180°.

So to determine the third angle of the given triangles, we subtract the sum of the other two sides from, 180°.

The third angle = 180° - (the first angle + the second angle).

Step 2:

For triangle ABC,

[tex]m\angle B=180^{\circ}-(\angle A+\angle C)[/tex],

[tex]m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.[/tex]

So [tex]m\angle B= 41^{\circ}.[/tex]

For triangle DEF,

[tex]m\angle F=180^{\circ}-(\angle D+\angle E)[/tex],

[tex]m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.[/tex]

So [tex]m\angle F= 70^{\circ}.[/tex]

Step 3:

For triangle GHI,

[tex]m\angle H=180^{\circ}-(\angle G+\angle I)[/tex],

[tex]m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.[/tex]

So [tex]m\angle H = 61^{\circ}.[/tex]

For triangle JKL,

[tex]m\angle K=180^{\circ}-(\angle J+\angle L)[/tex],

[tex]m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.[/tex]

So [tex]m\angle K= 56^{\circ}.[/tex]