the radius of the circular base of a cone is (3x-2)m. if its slant height is (9x^2 - 6x)m, express the cone’s surface area as factored polynomial in x.

NOTE: SA= πrs+πr^2

Answer:

109

Step-by-step explanation:

Three consecutive integers:

Sum of them:

The smallest integer out of three is 109

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3 consecutive integers = x+(x+1)+(x+2) or 3x+3 (x is the smallest number)

(Consecutive means one after another)

So 3x+3 = 330.

Now subtract 3 from both sides.

(3x-3)=3x

(330-3)=327

The left side is 3x and the right side is 327.

The equation now is 3x=327.

Now divide each side by 3 (so x is isolated)

3x÷3=x

327÷3=109

The left side is x and the right side is 109.

The final equation is x=109.

Since x is the smallest of these integers we don't have to do anything else.

Okay, so let's check the answer now. 109+110+111=330.

So the smallest of the 3 consecutive numbers is 109.

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Answer:

Answer:

True

Step-by-step explanation:

Answer:

  A.  True

Step-by-step explanation:

The graph passes the horizontal line test, so the inverse relation is a function.

__

The horizontal line test requires any horizontal line intersect the graph in at most one place.

Answer:

0

Step-by-step explanation:

Group like terms= 3r-3r-50+50

Add similar elements= -50+50

Answer=0

I hope this helps!

Answer: D: x = {-3, -1, 1}

Step-by-step explanation:

Domain refers to the x-values of the coordinates.

Coordinates are in the form (x, y) so we are looking for the values on the left side of the parenthesis.

(-3, -2) --> x = -3

(-3, 0)  --> x = -3  already listed above so no need to list it again

(-1, 2)  --> x = -1

(1, 2)  --> x = 1

the x-values are: -3, -1, & 1

so the domain is: x = {-3, -1, 1}

Answer:

Domain = -3, -1, 1.

Step-by-step explanation:

Let's find Domains of x-coordinates of the following.

1) (-3, -2) => (x = -3)

2) (-3, 0) => (x = -3)

3) (-1, 2) => (x = -1)

4) (1, 2) => (x = 1)

Hence, value of x = domain .

These x values lie on the x-coordinates .

[tex] \Large{ \boxed{ \mathbb{ \pink{SOLUTION:}}}}[/tex]

The AP would be like:

Now,

➝ First term = 1

➝ Common difference = 2

➝ No. of terms = 50

By using formula,

[tex] \large{ \boxed{ \rm{S_n = \frac{n}{2} \bigg(2a + (n - 1)d \bigg)}}} [/tex]

Here,

Proceeding further,

➝ S50 = 50/2{ 2 × 1 + (50 - 1)2 }

➝ S50 = 25{ 2 + 49 × 2 }

➝ S50 = 25{ 100 }

➝ S50 = 2500

⛈️ Sum of 50 terms of AP = 2500

Shortcut trick:- n^2

Then, Sum of 50(n) terms = 50^2 = 2500

☘️ Hence, solved !!

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Answer:

2500

Step-by-step explanation:

The Sum of First 50 Odd Natural Numbers:

1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41+43+45+47+49+51+53+55+57+59+61+63+65+67+69+71+73+75+77+79+81+83+85+87+89+91+93+95+97+99

= 2500

Answer:

34n=42?

Step-by-step explanation

-16+5n=-7(-6+8n)+3

1.) multiply

-16+5n=42+-56n+3

2.) add like terms

-16+5n=-45+-56n

3.) find lower number, and add the opposite

29n+5n=42

4.) add n's

34n=42 ?

Answer:

Step-by-step explanation:

-16 + 5n = -7(-6 + 8n) + 3

Expand the terms in the bracket

That's

- 16 + 5n = 42 - 56n + 3

Group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

5n + 56n = 16 + 42 + 3

Simplify

61n = 61

Divide both sides by 61

We have the final answer as

Hope this helps you

Answer:

[tex]\huge\boxed{b=-8}[/tex]

Step-by-step explanation:

[tex]4b+8=3b\\\\4b+8-8=3b-8\\\\4b=3b-8\\\\4b-3b=3b-3b-8\\\\\boxed{b=-8}[/tex]

Answer:

b = -8

Step-by-step explanation:

4b+8=3b

Subtract 4b from each side

4b-4b+8=3b-4b

8 = -b

Multiply each side by -1

-8 = b

Answer:

Step-by-step explanation:

1.  Symbolically, we get:  62 - 5x < 40

2.  y - 7.3 < 3.4.  Solve for y by adding 7.3 to both sides, obtaining:

     y < 10.7    This is both the 'range' and the 'solution'

3a)      4b =  9b + 45, or -5b = 45, or b = -9

3b)      5a + 10 = 4a - 4

Combining like terms results in a = -14

Answer:

C. 3m+24/4

Step-by-step explanation:

Given that (3m/4 - 2) + 8

Then we solve

= (3m/4 - 8/4) + 8

= (3m - 8)/4 + 32/4

= (3m - 8 + 32)/4

= 3m + 24 /4

Therefore the answer is C

Alternatively, we can simplify the equation by

Given that, the equation is ( 3m/4 - 2 ) + 8

We then remove parenthesis

= 3m/4 - 2 + 8

= 3m/4 + 6

= 3m/4 + 24/4

Then add the numerators and leave the denominator

= 3m + 24 /4

This also equals option C.

Hence, it can be concluded that, the correct answer is Option C: (3m + 24)/4

Answer:(6,-7)

Step-by-step explanation:

you just flip in over the x axis so the only thing changing is y lol

Answer:

63 = x

Step-by-step explanation:

We know that a triangle's angles always add up to 180º. Since Line DC is a 180º line, we can subtract 128 from 180.

180 - 128 = 52º

The angle next to A is 52º.

Then, we add 52 and 65 to get the sum of the two angles.

52 + 65 = 117

Finally, subtract 117 from 180 to get our x.

180 - 117 = 63

x = 63

To check, add all the angle values together and if they equal to 180, your answer is correct.

63 + 52 + 65 = 180. Correct!

=======================================

Explanation:

Through the remote interior angle theorem, adding the remote interior angles x and 65 results in the exterior angle 128. Note how the exterior angle is not adjacent to any of the interior angles (which is where the "remote" portion comes from).

x+65 = 128

x+65-65 = 128-65

x = 63

------------------

A longer method involves finding interior angle BAC using the given exterior angle

angle BAC = 180-(exterior angle DAB)

angle BAC = 180-128

angle BAC = 52

So far, the triangle BAC has two known interior angles 65 and 52. The missing angle x adds onto the previous two getting us 180

x+65+52 = 180

x+117 = 180

x = 180-117

x = 63

We get to the same x value.

Answer:

In domain: -2.

Not in domain: 2, 4.

Step-by-step explanation:

The domain of a square root function is all real numbers such that the expression under the square root is greater than or equal to 0.

So, set the expression under the square root greater than or equal to 0 and solve for x:

[tex]-2x\geq 0\\[/tex]

Divide both sides by -2. When dividing by a negative, we flip the sign:

[tex]x\leq 0[/tex]

So, the domain of the function is all real numbers such that x is greater than of less than 0.

-2 is less than 0. So, it is in the domain.

2 is not less than 0. So, it is not in the domain.

4 is not less than 0. So, it is also not in the domain.

Answer:

Step-by-step explanation:

Answer:

2 -

Step-by-step explanation:

if u flip the shape to make a diamond

Answer:

Cost of the pen = Rs.100

Step-by-step explanation:

Let the marked price = x

When the shopkeeper is selling for x, his gain = Rs. 20

Cost price = Marked price  - Gain = x - 20 --------(I)

After discount:

Discount = 10%

Marked price after discount = (100 - 10)% of x = 90% of x

                                               = 0.9 * x = 0.9x

When the shopkeeper is selling for 0.9x, his gain = Rs.8

Cost price = Marked price - gain = 0.9x - 8   -------(II)

From (I) and (II)

x - 20 = 0.9x - 8

x   = 0.9x - 8 + 20

x = 0.9x + 12

x - 0.9x = 12

0.1x = 12

x = 12/0.1

x = 120

Marked price of pen = Rs.120

Cost price = 120 - 20

Cost price  = Rs. 100

Answer:

y = -1

Step-by-step explanation:

Notice that the line x = 9 is a vertical line, therefore a line perpendicular to it will be a horizontal line of the form y = constant number.

Since we want it to go through the point (9, -1), then we know that that y value needs to be "-1", and the equation of the line will be given by the expression:

y = -1

Answer:

y =1

Step-by-step explanation:

[tex](9,-1)=(x ,y)\\\\x =m_1 =9\\m_2 = \frac{-1}{m_1} = \frac{-1}{9} = -\frac{1}{9} \\\\Substitute \:the \:values\:into ;\\y =mx+b\\\\-1 =-\frac{1}{9} (9) +b\\-1 = -1+b\\-1+1 = b\\0 =b\\m= 1 \\Substitute\:the\:new\:values\:into ;\\y = mx+b\\y = 1 x +0\\ y= 1[/tex]

Answer:

Your answer will be 1.35

Answer:

15

Step-by-step explanation:

OPTION 1:

We can use the distance formula to find the distance between these two points.

[tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

X2 is -9, X1 is 0, Y2 is -10, and Y1 is 2, so we can substitute inside the equation.

[tex]\sqrt{(-9-0)^2 + (-10-2)^2}\\\\\sqrt{9^2 + -12^2}\\\\\sqrt{81 + 144}\\\\\sqrt{225}\\\\15[/tex]

OPTION 2:

We can look at the change in x and the change in y and use the Pythagorean Theorem to find the missing length of the hypotenuse.

The x changes by 9, and the Y changes by 12.

[tex]a^2+b^2=c^2[/tex] is the Pythagorean Theorem. We know a and b, so we can substitute inside the equation.

[tex]9^2 + 12^2 = c^2\\\\81+144=c^2\\\\225=c^2\\\\c=15[/tex]

Hope this helped!

Answer: The distance is 15 units.

Step-by-step explanation:

Find the difference in the x and y coordinates and square them and add them together.

(0,2) and (-9,-10)  The x coordinates are 0 and -9  and the y coordinates are 2 and -10.

0-(-9) = 9

2-(-10) = 12

9^2 + 12^2 = d^2

  81 + 144 = d^2

   225 = d^2

d = [tex]\sqrt{225}[/tex]  

  d= 15

Answer:

[tex]\bold{\dfrac{11}{2 }}[/tex]

Step-by-step explanation:

Given the geometric series:

[tex]\{\dfrac{1}2, -1, 2, -4, ..... \}[/tex]

To find:

Sum of series upto 5 terms using the geometric series formula = ?

Solution:

Formula for sum of a n terms of a geometric series is given as:

[tex]S_n=\dfrac{a(1-r^n)}{1-r} \ \{r<1 \}[/tex]

[tex]a[/tex] is the first term of the geometric series

[tex]r[/tex] is the common ratio between each term (2nd term divided by 1st term or 3rd term divided by 2nd term ..... ).

Here:

[tex]a = \dfrac{1}{2}[/tex]

[tex]r = \dfrac{-1}{\dfrac{1}{2}} = -2[/tex]

[tex]n=5[/tex]

So, applying the formula for given values:

[tex]S_5=\dfrac{\dfrac{1}2(1-(-2)^5)}{1-(-2)} \\\Rightarrow S_5=\dfrac{1-(-32)}{2 \times 3} \\\Rightarrow S_5=\dfrac{1+32}{6} \\\Rightarrow S_5=\dfrac{33}{6} \\\Rightarrow \bold{S_5=\dfrac{11}{2}}[/tex]

So, the answer is

[tex]\bold{\dfrac{11}{2 }}[/tex]

Step-by-step explanation:

From the question

Perimeter = 2L + 2W

L = 24 units

W = 11 units

Substitute the values into the above formula

That's

P = 2(24) + 2(11)

P = 48 + 22

P = 70 units

Therefore the perimeter of the rectangle cannot be 60 units since the values when substituted into the above formula will give us 70 units

Hope this helps you

Answer:

[tex]\large \boxed{\mathrm{view \ explanation}}[/tex]

Step-by-step explanation:

∠BED is measuring 90 degrees (right angle).

The opposite angle of angle ∠BED will also be 90 degrees because of vertical angles.

∠AEC is measuring 90 degrees (right angle).

The angles on a line add up to 180 degrees.

∠AEC and ∠AEB add up to 180 degrees.

90 + ∠AEB = 180

∠AEB = 90

∠AEB is measuring 90 degrees (right angle).

Angles in a circle around the center add up to 360 degrees.

∠BED + ∠AEC + ∠AEB + ∠CED = 360

90 + 90 + 90 + ∠CED = 360

∠CED = 90

∠CED is measuring 90 degrees (right angle).

Answer:

Hope it helps u .

mark as brainlist

Answer:

A.  1.6 m/s²

Step-by-step explanation:

Use the formula given and solve for g.  Use the length for L and the time for T.

T = 2π√(L/g)

T/2π = L/g

(T/2π)² = L/g

g = L/((T/2π)²)

g = 1/((4.9/2π)²)

g = 1/(0.7799)²

g = 1/0.6082

g = 1.64

Answer:

You will earn $4,950.

Step-by-step explanation:

To find the Simple Interest:

S.I = P × R × T/100

S.I = P × R × T/100S.I = 15,000 × 5.5 × 6/100

S.I = P × R × T/100S.I = 15,000 × 5.5 × 6/100S.I = 150 × 5.5 × 6

S.I = P × R × T/100S.I = 15,000 × 5.5 × 6/100S.I = 150 × 5.5 × 6S.I = $4,950

Answer:

D. 360 cubic cm.

Step-by-step explanation:

The volume = l * w * h

= 12 * 6 * 5

360 cu cm.

The  volume of the rectangular prism is  360 cubic cm

A rectangular prism is a three-dimensional shape. It also known as a cuboid.

Characteristics of a rectangular prism

Volume = length x width x height

12 x 6 x 5 =  360 cubic cm

A similar question was solved here: https://brainly.com/question/12449923?referrer=searchResults

If you know the rules for differentiation, then

[tex]f(x)=\dfrac7x\implies f'(x)=-\dfrac7{x^2}\implies f'(1)=-7[/tex]

If you don't, you can use the definition of the derivative to first find [tex]f'(x)[/tex]:

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac7{x+h}-\frac7x}h=\lim_{h\to0}\frac{7x-7(x+h)}{hx(x+h)}=-\lim_{h\to0}\frac7{x(x+h)}=-\dfrac7{x^2}[/tex]

Plug in [tex]x=1[/tex] to get the same result.

Or, you can directly compute the value of the derivative using the limit definition:

[tex]f'(1)=\displaystyle\lim_{x\to1}\frac{\frac7x-7}{x-1}=\lim_{x\to1}\frac{7(1-x)}{x(x-1)}=-\lim_{x\to1}\frac7x=-7[/tex]

Thousand

Please Mark As Brainliest

Answer:

One thousand

Step-by-step explanation:

Answer:

2n-7

Step-by-step explanation:

the product of 2 and a number is 2 times a number, so number is n. (this is multiplicaiton) it then becomes 2n. 7 less than that is 2n-7. (If it's less than, it goes after the variables 2n)

Explanation:

7 less --> -7

product of 2 and a number --> 2x

Answer:

2x-7

I hope this Helps!!

Answer:

D

Step-by-step explanation:

So we are given the limit:

[tex]\lim_{x \to 0} (x^2+10)[/tex]

To figure out this limit, we can use direct substitution. Simply substitute 0 for x and then simplify. Therefore:

[tex]\lim_{x \to 0} (x^2+10)\\=(0)^2+10\\=0+10\\=10[/tex]

Therefore, the limit equals 10.

Answer:

0.3

Step-by-step explanation: