In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.

5x-9 = 3x+3

2x-9 = 3

2x = 12

x= 6

plz mark branliest, hopoe this helps :)

Answer:

B

Step-by-step explanation:

you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.

The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

From the question, we are to determine the product of the given polynomials

The given polynomials are

(8x^2-4x-8) (2x^2+3x+2)

Their product can be determined as follows

[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]

[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]

Clear the brackets

[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]

Now, collect like terms

[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]

Simplifying

[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

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Answer:

The second term becomes the reciprocal and then you multiply the first term by the second term

Answer:

A. second

Step-by-step explanation:

When dividing fractions, we always take the second term and flip that. In other words, we convert the second term into its reciprocal. Remember the phrase "flip the guy, and multiply!" Essentially, the "guy" just refers to the second term.

For example, if we have 1/3 ÷ 2/5, in order to solve this, we flip the second term, which is 2/5 so that it becomes 5/2 and then multiply:

1/3 ÷ 2/5 = 1/3 × 5/2 = 5/6

The answer is thus A.

~ an aesthetics lover

Answer:

216 cubic inches

Step-by-step explanation:

We want to simplify:

102 * 4 - 3(8 * 8 * 1)

We will apply BODMAS:

Solving the Bracket first:

102 * 4 - 3(64)

102 * 4 - 192

=> 408 - 192

= 216 cubic inches

He will need 216 cubic inches of packing foam.

Answer:

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part

Answer:

3x - y = - 7

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (- 2, 1) , thus

y - 1 = 3(x + 2) ← distribute

y - 1 = 3x + 6 ( subtract 6 from both sides )

y  - 7 = 3x ( subtract y from both sides )

- 7 = 3x - y, that is

3x - y = - 7 ← in standard form

Answer:

Factors: 5x, 3x²y⁵   Not Factor: 10x⁴y³

Step-by-step explanation:

5x is a factor because 15x²y⁶= 5x•3xy⁶

3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y

10x⁴y³ isn't a factor because 15:10=1.5 isn't integer

Answer:

SSS

Step-by-step explanation:

I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)

Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.

Answer:

The final cost is $43.2

Step-by-step explanation:

We have the following equation:

[tex]C=p(1+r)[/tex]

Where C is the final cost, p is the price before tax and r is the tax rate.

So, to calculated the final cost for a $40 item after 8% tax, we need to replace p by 40 and r by 0.08 and calculate the value of C as:

[tex]C=40*(1+0.08)=43.2[/tex]

Therefore, the final cost is $43.2

Answer: $43.20

Step-by-step explanation: The simplest way to do it (my way) is i first used (1 + r), which is (1 + 8%), that gave me 1.08, then I did the total amount, $40x1.08, which equals $43.20. This may not be the right way to do it, but it is the simplest.

Hope this helped :)

Answer:

She is wrong

Step-by-step explanation:

Let us use the scale 1 : 75 to find the length of the gym on the scale drawing.

The scale means that 1 m on the drawing represents 75 m in real life.

Therefore, if the length of the gym is 12.3 cm, then the length of the gym in the scale drawing is:

12.3 / 75 = 0.164 m

Converting to cm:

1 m = 100 cm

0.164 m = 0.164 * 100 = 16.4 cm

She is wrong.

Answer:

4/5

Step-by-step explanation:

y = 4/5 x -3

This is written in slope intercept form

y =mx + b where m is the slope and b is the y intercept

the slope is 4/5 and the y intercept is -3

The value of angle x is 57.1 degrees.

Here we have given an angle is 38degee and the sides of the triangle are 11cm and 8 cm.

[tex]sin(x)=\frac{opposite side }{hypotenuse}[/tex]

Therefore by using the formula for the attached figure we have

[tex]sin(38^0)=\frac{y}{11}\\\\y=11sin(38^0)\\\\y=6.71[/tex]

Similarly, for the second triangle for the value of x

we have,

[tex]sinx=y/8=6.71/8=0.84\\\\x=sin^-1(0.84)=57.1^0[/tex]

Therefore we get the value of angle x is 57.1 degrees.

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Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x - 5y = 2

5y = 12x - 2

Divide both sides by 5

y = 12/5x - 1/5

Comparing with the above formula

Slope / m = 12/5

Since the lines are parallel their slope are also the same.

Slope the parallel line = 12/5

Equation of the line using point (2,3) is

[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]

Multiply through by 5

That's

5y - 15 = 12(x - 2)

5y - 15 = 12x - 24

We have the final answer as

Hope this helps you

Answer:

Our expressions is f(x) = 3|x-7|-7

Let's calculate the limits in +∞ and -∞

So the right staement is B

As x approaches positive infinity, f(x) approaches negative infinity.

A relation is a function if it has only One y-value for each x-value.

The function f(x) = 3|x − 7| − 7 is a piecewise function, where the absolute value function has two cases depending on the sign of (x - 7).

When (x - 7) is positive, the function becomes 3(x - 7) - 7 = 3x - 28, and when (x - 7) is negative, the function becomes -3(x - 7) - 7 = -3x + 14.

As x approaches positive infinity, both cases approach negative infinity because the dominant term in each case is the linear term (3x or -3x) as x becomes large.

Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches negative infinity.

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Answer: If point B is on the same line and the same distance from points A and C,  the location is (-1.5, 4,5)

Step-by-step explanation: For point B to be the same distance from the other two points, it must be halfway between them.

for the x-value, find the number that is halfway between 0 and -3. That is -1.5

For the y-value, find the number that is halfway between 4 and 5. That is 4.5

The coordinate for point B is (-1.5, 4.5)

Answer:

Below.

Step-by-step explanation:

cos2a = 2 cos^2 a - 1

cos^4a =  8cos^4 a - 8cos^2 a + 1

Right side of the identity =

1 /8(3 + 4cos2a + cos4a)​

= 1/8( 3 + 4(2 cos^2 a - 1) + 8cos^4 a - 8cos^2 a+1)

= 1/8 (3 + 8 cos^2 a - 4 + 8 cos^4 a - 8cos^2 a + 1)

= 1/8 (8cos^4 a)

= cos^4 a = the left side.

I realised that I should have derived the identity for cos 4a as well , which i have done in the picture.

The given identity, cos⁴a = 1/8(3 + 4cos2a + cos4a) is proved.

To prove a given identity, say f(a) = f(b), we proceed to simplify any of the expressions among the L.H.S. f(a) and the R.H.S. f(b), to get the other term. If we get the simplified form as the other term, our identity holds and is proved.

We know cos2A = 2cos²A - 1.

Going by the same formula, we derive the value of cos4A.

cos4A = 2cos²2A - 1

or, cos4A = 2(2cos²A - 1)² - 1, putting value of cos2A

or, cos4A = 2(4cos⁴A - 4cos²A + 1) - 1, (expanding (2cos²A - 1)² using the formula of (a-b)² = a² -2ab + b²)

or, cos4A = 8cos⁴A - 8cos²A + 2 - 1, (expanding)

or, cos4A = 8cos⁴A - 8cos²A + 1, (simplifying)

∴ cos4A = 8cos⁴A - 8cos²A + 1.

Given identity to us is, cos⁴a = 1/8(3 + 4cos2a + cos4a).

To prove the identity, we proceed with the R.H.S.:

= 1/8(3 + 4cos2a + cos4a)

We put values of cos2A and cos4A in this expression, to get

= 1/8(3 + 4(2cos²a - 1) + (8cos⁴a - 8cos²a + 1))

Expanding the equation, we get

= 1/8(3 + 8cos²a - 4 + 8cos⁴a - 8cos²a + 1)

Simplifying, we get

= 1/8(8cos⁴a) = cos⁴a = L.H.S.

Hence, the given identity is proved.

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Answer:

Let,O and P be the events of getting odd number and any other number except 4 respectively.

n(S)=6

O=(1,3,5) so, n(O)=3

P=(1,2,3,5,6) so, n(P)=5

So,probability of getting an odd number and any other number except 4 will be

n(O)/n(S) × n(P)/n(S)

=3/6 × 5/6

=5/12

May be it's the answer I guess. Hope you're clear with it:-)

Answer:

2/5

Step-by-step explanation:

4ounces of coffee in cup  1

4 ounces of cream in cup 2

In the first step  pour 4/2=2 ounces of coffee from cup 1 to cup 2, getting:

2 ounces of coffee in cup 1

2 ounces of coffee and 4 ounces of cream in cup 2

In the second step we pour 2/2=1 ounce of coffee and 4/2=2 ounces of cream from cup 2 to cup 1, getting:

2+1=3 ounces of coffee and 0+2=2ounces of cream in cup 1

so the answer is 2/5

Answer:

13

Step-by-step explanation:

We have:

8a^2 + 2b^2 = 10

Dividing both sides by 2,

=> 4a^2 + b^2 = 5

or (2a)^2 + b^2 = 5

We also have ab = 2

=> (2a + b)^2

= (2a)^2 + 2(2a)(b) + b^2

= (2a)^2 + b^2 + 4ab

= 5 + 4(2)

= 5 + 8

= 13

Answer:

add the y coordinates of the two lines and divide by 2

Step-by-step explanation:

½[0+(-12)]

½[0-12]

½[-12)

y co-ordinate of the midpoint is -6

Answer: Choice B) The conjecture is valid given the focus is on proportional equivalence of two sectors.

This is another way of saying "the two pie slices are the same percentage in area". By this, I mean the percentage of the entire cake. For instance, the shaded slice could be 20% of the entire circle area, for each circle.

It's probably easier to see this is the angle was 90 degrees (split the cake into 4 equal slices, only shade one slice). Or probably even easier if you cut the cake into two slices and only shade one slice (to form a central angle of 180 degrees). For the first example, the slice would be 25% of the whole area, while the second slice is 50%.

Choice C is close, but the two sectors are not the same area. This is because the bottom circle has a larger radius, and therefore its sector area is larger.

Answer:

If the expression is:

-3x + 12 = -3x + 12, infinite solutions

If the expression is:

-3x + 12 = -3x - 12, no solutions

Step-by-step explanation:

Step 1: Distribute

-3x + 12 = 3x = 12

If both lines have the same slope and same y-int, they are the same line and therefore have infinite solutions.

If both lines have the same slope but different y-int, then they are parallel and therefore have no solutions.

Answer:

12

Step-by-step explanation:

8.3 / .7

Multiply each by 10 to get rid of the decimal

83/7

We know that 84/7 =12 so this is close to 12

Answer:

She traveled 33 miles.

Step-by-step explanation:

11*3 = 33

Answer:

33

Step-by-step explanation:

11mph times 3 hours= 33 miles

Answer:

parabola; (x)^2-2(square root 3) xy+3(y)^2 +16 (square root 3) x+16=0

Step-by-step explanation:

edge’s possible answer 2020

Answer:

a = 1, b = 6

Step-by-step explanation:

The equation given is as follows;

P(x) = a·x³ + b·x² + 3·x - 10

The above equation has a factor of x + 5, therefore, we have;

P(-5) = 0 = a·(-5)³ + b·(-5)² + 3·(-5) - 10

-125·a + 25·b + (-15) - 10 = 0

-125·a + 25·b - 25 = 0

-125·a + 25·b  = 25...........(1)

Also, we are given that;

a·x³ + b·x² + 3·x - 10 divided by x + 1 as a remainder, R = -8, therefore;

P(-1) = -8 = a·(-1)³ + b·(-1)² + 3·(-1) - 10

-a + b - 13 = -8

-a + b = -8 + 13 = 5

-a + b = 5............................(2)

Multiply equation (2) by 25 and subtract from (1) gives

-125·a + 25·b - 25(-a + b) = 25 - 25×5

-100·a = 25 - 125 = -100

a = 1

Therefore, from equation (2) we have;

-1 + b = 5

b = 5 + 1 = 6.

Answer:

TRUE

Step-by-step explanation:

if it was b^4 x b^3 then false. but here, would would multiply b^4 by b^3 to make it 12 so true

sorry for bad explanation

Answer:

True

Step-by-step explanation:

If b=2, 2^4 is 16, and 16^3 is 4096.

Also 2^12 is 4096.

So they are equivalent.

Answer:

The evaluated answer to this equation is -482

Step-by-step explanation:

h = 5

g = 10

Plug in your numbers for the equation.

8 - 50(10) + 2(5)

Multiply -50 by 10 and multiply 2 by 5.

8 - 500 + 10

Subtract 8 by -500.

-492 + 10

Add 10 to -492.

-482

Answer:

Check Explanation

Step-by-step explanation:

The options for the question aren't available. But it is given that the micrometer screw gauge in question can measure up to a hundredth of a millimeter.

We now want to measure a ball with diameter that is roughly 1.5 cm.

1.5 cm = 15.00 mm

Since our micrometer screw gauge can measure up to a hundredth of a millimeter, the possible true diameter of the ball will range between 14.995 mm and 15.004 mm

The error in measurement can range from -0.004 mm to +0.005 mm.

The amount of error was picked based on the approximate measurements on the analogy micrometer screw gauge that the equipment will still classify as roughly 15 mm (1.5 cm)

Hope this Helps!!!

Answer:

1.715 cm ± 0.005 cm; The standard error was chosen as +(-) 1/2 the smallest unit that can be precisely measured on the device, or 0.01 cm.

Step-by-step explanation: