MATHEMATICS HIGH SCHOOL

Write the equation for f(x)=x^2But flipped over the x-axis, shifted 4 units down, and shifted 1 unit to the left.
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Answers

Answer 1

Answer:

Answer:

$f^\prime(x)=-(x+1)^2-4$

Step-by-step explanation:

We have the function:

$f(x)=x^2$

And we want to write its equation after being: 1) Flipped over the x-axis, 2) shifted 4 units down, and 3) shifted 1 unit to the left.

To denote a flip over the x-axis, we multiply the function by -1. Hence:

$f^\prime(x)=-x^2$

Is our function flipped over the x-axis.

To shift n units vertically, we simply add n to our function.

Since we are going 4 units downwards, we will add -4 to our function. Hence:

$f^\prime(x)=-x^2-4$

Finally, to shift n units horizontally, we substitute our variable $x$ for $(x-n)$ .

Since we are shifting 1 unit to the left, n=-1. Hence, we will substitute $x$ for $(x+1)$ . Therefore:

$f^\prime(x)=-(x+1)^2-4$

So, our final function is:

$f^\prime(x)=-(x+1)^2-4$

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Answers

Answer:34

Step-by-step explanation: 180-146=34

Answer:

The value of x is 6/5.

Step-by-step explanation:

To solve this problem, we can use the following steps:

Factor the number 146 into its prime factors. We get 146=2×73.

Since m and n are factors of 146, we know that one of them must be 2 and the other must be 73.

However, we are not told which factor is m and which is n. Therefore, there are two possible solutions:

m=2 and n=73, or

m=73 and n=2.

Which of the following gives an example of a set that is closed under multiplication? Choose all that apply.. . . . A. The product of a perfect cube and a perfect cube. B. The product of 0 and 0. C. The product of a whole number and a whole number. D. The product of a perfect square and a perfect square. . I think its b and c? help anyone...

Answers

All the four choices that are given in the question can be considered as as examples of a set that is closed under multiplication. The correct options among all the options that are given in the question are options "A", "B", "C" and "D". I hope that the answer has come to your help.

Answer:

The correct answer is:

Option: A , Option: B , Option: C , Option: D

Step-by-step explanation:

For a set to be closed under multiplication means if two elements are taken from that set then their multiplication must also belong to the same set.

The product of a perfect cube and a perfect cube.

Let a be a perfect cube of "m"

and b be a perfect cube of "n"

i.e.

$a=m^3\n\nand\n\nb=n^3$

Hence,

$a\cdot b=m^3\cdot n^3\n\ni.e.\n\na\cdot b=(mn)^3$

i.e.

$a\cdot b\ \text{is a perfect cube of mn}$

Hence, this set if closed under multiplication.

The product of 0 and 0.

when we take the product of 0 and 0 then the resultant is also zero.

Hence, this set is also closed under multiplication.

The product of a whole number and a whole number.

When we multiply a whole number to a whole number then the product is again a whole number.

This set is also closed under multiplication.

The product of a perfect square and a perfect square.

Let us take two elements of the set as x and y

i.e.

$x=a^2$

and

$y=b^2$

Hence,

$x\cdot y=a^2\cdot b^2\n\ni.e.\n\nx\cdot y=(ab)^2$

i.e.

$x\cdot y\ \text{is\ also\ a perfect\ square}$

Hence, the set is closed under multiplication.

The mass of an electron is approximately 9 × 10-28 grams, while the mass of a neutron is approximately 2 × 10-24 grams. Which of the following is true?The mass of a neutron is approximately 2,000 times the mass of an electron.

The mass of a neutron is approximately 10,000 times the mass of an electron.

The mass of a neutron is approximately 20,000 times the mass of an electron.

The mass of a neutron is approximately 1,000 times the mass of an electron.

Answers

We simply divide the Mass of Neutron by Mass of electron

= 2 × 10⁻²⁴ / (9 × 10⁻²⁸)

= (2/9) × 10⁻²⁴ ⁻ ⁻²⁸

= (2/9) × 10⁻²⁴ ⁺ ²⁸

≈ 0.2222... × 10²⁸ ⁻ ²⁴

≈ 0.2222 × 10⁴

≈ 2222

This is approximately 2000 times.

So:

The mass of a neutron is approximately 2,000 times the mass of an electron

The first option. I hope this explains it.

Answer:

The mass of a neutron is approximately 2,000 times the mass of an electron

Step-by-step explanation:

= 2 × 10⁻²⁴ / (9 × 10⁻²⁸)

= (2/9) × 10⁻²⁴ ⁻ ⁻²⁸

= (2/9) × 10⁻²⁴ ⁺ ²⁸

≈ 0.2222... × 10²⁸ ⁻ ²⁴

≈ 0.2222 × 10⁴

≈ 2222

This is approximately 2000 times.

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?A f(x) = 1500(1.15)x

B f(x) = 1500(115)x

C f(x) = 1500(2.15)x

D f(x) = 1500(215)x

Answers

Answer:

Option (c) is correct.

$f(x)=1500(2.15)^x$ function representing the increase of bacteria every hour x,

Step-by-step explanation:

Given : A colony contains 1500 bacteria. The population increases at a rate of 115% each hour.

we have to find the function that represents the given scenario.

Let x represents the number of hours elapsed.

Given A colony contains 1500 bacteria

and number of bacteria is increasing at a rate of 115% each hour.

Using formula for Compound interest , we have,

$A=P(1+(r)/(100) )^t$

Where A is amount

T is time period

R is rate of interest

Here, P = 1500

T = x hours

R = 115%

Let f(x) be the function representing the increase of bacteria every hour.

Substitute, we have,

$f(x)=1500(1+(115)/(100) )^x$

Simplify, we get,

$f(x)=1500(1+1.15)^x$

$f(x)=1500(2.15)^x$

Thus, $f(x)=1500(2.15)^x$ function representing the increase of bacteria every hour x,

its f(x)=1500(2.15)x so c hope this helps

I need help please help me

Answers

A because the price went up after a 35%

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? in cubic inches

Answers

To find out how much wax is needed for the candles we need to figure out the volume of each candle. We know radius r=0.5 inches and height h=3 inches of the smallest candle and we know that the middle candle has r2=2r=1 inch and h2=2h=6 inches and the biggest candle has r3=3r=1.5 inches and h3=3h=9 inches. So now we need the formula for volume: V=pi*r^2*h and we simply plug in the numbers. First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

Answer:

First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

Step-by-step explanation:

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