Given f(t)=t to the power of 4 +t² -5, find the value of f(b) - f(-b)

Answers

Answer 1

Answer: $f(t)=t^4+t^2-5\n \n f(b)-f(-b)=b^4+b^2-5-[(-b)^4+(-b)^2-5]\n \n f(b)-f(-b)=b^4+b^2-5-b^4-b^2+5\n \n \boxed{f(b)-f(-b)=0}$

Answer 2

Answer: $f(b)-f(-b)=b^4+b^2-5-((-b)^4+(-b)^2-5)\n f(b)-f(-b)=b^4+b^2-5-(b^4+b^2-5)\n f(b)-f(-b)=b^4+b^2-5-b^4-b^2+5\n f(b)-f(-b)=0$

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How many hundredths are in one tenth? Explain using pennies and dimes.

Answers

Answer:

11 ways

100 Pennies & 0 Dimes

90 Pennies & 1 Dimes

80 Pennies & 2 Dimes

70 Pennies & 3 Dimes

60 Pennies & 4 Dimes

50 Pennies & 5 Dimes

40 Pennies & 6 Dimes

30 Pennies & 7 Dimes

Step-by-step explanation:

Final answer:

There are 10 hundredths in one tenth. This can be understood by considering that a dime, representing one tenth of a dollar, is equivalent to 10 pennies, each penny representing one hundredth of a dollar.

Explanation:

In terms of decimals, one tenth is represented as 0.1 and a hundredth is represented as 0.01. Given this, there are 10 hundredths in one tenth (because 0.1 divided by 0.01 equals 10). To understand this using pennies and dimes, consider one dime (which represents one tenth of a dollar) and a penny (which represents one hundredth of a dollar). As there are 10 pennies in a dime, we can conclude that there are 10 hundredths in one tenth.

Learn more about Decimals here:

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1. If the expression 9y − 5 represents a certain number, which of thefollowing could NOT be the translation?

a. five less than nine times y

b. five less than the sum of 9 and y

c. the difference between 9y and 5

d. the product of nine and y, decreased by 5

Answers

After examining all options, we find that each one can be represented by the expression 9y - 5. Therefore, there is no option that could NOT be the translation of the given expression.

To find the translation that could NOT be represented by the expression 9y - 5, we need to compare each option with the given expression and determine if they are equivalent or not.

The given expression is: 9y - 5

Now, let's examine each option:

a. five less than nine times y

This option can be represented as 9y - 5, so it is equivalent to the given expression.

b. five less than the sum of 9 and y

This option can be represented as 9 + y - 5, which simplifies to 9y - 5. So, it is also equivalent to the given expression.

c. the difference between 9y and 5

This option can be represented as 9y - 5, so it is equivalent to the given expression.

d. the product of nine and y, decreased by 5

This option can be represented as 9y - 5, so it is also equivalent to the given expression.

To know more about expression:

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Answer:

b. five less than the sum of 9 and y

Which shows the dimensions of two rectangular prisms that have volumes of 72 cm3 but different surface areas? A. 6 cm by 3 cm by 4 cm; 12 cm by 2 cm by 3 cm B. 2 cm by 4 cm by 9 cm; 9 cm by 4 cm by 2 cm C. 3 cm by 3 cm by 8 cm; 2 cm by 6 cm by 8 cm D. 6 cm by 3 cm by 4 cm; 9 cm by 4 cm by 3 cm

Answers

To solve, lets find the volumes of all of the options...

V=l*w*h

A.
6*3*4=72cm³
12*2*3=72cm³

B.
2*4*9=72cm³
9*4*2=72cm³

C.
3*3*8=72cm³
2*6*8=96cm³

D.
6*3*4=72cm³
9*4*3=108cm³

We can conclude that C & D aren't the answer, since they contain prisms that don't have a volume of 72cm³.

Now lets solve for the surface area of A and B...

A.
sA=2(wh+lw+lh)=2(6*3+4*6+4*3)=2(18+24+12)=2(54)=108cm²
sA=2(wh+lw+lh)=2(12*2+3*12+3*2)=2(24+36+6)=2(56)=112cm²

B.
sA=2(wh+lw+lh)=2(2*4+9*2+9*4)=2(8+18+36)=2(62)=124cm²
sA=2(wh+lw+lh)=2(9*4+2*9+2*4)=2(36+18+8)=2(62)=124cm²

A is the only option with both similar volumes of 72cm³ and different surface areas...

Answer=A

Answer:

Step-by-step explanation:

A, is the answer

Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 7m x 7m.

Answers

Putting this as an arithmetic sequence gives:

$u_n = 150+200(n-1)$

The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L

The sum of an arithmetic series can be written as:

$S_n=n/2 [2a+(n-1)d] = 784 000\nn/2[2(150)+(n-1)200] = 784 000\nn[300+200(n-1)=1 568 000\n300n+200n^2-200n = 1 568 000\n200n^2+100n- 1 568 000 = 0\n2n^2 +n- 15680 = 0\nn= 88.2...,-88.7$

n has to be positive, so we get

n = 88.2 hours (3 s.f.)

Volume of tank = (16m)(7m)(7m) = 784 m³

Conversion of m³ to L:
(784 m³) × (1000L / 1m³) = 784,000 L

Rate in the 1st hour:
150 liters/hr

Rate in the 2nd hour:
350 liters/hr

Rate in the 3rd hour:
550 liters/hr

It is apparent that the Fill Rate is increasing by 200 liters/hr every subsequent hour . . . so that can be represented by the following equation

where:
t = number of hours

Fill rate (i.e. volume of water filled into tank within the specified hour) = 150 + 200(t - 1)

For t = 1 . . . Fill rate = 150 L/hr
For t = 2 . . . Fill rate = 350 L/hr
For t = 3 . . . Fill rate = 550 L/hr

Because after every hour there has been more water added to the tank, this problem can be represented as a geometric sequence in order to account for the compounding of the volume after each time step, but it can also be tabulated (which seems to me to be the more direct/simple approach), so I will build a table that accounts for the increasing Fill Rate and the compounding of water volume after each time step . . .

(see attached)

The answer (after all of this) is . . . t = 88 hrs 17 1/2 mins (approx)

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10

(-8/2)^2 = 16

What is the function written in vertex form?
A.f(x) = 3(x + 4)2 – 6
B.f(x) = 3(x + 4)2 – 38
C.f(x) = 3(x – 4)2 – 6
D.f(x) = 3(x – 4)2 – 38

Answers

Following the steps already shown to transform the given function into the vertex form, we have:

f(x) = 3(x2 - 8x + 16) + 10 - 3(16)
f(x) = 3(x - 4)(x - 4) + 10 - 48
f(x) = 3(x - 4)2 - 38

Therefore, the function written in vertex form is:
D.f(x) = 3(x – 4)2 – 38

The vertex form has the general form of:

y = a(x-h)^2 + k

We have the given equation:

f(x) = 3x^2 – 24x + 10

f(x) - 10 + 3(16) = 3(x^2 -8x + 16)
f(x) + 38 = 3(x - 4)^2
f(x) = 3 (x-4)^2 -38

Then, the correct answer is D.

A model is made of a car. The car is 8 feet long and the model is 10 inches long. What is the ratio of the length of the car to the length of the model?

Answers

Like I said in one of your questions ratios are just fractions
8/10 is what you get, but you need to simplify it to get
4/5

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