Work out the value of (2x10^4)+(7x10^3) in standard form

We're given

(0, 144)

(1, 48)

(2, 16)

(3, 16/3)

[tex]f(x) = a*b^x\\144 = a*b^0\\144 = a\\[/tex]

now that we know a, we can find b

[tex]f(x) = 144*b^x\\48 = 144*b\\b = \frac{48}{144}\\b = \frac{1}{3}[/tex]

[tex]f(x) = 144*(\frac{1}{3})^x[/tex]

Sum of three terms in a GP = 7

Product of the numbers = 8

G.P

Let the three numbers be a/r , a , ar where a is the first term and r is the common ratio.

So,

⟹ a/r + a + ar = 7 -- equation (1)

And,

⟹ (a/r) * a * ar = 8

⟹ a³ = 8

⟹ a = ³√8

⟹ a = 2

Substitute the value a in equation (1).

⟹ 2/r + 2 + 2r = 7

⟹ (2 + 2r + 2r²)/r = 7

⟹ 2 + 2r + 2r² = 7r

⟹ 2r² + 2r - 7r + 2 = 0

⟹ 2r² - 5r + 2 = 0

⟹ 2r² - 4r - r + 2 = 0

⟹ 2r(r - 2) - 1 (r - 2) = 0

⟹ (2r - 1)(r - 2) = 0

★ 2r - 1 = 0

⟹ 2r = 1

⟹ r = 1/2

★ r - 2 = 0

⟹ r = 2

If r = 1/2 ;

a/r = 2/(1/2) = 2 * 2 = 4

a = 2

ar = 2 * 1/2 = 1

If r = 2 ;

a/r = 2/2 = 1

a = 2

ar = 2 * 2 = 4

∴ Required GP is 4 , 2 , 1 or 1 , 2 , 4.

I hope it will help you.

Regards.

Step-by-step explanation:

Assume that the 4 terms are a/r, a , ar, ar2.

Product of first 3 terms = a3 =8

=> a=2

Sum of last 3 terms :

a(1 + r + r2) = 14

=> r2 + r - 6 = 0

Solving the above equation r= -3 or 2

So the terms are

-2/3, 2, -6, 18

Or

1, 2, 4, 8

Answer:0.0049

Step-by-step explanation: You move the decimal 3 places to the left because its negative which gives you 0.0049

See attachment for math work and answer.

Answer:

1.99 per pound means the cost of 1 pound is 1.99!!

Step-by-step explanation:

Unit rate means the rate of 1 item

Answer:

The slope should be -5/8

Step-by-step explanation:

The equation used to find the slope using a table is:

[tex]\frac{y2-y1}{x2-x1}[/tex]

To get the values, take two points from the table. For example:

(8, -5) and (16, -10)

Write and classify them as (x1, y1) and (x2, y2). Knowing that these values equal the numbers, put the numbers in the equation above, and you should find the slope.

Answer:

is this a real question???

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

2,1 .     4,4 .     5,2

Step-by-step explanation:

Answer:

a' (2,1)

b'(4,4)

c'(5,2)

(x,y)→(x+1,y+4)

Step-by-step explanation:

So the <a'b'c' is <abc translated 1 unit to the right and 4 units up. Whenever it says to move to the right or the left it has to do with the x axis. When you move to the left its subtraction and when you move to the right you addition.

When ever is say to move up or down it has to do with the y-axis. when you move up its addition and when you move down its subtraction. Sooo since the question said to move it to the right and up theyre both going to be addition. Thats why in the translation theyre both addition sign.

Im really bad at explaining things but hope this helps:)

Answer:

indecsaty

Step-by-step explanation:

the indecsaty of the line more known as a slope is the other name

See attachment for math work and answer.

Answer:

1. If its radius is 2 inches, the height is 36 inches.

2. If its radius is 2 inches, the height is 16 inches.

3. If its radius is 2 inches, the height is 4 inches.

Step-by-step explanation:

Here is the complete question:

There are many cylinders with a volume of 144[tex]\pi[/tex] cubic inches. The height [tex]h(r)[/tex] in inches of one of these cylinders is a function of its radius [tex]r[/tex] in inches where [tex]h(r) =\frac{144}{r^{2} }[/tex] .

1. What is the height of one of these cylinders if its radius is 2 inches?

2. What is the height of one of these cylinders if its radius is 3 inches?

3. What is the height of one of these cylinders if its radius is 6 inches?

Step-by-step explanation:

1. To determine the height of one of the cylinders if its radius is 2 inches,

From the question,

Since height [tex]h(r)[/tex] of one of these cylinders is a function of its radius [tex]r[/tex], and

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 2 inches

[tex]h(r) =\frac{144}{2^{2} }[/tex]

[tex]h(r) =\frac{144}{4 }[/tex]

[tex]h(r) = 36 inches[/tex]

Hence, the height is 36 inches

2. To determine the height of one of the cylinders if its radius is 3 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 3 inches

[tex]h(r) =\frac{144}{3^{2} }[/tex]

[tex]h(r) =\frac{144}{9 }[/tex]

[tex]h(r) = 16 inches[/tex]

Hence, the height is 16 inches

3. To determine the height of one of the cylinders if its radius is 6 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 6 inches

[tex]h(r) =\frac{144}{6^{2} }[/tex]

[tex]h(r) =\frac{144}{36 }[/tex]

[tex]h(r) = 4 inches[/tex]

Hence, the height is 4 inches.

Answer:

5240

Step-by-step explanation:

Answer:

5) 36

6) 113

Step-by-step explanation:

5)

As a reminder, complementary angles add up to 90; therefore, we can set up an equation:

(5x+4)+(3x+6)=90

8x+10=90

8x=80

x=10

Now that we know x, we can plug x as 10 into the original expression for angle A:

3(10)+6

=30+6

=36

6)

As a reminder, supplementary angles add up to 180; therefore, we can set up an equation:

(5x+8)+(3x+4)=180

8x+12=180

8x=168

x=21

Now that we know x, we can plug x as 21 into the original expression for angle D:

5(21)+8

=105+8

=113

Answer:

0

Step-by-step explanation:

it has a zero slope

0,0

6,0

0-0=0

6-0=6

0/6 is 0

Answer: 8¹⁰

Explanation: Since these two powers have the same base of 8, you can

multiply them together by simply adding their exponents to get 8¹⁰.

A common mistake in this problem would be to

multiply the bases together and give an answer of 64¹⁰.

It's important to understand however that the 8's can't be

multiplied together because they are not coefficients, they are bases.

When applying your exponent rules, your base will never change.

Answer:

The overall change is 116points gained

Step-by-step explanation:

Points gained = 12points

Points lost  = 114points

Points gained  = 218points

Unknown:

Overall change in its value  = ?

Solution:

 The overall change  = Total points gained  - Total points lost

                                    = (218 + 12) - 114

                                     = 116points

The overall change is 116points gained

Answer:

its 116

Step-by-step explanation:

12 - 114

-102 + 218 = 116

Answer:

4 + x²

Step-by-step explanation:

Given problem:

    4 more then a number squared

Problem:

  Give the expression form;

Solution:

  Let the number x;

So;

   4 more than x squared:

          4 + x²

Answer:

60/24

Step-by-step explanation:

Answer:

StartFraction 60 hours Over 1 EndFraction times StartFraction 24 days Over 1 hour EndFraction

Step-by-step explanation:

I'm sorry if this is wrong

Answer:

r=-2.00000

s=2.00000

Answer: y=4x-5

Y=4x-5

Answer:

Step-by-step explanation:

1st one is 62.5 kilogramic meter

2nd one is 1 kilo kilogram/cubic meter

Step-by-step explanation:

1)First calculate the volume

v=Pir²h

v=3.15×4²×4

v=201mm³

p=m/v

p=0.250/0.201

p=1.24Kg/m³

2)v=3/4pi r³

v=3/4×3.14×2³

v=33.5m³

p=m/v

p=2/33.5

p=0.0597kg/m³

Answer: Reflect across the Y and and move it 7 down

Step-by-step explanation: Reflecting across the Y will turn the (X,Y) into (-X,Y) then you just count how many places the image is away from the preimage.

Answer:

This is so easy question .

I can do.

Step-by-step explanation:

1) Option II (1)

2) Option III (-5)

3) IV (None of these)

4) III (-4)

Answer:

1. The numerical coefficient of x^2y^2 is 1

2. -5

3. Monomial

4. -4(I know its x squared)

Step-by-step explanation:

1. We know if we multiply any number or variable with 1 it remains same.

here there is no number before (x^2)(y^2) so we assume it as 1.

Hence the answer is 1.

2. numerical coefficient is a constant multiplier of the variables in a term. In the term -5x2y, the numerical coefficient is -5. In the expression ax2 + bx + c, the numerical coefficient of the x2 term is "a" and the numerical coefficient of the x term is "b". "c" is properly referred to as the constant term.

3. in monomial there is only one term and pqr is only one term. binomial requires two terms like abc, pqr. and trinomial requires three terms like abc, pqr, mno.

4. -1^2 - 5 = -1 - 5 = -4 I know in rules of subtracting integer it equals to -4

To subtract integers, change the sign on the integer that is to be subtracted.

If both signs are positive, the answer will be positive.

If both signs are negative, the answer will be negative.

If the signs are different subtract the smaller absolute value from the larger absolute value.

Answer:

I used a math calculator by a math calculator service

Step-by-step explanation:

Answer:

x ≥ 15

Step-by-step explanation:

5x + 3 ≥ 48

Group like terms

5x ≥ 48 – 3

5x ≥ 45

divide both sides by 5

5x/5 ≥ 45/5

x ≥ 15

Answer:

$216

Step by step

Explanation:

First we subtract  $ 20 from  $ 84  giving us a total of  $ 64 and when we add that to  $ 152  we get  $ 216

.

Answer:

-60

Step-by-step explanation:

Answer:

[tex]130.2845\leq h\leq 137.7245[/tex]

Step-by-step explanation:

Given an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur by the equation

[tex]|h - (2.47f + 54.10)| \leq 3.72[/tex]

If an adult female measures her femur as 32.25 centimeters, we can determine the possible range of her height by plugging f = 32.25cm into the modelled equation as shown:

[tex]|h - (2.47(32.25) + 54.10)| \leq 3.72\\|h - (79.9045 + 54.10)| \leq 3.72\\|h - (134.0045)| \leq 3.72\\[/tex]

If the modulus function is positive then:

[tex]h - 134.0045 \leq 3.72\\h \leq 3.71+134.0045\\h\leq 137.7245[/tex]

If the modulus function is negative then:

[tex]-(h - 134.0045) \leq 3.72\\-h+134.0045 \leq 3.72\\-h\leq 3.72-134.0045\\-h\leq -130.2845\\[/tex]

multiply through by -1

[tex]-(-h)\geq -(-130.2845)\\h\geq 130.2845\\130.2845\leq h[/tex]

combining the resulting inequalities, the estimate of the possible range of heights will be [tex]130.2845\leq h\leq 137.7245[/tex]

Answer:

An)  is a value that does not change​?  yes