Select the correct answer. Which number is a rational number? A. B. C. D.

Answer:

£40000

Step-by-step explanation:

→ Set up an equation

x × 0.6 = 24000

→ Divide both sides by 0.6

x = 24000 ÷ 0.6 = 40000

By hit and trial of each option and also by graph, solutions to f(x) = 3ˣ and  g(x)=2x-1 will be 0 and 1.

given functions are,

[tex]f(x) = 3^x\\\\g(x) = 2x+1[/tex]

let us put x=0

f(0) = 1

g(0) = 1

f(0)=g(0)=1

so 0 will be a solution.

let us put x=1

f(1)= 3

g(1) = 3

f(1)=g(1)=3

so 1 will be also a solution

let us put x=2

f(2) = 9

g(2) = 5

f(2)≠g(2)

so 2 will not be solution.

x=-2 and x=-1 clearly will not be solution because,

g(-2) = negative value but f(x) cannot be negative, being an exponential function.

Any function in form f(x)= pˣ, where p≥1, is called an exponential function.

therefore, solutions to f(x) = g(x) will be 0 and 1.

to get more about exponential function refer to:

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Answer:

The answer is 11/35, Hope this helps!

Stay safe, and have a very nice rest of the day!

Answer:

1   1   5

6÷5=6

Step-by-step explanation:

Answer:

440$

Step-by-step explanation:

55 x 4=220

50 x 4=200

440$

I hope this is correct if not im sorry

Answer:

$ 205

Step-by-step explanation:

55+50x

x= number of hours minus the first hour (3)

so 55+50(3) = $205

Answer:

[tex]3(x - \frac{ - 7 + \sqrt{73} }{6} )(x - \frac{ - 7 - \sqrt{73} }{6} )[/tex]

Step-by-step explanation:

Here is your answer ☝

Answer:

First term: 6

Common difference:  15/4

Step-by-step explanation:

General form of arithmetic progression:

[tex]a_n=a+(n-1)d[/tex]

(where [tex]a[/tex] is the initial term and [tex]d[/tex] is the common difference between terms)

Question (a)

[tex]\implies a_3=a+(3-1)d=a+2d[/tex]

[tex]\implies a_9=a+(9-1)d=a+8d[/tex]

[tex]\implies a_{25}=a+(25-1)d=a+24d[/tex]

Question (b)

General form of a geometric progression:  [tex]a_n=ar^{n-1}[/tex]

(where [tex]a[/tex] is the initial term and [tex]r[/tex] is the common ratio)

Therefore, the first three terms of a geometric series are:

[tex]a_1=ar^0=a[/tex]

[tex]a_2=ar^1=ar[/tex]

[tex]a_3=ar^2[/tex]

To find the common ratio:

[tex]r=\dfrac{ar^2}{ar}=\dfrac{ar}{a} \implies \dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]

If the 3rd 9th and 25th terms of an arithmetic progression form the first three consecutive terms of a geometric series, then inputting these into the above formula for r:

[tex]\implies \dfrac{a+24d}{a+8d}=\dfrac{a+8d}{a+2d}[/tex]

[tex]\implies (a+24d)(a+2d)=(a+8d)(a+8d)[/tex]

[tex]\implies a^2+26ad+48d^2=a^2+16ad+64d^2[/tex]

[tex]\implies 10ad=16d^2[/tex]

[tex]\implies 10a=16d[/tex]

The 6th and 7th terms of the arithmetic progression are:

[tex]a_6=a+5d[/tex]

[tex]a_7=a+6d[/tex]

If the sum of the 7th and twice the 6th term of the arithmetic progression is 78, then:

[tex]\implies a_7+2(a_6)=78[/tex]

[tex]\implies (a+6d)+2(a+5d)=78[/tex]

[tex]\implies 3a+16d=78[/tex]

Substituting  [tex]10a=16d[/tex]  into  [tex]3a+16d=78[/tex]  and solving for a:

[tex]\implies 3a+10a=78[/tex]

[tex]\implies 13a=78[/tex]

[tex]\implies a=6[/tex]

Substituting [tex]a=6[/tex] into  [tex]3a+16d=78[/tex]  and solving for d:

[tex]\implies 3(6)+16d=78[/tex]

[tex]\implies 16d=60[/tex]

[tex]\implies d=\dfrac{15}{4}[/tex]

Answer:

f(x)=-4x-1

Step-by-step explanation:

f(x)=ax+b

a=-4/slope

b=-1/y-intercept

f(x)=-4x-1

Answer:

x = 10

Step-by-step explanation:

61 - 21 = 40
40 / 4 = 10
x = 10

[tex]sin3( \alpha ) = 3 \sin( \alpha ) - 4 { \sin^{3} ( \alpha ) }[/tex]

[tex]2( 3 \sin( \ \frac{\pi}{18} ) - 4 { \sin^{3} ( \ \frac{\pi}{18} ) })[/tex]

[tex]2(sin3( \ \frac{\pi}{18} ))[/tex]

[tex]2( \sin( \frac{\pi}{6} ) )[/tex]

[tex]2 \times \frac{1}{2 } = 1[/tex]

Answer:

Philip, after 12 seconds, is 13.44 meters farther ahead after 12 seconds

Step-by-step explanation:

Philip

6.59 x 12 = 79.08

Mary

5.47 x 12 = 65.64

79.08 - 65.64 = 13.44

Answer and explanation:

There's 3 one dollar bills

2 five dollar bills

and 2 ten dollar bills

and 1 twenty dollar bill

3+2+2+1=8

Part A: The probability of selecting 5 is 2/8 and the probability of selecting 10 is also 2/8 and both of them are the same, 1/4.

Part B: The probability of selecting a one dollar bill is 3/8 and the probability of selecting a twenty dollar bill is 1/8 because there are 3 one dollar bills in 8 bills and 1 twenty one dollar bill in 8 bills only.

Answer:

$1248

Step-by-step explanation:

I = 960 x 3 x 0.1

= 2880 x 0.1

= $288

Amount

= 960 + 288

= $1248

Answer:

Distributitive Property

Step-by-step explanation:

The correct justification for the first step in solving the provided equation is that the first step should be distributive Property

Property of equality says that by performing any mathematical operation, of both sides of a expression does not change the original value of the equation.

The equation given in the problem is,

[tex]3(x - 4) + 1 = 12x[/tex]

To solve the above equation, we need to open the brackets of the equation. To do this, we need to use the distributive property of the equality.

This can be done by multiplying the number 3 inside the bracket (x-4). This operation simplify the equation, to solve it further. Therefore,

[tex]3x - 3\times4 + 1 = 12x\\3x - 12 + 1 = 12x[/tex]

Hence, the correct justification for the first step in solving the provided equation is that the first step should be distributive Property.

Learn more about the property of equality here;

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Answer:

3(x-2)

=3x-6

by using BODMAS

SOLUTION:

=) (a + 2a)/3a

=) 3a/3a

=) 1

Answer:

Step-by-step explanation:

↝m√p + n√p -√p

↝√p(m+n-1)

↝(m+n-1)√p = √p(m+n-1)

↝(m-n+1)√p ≠ √p(m+n-1)

↝(m-n-1)√p ≠√p(m+n-1)

hence, option 1st is correct ✓

Option A

Let's verify

[tex]\\ \rm\Rrightarrow (m+n-1)\sqrt{p}[/tex]

[tex]\\ \rm\Rrightarrow m\sqrtp}+n\sqrt{p}-\sqrt{p}[/tex]

Hence verified

Answer:

Step-by-step explanation:

This is called a 'System of equations'.

Say that you have these two expressions, and the unknown is "b".

5b = y

4b+2 = y

Now we can solve two ways; graph it or solve it.

Solving it, we can see that they both equal y, so:

5b=4b+2

move 4b to the left side by subtraction:

(5b-4b) =2

b = 2

let's see what y equals when b = 2

5 * 2 = y

10 = y

Graphing it we see they intersect, or solve at

(2,10) or b=2, y=10

Hope this helps!

Answer:

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times {7}^{2} \\ = 3.14 \times 49 \\ = 153.86 \: {km}^{2} \\ [/tex]

Answer:

no haha

Step-by-step explanation:

Answer:

10 is B. 9 is 28.8

Step-by-step explanation:

Answer:

840

Step-by-step explanation:

b x h = 42 x 20

Answer:

The vertex form would be  y =  (x+2)^2

The factored form would be y = (x-2)(x-2)

The standard form would be y = x^2-4x+4

Step-by-step explanation:

To find this, you know that the vertex is 2 left from the center, so you have h = -2, and k = 0 since it isnt shifted up. The graph isn't shifted up either, so a=1.

The vertex form would be:  y = a(x-h)^2+k

                                                 =  (x+2)^2

The factored form would be y = (x-2)(x-2)

The standard form would be y = x^2-4x+4

Your welcome, and comment if you have any questions! :D

Answer:

Formula for area is length times width

So 2x × x = 2x^2

E. G.

2×2×2=8

And can also be written as 2^3

Meaning 2×2×2

So in this instance x × x=x^2

In front of the length x imagine a 1

So 2×1=2

Therefore 2x^2

Answer:

Area = 2x²

Step-by-step explanation:

Area = L x W

L = 2x

W=x

 x*2 =2x

x*x =x²

 Area = 2x²

Answer:26!

Step-by-step explanation:

((23) -  4) +  ((52 -  6) +  3)

(23 -  4) +  22

26

Hope this helps! ^w^

Answer:

5x2−115x+49

Step-by-step explanation:

hope it helps

5x²-115x+49 is the required dividend.

A dividend is a number that is being divided, if 2x is a dividend and 2 is a divisor, then it gives remainder 2, when 2x is divided by 2.

The given polynomial is,

5x²-13x+47-102x+2

To find dividend, simplify this polynomial,

5x²-115x+49

This is the required dividend.

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Answer:

x = -1, y = 2

Step-by-step explanation:

plug the first equation into the second to get: 4x-20x=16

simplify: -16x=16

therefore, x = -1, and y = 2