Convert the number below from exponential to standard notation.6(104) + 4(103) + 8(102) + 1(101) + 7(100)

6,481,700
648.17
648,170
64,817

Answers

Answer 1
Answer: 6(10^4) + 4(10^3) + 8(10^2) + 1(10^1) + 7(10^0)\n\n = 6(10,000) + 4(1,000) + 8(100) + 1(10) + 7(1)\n\n=60,000 + 4,000 + 800 + 10 + 7\n\n = \boxed{\bf{64,817}}

Your answer is D.

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What is the solution of the system? Use substitution. 4x – y = 5
3x – 7 = 2
A) (3, 7)
B) (7, -7)
C) (-3, 7)
D) (3/4, 2/5)

Answers

Hi

We need to solve 3x-7=2 for x

Let's start by adding 7 to both sides

3x-7+7=2+7

3x=9

Now just divide both sides by 3 so we can find the value for x

3x/3=9/3

x=3

Now substitute 3 for x in 4x-y=5 so we can find the value for y

4x-7=5

4(3)-y=5

-y+12=5

Add -12

-y+12-12=5-12

-y=-7

Now divide both sides by -1 so we can find the positive value for y

-y/-1=-7/-1

y=7

The answer is A

(3,7)

Good luck:0


If f(x)=3x+7 and g(x)=2x-5 find g(f(-3))

A. -26 B.-9 C. -1 D. 10

Answers

The value of g(f(-3)) would be -9 which is the correct answer would be an option (B).

What exactly is a function?

A function is defined as a mathematical phrase that specifies a connection between two variables in algebra.

We have been given the functions below as

f(x) = 3x + 7 and g(x) = 2x - 5

We have to determine the value of g(f(-3))

Substitute the value of f(x) = 3x + 7 in the g(x) = 2x - 5 to get g(f(x))

⇒ g(f(x)) = 2(3x + 7) - 5

Apply the distributive property of multiplication,

⇒ g(f(x)) = 6x + 14 - 5

⇒ g(f(x)) = 6x + 9

Substitute the value of x = -3 in the g(x) = 2x - 5 to get g(f(-3))

⇒  g(f(-3)) = 6(-3) + 9

⇒  g(f(-3)) = -18 + 9

⇒  g(f(-3)) = -9

Therefore, the value of g(f(-3)) would be -9.

Learn more about the functions here:

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f(x)=3x+7 \n g(x)=2x-5 \n \n g(f(-3)) = ? \n \nf(-3)=3x+7 =3 \cdot (-3)+7=-9+7=-2 \n \n g(-2)=2x-5 =2*(-2)-5=-4-5 = -9\n \n g(f(-3)) = -9 \n \n Answer: \ B.) \ \ -9

Find the area of the figure to the nearest tenth.a.

77.9 sq mm

c.

70 sq mm


b.

72.5 sq mm

d.

540 sq mm

Answers

Look at the picture in the attachment.
The area of the figure is equal to the sum of the areas A₁ and A₂.

A_1=9 \ mm * 4.8 \ mm=43.2 \ mm^2 \nA_2=(9 \ mm * 7.7 \ mm)/(2)=(69.3 \ mm^2)/(2)=34.65 \ mm^2 \n \nA=43.2 \ mm^2 + 34.65 \ mm^2=77.85 \ mm^2 \approx 77.9 \ mm^2

The answer is A.

In the function f (x)=(x-2)^2+4, the minimum value occurs when x is... (a) -2(b) 2
(c) -4
(d) 4

Answers

Hello,

y=a(x-h)²+k has the vertex (h,k)
If a>0 it is a minimum
if a<0 it is a maximum

Here h=2 and k=4

The minimum is 2
Answer B.

If 3 waves happen in 6 seconds how many happen in 1 second? How do I solve this and what's the answer?

Answers

you would do 3 divided by 6 and that would give you th answer and the answer is 0.5 so that would mean half a wave happens every second

Pls explain me how to solve this

Answers

|f(x)| is equivalent to 2 equations
f(x) when f(x) >= 0 OR -f(x) when f(x)< 0

so |x-11| > 4 is equivalent to
x-11 > 4 when x-11 >= 0 OR
-(x-11) > 4 when x-11 < 0

rearrange
x-11 > 4 when x-11 >= 0 we get
x > 15 when x >= 11 ... means x > 11

-(x-11) > 4 when x-11 < 0 we get
x < 7 when x < 11 ...means x < 7

so we have. x < 7 OR x > 11 for this inequality which is not the correct answer

... now... what is solution for |x-11| < 4
you can try to work as above and should come up with the solution just 'the opposite' which is x > 7 OR x < 11 [ 7 < x < 11 ]

then you work for c) and could work or guess for d)