If f (x)=2^x-1 +3 and g(x) = 5x-9 what is (f-g)(x)

Answers

Answer 1

Answer: $( f - g )( x )$
_________________

$f(x) - g(x)$

$= ( 2^(x-1) +3) - (5x-9)$

$= 2^(x-1) - 5x + 12$

Answer 2

Answer: ( f - g )( x ) = f( x ) - g( x ) = 2^x-1 + 3 - 5x + 9 = 2^x-1 - 5x + 12 ;

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A scale drawing of an office space uses a scale of 2 inches in 3 yards the scale drawing has an area of 16 in.² what is the area of the actual office space

Answers

Answer:

36 Square Yards

Step-by-step explanation:

The Scale Drawing uses a ratio

2 Inches : 3 Yards

Therefore,

1 Inch = 3/2 Yards

If the area of the scale drawing is 16 Inch²

To get the area of the actual office, we multiply by the square of the scale factor.

Scale Factor=3/2

Therefore:

The area of the actual office space

=16X(3/2)² Square Yards

=36 Square Yards

Answer:

36 square yards.

Step-by-step explanation:

This question is solved with rule of three and ratios

We know that 2 inches is equivalent to 3 yards, and the area in the drawing is 16 square inches.

so if

2 inches ---- 3 yards then 1 inch is 3/2 yards.

Let's say that the office is 8 inches x 2 inches = 16 squared inches

Then, if we convert it to yards,

8 inches would be: $8((3)/(2))=12$ yards

and 2 inches would be: $2((3)/(2))=3$ yards

Then, the area of the office would be 12 x 3 = 36 squared yards.

How many grams are in 17 kilograms?

Answers

There are 17000 Grams in 17 Kilograms.
1 Kilogram = 1000 Grams

PLEASE HURRY According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth.P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction

0.024

0.031

0.132

0.309

Answers

Answer:

0.309

Step-by-step explanation:

→ Utilise the binomial distribution formula

$p=nCr*p^(n) *q^(n-r)$

→ It first will be 5C2 as there is 5 possible voters but he wants 2 voters

$p=5C2*p^(n) *q^(n-r)$

→ Then it will be $0.3^(2)$ as the probability they are in favour is 0.3 and we get the n from the 2 number for the 5C2

$p=5C2*0.3^(2) *q^(n-r)$

→ There for q will be 0.7 as it is the other probability left and the power will be 3 as it is n - r

$p=5C2*0.3^(2) *0.7^(3)$

→ Then getting 0.3087 which is 0.309

Answer:

Option D) 0.309

Step-by-step explanation:

Correct on edge

PLEASE HELPWhat is the perimeter of DEFG, shown?

A. 26.12
B. 18.06
C. 36.12
D. 13.06

Answers

The answer is the option A: A. 26.12

The explanation is shown below:

1. As you need the perimeter, you can divide the figure into three triangles (as you can see in the figure attached) to calculate the length of the diagonal lines, which would be the hypotenuses of the triangles.

2. You must apply the Pythagorean Theorem to calculate the hypotenuse of each triangle:

- Red triangle (The legs are 3 and 4):

$h=\sqrt{3^(2)+4^(2)} =5$

- Blue triangle (The legs are 1 and 2):

$h=\sqrt{1^(2)+2^(2)} =2.23$

-Green triangle (The legs are 3 and 5):

$h=\sqrt{3^(2)+5^(2)} =5.83$

3. The figure has is symmetric with respect to the y-axis. So, you can multiply the sum of the hypotenuses obtained by two to calculate the perimeter:

$Perimeter=2(5+2.23+5.83)=26.12$

Which counterexample disproves this statement?
for all integers x, 1/x less than or equal to x

Answers

One counter example would be -2. -1/2 is more than -2.

ActivityThe equation y = x + 1 represents plane A and y = -x + 21 represents plane B, where x is the time in minutes and y is the fuel in tons.

Part A
Go to your math tools and open the Graph tool to graph the two sets of equations. To see where the two lines intersect, change the scale so that the x-axis goes from 0 to 30 and the y-axis goes from 0 to 12. Paste a screenshot of the resulting graph in the answer space.

Part B
At which point do the lines intersect?

Part C
Do the coordinates of the point of intersection satisfy both equations simultaneously?

Answers

Answer:

Part-A: refer to the attachment

Part-B: (10,11)

Part-C: yes

step-by-step explanation:

Part-A:

refer to the attachment

(I used a online graphing calculator to graph the equations which made the work easy)

Part-B:

When two lines share exactly one common point, they are called the intersecting lines and thepointis called thepointof interception

Looking at the graph,we can understand that the two lines share a common point at (10,11),

hence,

The lines intercept at the point (10,11)

PartC:

well, to find the answer of this part, we can consider doing equality check by substituting the value of the point we got.

The point (10,11) means that the left and right hand side of both of the equations i.e $\text{y=x+1 and y=-x+21}$ are equal when x and y equal to 10 and 11 respectively.