Which of the following functions represents an exponential decay with a 15% rate of change where A represents the initial value and x represents time in years

[tex] \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 12.4 \times 18 \\ 6.2 \times 18 \\ 111.6 {cm}^{2} [/tex]

Answer:

x= 5

Step-by-step explanation:

Since RQ= PQ,

3x= 15

Divide both sides by 3:

x= 15 ÷3

[tex]\textcolor{red}{x = 5}[/tex]

[tex]\textcolor{steelblue}{\text{Prove for RQ}= \text{PQ}}[/tex]

Let SP= x

RS= SP= x (given)

Let SQ= y

Applying Pythagoras' Theorem,

In triangle QRS

(RQ)²= (RS)² +(SQ)²

(RQ)²= x² +y²

[tex]RQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

In triangle QPS

(PQ)²= (SP)² +(SQ)²

(PQ)²= x² +y²

[tex]PQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

Thus, RQ= PQ.

Answer:

Step-by-step explanation:

3x = 15

3x/3 = 15/3

x = 5

3(5) = 15

Answer:

6468 mm²

Step-by-step explanation:

Given:

Therefore, the area of the small rectangle is:

= width × length

= 21 × y

= 21y mm²

From inspection of the larger rectangle

Therefore, the area of the larger rectangle is:

= width × length

= 84(2y + 21)

= 168y + 1764 mm²

We know that the area of the larger rectangle is 11 times the area of the smaller rectangle. Therefore,

⇒ 11 small rectangles = larger rectangle

⇒ 11(21y) = 168y + 1764

⇒ 231y = 168y + 1764

⇒ 63y = 1764

⇒ y = 28

Therefore, the missing side length of the smaller rectangle is 28 mm.

Finally, to find the area of the larger rectangle, substitute the found value of y into the found expression for its area:

⇒ area = 168y + 1764

⇒ area = 168(28) + 1764

⇒ area = 4704 + 1764

⇒ area = 6468 mm²

Answer:

-4

Step-by-step explanation:

if you divide a negative number by a positive number, you will get a negative number

Answer:

-4

Step-by-step explanation:

-(4×3)/3

by crossing both 3 out

-(4) remains

Answer: B

Step-by-step explanation:

These are vertical angles, so x+97=2x+32, meaning x=65.

So, the measure of angle 1 = 65 + 97 = 162 degrees

The value of m∠1, given that m∠1 = x + 97 and m∠2 = 2x + 32 is 162° (2nd option)

First, we shall list out the given parameters from the question. This is given below:

Next, we shall obtain the value of x. Details below:

m∠1 = m∠2 (vertically opposite angle)

x + 97 = 2x + 32

Solving for x, we have:

97 - 32 = 2x - x

65 = x

Thus,

x = 65

Now, we shall obtain the value of m∠1 as follow:

m∠1 = x + 97

x = 65

Therefore,

m∠1 = 65 + 97

= 162°

Thus, the value of m∠1 is 162° (2nd option)

Learn more about vertically opposite angle:

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#SPJ2

Answer:

x=9

Step-by-step explanation:

divide 4 by 4 to get 1

x-1=8

9-1=8

Hey there!

x - 4/4 = 8

x - 1 = 8

ADD 1 to BOTH SIDES

x - 1 + 1 = 8 + 1

CANCEL out: -1 + 1 because it give you 0

KEEP: 8 + 1 because it give you the x-value

NEW EQUATION: x = 8 + 1

SIMPLIFY IT!
x = 9

Therefore, your answer is: x = 9

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

12

Step-by-step explanation:

[tex] \sqrt{ - 72k} \\ \\ = \sqrt{ - 72( - 2)} \\ \\ = \sqrt{144} \\ \\ = 12[/tex]

Answer:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

=12

Answer:

A makes 10 parts in 1 hour

B makes 4 parts in 1 hour.

then,

A makes 120 parts in a hour.

B makes 48 parts in a hour

Hope this helps!

Mark Brainlest!!!!!

Step-by-step explanation:

Answer:  3 out of 19  

Step-by-step explanation:

Answer:

P(caramel) = 3/10

P(raspberry) = 1/3

Step-by-step explanation:

Given:

⇒ Total chocolates = 3 + 3 + 4 = 10

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(picking \ caramel \ chocolate) = \dfrac{3}{10}[/tex]

If the picked caramel chocolate is NOT replaced then:

[tex]\sf \implies P(picking \ raspberry \ chocolate) = \dfrac39=\dfrac13[/tex]

Answer:

Step-by-step explanation:

16 ticks, the pointer is on 12. there fore it is the second answer.

2 3/4 lb

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$34000\\ P=\textit{original amount deposited}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ t=years\dotfill &9 \end{cases} \\\\\\ 34000=Pe^{0.049\cdot 9}\implies 34000=Pe^{0.441}\implies \cfrac{34000}{e^{0.441}}=P\implies 21875.35\approx P[/tex]

Answer:

  B

Step-by-step explanation:

The first step of any problem solution is look at the given information. Here, we are given the equation of a line in (almost) standard form, and we want to match the equation with a graph. We notice that the coefficients of the variables are factors of the constant, so the intercepts are integer values easily found.

We can compare the line's intercepts to those shown on the graphs to choose the correct graph.

x-intercept

The x-intercept is found by setting y=0 and solving for x:

  -3x +5(0) = -15

  x = -15/-3 = 5

Only one graph shows a line with an x-intercept of (5, 0): graph B.

y-intercept

We can confirm graph B by finding the y-intercept. For this, we set x=0 and solve for y.

  -3(0) +5y = -15

  y = -15/5 = -3

Graph B also has a y-intercept of (0, -3), confirming it is the correct choice.

_____

Additional comment

Part of "look at the given information" is "look at the answer choices." What you look for is what makes one choice different from the others. Here, the lines have x- and y-intercepts of ±3 and ±5. The y-intercepts are the same for graphs A and B, and for graphs C and D.

However, the x-intercepts are different for all of them. This tells you that finding the x-intercept is the fastest way to find the correct graph.

The word or phrase that describes the chances of Elizabeth winning the mountain bike if she buys all the tickets is likely.

If Elizabeth buys all the tickets, then she will most definitely win the raffle because she will have the winning ticket.

In probability, when an event is certain to happen, it is said that the event is "likely." It is therefore likely that Elizabeth will win the raffle.

Find out more on likely events at https://brainly.com/question/7130419.

Answer:

rectangle

Step-by-step explanation:

the question is asking what the shape of the cross section would be if it was perpendicular to the base. imagine a cylinder that you could slide a piece of paper into. what would be inside the cylinder? perpendicular to the base, it would be a rectangle. if it was parallel to the base, you'd then have a circle.

its C

One coffee maker's cost in 1983 was $20.85 if the current CPI is 153 option (a) is correct.

It is given that the CPI is currently 153 if a coffee maker costs $31.90 today. It is required to find how much did one cost in 1983.

It is defined as the tool to measure inflation that indicates between two periods how much cost is increased. It can be represented by [tex]\rm CPI_t[/tex] for the given time 't'

The formula for finding the CPI:

[tex]\rm CPI_t = \frac{C_t}{C_0}\times 100[/tex]

Where [tex]\rm c_t[/tex] is the cost in the current market

           [tex]c_0[/tex] is the cost at the given period.

We have in the question:

[tex]\rm c_t = \$31.90\\\\\rm CPI_t = 153[/tex]

Putting these values in the CPI formula, we get:

[tex]\rm 153= \frac{31.90}{C_0}\times 100\\\\\rm c_0 = \frac{3190}{153} \\\\\rm c_0 = \$20.84 \approx \$20.85[/tex]

Thus, one coffee maker's cost in 1983 was $20.85 if the current CPI is 153.

Learn more about the CPI here:

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Answer:

forty five thousand and nine hundreds twenty

Step-by-step explanation:

Answer:

C, they are congruent.

Step-by-step explanation:

Rotation only changes the position of the image, not the size. :)

Answer:

C. They were rotated around the origin since that is the only point in the plane you can use as the center of rotation.

explanation:

when you think about it and look at the other problems, they are all going around the center of the grid when rotated, specifically the key word is when rotated, when they are translated they go anywhere they want.

Answer:

th answer is 324

Step-by-step explanation:

i took the test

Answer: -2, 0

Step-by-step explanation:

The graph this represents this system is the second graph since the vertex of the absolute value function is at x=-2.

So, to find the solutions, we can find the intersection points. These are at x=-2 and x=0.

obcjkaosicabkajiuhcabaca

Answer:

384800 square centimeters (cm²); 3.848 × 107 square millimeters (mm²); 1.48572E-5 square miles (mi²); 46.0217 square yards (yd²)

Step-by-step explanation:

21b-32+7b-20b=

21b + 7b - 20b - 32

       8b            - 32

Hello!

21b-32+7b-20b=

21b +7b -20b -32

= 28b -20b - 32

= 8b -32

The inverse, converse and contrapositive of a statement are used to determine the true values of the statement

As a general rule, we have:

If a conditional statement is: If p , then q .

Then:

Using the above rule, we have:

Statement 1

All three statements above are true

Statement 2

All three statements above are also true

Read more about conditional statements at:

https://brainly.com/question/11073037

Step-by-step explanation:

All Natural Number (1,2,3,4,5...) are integers

All Whole numbers (0,1,2,3,4...) are not natural numbers (1,2,3,4...)

All integers are rational numbers

All real numbers are not irrational numbers as real nimber contain both rational and irrational numbers hence it is false.

Hence statement 1 and statement 3 are true

Answer:

The answeris D

Step-by-step explanation:

All whole numbers are natural numbers; natural numbers are numbers we use for counting 1, 2, 3....and so on, so that makes them whole because thay have no fraction, or decimils.

Answer:-7/8>-0.60

C is not true

Answer:

x<

−97

45

Answer:

b<

−38

5

n>

−22

3

p>

16

3

n>7