Plz help!! I need it ASAP

Midpoint of (2,4) and (2, -7)

slega [8]

Step-by-step explanation:

soln:

let,

(x1,y1) =(2,4)

(x2,y2)=2,-7)

Now,

By midpoint formula,

×= x1+x2

2

= 2+2

2

=4

2

=2,,

And,

Y=y1+y2

2

=4-7

2

= -3

2

Hence ,

The mispoint between points (2,4) and (2,-7) is (2,-3 )

2

6 0

2 years ago

Find the range of the following piecewise function.

mash [69]

Answer:

$\huge\boxed{[-5;\ -2)\ \cup\ [3;\ 13)}$

Step-by-step explanation:

The following piecewise functions are linear functions. The graph of any of them is a line segment.

We just need to calculate the value of the function at each end specified in the brace.

$y=3x-2\ \text{if}\ -1\leq x$

Substitute x =-1 and x = 0:

$x=-1\\y=3(-1)-2=-3-2=-5\\\\x=0\\y=3(0)-2=0-2=-2$

Range of this piece is [-5; -2)

$y=2x+3\ \text{if}\ 0\leq x$

Substitute x =0and x = 5:

$x=0\\y=2(0)+3=0+3=3\\\\x=5\\y=2(5)+3=10+3=13$

Range of this piece is [3; 13)

Therefore the range of the following piecewise function is:

$[-5;\ -2)\ \cup\ [3;\ 13)$

Look at the picture.

6 0

3 years ago

If 225.00 yields 27.00 in x years as simple interest at the rate of 4% per annum find x

Lyrx [107]

Answer:

3 years

Step-by-step explanation:

By simple interest formula:

$i = \frac{prt}{100} \\ \\ 27 = \frac{225 \times 4 \times x}{100} \\ \\ x = \frac{27 \times 100}{900} \\ \\ x = \frac{2700}{900} \\ \\ x = 3 \: years$

6 0

3 years ago

flying with wind, a small plane flew 410 mi in 2 h. Flying against the wind, the plane could fly only 380 mi in the same amount

Thepotemich [5.8K]

Answer:

197.5 mph.

Step-by-step explanation:

If flying with wind a small plane flew at 410 miles and 380 miles then the next step is to divide both speeds by two. This way you get the mph. So now it is 205 mph and 190 mph. Now we find the average of these two numbers and you get 197.5 mph.

7 0

3 years ago

John, Sally, and Natalie would all like to save some money. John decides that it would be best to save money in a jar in his clo

Radda [10]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) Is a exponential growth function

Part 5) $A=6,000(1.07)^{t}$

Part 6) $\$11,802.91$

Part 7) Is a exponential growth function

Part 8) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 9) $\$13,591.41$

Part 10) Natalie has the most money after 10 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

$y=mx+b$

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

so

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

$y=100x+300$

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

10 years=10(12)=120 months

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}$

$A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 5) Write the model equation for Sally’s situation

$A=6,000(1.07)^{t}$

see the Part 4)

Part 6) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 7) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 8) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 7)

Part 9) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 10) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

4 0

4 years ago

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