Consider the line y=-3/2x - 3
Find the equation of the line that is perpendicular to this line and passes through the point (3, 6).
Find the equation of the line that is parallel to this line and passes through the point (3, 6).

Answer:

b)

Step-by-step explanation:

The soccer coach is 3 years less than twice the age of his youngest team member.

In y = 2x - 3, x represents the youngest team member. y represents the soccer coach.

2x is twice the age of the youngest team member.

-3 is three years less.

Answer:

It would have no last term

Step-by-step explanation:

Answer:

x = 6 ± i√23

Step-by-step explanation:

x² − 12x + 59 = 0

Use quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-12) ± √((-12)² − 4(1)(59)) ] / 2(1)

x = [ 12 ± √(144 − 236) ] / 2

x = (12 ± √-92) / 2

x = (12 ± 2i√23) / 2

x = 6 ± i√23

The values of x are 1.2 or 10.8.

The given equation is x²-12x+59=0.

We need to find the value of x.

The standard form of a quadratic equation is ax²+bx+c=0.

Use quadratic formula [tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a}[/tex]

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

Now, a=1, b=-12 and c=59

[tex]x=\frac{12\pm\sqrt{(-12)^{2} -4\times 1\times 59} }{2\times 1}[/tex]

⇒x=1.2 or 10.8

Therefore, the values of x are 1.2 or 10.8.

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Answer:(1) The distance Soo Lin walks is a function of time = True

(2) The time it takes soo- in to walk a certain distance is a function of distance = False

Step-by-step explanation:

Since the distance walked, e in miles= 3.17t

Where t is time

From the equation,

time t is an independent variable, it does not dependent on distance e

Also

distance e is a dependent variable that depend on time t

Therefore,

Distance e is a function of time t.

While time t is not a function of distance e.

16,17,6

16-6 is 10 (range)

16+17+6=39

39/3 is 13. (mean)

Answer:

Both answer shown

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7 [/tex]

Step-by-step explanation:

Given: Little confusion is in the question

e^ln7 x1

i.e [tex]e^{ln 7x}[/tex]

To Find:

[tex]e^{ln 7x}= ?[/tex]

Solution:

We know Logarithmic identity as

[tex]\ln e = 1[/tex]

[tex]\ln e^{x} = x[/tex]

Similarly,

[tex]e^{\ln x}=x[/tex]

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7\times 1=7 [/tex]

Answer: C on edg

Step-by-step explanation:

Answer:

The total area of the farm land is  2520 sq. m

Step-by-step explanation:

Let us assume the total area of the farm land  = P sq. m

Now, two thirds of the area of a farm land was covered by wheat fields.

So, the area covered in Wheat field = [tex]\frac{2}{3}  \times P = (\frac{2}{3})P[/tex]

The area left which is not covered in wheat

= Total land - Land covered  in Wheat  

= [tex]P - (\frac{2}{3}) P =  (\frac{1}{3})P[/tex]

Also, the half of the remaining land is covered by pound.

So, the area covered in pound  = [tex]\frac{1}{2}  \times (\frac{P}{3} )  = (\frac{P}{6} )[/tex]

The other half is empty garden.

⇒The area empty garden  =   [tex]\frac{1}{2}  \times (\frac{P}{3} )  = (\frac{P}{6} )[/tex]

Also, the area of the garden = 420 sq. m

⇒[tex](\frac{P}{6})  =  420\\\implies  P = 6 \times 420 =  2520[/tex]

or, P  = 2520 sq. m

Hence, the total area of the farm land is  2520 sq. m

Yes it is. You would just plug in 10 for every instance of x so...

g(10) = 3(10)+4 = 30+4 = 34

answer: 34

Answer: g(10) = 34

Explanation: In this problem we are given the function g(x) = 3x + 4 and we are asked to find g(10).

In other words, if we put an x into our function, we get a 3x + 4 out so we are really being asked what happens if we put a 10 into the function.

Well if we put a 10 into the function, that's g(10) = and we get a 3(10) + 4 out.

Now all we have to do is simplify on the right side. 3 x 10 is 30 and 30 + 4 is 34. So g(10) = 34.

Answer: The bike cost $ 329

Step-by-step explanation:

1. Ist sentence

The local bike shop sells a bike and accessories package for $376.

Let the cost of one bike be $b

Let the cost of the accessories be $a

b + a = 376 .........…...... eqn(1)

2. Second sentence.

If the bike is worth 7 times more than the accessories.

Equation;

b = 7a

3. Substitute b into eqn 1

7a + a = 376

8a = 376

a = 376/8

a= 47

b= 7a = 7× 47 = 329

Therefore The bike cost $ 329

Answer:

A

Step-by-step explanation:

Complementary angles have a sum of 90 degrees

Answer:

A. 7degree + 83degree

Step-by-step explanation:

which satisfy with the formula

complementary angle = sum of two angles equal to 90 degree

7+83 =90

Answer:

x=20, -5

Step-by-step explanation:

x^2-15x-100=0

factor out the trinomial,

(x-20)(x+5)=0

zero property,

x-20=0, x+5=0

x=0+20=20

x=0-5=-5

She sold 98 small cups and 57 large cups

Step-by-step explanation:

Ashley had a summer lemonade stand

We need to find how many cups of each type she sold

Assume that Ashley sold x small cups and y large cups of lemonade

∵ Ashley sold x small cups of lemonade

∵ She sold y large cups of lemonade

∵ Ashley sold a total of 155 cups

∴ x + y = 155 ⇒ (1)

∵ The price of the small cup = $1.25

∵ The price of the large cup = $2.5

∵ The price of the all cups = $265

- Multiply x by 1.25 and y by 2.5 and add the two products,

  then equate the sum by 265

∴ 1.25x + 2.5y = 265 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2.5 to eliminate y

∵ -2.5x - 2.5 y = -387.5 ⇒ (3)

- Add equations (2) and (3)

∴ -1.25x = -122.5

- Divide both sides by -1.25

∴ x = 98

- Substitute the value of x in equation (1) to find y

∵ 98 + y = 155

- Subtract 98 from both sides

∴ y = 57

She sold 98 small cups and 57 large cups

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Answer:

4 is by SAS Postulate

5 is Definition of a Median

Step-by-step explanation:

hope this is right

Answer:

15/8

Step-by-step explanation:

63 3/8=507/8

65 1/4=261/4

-------------------

261/4-507/8=522/8-507/8=15/8

Q and S are parallel because the  93 degree and 87 degree angles are supplementary angles and when added together equal 180 degrees.

The answer is B.

Answer:

B

Step-by-step explanation:

if you move the angle 87 up to angle 93 on the line q they equall 180 showing you its parallel

To construct the linear function for the number of marriages per hour in the U.S., you calculate the number of marriages in one hour by dividing 3600 seconds by 13.4 seconds and rounding to the nearest whole number. The linear function is y = 269x, with the domain being non-negative hours (x) and the range being whole number marriages (y).

To construct a linear function representing the number of marriages in the U.S. as a function of time given in hours, we can start by determining how many marriages occur every second. Since there was one marriage every 13.4 seconds in 2000, we first convert an hour to seconds, which is 3600 seconds per hour. Then we divide 3600 by 13.4 to find how many marriages occur in an hour. This gives us approximately 268.66, which we can round to the nearest whole number, yielding about 269 marriages per hour.

Let's denote the number of hours as x and the number of marriages as y. Thus, the linear function is y = 269x. The domain of this function is the number of hours, which we can assume to be all non-negative real numbers (x >= 0), representing the continuous passage of time. The range of the function is the number of marriages, which also comprises non-negative whole numbers, as you wouldn't have a fraction of a marriage.

Answer:

C, $ 240,000.00

Step-by-step explanation:

Company cost: 393.29 + 151.44 + 46.39 = 591.12

Profit each computer: 1196.91 - 591.12 = 605.79

408 customers: 605.79 x 408 = 247162 ≈ 240000

Answer:

8

Step-by-step explanation:

4x ÷ y

x = 1/2

y = 1/4

4(1/2) ÷ 1/4

4 × 1/2 = 2

2 ÷ 1/4

2 × 4 = 8

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Answer:

1/12 of a mile.

Step-by-step explanation:

1. Find a common denominator. In this instance, we can use the denominator of 12 because both 3 and 4 are multiples of 12.

2. Multiply each fraction (numerator and denominator) to convert them.

1/3(4/4) = 4/12

1/4(3/3) = 3/12

3. Subtract.

4/12－3/12 = 1/12

Answer:

Step-by-step explanation:

Answer:

[tex]y=3/8 -3\\[/tex]

Step-by-step explanation:

Since the equation is in standard form, you have to the equation in y = mx + b format, to graph the equation, -3x -8y = 24 in y = mx + b format is y = [tex]\frac{3}{8}[/tex] - 3. Just graph the equation from there. I hpe this helps you!

Answer:

[tex]x=\frac{132}{25}[/tex]

Step-by-step explanation:

We have to solve for the value of "x". The equation is:

[tex]\frac{1}{3}(12+x)=8(6-x)[/tex]

We can use the distributive property shown below to simplify the expression and find the value of x.

Distributive property:  [tex]a(b+c)=ab+ac[/tex]

Now, we solve:

[tex]\frac{1}{3}(12+x)=8(6-x)\\4+\frac{1}{3}x=48-8x\\\frac{1}{3}x+8x=48-4\\8\frac{1}{3}x=44\\\frac{25}{3}x=44\\x=\frac{44}{\frac{25}{3}}\\x=44*\frac{3}{25}\\x=\frac{132}{25}[/tex]

This is the improper fractional value of "x". So,

[tex]x=\frac{132}{25}[/tex]

Answer:

x = 3 or x = 4

Step-by-step explanation:

Given

x² + 12 = 7x ( subtract 7x from both sides )

x² - 7x + 12 = 0 ← in standard form

(x - 3)(x - 4) = 0 ← in factored form

Equate each factor to zero ( zero product property ) and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase

Solution:

Given that Two years ago, Sally had 5,000 dogs in her dog shelter

Now she has 24,575 dogs

To find: rate of change

A rate of change is a rate that describes how one quantity changes in relation to another quantity

[tex]\text {rate of change }=\frac{\text { new value }-\text {original value}}{\text {original value}} \times 100[/tex]

[tex]\begin{array}{l}{\text { rate of change }=\frac{24,575-5000}{5000} \times 100} \\\\ {\text { rate of change }=\frac{19575}{5000} \times 100=391.5}\end{array}[/tex]

Thus the rate of change is 391.5 % increase

There were 18 single rooms and 6 suites booked.

Step-by-step explanation:

Given,

Cost of one single room = $90

Cost of one suite = $150

Total rooms booked = 24

Total amount earned = $2520

Let,

Number of single rooms = x

Number of suite = y

According to given statement;

x+y=24     Eqn 1

90x+150y=2520    Eqn 2

Multiplying Eqn 1 by 90

[tex]90(x+y=24)\\90x+90y=2160\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](90x+150y)-(90x+90y)=2520-2160\\90x+150y-90x-90y=360\\60y=360[/tex]

Dividing both sides by 60

[tex]\frac{60y}{60}=\frac{360}{60}\\y=6[/tex]

Putting y=6 in Eqn 1

[tex]x+6=24\\x=24-6\\x=18[/tex]

There were 18 single rooms and 6 suites booked.

Keywords: linear equation, variable

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Answer: 2 and 7/12

Step-by-step explanation: To subtract 4 - 1 and 5/12, first subtract the fractions. Since 4 has no fraction, imagine the fraction 0/12.

Notice however that we can't subtract 0/12 - 5/12.

So, let's rewrite 4 and 0/12 as 3 + 1 and 0/12 or 3 + 12/12 by changing 1 and 0/12 into an improper fraction.

Now we have 3 and 12/12 - 1 and 5/12.

Now we can subtract our fractions 12/12 - 5/12 and we get 7/12. Next we subtract our whole numbers 4 - 1 to get 3.

So 5 - 1 and 5/12 is 2 and 7/12.

Answer:

A  increases slowly

B  decreases quickly

C  increases quickly

D  decreases slowly

Step-by-step explanation:

In the graph, the changes in the values of y for the values of x, are shown below.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used

In the given graph,

In interval A, the value of y increases slowly.

In interval B, the value of y decreases  quickly.

In interval C, the value of y increases quickly.

And in interval D, the value of y decreases slowly.

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Answer:

the music long is 2:30 hours

Step-by-step explanation:

1:10 + 2:30 = 3:40

Good Luck

Answer:

The time = 6.5 seconds and the maximum height reached by the rocket = 676 feet

Step-by-step explanation:

A path of a toy rocket thrown upward from the ground at a rate of 208 ft/sec is modeled by the quadratic function h(t) = -16[tex]t^{2}[/tex] +208t.

We have to find when the rocket will reach its maximum height.

When the rocket reaches its maximum height, [tex]\frac{dh}{dt}[/tex] = 0.

h(t) = -16[tex]t^{2}[/tex] +208t

[tex]\frac{dh}{dt}[/tex] = - 32t + 208 = 0

t = 6.5 seconds

At t = 6.5 seconds it is at maximum height.

Maximum height = - 16[tex]\times (6.5^{2} ) + 208\times 6.5[/tex]

                            = 676 feet

Answer:

Time taken = 6.5s . Maximum height = 676 feet.

Step-by-step explanation:

To find the maxima of height function use differentiation ie, h(t) will be maximum when [tex]\frac{dh(t)}{dt} = 0[/tex] .

[tex]h(t) = -16t^{2} + 208t\\\frac{dh(t)}{dt}= -32t + 208[/tex]

[tex]\frac{dh(t)}{dt} = 0[/tex] ⇒ -32t +208 = 0

32t = 208

[tex]t = \frac{208}{32} = 6.5[/tex]

For maximum height put t = 6.5  in h(t),

Maximum height = -16×6.5×6.5  + 208×6.5

=676 feet.

Step-by-step explanation: Pi is an irrational number 3.14159... which rounds to 3.14.

Mathematicians found out that when you try to write down what π is, the decimal the decimal places just keep going and going. This means it's impossible to find all the digits of π.

To solve many problems involving π, you just round it off to 3.14 and it will work. However, if you include more digits, your answer will be more accurate.

The first 100 digits of pi are below.

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

Pi, a key mathematical constant, can be approximated to 3.14 but extends infinitely. Each digit after the decimal point serves a purpose in precision in calculations. Digits form numbers and range from 0 to 9, with the decimal point establishing the value of the number.

The digits of pi, which is a mathematical constant representing the ratio of a circle's circumference to its diameter, are numerous as pi extends infinitely beyond the decimal point. However, in most contexts, it is approximated to 3.14. These first two digits are usually sufficient for common calculations in geometry, note that pi includes many more digits in its full representation.

When it comes to number rounding, it is worth noting that each digit after the decimal point matters. In terms of importance from left to right, a digit would be replaced by a zero if the next immediate number is 5 or above; this next number then either rounds up the previous number or maintains it depending on if it's below or above 5.

Digits are the components making up a number. They range from 0 to 9 and can be put in a sequence to form a variety of numbers. The placement of the decimal point also plays a vital role in establishing the numeric value of the number.

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