Jordan bikes at a speed of 8 2/3 mph. How many miles will he bike in:


45 minutes?

Just to be different we'll start with intercept intercept form which says the line through x intercept (a,0) and y intercept (0,b) is

[tex]\dfrac x a + \dfrac y b = 1[/tex]

Through (4,0) and (0,-2) that's

[tex]\dfrac{x}{4} + \dfrac{y}{-2} = 1[/tex]

Multiply through by the common denominator of 4 for standard form:

x - 2y = 4

For slope intercept form we solve for y

-2 y = -x + 4

y = (1/2) x - 2

We see our slope is (1/2) and we go through (4,0) so point slope form is

y - 0 = (1/2)(x - 4)

y = (1/2)(x-4)

The equation is y = 1/2(x - 4), and converting this to standard form results in x - 2y = 4.

To find the equation of the line that passes through the x-intercept (4,0) and y-intercept (0,-2), we need to derive its slope and then write the equation in different forms:

Step 1: Calculate the Slope

The slope (m) is given by
m = (y2 - y1) / (x2 - x1).
Using the given intercepts (4,0) and (0,-2):

m = (0 - (-2)) / (4 - 0) = 2 / 4 = 1/2

Step 2: Slope-Intercept Form

The slope-intercept form is
y = mx + b, where m is the slope and b is the y-intercept. We know that the y-intercept, b, is -2.

Thus, the equation in slope-intercept form is:

y = 1/2 x - 2

Step 3: Point-Slope Form

The point-slope form is given by
y - y1 = m(x - x1).
Using the point (4,0):

y - 0 = 1/2(x - 4)

Which simplifies to:

y = 1/2(x - 4)

Step 4: Standard Form

Standard form is
Ax + By = C. To convert our slope-intercept form (y = 1/2 x - 2) to standard form, we follow these steps:

Multiply both sides by 2 to eliminate the fraction:
2y = x - 4

Rearrange to get integer coefficients on the left side:
x - 2y = 4

Thus, the equation in standard form is: x - 2y = 4

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:

4 is by SAS Postulate

5 is Definition of a Median

Step-by-step explanation:

hope this is right

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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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

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:

the music long is 2:30 hours

Step-by-step explanation:

1:10 + 2:30 = 3:40

Good Luck

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:

It would have no last term

Step-by-step explanation:

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

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:

5 cubed, 5 (6-3), and 5 to the power of 6 divided by 5 cubed.

Answer:

5^(6-3), 5^6/5^3, 5^3 or the 1st and 3rd on the top row and the 2nd on the bottom row

Step-by-step explanation:

So, how exponent rules work is if x to the power of any number is multiplied by x to the power of any number, you add the exponents. For example, 5^6 multiplied by 5^-3 is 6-3 which is 3, so the answer is 5^3. If you are dividing, lets say you have 5^6/5^3, you subtract. It would be 6-3, and the answer would be 5^3. When you have x to the power of a number, and you have that in parenthesis, and there is an exponent on the outside, only then do you multiply the exponents, and you cannot multiply exponents if there are more than one term in the parenthesis. For example, (x^5)^5 = x^25 because 5x5 = 25. But, if you have (x-5)^2 you cannot multiply the 2 out on both terms, you have to instead use FOIL. Using these rules, you can find that each of the answers above is equal to the answer of the first equation, 5^3.

5^(6) x 5^(-3) = 5^(6-3) = 5^(3)

5^6/5^3 = 5^(6-3) = 5^(3)

5^3 = 5^3

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

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:

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:

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.

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:

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

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:

1500

Step-by-step explanation:

75 ballons in one package, mulitiply 75 by 20 to get 1500 total balloons

Answer:1500

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:

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:

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

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

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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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:

The better one? 8 oz

Step-by-step explanation:

You might be wondering why. You divide the cost by the oz. (or like a kind of capacity measurement or like weigh) For example, 2.16/ 8 is 0.27, that means per oz it is 0.27. Then, you find it for a 10 oz that costs 2.75, that is equal to 0.275. 0.275 is more than 0.27 so a 8 oz must be better to buy.

Answer: 8 oz drink

Step-by-step explanation: In this problem, we are asked to determine which of the following drinks is a better buy.

A 8 oz drink that for $2.16 or a 10 oz drink for $2.75.

Since the drinks that we are comparing are different sizes, to determine which drink is a better buy, we first need to find the unit price of each drink which in this case is the cost per ounce of each drink.

For our first drink, since $2.16 is the cost for 8 oz, to find the cost per ounce, we divide 8 into 2.16 to get 0.27. So the 1 ounce drink has a unit price of 0.27 cents per ounce.

For our second drink, since $2.75 is the cost for 10 oz, to find the cost per ounce, we divide 10 into 2.75 to get 0.275.

Finally we want to know which drink is a better buy so we are looking for the drink with the lower unit price. Since 0.27 cents is less than 0.275 cents, the 8 oz drink has the lower unit price and is therefore the better buy.

16,17,6

16-6 is 10 (range)

16+17+6=39

39/3 is 13. (mean)

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