−4x + 3y = 15, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 40km/hr.

the standard form of a quadratic is :  y = ax² + bx + c : (a ≠ 0 )

note that (x - 0 )² = x²

distributing by - 0.3 gives

y= - 0.3x² + 3 ← in standard form

with a = - 0.3, b = 0 and c = 3

Answer:

[tex]10 ^ {3m-2n} = 10 ^ z[/tex]

Where z = 3m-2n

Step-by-step explanation:

An important mathematical property about the powers is that when powers of equal base are divided, the same base is placed and the exponents are subtracted.

Then we can write 1000m and 100n as powers of the same base:

[tex]1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}[/tex]

Now we perform the division of powers of the same base (10)

[tex]\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}[/tex]

Finally

 [tex]10 ^ {3m-2n} = 10 ^ z[/tex]

Where z = 3m-2n

To express z in terms of m and n, rewrite the equation: 1000m / 100n = 10z. Then, simplify to 100m / 10n = z. So, z can be expressed as 10m/n.

The given equation is 1000m divided by 100n equals to 10z. To express z in terms of m and n, we need to isolate z. Let's proceed step by step:

So, z can be expressed as 10m/n.

https://brainly.com/question/953809

#SPJ2

Answer:

[tex]\boxed{F=\dfrac{9}{5}c+32}[/tex]

Step-by-step explanation:

[tex]\dfrac{5(F-32)}{9}=c\qquad\text{multiply both sides by 9}\\\\5(F-32)=9c\qquad\text{divide both sides by 5}\\\\F-32=\dfrac{9}{5}c\qquad\text{add 32 to both sides}\\\\\boxed{F=\dfrac{9}{5}c+32}[/tex]

Annual Percent Rate (APR) = 18%

Rate during the current billing cycle = 18/12 = 1.5%

Balance at the beginning of the billing cycle = 60.15

Payment   51.00

Balance                                                                 10.15

Purchase 91.27        

Balance                                                                - 81.12

Finance Charge 60.15 * 0.015 =                             0.90

New Balance                                                       - 82.02

x + x - 3 + 2x - 3 = 78  

4x = 84  

x = 21  

Answer: 21 Schnauzers.

The graph of the tangent function approaches vertical asymptotes at x=±π/2. The inverse function will have horizontal asymptotes of y=±π/2. The only viable choice among your graphs is ...

... Graph C

_____

The graph of the inverse of a function is the function's graph with the x- and y-coordinates swapped. Essentially, the graph is reflected across the line y=x. The graph of the tangent function has a vertical aspect. Its inverse has a horizontal aspect.

ANSWER

[tex]y=12[/tex]

EXPLANATION

One way is to make x the subject in one equation and substitute into the other.

[tex]2x+2=y[/tex]

[tex]\Rightarrow 2x=y-2[/tex]

[tex]\Rightarrow x=\frac{y}{2}-1--(1)[/tex]

The second equation is

[tex]2y=5x-1--(2)[/tex]

Let us put equation 1 in 2

[tex]\Rightarrow 2y=5(\frac{y}{2}-1)-1[/tex]

[tex]\Rightarrow 2y=\frac{5y}{2}-5-1[/tex]

[tex]\Rightarrow 2y=\frac{5y}{2}-6[/tex]

Multiplying through by 2 gives;

[tex]\Rightarrow 4y=5y-12[/tex]

[tex]\Rightarrow 4y-5y=-12[/tex]

[tex]\Rightarrow -y=-12[/tex]

[tex]\Rightarrow y=12[/tex]

D

given the 2 equations

2x + 2 = y → (1)

2y = 5x - 1 → (2)

Substitute y = 2x + 2 into (2)

2(2x + 2) = 5x - 1

4x + 4 = 5x - 1 ( subtract 5x from both sides )

- x + 4 = = - 1 ( subtract 4 from both sides )

- x = - 5 ( multiply through by - 1 )

x = 5

substitute x = 5 into (1)

y = (2 × 5 ) + 2 = 10 + 2 = 12 → D

Answer:

x     6  0    3    -3  

y     0  -2   -1   -3

Step-by-step explanation:

We substitute x value in the equation and find y.

When x =0, -6y = 12 or y =-2

Likewise all pairs are found out.

Similarly put y =0:  x = 6

When x =3, 2(3)-6y =12 :y =-1

When x=-3, 2(-3)-6y=12 or y = -3

Plot these on a graph and join the line.

Graph is attached below:

a. 2x-6y=12: y = (12-2x)/6.

b. Graph the line using (0,2) and (3,0).

(a) To create a table of values for at least 4 points, we can solve the equation for y in terms of x:

y = (12 - 2x) / 6

We can then choose different values for x and plug them into the equation to find the corresponding y values.

Here is a table of values for at least 4 points:

x y

0 2

3 0

-3 4

6 -2

(b) To graph the line, we can use the two points from the table of values that are closest to each other.

In this case, we will use the points (0, 2) and (3, 0).

First, plot the two points on the coordinate plane.  

Then, use a straightedge or ruler to draw a line that passes through both points.

Here is the graph of the line 2x − 6y = 12:

For similar question on Graph the line.

https://brainly.com/question/19040584

#SPJ3

Answer:

70.2

Step-by-step explanation:

Multiply the weight in pounds by the conversion factor.

[tex]156\,lb\times\dfrac{0.45\,kg}{1\, lb}=70.2\,kg[/tex]

Answer:

70.2 kilograms

Step-by-step explanation:

In order to calculate this you just have to do a rule of three, where you use the equivalence of the pounds by the kilograms, in the table you see that 1 pound equals .45 kilograms, so you use that for your equivalence:

[tex]\frac{1pound}{.45kilograms}= \frac{156 pounds}{x}[/tex]

[tex]x=\frac{165*.45}{1 pound}[/tex]

[tex]x=70.2 kilos[/tex]

So we know that the patient weights 70,2 kilograms.

Answer:

(0,2) and (1,14)

Graph is attached.

Step-by-step explanation:

Let us find  y intercept

When x=0, y  = f(x) =2

Hence one point is (0,2)

Other point is let x = 1,

y =12(1)+2 =14

(1,14) (0,2) are plotted and joined.

Graph is attached.

The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.

Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives

... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)

... 2x +z = -4 . . . . simplified

Likewise, we can add 3 times the second equation to the first to cancel y in that sum.

... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)

...15x +3y -12z +2x -3y +z = 123 -1

...17x -11z = 122 . . . . simplified

Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:

... 11(2x +z) +(17x -11z) = 11(-4) +122

...22x +17x = 78 . . . . . . simplify a little bit

... x = 78/39 = 2 . . . . . . divide by 39

From above, we find

... z = -4 -2x = -4 -2·2 = -8

... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1

The solution is (x, y, z) = (2, -1, -8).

_____

The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.

Answer:

(0,-5) , (1,-2) , (0,1) and (-1,1)

Step-by-step explanation:

-2x + y ≥ -4

y ≥ 2x - 4

Taking a point (0,-5):

-5 ≥ 0 - 4 , 5 ≥ -4

This situation is true.

Taking a point (3,-1):

-1 ≥ 2(3) - 4 , -1 ≥ 2

This situation is not true.

Taking a situation (1,-2):

-2 ≥ 2(1) - 4 , -2 ≥ -2

This situation is true.

Taking a point (0,1):

1 ≥ 0 - 4 , 1 ≥ -4

This situation is true.

Taking a point (-1,1):

1 ≥ 2(-1) - 4 , 1 ≥ -6

This situation is true.

The correct answers are

(−1, −1)

(5, −12)

(0, 1)

Have a nice day!

Rewriting this symbolically, (-3/8)n = -0.1.  Let's solve for n.  To do this, multiply both sides of the equation by (-8/3).  This results in n = 8/30, or n= 4/15.

Answer:

The edge length of the storage cube is 30 centimeters.

Step-by-step explanation:

All sides/edges of a cube has equal length.

Let's take the length of a edge as [tex]a[/tex] centimeters.

The volume a the cube = Height * Width * Length

All height, width and length are equal([tex]a[/tex] centimeters).

Now we can write the equation again as,

The volume a the cube = [tex]a*a*a[/tex]

Volume of the cube is given as 27,000 cubic centimeters.

Therefore,

[tex]a*a*a=27,000[/tex]

[tex]a=\sqrt[3]{27,000}[/tex]

[tex]a=30[/tex]

Therefore, the edge length of the storage cube is 30 centimeters.

40% of $350, 000

40% = [tex]\frac{40}{100}[/tex] = 0.4, hence

expected amount = 0.4 × $350, 000 = $140, 000

I think you need to think about the problem carefully. My guess is 1,that's my guess. sorry i couldn't give an accurate answer or you divide 300 by 5

Answer:

60

Step-by-step explanation:

If an odd number of minus signs are involved in a product or quotient, the sign of the result is negative. Otherwise, it is positive.

Examples:

(-1)(-1) = 1

(-1)(-1)(-1) = -1

(-1)/(-1) = 1

(-1)(-1)/(-1) = -1

The product of two positive numbers is positive:  (+)(+) = (+).

The product of one positive number and one neg number is neg:  (+)(-) = (-).

The product of two negative numbers is positive:  (-)(-) = (+)

x < 4

given x - 1 < 3 ( add 1 to both sides )

x < 4

or x ∈ ( - ∞, 4 ) ← in interval notation

We assume the slope is a constant, so the rise is proportional to the run.

... y/(4 ft) = (31 ft)/(3 ft)

... y = (4/3)·(31 ft)

... y = 41 1/3 ft = 41 ft 4 in

Answer:

y=-1

Step-by-step explanation:

The first step to solving this problem is to write it out like this-->

4x+2y=6

x-3y=5    

Next you want to eliminate the X's or the Y's, I chose to elininate the X's-->

4x+2y=6

-4(x-3y=5) [You MUST distribute the -4 to each of the numbers in the equation]

Then you get--->

4x+2y=6

-4x+12y=-20 Then you add them top to bottom--->

0x+14y=-14 [At this point you dont have to write the X]Next you solve for y-->

14y=-14 Divide both sides by 14, in order to get the y by itself-->

y=-1 And theres your answer hope it helps :D

we have the 2 equations

4x + 2y = 6 → (1)

x - 3y = 5 → (2)

multiply (2) by 4

4x - 12y = 20 → (3)

(3) - (1) to eliminate the terms in x

- 14y = 14 ( divide both sides by - 14 )

y = - 1

substitute y = - 1 into (1) and solve for x

4x - 2 = 6 ) add 2 to both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is x = 2, y = - 1

As t/3 it means that 0.5% every 3 years.

So n will be 3 years , 36 months

Solution:

The Given model to Predict the population

[tex]P=P_{0}(1.005)^{\frac{t}{3}[/tex]

                               ----------------------------------(1)

The population increases by 0.5 % every n months.

Initial Population = 215

Final Population

[tex]=215+215\times \frac{0.5}{100}\\\\=215+1.075\\\\=216.075[/tex]

Substituting the value of , Initial and final Population in equation 1,

[tex]216.075=215\times (1.005)^{\frac{t}{3}}\\\\  (1.005)^{\frac{t}{3}}=\frac{216.075}{215}\\\\  (1.005)^{\frac{t}{3}}=(1.005)^{1}\\\\ \frac{t}{3}=1\\\\ t=3[/tex]

t=3 years =36 months

The value of n is equal to 36 months.

Running 2 miles at 8:15 per mile takes 16:30 minutes.

Running 3 miles at 7:12 per mile takes 21:36 minutes.

The total running time is 16:30 + 21:36 = 38:06 minutes. That length of time after 6:52 am is 7:30:06 am.

You get home for breakfast at 6 seconds past 7:30 am.

By adding the times spent on each individual run to your start time, you should arrive home at approximately 7:30 am.

To begin with, this is a question about time calculation, where you need to know exactly how to calculate time durations. First, you start running at 6:52 am. Your easy pace is 8 minutes 15 seconds, or 8.25 minutes, per mile and you do this once before and once after your tempo run. So, for 2 miles, it's 2*8.25 = 16.5 minutes.

Then you have a tempo pace at 7 minutes 12 seconds, or 7.2 minutes, per mile. You run 3 miles at tempo pace, so that's 3*7.2 = 21.6 minutes.

Adding these two results together, you have a total running time of 38.1 minutes (16.5 minutes easy pace + 21.6 minutes tempo pace). Adding this to your start time of 6:52 am gives you a rough end time of 7:30 am. Please note that this estimation rounds your running time to the nearest minute.

https://brainly.com/question/34080240

#SPJ2

I hope this might be able to help you.

Since the value of the car slowly decreases each year and each year is represented by y, the function is 24,000-1750y=f(x).

We have to break each degree in terms of 90

A) [tex]sin180^\circ=sin(90\times2+0)[/tex]

Which is in third quadrant, therefore sine is negative hence

[tex]sin(90\times2+0)= -sin0 ^\circ = 0[/tex]

B) [tex]cos180^\circ =cos(90\times2+0)[/tex]

Which is in third quadrant, therefore cosine is negative hence

[tex]cos(90\times2+0)= -cos0^\circ = -1 [/tex]

C) [tex] tan180^\circ=tan(90\times2+0)[/tex]

Which is in third quadrant, therefore tangent is positive hence

[tex]tan(90\times2+0)= tan0^\circ = 0[/tex]

D) [tex]csc180^\circ=csc(90\times2+0)[/tex]

Which is in third quadrant, therefore cosec is negative hence

[tex]cosec(90\times2+0)= -csc0^\circ =[/tex]not defined

E)[tex]sec180^\circ=sec(90\times2+0)[/tex]

Which is in third quadrant, therefore secant is negative hence

[tex]sec(90\times2+0)= -sec0^\circ = -1 [/tex]

F) [tex] cot180^\circ=cot(90\times2+0)[/tex]

Which is in third quadrant, therefore tangent is positive hence

[tex]cot(90\times2+0)= cot0^\circ = [/tex] not defined

Hence only [tex] cos 180^\circ [/tex] and

[tex] sec180^\circ [/tex] have value -1

Hope this will help

Answer:

Cos and Sec

Step-by-step explanation:

thats the short of the guy above

The commutative property of addition lets you rearrange this to

(3/4 +5/3) - 2/3

The associative property of addition lets you regroup this to

3/4 + (5/3 -2/3)

= 3/4 + 3/3

= 1 3/4 . . . . take your pick of the final form

= 7/4

= 1.75

12 gallons of white paint

divide 20 gallons by 5 to obtain 1 part of the ratio

[tex]\frac{20}{5}[/tex] = 4 gallons ← 1 part

white paint = 3 × 4 = 12 gallons ← 3 parts

30 percent

22% of 200 is 44, 44 students play football

12 of 200 is 24, 24 students play baseball

44+24=68

The teams have a total of 68 players

because 8 play both sports you subract 8

68-8=60

The answer is a tolal of 60 students play sports

I think the answer is 60

Correctly written, your identity would tell you ...

... (sum of cubes) - 3·(product) = (sum of integers)·((sum of squares) - (sum of any two products))

Filling in the given numbers, you have ...

... 684 - 3·210 = (sum of integers)·(110 -107)

... 54 = (sum of integers)·3 . . . . . simplify

... sum of integers = 54/3 . . . . . . divide by the coefficient of the variable

... sum of integers = 18

_____

Integers 5, 6, and 7 meet these conditions.