help me out this is important ot me to get an A

Answer:

Step-by-step explanation:

No. of miles driven in 1 gallon = 30 miles.

since we have to distance traveled in miles.multiply LHS and RHS by x

No. of miles driven in 1*x gallon = 30*x miles.

No. of miles driven x gallons = 30*x = 30x miles

As given that

the number of miles Bill travels is represented by y

gas used is x

then

y = 30x

=> x = y/30

Thus, Bill's car uses y/30 gallon gas to travel Y miles.

Answer:

Part a: Bill’s car travels 30 miles per gallon of gas. If y represents the number of miles the car travels on x gallons of gas, the equation that represents this situation is y = 30x.

Part b:       gallons of gas (x) miles (y)

                                    1         30

                                    2        60

                                    3        90

Part c: There is no x-value that would lead to multiple y-values.

Part d: Yes, y = 30x is a function, because for every input, or x-value, there is only one output, or y-value.

Step-by-step explanation:

edmentum answers 100% correct

Answer:

(x + 2) , (x + 3) are factors

Step-by-step explanation:

Given

x² + 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)

The factors are + 2  and + 3, since

2 × 3 = 6 and 2 + 3 = 5 , thus

x² + 5x + 6 = (x + 2)(x + 3)

Answer:

Step-by-step explanation:

Let y(t) be the amount of salt in the tank after time t.

(A) Incoming rate = 0 (due to Pure water having no salt)

(B) Mixed solution comes out at 150 L/min. Initially the tank has 15,000 L of brine with 24 kg of salt.

concentration of salt at time t  = y(t) / 15000 kg/L

Outgoing rate = y(t)/15000 * 150 = y(t) / 100

(C) we know that,

[tex]\frac{dy}{dx} =(incoming\ rate) - (outgoing\ rate)[/tex]

[tex]\frac{dy}{dx} =0-\frac{y(t)}{100} = \frac{-y(t)}{100}[/tex]

Separate variable and integrate

[tex]\int {\frac{dy}{y} } = - \int {\frac{1}{100} } \, dt[/tex]

[tex]ln|y|=-\frac{1}{100}t + D[/tex]

[tex]y=e^{D} e^{\frac{-t}{100} }[/tex]

[tex]y= Ce^{\frac{-t}{100} }\ [C=e^{D} ][/tex]

At t= 0 , y(0) = 24 kg

[tex]24=C\ e^{0}[/tex]

C= 24

(D) Therefore, the amount of salt in the tank after time t :

[tex]y(t)=24e^{\frac{-t}{100} }\ kg[/tex]

Answer:

population parameter

Step-by-step explanation:

A population  is said to be category of individuals under study.

A population parameter is a numerical value which provides a summary to a measure of an average or percentage which describes the entire population under a study.

In a Normal Curve, the population parameter can be a population mean or population standard deviation , population proportion which represent the population.

∴

The average SAT score of  1356 in the given study  is a population parameter

Answer:

3(6)

??

Step-by-step explanation:

Answer:

a) 2 h 45 min

b) 2 h 50 min

c) 2 h 20 min

d) 3 h 20 min

Step-by-step explanation:

Answer:

a) hours: 9 hours 15 minutes

minutes: 555

b) hours: 9hours 10 minutes

minutes: 550

c) hours: 2hours 20 minutes

minutes: 140

d) hours: 3 hours 20 minutes

minutes: 200

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

Intersecting Chords Theorem: ab = cd

Step 1: Label our variables

a = x

b = x - 11

c = x - 8

d = x - 5

Step 2: Plug into theorem

x(x - 11) = (x - 5)(x - 8)

Step 3: Solve for x

x² - 11x = x² - 8x - 5x + 40

x² - 11x = x² - 13x + 40

-11x = -13x + 40

2x = 40

x = 20

Answer: x=20

Step-by-step explanation:

[tex]ab=cd[/tex]

[tex]x(x - 11) = (x - 5)(x - 8)[/tex]

[tex]x^2 - 11x = x^2 - 13x + 40[/tex]

[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]

[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]

Perimeter:

P = 4s = 4•17 = 68 cm

Answer:

[tex]\large \boxed{\sf \bf \ \ x^2-6x+45 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

You need to develop the expression.

[tex]y=(x-3)^2+36\\\\=x^2-2 * 3 * x +3^2+36\\\\=x^2-6x+9+36\\\\=x^2-6x+45[/tex]

Thank you.

Answer:

D

Step-by-step explanation:

Answer:

C = 35x pence

Step-by-step explanation:

1 pen costs 15 , thus x will cost 15x

1 ruler costs 20, thus x will cost 20x

Total cost (C) will then be

C = 15x + 20x = 35x pence

The total cost of pens and rulers, C = 35x pence

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cost 1 pens is 15.

Then, cost for x pen is 15x

Cost of 1 ruler is 20

Then, cost of x ruler is 20x

So, the total cost is

= 15x + 20x

= 35x

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Answer:

See below.

Step-by-step explanation:

[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]

First, use the co-function identity:

[tex]\sin(90-x)=\cos(x)[/tex]

We can turn the second term into cosine:

[tex]\sin(20)=\sin(90-70)=\cos(70)[/tex]

Substitute:

[tex]\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]

Now, use the sum to product formulas. We will use the following:

[tex]\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})[/tex]

Substitute:

[tex]\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)[/tex]

Use the even-odd identity:

[tex]\sin(-x)=-\sin(x)[/tex]

Therefore:

[tex]\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]

Replace the second term with the original term:

[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]

Proof complete.

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer: x=0.125 or 1/8

Step-by-step explanation:

[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]

add 3/4 on both sides

[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]

[tex]7x=6x+\frac{1}{8}[/tex]

subtract 6x on both sides

[tex]x=\frac{1}{8}[/tex]

Answer:

x = 1/8

Step-by-step explanation:

7x - 3/4 = 6x - 5/8

7x - 3/4 + 3/4 = 6x - 5/8 + 3/4

7x = 6x + 1/8

7x - 6x = 6x + 1/8 - 6x

x = (6x - 6x) + 1/8

x = 1/8

Answer:

C is a function

Step-by-step explanation:

We can use the vertical line test.  If a vertical straight lines passes through the graph more than one, it is not a function

A and B are not functions

C is a function

Answer:

6:30 pm

Step-by-step explanation:

Given the following :

Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively.

Time when all four machines gave out signal simultaneously = 5:00 pm

To find the time all four will give out the next simultaneous signal :

Take the lowest common factor of the four intervals :

L. C. M of 24, 27, 30, 50

Using the Lowest Common Multiple calculator :

L. C. M. = 5400

5400 seconds.

Adding 5400 seconds to the last time a simultaneous signal was produced :

5:00 pm + 5400 seconds

5400 seconds = (5400/60) = 90 minutes = 1hour 30 minutes

5:00 pm + (1 hour 30 minutes)

= 6:30 pm

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

768 libras de fuerza

Step-by-step explanation:

Tenemos que encontrar la ecuación que los relacione.

F = Fuerza necesaria para evitar que el automóvil patine

r = radio de la curva

w = peso del coche

s = velocidad de los coches

En la pregunta se nos dice:

La fuerza requerida para evitar que un automóvil patine alrededor de una curva varía inversamente con el radio de la curva.

F ∝ 1 / r

Y luego con el peso del auto

F ∝ w

Y el cuadrado de la velocidad del coche

F ∝ s²

Combinando las tres variaciones juntas,

F ∝ 1 / r ∝ w ∝ s²

k = constante de proporcionalidad, por tanto:

F = k × w × s² / r

F = kws² / r

Paso 1

Encuentra k

En la pregunta, se nos dice:

Suponga que 400 libras de fuerza evitan que un automóvil de 1600 libras patine alrededor de una curva con un radio de 800 si viaja a 50 mph.

F = 400 libras

w = 1600 libras

r = 800

s = 50 mph

Tenga en cuenta que desde el

F = kws² / r

400 = k × 1600 × 50² / 800

400 = k × 5000

k = 400/5000

k = 2/25

Paso 2

¿Cuánta fuerza evitaría que el mismo automóvil patinara en una curva con un radio de 600 si viaja a 60 mph?

F = ?? libras

w = ya que es el mismo carro = 1600 libras

r = 600

s = 60 mph

F = kws² / r

k = 2/25

F = 2/25 × 1600 × 60² / 600

F = 768 libras

Por lo tanto, la cantidad de fuerza que evitaría que el mismo automóvil patine en una curva con un radio de 600 si viaja a 60 mph es de 768 libras.

Answer:

the answer is 3

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

x+37+x+37+90 = 180

2x + 74 = 90

2x = 16

x = 8

Answer:

x=8°

Step-by-step explanation:

JI is a diameter and K is on the circumference of a circle.

∴∠JKI=90°

also KJ=KI=x(say)

tan (x+37)=y/y=1=tan 45

so x+37=45

x=45-37=8°

Answer:

d. (9, 13)

Step-by-step explanation:

5x-3y=6  /*6

6x-4y=2  /*(-5)

30x - 18y = 36

-30x +20y = - 10

            2y = 26

              y = 13

5x-3y=6

5x - 3*13 = 6

5x - 39 = 6

5x = 45

x = 9

(9, 13)

Answer:

x=36

Step-by-step explanation:

180-x=180-2x +180-4x

180-x = 360 -6x

5x =180

36 = x

Answer:

√137

Step-by-step explanation:

[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]

Step-by-step explanation:

Example 1:

a+c=b+c then a=b

First let the value of a and b be different (not equal)

a=5

b=7

c=10

a+c=b+c

5+10=7+10

15≠17

Example 2:

Let the value a and b be equal (the same)

a=5

b=5

c=10

a+c=b+c

5+10=5+10

15=15

So when,

a+c and b+c is equal, a and b are always equal.

Hope this helps ;) ❤❤❤

Answer:

a=b

Step-by-step explanation:

Reason:

a+c=b+c

a-b=c-c

c-c would be 0

if a-b=c-c=0

a-b=0

Only if a=b can a-b=0

You can also take it as:

b-a=c-c (a+c=b+c)

b-a=0=c-c

Therefore b=a

By the way even I am a BTS army

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

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Best way to solve this is by using

[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

[tex]where \: s = \frac{a + b + c}{2} [/tex]

s=(12+8+17)/2

=18.5

using the formulae

area =43.5

Answer:

3.03 • 10⁻³ is scientific notation

0.00303 is decimal form

Answer:

25 + 10h = 50+5h

Step-by-step explanation:

Black Diamond Ski Resort

25 + 10h

Bunny Hill Ski Resort

50+5h

We want when they are equal

25 + 10h = 50+5h

Answer:

10x + 25 = 5x + 50

Step-by-step explanation:

Answer:

Daily pay= $18

5 days pay = $90

Step-by-step explanation:

Archer's daily pay =p

Pay for 5 days= 5p

Gas = 1/2 of 5p

= 1/2 × 5p

= 5p/2

Water = $5

Balance = $40

5p = 5/2p + 5 + 40

5p - 5/2p = 45

10p -5p /2 = 45

5/2p = 45

p= 45÷ 5/2

= 45 × 2/5

= 90/5

P= $18

5p= 5 × $18

=$90

The equation to determine Archer's daily pay is

5p = 5/2p + 5 + 40

Divide both sides by 5

p = 5/2p + 45 ÷ 5

= (5/2p + 45) / 5

p= (5/2p + 45) / 5

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Greetings from Brasil...

In this case, we can say:

Domain = [0; 6]

Image = [3; 192]

see attachment