a truck and a car drive uniformly among the expressway from city a to city b. The truck leaves at 09:15 am and arrives at 1:15 pm. The car leaves at 10:00 am and arrives at 12:45 pm. At what times does the car overtake the truck? please help

Answers

Answer 1

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.


Related Questions

Victor is in the 28% tax bracket.
a. How much will a $900 tax credit save him?
b. how much will a $900 charitable contribution save him if he itemized his deductions?​

Answers

Incomplete question. I've made some assumptions to provide clarity.

Answer:

a. $45,743.07

b. $44,843.07

Step-by-step explanation:

Let's assume Victor is a single filer with an income of $100,000.

Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:

- 10 percent on the first $9,325 = 10% x 9525 =$932.5

- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6

- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25

- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72

Total=  $46,643.07

Minus $900 tax credit= $46,643.07-$900= $45,743.07

Minus $900 charitable contribution = $45,743.07-$900= $44,843.07

According to the histogram below, how many people took the test? 39 9 16 23

Answers

The correct answer is D. 23

Explanation:

Histograms similar to other graphs represent numerical information, usually by using bars, as well as ranges. For example, in the case presented the information presented belongs to the scores obtained in a test, which are shown using ranges. Moreover, it is possible to know the total of people that took the test by adding each of the frequencies, as the frequency in the y-axis shows the number of times the range repeated and it is expected each grade registered belongs to 1 person. This means the total of people is equal to 2 (score from 60-69) + 9 (score from 70-79) + 7 (score from 80-89) + 5 (score from 90-99) = 23 people.

Answer:

the answer is 23

Step-by-step explanation:

hopes this helps:)

WHY IS THERE ANY HELP? PLEASE Solve the system of equations by using the substitution method. [tex]\left \{ {{x+y=6} \atop {x=2y}} \right.[/tex] Is there a solution, no solution, or infinite number? If there's a solution, what's the ordered pair?

Answers

Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

HELLPPPPPPPPPPPPP Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract 60 from each side of the equation. Next, add 64 to each side of the equation to complete the square. Now, write x² - 16x + 64 = -8 as ✔ (x - 8)² = -8

Answers

Answer:

x = 8 ± 2i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² - 16x + 60 = - 12 ( subtract 60 from both sides )

x² - 16x = - 72

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64, thus

(x - 8)² = - 8 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )

x = 8 ± 2i[tex]\sqrt{2}[/tex]

The solution of the given expression is ±2√2i+8

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that

x² - 16x + 60 = - 12

Then subtract 60 from both sides;

x² - 16x = - 72

To complete the square then add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64,

(x - 8)² = - 8 ( take the square root of both sides )

x =  ±2√2i+8

Learn more about equations here;

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Which system of equations represent the matrix shown below?

1 2 -1| 8
-1 0 3| 15
1 -2 4| 18

A. x + 2y + z =8
x + y + 3z =15
x + 2y + 4z =18

B. x + 2y + z =8
x + 3z =15
x + 2y + 4z =18

C. x + 2y - z =8
-x + y + 3z =15
x - 2y + 4z =18

D. x + 2y - z =8
-x + 3z =15
x - 2y + 4z =18

Answers

Answer:

the solution to the problem is D

∫ ex (sec x + tan²x) dx = ? a) eˣsec²x b) eˣsecx c) eˣtan²x d) eˣtanx

Answers

None of these options seem to be correct. You can check each result by differentiation:

[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]

[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]

[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]

[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]

But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...

Let a and b be real numbers where a=/b=/c=/0 which of the following functions could represent the graph below?

Answers

Answer: The second option;  y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

Ok, we have that a and b are real numbers different than zero.

In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:

y = x*(x - a)^3*(x - b)^3

then when x = 0 we would have:

y = 0*(0-a)^3*(0-b)^3 = 0

But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.

So the remaining options are:

y = (x - a)^2*(x-b)^4

y = (x - a)^5*(x - b)

Now, another thing you can see in the graph is that it is always positive.

Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.

(For example, if x > a and x < b we would have a negative value for y)

Then the only remaining option is y =  (x - a)^2*(x-b)^4

Answer:

B.y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

EDGE 2020 Brainliest please

what is 3141 times X. x=5783978

Answers

Answer:

18167474898

Step-by-step explanation:

I used a calculator.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Smoothing a time series of observations A. is a form of statistical cheating. B. allows statisticians to use less data than would otherwise be required. C. renders the resultant forecast unusable. D. is used to reveal an underlying pattern in the data.

Answers

Answer:

D. is used to reveal an underlying pattern in the data.

Step-by-step explanation:

Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.

Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.

Help me fast please

give the coordinates of the
foci,vertices,and convertices of the ellipse with equation x²/169 + y²/25 = 1​​

Answers

Answer:

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Step-by-step explanation:

For this problem we have the following equation given:

[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]

If we compare this with the general expression of an ellipse given by:

[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

A parallelogram has side lengths of 13 and 17 and an
angle that measures 64º.
What is x, the length of the diagonal, to the nearest
whole number?

Answers

Answer:

[tex] x = 16 [/tex]

Step-by-step explanation:

x = length of diagonal, can be calculated using the Law of Cosines as explained below:

a² = b² + c² - 2bc(cosA),

Where,

a = x

b = 17

c = 13

A = 64°

Plug in the values into the formula:

[tex] x^2 = 17^2 + 13^2 - 2(17)(13)*cos(64) [/tex]

[tex] x^2 = 289 + 169 - 442*0.4384 [/tex]

[tex] x^2 = 458 - 193.77 [/tex]

[tex] x^2 = 264.23 [/tex]

[tex] x = \sqrt{264.23} [/tex]

[tex] x = 16.255 [/tex]

Length of diagonal, [tex] x = 16 [/tex] (to nearest whole number)

Sam invest $4000 in an account that compounds interest continuously and earns 5.5% how long will it take for his money to reach $80,000 round to the nearest 10th of a year

Answers

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

I have a total of 10 gigabytes of data on my computer, x gigabytes are movies, pictures take up half the amount of space that movies do and the rest is music. How many gigabytes of music is stored on my computer?

Answers

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

The amount of gigabytes of music stored on the computer is:

[tex]y = 5 - x[/tex]

In which x is the amount stored in movies.

We solve this question representing the amount of music as a variable, that I will call y.

The total amount of data is 10 gigabytes.

Division of the 10 gigabytes:

Half in pictures, that is, 10/2 = 5 gigabytes.

x are movies.

The rest, y, are music.

Thus, since the sum of this all is 10, we have that:

[tex]5 + x + y = 10[/tex]

[tex]y = 10 - 5 - x[/tex]

[tex]y = 5 - x[/tex]

Thus, the amount of gigabytes of music stored on the computer is [tex]y = 5 - x[/tex], considering x as the amount of gigabytes of movies stored.

A similar question is found at https://brainly.com/question/22789267

WHY CAN'T ANYONE HELP ME? PLEASE What one is the standard form of the equation y = – 1/4 x – 2? A. x + 4y = 8 B. x + 4y = – 2 C. x + 4y = – 8 or D. –x + 4y = – 8

Answers

Answer:

C. x+4y=-8

Step-by-step explanation:

The standard form of an equation is Ax+Bx=C

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

Multiply 4 by both sides

4y= -x-8

1+4y= -8

Marcus made a sail for his toy boat. If the sail is 5 inches long and the top angle of the sail is 40°, what is the width of the bottom of the sail (w) to the nearest tenths place?

Answers

Answer:

4.2 in

Step-by-step explanation:

let us first visualize the sail as a triangular shape

the angle of the triangle from top is 40°

the height of the triangle is give as 5 in

we can apply SOH CAH TOA to solve for the base of the sail

the opposite = the base of the sail

the adjacent = the height of the sail= 5 in

therefore

Tan∅= Opp/Adj

Tan(40)= Opp/5

Opp= Tan(40)*5

Opp= 0.8390*5

Opp= 4.195 in

Hence the width of the sail is 4.2 in to the nearest tenths

Answer:

4.2

Step-by-step explanation:

A new furnace for your small factory will cost $29,000 and a year to install, will require ongoing maintenance expenditures of $1,200 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 2,800 gallons per year. Heating oil this year will cost $2 a gallon; the price per gallon is expected to increase by $0.50 a year for the next 3 years and then to stabilize for the foreseeable future. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value. The discount rate is 6%.

Answers

Answer:

Net present value is $61,058.

Step-by-step explanation:

Net present value is the difference between present value of cash inflows and the present value cash outflows over the period of time. NPV method is used in capital budgeting to analyze profitability of the project.

Less: initial cost is $29,000

Add: Year 1: Cost saving due to new furnace is $5,600 (2,800 oil gallons * $ 2 per gallon)

Year 2: Cost saving due to new furnace is $7,000 (2,800 oil gallons * $ 2.50 per gallon)

Year 3- 20: Cost saving due to new furnace is $8,400 (2,800 oil gallons * $ 3 per gallon)

Less : Maintenance expenditure is $1,200

The furnace will benefit for 20 years and the price per gallon will increase by $0.50 year.

The annuity factor is applied at discount factor of 6% and then present value of each cash inflow and outflow is calculated. The net present value is $61,058.

expand(x+y2)2 plzzzzzzzzzzzzzzzz​

Answers

Answer:

[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]

Hope it helps!!❤❤Please mark me as the brainliest!!!

Thanks!!!!

In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠CAB ≅ ∠SAB ∠CAS ≅ ∠BAS

Answers

Answer:

∠CAB ≅ ∠SAB is not true

Step-by-step explanation:

CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.

So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

sap

Step-by-step explanation:

What is the missing term in this arithmetic sequence? 9, 14, 19, __, 29, 34, …

Answers

Answer: 24 because you add 5 for every number ex: 9+5=14

Answer:

24

Step-by-step explanation:

The difference can be calculated by subtracting the second term with the first term.

d = 14 - 9

d = 5

The difference is 5.

Add 5 to 19.

19 + 5 = 24

Solve for X in the equation, where X = 3A − 2B

Answers

Answer:

work is shown and pictured

Answer:

Image is attached.

Solve the right triangle.
A = 48.31º. c = 49.9​

Answers

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]

Which expression is a cube root of -2

Answers

Answer:

∛-2

Step-by-step explanation:

The aritmetic expressión is:

∛-2

The graph of a linear function is given below. What is the zero of the function?

Answers

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

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

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

[tex]y=-\frac{3}{2}x-3[/tex]

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire

Answers

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

In the question it is given that the sprinklers activate correctly or not independently. The number of outcomes are two i.e. sprinklers activate correctly or not.

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

6t+7−2+t combine the like terms to create an equivalent expression

Answers

Answer:

7t+5

Step-by-step explanation:

Answer:

7t +5

Step-by-step explanation:

6t+7−2+t

Combine like terms

6t+t  + 7-2

7t +5

8. Which statement is always true?
A. 9 times a number is always odd.
B. 9 times a number is always even
C. 10 times a number is always odd.
D. 10 times a number is always even.​

Answers

Answer:

D

Step-by-step explanation:

Any number multiplied by an even number will always be even. 10 is an even number.

Answer:

d. 10 times a number is always even

Step-by-step explanation:

multiples of 9 contain 81 and 36 which one is even and the other is odd

multiples of 10 ONLY contain even numbers because   the unit digit for a multiple of 10 is 0.

So whenever you multiply a number by 10 it will be even

Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. ∫ 3 0 | 8 x − 10 | d x

Answers

Please find attached

thank you

The area of Integral is 19 sq units.

What is Integral?

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives. The terms antiderivative and primal are additional terms for integral.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

Given:

∫ 3 0 | 8 x − 10 | d x

Now, the graph touches the x axis  

when 8x- 10 = 0

x= 10/8

x= 5/4

and, When x = 0, y = 10.

So, the limit range will be x = 0 to x = 5/4.

Now, Area of First triangle

= 10 x 5/4 x 1/2

= 25/4

and, Area of second triangle

= 14 x (3- 10/8) x 1/2

= 7 x 7/4

= 49/4

Hence, the total Area = 25/4 + 49/4 = 19 sq. units

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Please help! I’ll mark you as brainliest if correct

Answers

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Which set of integers does NOT represent the lengths of the sides of a triangle? A. {6,6,11} B. {9,10,11} C. {4,8,12} D. {4,7,9}

Answers

Answer:

C

Step-by-step explanation:

I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.

So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.

Consider the line y=2x-7 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answers

Answer:

The slope of the given line is 2

Answer -1/2 is the line perpendicular

Step-by-step explanation:

This can be rewritten in fraction form as 2/1 since x/1 = x.

Answer: parallel line = 2x, perpendicular line = -1/2x

Explanation:

In order to have a parallel line:

The slope have to be the same as the original which is 2x

In order to have a perpendicular line:

The slope have to be the opposite reciprocal of the original slope

Which is -1/2x
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