Mathematics High School

Which is the distance betweeen parallel lines with the equations 3x - 5y = 1 and 3x-5y=-3

Answers

Answer 1

Answer:

Distance between the two parallel lines

[tex]d = \frac{4}{\sqrt{34} } = 0.6859[/tex]

Step-by-step explanation:

Step(i):-

Given the two equations are 3 x - 5 y = 1 ...(i)

and 3 x - 5 y = - 3....(ii)

Distance between the two parallel lines

[tex]d = \frac{|C_{1} - C_{2} | }{\sqrt{a^{2}+b^{2} } }[/tex]

Given equations

a = 3 , b = -5 and C₁ = 1 and C₂ = -3

Step(ii):-

Distance between the two parallel lines

[tex]d = \frac{|C_{1} - C_{2} | }{\sqrt{a^{2}+b^{2} } }[/tex]

[tex]d = \frac{|1 - (-3)| }{\sqrt{9+25 } }[/tex]

[tex]d = \frac{4}{\sqrt{34} }[/tex]

Final answer:-

Distance between the two parallel lines

[tex]d = \frac{4}{\sqrt{34} }[/tex]

Answer 2

Answer:

The Answer is C. The person above is almost correct, but they did not simplify to 2sqrt34/17

Step-by-step explanation:

Related Questions

PLS HELP ASAP! A decoration is packed in a box shaped like a cube. The decoration has a volume of 651 cm3. Approximately how much empty space remains in the box?

Answers

This question is incomplete.

Find attached to this question the diagram of the cube.

Reference for the attached image: This diagram was obtained from Education Quality and Accountability Office (EQAO) PDF

Answer:

128cm³

Step-by-step explanation:

The diagram of the box shows it has a side length of 9.2cm

Volume of a cube =( Length)³

Volume of a cube =( 9.2cm)³

= 778.688cm³

We are told in the question that the decoration packed in the cube has a volume of 651 cm³.

The amount of empty space remaining in the box is calculated as:

778.688cm³ - 651cm³

= 127.688cm³

Approximately to the nearest whole number = 128cm³

Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

Answers

Answer:

11.67

Step-by-step explanation:

Data given in the question

∠ADC = 42°

∠BAC = 68°

Let us assume that AC be Y

Now

In ΔACD

tan 42° = AC ÷ CD = Y ÷ x ...............................(i)

In ΔACB

tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)

Now take the value of Y from the equation (ii)

Y = 26 ÷ Tan 68° ...................... (iii)

Now place the value of Y in equation (i)

So,

Tan 42° = 26 ÷ tan 68° × X

X = 26 ÷ tan 68° × Tan 42° ......................(iv)

Now placing the values of tan 42° and tan 68° in equation (iv)

So,

X = 26 ÷ 0.900 × 2.475

= 11.67

The tan 42° = 0.900

And, the tan 68° = 2.475

PLZ HURRY How many solutions does this system have? y = 3 x minus 5. y = negative x + 4.

Answers

Answer:

one is correct.

Step-by-step explanation:

because it have one solution when you graph it

Answer:

One solution (2.25,1.75)

Step-by-step explanation:

Well first we need to graph the following

[tex]y=3x-5[/tex]

[tex]y=-x+4[/tex]

So look at the image below.

So looking at the image below we can tell that the system only has one solution (2.25,1.75).

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

x-2 is a factor so x = 2 is a root of f(x)

This is because f(x) = (x-2)*g(x) for some polynomial g(x). We don't have to worry about what g(x) is equal to as it doesn't affect the status of the root we're after.

So,

f(x) = 0

(x-2)*g(x) = 0

x-2 = 0 or g(x) = 0

x = 2 or g(x) = 0

This shows how the factor x-2 leads to the root x = 2

Therefore, f(2) = 0

Answer: Choice D

Answer:

F ( 2 ) = 0

Last one is the correct option.

Step-by-step explanation:

A root or zero of a polynomial are the value (s) of X that cause the polynomial equal to zero.

y = 0

It is x- intercept. The root is the x-value.

Hope this helps...

Good luck on your assignment..

A little help would be nice :')

Answers

Answer:

(2,6)

Step-by-step explanation:

x+2y = 14

y = x+4

Substitute x+4 into the first equation for y

x+2(x+4) = 14

Distribute

x+2x+8 = 14

3x+8 = 14

Subtract 8 from each side

3x+8-8 = 14-8

3x = 6

Divide by 3

3x/3 = 6/3

x = 2

Now solve for y

y = x+4

y =2+4

y =6

(2,6)

Answer:

D. (2, 6)

Step-by-step explanation:

Put y as x+4 in the first equation and solve for x.

x + 2(x + 4) = 14

x + 2x + 8 = 14

3x = 14 - 8

3x = 6

x = 2

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

y = 2 + 4

y = 6

Tanya can wash a car and vacuum its interior in 22 hours. Pat needs 55hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car?

Answers

Answer:

1 hour 26 Minutes

Step-by-step explanation:

Tanya needs 2 hours to do the job.

Pat needs 5 hours to do this same job.

Tanya's rate [tex]=\frac{1}{2}[/tex]

Pat's rate[tex]=\frac{1}{5}[/tex]

Let the number of hours it will take both of them =x

Rate when two of them work together [tex]=\frac{1}{x}[/tex]

Therefore:

[tex]\frac{1}{2}+\frac{1}{5}=\frac{1}{x}\\$Taking lowest common multiple$\\\frac{5+2}{10}=\frac{1}{x}\\\\\frac{7}{10}=\frac{1}{x}\\\\$Cross multiply$\\7x=10\\x=1.43$ hours[/tex]

[tex]0.43 X 60 =25.8 \approx 26$ minutes[/tex]

Therefore: 1.43 hour = 1 hour 26 Minutes

It will take both of them approximately 1 hour 26 minutes to the job.

On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?

Answers

Answer:

The temperature after 10 hours is -9 ºF.

Step-by-step explanation:

This statement can be translated mathematically as follows. The temperature after 10 hours from sunrise is:

[tex]T = -10\,^{\circ}F + \left(1\,\frac{^{\circ}F}{h} \right)\cdot (7\,h)+ \left(-2\,\frac{^{\circ}F}{h} \right)\cdot (3\,h)[/tex]

[tex]T = -9\,^{\circ}F[/tex]

The temperature after 10 hours is -9 ºF.

Answer:

The answer is in the picture

Step-by-step explanation:

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the speed of the truck.

Answers

Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

[tex]t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}[/tex]

The sum of these times must be equal to the total time of the trip, therefore:

[tex]t_{stage1} + t_{stage2} = 5[/tex]

[tex]\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10[/tex]

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Find the product of the following.
i) –5a2bc, 6ab, 8abc2
ii) –3x2y and (5y – xy)
iii) x2y2z2 and (xy – yz + zx)
iv) (p+6)and (q–7)
v) (2x+7)and(x2 –5x+6) vii) (x + y + 5) and (2x – 2y – 3)
PLEASE I NEED THE ANSWER NOW

Answers

Answer:

i) -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) -15x²y² + 3x³y²

iii)x³y³z³ - x²y³z³ + x³y²z³

iv) pq -7p+6q-42

v)9x²-33x +42

vii) 2x² - 2y² + 7x -13y - 15

Step-by-step explanation:

To find product here means to multiply the algebraic expressions together

i) (–5a²bc)×(6ab)×(8abc² )

multiply like terms together

= -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) (–3x²y) ×(5y – xy)

(–3x²y)×(5y) – (–3x²y) ×(xy)

multiply like terms together