Mathematics College

The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is

Answers

Answer 1

Answer:

Step-by-step explanation:

eq. of line x-3y-6=0

3y=x-6

y=1/3 x-6/3

y=1/3 x-2

its slope m1=1/3

y=2x+5

slope m2=2

if α is the angle between the lines then

[tex]tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ\\[/tex]

Related Questions

For a certain kind of plaster work, 1.1 cu yd of sand are needed for every 100 sq yd of surface. How much sand will be needed for 280 sq yd of surface
cu yd of sand will be needed for 280 sq yd of surface.

Answers

308 cubic yards of sand will be needed for 280 square yards of surface.

How to find the cubic yards?

If 1.1 cubic yards of sand are needed for every 100 square yards of surface, we can find the amount of sand needed for 280 square yards of surface using the proportion:

1.1 cu yd / 100 sq yd = x cu yd / 280 sq yd

To find the value of x, we can cross-multiply and solve for x:

1.1 cu yd * 280 sq yd = x cu yd * 100 sq yd

x = 1.1 cu yd * 280 sq yd / 100 sq yd

x = 308 cu yd

So, 308 cubic yards of sand will be needed for 280 square yards of surface.

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What is the properties of (10c - 4) + 11d?

Answers

Answer:

10c-4+11d Welcome :D

Step-by-step explanation:

Identify the value of x that makes each pair of ratios equal
5:15 and x:3

Answers

The ratio for 5 / 15 based on the information is 1:3. The value of x is 1.

How to illustrate the ratio?

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

The ratio for 5 / 15 will be:

= 5 / 15

= 1 / 3

= 1:3

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Write an equation of the line that passes through each pair of points (9,2) (-2,6)

Answers

y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6).

What is equation?

A group of numbers and variables without an equal sign are known as a numerical expression. A set of numbers and variables with an equal sign is referred to as an equation.

Once you are familiar with these terms, you will realise that an equation is just two expressions joined by an equal sign. You can also write expressions, equations, and simplify equations.

To find an equation of the line that passes through each pair of points (9,2) (-2,6) we need to find slope and convert it to y-intercept form

Slope formula = y - y₁ = m(x - x₁)

Putting the values in the formula we get

2 - 6 = m(9 - (-2))

-4 = m(11)

m = -4/11

As we have found slope, we can find the slope intercept form i.e.

y - 2 = -4/11(x -9)

y = (-4/11)x + 3.27 + 2

y = (-4/11)x + 5.27

Thus, y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6)

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1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval
-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.

Answers

On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1

What is factor?

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

The factors of 5 are -

5and 1

as 5 = 5 X 1

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How many 5 card hands are possible with a 52-card deck?

Answers

How many 5-card hands are possible with a 52-card deck?

Answer:

Only 10, there will still be 2 cards left though.

Step-by-step explanation:

You're welcome.

Which of the following is the product of the rational expressions shown
below?
2/x+1 • 5/3x

A. 5(x+1)/6x
B. 5/x^2+3
C. 10/3x+3
D. 10/3x^2+3x

Answers

Answer:

D. 10/3x^2+3x

Step-by-step explanation:

The product of the two rational expressions is:

(2/x+1) * (5/3x)

Multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:

(2*5) / (x+1) * (3x)

Which simplifies to:

10 / (x^2 + x)

So the correct answer is:

D. 10/3x^2+3x

You put $600 in an account. The account earns $31 simple interest in 10 months. What is the annual interest rate? need % answer

Answers

The annual interest rate that yields $31 from $600 in 10 months is 6.2%

What is an interest earned on an amount?

An interest is the amount earned by placing a sum of money in a savings account or in an investment.

The principal amount you put in the account, P = $600

The amount (interest) earned in 6 months, I = $31

The duration over which the interest of $31 is earned, T = 10 months

The annual interest rate is found as follows;

The annual interest rate is the interest rate per year

The number of months in a year = 12 months

The formula for the simple interest, I, is presented as follows;

I = P·R·T

Where;

I = The simple interest earned

P = The principal amount saved in the account

R = The annual interest rate

T = The time duration the amount was saved in years

12 months = 1 year

Therefore; 10 months = (1/12) × 10 year = (5/6) year

The time, T, of 10 months = (5/6) year

31 = 600 × R × (5/6)

R = 31/(600 × (5/6)) = 0.062

0.062 in percentage is 0.062 × 100 = 6.2%

The annual interest rate, R = 6.2%

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Important

Given AABC ~ ADE F, determine the following information.

Determine the measure of LB. Show the work that leads to your answer.

Determine the length of EF. Show the work that leads to your answer.

Answers

Answer:

m∠B = 83°

EF = 10

Step-by-step explanation:

Two triangles are similar if their corresponding angles are the same size.

Therefore if ΔABC ~ ΔDEF then:

∠A ≅ ∠D = 24° ∠B ≅ ∠E∠C ≅ ∠F = 73°

Interior angles of a triangle sum to 180°:

⇒ m∠A + m∠B + m∠C = 180°

⇒ 24° + m∠B + 73° = 180°

⇒ m∠B + 97° = 180°

⇒ m∠B = 83°

In similar triangles, corresponding sides are always in the same ratio.

Therefore if ΔABC ~ ΔDEF then:

⇒ AB : DE = BC : EF = CA : FD

⇒ 12 : DE = 8 : EF = 16 : 20

Therefore, to find the length of EF:

[tex]\implies \sf 8 : EF = 16 : 20[/tex]

[tex]\implies \sf \dfrac{8}{EF} = \dfrac{16}{20}[/tex]

[tex]\implies \sf 8 \cdot 20= 16 \cdot EF[/tex]

[tex]\implies \sf160= 16 \cdot EF[/tex]

[tex]\implies \sf EF=\dfrac{160}{16}[/tex]

[tex]\implies \sf EF=10[/tex]

Solve the following problem using the substitution method. Please make sure to show all of your work.

6x - 3y = 1
y = -2x - 5

Answers

Answer:

x=-7/6, y=-8/3. (-7/6, -8/3).

Step-by-step explanation:

6x-3y=1

y=-2x-5

-------------

6x-3(-2x-5)=1

6x+6x+15=1

12x+15=1

12x=1-15

12x=-14

x=-14/12=-7/6

y=-2(-7/6)-5=7/3-5=7/3-15/3=-8/3

Multiply. Write your answer as a decimal.
-0.05 × (-0.5)

Answers

The solution for the given decimal multiplication is 0.025.

What are decimal numbers and how do you multiply them?

To multiply two decimal numbers, first multiply the values without the decimal points.

The digits in the factors that follow the decimal point should now be added together.

Following that, the dot should be placed in the product so that it has the same number of digits as the total number of factors.

If there are more decimal places than digits in the number, place zeroes immediately after the dot.

If there are more decimal places present compared to digits in the product, fill the decimal places with zeroes immediately after the dot.

For the given question, multiply -5 * -5 = 25

Now the total digits after the decimal point in factors are 3.

But there are only 2 digits in 25.

So fill the decimal place with a zero.

Therefore the product of given decimal numbers is 0.025.

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What is 4, 700, 000 in scientific notation?
A. 4.7 x 105
B. 4.7 x 106
C. 4.7 x 107
D. 4.7 x 108

Answers

It would be 4.7 x 10^6
You would move the decimal place 6 numbers to the left.

Answer:

4,700,000 can be written as 4.7 × 10⁶ in scientific notation

Scientific notation:Scientific notation, also called power of 10 notation.It is a method of writing extremely large and small numbers.

For Example:

10 = 1 × 10¹ 100 = 1 × 10² = 10²1200 = 1.2 × 10³

Here,

1200 can also be written as

12 × 100

we know that, 100 = 10²

so,

12 × 10²

Remember

Decrease the base increase the power and vice-a-versa

1.2 × 10³

3 / 3/4=, 5 / 3/4=, 8 / 4/7=, 6 / 3/5=, 2 / 5/8=, and 4 / 8/9= simplify them all

Answers

On simplifying the values obtained for the fractions are - 3 / 3/4= 4, 5 / 3/4= 6.66, 8 / 4/7= 14, 6 / 3/5= 10, 2 / 5/8= 3.2 and 4 / 8/9= 4.5.

What is fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The first fraction is 3/(3/4).