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

Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The following equations are equivalent:

2 + x = 5

x + 1 = 4

Negative 5 + x = negative 2

This is because, in each equation, x is the same variable, and it has the same value on both sides of the equation.

In the first equation, x is equal to 3.

In the second equation, x is equal to 3

In the third equation, x is equal to -3

Note that the equation 9 + x = 6 and x + (negative 4) = 7 are not equivalent as these equations have different values for x.

the solid below is made from cubes.
find its volume

Answers

Answer:

Step-by-step explanation:

Question 9 of 10
What is the product of the following numbers? Use a scientific calculator to
find the answer.
5.56 x 104 x 2.43 x 106
A. 2.23 x 10-2
OB. 1.97 x 10²1
C. 1.35 × 1020
OD. 1.35 x 10¹1

Answers

I’m not too sure, I got 148943.0592, so I don’t no which that equals

WILL MARK BRAINLIEST! please help with easy geometry problem!! :) and give explanation and steps too

Answers

Therefore , the solution to the given problem of triangle comes out to be x =20 degree and y = 20 degree.

Defining a triangle

In a plane, any three points can be joined to form triangles, that have 3 components and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

Given : 140 degree

Since it is a scalar triangle

two sides will have equal angle,

Thus ,

x=y

=> x+ x + 140 =180

=> 2x = 180-140

=> 2x =40

=> x =20

Therefore , the solution to the given problem of triangle comes out to be

x =20 degree and y = 20 degree.

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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

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]

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

Sallu car has an average fuel economy of 28 miles per gallon the capacity of the fuel tank is 16

Answers

The number of miles Sallu car will travel with 16 gallons fuel capacity if he travelled 28 miles per gallon is 448 miles.

How many miles can a full tank capacity travel?

If Sallu car can travel 28 miles using 1 gallon of fuel;

then, Sallu car will travel x miles using 16 gallons of fuel.

Based on the given task content; we can solve the task using the concept of ratio.

A ratio is a number representing a comparison between two named things.

It also refers to the relative magnitudes of two quantities usually expressed as a quotient.

Equate the ratio of miles travelled to gallons of fuel used

28 miles : 1 gallon = x miles : 16 gallons

28/1 = x / 16

28 × 16 = x × 1

448 = x

Therefore, Sallu car will travel 448 miles using 16 gallons of fuel.

Answers

By applying pythagorean theorem and perimeter formula, The answer is D 9+[tex]\sqrt{2}[/tex] +[tex]\sqrt{5}[/tex]

What is pythagorean theorem?

The Pythagorean theorem is a fundamental result in mathematics named after the ancient Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

What is perimeter?

Perimeter is a measure of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The formula for perimeter depends on the shape. For example, the perimeter of a rectangle is twice the sum of its length and width, while the perimeter of a circle is equal to its circumference.

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Ed’s birthday is less than 16 days away.

Part A
Ann writes the inequality d ≤ 16, where d equals the number of days, to represent this scenario.

Choose the best explanation for Ann’s error.
A.
Ann should have used 16d because it is less than 16 days away. B.
Ann should have switched the inequality symbol to greater than or equal to. C.
Ann should have switched the inequality symbol to not include 16 as a possible choice. D.
Ann should have used the not equals sign to compare the two sides of the inequality.
Part B
Select the correct inequality symbol to complete the inequality.

d
Choose...
16

Answers

Ann should have switched the inequality symbol to not include 16 as a possible choice. The correct answer would be an option (C).

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per the question, we have been given that Ed's birthday is less than 16 days

away and that Ann writes the inequality

d ≤ 16, where d equals the number of days, to represent this.

Thus, He should have switched the inequality symbol to not include 16 as a possible choice.

Hence, the correct answer would be an option (C).

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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.

Is this SSS, ASA, SAS, or AAS? I’m pretty sure it’s either sss or sas because there are already two sides but I’m not sure!! Please help:,)

Answers

Therefore , the solution of the given problem of congruent comes out to be in this case we have two side equal and one side common so it is sss

What in mathematics is a congruence?

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

How does SSS work?

SSS definitions. an autonomous government organization responsible for overseeing military conscription. Selective Service and Selective Service System are synonyms. independent agency kind. a federal agency that was established by a congressional act and is unrelated to the executive departments.

In this case we have two side equal and one side common so it is sss

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What is the equation in slope intercept form of the line that passes through the y-intercept (0, -4) and has a slope of 5?
O y = 5x + 28
O y = 5x + 4
O y = 5x-4
O y = 5x-28

Answers

The equation in slope-intercept form of the line that passes through the point (0, -4) and has a slope of 5 is y = 5x - 4.

What is slope intercept form ?

The form of a line's slope intercept is one of the most common ways to represent a line's equation. The slope intercept formula can be utilized to find a line's equation given its slope and y-intercept for a straight line ( the y-coordinate of the point where the line intersects the y-axis). For a line to exist, every point along the line must be satisfied by its equation. This straight line equation, which is represented as, can be resolved in a number of ways.

1. Slope-intercept form

2. Two-point form

3. Intercept form

4. Point slope form

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Joey wants to buy several tickets to the next Jastin Timberlake concert. Each ticket will cost $150. Create a table of values to show the cost of buying up to 5 tickets. Show your work in the box

Answers

Ticket #1 ║ Ticket #2 ║ Ticket #3 ║ Ticket #4 ║ Ticket #5

$150 $300 $450 $600 $750

Step-by-step explanation:

The table shows tickets #1-5, but if you want to go up to tickets #6 and #7, then Ticket #6 would be $900, and Ticket #7 would be $1,050. Due to each ticket being equivalent to $150, you get your answer by adding 150 for each ticket or multiplying 150 × 7.

The number of CD's sold since April 8 at a music store can be
modeled by the function N(d) = 12d +35 and the price per
CD can be modeled by P(d) = 0.3d2 - d+5, where d is
the number of days since April 8.
of revenue
According to this model, what is the total amount of rev
generated by the store's CD sales on April 18?

Answers

The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.Markup on selling price is 27 %.

How do you calculate markup on selling price?

The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage.

Below, you'll find various possible formats for the markup formula or equation.

The selling price given as = $ 15

The cost per CD is = $ 11

The total profit = Selling price - Cost

Total profit per CD = $ 15 - $ 11

Total profit per CD = $ 4

The markup on selling price is calculated as - Total profit ÷ Selling price × 100

Markup on selling price = $ 4 ÷ $ 15 × 100 =26.6666 % or 27 %.

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Tyrell is traveling to Chicago, Ilinois. He takes a cab service from the airport to his hotel.
The table shows the linear relationship between the number of miles the
Cab Fare
Number of Miles Total Fee
$15.00
5
$19.50
7
$22.50
10
$27.00
15
$34.50
What does the y-intercept mean in this situation?
O When the cab travels 0 miles, the total fee will be $1.50.
O When the cab travels 0 miles, the total fee will be $12.00.
O For every additional
mile the cab travels, the total fee increases by $1.50.
O For every additional mile the cab travels, the total fee increases by $12.00.

Answers

Y-intercept linear 12 shows that the total cost will be $12.00 when the taxi travels 0 miles.

How do you define a linear relationship?

the connection between two variables that, when plotted on the coordinate plane, forms a straight line. The term "linear expression" refers to both the linear equation and the expression that depicts a linear relationship.

(2, 15), (5, 19.50), (7, 22.50), and (10, 27) are the coordinates (15, 34.50)

We will obtain a straight line if we plot the points on the XY coordinate system. The line crosses the Y axis at 12.00, as can be seen. As a result, the y-intercept is 12.00, and its coordinate is (0,12)

The y-intercept in this case is 12, which indicates that the total cost will be $12.00 even if the taxi travels 0 miles.

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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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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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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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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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For which addition equation can you make a 10 to add?
24+14=
7+25=
76+3=
26+14=

Answers

Nothing is 10 for this equation

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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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

Lily received 50 postcards. 16% of them were from Thailand. After he received ostcards from Thailand, the percentage of Thailand postcard increased to 30%. How many Thailand postcards did he receive?

Answers

Answer:

Step-by-step explanation:

Final answer: Lily received 10 postcards from Thailand.

Explanation: Number of postcards=50

Percentage of postcards from thailand= 16

Number of postcards from Thailand= 16/100*50= 8

Now, he received some postcards from Thailand. Let the number of postcards received from Thailand be x. Therefore,

Number of postcards=50+x

Number of postcards from Thailand= 8+x

We know that the percentage of postcards from Thailand now is 30.

Therefore,

30=(8+x/50+x)*100

0.3(50+x)=8+x

15+0.3x=8+x

0.7x=7

x=10

Therefore, he received 10 postcards from Thailand.

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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).