Answers
The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.
What is a straight line called?An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.
A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.
y=mx+c
Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.
[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]
[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]
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Related Questions
Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)
Answers
Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)
What is Midpoint of LineThe midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Substituting the values into the formula;
M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2
M(x , y) = -6/2, 0/2
M(x, y) = -3, 0
The coordinate of midpoint is (-3, 0)
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3a+2b
Help me please
I can’t do it
Answers
Answer:
Question is not clear
Step-by-step explanation:
Question 4 of 10
Find the difference. Enter your answer in the box below as a fraction, using
the slash mark (/) for the fraction bar.
8-7
14 14
Answers
There is a 2/17 difference between 16/17 and 14/17 as 17 is the shared denominator of both fractions.
what is fractions ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
Given,
To get the difference between 16/17 and 14/17, discover their common denominator first.
17 is the shared denominator of both fractions.
To solve, multiply the result by the numerator of the fractions, then divide the sum by the common denominator:
16 - 14/17 (16 - 14) = 2/17 is the solution.
Therefore, there is a 2/17 difference between 16/17 and 14/17.
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Which symbol makes the number sentence true?
-2.5O 10/4
A. <
B. >
C. =
Answers
Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry
Step-by-step explanation:
Which sentence is incorrect?
A. -3 > -8
B. -4 > -7
C. -2/5=0.4
D. -5/2=0.4
Answers
Answer:
D
Step-by-step explanation:
4.75% as a fraction in simplest form
Answers
Answer: 19/400
Step-by-step explanation:
4.75% = 4.75/100 (in fractions)
= 475/10000 (multiply by 100 for both the numerator and denominator)
= 19 / 400 (divide by 25 for both the numerator and denominator)
How do I know it is 25 for the last step?
Obtain the highest common factor of 475 and 10000. The highest common factor of these two numbers is 25.
Can someone answers this
Answers
Answer: ( see image )
Step-by-step explanation:
Please help me, I need help asap !! I can’t figure it out
Answers
when you make them have a common denominator you get 30/35 wants to get down to 7/35
when you subtract them you get 23/35, meaning you have to take off 23/35 inches of the pipe in order to get it to 1/5
the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities
Answers
The number of months Mark can have the phone is given by the equation
A = 11.4 months
What is an Equation?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.
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 data ,
Let the number of months be represented as = A
Now , the equation is
Now , the total amount with Mark = $ 146.43
The initial amount for the smartphone = $ 33
The amount per month for 2GB is = $ 9.95
So , the amount for A months = $ 9.95 ( A )
So , the equation will be
Initial amount for the smartphone + the amount for A months = total amount with Mark
Substituting the values in the equation , we get
33 + 9.95 ( A ) = 146.43 be equation (1)
On simplifying the equation , we get
Subtracting 33 on both sides of the equation , we get
9.95 ( A ) = 113.43
Divide by 9.95 on both sides of the equation , we get
A = 11.4 months
Therefore , the value of A is 11.4 months
Hence , the number of months is 11.4 months
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Find the equivalent measures. Express as a decimal
(a) 250 cm =
Answers
The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.
The sum of two angles is 85, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.
Answers
Therefore , the solution of the given problem of angles comes out to be equation : x+ y =85°.
'
An angle is what?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.
Here,
Given :
Let two angles be x and y is
=> x+ y =85°
So, the equation is represented as x+ y =85°.
Therefore , the solution of the given problem of angle comes out to be equation : x+ y =85°.
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The physician orders 150 mg/5 kg. The patient’s weight is 75 kg. How many grams of medication has the physician ordered?
Answers
Answer: 2.25 grams
Step-by-step explanation:
In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.
[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex] [cross multiply]
[tex]11250=5x[/tex] [divide both sides by 5]
[tex]x=2250mg[/tex]
We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.
[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex] [cross multiply]
[tex]1000y=2250[/tex] [divide both sides by 1000]
[tex]y=2.25[/tex]
Therefore, we need to give 2.25 grams.
PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.
How many pounds of cement does he use?
Answers
The pound of cement used based on the information will be C. 2 pounds.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.
The pound of cement used will be:
Gravel = 1 2/3 × 3
= 5 pounds
Cement used will be:
= 2/5 × 5.
= 2 pounds.
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[NEED HELP ASAP] How do I find the surface area of the shape in the picture?
Answers
When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.
How do I find the surface area of the shape in the picture?The surface area of the shape in the picture is approximately 300.4 cm².To calculate this, use the formula for the surface area of a triangular prism, which is SA = 2(bhl) + 2(bh + la).In this case, b = a = 4 cm, h = 12 cm, and l = s = 4.6 cm, so the calculation is SA = 2(4 x 12 x 4.6) + 2(4 x 4.6 + 4 x 12) = 300.4 cm².To calculate the surface area of the shape in the picture, you need to first calculate the area of the rectangle, triangle and circle.The rectangular portion has a height of 12 cm and a length of 4 cm, so the area is 48 cm^2.The triangle has a height of 12 cm and a base of 4 cm, so the area is 24 cm^2. The circle has a radius of 4.6 cm, so the area is 66.48 cm^2. Therefore, the total surface area of the shape is 138.48 cm^2. To calculate the surface area, you need to add the area of each of the components.For example, the area of the rectangle is 48 cm^2, the area of the triangle is 24 cm^2, and the area of the circle is 66.48 cm^2.The total surface area of the shape is then the sum of all these components, which is 138.48 cm^2.In this example, the rectangular portion, triangle and circle each had to be calculated separately in order to find the overall surface area.To learn more about the surface area of a of the prism refer to:
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2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km
Answers
It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:
Speed = distance / time
Distance = Speed * time
The spaceships are moving at 110000 km/h
The distance covered by each in x hours is:
Distance = 110000 * x = 110000x
Since they are 7100 km apart, hence:
110000x + 110000x = 7100
220000x = 7100
x = 0.03227 hours = 116.18 seconds
It would take 116.18 seconds for the spaceships to meet.
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Can somebody help me? I need help please
Answers
By using concept of angle relationship, we get x equal to 27°.
What are angle relationships defined as?We compare the position, measurement, and congruence of two or more angles when we talk about angle relationships. For instance, two pairs of vertical angles are created when two lines or line segments intersect.
∠BAF+∠EAF=180°
∠EAF=180° - 138°
∠EAF=42°
Since, ∠EAF and ∠BAC are vertically opposite angle,
Hence,
∠EAF = ∠BAC =42°
Again,
∠EAD+∠DAC+BAC=180°
4x+30°+42°=180°
4x=180°-72°
4x=108°
x=27
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hich are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representations of the inequality are
-6x + 15 < 10 - 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Solving inequality and determining the correct representationsFrom the question, we are to determine the correct representations of the inequality
From the given information,
The given inequality is
-3(2x - 5) < 5(2 - x)
To determine the correct representations, we would proceed to solve the inequality
Solving the inequality
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x
This is one of the representations of the inequality
Then,
Collect like terms
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
Multiply through by -1
x > 5
If the solution is represented on a number line, we would have a number line from negative 3 to 3 with an increments of 1 and an open circle at 5 and a bold line starts at 5 and is pointing to the right.
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How do I write an equation for this relationship (where y represents the number of blocks and x represents the stage number).
Answers
The equation of the line is y = 4x + 1 , where the slope of the line is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of blocks be y
Let the stage number be x
Let the first point be represented as P = P ( 1 , 5 )
Let the second point be represented as Q = Q ( 2 , 9 )
Now , the slope of the line between the points be
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 5 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 4 ( x - 1 )
On simplifying the equation , we get
y - 5 = 4x - 4
Adding 5 on both sides of the equation , we get
y = 4x + 1
Therefore , the value of A is y = 4x + 1
Hence , the equation of line is y = 4x + 1
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what's the y intercept of y=-2x+ -20
Answers
Answer: y=20-2x
Step-by-step explanation:
If a jacket is marked up 75% to be $350 and a month later is 20% off and then two weeks later is 30% off how much money did the company gain or lose
PLEEEEASE HELP!!!!!
Answers
280 AND 245 RS the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs
How to calculate discount price in rupees?For example, you may want to calculate the sale price of a shirt that regularly costs Rs 1,000. If the shirt is 20% off, you must convert 20% to a decimal (20/100 = 0.2). You have Rs 1,000 * 0.2 = Rs 200. You then subtract the discount from the original price as Rs 1,000 – Rs 200 = Rs 800.Discount is the difference between the marked price (list price) and the selling price of an article. Therefore, the formula used to calculate discount is: Discount = List price - selling price.For example, $100 invested today in a savings scheme that offers a 10% interest rate will grow to $110. In other words, $110, which is the future value (FV), when discounted by the rate of 10% is worth $100 (present value) as of todayTo learn more about discount price refers to:
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Complete the table using the function c = 12m - 17.
Answers
Step-by-step explanation:
c = 12m - 17
m = 2
c = 12×2 - 17 = 24 - 17 = 7
m = 4
c = 12×4 - 17 = 48 - 17 = 31
m = 8
c = 12×8 - 17 = 96 - 17 = 79
b) The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle. (10 points)
Answers
[tex] \div 7841562130. = 98[/tex]
Answer:
123459c
Step-by-step explanation:
round
The ratio 81:108 in the simplest form
Answers
The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.
Given that M =
2x 2
93
calculate the value(s) of x for which [M] = 0.
Answers
M equal 0 calculate
Judi is making a rope ladder. She uses 1/2 yard of for each step. How many yards of rope can she make for step?
Answers
The number of yards of rope she can make for the step is 3 yards
How to determine the number of yards of rope she can make for the step?From the question, we have the following parameters that can be used in our computation:
Yards of rope per step = 1/2 yards per step
Total number of steps = 6 steps
The number of yards of rope she can make for the step can then be calculated using the following equation
The number of yards of rope = Total number of steps * Yards of rope per step
Substitute the known values in the above equation, so, we have the following representation
The number of yards of rope = 1/2 * 6
Evaluate
The number of yards of rope = 3
Hence, the number of yards of rope is 3
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Complete question
Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answers
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run? m
Answers
Answer:
If we assume she runs around it once and since they tell us its a square: 27x4=108
Step-by-step explanation:
solve number 13 please
Answers
The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .
What is expression ?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.
Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :
G = 6t^4+ 3t³ – 2t² + 5t + 60
I = 3t^4 - 3t³ + 5t² - 5t + 45
where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.
A new model {A} for the total number of new green tea and fruit juice sales can be written as -
{A} = {G} + {I}
{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45
{A} = 9t^4 + 3t² + 105
Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105
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Please help. Assignment is due today. I am terrible with math, I don't understand this. Thanks in advance.
Answers
Answer:
a. A' (-3, -1) B' (3, 2) C' (6, 0); b. A' (-1, -3) B' (1, 6) C' (2, 0); c. A' (-2, -3) B' (2, 6) C' (2, 0)
Step-by-step explanation:
Solutions for graph a, b and c are attached.
a. (x, y) to (3x, y)
A' (-3, -1) B' (3, 2) C' (6, 0)
b. (x, y) to (x, 3y)
A' (-1, -3) B' (1, 6) C' (2, 0)
c. (x, y) to (2x, 3y)
A' (-2, -3) B' (2, 6) C' (2, 0)
REMEMBER: Connect the lines to make the triangles for each graph BEFORE submitting.
Jahnay is following this recipe to make cakes. Jahnay uses 780 g of butter. How many cakes is Jahnay making? Recipe: Makes 1 Cake 120 g sugar 130 g butter 260 g flour 3 eggs
Answers
Jahnay is making 6.5 cakes from the given ingredients.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Recipe: Makes 1 Cake = 120 g sugar + 130 g butter + 260 g flour + 3 eggs.
Jahnay is following this recipe to make cakes.
Jahnay uses 780 g of butter.
To find the number of cakes:
Use division operation,
780 ÷ 120,
= 780/120
= 78/12
= 6.5
Therefore, Jahnay makes 6.5 cakes.
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