Answer:
[tex]y = - \frac{1}{5} x + 4[/tex]
Step-by-step explanation:
The slope-intercept form equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope.
[tex]\boxed{\text{Slope}= \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Slope of line, m
[tex] = \frac{6 - 3}{ - 10 - 5} [/tex]
[tex] = \frac{3}{ - 15} [/tex]
[tex] = - \frac{1}{5} [/tex]
Substitute value of m into equation:
[tex]y = - \frac{1}{5} x + c[/tex]
Substitute any point the line passes through into the above equation:
When x= 5, y= 3,
[tex]3 = - \frac{1}{5} (5) + c[/tex]
3= -1 +c
c= 3 +1
c= 4
Substitute the value of c into the equation:
[tex]y = - \frac{1}{5} x + 4[/tex]
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ABCD is a rectangle. Find angles a and b, giving reasons with each step.
Answer:
a = 45°b = 23°Step-by-step explanation:
If I name the centre (intersection of diagonals) as O, Angle AOD will be equal to 68°
[Opposite angles are equal]
The diagonals bisect the 4 corner angles of a rectangle in equal halves. So, a = 45°
Also, Angle ADO = 90° - b
[Each of the four angles in a rectangle = 90°]
And In [tex]\triangle[/tex] AOD,
=> Angle AOD + Angle ADO + Angle OAD = 180°
=> 68° + 90° - b + 45° = 180°
=> 203° - b = 180°
=> b = 23°
Raymond A circular table of diameter 91cm was decorated all round the flowers placed at interval of 11cm.How many flowers were used?
The total flowers used = 25 flowers . To determine the number of flowers, we calculate the circular table's diameter.
What is a circle's circumference?In other words, if the circle were stretched and straightened out to a line segment, the circumference would match the circle's arc length. In general, the circumference of any closed figure is measured by the length of its arc. The term "circumference" can also refer to the circle's actual location, which corresponds to the edge of a disk.
Circumference, C = π x diameter
= 3.14 x 91
= 285.88
No. of flowers = 285.88/11 = 25.98
Hence 25 flowers were used.
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Combine the like terms to create an equivalent expression.
8x - 1 - 2y + 4 =
pls help!!!
The equivalent expression of 8x - 1 - 2y + 4 is
8x - 2y + 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
8x - 1 - 2y + 4
Combine the like terms.
8x - 2y + 3
Thus,
The final expression is 8x - 2y + 3.
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-2/3y -3/4 =5
What does y equal
{3x+y=9,5x-3y=1} which first step for solving the given system using substitution results in an equation without fractions
The best first step for solving the given system using substitution while avoiding fractions: Solve for y in the first equation
What is substitution method ?The substitution method is an algebraic strategy for resolving simultaneous linear equations. This approach, as the name suggests, involves substituting the value of one variable from one equation into the second equation.
Given that: the system of equation:
( 3x + y = 9 ) .....[1]
( 5x - 3y = 1 ) .....[2]
We can write equation [1] as:
y = 9 - 3x
Using substitution substitute equation ( y = 9 - 3x ) into [2] we have;
5x - 3(9 - 3x ) = 1
Therefore, the optimum first step for applying substitution and avoiding fractions to solve the given situation is:
Solve for y in the first equation.
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If a pizza delivery van travels at 80km/h, how far will it travels in 8 hours?
Answer:
640 km
Step-by-step explanation:
80km/h, x 8 hours = 640 km
I need help divisible rules
========================================================
Explanation:
The divisibility rule for 8 is we look at the last three digits only.
The 083 is what we focus on
Is 083, aka 83, a multiple of 8? The answer is no because 83/8 = 10.375 is not a whole number result. The closest multiples are 80 and 88.
So if the number ended with something like 080 or 088, then we would have a multiple of 8 in the much larger number.
But 083 is not a multiple of 8, so the original number isn't either.
Each chess piece has a path that it can follow to move. The rook, which begins in square a8, can only move vertically or horizontally. The knight, which begins in square b8, can move two squares horizontally and then one square vertically, or two squares vertically and one square horizontally. The bishop, which begins in square f 8 , can only move diagonally.
b. After two moves, the rook is in square d3. Describe a possible translation to describe the two moves.
Part a: The possible locations for the knight after two moves are a7, a5, e7 or e5.
Part b: A rook would have to move down 5 spaces and right 3 spaces, according to one possible translation.
How to describe a chess?One of the most well-known and oldest board games, played between two opponents on a checkered board with specifically made contrasting pieces, usually white and black After White moves first, players take turns in compliance with fixed rules, each attempting to force the opponent's main piece, the King, in to the checkmate—a position in which it cannot avoid capture.
Chess is played on a 64-square board divided into eight vertical rows known as files as well as eight horizontal rows known as ranks. These squares alternate among two colors: one light (white, beige, or yellow) and one dark (black or green). The board is positioned between the two competitors so that each has a light-colored square in the upper right corner.Niw, as per the given question;
Part a: The knight's first move can be to a6 (green square 1) or c6 (red square 1). If he lands on a6, he can move on to c7 or c5. He can land on a7, a5, e7, or e5 if he lands on c6.
Part b: The rook would have to move 5 spaces down and 3 spaces right.
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The complete quesion is-
Each chess piece has a path that it can follow to move. The rook, which begins in square a8, can only move vertically or horizontally. The knight, which begins in square b8, can move two squares horizontally and the one square vertically, or two squares vertically and one square horizontally. The bishop, which begins in square f8, can only move diagonally.
a. The knight moves 2 squares vertically and 1 square horizontally on its first move, then two squares horizontally and 1 square vertically on its second move. What are the possible locations for the knight after two moves?
b. After two moves, the rook is in square d3. Describe a possible translation to describe the two moves.
What minimum information is sufficient to determine congruency for each of the following?
a) two squares
b) two rectangles
c) two parallelograms
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.
What is mean by congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If two line segments are the same length, they are said to be congruent.If two angles have the same measure, they are said to be congruent.If two circles have the same diameter, they are congruent.If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.Two rectangles are congruent if both of them have the opposite sides are equal. Two squares are congruent if both of them have the same edges.To learn more about congruency refer to:
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Find the least common multiple of each pair of polynomials.
x² - 1 and x² + 2x + 1
The least common multiple of each pair of polynomials x² - 1 and
x² + 2x +1 is equal to (x-1)(x+1)².
As given in the question,
Given pair of polynomial are x² - 1 and x² + 2x +1
Simplify each pair of polynomial by factorizing them
Apply a² -b² =(a-b)(a +b)
x² -1 =(x-1)(x+1)
Apply (a +b)² =a² +2ab +b²
x² + 2x + 1 =(x+1)²
Least common multiple of (x-1)(x +1) an (x+1)² =(x-1)(x+1)²
Therefore, the least common multiple of each pair of polynomials x² - 1 and x² + 2x + 1 is equal to (x-1)(x+1)².
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The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days.
b. What is the equation of the line in standard form?
4y - 7x = 0 is the equation of the line in standard form.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
To find standard equation of a line we will use points (0,0) and (80,140)
Lets fine the slope of given data, slope, m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
m = [tex]\frac{140- 0}{80- 0}[/tex]
m = 140/80
m = 7/4
We can now make the slope intercept form that is y = mx
with the given data,
y = 7/4(x)
4y = 7x
subtract 7x both the side and we get
4y - 7x = 0
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Name the circle, a radius, a chord, and a diameter of the circle.
(a). Using the concept given above, PC and AB are the circle's chords.
(b). In the given figure, OC, OP, OA and OB are the radii of the circle.
(c). A chord which is not the diameter of the circle is PC.
What is meant by Circle?A circle is a shape in which all points are the same distance from the center. Circles are named after their centers. Therefore, the right circle is called circle A because its center is at point A. Real-world examples of circles include (the surface of) wheels, dinner plates, and coins.
(a). Circle chords are two-point line segments that connect two different places on the circumference of a circle.
Using the concept given above, PC and AB are the circle's chords.
(b). Line segments formed by joining any point on the boundary on the circle with the center of the circle are known as radii of the circle.
In the given figure, OC, OP, OA and OB are the radii of the circle.
(c). A chord which passes through the center of the circle is known as diameter of the circle.
A chord which is not the diameter of the circle is PC. ( By using the definition of chord and diameter of the circle.)
The complete question is:
In figure, O is the center of the circle
(a) Name all chords of the circle
(b) Name all radii of the circle
(c) Name a chord, which is not the diameter of the circle
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What is the probability of getting a sum of 6 when rolling two number cubes?
Answer:
The probability of rolling a sum of 6 with two dice is 5/36.
here is you answer
I think you like it
y varies directly with x .If y= -5/8 when x= 3/2 , find x when y=(2/5)
The required value of the constant of proportion and x is (-12 / 5) and (⅙) respectively.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation and x
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Now, find k for, given x = 3 / 2 and y = -5 / 8, we need to put these values in equation 1, i.e.
-5 / 8 = k(3 / 2)
k = -12 / 5
Further, calculate x for given y = (⅖) and constant of proportion = -12/5 i.e.
2 / 5 = (- 12 / 5) × (x)
x = -⅙
Hence, the required value of constant of variation and z is -12 / 5 and -⅙ respectively.
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Write an example from daily life that uses each type of real number.
integers
Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
What is real numbers?The value of a continuous quantity that may be used to describe a distance along a line is known as a "real number" in mathematics (or alternatively, a quantity that can be represented as an infinite decimal expansion).In one dimension, real numbers may be used to quantify things like distance, velocity, acceleration, force, momentum, and other physical quantities that can be measured (roughly) physically.Positive and negative numbers, as well as the zero, are real numbers.Since they do not belong to the imaginary number system, they are known as real numbers. For example, the square root of -1 is an imaginary number that cannot be quantified.Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
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Liz and Sucely were texting. The number of texts that Sucely sent was three times the difference of the number of texts liz send and the number 5.If Sucely sent 21 texts, how many texts did Liz send?
Answer:
12
Step-by-step explanation:
We'll give Sucely the variable s and Liz l.
s = 3(l - 5)
21 = 3(l - 5) distribute the 3
21 = 3l - 15 add 15 to each side
36 = 3l divide each side by 3
12 = l
So, Liz sent 12 texts
Cindy is shopping for a new desk chair at a store where the desk chairs are 50% off. She also has a coupon for 50% off any one item. Cindy thinks that she can now get the desk chair for free. Is this true? If not, what will be the percent off she will receive with both the sale and the coupon?
Cindy thinks that she can now get the desk chair for free which is false. Then the percent off that she will receive with both the sale and the coupon will be 75%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Let X be the price of a new desk chair.
Cindy is shopping for a new desk chair at a store where the desk chairs are 50% off. Then the cost of a new desk chair after 50% off will be
⇒ 50% of X
⇒ 0.50X
She also has a coupon for 50% off any one item. Then the cost of a new desk chair after applying the coupon of 50% will be
Cost = 50% of 0.50X
Cost = 0.25X
Cindy thinks that she can now get the desk chair for free which is false.
Then the percent off that she will receive with both the sale and the coupon will be
Discount = [(X - 0.25X) / X ] * 100
Discount = 0.75 x 100
Discount = 75%.
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Solve the following compound inequality:
−3(x + 7) − 15 > 2x + 4 or −2x + 6 < 4(x − 3)
a
x < −8 or x > 3
b
x > −8 or x < 3
c
x < 8 or x > −3
d
x > 8 or x < −3
Answer: a
Step-by-step explanation:
[tex]-3(x+7)-15 > 2x+4\\\\-3x-21-15 > 2x+4\\\\-3x-36 > 2x+4\\\\-36 > 5x+4\\\\-40 > 5x\\\\x < -8[/tex]
[tex]-2x+6 < 4(x-3)\\\\-2x+6 < 4x-12\\\\6 < 6x-12\\\\18 < 6x\\\\x > 3[/tex]
Taking the union, we get that [tex]x < -8[/tex] or [tex]x > 3[/tex].
Two suitcases are similar rectangular prisms. The smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long.
a. What is the scale factor of the prisms?
The scale factor of two suitcases that are similar rectangular prisms is 5/4.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar rectangular prisms:
length of A / length of B = width of A / width of B = height of A / height of B
Scale factor refers to the ratio of the corresponding dimensions of similar solids.
If the smaller suitcase is 68 centimeters long and the larger suitcase is 85 centimeters long, then the scale factor is:
scale factor = length of larger suitcase / length of smaller suitcase
scale factor = 85 cm / 68 cm
scale factor = 5/4
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Pedro and Amelia share a common investment goal and once they reach their goals, they will withdraw their money.
Amelia starts out with twice as much money as Pedro and it takes Pedro 6 times longer than Amelia to reach this goal.
They both use the same bank that provides a 4% annual interest rate compounded quarterly.
Work out how long it takes Pedro to reach his investment goal.
The number of years that Pedro took to reach his investment goal will be 52.5 years.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Amelia and Pedro have the same financial objective, and if they achieve it, they will withdraw their funds. Pedro starts off with twice as much money as Amelia, but it takes him six times as long to get there. Both of them use the same bank, which offers a 4% annual interest rate that is compounded every three months. Next, we have
n' = 4n
r/4 = 2 x 0.04 / 4 = 0.02
Let x be the amount of money invested by Pedro. Then the amount of money invested by Amilia will be 2x.
Let n be the number of years. Then for Pedro, the number of years will be 6n.
Then the equation when investment gets doubled will be
4x = 2x(1 + 0.02)⁴ⁿ
2 = 1.02⁴ⁿ
Taking log on both sides, then we have
ln 2 = 4n ln 1.02
4n = 35
n = 8.75 years
Then the number of years that Pedro took to reach his investment goal will be
6n = 6 x 8.75 = 52.5 years
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factorize -b^2+48c^2+8bc
Answer:
(4c + b)(12c - b)
Step-by-step explanation:
- b² + 48c² + 8bc ← rearrange
48c² + 8bc - b² ( split the middle term )
= 48c² + 12bc - 4bc - b² ( factor first/second and third/fourth terms )
= 12c(4c + b) - b(4c + b) ← factor out (4c + b) from each term
= (4c + b)(12c - b)
In this problem, you will use dynamic geometric, software to investigate line and rotational symmetry in regular polygons.
a. Use The Geometer's Sketchpad to draw an equilateral triangle. Use the reflection tool under the transformation menu to investigate and determine all possible lines of symmetry. Then record their number.
The equilateral triangle has three symmetry lines.
What do we mean by rotational symmetry?In geometry, rotational symmetry, also recognized as radial symmetry, is the property that a shape has when it looks the same after a partial turn rotation. The degree of rotational symmetry of an object is the number of distinct orientations in which it appears exactly the same for each rotation.Certain geometric objects, such as squares rotated 90°, are partially symmetrical when rotated at certain angles; however, the only geometric objects that are fully rotationally symmetric anywhere at an angle are spheres, circles, and other spheroids.So,
The Geometer's Sketchpad is indeed a commercial interactive geometry software program that allows you to experiment with Euclidean geometry, algebra, calculus, and other areas of mathematics. In this question, we must draw an equilateral triangle in the Geometer's Sketchpad and then use the reflection tool from the transition menu to investigate and determine all possible lines of symmetry. Then write down their number. Now we'll draw the figures on the Geometer's Sketchpad.Step 1:
Create an equilateral triangle and label its vertices A, B, and C. Draw a perpendicular line A to BC.In the line, reflect the triangle. Display the reflected image's labels. This line is the line of reflection if the image maps to the original.Step 2:
Next, draw a line perpendicular to AC through B.In the line, reflect the triangle. Display the reflected image's labels. This line is the line of reflection if the image maps to the original.Step 3:
Draw a line C perpendicular to AB now. In the line, reflect the triangle.Display the reflected image's labels. This is the line of reflection if the image includes the original.(Refer to the graphs below)
Therefore, the equilateral triangle has three symmetry lines.
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Which of the following choices will simplify
7-5(3)^2
The simplified form the expression (7 - 5(3)²) is -38.
What is the simplified form of the given expression?Simplification is the process involved in replacing a mathematical expression by an equivalent one which is that is usually simpler and shorter.
For example;
a + b + 2a + 2b = 3a + 3b.
Given the expression in the question;
7 - 5(3)²
Simply each term, raise 3 to the power of 2
7 - 5(3)²
7 - 5(9)
Multiply -5 and 9
7 - 5(9)
7 - 45
Subtract 45 from 7
-38
Therefore, the simplified form the expression (7 - 5(3)²) is -38.
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Write an equation for each transformation of y=x .
Vertical compression by a factor of 1/4 .
Vertically Stretching and Compressing
Multiplying a function by positive constant yields a function whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done. You get vertical compression.
Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
Solution:
To write the equation of the function y = x with a vertical compression by a factor of 1/4, we will use the formula given below:
y = a · x
This equation means y = a · x, and a is the vertical compression/stretch. Since a = 1/4, we can substitute 1/4 for a.
Therefore, the answer is D, y = 1/4x.
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A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 40-kilogram crates that can be loaded into the shipping container.
If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
Inequalityx is the integer
First step is to formulate the inequality
40x≤ 25,500-6,400
Now let determine the x by using the inequality
40x≤ 25,500-6,400
40x≤19,100
x=≤19,100/40
x=≤ 477.5
Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
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Can anyone please solve these two questions
For the function f(2) = 9:
1. The value of the output is: 9
2. The value of the input is: 2.
How to Solve a Function?The function, f(2) = 9 is interpreted as, for an input value of 2, we would get an output value of 9.
This means that, when x (independent variable or input) is 2, y (dependent variable or output) would be 9.
Thus, given the function f(2) = 9, we have the following:
1. The value of the output is: 9
2. The value of the input is: 2.
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The opposite of the difference between x and 4
Please help!!
Answer:
It would be the sum of x and 4
Step-by-step explanation:
What is wrong with the following statement? If t, then r t = S.
The correct statement for the expression is that 't' should be multiplied by 's'.
Given r/s = t and explain what is wrong with the statement as r * t = s.
Given expression as r/s = t
We can write this expression as
r/s = t/1
By cross multiplication on both sides we get
r * 1 = t * s
r = t * s
This is the correct expression we get. But the given statement r * t = s is false.
We conclude this as 't' should be multiplied by 's'.
Hence, the correct option is option B is correct.
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Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 65,72,88
Given set of numbers 65, 72, 88 represent an acute triangle.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 65² + 72²
= 4225 + 5184
= 9409
= 97²
And 88² = 7744
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, given set of numbers 65, 72, 88 represents an acute triangle.
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Simplify each expression by rationalizing the denominator.
2 / √2
The simplified expression after rationalizing the denominator is [tex]\sqrt{2}[/tex].
The given expression is,
2 / √2 equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{2}[/tex] .
To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{2}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{2}[/tex] we will get,
2 / [tex]\sqrt{2}[/tex] = (2 × [tex]\sqrt{2}[/tex])/([tex]\sqrt{2}[/tex] ×[tex]\sqrt{2}[/tex] )
On further simplifying the expression , we will get
= 2[tex]\sqrt{2}[/tex] / 2
= [tex]\sqrt{2}[/tex]
So, we can conclude that the simplified expression after rationalizing the denominator is [tex]\sqrt{2}[/tex].
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