The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)
What is a system of equations?A system of equations are two (or more) equations that have common variables.
The system of equation is presented as follows;
20·x + 20·y = -2
2·x + 5·y = -8
The specified possible solution of the equation is; (1, -2)
Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;
20·x + 20·y = -2
20·y = -2 - 20·x
y = (-2 - 20·x)/20
Therefore; y = (-2 - 20 × 1)/20 = -1.1
When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2
Evaluating the second equation, we get;
2·x + 5·y = -8
5·y = -8 - 2·x
y = (-8 - 2·x)/5
Plugging in x = 1, we get;
y = (-8 - 2 × 1)/5 = -2
When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation
The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;
y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5
Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5
-10 - 100·x = -160 - 40·x
60·x = 150
x = 150 ÷ 60 = 2.5
x = 2.5
y = (-2 - 20 × 2.5)/20 = -2.6
y = -2.6
The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)Learn more about systems of linear equations here: https://brainly.com/question/11867840
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1. From the information given in the triangles, are these triangles always, sometimes, or never congruent?
A. always
B. sometimes
C. never
D. cannot be determined
On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here,
AB = DE
BC = EF
AC = DF
so, by SSS both triangles are similar
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Write an equation in slope-intercept form for the line that passes through the given
point and is perpendicular to the graph of the equation.
24. (−5, 2), y = ¹⁄2x − 3
Please explain how to get the answer too.
Answer:
Step-by-step explanation:
perp. -2
y - 2 = -2(x + 5)
y - 2 = -2x - 10
y = -2x - 8
How do you find the longest angle?
The longest angle is the straight line, or 180 degrees. To find it, draw two lines so that they form a straight line. Then measure the angle between the two lines using a protractor.
What is angle?Angle is a figure formed by two lines or rays intersecting each other. It is measured in degrees, and is generally represented by the symbol ∠. The lines or rays that form the angle can be extended indefinitely, and the angle can be either acute, obtuse, right, reflex, or full. An acute angle is one that is less than 90°, an obtuse angle is one that is greater than 90°, a right angle is one that is exactly 90°, a reflex angle is one that is greater than 180°, and a full angle is one that is 360°.
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Six times a number less 20 is the same as four times the same number increased by 6. Find the number
Answer:
13.
Step-by-step explanation:
SolutionLet X be the number.
Given information from the question, we can formulate an equation:
Six times a number less 20 = 4 times the same number increased by 6
6X - 20 = 4X + 6
From the equation, we can solve for X.
6X - 4X = 6 + 20
2X = 26
X = 26 ÷ 2
X = 13
Therefore the number is 13.
The value of the unknown number is = 13.
Let the unknown number be expressed by the variable = x.
According to the question, the mathematical linear equation in one variable that is 'x' can be expressed as:
=> 6x - 20 = 4x + 6
=> 6x - 4x = 6 + 20
=> 2x = 26
=> x = 26/2
=> x = 13
Therefore, the value of 'x' which is the unknown number is 13.
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An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true
The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
What is an apothem of a polygon?
A line segment from a regular polygon's centre to one of its sides is known as the apothem.
The given options are the following:
a)The apothem can be found using the Pythagorean theorem.
b)The apothem can be found using the tangent ratio.
c)The perimeter of the equilateral triangle is 15 cm.
d)The length of the apothem is approximately 2. 5 cm.
e)The area of the equilateral triangle is approximately 65 cm².
Now we will see if each option is true or not
a) From below figure,
b = 8.7 / 2 = 4.35 cm
From right angled triangle ΔABD,
Using Pythagorus Theorem,
a² + b² = 5²
a² + 4.35² = 5²
a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm
Apothem can be found using Pythagorus Theorem.
b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.
So from ΔABD,
tan 30° = a / 4.35
0.577 = a / 4.35
a = 2.5 cm
The apothem can be found using tangent ratio.
c) Perimeter of given equilateral triangle = 3 × side length
= 3 × 8.7 = 26.1 cm
This option is false.
d) From options (a) and (b) we found that length of apothem a = 2.5 cm
Therefore this option is true.
e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]
= 32.8 cm²
Therefore this option is false.
Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
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Please answer the question below
Part A) based on your answer to answer to part a, are there any values that can be eliminated from the solution set
The values that can be eliminated from the solution set of the inequality are given as follows:
Values of x ≤ 0.
How to calculate the perimeter of a rectangle?The perimeter of a rectangle of length l and height h is given by the formula presented as follows:
P = 2(l + h).
The dimensions for this problem are given as follows:
Length l = x + 4.Height h = x.The perimeter must be less than 120, hence the inequality is given as follows:
2(x + 4 + x) < 120
4x + 8 < 120
4x < 112
x < 28.
However, a side length must assume positive values, meaning that values of x ≤ 0, that is, zero and negative values, are eliminated from the solution.
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Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
20q ^10 - 10q⁹+ 30q^8 + 20q^7
The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
What is the greatest common factor?The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).
The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.
the factor of 20q¹⁰ is 2*2*5*q*q*q*q*q*q*q*q*q*q
the factor of 10q⁹ is 2*5*q*q*q*q*q*q*q*q*q
the factor of 30q⁸ is 2*3*5*q*q*q*q*q*q*q*q
the factor of 20q⁷ is 2*2*5*q*q*q*q*q*q*q
So that the common factor of all the above terms is 2*5*q*q*q*q*q*q*q
the common factor of all the above terms= 10q⁷
So that the greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
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Karen made 5 less than 4 times the number of free
throws that Kimi made. Write an expression in
simplest form that represents the total number of free
throws made by both players.
I don’t understand how to get my answer
answer:
5x-5
step-by-step explanation:
from the question, it can be determined that karen makes 4x-5 (x representing the amount of free throws made by kimi). since the question is asking you to find the total or sum of their free throws, you add 4x-5 and x to get the answer above. hope that helps!
Why is it called revolution?
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
Revolution is a term used to refer to a dramatic and sudden change in a situation, especially a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another, thus making it a revolution.
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
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How much faster is parallel computing?
The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.
What is parallel computing?The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.
Here,
Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.
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Raina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges and allows unlimited mileage. Company B has an initial fee of and charges an additional for every mile driven. For what mileages will Company A charge less than Company B
For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.
For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.
For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:
Total cost = initial fee + (mileage * additional cost per mile)
For Company B, this would be:
Total cost = $30 + (mileage * $0.50)
To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:
$50 <= $30 + (mileage * $0.50)
To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:
$20 <= (mileage * $0.50)
Then, we can divide both sides by $0.50:
40 <= mileage
So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
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What is the value of log2 log32?
the value of log2 log32 is 0.5899 and the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.J
The logarithmic equation that has the same solution as x-4=2^3 is log2(x-4)=3.
Logarithm
The logarithm of a number can be calculated from the following relationship:
Thus, the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
So, we have that the third expression
Therefore, this expression is the one corresponding to x-4=2^3.
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What is the largest positive multiple of $12$ that is less than $350?$
Answer: 348
Step-by-step explanation: 12*29 = 348, which is the largest multiple less than 350.
What are the 3 algorithms?
Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.
What is algorithm?An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).
Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.
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2789\36 help me psss i have to take this test lie be so fl i like right nowww pls haelp me
Answer:
77.472222 etc
Step-by-step explanation:
F= 5 9 (K−273)+32space, F, equals, start fraction, 9, divided by, 5, end fraction, left parenthesis, K, minus, 273, right parenthesis, plus, 32 In order to convert a temperature in Kelvin, KKK, into a temperature in degrees Fahrenheit, FFF, the equation above can be used. Which of the following equations correctly expresses the temperature in Kelvin in terms of the temperature in degrees Fahrenheit?
The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
The given expression:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
Conversion from Kelvin (K) to degrees Fahrenheit (F)To find the formula for K
The formula for K is obtained by making K the subject of the formula as shown below:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
subtract 32 from LHS.
[tex]F-32 = \frac{9}{5} (K-273)[/tex]
multiply 5 with LHS
[tex]5(F-32) = 9(K-273)[/tex]
Take numerator 9 to LHS
[tex]\frac{5}{9}(F-32) = K-273[/tex]
take -273 from RHS to LHS
[tex]\frac{5}{9}(F-32) + 273 = K[/tex]
Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
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Please help.. what am I missing on this?
A. 78
B. 12.75
C. 136.5
D. 12
Answer:
A. 78
Step-by-step explanation:
You want the measure of one base angle of an isosceles triangle when it is given as (6x+6)° while angle K is given as 2x°.
Angle relationsYou don't need to solve any equations to determine the correct answer choice. You just need to understand the relationship between angles in an isosceles triangle.
The two base angles in an isosceles triangle are congruent, so neither can be more than 90°. (Eliminates choice C.)
The base angle at (6x+6) is more than 3 times angle K at (2x), so the base angle cannot be as little as 12.75. (Eliminates choices B and D.)
The only viable answer choice is A. 78°.
SolutionThe sum of angles in any triangle is 180°. The two base angles in an isosceles triangle are the same measure, so we have ...
(6x +6)° +(6x +6)° +2x° = 180°
14x +12 = 180 . . . . . . . . . . . divide by °, collect terms
14x = 168 . . . . . . . . . . subtract 12
x = 12 . . . . . . . . . . divide by 14
∠D = (6x +6)° = (6·12 +6)° = 78°
__
Additional comments
We are referring to the angle marked 2x° as "angle K" because Brainly doesn't like the word a.pex to show up in an answer.
We know triangle DKT is isosceles because the sides are marked with a single hash mark. The congruent base angles are opposite the congruent sides.
An altitude from K to segment DT would divide the triangle into two congruent right triangles, each with its half of angle K being x°. Then angles K/2 and T are complementary to that, so you could write ...
6x +6 +x = 90 ⇒ 7x = 84 ⇒ x = 12 ⇒ ∠D = 90° -12° = 78°
Once again, recognition that 6x+6 is somewhat greater than x means that angle D must be somewhat more than 45°. (The larger of two things is always greater than half their sum.)
Which is closest to the quotient 4,367 -- 0. 004?
1,000
10,000
100,000
1,000,000
Answer: 1000
Step-by-step explanation:
i took this quiz before ! !
Emmet had c caramels. Then his sister took 5 of the caramels. Write an expression that shows the number of caramels Emmet has left.
Answer:
C - 5
Step-by-step explanation:
We know
Emmet had c caramels
His sister took 5 caramels, that means subtract 5, so the equation is
c - 5
1. Find the radian measures that correspond to the degree measures 330° and 135°
Answer:
Converting from degrees to radians is actually very simple, it is a one step unit conversion.All we need to know to solve this is that (π)radians=(180)degrees Therefore 135degrees⋅(π)radians180degrees=(135180)π radians =3π4 radians
Step-by-step explanation:
hope this helps
Evaluate the expression!!
The given expression is equivalent to 22 for x = 17 and y = 12.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
2x - y
For x = 17 and y = 12, we can evaluate the expression as -
2 x 17 - 12
34 - 12
22
Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.
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Select the correct answer from each drop-down menu. the function has been transformed, resulting in function h. to create function h, function f was translated 2 units , translated 4 units , and reflected across the _______.
Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4
Step (i): The type of transformation change of the function
a) The translated left "c" units are x - c;
b) The translated right "c" units are x + c
Step (ii) The given function is translated "2" units right side, then the new function is
h(x) = (x + 2 )3followed by the translated "4" units left sides and reflected across the y-axis.
Now the new function is h(x).
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To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Answer:
135.5 m
Step-by-step explanation:
Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.
Law of SinesGiven one side and two angles we can solve the triangle using the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.
A + B + C = 180°
46° +103° +C = 180° . . . use the given measures
C = 31° . . . . . . . . . . . . . subtract 149°
Now, we can find 'a' from ...
a/sin(A) = c/sin(C)
a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m
The distance from B to the tree at C is about 135.5 meters.
Can someone help me step by step !!
Answer:
[tex]x=\sqrt{153}[/tex]
Step-by-step explanation:
[tex](\overline{BC})^2 = (\overline{AB})^2 + (\overline{AC})^2\\\\(13)^2=(x)^2+(4)^2\\\\169 = x^2+16\\\\169-16=x^2\\\\153=x^2\\\\\sqrt{x^2} = \sqrt{153}\\\\x=\sqrt{153}[/tex]
You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score $x$ without the penalty.
Your score without the penalty is 9.424.
To find your score without the penalty, we need to add 0.3 points back to your final score of 9.124. We can use the linear equation:
x = 9.124 + 0.3
This equation represents the original score, represented by x, plus the penalty of 0.3. To solve for x, we need to add 0.3 to 9.124:
x = 9.124 + 0.3
x = 9.424
So your score without the penalty is 9.424.
In this equation, x is being used to represent the original score, before the 0.3-point penalty was applied. The equation x = 9.124 + 0.3 represents that the original score was 9.124 and 0.3 points were taken off due to stepping out of bounds. By solving the equation, we are able to find the original score without the penalty which is 9.424
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6. Shenandoah's test scores were 70, 80, 80, and 90. What was his weighted average if the
tests were weighted 1, 3, 5, and 4, in that order?
The weighted average of Shenandoah's test scores is 82.3.
What is the weighted average?
To find a weighted average, multiply each number by its weight, then add the results. If the weights don't add up to one, find the sum of all the variables multiplied by their weight, then divide by the sum of the weights.
To calculate a weighted average, we need to multiply each score by its corresponding weight, and then add those products up and divide by the sum of all the weights.
To calculate a non-weighted average such as a mean average, all we need to do is, sum up, the scores and divide this sum by the number of scores. For a weighted average, each score must have a frequency attached to it. This frequency is called specific weight.
So in this case,
Weighted average = (701 + 803 + 805 + 904) / (1+3+5+4) = (70 + 240 + 400 + 360) / 13 = 1070/13 = 82.3
Hence, The weighted average of Shenandoah's test scores is 82.3
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How do you find the sides of an isosceles triangle given the angles?
To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.
An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.
For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:
Side AB = Side BC = (Side AC) x (Sin A / Sin B)
Where A and B are the angles of the triangle and Side AC is the known side length.
Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).
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how do i answer this q
Answer: -1/4
Step-by-step explanation:
Rate of change is just another term for slope. To calculate slope, we just need any 2 points on the graph and apply the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m=\frac{1-2}{4-0} =\frac{-1}{4} =-\frac{1}{4}[/tex]
This means -1/4 is the rate of change.
At a benefit concert, fifteen bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?
On solving the provided question, we can say that - he need 56 answers he need to get correct if he want a grade of 80 percent on a test with 70 questions
what is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.
Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.
So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.
20% of 70
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