The level of a line's slope indicates its steepness.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates.Example -
This line goes through the points (0,0) and (4,4).
Now, slope = (y₂ - y₁) / (x₂ - x₁)
slope = (4 - 0) / (4 - 0)
slope = 4 / 4
slope = 1
So, from the above calculation it is shown that, the slope of the line is 1.
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How do you prove that a triangle is similar by SSS?
"If in two triangles, sides of one triangle are proportionate to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and consequently the two triangles are comparable," asserts the Side-Side-Side (SSS) criteria.
Take a look at the triangles below.
- We can see that all three pairs of the sides of these triangles are congruent. - This is also known as "side-side-side" or "SSS." According to the SSS criteria for triangle congruence, two triangles are congruent if they have three pairs of congruent sides.
SSS Congruence Rule Theorem
When one triangle's three sides are identical to the corresponding three sides of another triangle, two triangles are said to be congruent.
The aforementioned theorem will now be proven.
Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.
To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]
Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]
Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].
Join SQ and SR.
In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],
BC=QR Given
[tex]\angle C B A=\angle R Q S[/tex] By construction
[tex]\angle B C A=\angle Q R S[/tex] By construction
[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence
[tex]\angle A=\angle S[/tex] By CPCTC
AB=SQ By CPCTC
AC=SR
Now, AB=PQ and AB=SQ => PQ=SQ
Similarly, AC=PR and AC=SR => PR=SR
Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]
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State all integer values of x in the interval 1 ≤ x ≤ 8 that satisfy the following
inequality:
5x − 8 > 6
Answer:
3,4,5,6,7.
Step-by-step explanation:
if yk, yk
A water park charges a rental fee plus $2.00 per hour for lockers. The total cost of 5 hours is $13.00. Assume the relationship is linear. Find the rate of change and the rental fee.
how to determine sample size needed for confidence intercal when population standard deviation not known
When the population standard deviation is not known, the sample size needed for a confidence interval can be determined using the t-distribution.
The t-distribution is used to calculate the margin of error, which is the amount of variation that is allowed in the sample results. The sample size needed for a confidence interval is determined by calculating the critical value of the t-distribution for a given level of confidence and degree of freedom. The degree of freedom is the number of independent observations in the sample minus one.
The confidence level determines the critical value of the t-distribution, which is used to calculate the margin of error. The sample size is then calculated by dividing the margin of error by the desired confidence level. This method allows us to determine the sample size needed for a confidence interval even when the population standard deviation is unknown.
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There were 17 unny day thi year, which wa 18 fewer than lat year. Two year ago , there were three time a many unny day a there were thi year. How many unny day were there in all three year?
The total number of sunny days for the three years is 103 days.
This year there were 17 sunny days.
There were 17 sunny days this year, 18 fewer than last year. This is to mean that, last year, sunny days were 18 days more than this year, Which can be found by;
18+17 = 35 sunny days
Sunny days two years ago were three times the sunny days this year which is;
3×17 = 51 sunny days
Therefore, the total number of sunny days for the three years is calculated by adding the total number of sunny days for the three years:
17 + 35 + 51 = 103 sunny days
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The graph shows the the number of mistakes made on an exam. How many students made four or more mistakes?
Which has a vertex at (-2,-3)?
A) y = x² + 4x+1
B) y = x² + 4x - 1
C) y = x² - 4x + 1
D) y = x² - 4x-1
How do you prove AAS congruence rule?
The two triangles are congruent if two angles and a non-included side of one triangle are congruent with two angles and the corresponding non-included side of a second triangle. So it was proved.
The two triangles are congruent if two angles and a non-included side of one triangle are congruent with two angles and the corresponding non-included side of a second triangle.
If angle ad, side ac-df, and angle cf are present, then ABCDEF is true.
To support: By the angle sum property, ABC DEF A+B+C=180° ______ (1)
In DEF D+E+F=180°___________ (2) (By angle sum property)
From (1) and (2), A+B+C= D+E+F A+E+F= D+E+F
(Given B=E and C=F) A=D ____________________ (3)
Currently, in ABC and DEF A=D (from (3))
AC = DF (Given)
C=F (Give (AAS congruency)
So it was proved.
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What is the sum of roots of x2 +5 x 6 0?
The sum of roots of x2 + 5x + 6 = 0 is -5.
x2 + 5x + 6 = 0
To find the sum of roots, we need to factor the equation :
x2 + 5x + 6 = 0
x2 + 3x + 2x + 6
= 0
x(x + 3) + 2(x + 3)
= 0
(x + 3)(x + 2) = 0
x = -3, -2
Sum of Roots = -3 + (-2) = -5
x2 + 5x + 6 = 0
To find the sum of roots, we need to factorize the given equation. To do that, we can divide the equation into two parts, x2 + 3x and 2x + 6. We can factorize the first part as x(x + 3) and the second part as 2(x + 3). Then, we can multiply both parts to get the factorized equation, (x + 3)(x + 2) = 0. We can solve this equation to get the roots, x = -3 and -2. Finally, we can add both roots to get the sum of roots, -3 + (-2) = -5.
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|3t+6| =9
A. n= -5
B. n= 1
C. n= -1 or 1
D. n= -5 or 1
Answer:
C, n= -1 or 1.
Step-by-step explanation: The bars around 3x+6 are absolute value bars (| |), meaning that whatever lies inside of them will turn positive. An example: |-9| ➡️ 9. So, since we do have the absolute value bars, multiplying 3 by -1 would not effect the equation. So therefor we could use a regular 1 or a negative one to make the equation equal to 9.
A triangle has two sides of length 8.3 and 3.4. What compound inequality describes the possible lengths for the third side, x?
Using Pythagoras theorem the compound inequality for the possible length is 7.6 ≤ x ≤ 9
Pythagoras TheoremPythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
To find the possible value for the third side, we have to use Pythagoras formula which is given as;
x² = y² + z²
In the first scenario, we would assume the third side is the hypothenuse
x² = 8.3² + 3.4²
x = 9
In the second scenario, we would assume the third side is one of the legs of the triangle and the formula will change to
8.3² = y² + 3.4²
y² = 8.3² - 3.4²
y = 7.6
Writing a compound inequality to show the possible length
7.6 ≤ x ≤ 9
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How do you solve for y in a triangle?
Either Pythagorean Theorem or the Law of Cosines is used to solve for y in a triangle, you can use either of these equations.
The Pythagorean Theorem states that the sum of the squares of the two shorter sides of the triangle is equal to the square of the longest side. This is written as:
a2 + b2 = c2,
where a and b are the lengths of the two shorter sides, and c is the length of the longest side. In this equation, y is the length of the longest side.
The Law of Cosines states that:
a2 = b2 + c2 - 2bc cos A
where A is the angle opposite side a. In this equation, y is side a.
Therefore, to solve for y in a triangle, you can use either the Pythagorean Theorem or the Law of Cosines, depending on the information given.
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Show that x(x - 1)(x + 1) = x³ - x
x (x - 1) (x + 1) = [tex]x^{3}[/tex]- x
Distribute
1. (x + 1) [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3}[/tex] - x
2. Distribute
(x + 1) [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3}[/tex] - x
[tex]x^{3 }[/tex] + 1 [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3 }[/tex] - x
3. Multiply by 1
[tex]x^{3 }[/tex] + 1 [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3 }[/tex] - x
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3 }[/tex] - x
4. Distribute
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - x (x + 1) = [tex]x^{3 }[/tex] - x
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - ([tex]x^{2}[/tex] + x) = [tex]x^{3 }[/tex] - x
5. Distribute
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - ([tex]x^{2}[/tex] + x) = [tex]x^{3 }[/tex] - x
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - [tex]x^{2}[/tex] - x = [tex]x^{3 }[/tex] - x
6. Combine like terms
[tex]x^{3 }[/tex] + [tex]x^{2}[/tex] - [tex]x^{2}[/tex] - x = [tex]x^{3 }[/tex]- x
[tex]x^{3 }[/tex] - x = [tex]x^{3 }[/tex] - x
7. Move terms to the left side
[tex]x^{3 }[/tex] - x = [tex]x^{3 }[/tex] - x
[tex]x^{3 }[/tex] - x - ([tex]x^{3 }[/tex] - x) = 0
8. Distribute
[tex]x^{3 }[/tex] - x - ([tex]x^{3 }[/tex] - x) = 0
[tex]x^{3 }[/tex] - x - [tex]x^{3 }[/tex] + x = 0
9. Combine like terms
[tex]x^{3 }[/tex] - x - [tex]x^{3 }[/tex] + x = 0
- x + x = 0
10. Combine like terms
- x + x = 0
0 = 0
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Is 1 and 2 a square number?
According to square numbers , 1 is a square number while 2 is not .
What does Squaring mean ?
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.
When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
Thus , 1 is a square number while 2 is not .
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What is the value of K if X 1 is a factor of 4x³ 3x² 4x K?
The value of k is -3, if x-1 is a factor of 4x³+3x² −4x + k
Quadratic Equation:
A quadratic equation is a second-order algebraic equation in x. The quadratic equation in standard form is ax2 + bx + c = 0. where a and b are the coefficients, x is the variable, and c is the constant term. The first condition of the quadratic equation is that the coefficients of x² are non-zero terms (a ≠ 0). To write a quadratic equation in standard form, first write the x² term, then the x term, and finally the constant term. The numbers for a, b, and c are generally written as whole numbers, not as fractions or decimals.
According to the Question:
Let P(x) = 4x³+3x² −4x + k
Given, (x−1) is a factor of P(x)
x−1 = 0
x= 1
∴ p(1) = 4×(1)³+3×(1)² −4×(1)+k = 0
⇒ 4+3−4+k = 0
⇒ k+3=0
⇒ k=−3
Hence, the value of k is −3.
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The second term of a geometric sequence is 6 and the fifth term is 48, what is the nth term of
the sequence?
Answer:
1536
Step-by-step explanation:
Answer:
3,6,12,24,48,96,192,384,768,1536
I don't know which term you need so i mentioned all terms
What is the slope of the line y =- 3x 1 3?
The slope of the line y =3x(1 ,3) is 3.
Describe slope.The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same). In math, we frequently want to quantify the steepness. Slopes B and C are clearly higher than slope A. While slope A is just four units high, they are both seven units high. Therefore, it would seem that height and steepness are related.
Given
Equation
y = 3x (1,3)
Using slope intercept form,
y = mx + b
m = slope
m = 3
The slope of the line y =3x(1 ,3) is 3.
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2/9x18
Please show step by step example
Which shape has 4 sets of parallel lines?
Answer:
Octagon
Step-by-step explanation:
An octagon has 4 sets of parallel lines and 8 sides.
What value of b will cause the system to have an infinite number of solutions 6 3 3 6?
The value of b when the system has an infinite number of solutions is 12.
The Given equations are
y=6x-b ---(1)
6=3x+3y ----(2)
If the system has an infinite number of solutions, then equation 1 is equal to equation 2
If a pair of linear equations have unique or infinite solutions, then the system of equation is said to be a consistent pair of linear equations
Isolate variable y in equation 2
2=x+y
Multiply by 6 on both sides
y=6x-12 -----(3)
To find the value of b, equate equation 1 and equation 3
6x-b=6x-12
b=12
Thus the value of b=12.
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what factors predict how much money a film will earn? a data scientist at a top movie studio fits a multiple regression model to predict domestic gross earnings ($ millions) from: the film budget ($ millions), the film run time (minutes) average rotten tomatoes rating score [0, 100] gross
Therefore, the solution to this problem is the option 3) Gross =$204.1 million is the correct option.
What is regression model ?Regression analysis, which is used in statistical modeling, is a collection of statistical procedures for determining the associations between a dependent variable and one or more independent variables.
Here,
Given: Multiple regression model to predict domestic gross earning.
=> Gross = -27 + (1.1*Budget)-(0.43*runtime)+(2.6*return) + error
We have,
budget = $75 million
runtime = 120 minute
rotten tomatoes =77
=>Gross = -27 + (1.1*75)-(0.43*120)+(2.6*77)
=> Gross =$204.1 million
Therefore, the option 3) Gross =$204.1 million is the correct option.
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PLEASE HELP!!!!!!!
Use the expression below. -4b + 8c + 12-8b-2c +6 Part A Simplify the expression. Enter your answers in the boxes. b+ C+
Answer:
Option D is correct answer
Step-by-step explanation:
-4b + 8c + 12 - 8b - 2c + 6
-4b - 8b + 8c - 2c + 12 + 6
-12b + 6c + 18
Take 6 as common
6(-2 + c + 3)
Thus, The answer is 6(-2 + c + 3)
Last summer, Sheila decided to measure change in a swimming pool's
water level each week. There was a hot and dry spell that lasted 4
weeks and the water level dropped the following amounts each week
Sheila measured the level: 8 millimeters in the first week, 5 millimeters
in the second week, 12 millimeters in the third week, and 5 millimeters
in the fourth week. Express the total gain/loss of water over the 4
weeks as an integer
Sheila measured the water level in the swimming pool every week for 4 weeks and found that the water level decreased by 8 millimeters in the first week, 5 millimeters in the second week, 12 millimeters in the third week and 5 millimeters in the fourth week. The net result was a loss of 10 millimeters of water over the 4 week period.
Sheila wanted to track the changes in the water level of a swimming pool over time. She measured the level every week for 4 weeks. In the first week, the water level dropped by 8 millimeters. In the second week, the level dropped by 5 millimeters. In the third week, the level dropped by 12 millimeters. Finally, in the fourth week, the level dropped by 5 millimeters. The net result of these measurements was a loss of 10 millimeters of water over the course of the 4 week period. This indicates that the hot and dry spell had a negative effect on the water level in the pool.
Total Water Loss = 8 millimeters + 5 millimeters + 12 millimeters + 5 millimeters = 30 millimeters
Total Water Gain = 0 millimeters
Net Loss = Total Water Loss - Total Water Gain = 30 millimeters - 0 millimeters = -10 millimeters
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Which equations are continuous?
Any equation that does not contain a discontinuity, defined as a point where the graph of the equation has a sudden break or jump, is considered continuous. Examples of continuous equations include linear equations, polynomial equations, and exponential equations.
Continuity is an important concept in mathematics and related disciplines. A continuous equation is defined as any equation that does not contain a discontinuity, which is a point where the graph of the equation has a sudden break or jump. Discontinuous equations are equations with discontinuities that cause the graph of the equation to have sudden jumps or breaks. Linear equations, polynomial equations, and exponential equations are all examples of continuous equations, since they do not contain any discontinuities. Continuous equations are important because they are used in many areas of mathematics, such as calculus, to solve problems and understand the behavior of certain function
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What is the discriminant of 2x² 5x 3 0?
The discriminant of a quadratic equation is equal to the expression (b^2 - 4ac) where a, b, and c are the coefficients of the equation. In this case, the discriminant is equal to (5^2 - 4(2)(3)) = 25 - 24 = 1.
The discriminant of a quadratic equation is a numerical value that can be used to determine the nature of its roots. The discriminant is equal to the expression (b^2 - 4ac) where a, b, and c are the coefficients of the equation. In this case, the equation is 2x² 5x 3 0. We can identify the coefficients of the equation as a = 2, b = 5, and c = 3. Using the formula, the discriminant is equal to (5^2 - 4(2)(3)) = 25 - 24 = 1. This means that the equation has two real and equal roots, as the discriminant is equal to zero. This can be seen by factoring the equation, which gives us (2x - 3)(x + 1) = 0. The roots of the equation are then x = 3/2 and x = -1.
Discriminant = b^2 - 4ac
= (5)^2 - 4(2)(3)
= 25 - 24
= 1
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What is the exact value of x?
5·215x=16
Answer:
X=log 3.2/5 log 21
Step-by-step explanation:
X=0.0764094
How many terms are there in the expression 5xy +9yz+ 3zx 5x 4y?
What is the base area B?
The space occupied by the flat surface of a cylinder's base, also known as the base area, is quantifiable.
Given,
Base area of cylinder;
The amount of space that a flat surface at the base of a cylinder occupies is known as the base area. Since the cylinder's base is a circle, the base area of the cylinder is actually an area of a circle.
Formula for base area;
The cylinder's base area is calculated by multiplying the square of its radius by π.
Then,
"πr²" is the formula for the cylinder's base area with radius r.
That is,
Base Area of a Cylinder = (π × radius²) square units.
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Complete question is here;
What is the base area B of cylinder?
Answer the geometry question
Answer:
52 degrees
Step-by-step explanation:
The 3 angles of a triangle add up to 180 degrees
To find angle C, use 180 - B - A = C
180 - 85 - 43 = 52
Given: ABCD is a parallelogram; line FD is congruent to line BE
Prove: Line A F is congruent to line EC
From the parallelogram AECF, lines A F is similar to E C.
How to determine congruent lines?You should know that two or three lines are congruent if they are the same or if they look alike.
The given parameters are
Parallelogram A E CF (given)
Parallelogram A B C D given
In every parallelogram, opposite side are parallel and similar
From parallelogram ABCD, line AB = DC = FD
Also, AB=DC=BE
In the figure also, ΔAFD=ΔBCE (similar triangles)
Therefore, A F similar to E C
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