The slοpe οf the line is –4/13
Slοpe οf the line:The slοpe fοrmula is used tο calculate the slοpe οf a straight line passing thrοugh twο given pοints. It is alsο knοwn as the gradient fοrmula. The slοpe fοrmula is as fοllοws: slοpe = (change in y) / (change in x)
where "change in y" represents the difference between the y-cοοrdinates οf the twο pοints and" change in x" represents the difference between the x-cοοrdinates οf the twο pοints. Hence slοpe fοrmula can be given as slοpe = (y₂ - y₁) / (x₂ - x₁)
Here we have
The line passes thrοugh (–3, 2) and (10, –2)
Take (x₁, y₁) = (–3, 2) and (x₂, y₂) = (10, –2)
Using the fοrmula, m = (y₂ - y₁)/(x₂ - x₁)
Slοpe οf the line (m) = (–2 –2 )/(10 –(–3))
= (–4 )/(10 + 3)
= –4/13
Hence,
The slοpe οf the line is –4/13
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suppose you build a model of a concert hall using a scale factor of 18. how will the surface area of the actual concert hall compare to the surface area of the scale model? what about the volume?
The Surface area of the actual concert hall is 324 times as great as the surface area of scale model A
Given that,
Imagine creating a music hall model with a scale factor of 18.
To find : How will the scale model's surface area and the real music hall's surface area compare? Considering the volume
A new concert hall using a scale factor is 18.
then,
Scale = Dimension on module / Actual dimension
Area =k²
Where
K = Scale factor
Surface area of actual concert hall = (18)²
= 324
Thus, the Surface area of the actual concert hall is 324 times as great as the surface area of scale model A.
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When Landon overdrafts from his checking account, his bank moves $50 from his savings account into his bank account and charges him $5 (from his checking account) as a penalty each time it happens. If Landon had $75.32 in his checking account and he wrote a check for $113.85, how much money would he have in his checking account after the check is cashed and the bank handles his overdraft?
Answer:
Landon would have -$43.53 in his checking account after the check is cashed and the bank handles his overdraft.
Step-by-step explanation:
5. A student surveyed 100 adults who took either vitamin C, zinc, or echinacea
supplements to prevent getting a cold. The adults were asked if they had a cold or no
cold in the last 30 days. The results are shown in the table.
vitamin C
zinc
no cold cold
41
echinacea
total
12
21
74
15
5
6
total
26
56
17
27
100
a. What proportion of adults in the survey took echinacea?
b. What proportion of adults who took vitamin C reported having a cold in the last
30 days?
c. What proportion of adults who reported having a cold took zinc?
The proportions for this problem are given as follows:
a) Took echinacea: 0.27.
b) Having a cold in the last 30 days, of those who took Vitamin C: 0.2679.
c) Took zinc, of those having a cold: 0.1923.
How to calculate the proportions?The proportions are calculated as the division of the number of desired outcomes by the number of total outcomes.
The survey is composed by 100 adults, and of those, 27 took echinacea, hence the proportion is of:
27/100 = 0.27.
56 adults took vitamin C, and of those, 15 reported a cold in the last 30 days, hence the proportion is of:
15/56 = 0.2679.
26 students had a cold in the last 30 days, and of those, 5 took zinc, hence the proportion is calculated as follows:
5/26 = 0.1923.
Missing InformationThe table is given by the image shown at the end of the answer.
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Which matrix can be multiplied to the left of a vector matrix to produce another vector matrix?
The matrix that can be multiplied to the left of a vector matrix to produce another vector matrix given as follows:
A. [2;5].
What is a vector matrix?A matrix is also called a vector matrix when it has either only one row or only one column.
In multiplication of matrices, the rows of the left matrix are multiplied by the columns of the right matrix, and the dimensions are given as follows:
the number of rows of the left matrix.the number columns of the right matrix.The matrix in this problem that we are going to multiply is the right matrix, meaning that we want a matrix with one column, and more than one row, which is given by option A.
(a matrix with only one element, as is the case for option D, is not considered a vector matrix).
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At what y points on the curve xy = 25 is the tangent line parallel to 5x + y = 0?
The point at which =the curve xy = 25 is the tangent line parallel to 5x + y = 0 is y = ± 5√5 so, option A is correct.
What is line?
A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.
Given:
the curve xy = 25 and the equation of the line is 5x + y = 0,
The equation of line parallel to line 5x + y = 0 will be,
y = mx + c
y = -5x + c (y = -5x)
The line will be in the curve as it is tangent, so,
xy = 25 and y = -5x + c line have a solution,
Solve the above equation as shown below,
y = ± 5√5
Thus, the point y = ± 5√5 the line is tangent to the curve.
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8 The graph shows four ordered pairs that represent ratios. Which
ordered pair represents a ratio that is not equivalent to the others?
A (2,12)
B (3,18)
C (5,24)
D (6,36)
C (5,24) ordered pair represents the ratio that is not equivalent to the others.
What is a ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Consider first pair A, the ratio is given by
2/12 = 1/6
Consider next pair B, the ratio is given by
3/18 = 1/6
Consider next pair C, the ratio is given by
5/24 is not equat to 1/6
Consider next pair D, the ratio is given by
6/36 = 1/6
Hence, the ordered pair represents a ratio that is not equivalent to the others is C (5,24).
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NEED HELP ASAP!!! please help!!!
Answer:
x=21
Step-by-step explanation:
rs= 6(x-9)
rt=2(2x-6)
rs=rt
6(x-9)=2(2x-6)
6x-54=4x-12
2x=42
x=21
please help meee!!!!
The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,
What is the linear pair angles?
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
We have,
Angles:
6x° + 35°
z°
8x° + 51°
To find the values of x and z
from the given figure
Linear pair angles:
6x° + 35° + 8x° + 51° = 180
14x° + 86° = 180
14x° = 180° - 86°
14x° = 94°
x° = 94°/14°
x° = 6.71°
Vertically opposites angles are equal
6x° + 35° = z°
z° = 6( 6.71°)° + 35
z° = 40.26 + 35
z° = 75.26°
Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.
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The endpoints of AB are A(-8, 1) and B(4, -7).
What are the coordinates of point Con AB that is
34
the distance from point A to point B?
∞
6
4
The Co-ordinates of the point C that divides the line in the ratio of 3:4 is (-20/7, -17/7)
What is Section Formula?
The Section formula is used in coordinate geometry to compute the ratio of a line segment split by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle. It is used in physics to determine the centre of mass of systems, equilibrium locations, and so on.
Solution:
A(-8, 1) and B(4, -7)
Ratio is 3:4
Section Formula is (mx2 + nx1/ m + n), (my2 + ny1/ m + n)
m = 3 and n = 4
Co-ordinates of C are (3*4 + 4*(-8)/ 3+4), (3*(-7) + 4*1 / 3+4)
= (12 - 32 / 7), (-21 + 4 / 7)
= (-20/7, -17/7)
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let g be a polynomial function of x where g(x) = 2x^3 + 5x^2 - 28x - 15 Given (x - 3) is a factor of g, what is the reminder of g(x) + (x - 3)?
The remainder of polynomial g(x) divides (x - 3) that is g(x) / (x - 3) is 0.
What is polynomial?
A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.
Given: g(x) = 2x^3 + 5x^2 - 28x - 15
(x - 3) is a factor of g(x).
We have to find the remainder of g(x) / (x - 3).
Consider,
2x^2 + 11x + 5
[tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]
- 2x^3 -6x^2
____________________________
11x^2 - 28x
- 11x^2 - 33x
____________________________
5x - 15
- 5x - 15
_______________________________
0
Hence, the remainder of polynomial g(x) divides (x - 3) that is
g(x) / (x - 3) is 0.
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Division of Polynomials
1). 2x^3 - x^2 + 3x - 4 / x + 5
2). X^4 - 8x^2 + 2x + 7 / x+5
3). 2x^3 + x^2 - 8x + 15 / x^2 + 2x - 1
Division of Polynomials is [tex]$$2 x^2-11 x+58-\frac{294}{x+5}$$[/tex] , [tex]$$x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex], [tex]2 x-3+\frac{12}{x^2+2 x-1}[/tex].
What is Polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
1). [tex]\frac{2 x^3-x^2+3 x-4}{x+5}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{2 x^3-x^2+3 x-4}{x+5}: \quad \frac{2 x^3-x^2+3 x-4}{x+5}=2 x^2+\frac{-11 x^2+3 x-4}{x+5} \\& =2 x^2+\frac{-11 x^2+3 x-4}{x+5}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{-11 x^2+3 x-4}{x+5}: \frac{-11 x^2+3 x-4}{x+5}=-11 x+\frac{58 x-4}{x+5} \\& =2 x^2-11 x+\frac{58 x-4}{x+5}\end{aligned}$$[/tex]
Divide [tex]$\frac{58 x-4}{x+5}: \quad \frac{58 x-4}{x+5}=58+\frac{-294}{x+5}$[/tex]
[tex]$$=2 x^2-11 x+58+\frac{-294}{x+5}$$[/tex]
Simplify
[tex]$$=2 x^2-11 x+58-\frac{294}{x+5}$$[/tex]
2.[tex]\frac{x^4-8 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{x^4-8 x^2+2 x+7}{x+5}: \quad \frac{x^4-8 x^2+2 x+7}{x+5}=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$[/tex]
[tex]=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{-5 x^3-8 x^2+2 x+7}{x+5}: \frac{-5 x^3-8 x^2+2 x+7}{x+5}=-5 x^2+\frac{17 x^2+2 x+7}{x+5}$[/tex]
[tex]=x^3-5 x^2+\frac{17 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{17 x^2+2 x+7}{x+5}: \quad \frac{17 x^2+2 x+7}{x+5}=17 x+\frac{-83 x+7}{x+5}$[/tex]
[tex]$$=x^3-5 x^2+17 x+\frac{-83 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{-83 x+7}{x+5}: \quad \frac{-83 x+7}{x+5}=-83+\frac{422}{x+5}$[/tex]
[tex]$$=x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex]
3.
[tex]\begin{aligned}& \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}: \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}=2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& =2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{-3 x^2-6 x+15}{x^2+2 x-1}: \frac{-3 x^2-6 x+15}{x^2+2 x-1}=-3+\frac{12}{x^2+2 x-1} \\& =2 x-3+\frac{12}{x^2+2 x-1}\end{aligned}[/tex]
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which expression in the simplest form of
The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.
What is simplest form?Expressions are rewritten in a compact and unlike terms-free manner when they are simplified. Expressions are simplified by combining like phrases, resolving any provided brackets, and only leaving unlike terms that cannot be further reduced in the final simplified expression.
The given expression is -(2x³+x²)+3(x³-4x²)
Simplify the given expression as follows
-2x³-x²+3x³-12x²
= x³-13x²
The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.
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Given f(x) = x² + 4x, find the average rate of change of f(x) on the interval [4, 4+h]. Your answer will
be an expression involving h.
Step-by-step explanation:
please refer to the attached sketch for the answer.
Evaluate. Remember Order of
Operations! (PEMDAS)
4-(7+2)÷3= [?]
Answer: 1
Yessssssssssssssss
Solve the Cryptarithm,
BIRD
FOOD
+GRID
which equals GRAIN.
Also note that food is a multiple of 1279 and that it is a prime number.
Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378==13674.
What is a cryptarithmetic problem?Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.
What is reverse cryptarithm?A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.
since the digits used are 0 to 9.
first letter can't be zero.
and we can't repeat the same digit for same different alphabets.
Using these rules with the condition that food is multiple of 1279.
The answer is : 9738+2558+1378==13674
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Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378 =13674.
What is a cryptarithmetic problem?
Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.
What is reverse cryptarithm?
A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.
since the digits used are 0 to 9.
first letter can't be zero.
and we can't repeat the same digit for same different alphabets.
Using these rules with the condition that food is multiple of 1279.
The answer is : 9738+2558+1378 = 13674
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A triangle has angle measures of 45 degrees, 45 degrees, and 90 degrees. Which statement is true about the lengths of the sides? Each side has a different length. Two sides have the same length, which is less than the length of the third side. The three sides have the same length. The sum of the lengths of two sides is equal to the length of the third side.
The sum of the lengths of two sides is equal to the length of the third side is 45°.
What is Triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.As we discussed in the introduction, a triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides. This is one of the important parts of geometry. Some major concepts, such as Pythagoras theorem and trigonometry, are dependent on triangle properties. A triangle has different types based on its angles and sides.To learn more about vertex of the triangle refer to:
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What is the solution to the system of equations graphed below ?
Answer: (6, -1)
Step-by-step explanation:
<3
find the value of y² when y=-9
Answer:
81
Step-by-step explanation:
y = -9
y² = (-9)² = 81
?
What is an equation of the line that passes through the point (8, -7) and is parallel
to the line x + 2y = 18?
Parallel/Perpendicular Through Point
The equation of the line that passes through point (8, -7) and parallel to the line x + 2y = 18 is
y = -x/2 - 3How to find the equation of the lineA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable
y = output variable
m = slope
x = input variable
c = y intercept
x + 2y = 18
rewriting gives : y = -x/2 + 9
when the line is parallel the slope is equal hence the slope of the line is -1/2.
using the point slope formula for point (8, -7) which is
(y - y') = m(x - x')
(y + 7) = -1/2(x - 8)
y + 7 = -x/2 + 4
y = -x/2 - 3
the equation of the line is y = -x/2 - 3
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what is the square root of 1476
associative analyses cannot determine whether stable relationships exist between two variables. true false
Associative analyses cannot determine whether stable relationships exist between two variables.
The statement is False
Now, According to the question:
There are statistical analyses beyond simple descriptive measures, statistical inference, and differences tests including associative analyses which determine whether a stable relationship exists between two variables.
Associative analysis is an approach that is used to analyses the peoples mental representation , focusing on meaning and similarities and differences across the culture. It determined that relationship that is hidden in the large data set. It determine the relationship in between two variable as well.
Hence, Associative analyses cannot determine whether stable relationships exist between two variables.
The statement is False
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Which of the following statement is false? a. all isosceles triangles are similar b. all quadrilateral triangle are similar c. all circle are similar
d. none of the above
The statement that is false is A.. all isosceles triangles are similar
What is an isosceles triangles?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
An isosceles triangle has two of its three sides with equal lengths, and its two base angles are also equal. Although two isosceles triangles can have two sides that are equal on their own, they may not be similar because their sides may be of a different measurement.
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what is equilvalent to the square root of -2.
Answer:
1.4142135623730951i
Step-by-step explanation:
Did it help pls make me the brainliest and you can round your answer to how you want it and if not that's you answer thank you.
A bag contains 12 red marbles, 14 yellow marbles, and 3 green marbles.
If I marble is chosen at random, which is the probability that it will be a blue marble?
Answer:1/3
Step-by-step theexplanation:1/3 is the probablility of the marbles
PLEASE PLEASE PLEASE help, I will mark brainliest, this is for my final. In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ
Answer:
EL/EF
OS/OJ
Step-by-step explanation:
Tangent is equal to opposite/adjacent
There is a line whose y-intercept is 10 and whose slope is 0. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in
simplest form.
Answer:
Below
Step-by-step explanation:
A line with slope = 0 is a horizontal line
for y = mx + b form this would be
y = (0)* x + 10
y = 10
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game.
How many points did Carlos score?
The number of points that Carlos score based on the information is 19 points.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
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 written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
In this.case, Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos.
Let Carlos point = x
Fabio point will be = 2x - 7
The equation will be:
2x - 7 = 31
2x = 31 + 7.
2x = 38
Divide
x = 19
Carlos had 19 points
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In the figure below, m ABD=100, and m<1 is four times m<2. Find m<2.
The unknown angle in the intersecting lines is as follows:
m∠2 = 20 degrees
How to find the angles when line intersect?In the figure m∠ABD is 100 degrees and m∠1 is four times m∠2. Therefore, let's find the angle m∠2.
From the diagram, the sum of angle ABC and angle CBD is equals to angle ABD.
Therefore,
m∠ABD = 100 degrees
m∠ABC = m∠2
m∠CBD = m∠1
Therefore,
let
x = m∠2
m∠1 = 4x
Hence,
100 = 4x + x
5x = 100
divide both sides by 5
x = 100 / 5
x = 20 degrees
Therefore,
m∠2 = 20 degrees
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A speed skater goes around a turn with a 25 m radius. The skater has a velocity of 15 m/s and experiences a centripetal force of 720 N. What is the mass of the skater?
Answer:
80 kg
Step-by-step explanation:
To find the mass of the skater, you can use the formula for centripetal force:
F_centripetal = m * v^2 / r
Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
Plugging in the values you know, you get:
720 N = m * (15 m/s)^2 / 25 m
Solving for m, you find that the mass of the skater is:
m = 720 N * 25 m / (15 m/s)^2
= 720 N * 25 m / 225 m^2/s^2
= 80 kg
So the mass of the skater is approximately 80 kilograms.
based on this data, what is a reasonable estimate of the probability that todd runs more than 15\text{ km}15 km15, start text, space, k, m, end text tomorrow?
The reasonable estimate of the probability that Todd runs 5/13.
We know that,
Experimental probability = Number of favorable outcomes/total number of outcomes.
Experimental probability, also called empirical probability, is based on real experiments and rational records of what happened. A series of real-world experiments are conducted to determine the occurrence of events. Experiments with undetermined results are called random experiments. The results of such experiments are uncertain. Repeat the random experiment several times to determine its probability. Experiments are repeated a specified number of times, and each repetition is called a trial. Mathematically, the formula for experimental probability is defined as:
Probability of event P(E) =
frequency of occurrence of event / total number of trials.
According to the question:
The number of favorable outcomes are 5.
The total number of outcomes are 2 + 3 + 3 + 5 = 13.
Therefore, the reasonable estimate of the probability that Todd runs is 5/13.
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