Therefore the slope of the line joining the points (2,2) and (6,8) is equal to 2/3.
What is meant by slope?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The formula for finding the slope of a line is [tex]m= \frac{X2-X1}{Y2-Y1}[/tex].
Where (X1, Y1) and (X2, Y2) are the points on the line.
The given points are (2,2) and (6,8).
Therefore slope is
[tex]m=\frac{6-2}{8-2} \\m=\frac{4}{6} \\m=\frac{2}{3}[/tex].
The slope is 2/3.
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A submarine in the middle of the ocean at a depth of 115 feet and dives to a depth of four times its initial death rate in submarines death as an integer
The integer number that represents the submarine's depth is given as follows:
-460.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
The concepts of height and depth are given as follows:
Height is above the sea level, hence it is represented by positive integers.Depth is above the sea level, hence it is represented by negative integers.A submarine in the middle of the ocean at a depth of 115 feet, hence the integer that represents the initial depth is given as follows:
-115.
The submarine dived to a depth that is four times the initial depth, hence the integer that represents the final depth is given as follows:
4 x -115 = -460.
(meaning that the final depth of the submarine is of 460 feet).
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Find a word problem 4=3/4x+0
Answer:
x=16/3
Step-by-step explanation:
4=3/4x+0
4=3x/4
4=3x/2square
4times4=16
3x/3=16/3
x=16/3
Can u please help...................
Answer:
(-2, 2)
Step-by-step explanation:
You want the circumcenter of the triangle with vertices A(2, -3), B(2, 7), and C(-6, -3).
CircumcenterThe circumcenter is the center of the circle that circumscribes the triangle. Here, the triangle is a right triangle, so the circumcenter is the midpoint of the hypotenuse.
MidpointThe midpoint of segment BC is the average of the coordinates of B and C:
X = (B +C)/2 = ((2, 7) +(-6, -3))/2 = (2 -6, 7 -3)/2 = (-4, 4)/2
X = (-2, 2)
The circumcenter is (-2, 2).
__
Additional comment
The right angle subtends an arc of twice its measure, 180°, so the circumscribed triangle occupies a semicircle, and the hypotenuse is a diameter. That puts the center of the circle at the midpoint of the hypotenuse.
The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?
The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.
We will calculate the interquartile range and us the rule 1.5 .
The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.
IQR = Q3 - Q1
Therefore, interquartile range becomes,
IQR = 17 - 13
IQR = 4
Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first
4 * 1.5 = 6
and then,
17 + 6 = 23
on applying the rue we will get ,
13 - 6 = 7 .
This value means that there is no outlier in the displayed data set.
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What are the 3 parts to a chemical word equation?
The three main parts to a chemical word equations are the reactants , the products and the arrow .
What is a Chemical Equation ?
A chemical equation is defined as a representation of a chemical reaction expressing it in in terms of symbols of the substances.
The three main parts of the Chemical Equation are :
(i) The Reactants : During a chemical reaction, these elements combine and undergo some chemical changes. They are present on left side of reaction equation.
For Example : [tex]CH_{4} + 2O_{2}[/tex] ;
(ii) The Arrow : It indicates formation of products from reactant . It is represented as " → " ;
(iii) The Products : Products are the result of chemical reactions between their reactants. It is present on right side of the chemical equation.
For example, : [tex]CO_{2} +2H_{2} O[/tex]
So , overall Chemical Equation can be written as : [tex]CH_{4} + 2O_{2}[/tex] → [tex]CO_{2} +2H_{2} O[/tex] .
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What are the 3 linear equations?
The 3 linear equations are
1. y = mx + b
2. ax + by = c
3. x/a + y/b = 1
1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.
2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.
3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.
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what is x^2(2x^2+8)?
Answer:
2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8) When you are multiplying powers that have the same bases, you add the exponents.
find the missing part of the proof for m A. m B. m C. m D. m
Therefore, K= 66 degrees, LK length = 22 unit, and LK length = 22 unit are the answers to the specific problem of angles.
Angles are what?A geometrical angled construction is constructed from two rays that converge at the summit, or center, of both the angle and are referred to as the face and the vertex, respectively. Guess it depends on how they're situated, it is possible for two rods to create an angle together within plane. When two planes collide, an inclination is also formed. Diahedral angles are the term used to refer to them. Light beams or lines in euclidean geometry can have a wide variety of shapes or angles for the same termination. The phrase "angle" in English is based on the Latin term "angulus," which meaning "horn." the vertex.
Here,
Given: MKL M = 24 degree right triangle
K is 90 degrees, etc.
Thus,
=> ∠L + ∠M +∠K =180
=> 90 + 24 + ∠K = 180
=>∠K =180-114
K equals 66 degrees.
and
The formula for LK length is 22.
The formula for LK length is 22.
In light of this, the answer to the angle problem is
K=66 degrees, and LK length=2 units. LK length equals two units.
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A local boys club sold 196 bags of mulch and made a total of $357. It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag. How many bags of each kind of mulch did it sell?
Total 56 bags of hardwood and 140 bags of pine bark bags are sold.
In the given question, a local boys club sold 196 bags of mulch and made a total of $357.
It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.
We have to find how many bags of each kind of mulch did it sell.
Let total number of x bags of hardwood sell.
Let total number of y bags of pine bark sell.
Now the equation should be
2x + 1.75y = 357............................(1)
Total number of bags sold 196.
So x + y = 196............................(2)
From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.
2(196 - y) + 1.75y = 357
392 - 2y + 1.75y = 357
392 - 0.25y = 357
Subtract 392 on both side, we get
-0.25y = -35
Divide by -0.25 on both side, we get
y = 140
Now putting the value of y in x = 196-y
x = 196 - 140
x = 56
Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.
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Question 2
In 2007 the US Census Bureau reported that 71.3% of American families owned their
homes. The city council is debating on whether to offer tax breaks to first time
homebuyers, but they only want to do so if there is strong evidence that the rate of
home ownership has increased since 2007 since it will cost the city money to do so.
a) What are the null and alternative hypothesis?
b) Describe a Type I error in context along with the consequence.
c) Describe a Type Il error in context along with the consequence.
d) Which is a more serious error in this context? Justify your answer
e) For each type of error, tell who would be harmed.
(These are questions to answer, not answer choices.)
The answer to all the questions is explained below with justifications.
What is hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.
a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.
The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.
b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.
The type II error is the null hypothesis is false and we assumed it to be true
that is less than 71.3% of American families owned their homes and the council provides tax breaks.
c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.
d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.
e) For type I error house owners will be harmed and for type II error counsel will be harmed.
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Which inequalities are true? Check all that apply. You
can use the tool on the right to help you.
5/6 > 4/6
3/8< 5/8
4/5 <2/5
4/7> 6/7
2/31/3
The true inequalities are:
5/6 > 4/6
3/8< 5/8
2/3 > 1/3
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
5/6 > 4/6
0.833 > 0.667
so, this inequality is true.
3/8 < 5/8
0.375 < 0.625
so, this inequality is true.
4/5 < 2/5
0.8 < 0.4
so, this inequality is false.
4/7 > 6/7
0.571 > 0.857
so, this inequality is false.
2/3 > 1/3
0.667 > 0.333
so, this inequality is true.
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To get to his parents' house, Dylan would have to drive due north 8 miles. To get to his
grandparents' house, he would have to drive due east 5 miles. What is the straight-line
distance between the parents' and grandparents' houses? If necessary, round to the nearest
tenth.
When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.
what is pythagoras theorem ?The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.
given
by pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]
The homes of the parents and grandparents are thus 9 miles apart in a straight line.
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please help i need help asap i have class in 2 hours pls
The value of x, given the angles next to the triangle, can be found to be 38 °
How to find the value of x ?To find the value of x, you first need to find the value of the other angles in the triangle.
Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:
= 180 - 134
= 46 °
The angle to the bottom right is:
= 180 - 84
= 96 °
The angles in a triangle add up to 180 ° so the value of x would be:
= 180 - 46 - 96
= 38 °
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is y = 1/3x + 4 proportional
The following system of equations is _____.
y = - x +
2x + 6y = 4
independent
inconsistent
equivalent
Answer:
"equivalent"
Step-by-step explanation:
Right!!
Shaheen ha many triangular piece, each of area 1 q. Unit and many rectangular piece, each of area 2 q. Unit
If Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit she arranges these to form the given shape then the area of shape is 14 Square Units .
The Area of one triangular piece is given as = 1 Sq . Unit ;
The Area of one rectangular piece is = 2 Sq. Unit ;
From the shape given below ,
we can see that the shape has 4 triangular pieces and 5 rectangular pieces .
So , total area of given shape is ⇒[tex]4\times Area Of Triangle + 5\times Area Of Rectangle ;\\[/tex]
Substituting the values of Area ,
we get ;
[tex]Total Area = 4\times 1 +5\times 2[/tex]
= [tex]4+10[/tex]
= 14 Sq . Units .
Therefore , the area of the given shape is 14 Sq. Units .
The given question is incomplete , the complete question is
Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit .
If she arranges these to form a shape as shown below, what would be the area of this shape ?
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When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.
g c
4 15.80
8 31.60
11 43.45
15 57.25Choose all of the following statements that are true.
Select one or more:
a.
The range is {15.80, 31.60, 43.45, 57.25} .
b.
The set of independent values is {15.80, 31.60, 43.45, 57.25}.
c.
The range is {4, 8, 11, 15}.
d.
none of these
e.
The set of independent values is {4, 8, 11, 15}.
The two statements that are true about the table are:
A) "The range is {15.80, 31.60, 43.45, 57.25} ."
B) "The set of independent values is {4, 8, 11, 15}."
Which statements are true?Here we have the table for number of gallons and the costs of these:
g c
4 15.80
8 31.60
11 43.45
15 57.25
The statements that are true about that table are:
"The range is {15.80, 31.60, 43.45, 57.25} ."
This is true, the cost is the output of the table, thus, the range is that.
"The set of independent values is {4, 8, 11, 15}."
This is also called the domain, which is the input, in this case, the number of gallons of gas.
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Compare the function ƒ(x) = 4x + 2 to the function shown in the graph. Which statements are correct?
Responses
A The function ƒ(x) = 4x + 2 has a greater rate of change than the graphed function.The function ƒ(x) = 4x + 2 has a greater rate of change than the graphed function.
B The graphed function has a greater rate of change than the function ƒ(x) = 4x + 2.The graphed function has a greater rate of change than the function ƒ(x) = 4x + 2.
C The function ƒ(x) = 4x + 2 has a x-intercept with a greater value than the graphed function.The function ƒ(x) = 4x + 2 has a x-intercept with a greater value than the graphed function.
D The function ƒ(x) = 4x + 2 and the graphed function have the same slope.The function ƒ(x) = 4x + 2 and the graphed function have the same slope.
E The graphed function has a y-intercept with a greater value than the function ƒ(x) = 4x + 2.
The correct statement regarding the comparison of the linear functions f(x) and the graphed function is given as follows:
A. The function ƒ(x) = 4x + 2 has a greater rate of change than the graphed function.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial value.The function f(x) is given as follows:
f(x) = 4x + 2.
The parameters are given as follows:
Rate of change of 4.Intercept of 2.For the function g(x), we have that:
The rate of change is of 2, as when x increases by 2, y increases by 4, hence m = 4/2 = 2.The intercept is of 4, as the function crosses the y-axis at y = 4.Hence the correct option is given by option a, as the function f(x) has a greater rate of change, of 4, compared to the graphed function, of 2.
Missing InformationThe graphed function is given by the image presented at the end of the answer.
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Please help me, find the circumference of the circle use 3.14
Felix's dinner costs $16.49. Felix pays a $20 bill. About how much change did he receive? Show your work.
Answer: He received $3.51 in change.
Step-by-step explanation:
To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).
It will look like this:
$20.00 - $16.49 = $3.51
Answer:3 dollars and 51 cents
Step-by-step explanation:
What is the revolution of the Earth and Moon?
The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.
The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.
The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of 27.32 days.
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f(x) and g(x) below, find the value of f(g(-3)).
f(x) = 4x - 1
g(x) = 2x² + 7x - 3
Answer:
[tex]f(g(-3))=-25[/tex]
Step-by-step explanation:
[tex]g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25[/tex]
50PTS 50PTS 50PTS [D•O•N•T E•X•P•L•A•I•N]
Answer:x=20
Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get 8x+20 = 180, this can be simplified to 8x=160 or x = 20
Answer:
x = 20°
Step-by-step explanation:
Given angles,
→ 5x + 9
→ 3x + 11
Forming the equation,
→ (5x + 9) + (3x + 11) = 180°
{Because, sum of two angles in a straight line leads to 180°}
Now the value of x will be,
→ (5x + 9) + (3x + 11) = 180°
→ 5x + 3x + 9 + 11 = 180°
→ 8x + 20 = 180°
→ 8x = 180° - 20
→ x = 160/8
→ [ x = 20° ]
Hence, the value of x is 20°.
Could someone give me a hand here I’m rlly in a rush I needa get this over with
Answer:
c = √52
Step-by-step explanation:
applying pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' the hypotenuse.
Substitute values:
6² + 4² = c²
c² = 36 + 16
c² = 52
c = √52
(a-b)(a+2)-(a+b)(a-2)
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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Luc is investigating dilations of scale factor 2 of the line y = -4x +3. He claims that for some centers of dilation, the line will remain the same. Which centers of dilation could be used to support Luc's claim? Select ALL that apply.
Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.
To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.
For the origin (0, 0):
Point A: (x, y) = (0, 3)
Point B: (x, y) = (-4, -3)
Dilated Point A: (x, y) = (0, 6)
Dilated Point B: (x, y) = (-8, -6)
Equation of the dilated line: y = -4x + 6
This shows that the line is dilated with scale factor 2, but is the same line.
For the point (3, -4):
Point A: (x, y) = (3, -1)
Point B: (x, y) = (-1, -7)
Dilated Point A: (x, y) = (6, -2)
Dilated Point B: (x, y) = (-2, -14)
Equation of the dilated line: y = -4x + 3
This shows that the line is dilated with scale factor 2, but is the same line.
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What is the solution to the pair of simultaneous equations 2x y 5 3x 2y 4?
The solution to the pair of simultaneous equations 2x + y = 5 and 3x - 2y = 4 is (2, 1).
A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.
Given two linear equations in x and y,
2x + y = 5 (equation 1)
3x - 2y = 4 (equation 2)
Use substitution method to find its solution. Express the first equation as y in terms of x and substitute the value of y to the second equation.
2x + y = 5 (equation 1)
y = 5 - 2x
3x - 2y = 4 (equation 2)
3x - 2(5 - 2x) = 4
3x - 10 + 4x = 4
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.
3x - 10 + 4x = 4
7x = 14
x = 2
Substitute the value of x in the first equation and solve for y.
y = 5 - 2x
y = 5 - 2(2)
y = 5 - 4
y = 1
Hence, the solution of the given system of equations is (2, 1).
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Susan earns $10 per hour tutoring elementary students in math. She also earns $15 per
hour cleaning in the library. Her goal each week is to earn at least $240 while working no
more than 20 hours.
Let e represent the number of hours Susan works in one week tutoring elementary students,
and let c represent the number of hours Susan works in one week cleaning the library.
Which inequalities represent Susan's weekly goal of earning money?
Inequalities represent Susan's weekly goal of earning money are:
c + e ≤ 20
15c + 10e ≥ 240
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
Given that,
Susan earns $10 per hour tutoring elementary students in math.
She also earns $15 per hour cleaning in the library.
Her goal each week is to earn at least $240 while working not more than 20 hours.
Thus, the equation of inequality:
c + e ≤ 20
15c + 10e ≥ 240
Here, e represent the number of hours Susan works in one week tutoring elementary students.
c represent the number of hours Susan works in one week cleaning the library.
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Solve this problem?
step by step
Answer:
[tex]x = \sqrt{87}[/tex]
Step-by-step explanation:
So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:
[tex]13^{2} + x^{2} = 16^{2}[/tex]
Now, we will simplify the equations:
[tex]169 + x^{2} = 256[/tex]
Then, we will subtract 169 from both sides, giving us:
[tex]x^{2} = 87[/tex]
Square rooting both sides gives us:
[tex]x = \sqrt{87}[/tex]
And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.
Hope this helped