The linear equation that passes through the two given points is:
y = (-1/3)*x - 2/3
How to write the equation of the line with the two points?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (4, -2) and (-2, 0), then the slope is:
a = (0 + 2)/(-2 - 4)= 2/-6 = -1/3
y = (-1/3)*x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-2, 0) we will get:
0 = (-1/3)*-2 + b
0 = 2/3 + b
-2/3 = b
The linear equation is y = (-1/3)*x - 2/3
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Question 2 Part A:
An industrial copy machine has the ability to edit image dimensions by reducing it by a certain percentage
each time it copies. A design began with a length of 24 inches, represented by the point (0,24). After going
through the copy machine once, the length is 18, represented by the point (1,18).
Double click and enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)*
In the function, f(x) = a(b)ˣ the value of a and b is
a = 24b = 0.75How to find the value of a and bThe function defined by f(x) = a(b)ˣ is a exponential function
Where
a is the starting function
b is the base function
The starting function from (0,24)
24 = a(b)ˣ
a = 24
using (1, 18), we solve for the base
18 = 24(b)
b = 0.75
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Mary invests £12000 into a savings account. The account 1.5% compound interest per year. Work out the value of her investment after 2 years.
Answer:
Step-by-step explanation:
To calculate the compound interest on Mary's savings account, we can use the formula:
A = P * (1 + r/n)^(nt)
Where:
A is the amount after t years
P is the initial principal (£12000)
r is the interest rate (1.5%)
n is the number of times the interest is compounded in a year (let's assume it's compounded annually)
t is the number of years (2)
So, plugging in the values, we get:
A = £12000 * (1 + 0.015/1)^(1 * 2)
A = £12000 * (1.015)^2
A = £12000 * 1.0302
A = £12363.84
So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.
Sarah, James, and Matthew are on a team in a game show. In the game, Sarah always earns $5$ points, Matthew always earns $-2$ points, and James always earns $3$ points. To calculate their team's score, they multiply the first person's score by the second person's score, then subtract the third person's score. If they can choose the order in which they play the game, what is the maximum possible score that their team can earn?
Answer:
17
Step-by-step explanation:
5 x 3 = 15
15 - (-2) = 17
Sarah goes first, James goes second, and Matthew goes third.
Consider the line 9x-8y=-9.
Find the equation of the line that is parallel to this line and passes through the point (−3, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 4).
Equation of parallel line:
Equation of perpendicular line:
1
=
X
0=0
5
A plane traveled 3900 miles with the wind in 6.5 hours and 3120 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer:
the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
Step-by-step explanation:
Step 1: Define the variables
Let's call the speed of the plane in still air "V". Let's call the speed of the wind "W".
Step 2: Write an equation for the distance traveled with the wind
The distance traveled by the plane with the wind in 6.5 hours can be represented by the equation:
D1 = (V + W) * t
where D1 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3900 = (V + W) * 6.5
Step 3: Write an equation for the distance traveled against the wind
The distance traveled by the plane against the wind in 6.5 hours can be represented by the equation:
D2 = (V - W) * t
where D2 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3120 = (V - W) * 6.5
Step 4: Solve for the speed of the wind
We can now use the two equations from Steps 2 and 3 to solve for the speed of the wind.
First, let's rearrange the equation from Step 2 to isolate "W":
W = (3900 / 6.5) - V
Next, substitute this expression for "W" into the equation from Step 3:
3120 = (V - ((3900 / 6.5) - V)) * 6.5
Expand the right side of the equation:
3120 = (V - 3900 / 6.5 + V) * 6.5
Simplify the equation:
3120 = 2V * 6.5 - 3900
Divide both sides of the equation by 2:
1560 = V * 6.5 - 1950
Multiply both sides of the equation by 2:
3120 = V * 13 - 3900
Add 3900 to both sides of the equation:
7020 = V * 13
Divide both sides of the equation by 13:
V = 540
Step 5: Solve for the speed of the wind
Now that we know the speed of the plane in still air, we can use the equation from Step 2 to find the speed of the wind:
W = (3900 / 6.5) - V
Substitute the value of "V" that we found in Step 4 into the equation:
W = (3900 / 6.5) - 540
Simplify the equation:
W = 280
Step 6: Conclusion
Therefore, the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
B) The area of a triangle = ½ the base the
height
What is the area of an equilateral triangle where
every side measures 10 cm?
The area of the equilateral triangle with side length 10 cm is 25 cm².
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
To find the area of an equilateral triangle, we need to find the height first. The height of an equilateral triangle is equal to the length of the perpendicular line from the center of the triangle to one of its sides.
To find the height, we can divide the equilateral triangle into two 30-60-90 triangles. The height is equal to half of the hypotenuse of one of these triangles, which can be calculated as:
10 cm / 2 = 5 cm
Now that we have the height, we can find the area of the equilateral triangle as follows:
Area = ½ * base * height
Area = ½ * 10 cm * 5 cm
Area = 25 cm²
Hence, The area of the equilateral triangle with side length 10 cm is 25 cm².
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Determine if the points are solution points to the inequalities below. If the point is a solution, enter yes.
If the point is not a solution, enter no. Enter yes or no in lower case letters (no capital letters).
a. Is (2, 10) a solution to y < 12- x?
b. Is (3, 13) a solution to y ≤ 15 - x?
c. Is (4, 19) a solution to y > 19 - x?
d. Is (5, 13) a solution to y ≥ 12 - x?
The solution is;
a. (2, 10) is not a solution to y < 12- x.
b. (3, 13) is a solution to y ≤ 15 - x
c. (4, 19) is a solution to y > 19 - x
d. (5, 13) is not a solution to y ≥ 12 - x
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
A Set of such values is called a solution set to the considered equation or inequality.
Substitute the values where the variables are, and simplify to the point where you can tell whether the statement is true.
Each ordered pair is (x, y), thus the first value gets substituted for x; the second value gets substituted for y.
a. (2, 10)
11 < 13 -2 = 11
no
b.(3, 13)
8 ≤ 16 -3 = 13
yes
c. (4, 19)
20 > 18 -4 = 14
yes
d. (5, 13)
9 ≥ 15 -5 = 10
no
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subtract 1/2h - 1 from 3/4h + 4
Answer:
= -1+12h.
Step-by-step explanation:
I guess my answer is correct
What is the Volume of the prism below
Answer:
140
Step-by-step explanation:
(5*7*8)/2= 280/2 =140
Multiplying a number by which of the following would result in a smallest number?
O 10-1
O 10⁰
O 10¹
102
You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To volume to fill the rectangular garden is 8.99 cubic yard
What is the volume to fill the gardenTo determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.
inch to yard
6 inch = 0.17 yard
Feet to yard
28 feet = 9.33 yard
17 feet = 5.67 yard
The volume of the rectangular garden is given as;
v = l * w * h
l = lengthw = widthh = heightSubstituting the values;
V = 0.17 * 9.33 * 5.67
v = 8.99 cubic yard
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Simplify the following expression using rational exponents. Assume all variables are positive.
(4y2/5)^2
A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.
What is meant by rational exponent?Exponents that are fractions with the denominator a root and the numerator a power are known as rational exponents. For instance, 813 is another method to write 38, while 1612 is another way to write 16. A fractional exponent is a rational exponent. For instance, the number 4 can be written as 412 4 1 2. Though they can be challenging to use at first, rational exponents can actually make some issues simpler.The ability to express rational exponents in pq form as opposed to irrational exponents in pq form is one of the key distinctions between the two types of exponents. Rational exponents are rational numbers, whereas irrational exponents are infinite or non-repeating decimals.Given,
[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]
Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]
[tex]$=\frac{16 y^4}{5^2}[/tex]
The we get,
[tex]$& =\frac{16 y^4}{25}[/tex]
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PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
Given the functions f(x) = x3 + x2 – 2x + 3 and g(x) = log(x) + 2, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2 have same range as (-∞,∞) or {y : y∈R}.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given functions are -
f(x) = x³ + x² - 2x + 3
g(x) = log(x) + 2
The graph for function f(x) is plotted.
The function f(x) is a cubic function.
The domain for the function is (-∞,∞) or {x : x∈R}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (-2.37442376,0).
The y-intercept for the function is (0,3).
The graph for function g(x) is plotted.
The function g(x) is a logarithmic function.
The domain for the function is (0,∞) or {x : x>0}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (0.01,0).
The y-intercept for the function is not available.
Therefore, both functions have same range,
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can someone pls give me the percent equation to these? 100 points to the fellow that does and brainiest if correct. Also pls hurry, its due today
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
120 is what percent
of 400?
4% of 975 is what
number?
Answer:
Step-by-step explanation:
You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.
Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.
I used x to represent what we are looking for:
6.5% of $400 = x
0.065 * 400 = $26
12.5% of 100 = x
0.125 * 100 = $12.5
x of 650 = 130
130/650 = 0.2 which equals 20%
x of $4.50 = $5.40
5.40/4.50 = 1.2 which equals 120%
x of $28 = $8.40
8.40/28 = 0.3 which equals 30%
56% of x = $21.84
21.84/0.56 = 39
55% of x = $495
495/0.55 = 900
x of 400 = 120
120/400 = 0.3 which equals 30%
4% of 975 = x
0.04 * 975 = 39
Answer:
See below
Step-by-step explanation:
a. 6.5% of $400:
[tex]= \frac{65}{100}[/tex]× ($400)
= $260
b. 12.5% of $100:
[tex]= \frac{12.5}{100}[/tex] × ($100)
= $12.5
c. 130 is what percent of 650:
[tex]=\frac{130}{650}[/tex]×100%
= 20%
d. $5.40 is what percent of $4.50:
[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%
e. $8.40 is what percent of $28:
[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%
f. 56% of what number is $21.84:
=[tex]\frac{56}{100}[/tex]× number = $21.84
∴ Number = [tex]\frac{100}{56}[/tex]×$21.84
= $39
g. $495 is 55% of what number:
= $495 = [tex]\frac{55}{100}[/tex]× Number
∴Number = [tex]\frac{100}{55}[/tex]×($495)
= $900
h. 120 is what percent of 400:
= [tex]\frac{120}{400}[/tex]×100%
= 30%
i. 4% of 975 is what number:
= [tex]\frac{4}{100}[/tex]×975
= 39
Determine the value for m in the equation 1.4m = 0.42. HELP ASAP
Answer:
Below
Step-by-step explanation:
1.4 m = .42 divide both sides of the equation by 1.4 to get
m = .3 Done.
what could be a ratio between the lengths of the two legs of a 30-60-90 triangle
Answer:
Below
Step-by-step explanation:
One leg would be hyp * cos 30 and one would be hyp cos 60
hyp cos 30 : hyp cos 60
cos 30 : cos 60
= ratio sqrt (3) /2 : 1/2 or sqrt 3 : 1
In the figure below, which term best describes point W?
A. Centroid
B. Orthocenter
C. Circumcenter
D. Incenter
The term that best describes the point W in the triangle is given by the following option:
B. Orthocenter.
What is the orthocenter of a triangle?The orthocenter is the point where all three altitudes of a triangle will intersect.
An altitude is a line which passing through one of the three vertices of the triangle and is perpendicular to the opposite side relative to this vertex.
Hence point W is the orthocenter of triangle XYZ.
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Please help!! Due tomorrow morning!!
Directions: if QS represents an angle bisect or, solve for x.
(Ignore my answer)
The solution for x in the triangle is x = 52.5
How to solve for x in the triangle?
The bisector of an angle in a triangle divides the opposite side in the ratio of the sides containing the angle. That is:
PQ/QR = PS/SR
PQ = x, QR = 35, PS = 42 and SR = 70 - 42 = 28.
Therefore, we have:
PQ/QR = PS/SR
x/35 = 42/28
28*x = 42*35
28x = 1470
x = 1470/28
x = 52.5
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At a college, the ratio of faculty/staff to students is 3 to 13. If there are 4000
people at the college, how many students are there?
Answer:
Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.
According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:
3x / x = 3 / 13
To find the number of students, we can solve for x:
4x = 4000
x = 1000
So, there are 1000 students at the college.
if f (x) equals 3 (x+4), find f (2)
Answer:
f(2) = 18
Step-by-step explanation:
If f(x) = 3 * (x + 4)
Than f(2) = 3 * (2 + 4) (coz x is an argument)
f(2) = 3 * (2 + 4)
f(2) = 3 * 6
f(2) = 18
Find the limit………………
[tex]\lim_{p \to \(-8}[/tex] = -59
What is a Limit?
Limit is the values that a function approaches the output for the given input values.
How to calculate this
[tex]\lim_{p \to \(-8}[/tex] ( -[tex]p^{2}[/tex] - p -3)
when p = -8
By inserting the value of p
[tex]\lim_{p \to \(-8}[/tex] = {-(-8)^2 - (-8) - 3 }
open the bracket
[tex]\lim_{p \to \(-8}[/tex] = (-64 + 8 - 3 )
[tex]\lim_{p \to \(-8}[/tex] = ( - 59 )
So, [tex]\lim_{p \to \(-8}[/tex] =-59
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How do I do these questions ??
Consider the system of equations.
y = -5x-1
y = 2x+6
Choose the correct answer to each question.
What is the slope of the first line?
What is the slope of the second line?
How many times do the lines intersect?
C
How many solutions does the system have?
C
Costs of Starting Your Own Business
SHORT ANSWER
You are looking at a potential location to open your first spa. The rent is $21 per square
(annually), and the space is 1,800 square feet. How much rent would you pay each year? Each
foot
month?
The amount of money that would be paid for rent each year for the spa would be = $37,800
How to calculate the annual payment for the rent for spa?The area of the potential space for the opening of your first spa = 1,800 square feet.
The price for each square feet per year = $21
That is; = 1800× 21 = $37,800
Therefore, annual rent fees for the space which will be used for spa = $37,800.
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What needs to be done to an equation to find the slope and y intercept??
NEED HELP ASAP
Answer:
C. Solve for the variable y.
Step-by-step explanation:
You want to know what needs to be done to an equation to find the slope and y-intercept.
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx + b
This is a polynomial equation written in standard form with the terms in decreasing order of the power of the variable. In this equation, the coefficient 'm' is the slope of the line, and the constant 'b' is the y-intercept on the graph.
This equation can be obtained from other forms of the equation for a line by solving for y and arranging the terms to match this form. That is, to find the slope and y-intercept, what needs to be done is ...
C. Solve for the variable y.
__
Additional comment
The description "standard form" as used above applies to polynomials in general. Specific polynomial equations, as for lines, circles, ellipses, hyperbolas, have their own "standard form."
The form called "standard form" for a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a > 0. In the case of a horizontal line, b > 0.
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A total of 360 people voted in an election. The circle graph shows the results.
(a) How many people (number of people, not the percentage) voted for Goron?
Show your work.
(b) How many people (number of people, not the percentage) voted for Fishman
and Other? Show your work. PLEASE HELP
a. There were 126 people who voted for Goron.
b. There were 144 people who voted for Fishman.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given circle graph shows the results.
There were 360 people who voted in the election.
According to the question, the required solution would be as:
number of people who voted for Goron = 35% of 360
15% is expressed as 15/100 in fractional form
number of people who voted for Goron = (35/100) × 360
number of people who voted for Goron = 126
number of people who voted for Fishman = 40% of 360
number of people who voted for Fishman = (40/100) × 360
number of people who voted for Fishman = 144
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The missing figure has been attached below
Solve for the 2 unknown sides and the missing angle
The measure of other sides of a triangle are 15.11 units and 10.76 units.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
In the given triangle, ∠B=45°, ∠C=52° and AB=12 units.
By using angle sum property of a triangle,
∠A+∠B+∠C=180°
∠A+45°+52°=180°
∠A+97°=180°
∠A=83°
Now, by using sine rule, we get
sin83°/a=sin45°/b=sin52°/12
0.9925/a=0.7071/b=0.788/12
0.9925/a=0.788/12 and 0.7071/b=0.788/12
0.788a=11.91 and 0.788b=8.4852
a=11.91/0.788 and b=8.4852/0.788
a=15.11 units and b=10.76 units
Therefore, the measure of other sides of a triangle are 15.11 units and 10.76 units.
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Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results? Check all that apply. Sample more families/ sample families that have children who are not in seventh grade/ sample families that do not have children /sample families whose answer to the survey question is predetermined/ sample families living in every third house in the neighborhood
The correct options are sample more families, sample families having children who are not in seventh grade.
Sample families that do not have children. Sample families living in every third house in neighborhood.
To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:
Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.
Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.
Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.
Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of
sampling bias.
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Tomas estimated that he would need to throw 22.52m in fact he threw 21.36m what is the percentage error
Answer:
5.15%
Step-by-step explanation:
Difference between estimated throw and actual throw
= estimated - actual
= 22.52 - 21.36
= 1.16 m
As a fraction of estimated throw:
1.16/22.52
As a percentage:
1.16/22.52 x 100 = 5.15%
