What is a linear equation?
Answers
Answer: A linear equation follows a pattern where there is a specific change in y value for every change in x, the general form of the linear equation is as follows:
\(y(x)=mx+b\rightarrow(1)\)Where the constant m and b are slope and y-Intercept.
\(m=\frac{\Delta y}{\Delta x}\)The graph of the linear equation with m = 1 and b = 0 is as follows:
\(\begin{gathered} m=,b=0 \\ \\ \therefore\Rightarrow \\ \\ y(x)=x \end{gathered}\)Note! For every change in x there is a fixed change in y.
Related Questions
WILL MARK BRAINLIEST
Use the function below to find F(3)
F(x)=(1/5)^x
Answers
The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.
What is a function?A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.
A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.
F(x)=(1/5)ˣ
F(3)=(1/5)³
F(3)=1/125
Hence, the value of the function F(3) will be 1/125.
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Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
Answers
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
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Please solve the picture I just send
Answers
The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.
To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:
Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)
Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).
i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.
The radius of the circle is half the length of PN. Therefore, the radius is given by:
Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)
Substituting the values into the equation, we get:
\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)
ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.
The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:
m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75
The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.
Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:
y - (-2) = (-4/3)(x - 7)
y + 2 = (-4/3)x + 28/3
y = (-4/3)x + 22/3
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Susie is visiting Germany from the U.S. One day she stopped by a market and found a stall selling tomatoes for 1.74 euro per kilogram. If 1 euro was worth 1.09
dollars that day, how much did the tomatoes cost in dollars per pound?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of
the equation.
Answers
The cost of the tomatoes, in dollars per pound, using proportions, is of:
$0.86 per lb.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.
In this problem, the costs is obtained as follows:
Cost: 1.74 euros per kilogram.Exchange ratio: 1 euro = 1.09 dollars.Hence the cost in dollars per kg of the tomatoes is obtained as follows:
1.74 x 1.09 = $1.8966 per kg.
The relationship between kg and pounds is given as follows:
1 kg = 2.20 lb.
Hence the cost is written as follows:
$1.8966 per 2.20 lb.
The cost per pound of the tomatoes is of:
1.8966/2.20 = $0.86 per lb.
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What is the value of the x-coordinate of point A?
(a) sin(pi/5)
(b) cos (pi/5)
(c) sin (6pi/5)
(d) cos (6pi/5)
(e) sin (9pi/5)
Answers
Answer:
D.) cos(6π/5)
Step-by-step explanation:
In a unit circle, cosine is defined as x-coordinate and sine is defined as y-coordinate.
This is because cosine is defined as x/r but since it’s a unit circle, r = 1 therefore, cosine = x,
Sine is defined as y/r but it’s a unit circle so sine = y.
Therefore, we ignore choices with sine.
Next, since this π/5 angle is in the third quadrant. π/5 is supposed to be in the first quadrant so to convert from first quadrant angle or reference angle to the third quadrant angle or opposite side, add the reference angle or π/5 by π.
Therefore, π/5 + π = π/5 + 5π/5
= 6π/5
Since we want to find x-coordinate which is cosine, therefore.
The answer is cos(6π/5)
This unit focused, in part, on relationships in triangles. A triangle is the simplest type of
polygon and is frequently used in construction. Explain why triangles are often used to
build bridges, roofs, buildings, and other structures. Which properties of a triangle make
it a desirable geometric shape for these applications? Which type of triangle is best?
Why is the triangle preferred over other types of polygons? Explain.
Answers
Answer:
triangles have a specific geometric shape.Because they have three sides, the pythagorean theorem for right angled triangle.
Triangles are often used to build bridges, roofs, buildings, and other structures because truss made of shape of a triangle gives better load distribution.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Triangle shape trusses are used to build bridges, roofs, buildings, and other structures, as triangle shape trusses distribute the load in a pattern such as a load on one vetex distributed to two sides or a load on two sides distributed to one vertex of trusses and so on.
Thus, Triangles are often used to build bridges, roofs, buildings, and other structures because truss made of shape of a triangle gives better load distribution.
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Given that f(x) = x + 3
a) Find f(2)
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
In the above question, it is given that :
\(\qquad \sf \boxed{ \sf f(x) = \frac{x + 3}{2} }\)
A.) Find f(2) :
\(\qquad \sf \dashrightarrow \: f(2) = \dfrac{2 + 3}{2} \)
\(\qquad \sf \dashrightarrow \: f(2) = \dfrac{5}{2} \)
or
\(\qquad \sf \dashrightarrow \: f(2) = 0.5\)
B.) Find \({ \sf {f}^{-1}(x) } \) :
\(\qquad \sf \dashrightarrow \: let \: y = f (x) \)
so, we can write it as :
\(\qquad \sf \dashrightarrow \: y = \dfrac{x + 3}{2} \)
\(\qquad \sf \dashrightarrow \: 2y = x + 3\)
\(\qquad \sf \dashrightarrow \: x = 2y - 3\)
Now, put x = \({ \sf {f}^{-1}(x) } \), and y = x and we will get our required inverse function ~
\(\qquad \sf \dashrightarrow \: f {}^{ - 1}(x) = 2x- 3\)
C.) Find \({ \sf {f}^{-1}(12) } \) :
\(\qquad \sf \dashrightarrow \: f {}^{ - 1}(12) = 2(12)- 3\)
\(\qquad \sf \dashrightarrow \: f {}^{ - 1}(12) = 36- 3\)
\(\qquad \sf \dashrightarrow \: f {}^{ - 1}(12) = 33\)
f(ə) =
g(x) = (x - 2)2 – 7
We can think of g as a translated (shifted) version of f.
Complete the description of the transformation,
Use nonnegative numbers.
To get the function g, shift f up/down v
by
units and to the
right/left
by
units.
Answers
Answer: To get function g, shift f DOWN by 7 units and to the RIGHT by 2 units
Step-by-step explanation: g(x)= (x-2)^2-7 since they’re both negatives it should be the opposite. An example would be g(x)=(x+3)^2+5, f goes UP for positive by 5 units, left by 3 units.
An elevator travels 310 feet in 10 seconds.
1. At that speed, how far can this elevator travel in 12 seconds?
Answers
Answer:
372
Step-by-step explanation:
1 sec=31 feet
10 sec=310 feet
12 sec=372 feet
Which of the following units are units of capacity? Select all that apply.
Answers
The length of a rectangle is 3 meters less than
twice its width. The area of the rectangle is
104 m²2. Find the dimensions of the rectangle.
Answers
Therefore, the length of a rectangle is 13m and width is 8m
What is area?A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.
Here,
width=x
length=2x-3
Area =l x w
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4
x= 8m
Thus width = 8m
length = 2(8)-3 = 13m
Therefore the length of a rectangle is 13m and width is 8m
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Convert. (13/5) into a mixed number.
Answers
Answer:
2 3/5 :)
Step-by-step explanation:
please help school is literally about to end
Answers
Answer:
192 is the answer
Step-by-step explanation:
Answer:
SA = 272 sq in
Step-by-step explanation:
SA = 2(8 x 2) + 2(8 x 12) + 2(2 x 12)
= 2(16) + 2(96) + 2(24)
= 32 + 192 + 48
= 272 sq in
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
Answers
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)
16.67% probability = 0.1667
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An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the other ends of the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. How far across is the sink hole?
d. What is the perimeter of the triangle ABC?
Answers
A) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
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Answer:
Step-by-step expA) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?
A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
lanation:
crystal wants to buy a bag of red delicious apples one bag has a price of $4.50 what is the unit price per apple HEEEEEELP ASAP
Answers
Answer:
How many apples are in a bag?
Step-by-step explanation:
Which of the following is not a rational number? (Select all that apply.)
6.725
0.0625
2.713
0.65
Answers
Answer:
Step-by-step explanation:
All of them are rational.
Irrational numbers go on forever, like 10/3=3.33333333...
Pi is an irrational number because it goes on forever.
The sum of three consecutive natural numbers is 891, find the numbers.
The three numbers in increasing order are _____ , _____ and _____
Answers
The three numbers in increasing order are 296. 297 and 298
How to determine the valueLet the consecutive natural numbers be;
first number = x
second number = x + 1
Third number = x + 2
Now, substitute the values, we get;
x + x + 1 + x + 2 = 891
collect the like terms
x + x + x = 891 - 3
Add or subtract the like terms, we get;
3x = 888
Divide the value by the coefficient of x, we get;
3x/3 = 888/3
Divide the values
x = 296
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Drag the digits 0 to 9 to the boxes to create an original rectangle and a scaled copy.
Answers
Answer:
900 degrees
Step-by-step explanation:
I did this on my quiz
Find the constant rate of change for each linear function and interpret its meaning
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}\)
Divide. −3.52−2.2 What is the quotient
Answers
The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
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What’s the missing value of y=-2+4
Answers
Answer:
y=2
Step-by-step explanation:
Answer:
y = 2
Step-by-step explanation:
-2 + 4 = 2
therefore, y = 2
Ratios Question 2
A roll of nickels has a $2 value. Which of these tables
correctly shows the ratios of different numbers of rolls
of nickels to their values?
Select
2
4
Value
512 516
12
16
Value
3
512
12
16
59
2
V2
Answers
Multiply: -
2/3 x 6/7
Put your answer in lowest terms.
A. 4/7
B. 4/21
C. 12/21
D. 3/7
Answers
Answer:
It should be -4/7
Step-by-step explanation:
I hope i helped. And If you can, can you help me by subing to my YT. It’s called Not Claz and it is the same profile pick I have on Brainly.
Hello, is there anyone here a pharmacy technician?
Answers
Maybe
Explanation:
…
PLEASE HELP ILL GIVE BRAINLIESTTTT
Answers
Answer:
about 5.1 units
Step-by-step explanation:
to find the length between two points you can use the pythaogorean theorem
5^2 + 1^2 = c^2
25 + 1 = c^2
26 = c^2
c is about 5.09901
rounding to the nearest tenth we get 5.1
Need help, thanks!!!!!
Answers
When interpreted, the figures of the delivery times of the pizza shops shows that D. The means are nearly equal, but the variation is significantly greater for the second shop than for the first.
What do the delivery times mean ?This means that, on average, the second pizza shop delivers pizzas slightly faster than the first shop. However, the delivery times for the first shop are more consistent (less variable) than the second shop.
The standard deviation for the first shop (4 minutes) is much lower than the second shop (21 minutes), indicating that the delivery times for the first shop are clustered closely around the mean delivery time, whereas the delivery times for the second shop are more spread out. If delivery time is the only consideration, one may prefer the first shop as it has more consistent delivery times.
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Solve each equation please?
6) 3x - 5 = 10
7) 36 = 4x + 12
8) 3(x + 2) = 36
9) 7(2x - 15) = 63
Answers
Answer:
6) x=5
7)x=6
8)x=10
9)x=12
Step-by-step explanation:
6) 3x-5=10. 7) 36=4x+12. 8) 3(x+2)=36
+5 +5. - 12. - 12. 3x + 6=36
3x = 15. 24 = 4x. - 6. -6
÷3. ÷3. ÷4. ÷4. 3x=30
x=5. 6 = x. x = 10
9) 7(2x-15)=63
14x - 105=63
+105. +105
14x = 168
÷14. ÷14
x=12
Graph the circle (x - 3)^2 + (y + 3)^2= 36.
Answers
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
Answers
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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