Using the Pythagoras threoem,
the possible value of k are 6 or 1 in right angled triangle.
We have given that,
There is a triangle say, ∆ABC with vertices A(1,2) ,B(k , 2) and C(6,7).
and angle, B = 90°
that is this is a right angled triangle with angle ABC is 90° .
we have to find out the value of k .
Using Pythagoras threoem,
AB² + BC² = AC²---(*)
where, AB ,BC and AC are sides of ∆ABC.
using distance formula, we find length of sides of ∆ABC . let coordinates of A (a₁,b₁) and B(a₂,b₂)
AB = √(a₂ - a₁)² + (b₂-b₁)²
put a₁ = 1 , b₁ = 2 , a₂ = k , b₂ = 2
AB² = (k - 1)² + (0) = (k-1)²
similarly we can easily calculate the length of other sides of ∆ABC.
BC² = (6-k)² + 25
AC²= (5)² + (5)² = 50
putting all sides value in above formula,
50 = (k-1)² + (6-k)²+ 25
=> 25 = k² + 1 - 2k + 36 + k² - 12k
=> 2k² - 14k + 12 = 0
=> k²- 7k +6 = 0
this is a quadratic equation we solve it and find out value of k
using , roots formula
k = { -(-7) +- √(-7)^2 - 4(1)(6)}/2×1
=> k = either( 7 + √25) /2 or (7- √25)/2
=> k = either 6 or 1
Hence , the possible value of k are 6 or 1
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Determine the value of b in the equation b3 = −125. b = −5 b = 5 b = −41.7 b = 41.7
The value of b in the equation [tex]b^{3}[/tex] = 125 will be 5. Option (b) is correct.
The question is about the system of equations. According to the question, we have the following equation:
b³ = 125.
We can find the value of b by simplifying and using the rules of equations.
First, we need to Factorize 125 on the right-Hand side, we get.
b³ = 5.5.5 = 5³
Hence we get,
b³ = 5³
We know that if there are two expressions that are equal and we add, subtract, multiply or divide into both sides of the equation, the resulting equation will also be equal. So, Multiply both sides by the cube root, and we get:
[tex]\sqrt[3]{b^{3}} = \sqrt[3]{5^{3}}[/tex]
[tex](b^{3})^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}}[/tex]
[tex](b})^{\frac{3}{3}} = (5})^{\frac{3}{3}}[/tex]
[tex](b})^1 = (5})^1[/tex]
So we get the value of b = 5, hence the correction option will be (b).
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studies show that gasoline use for compact cars sold int he untied states is normally distirbuted with a mean use of 25.5 miles per gallon and a standard deviation of 4.5 miles per gallon. what eprcentage of compact obtains 30 or more miles per gallon
0.1587 is eprcentage of compact obtains 30 or more miles per gallon by standard deviation.
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.
P(X> 30 )
Normal distribution
μ = 25.5
σ = 4.5
P(X > 30 ) = Area to the right of 30
we convert this to standard normal using z = x - μ/σ
z = 30 - ( 25.5 )/45 = 1.00
P(Z > 1.00 ) = Area to the right of 1.00
P( X > 30) = P( Z > 100) = 1 - P( Z < 1.00 ) = 1 - 0.8413
= 0.1587
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Caroline buys 5 rubbers and 5 crayons for £10.
Elliot buys 1 rubber and 2 crayons for £2.75.
Work out the cost of one rubber and one crayon.
Answer:
5R + 5C = 1000
1R + 2C = 275
(1R + 2C = 275) x 5 = 5R + 10C = 1375
(5R + 10C = 1375) - (5R + 5C = 1000) = 5C =375
CRAYON = 75p
RUBBER = 125p
there are 96 boys and 112 girls in a primary school . write the ratio of the boys to the girls
Answer:
6 : 7
Step-by-step explanation:
the ratio of
boys : girls
= 96 : 112 ( divide both parts by 16 )
= 6 : 7
Which table represents the function y = -2x + 4?
Input x 0 1 2
Output y 4 7 10
Input x 0 1 2
Output y 4 2 0
Input x 0 1 2
Output y 4 6 8
Input x 0 1 2
Output y 3 4 5
The table that represents the function y = -2x + 4 is: the second table.
How to Find the Function that Represents a Table?Considering the third table representing a function given:
x | y
0 4
1 2
2 0
Find the slope (m) using the two points (1, 2) and (2, 0):
Slope (m) = change in y / change in x = (0 - 2) / (2 - 1)
m = -2/1
m = -2.
The y-intercept (b) = 4.
Substitute m = -2 and b = 4 into y = mx + b:
y = -2x + 4
Therefore, the second table represents the function y = -2x + 4.
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How is the area of a triangle formed by the Midsegments of a triangle related to the area of the original triangle use an example to justify your answer?.
A triangle's midsegment is the section created by joining any two of its sides at their midpoints.
Simply said, it equally splits the two triangle sides. A side is divided into two equal segments at its halfway. The middle segment of the triangle ABC is DE, as shown in the image below. Segment AB is divided into two equal portions at point D, and segment CB is divided into two equal parts at point E. The base of the triangle is the side on which the midsegment does not meet. The segment created by joining the midpoints of a trapezoid's two legs is known as the midsegment. Despite the fact that a trapezoid's midsegment is also helpful
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Write a recursive formula for the sequence described.
It follows a plus one pattern: 8, 9, 10, 11, 12, ...
The recursive formula for the given sequence is, [tex]a_n=a_n_-_1+1[/tex].
What is recursive formula?
Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula
[tex]a_n=a_n_-_1+d[/tex]. [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.
Consider the given sequence,
8, 9, 10, 11, 12, ...
Here each next term is defined by it's preceding term by adding 1 in each preceding term.
That is,
9 = 8 +1
10 = 9 + 1
11 = 10 + 1
12 = 11 + 1
Hence, the recursive formula for the sequence is, [tex]a_n=a_n_-_1 + 1[/tex].
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a rectangular room twice as long as it is wide would contain 145 square feet more if each side were one foot longer. what is the length of the room?
The length of the room will be 96 ft after increasing each side by 1 foot.
Let L be the length of the room and W be the width of the room.
Given , L = 2W.
Area , A = LW
= 2W × W
= 2W²
On increasing each side by 1 foot, new area is A' = (L + 1)(W + 1)
= (2W + 1)(W + 1)
= 2W² + 3W + 1
Since, the room would contain 145 ft more if each side were increased by 1 foot, then its new area is A' = A + 145 = 2W² + 3W + 1
2W² + 145 = 2W² + 3W + 1
145 = 3W + 1
3W = 145 - 1
3W = 144
W = 144/3
W = 48 ft.
Since its length L = 2W, substituting W = 48 into the equation, we have
L = 2(48)
L = 96 ft
Therefore the length of the room will be 96 ft.
The area of a rectangle in a two-dimensional plane is the area that it occupies. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.
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Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,P(5) = 1/6, P(6) = 0.(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,P(spades) = 16/52.Part (a) The distribution is legitimate.Part (b) The distribution is not legitimate.Part (c) The distribution is legitimate.
From the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
How to know legitimate probability distribution?We should know that Probability is the chance of occurrence of an even (E) over a period of time.
A legitimate probability distribution must be that which adds up to 1 and cannot be negative.
Legitimate Distribution= P(a)+P(b)+P(c)+.....+P(n)
Where a,b,c and n are Probabilities of events.
From the given Parameters
(a) Rolling a die to record P(1) =0, P(2)=[tex]\frac{1}{6}[/tex], P(3)=[tex]\frac{1}{3}[/tex], P(4)=[tex]\frac{1}{3}[/tex], P(5)=[tex]\frac{1}{6}[/tex], P(6)=0
Add up the probabilities to get 1
⇒0+[tex]\frac{1}{6} +\frac{1}{3}+\frac{1}{3}+\frac{1}{6}+0[/tex]
⇒[tex]\frac{0+1+2+2+1+0}{6}[/tex]
P(E)=[tex]\frac{6}{6}=1[/tex]
This implies that the distribution is legitimate
(b) Choosing a college student at random,
Add up the probabilities to get 1
P(female full time)+P(male full time)+P(female part time)+P(male part time)
⇒0.56+0.44+0.24+0.17
=1.41
The probability of the distribution is not legitimate because it is greater than one.
(c) Deal a card from a shuffled deck.
Add up the probabilities to get 1
P(club)+P(diamond)+P(hearts)+P(spades)
[tex]\frac{12}{52} +\frac{12}{52}+\frac{12}{52}+\frac{52}{16}[/tex]
[tex]\frac{12+12+12+16}{52}[/tex][tex]\frac{52}{52}=1[/tex]
The distribution is legitimate because the sum of the probabilities is
equal to 1
In conclusion, from the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
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At 98°F, a certain insect chirps at a rate of 88 times per minute, and at 107°F, they chirp 151 times per minute. Write an equation in slope-intercept form that represents the situation.
The equation in slope-intercept form that represents the situation is y = 7x - 598
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
The ordered pair are ( 98, 88) and (107, 151)
Equation of line in slope-intercept form is y = mx + c
at x = 98, y =88
so that by substituting we have,
88 = 98m + c -------------------1
at x = 107, y = 151 and by substituting we have
151 = 107m + c -----------------2
subtract equation 1 from 2
63 = 9m
m = 63/9
m = 7
substitute m = 7 in equation 1
88 = 98(7) + c
c = 88 - 686c
c = -598
substitute m and c for their values equation becomes
y = 7x - 598
In conclusion, the equation in slope-intercept form is y = 7x - 598
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Pythagorean Theorem of an equilateral triangle?
The Pythagorean Theorem of an equilateral triangle is a²+b²=c²
What is meant by an equilateral triangle?The height of an equilateral triangle is defined as a line drawn from any vertex on the opposite side of the triangle. This is the opposite side's perpendicular bisector. This means it cuts the opposite side in half and produces a 90° angle with it. The altitude that separates an equilateral triangle into two congruent right-angled triangles is also known as the triangle's height.
To calculate the missing side lengths of an equilateral triangle, use the Pythagorean theorem and the height of the right triangles within the equilateral.
The area of an equilateral triangle can therefore be determined using the formula A = 3/4 (a2).
The Pythagorean Theorem of an equilateral triangle is,
a(√3/2a)+b(√3/2b)=c(√3/2c)
√3/2a²+√3/2b²= √3/2c²
√3/2(a²-b²)= √3/2(c²)
a²+b²=c²
This is the Pythagorean Theorem of an equilateral triangle.
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How to determine if a graph represents y as a function of x?.
Answer:
Step-by-step explanation:
If it is not possible to draw a vertical line to touch the graph of a function in more than one place, then y is a function of x. For Example: Use the vertical line test to determine if the graph depicts y is a function of x.
State the complementary event of rolling a die and getting a number less than 3.
The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3 is the event and its complement is P' = n > 3.
What is the complement of an event?The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."
If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.
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Show that the flux of F =e_{r}/r^2 through a sphere centered at the origin does not depend on the radius of the sphere.
Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F
and 014≤ 640 ≤ 2TT outward normal is
(r = 18) = √x² + y²+z2)
= F = ૪ 3
flux = [[Finds
. Rsing dodo = 83
(from put value of n
13 sind do do 23
2 TT, TT sing do do
R 11 R [["e. / sind dado (r= 171 = radius of ephare)
Π 2T ए [e" [" sind do do= ["- Casp" "do 0
[-(-1-1) do 2TT = 2x (2-0) 2 = do flux
flux = [[F·ñ-ds S = 4π
The flux is 411 and it depends on radius 'R'
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A pendulum of length L cm has time period T seconds.
T is directly proportional to the square root of L.
The length of the pendulum is increased by 40%.
Work out the percentage increase in the time period.
The percentage increase in the time period is 6.3245%.
Given:
A pendulum of length L cm has time period T seconds.
T is directly proportional to the square root of L.
The length of the pendulum is increased by 40%.
Let L1 and T1 be the increased pecentage.
T α [tex]\sqrt{L}[/tex]
T/[tex]\sqrt{L}[/tex] = constant
T/[tex]\sqrt{L}[/tex] = T1/[tex]\sqrt{L1}[/tex]
T1 = [tex]\sqrt{L1}[/tex] * T/[tex]\sqrt{L}[/tex]
= [tex]\sqrt{L1/L}[/tex]* T
= [tex]\sqrt{40/100 *L / L}[/tex] * T
= [tex]\sqrt{0.4}[/tex] * T
= [tex]\sqrt{0.4} *100[/tex]
= 6.3245% T
Therefore The percentage increase in the time period is 6.3245%.
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FILL IN THE BLANK. Overall, available research suggests jurors exposed to pretrial publicity are ________________ to favor the ________________.
Answer:
Overall, available research suggests jurors exposed to pretrial publicity are more likely to favor the prosecution.
Solve the following inequality: -4x
+ 14 ≤ 54
The solution to the inequality is solved as: x ≥ -10.
How to Solve an Inequality?To solve an inequality means to find the possible values of the variable in the inequality that will make it true.
Given the inequality:
-4x + 14 ≤ 54
Subtract 14 from both sides of the inequality:
-4x + 14 - 14 ≤ 54 - 14 [Subtraction property of equality]
-4x ≤ 40
Divide both sides by -4 then change the inequality sign:
-4x/-4 ≥ 40/-4 [division property of equality]
x ≥ -10
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Which statement correctly describes the relationship between the graph of f (x) and the graph of g (x) =f (x) - 4?
A) The graph of g(x) is the graph of f(x) translated 4 units down.
B) The graph of g(x) is the graph of f(x) translated 4 units left.
C)The graph of g(x) is the graph of f(x) translated 4 units right.
D)The graph of g(x) is the graph of f(x) translated 4 units up.
The statement which describes the relationship between the graph of f (x) and the graph of g(x) = f (x) - 4 is the graph of f(x) translated 4 units down.
What is meant by standard form of transformation?The standard form of transformation can be described as,
g(x) = f(x + a) + b .... (1)
If a > 0, then the graph of f(x) shifts left side by a unit and if If a < 0, then the graph of f(x) shifts right side by a units.
If b > 0, then the graph of f(x) shifts upward by b unit and if If a < 0, then the graph of f(x) shifts downward by b units.
Since the relationship between the graph of f(x) and g(x) exists,
g(x) = f(x − 4)
From (1), we get
The value of a exists -4, therefore the graph of f(x) translated 4 units down.
The value of a function exists defined on a graph by the vertical distance from the x-axis. When that vertical distance exists reduced by 4, the corresponding point exists shifted down 4 units.
Therefore, the correct answer is option A) The graph of g(x) is the graph of f(x) translated 4 units down.
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determine the seating capacity of an auditorium with 20 rows of seats if there are 25 seats in the first row, 29 seats in the second row, 33 seats in the third row, 37 seats in the fourth row, and so on.Total number of seats=_____.
The total number of seats are 1260 in an auditorium.
The number of seats will be calculated by the arithmetic progression -
S = n/2 [2a + (n-1)d], where s is the number of seats, n is number of rows, a is the number of seats in first row and d is the number of extra seats added in each row.
d = 29 - 25
Performing subtraction
d = 4
Keep the values in formula -
S = 20/2 [(2×25) + (20 - 1)×4]
Performing multiplication and subtraction
S = 10 [50 + (19×4)]
Performing multiplication
S = 10 [50 + 76]
Performing addition
S = 10 [126]
Performing multiplication
S = 1260
Hence, there are 1260 seats.
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Mr. Cho received a container of fresh eggs. He sold 1/3 of the eggs in the morning and sold 320 eggs in the afternoon. At the end of the day, he found that 1/4 of the egs were not sold. How many eggs did he receive in the beginning?
Answer:
768
Step-by-step explanation:
Define the variable:
Let x be the number of eggs Mr Cho received in the beginning.Given information:
Mr Cho sold 1/3 of the eggs in the morning.Mr Cho sold 320 eggs in the afternoon. At the end of the day, Mr Cho found that 1/4 of the eggs were not sold.Create an equation with the defined variable and the given information:
[tex]\implies x - \dfrac{1}{3}x-320=\dfrac{1}{4}x[/tex]
Solve for x:
[tex]\implies \dfrac{2}{3}x-320=\dfrac{1}{4}x[/tex]
[tex]\implies \dfrac{2}{3}x-320-\dfrac{1}{4}x=\dfrac{1}{4}x-\dfrac{1}{4}x[/tex]
[tex]\implies \dfrac{5}{12}x-320=0[/tex]
[tex]\implies \dfrac{5}{12}x-320+320=0+320[/tex]
[tex]\implies \dfrac{5}{12}x=320[/tex]
[tex]\implies 12 \cdot \dfrac{5}{12}x= 12 \cdot 320[/tex]
[tex]\implies 5x=3840[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{3840}{5}[/tex]
[tex]\implies x=768[/tex]
Therefore, Mr Cho received 768 eggs in the beginning.
Total eggs be x
Form a equation
x-x/3-320=x/4x-320=x/4+x/3x-320=7x/1212x-3840=7x5x=3840x=768You want a 95% confidence interval for average pizza delivery time. A sample of 10 pizzas has an average delivery time of 34 minutes and a sample standard deviation of 5. 2 minutes. What t value do you use in your formula for the confidence interval?.
Write : linear equation to represent the line shown on the graph.
The equation of the line that passes through the points (0,-2) and (3,2) is 4x-3y-6 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
In the given graph,
The points are (0,-2) and (3,2)
To find the equation of the line,
Find slope by using formula m = (y₂-y₁)/(x₂-x₁)
m = (2-(-2))/(3-0)
m = 4/3
The equation of line is,
y-y₁ = m (x-x₁)
y-(-2) = 4/3(x-0)
y+2 = 4/3x
3y+6 = 4x
4x-3y-6 = 0
The required equation of line is 4x-3y-6 = 0.
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An ice cream factory make 320 quart of ice cream in 10 hour. How many quart could be made in 48 hour
Answer:
In 48 hours the ice cream factory can make 1,680 quarts.
Step-by-step explanation:
Multiply UNIT RATE 35 by 48 to answer your first question.
If 1 2 gallon of paint covers 1 12 of a wall, then how many quarts of paint are needed for the entire wall?.
If 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.
One gallon is equal to 4 quarts.
The amount of gallon that covers 1/12 of a wall = 1/2.
1/2 gallon = 2 quarts
This means that 2 quarts are needed to cover 1/12 of a wall.
Now, the number of quarts needed to cover the entire wall = 1/12 × 2= 1.
Therefore, if 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.
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The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y= -0.0127 + 0.0180x Suppose that the legal limit to drive is a blood alcohol content of 0.08.
0.0027 is the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression.
Given that,
In 16 male college students, the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression. This research produced the regression equation shown below: y= -0.0127 + 0.0180x Suppose a blood alcohol level of 0.08 is required to legally operate a vehicle.
We know that,
When five bears d, use x=5 to calculate the blood alcohol concentration.
y= -0.0127+0.0180*5=0.0773
So, his alcohol level is 0.0773 . this is clearly below legal level of 0.08
Then difference between his level and legal level= 0.08-0.0773= 0.0027
So, correct answer is
0.0027 below the legal limit
Therefore, 0.0027 is the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression.
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In preparing for the upcoming holiday season, fresh toy company (ftc) designed a new doll called the dougie that teaches children how to dance. the fixed cost to produce the doll is $100,000. the variable cost, which includes material, labor, and shipping costs, is $31 per doll. during the holiday selling season, ftc will sell the dolls for $39 each. if ftc overproduces the dolls, the excess dolls will be sold in january through a distributor who has agreed to pay ftc $10 per doll. demand for new toys during the holiday selling season is extremely uncertain. forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. the normal probability distribution is assumed to be a good description of the demand. ftc has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision. (a) determine the equation for computing ftc's profit for given values of the relevant parameters (e.g., demand, production quantity, etc.). using this equation, compute ftc's profit (in dollars) when realized demand is equal to 60,000 (the average demand).
The equation for ftc's profit is Profit = Sales – (Variable Cost + Fixed Cost)
According to the question,
The fixed cost to produce the doll = $100,000
Variable cost = $31
Selling price during holiday season = $39
Selling price during January = $10
Demand of new toys follows normal distribution
average sales = 60,000
Standard deviation = 15,000
Demand assumed in normal distribution = 60,000
The equation for ftc's profit ;
Let demand be d , production quality be p , fixed cost be x and variable cost be y
Maximum Profit:
Profit = Sales – (Variable Cost + Fixed Cost)
During the holiday season, For 40,000 dolls
Sales = 40,000 * 39 = $1,560,000
profit = $1,560,000 – (x+ y)
Variable Cost = 31*40,000 = 1,240,000
Fixed Cost = $100,000
Total Cost = 1,240,000+100,000 = $1,340,000
Profit = 1,560,000 – 1,340,000
= $220,000
Maximum Profit = $220,000
Average Profit: Off season sale price * Demand =$10*40,000
= $400,000
average sales = ($400,000 + 1,560,000 ) / 2=$1960,000/2
= $980,000
Average profit = 980,000 – 73,000= $972,700
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How do you write an equation in slope-intercept form of the line that is perpendicular to a graph?.
The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.
The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.
The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.
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Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece of poster board and then folding up the sides. The volume v(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts.
The expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.
It is given that:
Andre wants to make an open-top box by cutting out the corners of a 22-inch by 28-inch piece of poster board and then folding up the sides.
As we know,
The volume of the box = length×width×height
V = (28 - 2x)(22 - 2x)(x)
Plug x = 2
V = (28 - 2×2)(22 - 2×2)(2)
V = (24)(18)(2) cubic inches.
V = 864 cubic inhces
Since x measures length, it is not possible for it to be smaller than zero. In addition, since the width of the box's bottom cannot be less than zero.
Thus, the expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.
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a petty cahs fund was established with a $360 balance. it currently has cash of $42 and petty cash tickets totaling $318.
A credit to cash for $318 would be included in the entry to replenish the fund.
What is Balance?The balance is the sum owing on an account in banking and accounting. The term "balance" in accounting refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a certain financial period. The account shows a negative balance when total debits exceed total credits. There is just one rule in the balancing method: Perform the identical action on both sides of the equal sign so that only the unknown variable is left on one side.
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If you travel 4 km south, 2 km north, 5 km south, and 5 km north, what is your displacement?.
Answer:
2 km
Step-by-step explanation:
