The line parallel to line AB will have the same slope with different
y-intercepts.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines parallel to each other have the same slope with a different y-intercept.
Suppose the line AB has an equation y = mx + b.
∴ The line parallel to line AB will have an equation y = mx + c.
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Answer:
y=1/2x-3
Step-by-step explanation: if you are using edmentum this is correct.
If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
If 1200 square centimeters of material is available to make a box with a square base and an open top,
The largest possible volume of the box is V = 4000cm^3.
We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.
the dimensions of the box.
Square base implies the length and width are the same.
Let x = length/width.
The box has a height as well.
Let h = height
the surface area ; S.
S = (area of base) + (area of 4 walls)
The area of the base is x^2
The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.
S = x^2 + 4xh
And we know that S = 1200cm^2, so
x^2 + 4xh = 1200
Let's solve for h.
4xh = 1200 - x^2
h = (1200 - x^2) / (4x)
we require the volume formula.
V = (length) x (width) x (height)
And we know all of these.
V = (x)(x)(h)
V = (x^2) h
putting h = (1200 - x^2) / (4x) in the formula
V = (x^2) ( 1200 - x^2)/(4x)
We get a cancellation,
V = x(1200 - x^2)/4
V = (1/4)x (1200 - x^2)
This will be our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have
V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]
Simplify,
V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]
V'(x) = (1/4) [ 1200 - 3x^2 ]
V'(x) = (1/4) [ 3(400 - x^2) ]
V'(x) = (3/4) [ 400 - x^2 ]
To maximize, make V'(x) = 0, and solve for x.
0 = (3/4) [ 400 - x^2 ]
0 = 400 - x^2
x^2 = 400
x = +/- 20
Therefore,
x = { 20, -20 }
However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means
x = 20.
This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
Therefore,
V(20) = (1/4) (20) (1200 - 20^2)
V(20) = (1/4) (20) (1200 - 400)
V(20) = (1/4) (20) (800)
V(20) = (20/4)(800)
V(20) = 5(800)
V = 4000cm^3
Hence the answer is, the largest possible volume of the box is V = 4000cm^3.
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Find the product in simplest form.
1. 13 × 11 (1 point)
019¹
011
4
081
4
0152/12
4
Answer:
19 1/4
Step-by-step explanation:
1 3/4 × 11 = 7/4 × 11/1 = 77/4 = 19 1/4
True or false
a consumer has a budget of 90 monetary units and (s)he is considering buying two products: flowers (x) and chocolate (y). the price of x is 3 and the price of y is 5. if the price of x, px, increases to 5 the vertical intercept remains the same, while the slope will be flattened (smaller). true
false
question 2
0. 25 points
if px increases to 5 both the vertical intercept and the slope remains the same. true
false
question 3
0. 25 points
if py increases to 6 the vertical intercept change and the slope will be flattened (smaller). true
false
question 4
0. 25 points
if py increases to 6 the vertical intercept will be the same and the slope will be steeper
Answer:
false
Step-by-step explanation:
question 4
0. 25 points
if py increases to 6 the vertical intercept will be the same and the slope will be steeper
Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. Responses m∠1=m∠5 the measure of angle 1 equals the measure of angle 5 m∠7=m∠11 the measure of angle 7 equals the measure of angle 11 m∠5=m∠12 the measure of angle 5 equals the measure of angle 12 m∠4=m∠5 the measure of angle 4 equals the measure of angle 5 three lines a, b, and c that look somewhat horizontal. they are cut by a transversal forming 12 angles. line a intersects the transversal for form angles 1, 2, 4, 3 clockwise starting from the top left. line b intersects with the transversal to form angles 5, 6, 8, 7 clockwise starting from top left. line c intersects with the transversal to form angles 9, 10, 12, and 11 clockwise starting from top left. Skip to navigation
By using the properties of parallel lines, the result obtained is-
The correct options are first, second and fourth
What are parallel lines?
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Here,
From the figure,
For the first option,
m∠1=m∠5 [Corrosponding angles are equal]
First option is correct
For the second option,
m∠7=m∠11 [Corrosponding angles are equal]
Second option is correct
For the third option,
m∠5 ≠ m∠12 [ c is not parallel to b]
Third option is wrong
For the fourth option,
m∠4 = m∠5 [Alternate interior angle are equal]
Fourth option is correct
So the correct option are first, second and fourth
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Complete Question
The diagram has been attached
Answer: The answer is below
Step-by-step explanation:
This item has two parts: Part A and Part B. Use the information to complete Part A and Part B.
Two populations of bacteria increased at exponential rates. The table shows the bacteria population size for sample A, A(x), after x weeks.
x 0 1 2 3 4
A(x) 100 300 900 2,700 8,100
The graph shows the bacteria population size for sample B, B(x) = 500(2)x, after x weeks.
Part A
Which bacteria sample had a smaller initial population? What was that value?
Sample A; 100 bacteria
Sample A; 300 bacteria
Sample B; 2 bacteria
Sample B; 500 bacteria
Part B
Compare the population of each sample on the 5th week. Which sample was larger and by how much?
Sample A; 24,300
Sample A; 8,300
Sample B; 40,300
Sample B; 16,000
A. The bacteria sample that had a smaller initial population is;
Sample A; 100 bacteria.
B. The sample that was larger in the 5th week was;
Sample A; by 8,300.
How to solve Exponential functions?
An exponential function is defined by the general expression;
y = abˣ
where;
a is initial value.
b is rate of change.
For Sample A, the values of the above parameters are given as;
a = 100
b = 3
Thus, the exponential function is:
f(x) = 100(3)ˣ
In the 5th week, the population will be calculated as;
f(5) = 100 * 3⁵
f(5) = 24300.
For Sample B, the exponential function is expressed as:
g(x) = 500(2)ˣ
In the 5th week, the population will be;
g(5) = 500 * 2⁵
g(5) = 16000.
The difference of the larger population in Sample A and the smaller population in Sample B is;
24300 - 16000 = 8300.
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for a summer bbq you have 30 friends coming over. how many picnic tables do you need if you can seat 4 people at each picnic table?
Answer:
You need 8 picnic tables.
Step-by-step explanation:
You need 8 picnic tables because there are 30 friends and 4 sits at each table, and 4 x 8 is 32. There is 2 more extra seats. But it does fit all 30 friends.
Answer fast please!! will give brainiest
Answer:
8
Step-by-step explanation:
you divide so you can get the average
Answer:
in average she makes 8 friend in a week.
Step-by-step explanation:
You divide 80 by 9 that is 8 remaining 1, so yeah.
how many ways are there to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?
There are 2520 ways to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.
There are a total of seven different ways for eight individuals to sit around a circular table: (8-1)!=7!. We are using the concept of circular permutation.
By using circular permutation we have,
7!=5040
All of the seating is included in these 5040 ways. Given that everyone has the same two neighbors, regardless of whether they are left or right neighbors, two seating are said to be equal. To achieve the desired outcomes, we must divide the total number of methods by 2.
5040/2
=2520 ways
Therefore, there are 2520 ways to seat 8 people around circular table where two seating are considered the same.
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the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi?
the probability that the mean tire pressure of the sample is less than 69 psi 0.2030
The formula of the z-score is z = (x - μ)/σ, where
x is the score
μ is the mean
σ is the standard deviation
given,
a mean of 70 pounds per square inch
μ = 70
the standard deviation of 1.2 psi.
σ = 1.2
the sample is less than 69
x=69
so on substituting
z=(69-70)/1.2
z=-1/1.2
z=-0.83
The value corresponding to the z score is 0.2030 i.e 20.30%
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Thando divided 1572 by a certain number,and got an answer of 104,remainder 12 what number did she divide 1572
The number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
The dividend = 1572,
The quotient = 104,
The reminder = 12
Calculate the divisor by the following formula,
Dividend = Divisor × quotient + Reminder
Substitute the values,
1572 = Divisor × 104 +12
Divisor = 15
Therefore, the number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
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Evaluate the function. f(x)=-x^{2}+3x+11 Find f(−1)
The function f(x) = [tex]-x^2 + 3x +11[/tex] of the value is 7.
Given,
In the question:
The function is given as:
f(x) = [tex]-x^2 + 3x +11[/tex]
To find the f(-1)
Now, According to the question:
The function is :
f(x) = [tex]-x^2 + 3x +11[/tex]
To put the value of x = -1 in above function's equation:
f(x) = [tex]-x^2 + 3x +11[/tex]
f(-1) = [tex]- (-1)^2 + 3(-1) +11[/tex]
Solve the equation:
Determine the sign:
f(-1) = -1 -3 +11
Calculate the sum or difference:
f(-1) =7
Hence, The function f(x) = [tex]-x^2 + 3x +11[/tex] of the value is 7.
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Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house. What is the shortest distance between caroline’s and mattie’s houses?.
The shortest distance between Caroline's and Mattie's houses is 10 block.
Let Caroline started from point A and goes towards north 6 blocks to O. and goes to B 8 blocks in east.
AO = 6
BO = 8
Formula for the Shortest distance can be solve by pythagoras theorem:
[tex]AB^{2} = AO^{2} +OB^{2}[/tex]
[tex]AB^{2} = 6^{2} +8^{2}[/tex]
[tex]AB^{2} = 36+64[/tex]
[tex]AB^{2} = 100[/tex]
[tex]AB = \sqrt{100}[/tex] can
[tex]AB = 10[/tex].
The shortest distance AB = 10 block.
#1234
10 blocks are the shortest distance between Caroline and Mattie's homes.
Given data,
Caroline steps outside and makes a 6 block trek to the north. To go to Mattie's house, she does a turn and travels 8 blocks to the east.
To get the shortest distance between Caroline and Mattie's houses we need to it as a triangle and apply the Pythagorean theorem.
Pythagorean theorem:
The well-known geometric axiom is that the hypotenuse (the side across from the right angle) of a right triangle is equal to the sum of the squares on its legs. Or, in popular algebraic form, a² + b² = c².
The shortest distance (c);
Let, a = 6
b = 8
⇒ a² + b² = c²
6² + 8² = c²
36 + 64 = c²
c = [tex]\sqrt{100}[/tex]
c = 10
Therefore, the shortest distance between Caroline’s and Mattie’s houses is 10 blocks.
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Suppose that 17 inches of wire costs 85 cents. At the same rate, how much (in cents) will 13 inches of wire cost?
Answer:
65 cents
[tex]85 \div 17[/tex]
85/17 =5
so for 1 inch of wire is 5 cents but we want to know for 13 inches
so times 5 by 13
5cents*13=65cents
Pls Help I will give brainliest to whoever is first and correct. And answer all questions!
Answer:
The original equation
Distributive property
subtract 5x from both sides
add 12 to both sides
divide both sides by -14
A train travels 1 kilometre in 1 minute 20 seconds At this rate, how many kilometres will the train travel in 1 hour?
The train will travel for approximately 50 kilometres in 1 hours.
How to find the time in hours the train covers?The train travels 1 kilometre in 1 minute 20 seconds.
At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;
Therefore, lets convert 1 minutes and 20 second to hours.
20 seconds = 0.333333 minutes
Hence,
60 minutes = 1 hour
1.33333 minutes = ?
cross multiply
time in hours = 1.3333 / 60
time in hours = 0.02222221666
Therefore,
0.02 hours = 1 km
1 hours = ?
number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km
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there are 280 counters in a bag
1/2 of the counters are red
2/5 of the counters are yellow
the rest are green
work out the number of green counters in the bag
Answer:
84 counters
Step-by-step explanation:
⅖ + ½ = 7/10
10 - 7 = 3
280 ÷ 10 × 3 = 84
Answer:
28
Step-by-step explanation:
1/2×280=140(red counters)
2/5×280=112(yellow counters)
140+112=252
280-252=28(green counters)
5 times a number decreased by 2 is 4. What is the number? Show work if you can.
If 120% of a is equal to 80% of b, then what is a+b?
After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.
In the given equation,
If 120% of a is equal to 80% of b, then we have to find the value of a+b.
We firstly express the statement in the algebraic equation.
It is given in the statement that 120% of a.
We write it as 120%×a.
From the statement, 80% of b.
We write its as 80%×b.
Both are equal to each other.
So the expression should be
120%×a=80%×b
Divide by 12% on both side
120%/120% ×a=80%/120% ×b
Simplifying
a=80%/120% ×b
As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.
So a=80/120 ×b
Divide by b on both side
a/b=80/120 ×b/b
a/b=80/120
Simplifying the ration
a/b=2/3
Hence, the value of a=2 and b=3.
Now finding the value of a+b.
a+b = 2+3
a+b = 5
Hence, if 120% of a is equal to 80% of b, then a+b is 5.
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(8a+5b-4) and (3b-5)
Answer:
a =-13/24 b = 5/3
Step-by-step explanation:
From given
8a + 5b = 4 (1)
3b = 5 (2)
Using (2)
b = 5/3
Putting the value of b into (1) gives
8a + 5(5/3) =4
8a + 25/3 = 4
8a = 4 - 25/3
8a = -13/3
a = -13/(3*8)
a = -13/24
In the diagram below of triangle ABC,
D is the midpoint of AC and E is the
midpoint of BC. If DE = 34 - 6x,
and AB = 28 - 4x, what is the measure
of DE?
A
Answer:
DE =
Submit Answer
D
C
E
B
Using midpoint theorem the value of DE is 4.
What is midpoint theorem?
According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."
Here using midpoint theorem we know that ,
=> DE = 1/2 AB
Here DE=34-6x and AB=28-4x.
=> 34-6x=1/2(28-4x)
=>68-12x=28-4x
=> 12x-4x=68-28
=> 8x = 40
=> x =5.
Now put x=5 into DE then,
=> DE=34-6(5)=34-30 = 4.
Therefore using midpoint theorem value of DE is 4.
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help me pleaseeeeee?
Answer: 90
Step-by-step explanation:
VolBigCube = 1.5x1.25x0.75 = 1.40625 in^3
VolSmallCube = 0.25x0.25x0.25 = 0.015625 in^3
VolBigCube/VolSmallCube = 1.40625/0.015625 = 90
The perimeter of a rectangle is 72 inches. Its length is 6 inches greater than twice its width. Write and solve a system of equations that represents this situation.
f(x) =
g(x)=
solution:
Answer:
Step-by-step explanation:
first up, the perimeter is 4 side added up. so we do 72/4= which equals 18. we need to apply the 6 to the sides so we do 6/2=3 18/3=15 f=15 18+3= 21 one side is 15 & the other side is 21 to double check, 21+15*2= 72
what is the rate of change of the function y=4x-2
Answer: 4
Step-by-step explanation: x is multiplied by 4
define the semantics (inference rule) of the if statement: {p} if (e) s1 else s2 {q}. hint: one way to prove it is to do a case analysis. if e is true, the whole statement is equivalent to what? if e is false, the whole statement is what? formulate it as an inference rule.
The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).
In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.
A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.
(S1, S2, ........, Sn)/S
According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.
Given,
{P} if (E) S1 else S2 {Q}
The inference rule is
We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}
i.e. {E and P} S1 {Q},{not E and P} S2 {Q}
So the inference rule is:
({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})
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Katrina needs 3/5 kilogram of flour for a recipe her mother has 3/7 kilogram of flour in her pantry is this enough flour for the recipe if not how much more will she needs
The flour that Karina's mother has won't be enough for the recipe and she requires extra 3/20 together with the quality owed by the mother.
What is flour ?Flour is defined as a food product that is the main ingredient for baking of different recipes such as cakes, breads, plate pies just to mention a few.
The amount of flour needed by Karina for the recipe= 3/5 = 0.6.
The amount of flour owed by the mother = 3/7 = 0.45
The difference between the available flour = 0.6 - 0.45 = 0.15
This shows that extra flour of 0.15 or 3/20 is needed in addition to the quantity of flour owed by the mother to be able to make the recipe.
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5 A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Zoe measures the distance from
the pole to the stake and from the pole to the tower, as shown in the diagram below.
Find the length of the guy wire, to the nearest foot.
The length of the guys wire to the nearest foot is 56 feet.
How to find the length of the guy wire?The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.
The situations forms a right angle triangle.
Therefore, the length of the guy wire can be found as follows:
Using trigonometric ratios, we can find the angle the guy wire made with the ground.
tan ∅ = opposite / adjacent
tan ∅ = 5 / 1
∅ = tan ⁻¹ 5
∅ = 78.690067526
∅ = 78.69°
Therefore, let's find the length of the guy wire using the angle.
cos 78.69° = adjacent / hypotenuse
0.1961172908 = 11 / h
h = 11 / 0.1961172908
h = 56.088884361
Therefore,
length of the guy wire = 56 feet
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Elliot buy 5 ruler and 3 rubber for £5. 5. Mia buy 3 ruler and 2 rubber for £3. 5. Work out the cot of one ruler and one rubber
The cost ruler is £ 1.5 and the cost of rubber is £ 1.0.
Cost of 01 ruler be x pound.
Cost of 01 rubber be y pound.
according to question,
[tex]5x + 3y = 5.5[/tex] ------------------------------------ (1)
[tex]3x + 2y = 3.5[/tex] ------------------------------------(2)
multiplying equation (2) by 2 and equation (1)
[tex]10x + 6y = 11[/tex] -------------------------------------(3)
[tex]9x + 6y = 10.5[/tex] -------------------------------------(4)
subtracting equation (4) by (3), we get
[tex]x = 0.5[/tex]
putting the value of [tex]x = 0.5[/tex] in equation (2),
3×0.5 + 2y = 3.5
⇒1.5 +2y = 3.5
⇒2y= 2.0
⇒y = 1
∴ the cost of ruler is £ 0.5 and the cost of £1.0
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If you dealt 4 cards from a shuffled deck of 52 cards without replacement, what is the probability that all 4 cards are face cards?.
The probability of getting face card in all 4 attempts is 0.0018 approximately.
What are face cards?
Any of the twelve cards in a deck with an image of a face on it is referred to as a face card. King, Queen, and Jack are the face cards in this deck.
Main Body:
Jack, Queen, and King are face cards, each of the four suits has one of each, so 12 face cards.
12/52 is the chance that the first one will be a face card.
Then it’s 11/51, 10/50, and 9/49.
And the chance for all four is thus all four multiplied together.
(12 / 52) * (11 / 51) * (10 / 50) * (9 / 49) = 0.001828
Hence the probability of getting face card on all attempt is 0.0018
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URGENT
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $55 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2575. How long did each mechanic work?
The first mechanic worked 20 hours and the second mechanic worked 5 hours
The work charge of first mechanic = $115 per hour
The work charge of second mechanic = $55 per hours
Total number of hours they worked = 25 hours
The total amount they charged = $2575
Consider the number of hours that first mechanic work as x and second mechanic as y
Then the equations will be
x + y = 25
x = 25 -y
The second equation
115x + 55y = 2575
Here we have to use substitution method here
115(25-y) + 55y = 2575
2875 - 115y +55y = 2575
2875 -60y = 2575
60y = 2875 - 2575
60y = 300
y = 300 / 60
y = 5 hours
Then x = 25 - y
= 25 -5
= 20 hours
Hence, the first mechanic worked 20 hours and the second mechanic worked 5 hours
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Matrices (Please help, I have no idea what this is) 20 POINTS
a₁₁=1 of the given matrix.
What is Matrix?Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array.
Given Matrix is [tex]\left[\begin{array}{cccc}1&3&8&5\\5&4&6&2\\6&7&1&8\\2&9&3&7\end{array}\right][/tex]
The matrix will be in the form[tex]\left[\begin{array}{cccc}a_{11} &a_{12} &a_{13} &a_{14} \\a_{21} &a_{22} &a_{23} &a_{24} \\a_{31} &a_{32} &a_{33} &a_{34} \\a_{41} &a_{42} &a_{43} &a_{44} \end{array}\right][/tex]
The given matrix is a 4 cross 4 matrix, which has 4 rows and 4 columns.
a₁₁ means it is the first element of first row and first element of first column.
By comparing the given matrix with standard form a₁₁=1
Hence, a₁₁=1 of the given matrix.
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