Step-by-step explanation:
"t t hours" ????
you mean 11 hours ?
13 gallons now.
2 gallons are used (and therefore disappear from the tank) per hour.
so, in 5 hours 5×2 = 10 gallons will be used.
that leaves 13 - 10 = 3 gallons in the tank.
in 11 hours 11×2 = 22 gallons would have been used.
but there are only 13 gallons in the tank.
so, if he does not fill up, he will have 0 gallons left after 11 hours. in fact, already after 13/2 = 6.5 hours.
the point :
when you use 2 gallons per hour, that means in t hours you are using t × 2 or 2t gallons.
PLS HELP WITH THIS AND SHOW WORK SHOW WORK
Answer:
option 3
Step-by-step explanation:
6x + 3x² - 4x ← collect like terms
= 6x - 4x + 3x²
= x(6 - 4) + 3x²
= x(2) + 3x²
= 2x + 3x²
Answer:
Option 3: [tex]2x+3x^{2}[/tex]
Step-by-step explanation:
Combine like terms: [tex]6x-4x=2x[/tex]
Put the equation together: [tex]2x+3x^{2}[/tex]
The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].
Total area=
Help me please, thankss
The Area of given figure is 341.6 square.
According to the statement
we have to find the total area of given figure.
Here a= 10 and h= 11
So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))
where the a represent the base of given solid or sides of the equilateral triangle
And h represent the slant height of the solid.
So, Substitute the values in above formula then
A = 10(10 + √((10)^2 + 4(11)^2))
A = 10(10 + √((100 + 4(121))
A = 10(10 + √(100 + 484)
A = 10(10 + √(584)
A = 10(10 + 24.16)
A = 10(34.16)
A= 341.6
So, The Area of given figure is 341.6 square.
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Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The slope in question seven is 1. Below are the solutions to the remaining questions
In what means can Transformation occur ?Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.
Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise
2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.
3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2
4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.
5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0
6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.
7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be
Slope = Δy ÷ Δx
Slope = (5 - 4) ÷ (-10 + 11)
Slope = 1 ÷ 1
Slope = 1
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100 POINTS OKK!!!!
1. If y varies directly as x and y=5, when x=3, find the equation that relates x and y.
2. If v varies directly as w and v=21, when w=8. find the equation that relates v and w.
3. If p varies inversely with q and p=5 when q=6, find the equation that relates p and q.
4. If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.
5. The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1.5-foot-long board, how many pounds of pressure would he need to use to break a 6-foot-long board?
Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;
y = [tex]\frac{5}{3}[/tex] xv = [tex]\frac{21}{8}[/tex]wp = [tex]\frac{30}{q}[/tex]y = [tex]\frac{33}{x}[/tex]F = 5 poundsVariation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.
The required answers to the given questions are:
1. y [tex]\alpha[/tex] x
⇒ y = kx
where k is the constant of proportionality.
Given that, y = 5 and x =3, then;
5 = 3x
x = [tex]\frac{5}{3}[/tex]
Thus,
y = [tex]\frac{5}{3}[/tex] x
2. v [tex]\alpha[/tex] w
v = kw
Given: v = 21, w = 8
Then,
21 = 8k
k = [tex]\frac{21}{8}[/tex]
Thus,
v = [tex]\frac{21}{8}[/tex]w
3. q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]
y = [tex]\frac{k}{q}[/tex]
Given: q = 5, q = 6
Then,
5 = [tex]\frac{k}{6}[/tex]
k = 5 x 6
k = 30
Thus,
p = [tex]\frac{30}{q}[/tex]
4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]
y = [tex]\frac{k}{x}[/tex]
Given: y = 11, x = 3
Then,
11 = [tex]\frac{k}{3}[/tex]
k = 11 x 3
k = 33
Thus,
y = [tex]\frac{33}{x}[/tex]
5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]
F = [tex]\frac{k}{l}[/tex]
Given; F = 20 pounds, l = 1.5 ft
20 = [tex]\frac{k}{1.5}[/tex]
k = 20 x 1.5
k = 30
F = [tex]\frac{30}{l}[/tex]
When l = 6 ft, then;
F = [tex]\frac{30}{6}[/tex]
F = 5 pounds
The amount of force required is 5 pounds.
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GCSE MATHS PLEASE HELP
Answer:
A) y = 16/(x^2), B) 4/5
Step-by-step explanation:
For A, we can plug in some of the table values to check it. I will try 2 and 3
2. 4 = 16 / (2^2)
16/4 = 4
3. 16/9 = 16 / (3^2)
16/9 = 16/9
B) We can just input y into the formula 25 = 16 / (x^2)
This leaves us with +-4/5
Answer:
see explanation
Step-by-step explanation:
(a)
given y varies inversely as x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k substitute any ordered pair from the table into the equation
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , then
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is x = [tex]\frac{4}{5}[/tex]
A machine manufactuers 300 nails a day. how many did it produce in the month of april 2007
The machine produces 3000 nails in the month of April 2007.
Production of Nails in the Month of April
According to the given information,
Number of nails manufactured per day by the machine, x = 300
And, we know that April is the fourth month of a year which has total 30 days.
Hence, number of days the machine is manufacturing nails in the month of April, y = 30
So, the number of nails that will be produced by the machine in the month of April is given by,
N = Number of nails produced per day × Number of days in April
N = xy
N = 300 × 30
N = 9000
Therefore, the machine produces 9000 nails in the April month of year 2007.
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How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
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help pls im so confused
10(1^2*2^-2)
Answer:
2.5(or 5/2 or 2 1/2)
Step-by-step explanation:
Remember PEMDAS
10 * (1^2 * 2^-2)
10 * (1 * 0.25)
10 * 0.25 =
2.5
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.
Which equations are true for the values of x?The values of x given according to the task content are; x = –2 and x = 2.
By considering equation; x²-4 =0
x² = 4
x = ±2
Also, by considering 4x²= 16;
x² = 16/4 = 4
x = ±4.
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The triangle below is being reduced by a scale factor of two-thirds. What is the base of the new drawing? 15 m
Answer:
10
Step-by-step explanation:
A scale factor of 2/3 means multiplying all side lengths by 2/3
15*2/3=10
if there are 30 items to vote on in the local election, 240 people will choose to vote. For every batch of 3 items added to the ballot, 10 fewer people will vote. If all people who vote cast votes on every item, how many items should be placed on the ballot to maximize the total number of votes cast on all items
2 items should be placed on the ballot to maximize the total number of votes cast on all items.
According to the statement
items on which people vote = 30
people who will vote = 240
batch containing items = 3
number of batches formed = 10
now we find the number of items placed on ballot to maximize the number of votes.
we find the average number by each items got the vote.
Average = items in batch / total votes
Average = 3/240
but if we add 2 items in the ballot then average become half.
So, 2 items should be placed on the ballot to maximize the total number of votes cast on all items.
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The radius of circle A is 4.4 units.Which element of circle A has a measure of 27.65 units
Answer:
The circumference
Step-by-step explanation:
[tex]circumference \: = 2\pi \times radius \\ c = 2\pi(4.4) \\ c = 8.8\pi = 27.65[/tex]
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents lolas purchase
The graph that represents Lola's Purchase is as shown in the attached file.
How to interpret Inequality Graph?Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
Representing expense in the equation form gives us;
Expense on pencils + expense on erasers < 3
Thus;
0.25X + 0.50Y < 3
Dividing through by 0.25, we have;
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)
The correct graph is attached below.
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PR=
Help me please thanks so much
Formula: U*V=R*T
3*1=4*x
3=4x
x=3/4
Hope it helps!
Answer:
[tex]\sf PR =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Intersecting chords theorem:It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.
TP * PR = UP * PV
4 * PR = 3 * 1
[tex]\sf PR = \dfrac{3}{4}[/tex]
Given the following results from a spinner game after spinning 20 times.
What is the experimental probability of landing on red?
The experimental probability of landing on red is 7/20 or 0.35 or 35%
How to determine the experimental probability of landing on red?The complete question is added as an attachment
From the question, we have the following outcomes:
Red = 7
Green = 5
Blue = 5
Yellow = 3
The total number of spins is
Total = Red + Green + Blue + Yellow
This gives
Total = 7 + 5 + 5 + 3
Evaluate the sum
Total = 20
The experimental probability of landing on red is the calculated as:
P(Red) = Red/Total
Substitute the known values in the above equation
P(Red) = 7/20
Evaluate
P(Red) = 0.35
Express as percentage
P(Red) = 35%
Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%
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Point A is located in which quadrant?
IV
III
I
II
Answer:
Quadrant II
Step-by-step explanation:
This is because the top right is I, the top left
is II, the bottom left is III, and the bottom right is IV.
problem plot two points that are 8 88 units from point b bstart color #11accd, b, end color #11accd and also share the same x xx-coordinate as point b bstart color #11accd, b, end color #11accd.
The two points are B'=(-6,-8).
What is the plot?A plot is a graphical technique for depicting data collection, typically in the form of a graph that depicts the relationship between two or more variables. The storyline can be created either by hand or by computer. Previously, mechanical or electrical plotters were used.To plot the points:
Plot a new point that is 8 units down and also has the same x coordinate.
Given - Point B = ( -6, 0 )
Represent the new point with B':
In Point B = ( -6, 0 )
[tex]x=-6,y=0[/tex]
This means that B' has an x coordinate of -6.
Next, is to determine the y coordinate:
If a point (x,y) is translated b units down, the new point is (x, y, -b)
In this case:
The y coordinate of B is 0 and b = 8.
So, the new y coordinate is 0 - 8 = -8
So, we have B'=(-6,-8).
Therefore, the two points are B'=(-6,-8).
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Hi! It’d be really helpful if someone could explain he two questions below, thanks!
can someone please help me
Answer:
[tex]\frac{13\pi }{9}[/tex] radians
Step-by-step explanation:
to convert degrees to radians
degrees × [tex]\frac{\pi }{180}[/tex]
= 260 × [tex]\frac{\pi }{180}[/tex]
= 26 × [tex]\frac{\pi }{18}[/tex]
= 13 × [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{13\pi }{9}[/tex]
The circumference of a circular field is 222.94 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
35.5
Step-by-step explanation:
→ Write down the formula
2 × π × r = 222.94
→ Simplify
6.28 × r = 222.94
→ Divide both sides by 6.28
r = 35.5
Answer:
35.5 = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r where r is the radius
222.94 = 2 * 3.14 * r
222.94 = 6.28 r
Divide each side by 6.28
222.94/6.28 = r
35.5 = r
Jenna collects stamps. She puts the same number of stamps on each page and then inserts each page into one of her two stamp books. One of her stamp books has a total of 840 stamps. The other has 1008. What is the largest number of stamps that Jenna could be putting on each page
168 is the largest number of stamps that Jenna could be putting on each page
What is the Greatest Common Factor?
The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
So the largest number of stamps that Jenna could be putting on each page
would be gcd of 1008 and 840.
840 = 2 x 2 x 2 x 3 x 5 x 7
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.
∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.
Hence 168 is the largest number of stamps that Jenna could be putting on each page
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One number is 4 more than another and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following is the value of the smaller number?
The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding
Calculate the value of the numbers:Given that one number is 4 more than another,
⇒x = y + 4 (equation (1))
Their sum is 60,
⇒x + y = 60
y + 4 + y = 60 (From (1))
2y + 4 = 60
2y = 56 ⇒ y = 28
x = y + 4 = 28 + 4 = 32
Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.
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How to determine instantaneous rate of change with pi
The instantaneous rate of change of the function is 5/π
How to determine the instantaneous rate of change?The function is given as
[tex]f(x) =\cos(x - \pi) + 4[/tex]
Where
[tex]x = \pi[/tex]
Calculate f(π) as follows
[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]
This gives
[tex]f(\pi) =\cos(0) + 4[/tex]
Evaluate the expression
[tex]f(\pi) =5[/tex]
The instantaneous rate of change is then calculated as;
[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]
This gives
[tex]f'(x) = \frac{5}{\pi}[/tex]
Hence, the instantaneous rate of change of the function is 5/π
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y≤1/2x-3
y + 2x > 6
I need help solving this problem shjsdjjsjdndjskdjdkkdndnsjsjmsmskdndnd
Answer:
6-2x < y < ½x-3Step-by-step explanation:
The first part tells us that y is, or is anywhere below ½x-3
The second part tells us that above 6-2x
Since we don't know what x is, we cannot actually find y.
The best answer to this question is:
6-2x < y < ½x-3
Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.
Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.
In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?
Check the picture below.
The requried measure of the angle m∠C in the given circle is 15°.
In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.
Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82
Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.
∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°
Thus, the requried measure of the angle m∠C in the given circle is 15°.
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Having trouble can someone help me solve this
The function f(x) is vertically compressed to form g(x)
How to compare both functions?The functions are given as
f(x) =x^2
g(x) =3x^2
Substitute f(x) =x^2 in g(x) =3x^2
g(x) =3f(x)
This means that the function f(x) is vertically compressed to form g(x)
See attachment for the function g(x)
Also, both functions have the same domain and range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
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Which of the following parabolas has its vertex the furthest away from the x-axis
Oy
x² - 1
y = 3x² + 4
Oy
=
Y =
1/2x²
Oy = x² - 10
Question 12 (1 point)
Answer:
y=x^2-10
Step-by-step explanation:
If she was vaping every 15 minutes, assuming she was awake from 7 am- 11 pm (16 hours) how many times in a day would she vape?
Answer:
64 times
Step-by-step explanation:
16 hours to minutes: 16*60 = 960 minutes
vaping every 15 minutes: 960/15 = 64
The graph of y = f(x) is graphed below. Wat is the end behavior of f(x)?
PLEASE ASAP
Answer:
B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞
Step-by-step explanation:
F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).
Select the correct answer from each drop-down menu. a comic-strip writer churns out different numbers of comic strips each day. the writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8 the data in the distribution is . if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .
Mean = 3.5
Median = 3
Distribution is negatively skewed.
What is skew in the distribution?
The distribution has no skewness if the mean and median are equal.
The median exceeds the mean in a favorably skewed distribution.
The distribution is also negatively skewed if the median is lower than the mean.
Given,
Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]
Mean = [tex]\frac{56}{16}[/tex]
Mean = [tex]3.5[/tex]
Median = mid value of the data set when the values are arranged in ascending order
Here,
the two mid values = [tex]3, 3[/tex]
Median = [tex]\frac{3+3}{2}[/tex]
Median = [tex]\frac{6}{2}[/tex]
Median = [tex]3[/tex]
Now, as the mean is larger than the median therefore the distribution will be skewed negatively.
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
ヾ(•ω•`)o