To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.
What is a cylinder?In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.
A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.
To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.
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for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
Answer:
associative
combining
commutative
Step-by-step explanation:
1. associative property of addition since the grouping is changed
2. combining like terms since it's the addition of 4 and 6
3. commutative property of addition since it's a change of order
Find the area of the blue shape below. Use 3.14 for π
If anyone knows the answer please help!
Answer:
1413.86 ft^2.
Step-by-step explanation:
The diameter of the circle = 50 - 2(18)
= 50-36
= 14 ft.
So its radius is 7 ft.
The total area of the blue shape
= 2(35 * 18) + 3.14*7^2
= 1413.86 ft^2.
Prove that the number A= [tex]20^{8^{2014} } }+113 is composite
Cheese proof:
We can just prove that it is divisible by 3, which means that it is composite. We can use modular exponentiation, where if [tex]a \equiv b \pmod{n}[/tex] then [tex]a^x \equiv b^x \pmod{n}[/tex]. In this case, [tex]{-1}^{8^{2014}} \equiv 20^{8^{2014}} \pmod{3}[/tex]. This is much easier to calculate! Since [tex]8^{2014}[/tex] is even, [tex]-1^{8^{2014}}=1[/tex], meaning that now we only need to prove that [tex]0\equiv(1+113) \pmod{3}[/tex], which is obviously true.
I thought of the number that is between 104 and 140. The number is divisible by 6 and 15. What is my number?
Answer:
120
Step-by-step explanation:
Lets find the numbers multiples of 6 that are in the range from 104-140:
108, 114, 120, 126, 132, 138
Now out of these lets find which is divisible by 15
[tex]\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2[/tex]
120 Is the only solution in this set which is also equally divisible by 15, making it the answer.
The graph compares shoe sizes for a group of 100 two-year-old boys and a
group of 60 three-year-old boys.
Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13. The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys. For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
The number of two year old boys that wear a size 6 is greater than the number of three year old boys that wear a size 6 by 35.
How many more two year olds wear a size 6?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines called the whiskers and a box. The whiskers represent the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile
50% of the two year olds wear a size 6 = 50% x 100 = 50
25% of the three year olds wear a size 6 = 25% x 60 = 15
Difference in the number : 50 - 15 = 35
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A map has a scale of 1:5000000000 .
a. A road on the map is 10cm long . What is the real length of the road in km ?
b. The area of a farm of the map is 6 cm square . What is the real area of the farm in hectares ?
( 1 hectare = 10000 m square = 0.01 km square )
Considering the definition of scale, you obtain:
the real length of the road is 500,000 km.the real area of the farm is 300 hectares.Definition of mapA map is the conventional graphical representation of a portion of the earth or another celestial body that shows the size and position of elements of the landscape according to the selected scale and projection. That is, a map is a representation of a place, at a size smaller than the actual size.
Definition of scaleThe scale of a cartographic representation, or map scale (m), is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. In general, it is also defined as the ratio of the lengths of a linear element in the plane and its representation on the terrestrial reference surface.
That is, the scale of the map is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.
Real length of the roadA map has a scale of 1:5000000000. This indicates that 1 unit on the map is equivalent to 5,000,000,000 in reality.
You know that the road on the map is 10 cm or 0.0001 km long (knowing that 1 km= 100,000 cm).
Then you can apply the following rule of three: if by definition of scale 1 km on the map is equivalent to 5,000,000,000 km in reality, 0.0001 km on the map is equivalent to how much distance in reality?
[tex]real length of the road=\frac{0.0001 kmx 5,000,000,000 km }{1 km}[/tex]
real length of the road= 500,000 km
Finally, the real length of the road is 500,000 km.
Real area of the farmYou know that the area of a farm of the map is 6 cm square, 0.0006 m sr 0.00000006 hectares (knowing that 1 cm square= 0.0001 m square and 10,000 m square= 1 hectare).
Then you can apply the following rule of three: if by definition of scale 1 hectare on the map is equivalent to 5,000,000,000 hectares in reality, 0.00000006 hectares on the map is equivalent to how much area in reality?
[tex]real area of the farm=\frac{0.00000006 hectaresx 5,000,000,000 hectares }{1 hectare}[/tex]
real area of the farm= 300 hectares
Finally, the real area of the farm is 300 hectares.
SummaryIn summary, you get:
the real length of the road is 500,000 km.the real area of the farm is 300 hectares.Learn more about scale:
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What are the zeros of the polynomial function: f(x) = x^3 - x^2 – 6x ?
Answer:
x=0, x=3, x=-2
Step-by-step explanation:
factor the equation
x(x^2-x-6)
factor more
x(x-3)(x+2)
set it equal to 0
x(x-3)(x+2)=0
plug in numbers for x that would result in the answer being 0
0(0-3)(0+2)=0
3(3-3)(3+2)=0
-2(-2-3)(-2+2)=0
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
2p = 30 - 0
p = 15
4p = 4 × 15
= 60
In this case h = 0
So, we have (h,p) = (0,15)
So we get
We have equation: x^2 = 60(y-15)
y = x^2 / 60 + 15
What is a parabola?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
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A cube. the top face has points a, g, e, f and the bottom face has points b, h, d, c. the diagonal from a to e is startroot 288 endroot inches and the diagonal from a to d is startroot 432 endroot inches. what is the length of ed in the given cube? round to the nearest tenth of an inch if necessary. in.
The length of the line ed according to the description of the cube is; 8.5.
What is the length of ed in the given Cube?First, since the shape is a cube, it follows that the diagonal of the top face can be used to determine the length of the sides of the top face.
Therefore , we have; length of each side of the top face;
ag = ge = ef = fa = √288/2 = 6√2.
Also, the diagonal of a to d is; √432 = 12√3.
Hence, the length of ed in the group as evident from the length of sides of the cube's top face in which case,
Consequently, the length of line ed is;√432 × 8.5.
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I found this proof by induction that all people in canada are the same height, i was wondering what is the incorrect step?
Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all there is only one person!
Step 2: Therefore, statement S(1) is true.
Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k), it is also true for the next number (that is, n = k+1).
Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2) deducing from it that, in every group of k+1 people, everyone has the same age.
Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.
Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.
Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age (since we are assuming that, in any group of k people, everyone has the same age).
Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.
Step 9: Let R be someone else in G other than P or Q.
Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.
Step 11: Since P and R each belong to the group considered in step 8, they are the same age.
Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.
Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that everyone in G has the same age.
Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever it is true for n=k it is also true for n=k+1, so by induction it is true for all n.
The incorrect step in the induction that all people in Canada are the same height is; Step 9
How to prove Mathematical Induction?The principle of mathematical induction as follows:
For example, we have a set of natural numbers. Now, suppose that 1 is in the set. Now, we assume that anytime n is in the set, n + 1 is also in the set. Therefore we can say that every natural number is in the set.
The wrong step in the given mathematical Induction is Step 9. This is because;
We might not be to see anyone else in the arbitrary group G other than groups P or Q!
Recall that G is a group of k + 1 people. Thus, provided that k > 1, k + 1 > 2 and that a third person R in G does not exist, then the rest of the proof will work.
The steps above proves that;
S(k) = S(k + 1), for every k > 1.
Thus, we can also say that if S(2) is true, then it equally means S(3) is true and so on till infinity.
From our induction process written so far, we have see that S(1) was true. However, our induction step in the question does not show us that that S(1) = S(2) = true.
So: Thus, from the induction I have done It shows that S(1) not imply S(2) and as a result the proof is fallacious.
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Ramiro was on a two day road trip.on the first day he drove at an average speed of 40 mph.on the second day he drove at an average of 60 mph.if he drove 2 hours longer and went 20 miles farther on his first day find the total distance ramiro traveled on his road trip.
Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.
What is the relationship between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first day, we have that:
v = 40, t = t + 2, d = d + 20, hence:
40 = (d + 20)/(t + 2)
For the second day, we have that:
v = 60
60 = d/t
d = 60t
Then, replacing in the first equation:
40 = (60t + 20)(t + 2)
60t + 20 = 40t + 80
20t = 60
t = 3.
Then the distances are given by:
First day: d = 60t + 20 = 60 x 3 + 20 = 200 miles.Second day: d = 60t = 60 x 3 = 180 miles.Total: 200 miles + 180 miles = 380 miles.More can be learned about the relationship between velocity, distance and time at https://brainly.com/question/28143163
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Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.
How to determine angle <XYZ?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle XYZ will be given by this formula:
<XYZ = ½ × (m<WZ - m<XZ)
Substituting the given parameters into the formula, we have;
<XYZ = ½ × (175 - 105)
<XYZ = ½ × 70
<XYZ = 35°.
By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.
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Answer: 35
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line whose equation is ax by=c?
Answer:
b/a
Step-by-step explanation:
Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).
In the equation
ax + by = c,
the slope of the line is
-a/b
If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.
by = -ax +c
y = -a/b x + c/b
The slope is -a/b
So a perpendicular line would be opposite sign and flipped, b/a
At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of $30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
The average selling price of a ticket at the Algal Rhythms concert is $25
How to determine the average selling price of a ticket at the Algal Rhythms concert?The given parameters are:
75% of the tickets were sold for $30.
The remaining 25% were sold for $10.
The average selling price of a ticket at the Algal Rhythms concert is calculated using
Average = Sum of (Price * Percentage)
So, we have
Average = 30 * 75% + 10 * 25%
Evaluate the expression
Average = 25
Hence, the average selling price of a ticket at the Algal Rhythms concert is $25
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There are 6 dogs and 5 cats.
In how many different orders can these animals be placed in line if any animal can be next to any other animal?
In how many different orders can these animals be placed in line if the dogs and cats are lined up alternately?
(Hint - The first animal MUST be a dog)
In how many different orders can these animals be placed in line if the first and last animal in line must be a cat?
Using the arrangements formula, the number of orders is given as follows:
39,916,800 if no restrictions.86,400 if they are lined up alternatively.7,257,600 if the first and last must be cats.What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are no restrictions, the number of ways is:
[tex]A_{11} = 11! = 39,916,800[/tex]
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]
When the first and last are cats, we have that:
For the first and last animals, there are 5!/2! = 20 ways.For the middle 9 animals, there are 9! ways.Hence:
20 x 9! = 7,257,600.
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Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 48.
The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
According to thr question.
We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.
Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.
Now,
The total number of ways of selecting 6 numbers from 48
[tex]= ^{48} C_{6}[/tex]
[tex]= \frac{48!}{6!\times 42!}[/tex]
[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]
= 8835488640/6!
And, the total number of ways of selecting 6 incorrect numbers from 42
= [tex]^{42} C_{6}[/tex]
[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]
= 3776965920/6!
Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by
[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]
[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]
= 3776965920/8835488640
= 0.427
≈ 0.43
Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
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Select the correct answer. sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved?
The equation that Sean woul have solved using the cross multiplication would be option a.
How to solve the question through the use of cross multiplication[tex]\frac{10}{x^2-1} =\frac{15}{3x-3}[/tex]
We have to open the equation by using cross multiplication
10(3x - 3) = 15(x² - 1)
= 30x - 30 = 15x² - 15
we would have to factorize
30(x-1) = 15(x-1)(x+1)
We have to divide by 15(x-1)
2 = x + 1
take the like terms
2 -1 = x
x = 1
Hence the equation that has the extraneous solution is option a because the solution is 1.
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The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
7. Which of these statements is true?
A. 1-(-4)<4- (-2)
B. (-2)(3) > (-1)(-6)
C. 6÷
D.-(5-3)=-5-3
Answer:
A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6
Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
I need the algebraic proofs please!!!
Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6
Algebraic Proof for the Given Algebraic Equation
The given algebraic equation is,
(2x + 6)/5 = 4x - 3
2x + 6 = 5(4x - 3)
2x + 6 = 20x - 15
20x - 15 = 2x + 6
This algebraic equation can be written as,
20x - 2x - 15 = 6
18x = 15 + 6
18x = 21
x = 21/18
x = 7/6
Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.
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What are the y-intercept and the asymptote of g(x) = 3x – 5? (0, –5); y = 3 (0, –2); y = 5 (0, –4); y = –5 (0, 5); y = –3
The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
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Mrs. Bailey has equal numbers of nickels and quarters but the value of the quarters is $1.80 more than the value of the nickels. What is the total value of all coins together in dollars and cents
Total value of all coins together is $2.7
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
1 Nickel = $0.05 and 1 quarter = $0.25.
Let number of nickels and number of quarter be x.
According to the situation
x.(0.25) = $1.80 + x.($0.05)
x(0.25 - 0.05) = $1.80
x (0.2) = $1.80
x = $1.80/0.2
x = 9 coins
Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7
Thus total value of all coins together is $2.7.
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(e) ABCD is an isosceles trapezium. Prove that: (1) AC=BD (2) BE=CE (3) AE=DE
Answer:
look at attached image for the step-by-step proof. thanks for reposting this lol
A train to new york city leaves every 7 minutes. another train to boston leaves the station every 6 minutes. suppose it is 6:30 am right now. at what time will both trains leave the station together again if both of them left the station together at 6:30 am?
Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
What is LCM?The lowest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30. There are numerous ways for determining the least common multiples, just as there are for computing the greatest common divisors. One approach is to divide both numbers by their primes.To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:
If a train to New York City departs every 7 minutes and another to Boston departs every 6 minutes,The two trains then depart together after a time equal to the LCM of their individual intervalsLCM (7,6) = 42As a result, if they begin at the same time, they will depart at the same time every 42 minutes.If both trains left the station at 6.30 a.m., they will leave together again 42 minutes later, at 7.12 am.
Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
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X – 3 = 7 so X = thank
Answer:
x=10
Step-by-step explanation:
x-3(+3)=7+3
We need to add 3 to both sides to isolate x.
x=10
Answer:
x = 10Step-by-step explanation:
x - 3 = 7
x = 7 + 3
x = 10
(2x² – 3x)(3x² + 2x - 1)
Answer:
6x^4-5x^3-8x^2+3x
Step-by-step explanation:
-factor it using FOIL (first outside inside last)
(06.01 mc) what is the value of the expression 9 (fraction 1 over 2)4 ⋅ 48? 12 15 17 18
The value of the given expression is 105.
What are expressions?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find the value of the given expression:
Given function - 9 + (fraction 1 over 2)4 ⋅ 48Let, 9 + 1/2 ⋅ 4 ⋅ 48.Follow the PEMDAS order of operations:
Multiply and divide (left to right).
1/2 ⋅ 4 ⋅ 48 = 96 9 + 1/2 ⋅ 4 ⋅ 48 = 9 + 96Add and subtract (left to right)
9 + 96 = 105Therefore, the value of the given expression is 105.
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When we use the Distributive
Property, we multiply the number in
front of the parenthesis with each
term inside the parenthesis.
Enter the number that belongs in the green box.
3(4x + 2) = [?]x + [ ]
Answer:
12x+6
Step-by-step explanation:
Can i have brainliest
Answer: 12x + 6
Step-by-step explanation:
In Distributive property, you multiply each of the numbers in the parentheses by the outside number.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
Answer:
parallel
Step-by-step explanation:
//
Answer: these lines are parallel.
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]
Allen wants to buy colored pencils that cost $3.50. He has 2 dollars, 5 quarters, 2 dimes, and 7 pennies. Does he have enough money to buy the colored pencils
Answer:
Yes
Step-by-step explanation:
First we need to determine how much money Allen has
2 dollars = 2.00
5 quarters = 5 * .25 = 1.25
2 dimes = 2 * .10 = .20
7 pennies = 7 * .01 = .07
Add this together
2.00 + 1.25+.20+.07 =3.52
3.52 > 3.50
This is more than 3.50 so he has enough money to buy the pencils