Answer:
See below
Step-by-step explanation:
The given rational function is;
[tex]y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}[/tex]
The given function is not continuous where the denominator is equal to zero.
[tex](x+4)(x-4)(x+2)=0[/tex]
The function is discontinuous at [tex]x=-4,x=4,x=-2[/tex]
b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.
The point at x=-4 and x=4 are non-removable discontinuities(vertical asymptotes)
c) The equation of the vertical asymptotes are x=-4 and x=4
To find the equation of the horizontal asymptote, we take limit to infinity.
[tex]\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0[/tex]
The horizontal asymptote is y=0
Jerry pours 86 milliliters of water into 8 tiny beakers he measures an equal amount of water into the first 7 beakers he pours the remaining water into the eight beaker it measure 16 milliliters how many milliliters of water are in each of the first 7 beakers. Using the RDW process show how you got the answer.
Answer:
There are 7 milliliters of water in each of the first 7 beakers
Step-by-step explanation:
* At first lets read the problem
- There are 86 milliliters of water to pour into tiny beakers
- Jerry has 8 tiny beakers
- He pours same amount in seven of them
- He pours 16 milliliters in the 8th one
- we want to know how many milliliters in each of the 7 beakers
* Look to the attached drawing
- There are 8 shapes represent the tiny beakers
- Seven of them have same amount x
- The last one has amount 16 milliliters
- All of them have 86 milliliters
* Now lets write the steps to answer the problem
∵ The amount of water is 86 milliliters
∵ The 8th tiny beaker has 16 milliliters
∴ The amount of water in the 7 beakers = 86 - 16 = 70 milliliters
∵ Each one of the 7 beakers has x milliliters of water
∴ 7 × (x) = 70 ⇒ divide each side by 7
∴ x = 7 milliliters
* There are 7 milliliters of water in each of the first 7 beakers
Each of the first 7 beakers contains 10 milliliters of water.
1. First, we identify the total amount of water Jerry poured, which is 86 milliliters.
2. We know that the eighth beaker contains 16 milliliters of water.
3. To find out how much water was poured into the first 7 beakers, we subtract the amount in the eighth beaker from the total amount:
[tex]\[ \text{Water in first 7 beakers} = \text{Total water} - \text{Water in 8th beaker} \] \[ \text{Water in first 7 beakers} = 86 \text{ ml} - 16 \text{ ml} \] \[ \text{Water in first 7 beakers} = 70 \text{ ml} \][/tex]
4. Now, we divide the total water in the first 7 beakers by 7 to find out how much water is in each beaker:
[tex]\[ \text{Water per beaker} = \frac{\text{Water in first 7 beakers}}{\text{Number of beakers}} \] \[ \text{Water per beaker} = \frac{70 \text{ ml}}{7} \] \[ \text{Water per beaker} = 10 \text{ ml} \][/tex]
Therefore, each of the first 7 beakers contains 10 milliliters of water.
At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in 10 small candle holders and 4 large candle holders, using a total of 52 candles. On the west side, he replaced the candles in 2 small candle holders and 4 large candle holders, for a total of 36 candles. How many candles does each candle holder hold?
To solve this problem, we can set up a system of equations to represent the given information. Solving this system of equations, we find that each small candle holder holds 2 candles and each large candle holder holds 8 candles.
Explanation:To solve this problem, let's represent the number of candles each small candle holder holds as x and the number of candles each large candle holder holds as y. We can set up a system of equations to represent the given information:
For the east side: 10x + 4y = 52For the west side: 2x + 4y = 36We can solve this system of equations by eliminating one variable. Subtracting the equations, we get 8x = 16. Dividing both sides by 8, we find that x = 2. Substituting this value back into one of the equations, we can solve for y. Using the first equation, we have 10(2) + 4y = 52, which simplifies to 20 + 4y = 52. Subtracting 20 from both sides, we obtain 4y = 32. Dividing by 4, we find that y = 8. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.
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To find out how many candles each candle holder holds, set up a system of equations using the given information and solve for the variables. Each small candle holder holds 2 candles and each large candle holder holds 8 candles.
Explanation:To find out how many candles each candle holder holds, we need to set up a system of equations using the given information. Let's say the number of candles a small candle holder can hold is 's' and the number of candles a large candle holder can hold is 'l'.
From the east side, we have the equation 10s + 4l = 52. From the west side, we have the equation 2s + 4l = 36. Solving these equations, we can find the values of 's' and 'l', which will give us the number of candles each candle holder can hold.
We can eliminate 'l' by multiplying the first equation by 2 and the second equation by 5. This gives us 20s + 8l = 104 and 10s + 20l = 180. By subtracting the second equation from the first, we get 10l = 76. Dividing both sides by 10, we find that l = 7.6. Since we cannot have a fraction of a candle, we can approximate l to the nearest whole number, which is 8.
Substituting the value of l back into one of the original equations, we can find the value of s. Using the first equation, we have 10s + 4(8) = 52. Simplifying this equation gives us 10s + 32 = 52. Subtracting 32 from both sides, we find that 10s = 20. Dividing both sides by 10, we find that s = 2. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.
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This system of equations has an infinite number of solutions. Define the solutions algebraically, and allow z to represent all real numbers.
3x − 4y + 4z = 7
x − y − 2z = 2
2x − 3y + 6z = 5
x =
y =
z = all real numbers
Answer:
x = 1+12z, y = -1+10z, and z = z
Step-by-step explanation:
Step 1: Convert the system into the augmented matrix form:
• 3 -4 4 | 7
• 1 -1 -2 | 2
• 2 -3 6 | 5
Step 2: Multiply row 2 with -2 and add it into row 3:
• 3 -4 4 | 7
• 1 -1 -2 | 2
• 0 -1 10 | 1
Step 3: Multiply row 2 with -3 and add it into row 1:
• 0 -1 10 | 1
• 1 -1 -2 | 2
• 0 -1 10 | 1
Step 4: Replace row 1 with row 2 and multiply the updated row 2 with -1 and add it into row 3:
• 1 -1 -2 | 2
• 0 -1 10 | 1
• 0 0 0 | 0
Step 5: Multiply row 2 with -1 and add it in row 1:
0 1 -10 -1
• 1 0 -12 | 1
• 0 -1 10 | 1
• 0 0 0 | 0
Step 6: It can be seen that there are infinite solutions of this system since the last row is all zeroes. It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x - 12z = 1
• -y + 10z = 1
Step 7: Make x and y the subject of their respective equations:
• x = 1 + 12z
• y = -1 + 10z
So final answer is x = 1+12z, y = -1+10z, and z = z!!!
Which of the following equations is an example of inverse variation between variables x and y?
A. y = x + 7
B. y = 7x
C. y = x/7
D. y = 7/x
Answer:
D. [tex]y=\frac{7}{x}[/tex]
Step-by-step explanation:
Let y varies inversely with x.
Then we can write the variation equation:
[tex]y\propto \frac{1}{x}[/tex]
We introduce the constant of proportionality, k and obtain the inverse variation equation:
[tex]y=\frac{k}{x}[/tex]
From the given options, the only equation in this form is
[tex]y=\frac{7}{x}[/tex]
In this case, k=7 is the constant of proportionality or constant of variation.
Circle M is circumscribed about right triangle ABC with legs 6 meters and 8 meters.
What is the exact circumference of ⊙M
ABC is a right triangle, so AC has length given by
[tex]AC^2=(6\,\mathrm m)^2+(8\,\mathrm m)^2\implies AC=\sqrt{100\,\mathrm m^2}=10\,\mathrm m[/tex]
Then the circumference of circle M is [tex]10\pi\,\mathrm m[/tex].
Marti is filling a 10– inch diameter ball with sand to make a medicine ball that can be used for exercising. To determine if the medicine ball will be too heavy after it is completely full of sand, she did some research and found that there is approximately 100 pounds of sand per cubic foot. How heavy will the medicine ball be after it is filled with sand, rounded to the nearest pound? A.30 pounds B.58 pounds C.24 pounds D.83 pounds
Answer:
Option A. [tex]30\ pounds[/tex]
Step-by-step explanation:
step 1
Find the volume of the sphere ( medicine ball)
The volume is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
Convert inches to feet
Remember that
1 ft=12 in
[tex]r=5\ in=5/12\ ft[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(5/12)^{3}[/tex]
[tex]V=0.3029\ ft^{3}[/tex]
step 2
Find the weight of the ball
Multiply the volume in cubic foot by 100
[tex]0.3029*100=30.29\ pounds[/tex]
Round to the nearest pound
[tex]30.29=30\ pounds[/tex]
The medicine ball would be A. 30 pounds
Volume of the medicine ball
Since the medicine ball is a sphere, its volume is
V = πd³/6 where d = diameter of medicine ball = 10 in = 10 in × 1 ft/12 in = 0.8333 ft
So, substituting the value of the variable into the equation, we have
V = πd³/6
V = π(0.8333 ft)³/6
V = π(0.5787 ft³)/6
V = 1.818 ft³/6
V = 0.303 ft³
Mass of medicine ball
The mass of the medicine ball = mass of sand per cubic foot × volume of medicine ball
where
mass of sand per cubic foot = 100 lb/ft³ and volume of medicine ball = 0.303 ft³So,
mass of the medicine ball = 100 lb/ft³ × 0.303 ft³
= 30.3 lb
≅ 30 pounds
So, the medicine ball would be A. 30 pounds
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A coach is dividing a soccer team of 28 players into groups. If each group has the same number of players, what is the greatest number of groups there can be if each group has no more than 10 players?
Answer:
The only possible groups that could be made if each group have the same number of people is 2 groups of 14 or 4 groups of 7. Since each group cannot have more than 10 people, the only group left is 4 groups of 7.
James wants to pursue a career in engineering whereby he can offer services directly to the public. What certification should he get and who provides this certification?
James needs to obtain a certification of a (______) so that he can offer services directly to the public. The (______) conducts examinations that engineers must pass in order to acquire this certification.
blank 1. fundamental engineer, professional engineer, structural engineer
blank 2. NCEES, NICET, ABET
Answer:
Blank 1. Professional engineer
Blank 2. ABET( Accreditation Board for Engineering and Technology)
Please help me out ‼️
Answer:
7
Step-by-step explanation:
In similar triangles, corresponding elements are proportional. Then we get,
(2x + 1)/(x-1) = 10/4
4(2x +1) = 10(x-1)
8x + 4 = 10x - 10
8x = 10x - 14
2x = 14
x = 7
Hope it helps and if it does, please mark me brainliest...
Answer:
7
both sides are corresponding so triangleABC AB=AC.
At an elementary school carnival, students can draw a rubber duck out of a tub of water. Each duck has a number written on the bottom of it which correlates with a prize. There are a total of 8 ducks in the tub. Two ducks have a 5 on them, four ducks have a 6 on them, and two duck has a 7 on it. What is the expected value of a duck?
a. 8.25
b. 6.85
c. 25
d. 4
Please help!!!!
Answer: 4
Step-by-step explanation: I Am Almost Sure The Answer Is 4. I Did The Math Out And That Is What I Got.
Which equation represents the perpendicular bisector of the given line segment?
A) x = 0
B) y = 0
C) y = x
D) x = 10
Answer:
Option D. [tex]x=10[/tex]
Step-by-step explanation:
step 1
Find the midpoint of the given line segment
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
[tex]A(5,10),B(15,10)[/tex]
substitute the values
[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]
[tex]M=(10,10)[/tex]
step 2
Find the equation of the perpendicular bisector
we know that
The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)
therefore
the equation is equal to
[tex]x=10[/tex]
Answer:
10
Step-by-step explanation:
Bena bought a bottle of water for $ 1.29 and a pack of gum for $ 1.79.How much did bena give the clerk if she got $6.92 in change
Find the volume of this composite solid.
For this case we have that the figure shown is composed of a cylinder and a cone.
We have that the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
A: It's the radio
h: It's the height
Substituting the values:
[tex]V = \pi * (5) ^ 2 * 10\\V = \pi * 25 * 10\\V = 250 \pi \ m ^ 3[/tex]
On the other hand, the volume of a cone is given by:
[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]
Where:
A: It's the radio
h: It's the height
Substituting the values:
[tex]V = \frac {\pi * (5) ^ 2 * 4} {3}\\V = \frac {\pi * 25 * 4} {3}\\V = \frac {100 \pi} {3} \ m ^ 3[/tex]
Then, the total volume is:
[tex]V_ {t} = 250 \pi \ m ^ 3 + \frac {100 \pi} {3} \ m ^ 3[/tex]
Taking [tex]\pi = 3.14[/tex], we have to:
[tex]V_ {t} = 889.67 \ m ^ 3[/tex]
Answer:
Option D
each package contains 4 boxes each box contains a 7 pound bag of beans and a bag of rice the bags of rice are all identical
Answer:
28
Step-by-step explanation:
7*4
Answer:
28
Step-by-step explanation:
7*4
What is the value of COS H?
Round to four decimal places if needed.
Answer:
Final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].
Step-by-step explanation:
using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.
[tex]\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}[/tex]
[tex]\cos\left(H\right)=\frac{GH}{FH}[/tex]
[tex]\cos\left(H\right)=\frac{36}{85}[/tex]
[tex]\cos\left(H\right)=0.423529411765[/tex]
Hence final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].
Using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.
What is the Cosine Ratio?Cosine ratio is expressed as, cos ∅ = adjacent/hypotenuse of a right triangle.
Given:
∅ = H = ?Hypotenuse = 85Adjacent side = 36Therefore:
Cos H = 36/85
Cos H = 0.4235
Therefore, using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.
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A rectangle has a length of 6X +3 units and a width of eight units write a simplified expression for the area in square are you friends of this rectangle
Answer:
A = 48x + 24 (square units)
Step-by-step explanation:
L = 6x + 3
W = 8
A = L * W
A = 8(6x + 3)
A = 48x + 24
The woodlands middle school poll results show that about 79.3% of people who prefer pizza are students and about 81% of people who prefer burgers are students.
a : there is not enough evidence to support a relationship between lunch preference and role at school
b : there is evidence to support a relationship between lunch preference at school
Answer: A: there is not enough evidence to support a relationship between lunch preference and role at school
The relationship between poll result and the student preference is: option A, not enough evidence
Why is there no evidence?This due to the fact that the statistics in the question is incomplete. W do not have sufficient data that would be used for hypothesis testing.
Due to the fact above, we conclude that there is insufficient evidence to get the relationship between variables.
In conclusion, there is not enough evidence to support a relationship between lunch preference and role at school
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a box contains four $1 and six $5 bills. if three bills are selected at random without replacement, find the probability that all three are $5 bills.
A.27/125 B.1/4 C.1/6 D3/5
Answer:
C.1/6
Step-by-step explanation:
Initially the box has four $1 and six $5 bills. The probability of selecting a $5 bill in the first trial would be given as;
(number of $5 bills) / (total number of bills)
= (6)/(4+6) = 3/5
If in the first attempt we actually pick a $5 bill, the number of $5 bills will reduce by one to 5. Now, the probability of picking a $5 bill in the second attempt will be given as;
(new number of $5 bills) / (new total number of bills)
= (5)/(4+5) = 5/9
The new number of $5 bills will now be; 6 - 2 = 4 since we have already picked 2 without replacing them.
Now, the probability of picking a $5 bill in the third attempt will be given as;
(new number of $5 bills) / (new total number of bills)
= (4)/(4+4) = 1/2
Since the three attempts are independent, the probability of picking all three $5 bills is;
3/5 * 5/9 * 1/2 = 1/6
The probability of drawing three $5 bills from a box containing four $1 bills and six $5 bills, when the bills are drawn without replacement, is 1/6.
Explanation:The question is asking for the probability of drawing three $5 bills from a box containing four $1 bills and six $5 bills, given that the bills are drawn without replacement. This is a problem of combinatorial probability. We first find the total ways of selecting three bills from the box, then find the ways of selecting three $5 bills.
The total ways of selecting three bills is given by combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of bills and r is the number selected. In this case, n=10 (4 $1 bills and 6 $5 bills) and r=3. So, C(10,3) = 120.
The ways of selecting three $5 bills is C(6,3) = 20,
So the probability of drawing three $5 bills is 20/120 = 1/6.
Therefore, the correct answer is C. 1/6.
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My answers keep getting erased, even the ones that were actually perfectly fine and explained. The person who asked the question even said that I was right.
I'm just annoyed with Brainly at this point.
I need to add a question so.......
Find the answer to 749x832=?
Answer:
623168
Step-by-step explanation:
749x832=623168
Find (ƒ + g)(x) where ƒ(x) = 5x2 + 4, g(x) = 6x2 – x.
(ƒ + g)(x) = 11x2 – x + 4
(ƒ + g)(x) = 11x2 – 4x
To find (ƒ + g)(x) for the given functions ƒ(x) = 5x² + 4 and g(x) = 6x² - x, we add the like terms to get
(ƒ + g)(x) = 11x² - x + 4.
To find (ƒ + g)(x) where ƒ(x) = 5x² + 4, and g(x) = 6x² – x, we simply add the two functions together. We combine like terms to calculate the sum.
By adding the corresponding terms:
The x² terms: 5x² + 6x² = 11x² The x terms: Since there is no x term in ƒ(x), we only have the x term from g(x), which is -x.The constant terms: 4 from ƒ(x) and there is no constant term in g(x).Combining these, we get
(ƒ + g)(x) = f(x) + g(x)
(f + g)(x) = 11x² - x + 4.
Triangle ABC is similar to triangle DEF. The length of AC is 10cm. The length of BC is 16 cm. The length of DF is 8cm. What is the length of EF?
Answer: The length of EF=15 cm.
Step-by-step explanation:
John was born in 1951 and has been contributing to his own retirement plan as well as
Social Security for many years. John was trying to decide if he wanted to retire at 62 years of age rather than at 66 when he would reach full retirement age. According to the Social Security laws, John would receive a 25% reduction in his Social Security if he retired at 62. John went to the Social Security website and discovered that if he retired at 66 he would receive $2,460 a month in retirement from Social Security. How much would he receive if he retired at 62 rather than at 66?
a. $1,650 a month
b. $1,845 a month
c. $1,500 a month
d. $1,745 a month
Answer:
[tex]\boxed{\text{b. \$1845 a month}}[/tex]
Step-by-step explanation:
Amount if retired at 66 = $2460/mo
Less 25 % = 0.25 × 2460 = -615
Amount if retired at 62 = $1845/mo
John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.
HELP ASAP I WILL GIVE BRAINLIEST
Solve the following equation algebraically:
x^2=180
a.
-13.42, 13.42
b.
13.42
c.
-90, 90
d.
-12.42, 12.42
Answer:
A
Step-by-step explanation:
Taking the square root of both sides, you get
[tex]\sqrt{x^2} = \pm\sqrt{180}[/tex]
which simplifies to
[tex]x = \pm\sqrt{180}[/tex]
The square root of 180 is approximately 13.42 and since it is the plus or minus square root, the answer is A, -13.42, 13.42.
Final answer:
The equation x²=180 is solved by taking the square root of both sides, yielding two solutions: x = 13.42 and x = -13.42. Thus, option A is corect.
Explanation:
To solve the equation x² = 180 algebraically, we need to take the square root of both sides of the equation. This gives us two solutions, since both a positive and negative number squared will yield 180. The square root of 180 once calculated is approximately 13.42. Therefore, the two solutions are x = 13.42 and x = -13.42.
4. A garden store has the following miscellaneous flower bulbs in a basket.
* 6 amaryllins
* 7 daffodils
* 4 lilies
* 3 tulips
A customer bought 4 bulbs from the basket, one of each type of flower. If the next customer selects 1 of the remaining bulbs at random, which is the closest to the probability that customer will get an amaryllins bulb?
A. 30%
B. 31%
C. 38%
D. 45%
Final answer:
After removing one bulb of each type, the probability of the next customer getting an amaryllins bulb is 5/16, which is 31.25%. Thus, the closest answer provided is 31%, option B.
Explanation:
The question asks for the probability of the next customer getting an amaryllins bulb after four bulbs of different types have been removed from a basket containing miscellaneous flower bulbs. Initially, there were 6 amaryllins, 7 daffodils, 4 lilies, and 3 tulips. Since one bulb of each type was bought by the previous customer, we now have 5 amaryllins, 6 daffodils, 3 lilies, and 2 tulips remaining.
To find the probability of selecting an amaryllins bulb, we divide the number of amaryllins bulbs left by the total number of bulbs remaining:
Probability of selecting an amaryllins = Number of amaryllins bulbs remaining / Total number of bulbs remaining
Probability = 5 / (5 + 6 + 3 + 2) = 5 / 16
To convert this to a percentage, we multiply it by 100: (5 / 16) * 100 = 31.25%
Therefore, the probability is closest to 31%, which corresponds to option B.
What is the sum of the geometric sequence -1, 6, -36, ....if there are 7 terms.
A) -39,991
B) -6,665
C) 6,665
D) 39,991
Answer:
A) - 39,991
Step-by-step explanation:
Sum of geometric sequence formula is
[tex]S = a(\frac{1 -r^n}{1-r} )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1(\frac{1 -(-6)^7}{1-(-6)} )= -\frac{279937}{7} = -39991[/tex]
Answer:
The correct answer option is A) -39,991.
Step-by-step explanation:
We know that the sum of the geometric sequence is given by the formula:
[tex] S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r } [/tex]
where [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio and [tex]n[/tex] is the number of terms.
Here,
[tex]a_1 = -1[/tex]
[tex]r = -6[/tex]
[tex]n=7[/tex]
Substituting these values in the above formula to get:
[tex] S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) } [/tex]
S_n = -39,991
Choose all of the statements that correctly describe the transformation rule. Reflection over x-axis: (x, y) ? (?x, y) Reflection over y-axis: (x, y) ? (x, ?y) Rotation of 90° counter-clockwise about origin: (x, y) ? (?y, x) Rotation of 180° counter-clockwise about origin: (x, y) ? (?x, ?y) Rotation of 270° counter-clockwise about origin: (x, y) ? (y, ?x)
Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:
1. Reflection over x-axis:Consider the point [tex](x,y)[/tex], if you reflect this point across the x-axis you should multiply the y-coordinate by -1, so you get:
[tex]\boxed{(x,y)\rightarrow(x,-y)}[/tex]
2. Reflection over y-axis:Consider the point [tex](x,y)[/tex], if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:
[tex]\boxed{(x,y)\rightarrow(-x,y)}[/tex]
3. Rotation of 90° counter-clockwise about origin:Consider the point [tex](x,y)[/tex]. To rotate this point by 90° around the origin in counterclockwise direction, you can always swap the x- and y-coordinates and then multiply the new x-coordinate by -1. In a mathematical language this is as follows:
[tex]\boxed{(x,y)\rightarrow(-y,x)}[/tex]
4. Rotation of 180° counter-clockwise about origin:Consider the point [tex](x,y)[/tex]. To rotate this point by 180° around the origin, you can flip the sign of both the x- and y-coordinates. In a mathematical language this is as follows:
[tex]\boxed{(x,y)\rightarrow(-x,-y)}[/tex]
5. Rotation of 270° counter-clockwise about origin:Rotate a point 270° counter-clockwise about origin is the same as rotating the point 90° in clock-wise direction. So the rule is:
[tex]\boxed{(x,y)\rightarrow(y,-x)}[/tex]
Answer:Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:
Step-by-step explanation:
Eight less than seven times a number is the same as for l four more than three times a number. Find the number.
Question :- Eight less then seven times a number is the same as for l four more than three times a number. Find the number.
Answer :-
Let the number be x
Therefore,
[tex]=> 8-7x = 4+3x[/tex]
[tex]=> 8-4 = 3x+7x[/tex]
[tex]=> 4 = 10[/tex]
[tex]=> X = 5/4[/tex]
Hope it helps!
Bill is making accessories for the soccer team. He uses 791.86 inches of fabric on headbands for 32 players and 2 coaches. He also uses 273.28 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
There was 23.29 inches used on a headband for each player.
And 8.54 inches used on a wristband for each player.
Step-by-step explanation:To find out how much fabric for headbands and would beused for each player/person you would do
[tex]total \: fabric \: used \: \div \: total \: amount \: of \: people[/tex]
So, if you substitute the values in it is
[tex]791.86÷34=23.29 \: inches \: for \: 1 \: headband. \: [/tex]
And finally, to find how much fabric is used on a wristband for each player/person you would use the same formula.
[tex]273.28 \: \div 32 = 8.54 \: inches[/tex]
Find the value of the matrices
A) 17
B) 12
C) 15
D) 13
Answer:
option C is correct
Step-by-step explanation:
We need to find the determinant.
= -1(7*9 - 3*9)-( -3)(4*9 - 3*3) -2(4*9 -7*3)
= -1(63-27) +3 (36 - 9) -2( 36- 21)
= -1(36)+3(27)-2(15)
= -36+81-30
= 15
Option C is correct
It takes Ahmed 50 seconds on his bike to reach his friend's house 250 meters away. What is his average speed?
It takes 5 meters per second.
If you divide 250 by 50 you would get his average speed
The average speed of Ahmed is 5 meters per second.
Important information:
Time taken by Ahmed = 50 secondsDistance = 250 metersWe need to find the average speed of Ahmed.
Average speed:Formula for average speed is:
[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Using this formula, the average speed of Ahmed is:
[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]
[tex]\text{Average Speed}=5[/tex]
Thus, the average speed of Ahmed is 5 meters per second.
Find out more about 'Average speed' here:
https://brainly.com/question/633650