Answer:
The number of trees in each row is 21.
Step-by-step explanation:
Let us assume the number of trees in each row = m
So, the number of rows in the orchard = Number of trees in each row + 10
or, total number of trees in each row = (10 +m)
Now, Total number of Trees = Number of Rows x Number of trees in 1 row
⇒ 651 = m (m + 10)
[tex]651 = m^2 + 10m\\\implies m^2 + 10m - 651 =0\\or, m^2 + 31m 21m - 651 =0\\or, m(m +31) -21(m+31) =0\\\implies (m +31) (m-21) = 0[/tex]
⇒ (m +31) = 0, or (m-21) = 0
⇒ m= -31, or m = 21
Now, as m = The number of trees in each row, so m ≠ -31
So, m = 21
Hence, the number of trees in each row is m = 21.
10. A toy store received a shipment of 17 cases of
teddy bears. Use compatible numbers to estimate
the total number of teddy bears in the shipment.
12 bears per case
Answer: 204 teddy bears
Step-by-step explanation:
Answer:
17 x 12 = 204 teddy bears
Step-by-step explanation:
17 cases, 12 bears in each case
You could round 17 --> 20
You could round 12 --> 10
20×10=200
Deja has two baskets of berries. One of the baskets has 3 3/8 pounds of berries and the other basket has 2 7/8 pounds of berries. She is going to split the berries evenly among 4 people. Witch measure is the best estimate for the number of pounds of berries each person would receive.
A) 1 1/4 pounds
B) 1 5/8 pounds
C) 2 7/8 pounds
D) 3 3/16 pounds
Answer:
(b) The number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.
Step-by-step explanation:
The amount of berries in first basket = 3 3/8 pounds
Now, [tex]3\frac{3}{8} = 3+\frac{3}{8} = 3 + 0.375 = 3.375[/tex]
So, the amount of berries in first basket = 3.375 pounds
The amount of berries in second basket = 2 7/8 pounds
Now, [tex]2\frac{7}{8} = 2+\frac{7}{8} = 2 + 0.875 = 2.875[/tex]
So, the amount of berries in second basket = 2.875 pounds
Now, the total berries = Berries in ( First + Second) basket
= 3.375 pounds + 2.875 pounds
= 6.25 pounds
So, the number of pounds each person would have = [tex]\frac{\textrm{Total weight of viable berries}}{\textrm{4}} = \frac{6.25}{4} = 1.5625[/tex]
Now, [tex]1.5625 = 1 + 0.5625 = 1 + \frac{5625}{10000} = 1 + \frac{5}{8} = 1\frac{5}{8}[/tex]
So, the number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.
pls use the diagram to answer the question thanks
Answer:
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30°
Step-by-step explanation:
Given as :
It is shown in diagram as ;
The circle with different angles from angle 1 to angle 12
Now, The figure is the complete circle, and the measure of all angles in a circle = 360°
The measure of semicircle = 180°
and each quadrant is divided in to 3 angles
Each right angle is further divided into three 30° angles
Again ,
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30° Answer
The measure of the vertex angle of an isosceles triangle is 92. Find the measure of a base angle
Answer:
44°
Step-by-step explanation:
The sum of the angles in a triangle = 180°
In an isosceles triangle the base angles are equal, thus
base angle = [tex]\frac{180-92}{2}[/tex] = [tex]\frac{88}{2}[/tex] = 44°
Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.
An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 60 and an x intercept of 18 comma 0.
0 ≤ x ≤ 18, −3.33
0 ≤ x ≤ 18, −0.3
0 ≤ y ≤ 60, −3.33
0 ≤ y ≤ 60, −0.3
In order to play at the Cape Gerbil City Miniature Golf Club, a player has to pay the membership fee and pay for each round played. The total cost is represented by the function
T = 33.47r + 17.72, where T = the total cost (in dollars) and r = the number of rounds played.
Which of the following statements must be true?
A .The slope is the cost per round $33.47, and the y-intercept is the membership fee of $17.72.
B.The total cost is $51.19.
C.The slope is the cost per round $17.72, and the y-intercept is the membership fee of $33.47.
D.The slope is the membership fee of $17.72, and the y-intercept is the number of rounds played.
E.I don't know
Please answer
Final answer:
The correct statement must be that the slope of the equation is the cost per round of $33.47, and the y-intercept is the initial membership fee of $17.72, since the slope represents the additional cost per round and the y-intercept the initial cost at zero rounds.
Explanation:
In the function T = 33.47r + 17.72, which represents the total cost T of playing miniature golf as a function of the number of rounds played r, the coefficient of r represents the slope and the constant term is the y-intercept. The slope indicates the additional cost for each additional round of golf played, while the y-intercept represents the initial cost when no rounds are played, which can be interpreted as the membership fee. Therefore, the correct statement about the cost structure of the Cape Gerbil City Miniature Golf Club is A: The slope is the cost per round $33.47, and the y-intercept is the membership fee of $17.72.
Solve the system by elimination. 4x=−3y−10 9x+2y=6
Answer:
x = 2, y = -6Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x=-3y-10&\text{add}\ 3y\ \text{to both sides}\\9x+2y=6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=-10&\text{multiply both sides by 2}\\9x+2y=6&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+6y=-20\\-27x-6y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-19x=-38\qquad\text{divide both sides by (-19)}\\.\qquad\dfrac{-19x}{-19}=\dfrac{-38}{-19}\\.\qquad \boxed{x=2}[/tex]
[tex]\text{Put the value of}\ x\ \text{to the second equation:}\\\\9(2)+2y=6\\18+2y=6\qquad\text{subtract 18 from both sides}\\2y=-12\qquad\text{divide both sides by 2}\\\dfrac{2y}{2}=\dfrac{-12}{2}\\\boxed{y=-6}[/tex]
What happens to the energy that is stored in cells? Check all that apply.
A: It is released slowly.
B: It is released quickly.
C: It is released in a single reaction.
D: It is released in a series of reactions.
E: It is used by cells for repair and growth.
This is worth 20 points.
A, D & E
Cells store energy in the form ATPs. These molecules power al the biochemical activities that would not occur spontaneously. Examples of these bioactivities are the contraction of actin filaments, glycolysis cycle, replication of DNA, cell division, gene expression, cell repair and etcetera.
Step-by-step explanation:
All ATPs are not spent at the same time, and futhermore, they are constantly replaced by the continuous process of cellular respiration that captures the chemical energy in the glucose molecules and stores them in ATP. During the release of this energy to power the biochemical reactions, much of it is lost as heat energy and this is why living organisms are always warm.
Learn More:
For more on ATP energy check out;
https://brainly.com/question/2166757
#LearnWithBrainly
Answer: The multiple choice answers would be, A, D, and E.
Step-by-step explanation:
There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class had 15 boays and 6 girls. Mr Ben's class ahd 14 girls and 10 boys. In Ms. Ashley's class, 2/3 of the students wear glasses.
In Mr. Ben's class, 1/4 of the kids have others siblings in the school.
1. What fraction of the students in the school are in grade 4?
2. What fraction of the grade 4 students are boys?
3. What fraction of the grade 4 students are in Ms. Ashley's class?
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
Answer:
1. 45/482 of the students are in grade 4.
2. 5/9 of the students of the grade 4 are boys.
3. 7/15 of the grade 4 students are in Ms. Ashley's class
4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.
5. There are 14 students with glasses and 7 without glasses.
Step-by-step explanation:
1. Let's review the information given to us for solving the questions:
Number of students in the school = 482
Ms. Ashley's Grade 4 class = 21 students
Ms. Ashley's Grade 4 class boys = 15 students
Ms. Ashley's Grade 4 class girls = 6 students
Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students
Mr. Ben's Grade 4 class = 24 students
Mr. Ben's Grade 4 class boys = 10 students
Mr. Ben's Grade 4 class girls = 14 students
Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students
2. Let's answer all the questions:
1. What fraction of the students in the school are in grade 4?
(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school
21 + 24 / 482 = 45/482
2. What fraction of the grade 4 students are boys?
(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
15 + 10 / 21 + 24
25 / 45 = 5/9
3. What fraction of the grade 4 students are in Ms. Ashley's class?
Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
21 / 21 + 24
21 / 45 = 7/15
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class
24 - 6 / 24
18 / 24 = 3/4
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
There are 14 students with glasses and 7 without glasses.
Note: Same answer to question 14038475, answered by me.
5x - 9y=1
-7x + 2y = -5
9514 1404 393
Answer:
(x, y) = (43/53, 18/53)
Step-by-step explanation:
If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.
7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)
35x -63y -35x +10y = 7 -25
-53y = -18 . . . . simplify. Note the x-terms are gone.
y = 18/53 . . . . . divide by -53
__
Putting this value of y in the first equation, we get ...
5x -9(18/53) = 1
5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify
x = 43/53 . . . . . . . . . . divide by 5
The solution is (x, y) = (43/53, 18/53).
Given that LON is a right angle, find the measure of x.
Answer:
[tex]x=30\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠LOM+m∠MON=m∠LON ----> by angle addition postulate
we have
m∠LOM=2x°
m∠MON=x°
m∠LON=90° ----> is a right angle
substitute the values
[tex]2x+x=90[/tex]
solve for x
[tex]3x=90[/tex]
[tex]x=30\°[/tex]
Hey circular trampoline has an area of 132.2 ft.² what is the radius of the trampoline rounded to the nearest tenth
Final answer:
To find the radius of the circular trampoline, we can use the formula for the area of a circle and rearrange it to solve for the radius. The radius of the trampoline is approximately 6.5 ft (rounded to the nearest tenth).
Explanation:
To find the radius of the circular trampoline, we can use the formula for the area of a circle, which is A = πr². In this case, the area is given as 132.2 ft². We can rearrange the formula to solve for the radius:
r² = A/π
r² = 132.2/π
r ≈ √(132.2/π)
r ≈ √(42)
r ≈ 6.5 ft (rounded to the nearest tenth)
Final answer:
To find the radius of the trampoline, we use the formula for the area of a circle and rearrange it to solve for the radius. After substituting the given area and approximating π as 3.14, we find that the radius is approximately 6.5 ft when rounded to the nearest tenth.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given the area of the trampoline as 132.2 ft², we can solve for the radius using the area formula. We rearrange the formula to solve for the radius: r = √(A/π).
Substituting the given area and the approximate value for π (3.14), we get r = √(132.2/3.14). This simplifies to r = √(42.085...), which is approximately r = 6.487 ft. Rounding to the nearest tenth gives us a radius of 6.5 ft.
Which comparison is true?
O A. 0.3 > 0.09
B. 0.04 > 0.2
OC. 0.29 > 0.38
OD. 0.24 > 0.67
O E. 0.55 > 0.600
Answer:
0.3 > 0.09
Step-by-step explanation:
The comparison 0.3 > 0.09 is true.
0.3 = 0.300
0.300 > 0.009
All other options are false. They should have a less than sign instead of a greater than sign.
Final answer:
Upon comparison of decimal values in the given options, Option A (0.3 > 0.09) is the true comparison as 0.3 is greater than 0.09 when comparing the tenths place.
Explanation:
When comparing decimal numbers, you should look at the largest place value first and work your way to smaller place values to determine which number is larger. Let's evaluate each option:
A. 0.3 > 0.09: Comparing the tenths place, 3 is greater than 0. Therefore, this statement is true.
B. 0.04 > 0.2: Comparing the tenths place, 0 is less than 2. Therefore, this statement is false.
C. 0.29 > 0.38: Comparing the tenths place, both numbers are equal, but in the hundredths place, 9 is less than 8. Therefore, this statement is false.
D. 0.24 > 0.67: Comparing the tenths place, 2 is less than 6. Therefore, this statement is false.
E. 0.55 > 0.600: Comparing the tenths place, both numbers are equal, and in the hundredths place, 5 is equal to 0 followed by an additional 0, thus both numbers are equal and this statement is false.
Based on the above analysis, the correct answer is Option A. 0.3 > 0.09.
If the sum of a number and -3 is doubled the result is 1 half
times the number. Find the number
Answer:
-3
Step-by-step explanation:
2(x+-3)=1/2x
2x+6=1/2x
6=-1/2x
x=-3
Answer:
-3 is the write answer
Step-by-step explanation:
2(x+3)=1/2x
2x+6=1/2x
6=-1/2x
x=-3
solve for w: -5(3-w)+4=-5/6(24-6w)
Answer:
no solution
Step-by-step explanation:
well first you gotta distribute
-5(-3 - w) + 4 = -5/6(24 - 6w)
15 + 5w + 4 = -20 + 5w
19 + 5w = -20 + 5w
+20 +20
39 + 5w = 5w
-5w -5w
39 ≠ 0
therefore there is no solution (which is the answer)
(-4,6); slope = -3/4
Answer:
y-6=-3/4(x+4)
Step-by-step explanation:
y-y1=m(x-x1)
m=-3/4
y-6=-3/4(x-(-4))
y-6=-3/4(x+4)
Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!
What is the area of the triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
My answer - 11 1/2
919÷ 2
Round to the nearest whole
My answer-?
What is the area of a parallelogram with a base of 14.5 m and a height of 21 m?
The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and 150 grilled chicken salads. What is the ratio in simplest terms of grilled chicken salads sold to the total number of lunches sold?
My Answer- 1:3
What is the ratio of odd to even digits in the following number:
7,208,631
My Answer- 3:4
Given that one ton is equal to 2000 pounds, what is 5 tons?
My Answer- 400 or 1000
A table measures 3 feet across. How many inches is this?
My Answer-36
Answer:
The corresponding answers to the questions are 9.625 cm² , 459, 304.5m², 1 : 3 , 3:4 , 10,000 pounds , 36 inches.
Step-by-step explanation:
1.
Area of triangle = 0.5 x base length x height
Here base length = 5.5cm and height = 3.5cm
So area will be 0.5 x 5.5 x 3.5 cm² = 9.625 cm²
2.
919/2 rounding off to nearest whole
We know that the value of 919/2 = 459.5 .
So the nearest whole number value to which it can be rounded off is 459.
3.
We know that area of parallelogram is base length x height
Here, base length =14.5m and height = 21m
So area = 14.5 x 21 m² = 304.5m²
4.
No. of grilled cheese sandwiches sold = 200
No. of tacos sold = 100
No. of grilled chicken salads sold = 150
Total lunches sold = 200 + 100 + 150 = 450
So, ratio of chicken salads to lunches sold is 150 : 450 = 1 : 3
5.
Given number : 7,208,631
Odd digits here - 7,3,1 - 3 digits
Even digits here - 2,0,8,6 - 4 digits
So, ratio of odd digits to even digits is 3:4
6.
One ton = 2000 pounds
So 5 tons = 5 x ( 1 ton) = 5 x 2000 pounds = 10,000 pounds
7.
Table length = 3 feet
We know that 1 foot = 12 inches
So table length = 3 foot = 3 X 12 inches = 36 inches
What is the absolute value of -0.2
Answer:
0.2
Step-by-step explanation:
Absolute values are positive version of any number. So the absolute value of both 0.2 and -0.2 would be 0.2
A barn silo, excluding the top, is a cylinder. The silo is 7 m in
diameter and the height is 12 m. What is the volume of the silo?
The volume of the silo is 461.81 m³
Step-by-step explanation:
A barn silo, excluding the top, is a cylinder
The silo is 7 m in diameterIts height is 12 mWe need to find the volume of the silo
∵ The silo is shaped a cylinder
∵ The volume of a cylinder = base area × height
∵ The base is shaped a circle
∵ Area a circle = π r², where r is the radius of the circle
∴ The volume of the silo = π r² × h
∵ The diameter of the silo = 7 m
∵ The radius of a circle is half the diameter
∴ The radius of the silo = [tex]\frac{1}{2}[/tex] × 7 = 3.5 m
∵ The height of the silo = 12 m
- Substitute the values of r and h in the rule of volume
∴ The volume of the silo = π (3.5)² × 12
∴ The volume of the silo = 147 π = 461.81 m³
The volume of the silo is 461.81 m³
Learn more:
You can learn more about the volume in brainly.com/question/6443737
#LearnwithBrainly
Final answer:
The volume of a barn silo that is shaped like a cylinder with a diameter of 7 meters and a height of 12 meters is approximately 461.7 cubic meters.
Explanation:
To calculate the volume of the silo which is in the shape of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. The diameter of the silo is given as 7 meters, so the radius is half of that, which is 3.5 meters. The height of the silo is 12 meters. Plugging these values into the formula gives:
V = π × (3.5 m)² × 12 m
V = π × 12.25 m² × 12 m
V = π × 147 m³
Assuming π to be approximately 3.14159, the calculation results in:
V = 3.14159 × 147 m³ = 461.7 m³ (approx)
So, the volume of the silo is approximately 461.7 cubic meters.
3
Select the correct answer.
A square field was enlarged by adding 5 feet to the length and width of the original field. If the area of the enlarged field is 576 square feet, what
was the side length of the original field?
A.
29 feet
19 feet
C.
6 feet
D.
36 feet
Answer:
The answer is 19 feet or B.
Step-by-step explanation:
First you should know that a square has equal sides.
Then it tells you to add 5 feet on the original field. So you add 5 to 19 and you get 24. After that, you multiply the 24 by itself to get 576 feet.
You work 37 1/2 hours and earn $352.50. What is your hourly wage
Answer:
$9.40
Step-by-step explanation:
well since you work 37.5 hours and you earn $352.50 you divide them to get your hourly wage
352.5 ÷ 37.5 = 9.4
so your hourly wage is $9.40
Final answer:
To calculate the hourly wage, the total earnings of $352.50 should be divided by the total work hours of 37.5. The hourly wage comes out to be $9.40.
Explanation:
To find out your hourly wage, you need to divide your total earnings by the number of work hours. In this instance, you worked 37.5 hours (since 1/2 an hour is equivalent to 0.5 hours) and earned $352.50. So, your hourly wage would be calculated as follows:
Hourly Wage = Total Earnings ÷ Number of Work Hours
Hourly Wage = $352.50 ÷ 37.5 hours
Hourly Wage = $9.40 per hour
Therefore, your hourly wage is $9.40.
using the piling method, which of the following can be constructed from polygons alone? check all that apply
A. circle
B. pyramid (including the vertex)
C. cylinder
D. pyramid (not including the vertex)
E. prism
F. cone
Answer:
D. pyramid (not including the vertex)
E. prism
Step-by-step explanation:
D and E are the answers to this question.
D. pyramid (not including the vertex)
E. prism
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The function below represents the monthly expenses for an event planning company where f(x) represents the total monthly expenses for planning x events. If at the end of one month the expenses for the company were $12,350, then ___ events were planned
f(x) = 50(2x=1) + 300
Answer:
There were 120 events planned.
Step-by-step explanation:
We are given the following information in the question:
f(x) represents the total monthly expenses for planning x events.
[tex]f(x) = 50(2x+1) + 300[/tex]
Cost of expenses for the company at the end of one month = $12,350
We have to find the number of events planned that is we have to find the value of x.
[tex]f(x) = 50(2x+1) + 300 = 12350\\50(2x+1) + 300 = 12350\\100x + 50 + 300 = 12350\\100x + 350 = 12350\\100x = 12350-350\\100x = 12000\\\\x = \displaystyle\frac{12000}{100} =120[/tex]
Thus, there were 120 events planned.
Answer:
120
Step-by-step explanation:
i actually did just guess on that answer i didnt know what to put
Which table shows the relationship y= 1/2x?
The line segment shown is rotated 90° clockwise about the origin. What are the new coordinates of point B?
(3, - 4)
Imagine a rectangle with one corner on the origin and the opposite on the point. Rotate the rectangle about the origin and see where the point lands.
To find the new coordinates of point B after a 90° clockwise rotation around the origin, you apply the rotation rule: (x, y) becomes (y, -x). The original coordinates are needed to calculate the exact new position of point B.
Explanation:The student is asking about the result of a 90° clockwise rotation of a point around the origin in the Cartesian coordinate system. To find the new coordinates of point B after the rotation, we use the rule for 90° clockwise rotation, which is (x, y) becomes (y, -x). If the original coordinates of point B are (x₂, y₂), the new coordinates after the rotation will be (y₂, -x₂).
Without knowing the original coordinates of point B, we cannot give the exact new coordinates. However, if the student provides the initial coordinates, the new coordinates can be calculated using the rotation rule mentioned.
3x + 2 = x + 4 ( x + 2 )
Answer:
x = -3Step-by-step explanation:
[tex]3x+2=x+4(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\3x+2=x+(4)(x)+(4)(2)\\\\3x+2=x+4x+8\qquad\text{combine like terms}\\\\3x+2=(x+4x)+8\\\\3x+2=5x+8\qquad\text{subtract 2 from both sides}\\\\3x+2-2=5x+8-2\\\\3x=5x+6\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\3x-5x=5x-5x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3[/tex]
decide whether the pair of lines is parallel, perpendicular, or neither. 3x-6y=2 and 18x+9y=8
Answer: perpendicular
Step-by-step explanation:
Final answer:
The slopes of the two lines given by the equations 3x-6y=2 and 18x+9y=8 are 1/2 and -2 respectively. Since these slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Explanation:
To decide whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of the lines. The lines are given by the equations 3x-6y=2 and 18x+9y=8. To find the slope of each line, we must rewrite the equations in slope-intercept form (y=mx+b), where m represents the slope
For the first line, 3x-6y=2, we isolate y:
3x - 6y = 2-6y = -3x + 2y = (1/2)x - 1/3So the slope of the first line is 1/2.
For the second line, 18x+9y=8, we isolate y:
18x + 9y = 89y = -18x + 8y = -2x + 8/9The slope of the second line is -2.
Since the slopes of the two lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
Mr. Anderson drove 168 miles in 3 hours. He then drove the next 2 hours at a rate
of 5 miles an hour faster than the first rate,
How many miles did Mr. Anderson drive during th
hours?
Answer:
If you were asking how many miles in total: 290 miles.
If you were asking how many miles in the 2 hours: 122 miles
Step-by-step explanation:
In the first 168 miles,
[tex]Since \\v_1=168miles/3h=56 miles/h\\\\Thus \\v_2=v_1+5=56+5=61miles/h\\\\X_1=168miles\\X_2=v_2*2h=61*2=122miles\\X_1+X_2=168+122=290miles\\\\[/tex]
A farm is rectangular with an area of 1/2 square
miles. If the length of the farm is 1/3 miles, what
is its width? Input your answer as a fraction.
The width of a rectangular farm with area of 1/2 square mile and length of 1/3 mile is 1 1/2 miles.
Explanation:The area of a rectangle is found by multiplying length times width. In this case, we know that the area is 1/2 square mile and the length is 1/3 mile.
So we have the equation (Length) * (Width)= Area; so 1/3 * W = 1/2. To solve for W (width), you need to divide both sides of the equation by 1/3.You might remember that dividing by a fraction is the same as multiplying by its reciprocal. So, we divide 1/2 by 1/3, which is the same thing as 1/2 * 3/1. Doing this, we end up with the fraction 3/2, or 1 1/2.
So the width of the farm is 1 1/2 miles.
Learn more about Area of Rectangle here:https://brainly.com/question/15218510
#SPJ12
AB contains points (2, 1) and (-1, -8). What is the equation of the line parallel to AB that contains point (0, 2)?
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points that belong to the AB line:
[tex](x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope [tex]m = 3[/tex], then the equation will be of the form:
[tex]y = 3x + b[/tex]
We substitute the given point and find b:
[tex](x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b[/tex]
Finally, the equation is:
[tex]y = 3x + 2[/tex]
Answer:
[tex]y = 3x + 2[/tex]