D = M/12 + N/4 represents the relationship between Elena's distance in miles, D, and her biking speed.
Speed = distance/ time
Here, we are given that Elena bikes 20 minutes each day for exercise. She bikes at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes.
Therefore, distance covered by her in the first 5 minutes = speed x time
time = 5 minutes = 5/60 hours
= 1/12 hours
Thus, distance = M(1/12)
= M/12
Now, similarly, distance covered by her in the last 15 minutes = N(15/60)
=N/4
Thus, the total distance in miles, D, covered by her in the last 15 minutes = N(15/60)
= N/4
Thus, the total distance in miles, D, covered by her is D = M/12 + N/4
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Find measure.
m ∠ 6
The Measurement of ∠6 i.e. m∠6 is 120°
What is measurement of an angle ?The measurement of angle if the degree of that angle or we can also say that the angles are always measured in degrees. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360.
In the question
as ∠7 is an alternate angle to 60 degree,
thus ∠7 = 60°
According to sum of angle property :
∠7 + ∠6 = 180
60 + ∠6 = 180
∠6 = 180-60 = 120
Thus m∠6 = 120°
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The complete question is :
Find measure m∠6
2. Ms.Walker arrange her students into groups for the next school debate. When she groups them in 5s, 2 students are left out. When she groups them in 4s, 1 student is left out. When she groups them in 7s, 4 students are left out. What is the least number of students Ms.Walker has?
Answer:
8
Step-by-step explanation
we must find the total of the students to do that we look at when she grouped them in 7, 4 are left out so we multiple 4 miltiplied by 7 and we get 28, there are 4 left out so we add them. now we have a total of 32 students. 32 divided by 4 is 8
5/18 + 7/18
9/17+ 2 8/17
3 9/10 + 1 3/10
11/16 + 3/16
5 13/16 + 6 1/16
7/19 + 14/19
7/25 + 16/25
13/15 + 8/15
9/11 + 5/11
12 11/25
11 9/25
1.) 0.66666666666
2.) 3
3.) 5.2
4.) 0.875
5.) 11.875
6.) 1.10526315789
7.) 0.92
8.) 1.4
9.) 1.27272727273
10.) 12.44
11.) 11.36
Here ya go!
The approximate weights of two animals are 5.36 x 104 lbs. and 6.2 x 104 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits. 12 x 104 lbs. 5.9 x 104 lbs. 1.22 x 105 lbs. 1.2 x 105 lbs.
The total weight of the two animals is 5.9×10⁴ lbs.
In order to solve the question easily, firstly lets write the weight of each animal in standard form.
Weight of first animal = 5.36×10⁴
Weight of first animal = 53,600
Weight of first animal = 6.2×10⁴
Weight of first animal = 62,000
Now, the total weight of animals will be calculated by summing the two values.
Total weight = 53,600 + 62,000
Performing addition of total weight of animals
Total weight = 1,15,600 lbs
Writing the total weight in scientific notation -
Total weight = 1.15×10⁵ lbs
On rounding off, we get -
Total weight = 1.2×10⁵ lbs
Hence, the total weight of the two animals is 1.2×10⁵ lbs.
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-0.4-x=
−0.4−x=
\,\,-6(x-3.1)+6x
−6(x−3.1)+6x
Answer:
Step-by-step explanation:
I think you meant
-0.4 - x = -6(x - 3.1) + 6x
-0.4 - x = -6x + 6x + 18.6
-0.4 - x = 18.6
-x = 18.6 + 0.4
-x/-1 = 19/-1
x = -19
check
-0.4 - (-19) = -6(-19 - 3.1) + 6(-19)
18.6 = -6(-22.1) + (-114)
18.6 = 132.6 - 114
18.6 = 18.6
I need help with 1 and 2
The cost to rent a car is $19.50 plus $0.25 per mile. If you have $44
to rent a car, what is the greatest number of miles that you can
drive?
Can someone please help me out? I don’t really understand the problem.
Answer:
-3x+y=14
Step-by-step explanation:
add the x and -4x which gives you -3x
add the -y and 2y which is y
then -14 and 28 add up to 14
help plepqsqasseee im exhausted ONLY A,B AND C
Step-by-step explanation:
A) x(2x-4)
=2x^2-4x
B) 2y^2(3x+4y)
=6xy^2+8y^3
C) (x-3)(x+8)
=x^2+8x-24
Mark grew 9 flowers with 3 seed packets. With 5 seed packets, how many total flowers can Mark have in his garden? Assume the relationship is directly proportional.
Answer:
15
Step-by-step explanation:
9 seeds in 3 packets is a 3:1 ratio which means that there are 3 seeds per packet. With 5 packets you simply multiply 5 by 3
I need this answered please
What is the solution of the system of equations? r - 2x + 8y = -8 5x - 8y = 20
The solution of the given system of equations is (4,0)
We can use 3 methods to solve a system of equations:
- graphical method
- elimination method
- substitution method.
The given system of equation is:
-2x + 8y = -8 ....... (1)
5x - 8y = 20 ........(2)
Notice that in the both equations the coefficients of y are -8 and 8, hence if we add those coefficients, they will be cancelled out.
Therefore, we will choose elimination method.
Add equation (1) and equation (2)
-2x + 8y = -8
5x - 8y = 20 +
3x = 12
x = 12/3 = 4
Substitute x = 4 into equation (1):
-2x + 8y = -8
-2.(4) + 8y = -8
-8 + 8y = -8
Add 8 to both sides:
-8 + 8y +8 = -8 + 8
8y = 0
y = 0
Thus, the solution is (4,0)
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...............................................
Answer:
3
Step-by-step explanation:
1.5/1*2
40 times 40 equals what
Answer:
1600
Step-by-step explanation:
1600
Answer:
1600
Step-by-step explanation:
Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 2+7+12+ . . . . . . ; n=8
The given series is an arithmetic series. The sum of its first 8 terms is 156.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where d is the common ratio.
The given series is:
2+7+12+ . . . .
and the number of terms is 8.
In the given series:
a(1) = 2
a(2) = 7
a(3) = 12
Notice that the difference is constant,
d = a(3) - a(2) = a(2) - a(1)
= 7 - 2 = 5
Sum formula for the first n term of an arithmetic series is:
S(n) = n/2 . [2a(1) + (n - 1) . d]
Substitute n = 8, a(1) = 2, and d = 5
S(8) = 8/2 ( 2.(2) + (8 -1) .5)
S(8) = 4. 39 = 156
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I need this answered please
Bert is 11 kilometers away from brenda. both begin to walk toward each other at the same time. bert walks at 3 kilometers per hour. they meet in 2 hours. how fast is brenda walking?
2.5x4=10(Bert's walking distance)
22-10=12(Brenda's walking distance)
12/4=3
3km/h is Brenda's walking distance.
What is a Kilometer?The International System of Units (SI) defines the kilometer, sometimes known as the kilometer in American English, as one thousand meters (kilo- being the SI prefix for 1000). The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.
1 mile is equivalent to 1.609 kilometers. Both the mile and the kilometer are units of measurement. A mile is longer than a kilometer, nevertheless. A larger unit is a "mile."
1000 meters make up one kilometer. We use kilometers to calculate distance when traveling between two points.
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2 3 4 5 6 7 DOD
9
Look at the graph of the linear function.
-5-4-3-2-1
A
8
5
4
3
2
4
3
4
5
V
C
1
D
5
X
8
10
The rate of change between point A and point B is 2. What is the rate of change between point C and
-2
1
C
Answer:
show a picture
Step-by-step explanation:
Find the measure of the missing angles.
b
80°
Answer:
b=100 c=80
Step-by-step explanation:
How many groups of 1/9 are there In 2
Answer:
18
Step-by-step explanation:
Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet?
The elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet.
Here, we are given two elevation levels from the surface of the ocean.
One elevation is of -10 feet and another one is of -8 feet.
An elevation of -10 feet implies that the distance from the surface level is 10 feet.
On the other hand an elevation of of -8 feet implies that the distance from surface level is 8 feet.
Thus, by comparing the distances, we can see that elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet. To be more precise, it is 2(10-2) feet farther than an elevation of -8 feet.
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3. Plot 2 ordered pairs on the initial climb (first part of the rollercoaster going up) and determine the slope.
Points: Work to find Slope: Slope: ________
4. What is the equation of the line in slope-intercept form that represents your initial climb (first part of the rollercoaster going up)?
Equation: ___________
5. What is the domain and range of your entire roller coaster? (HINT: use compound inequalities)
Domain: Range:
6. a) Plot 2 ordered pairs at the top and the bottom of each hill (not the loop).
Hill 1 points: _________ Hill 2 points: _________
b) Find the rate of change going down each hill.
Work for Hill 1: Work for Hill 2:
Rate of change down Hill 1: _______ Rate of change down Hill 2: _______
c) Which hill is steeper? How do you know that hill is steeper?
Hill 1 or Hill 2 (circle/underline/pick one)
Explanation:
7. Is the roller coaster a function? Why or why not?
Function: YES or NO (circle/underline/pick one)
Explanation:
Using function concepts, it is found that:
3. Two ordered pairs are: (0, 0) and (130,260). The slope is of 2.
4. The equation of the line is of y = 2x.
5. The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
6. a)
For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).6. b) The rate of change down Hill 1 is of -5, while it is of -2 for Hill 2.
6. c) Due to the higher rate of change, Hill 1 is steeper.
7) The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
What are the two ordered pairs on the initial climb, what is the slope, and what is the equation of the line?Two ordered pairs are: (0, 0) and (130,260).
The slope is given by change in y divided by change in x, hence:
m = (260 - 0)/(130 - 0) = 2.
Considering the slope and the intercept(which is of 0, as when x = 0, y = 0), we have that:
The equation of the line is of y = 2x.
What are the domain and the range of the graph?The domain of a function is the set that contains all possible values of the input. In the graph, it is all the values assumed by the horizontal axis.The range of a function is the set that contains all possible values of the output. In the graph, it is all the values assumed by the vertical axis.Hence:
The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
Bottom and top of the hills:For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).The rates of change(change in height divided by change in length) are given as follows:
Hill 1: (-200)/40 = -5.Hill 2: -80/40 = -2.Due to the higher rate of change, Hill 1 is steeper.
Is the graph a function?A graph is a function if it has no vertically aligned points, that is, each value of the input is mapped to only one value of the output.
Hence:
The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
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Split 84 into two parts so that one part is five times the other part
a. The 9 th and 11 th terms of an arithmetic sequence are 132 and 98 . What is the 10th term?
The 10th term of an arithmetic sequence is found to be a₁₀ = 115.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a constant quantity (AP). Arithmetic Sequence is another name for it.
We'd come across a few specific terms in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be viewed in analysed in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the given question;
Let the 9th term be 'a₉' = 132.
The 11th term be 'a₁₁' = 98.
The 10th term be 'a₁₀'.
The AP must have contain equal common difference. So,
d = a₁₀ - a₉
d = a₁₀ - 132
And, also
d = a₁₁ - a₁₀
d = 98 - a₁₀
Since, a₁₀ - a₉ = a₁₁ - a₁₀ for forming an AP.
Equate the common difference.
a₁₀ - 132 = 98 - a₁₀
Bring the variable part on single side.
2a₁₀ = 98 + 132
2a₁₀ = 230
a₁₀ = 115.
Therefore, the value of the 10 th term is estimated as a₁₀ = 115.
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Need help with this please
The range of the function is represented by y ∈ [- 0.5, 3].
How to find the range of a function
Functions are relations between an input set named domain and an output set named range such that each element of the domain is related only to one element of the range. Graphically speaking, the range of the function is represented by the vertical axis of the Cartesian plane.
The picture shows that the range of the function is between - 0.5 and 3. Then, the range of the function is represented by y ∈ [- 0.5, 3].
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Translate the sentence into an equation.
Five less than the product of 3 and a number 6 equals .
Use the variable b for the unknown number.
Answer: b = 11/3 (or) 3.67
Step-by-step explanation:
Five less than the product of 3 and a number 6 equals .
five less = - 5
product of 3 and a number = (multiply) 3 x b
equals 6 = = 6
3b - 5 = 6
3b = 6 + 5
3b = 11
b = 11/3
b = 3.67 ( rounded )
HELP ASAP!!! WILL MARK BRAINLIEST!!!
Find the equation of the line that is perpendicular to y=2x+8 and passes through the point (8, -8).
A. y = 2x + 12
B. y = 1/2x - 4
C. y = -1/2x - 4
D. y = -2x + 12
Answer:
c. y = -1/2x - 4
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
y = 2x + 8 ← is in slope- intercept form
with slope m = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (8, - 8 ) into the partial equation
- 8 = - 4 + c ⇒ c = - 8 + 4 = - 4
y = - [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line
There are 66 markers
in the box. 20 markers
don't have tops. How
many more markers
don't have tops?
marketing
There are 20 markers with no tops and 46 markers with tops in the box.
What precisely are mathematical operations?A function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value is known as an operation.The complexity of the operation is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A constant is an operation with arity zero, also known as a nullary operation.An arity 3 operation, also known as a ternary operation, is the mixed product.So, there are 66 markers in the box.
20 markers don't have tops.Markers with tops:
66 - 20 = 46Therefore, there are 20 markers with no tops and 46 markers with tops in the box.
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The correct question is given below;
There are 66 markers in the box. 20 markersdon't have tops. How many more markers have tops?
17xy +4-3x
Term(s):
Coefficient(s):
Variable(s):
Constant(s):
Answer:
Terms: 17xy, 4, 3x
Coefficients: 17, 3
Variables: x, y
Constants 4, 3
Simplify the following expression completely :
Answer: x^29
Step-by-step explanation:
x^11 * x^18=
x^(11+18)=x^29
Answer:
= x²⁹
Step-by-step explanation:
x¹¹ · x¹⁸
= x¹¹ ⁺ ¹⁸
= x²⁹
