The speed of Makayla and Nathan are 12 mph and 20 mph respectively.
What is relation between speed and time?A moving body's speed is the distance it travels in one unit of time. If the distance is in kilometers and the time is in hours, the speed is in kilometers per hour. If the distance is expressed in meters and the time is measured in seconds, the speed is measured in meters per second.Let the speed of Makayla is 'x' mph.
and the speed of Nathan is 'y' mph.
The total distance travelled by both is 129 miles.
The time taken by each is 6 hours, same for both.
Speed = distance / time
Distance = speed × time
Makayla's covered distance = xt
Nathan's covered distance = yt
Total distance = xt + yt
xt + yt = 192
As, Nathan travels 8 mph faster than makayla.
The,
y = x + 8, t = 6 hours substitute;
xt + (x+ 8)t = 192
2x + 8 = 192/6
On simplification;
x = 12 mph (Makayla's speed)
Y = x + 8
y = 12 + 8
y = 20 mph (Nathan's speed)
Therefore, the speed of Makayla and Nathan are x = 12 mph and y = 20 mph respective;y.
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A square that is 6 m on a side is placed inside a rectangle that has a width of 11 m and a length of 18 m. What is the area of the region inside the rectangle that surrounds the square?
The area of the region inside the rectangle that surrounds the square is; 162 square meters
How to find the area of regular shapes?
We are given that;
Side length of square = 6 m
Width of rectangle = 11 m
Length of rectangle = 18m
Thus;
Area of rectangle = width * length = 11 * 18 = 198 square meters
Area of square = side * side = 6 * 6 = 36 square meters
Area of region inside rectangle not inside square = (area of rectangle) - (area of square) = 198 - 36 = 162 square meters
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please refer to the image
Brief The Question Please, Thank You
is 25 a perfect cube?
Answer: no 25 is a perfect square
Step-by-step explanation:
please help
maths geometry
(you can’t use congruency)
Step-by-step explanation:
ok, let's try this again. we need to explain congruence then in its details as an implicit part of the proof, as everything boils down to that.
due to AE = FC we also know that ED = BF.
because as ABCD is a parallelogram, it means AD = BC (and AB = DC).
and AD || BC, AB || DC.
as AD = AE + ED and BC = BF + FC, it means that
AE + ED = BF + FC
with AE = FC we can then simplify to
ED = BF.
as AD || BC, so is also ED || BF.
since the distance from E to D is the same as for B to F, it means that EB and DF must be equidistant to each other, and that means they are parallel.
and because ED || BF, that also means that both line segments are equidistant from each other, and that means that the connections between their end points (EB and DF) must have the same lengths.
therefore, the shape is a quadrilateral with 2 pairs of parallel and equally long line segments. and that is the definition of a parallelogram.
so, BEDF is a parallelogram.
find 1/3 + 3/43 sums and differences
Answer:
52/129
Step-by-step explanation:
How to solve math problem
Answer: by doing math
Step-by-step explanation:
Multiply.
4.62 x 10^6=???
Answer:
[tex]=4620000x[/tex]
Step-by-step explanation:
[tex]=1000000\cdot \:4.62x[/tex]
[tex]=4620000x[/tex]
Answer:
4620000
Step-by-step explanation:
4.62x10^6
1000000x4.62
Kevin takes 1500 steps to walk d meters from his home to the station. Each step is 90 centimeters correct to the nearest 10cm.
Find the lower and the upper bound for d
Distance of upper bond and lower bond is 120,000 and 150,000 centimeter
How to find Lower bound and Upper Bound?
Given:
Number of steps walk = 1500 steps
Each step count = 90 centimeters
Correction in each step = 10 cm nearest
Find:
Lower bound and upper bound for d
Computation:
Lower bound step length = 90 - 10
Lower bound step length = 80 centimeters
Upper bound step length = 90 + 10
Upper bound step length = 100 centimeters
Lower bound d = 1500 × 80
Lower bound d = 120,000 centimeters
Upper bound d = 1500 × 100
Upper bound d = 150,000 centimeters
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A line passes through ( - 1, - 1) and ( - 3, 5).
What is the equation of the line in slope-intercept form?
Answer:
y= -3x-4.
Step-by-step explanation:
1) the slope-interception form is:
y=slope*x+i, where i - interception;
2) using the given two points it is possible to calculate the slope:
[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]
then the required equation has the form:
y=-3x+i;
3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:
-1=-3*(-1)+i; ⇒ i=-4.
4) finally, the required equation is:
y=-3x-4.
P.S. the suggested way is not the shortest one.
NO LINKS!! Please help me with these problems. Part 9a1
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range: [0, ∞)Continuity: Point discontinuity (hole) at x = 3.Step-by-step explanation:
Given function:
[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]
DomainThe domain is the set of all possible input values (x-values).
Factor the denominator of the function:
[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]
The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.
Therefore, the function is undefined when x = -1 and x = 3.
Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).
RangeThe range is the set of all possible output values (y-values).
As the domain is restricted, the range is also restricted.
Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.
Therefore, there is a point discontinuity at x = 3.
Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.
Therefore, there is an infinite discontinuity at x = -1.
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]
Therefore, there are no stationary points and no minimum/maximum points.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]
[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]
[tex]\implies x+1 < 0 \implies x < -1[/tex]
[tex]\implies x+1 > 0 \implies x > -1[/tex]
Combine the intervals:
(-∞, -1) ∪ (-1, ∞)
Therefore:
The function is decreasing in the interval (-∞, -1) ∪ (-1, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: [0, ∞)
Continuity: Point discontinuity (hole) at x = 3.
Infinite discontinuity (vertical asymptote) at x = -1.
None
Decreasing function: (-∞, -1) ∪ (-1, ∞)
Symmetry: Neither
Cody decreased the speed of his car by 3.5 miles per second over a period of 60 seconds Find the average change in speed each second
Answer:
Step-by-step explanation:
To get your answer, you would want to use the expression -3.5/60. So your answer will be -0.058.
A universitys freshman class has 7600 studends. 73% of those students are najoring in computer science. How many students in freshman clsss are computer science majors?
There are 5548 students majoring in computer science.
This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.
Given that the total number of students in the university class is =7600
Also 73% of students are majoring in computer science.
Number of students majoring in computer science is = (73/100) of 7600
= 73×76
= 5548 students
So, the total number of students majoring in computer science is 5548.
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Greenwood Company manufactures two products—15,000 units of Product Y and 7,000 units of Product Z. The company uses a plantwide overhead rate based on direct labor-hours. It is considering implementing an activity-based costing (ABC) system that allocates all of its manufacturing overhead to four cost pools. The following additional information is available for the company as a whole and for Products Y and Z:
Activity Cost Pool Activity Measure Estimated Overhead Cost Expected Activity
Machining Machine-hours $ 231,000 11,000 MHs
Machine setups Number of setups $ 180,000 300 setups
Production design Number of products $ 94,000 2 products
General factory Direct labor-hours $ 260,000 10,000 DLHs
Activity Measure Product Y Product Z
Machining 9,000 2,000
Number of setups 60 240
Number of products 1 1
Direct labor-hours 9,000 1,000
Product Y would be allocated 20% of the machine setups cost
Product Z would be allocated 80% of the machine setups cost
What is activity-based costing?
Activity-based costing is a costing method where overhead cost of production are allocated based on the cost driver responsible for the overhead rather than using the plantwide overhead rate based on direct labor-hours.
In this case, we need to first of all determine the machine setups cost per per setups, based on the fact there 300 setups for both products Y and Z
machine setup cost per setup=Machine setups cost/Number of setups
Machine setups cost=$180,000
Number of setups=300
machine setup cost per setup=$180,000/300
machine setup cost per setup=$600
Total set up cost for product Y=60*$600=$36000
Total set up cost for product Y as %=$36,000/$180,000=20%
Total set up cost for product Z=240*$600=$144,000
Total set up cost for product Z as %=$144,000/$180,000=80%
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Choose the numbers that are equivalent to two and seven fifteenths.
fourteen fifteenths, 2.46 repeating where the 6 is repeating, 246.6%
fourteen fifteenths, 2.715, 271.5%
thirty-seven fifteenths, 2.46 repeating where the 6 is repeating, 246.6 repeating percent where the 6 is repeating
thirty-seven fifteenths, 2.715, 271.5%
The numbers that are equivalent to two and seven fifteenths are; thirty-seven fifteenths, 2.46 repeating where the 6 is repeating
How to simplify mixed fractions?
We want to find the numbers that are equivalent to two and seven fifteenths. This fraction is a mixed fraction and can be expressed as;
2⁷/₁₅
Converting this to an improper fraction gives us;
37/15
Now, in the first mixed fraction, we can turn the fraction into decimal like this; 2 + 7/15 = 2 + 0.46666 = 2.466666....
Thus, looking at the given options, the only correct option is;
C: thirty-seven fifteenths, 2.46 repeating where the 6 is repeating
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Given the following graphs of f(x) and g(x), find the value of lim x->7 f(g(x)) in simplest form.
The limit of the composite function is given as follows:
lim x->7 f(g(x)) = 2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
From the graph of g(x), we have that the lateral limits at x = 7 are given as follows:
[tex]\lim_{x \rightarrow 7^-} = \lim_{x \rightarrow 7^+} = -2[/tex]
Hence:
lim x->7 f(g(x)) = f(lim x->7 g(x)) = f(-2).
Looking at the graph of f(x), we have that:
f(-2) = 2.
Hence:
lim x->7 f(g(x)) = 2.
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a. Solve x + 8 - x + 8
b. If you simplify an equation and get 00, what can you conclude about the solution(s) of the original equation?
To solve an linear equation we need to use BODMAS rule.
Here the given equation is;
(x+8-x+8)
We know very well that if two like numbers have opposite sign and are added then it gets cancelled and gives zero as the result.
Similarly, here x and -x gets cancelled and we get 16 as the result.
If we get the solution of an equation as zero then we may say that the equation has no real solution. That means there are no values of the unknown which will complete the equation.
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How can you decompose one number to subtract? Why did you
choose that way? 696-275
The minuend and the subtrahend of 696 - 275 can be decomposed to give;
600 + 90 + 6
-
200 + 70 + 5
400 + 20 + 1
The decomposition into place values is chosen because of ease of reinforcing knowledge.
What is the decomposition method of subtraction?The decomposition method of subtraction involves decomposing the subtrahend, which is the smaller number and the place value of the numbers can be simply subtracted from the minuend.
In the subtraction, 696 - 275, the minuend is 696, while the subtrahend is 275.
Decomposing the subtrahend, gives;
275 = 200 + 70 + 5
Decomposing the minuend, gives;
696 = 600 + 90 + 6
The subtraction expression in the question, 696 - 275 gives;
696
-275
The above can therefore be decomposed as follows;
600 + 90 + 6
-
200 + 70 + 5
400 + 20 + 1
400 + 20 + 1 = 421
Therefore;
696 - 275 = 421
The reason the decomposition into place values of each digit is chosen is so as to make use of the easier understanding of subtracting numbers that are multiples of 10.
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Find (-18) + (-25) + 13
Answer: -30
Step-by-step explanation:
Answer:
the answer would be -30!!!
Step-by-step explanation:
i took the quiz.
The distance of the segment formed by the two points
is 15. What is the number that goes in the blank?
Explain or show your reasoning.
(-3,-4) (6, _)
The missing coordinate can either be - 16 or 8.
Let the missing coordinate be x.
Now, we know that the distance between (-3, -4) and (6, x) is 15.
Using the distance formula, we get that:
Distance² = (x₂ - x₁)² + (y₂ - y₁)²
Substituting the values in the formula, we get that:
15² = (6 + 3)² + ( x + 4)²
225 = 9² + x² + 16 + 8 x
225 = 81 +x² + 16 + 8 x
225 = x² + 8 x + 97
x² + 8 x - 128 = 0
x² + 16 x - 8 x -128 = 0
x ( x + 16) - 8 ( x + 16) = 0
(x + 16)(x - 8) = 0
x = -16 or x = 8.
Therefore, the missing coordinate can either be - 16 or 8.
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Solve P = 2L+ 2W for L.
Question content area bottom
L= ?
A line passes through the point point (-6, -5) and has a slope of - 4/3. Write an equation in slope-intercept firm for this line.
The equation in slope-intercept firm for this line is y = -4/3x - 13
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The given parameters are
Slope, m = -4/3
Point (x1, y1) = (-6, -5)
The linear equation is calculated as
y = m(x - x1) + y1
So, we have
y = -4/3(x + 6) - 5
Open the bracket
y = -4/3x - 8 - 5
Evaluate the difference
y = -4/3x - 13
Hence, the equation in slope-intercept firm for this line is y = -4/3x - 13
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what is 6561413+1000000=?
Answer:
7561413
Step-by-step explanation:
6561413+1000000= Equals Calculator Answer/////7561413
Answer:
7561413
Step-by-step explanation:
The calculator it equals 7561413
HELP ME pls. It’s hard im not gonna lie to you all
Answer:
greatest -( 9/36, -21/28, -7 )- smallest
Answer:
9/36
-7
-21/28
Step-by-step explanation:
You actually had them in the correct order
What is the quotient of negative 210 over negative 15?
The quotient of A = - 210 and B = - 15 is 14.
What is Euclid's Division Lemma ?The Euclid's Division Lemma says when a number 'a' is divided by a number 'b' gives the quotient to be 'q' and the remainder to be 'r' then the following relation -> a = bq + r exists, where 0 ≤ r < b.
Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]
Given two numbers A = - 210 and B = - 15
The resultant quotient when A is divided by B can be calculated using Euclid's division lemma. Initially, we will assume remainder [r] = 0.
If the quotient is in decimals, we will change the remainder according to it else if the quotient is a whole number, the remainder will remain 0.
Using Euclid's division lemma -
Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]
- 210 = - 15 x q + 0
- 210 = - 15 x q
q = - 210 / - 15 = 14
Since, the quotient is a whole number, the remainder will remain zero.
Therefore, the quotient of A = - 210 and B = - 15 is 14.
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The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 6 to 1.
M(-13, 20)
N (?, ?)
P(1-1)
If the point N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1, and the coordinates of M(-13, 20) and P(1-1), then the coordinates of "N" is
As per the question statement, N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1.
We are required to find out the coordinates of "N".
To solve this question, we need to know the formula to calculate the coordinates of a point (Say "c") that divides a line segment AB in the ratio of (m:n).
The formula goes as:
Abscissa of c [tex](x_{3})=\frac{mx_{2}-nx_{1} }{m-n}[/tex]
and, Ordinate of c [tex](y_{3})=\frac{my_{2}-ny_{1} }{m-n}[/tex]
where, [tex](x_{1}, y_{1})[/tex] are the coordinates of point A, while
[tex](x_{2}, y_{2})[/tex] are the coordinates of point B.
Using our given data in the above formulae, we get
Abscissa of N = [tex]\frac{(6*1)-[1*(-13)]}{6-1} =\frac{6-(-13)}{5}=\frac{6+13}{5}=\frac{19}{5}[/tex]
And, Ordinate of N = [tex]\frac{[6*(-1)-(1*20)}{6-1} =\frac{(-6)-20}{5}=\frac{-(20+6)}{5}=\frac{-26}{5}[/tex].
Hence, our concerned point N = [tex](\frac{19}{5}, \frac{-26}{5})\\[/tex].
Line Segment: In Euclidean geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints and it's length is given by the Euclidean distance between its endpoints.To learn more about Line Segments, click on the link below.
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Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answer: Sue fills 32/3 (Decimal form = 10.6667 containers)
Step-by-step explanation: 8 divided by 3/4 equals 32/3. If you need it in decimal form it's 10.6667
Please heart this or rate it :)
Answer:
10 2/3 containers BUT can only fully fill 10 containers
Step-by-step explanation:
to solve this equation you need to divide 8 by 3/4
8 / 3/4
that is
8/1 / 3/4
when dividing fractions you must flip the second number and multiply both numbers together
8/1 * 4/3
32/3 is your answer
or
10 2/3
she can fully fill 10 containers
Give the domain and the range for the relation.
{(3,1), (6,4), (9,9)}
Answer:
domain: {3,6,9}
range: {1,4,9}
Step-by-step explanation: take the x values in increasing order for domain and the y values in increasing order for range. Do not repeat values.
Find the perimeter of CDE
Answer:
4 + 4√2
Step-by-step explanation:
[tex]CD=\sqrt{\left( 4-4\right)^{2} +\left( -5 - (-1)\right)^{2} } \\\\\\ =\sqrt{\left( 0\right)^{2} +(-4)^{2} }\\\\\\\ = \sqrt{16 }\\\\\\ =4[/tex]
[tex]DE=\sqrt{\left( 2-4\right)^{2} +\left( -3 - (-5)\right)^{2} } \\\\\\ =\sqrt{\left(-2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}[/tex]
[tex]\text{\bf{EC} $=\sqrt{\left( 4-2\right)^{2} +\left( -1 - (-3)\right)^{2} } \\\\\\ =\sqrt{\left( 2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}$}[/tex]
Perimeter (∆CDE) = CD + DE + EC
= 4 + 2√2 + 2√2
= 4 + 4√2
≈ 9.7
Steven has a rope that is 6ft long. He cuts it into 9 pieces. How many are in each piece
Answer:2/3
Step-by-step explanation:
Financial Goals: Tutorial
Part C
? Question
Diego's cash flow is the difference of his monthly income, $3,000, and his total expenses, $2,715. Which equation
correctly represents Diego's cash flow?
O cash flow = $2,715 - $3,000
O cash flow = $3,000-$2,715
O $3,000 = $2,715 - cash flow
$3,000 = cash flow-$2,715
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Sep 6
7:56
The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.
What is the cash flow?Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.
Cash inflow = income - expense
$3,000 - $2,715
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