The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.
Here, we note the following
Let the person walking away from the elevator be X
Let the other person going up in the elevator be Y
Therefore after 15 seconds, their positions will be;
For X, 2 ft/sec × 15 s = 30 ft away from the elevator
For Y, 7 ft/sec × 15 s = 105 ft up in the elevator
At that instant, the distance between them is given as
d² = x² + y²
d=√ 30² +105² = 11925 ft²
d = √11925 ft² = 109.202 ft
The rate of change of the distance between the two people, X and Y is given as
[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]
(or)
[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]
Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec
Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]
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please help!.....Answer the questions about the following polynomial.
Answer:
The expression represents a cubic polynomial with 3 terms. The constant term is -1, the leading term is x^3, and the leading coefficient is 1.
Step-by-step explanation:
true or false: the highest weight edge in a graph will never be in an mst. if true, prove it. if false, show an example in which it is included.
False. Consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices.
The highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices.The definition of a minimum spanning tree states that it is a subset of edges of a graph that connect all of the vertices without forming any cycles, and with the minimum total weight. If a graph contains an edge with the highest weight, it may still be included in the MST if it is the only connection between two vertices. To illustrate this, consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices. In this case, the highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices, and thus the minimum total weight is achieved.
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what does it mean rational function
Answer: [Rational function definition]In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. In other words, it's a function that is the ratio of two polynomials. It is "Rational" because one is divided by the other, like a ratio.
Simplify
4a x 6a'
divide 8a
Answer: 3a
Step-by-step explanation:
(4a*6a)/8a
24a^2/8a
3a
[tex]4a\times6a[/tex]
[tex]4\times6=24\\4a\times6a=24a[/tex]
[tex]\dfrac{24a}{8a}[/tex]
[tex]=\fbox{3a}[/tex]
You wish to purchase a 14 pound bag of mixed nuts. Peanuts are $5.00 per pound and almonds are $6.00 per pound. How many pounds of peanuts should you buy if the entire bag costs $74.
[Please show and explain how you solved this word problem.]
Answer:
10 pounds
Step-by-step explanation:
You want to know the number of pounds of peanuts in a mix of $5/lb peanuts and $6/lb almonds that gives 14 pounds of nuts for $74.
SetupLet p represent the number of pounds of peanuts in the mix. The (14-p) is weight of almonds, and the total cost is ...
5p +6(14 -p) = 74
SolutionSimplifying the equation gives ...
-p +84 = 74
10 = p . . . . . . . . add p-74
You should buy 10 pounds of peanuts to make the 14 lb bag cost $74.
__
Additional comment
You notice that simplifying the equation gives p a negative coefficient. If you choose the variable to represent the more expensive contributor, then the coefficient of that comes out positive. (We like positive coefficients, as they tend to reduce errors.)
Here, the problem is requesting the amount of the lower cost contributor, so we used the variable to represent that.
Often, you are asked to solve mixture problems using a system of equations. Those would use a variable for each of the quantities, and the equations would be ...
p + a = 14 . . . . . . . total weight5p +6a = 74 . . . . . total costYou notice that substituting for 'a' gives the equation we used above.
a = 14 -p . . . . . . . . . . . . . write an expression for 'a'5p +6(14 -p) = 74 . . . . . use the expression for 'a'Jumping directly to this step saves a bit of written work, though the mental work is the same.
1/6+5.4 as a fraction in simpelest form
Answer: 167/30
Step-by-step explanation:
1/6 + 5.4
5.4 = 54/10
So we have 1/6 + 54/10
The common factor is 60
10/60 + 324/60
334/60
167/30
Answer:
1/6 + 5.4 = 167/30 = 5 17/30
Step-by-step explanation:
Conversion of a decimal number to a fraction: 5.4 = 54/
10
= 27/5
a) Write down the decimal 5.4 divided by 1: 5.4 = 5.4/
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
5.4/1
= 54/10
Note: 54/10
is called a decimal fraction.
c) Simplify and reduce the fraction
54/10
= 27 * 2/5 * 2
= 27 * 2/5 * 2 = 27/5
Add: 1/6 + 5.4 = 1/6 + 27/5 = 1 · 5/
6 · 5 + 27 · 6/
5 · 6
= 5/30 + 162/30 = 5 + 162/30
= 167/30
Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios. What is the unit rate of change of flour (y) to respect sugar (x)? That is, how much flour corresponds to one cup of sugar? The unit rate of change is 2.25. How do I graph this?
The unit rate of change of flour (y) with respect to sugar (x) will be 2.25.
What does the unit rate of change means?The unit rate of change means by how much times a specific quantity changes per unit change in other quantity. For a function, y = f(x), the unit rate of change is given by -r = Δy/Δx
[tex]\lim_{x \to \;0} (r) = \lim_{x \to \;0}[/tex] (Δy/Δx) = dy/dx
Given is that Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios as shown in the question.
We can write the rate of change as -
r = Δy/Δx
r = (y₂ - y₁)/(x₂ - x₁)
y₂ = [tex]$6\frac{3}{4}[/tex] = 27/4
y₁ = [tex]$4\frac{1}{2}[/tex] = 9/2
x₂ = 3
x₁ = 2
Using the values -
r = (27/4 - 9/2)/(3 - 2)
r = (27 - 18)/4
r = 9/4
r = 2.25
Therefore, the unit rate of change will be 2.25.
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question 18 the unexplained sum of squares measures variation in the dependent variable y about the a. y-intercept. b. mean of the y values. c. mean of the x values. d. estimated y values.
The unexplained sum of squares measures variation in the dependent variable Y about the estimated Y values. The correct answer is option D.
How do we calculate unexplained variation?The unexplained variation is the sum of the squared of the differences between the y-value of each ordered pair and each corresponding predicted y-value. The sum of the explained and unexplained variations is equal to the total variation.
Unexplained variance is also known as error variation or residual variation. It refers to the random fluctuations around the regression line which show as variation. This type of variation is the sum of squared differences among each ordered pair's y-value and the predicted corresponding y-value.
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What is the measure
of z?
16
z=[?]
Give your answer in simplest form.
Enter
The measure of z on the right triangle shown at the end of the answer is given as follows:
z = square root of 80.
How to obtain the measure of z?To obtain the measure of z, the first step is obtaining the measure of y, which is obtained using the geometric mean property, as follows:
y = square root of (16 x 4) = square root of 64 = 8.
The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.
For the smaller right triangle, we have that:
The two legs have measures of 4 and 8.The hypotenuse has a measure of z.Then the length of the hypotenuse z is obtained applying the Pythagorean Theorem as follows:
z² = 4² + 8²
z² = 16 + 64
z² = 80
z = square root of 80.
Missing InformationThe triangle is given by the image shown at the end of the answer.
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1. Judy took $20 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $4. The price of each drink was half the price of a bag of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
The graph of the linear function is attached below as it passes through the origin
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.
where;
m = slope of the lineb = y-interceptAssuming we let;
x = number of popcorn boughty = 1/2x = number of drinks boughtWe can write a linear function to model the problem given as
4x + 2y = 20
Graphing this linear equation;
Kindly find the attached graph below.
b) The graph of the linear function shows a straight line passing through the origin of the graph which is at a coordinate (0, 0)
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Let the number of popcorns be x and number of drinks be y.
The cost of popcorns is 4x and the cost of drinks is 2y as per question.
The total amount can be spent is $20.
It can be represented as function:
4x + 2y = 20Simplify by dividing both sides by 2:
2x + y = 10The intercepts are:
x = 0 ⇒ y = 10, the point (0, 10)y = 0 ⇒ 2x = 10 ⇒ x = 5, the point (5, 0)Part AThe graph is attached. It contains the line between the x- and y-intercepts
Part BUsing integer values of one variable between the intercepts helps to determine the other variable, that limits the spending amount to $20.
Example:
If Judy buys 2 bags of popcorn, the line will help to find the corresponding y-coordinate, 6 (number of drinks can be bought) by tracing with vertical line from x = 2 until intersection with the graph.Determine if the lines are parallel, perpendicular, neither or coinsiding..
y=-3x+7
y = 3x - 7
A Perpendicular
B neither
C Parallel
D Coinciding
Answer:
neither
Step-by-step explanation:
The slopes are neither equal nor negative reciprocal.
Answer:
B
Step-by-step explanation:
The lines are B. Neither.
To determine whether two lines are parallel, perpendicular, neither, or coinciding, we can look at their slope. The slope of a line is a measure of how steep the line is. It is calculated by taking the difference in the y-coordinates of two points on the line, and dividing it by the difference in the x-coordinates of those points.
In this case, the two lines have the equations y = -3x + 7 and y = 3x - 7. To find their slopes, we can plug in the coordinates of two points on each line, and then calculate the slope using the formula mentioned above.
For the first line, we can use the points (0, 7) and (1, 4) to calculate the slope:
Slope = (4 - 7) / (1 - 0) = -3
For the second line, we can use the points (0, -7) and (1, -4) to calculate the slope:
Slope = (-4 - (-7)) / (1 - 0) = 3
Since the slopes of the two lines are the opposite of each other (i.e. one is positive and the other is negative), the lines are not perpendicular or coinciding to each other. This means that they do intersect at a right angle, and are not parallel or coinciding. Therefore, the correct answer is B, neither.
Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
S:{−5}
S:{3}
S:{12}
S:{42}
The integer that makes the inequality 3(n − 6) < 2(n + 12) false is
S:{42}How to find the integer that makes the inequality falseThe integer that makes the inequality false is solved by substituting the values and solving the inequality
3(n − 6) < 2(n + 12)
for n = -5
substituting the value of n
3(-5 − 6) < 2(-5 + 12)
= -33 < 14
3(n − 6) < 2(n + 12)
for n = 3
substituting the value of n
3(3 − 6) < 2(3 + 12)
= -9 < 30
3(n − 6) < 2(n + 12)
for n = 12
substituting the value of n
3(12 − 6) < 2(12 + 12)
= 18 < 48
3(n − 6) < 2(n + 12)
for n = 42
substituting the value of n
3(42 − 6) < 2(42 + 12)
= 108 < 108 wrong
This is the only wrong solution since 108 = 108
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a variable subtracted from the left-hand side of a greater-than-or-equal to constraint to convert the constraint into an equality is known as a(n)
To change a greater than or equal to type constraint into an equality constraint, a variable is removed from the left side. It also goes by the name "negative slack variable."
Surplus variables, in terms of economics, signify the overfulfillment of the requirement.In order to change a less than or equal to type constraint into an equality, a variable is added to the left side of the constraint.The non-negative variables that are added to the LHS of the constraints in order to transform the inequality () into an equation are known as slack variables. The initial objective function with zero coefficients is expanded using such variables.Similar to slack variables, surplus variables have zero objective function coefficients and a coefficient in only one row. They serve as a measure of how much a constraint's left side is bigger than its right side.To know more about constraint check the below link:
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through:(0,-3), slope=7/2
The equation of the line would be 7x - 2y = 6.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
The required line passes through (0, -3) and the slope is 7/2.
By using the slope-point form of the line, we get
y - (-3) = (7/2)(x-0)
y + 3 = 7/2x
2y + 6 = 7x
7x - 2y = 6
Hence, the equation of the line would be 7x - 2y = 6.
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Question: Find the equation of the line passing through the point (0, -3) having slope 7/2.
Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20}. Find X n Y.
3
21
The values of X ∩ Y are 1, 3, 5, and 7.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, complements of sets.
We have,
X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Y = {-3, -1, 1, 3, 5, 7, 20}
Now,
X ∩ Y
= The values common to both sets.
= {1, 3, 5, 7 }
Thus,
X ∩ Y = {1, 3, 5, 7 }
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Rhianna bought a golf
club online. It cost
$121.25 plus 12% shipping
and handling. What was
the total cost?
The total cost of golf club including shipping and handling is $135.8.
What is cost?
A cost is the value of money that has been expended in the production or delivery of a good or service and is therefore no longer available for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to acquire it.
Given:
Rhianna bought a golf club online. It cost $121.25 plus 12% shipping and handling.
The cost of shipping and handling is,
$121.25 x 12% = $121.25 x 0.12 = $14.55
So, the total cost is,
$121.25 + $14.55 = $135.8
Hence, the total cost of golf club including shipping and handling is $135.8.
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Find the measure of <1
A. 145 degree
B. 36 degree
C. 109 degree
D. 35 degree
Please help!!!
Picture is provided
Answer:
A. 145 degree
Step-by-step explanation:
A triangle has 180 degree
109 + 36 = 145 degree
180 - 145 = 35 degree
35 degrees is the missing angle of the triangle. This angle must add with angle 1 equal to 180 degrees.
180 - 35 = 145 degree
So, the answer is A
Answer:
ANGLE 1 = 145°
Step-by-step explanation:
Angle 1 is right next to the EMPTY interior angle of the triangle and they are on a straight line!
This means, these two angles (angle 1 and the empty angle next to it) are supplementary angles!
Supplementary angles are angles on a straight line and they always add up to 180°
To find it, we need to find the degrees of the empty angle.
To find it, we need to look at the whole triangle.
Remember, all triangles equal 180°
Let's find this empty angle
180° - 109 - 36 = 35°
The empty angle = 35°
BUT WE ARE NOT DONE!
We are looking for angle 1, not the empty angle.
To find angle 1, we must remember that the empty angle (which we found was 35°) and angle 1 make a supplementary angle (which totals up to 180°)
Let's find angle 1, using subtraction.
180° - 35 = 145°
ANGLE 1 = 145°
or One angle of a triangle measures 70°. The other two angles are in a ratio of 3:8. What are the measures of those two angles?
Answer: The answer would be 9.125.
Step-by-step explanation:
I can't really find an explanation for it. Sorry.
The remaining angles are 80 and 30
The sum of angles of a triangle = 180
One angle is given as = 70
The sum of the remaining angles= 110
Now we apply the theory of ratios
The ratio between the angles are given as 3:8
So one angle will be 3 parts of 110 and other eight parts of 110
Total number of parts = 3+8 = 11
Angle 1 = (3*110)/11
= 30
Angle 2 = (8*110)/11
= 80
So the other two angles are 30 and 70.
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Help pls I inserted photo
In the △IGH, the measurement of the angles are m∠G = 114°, m∠H = 49°, and m∠I = 17°.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that,
m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°.
The sum of interior angles of a triangle is 180°.
Therefore,
m∠G + m∠H + m∠I = 180°
Putting m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:
(7x - 5)° + (3x - 2)° + x° = 180°
Combine like terms:
(7x + 3x + x) - (5 + 2) =180
11x - 7 = 180
Add 7 on both sides:
11x = 187
Divide both sides by 11:
x = 187/11
x = 17
Now putting x = 17 in m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:
m∠G = (7×17 - 5)° = 114°
, m∠H = (3×17 - 2)° = 49°
m∠I = 17°
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6x^2+30x+3
solve by quadratic formula
Answer:
Step-by-step explanation:
Suppose y varies directly with x, and y = -10 when x = 2 . What is the value of y when x = 12
A. 12
B. -24
C. -120
D. -60
Answer:
Step-by-step explanation:
y varies directly with x then, y=kx
for x = 2 and y= -10 we get:
-10 = 2k
k= -5
when x = 12
y = -5 * (12) = -60
D
Answer please ASAP!!!!!!!
Which graph represents the solution to the inequality 1.5 is greater than or equal to the product of a number and −0.75?
number line with closed circle on point on 0.5 with arrow shaded right
number line with open circle on point on negative 0.5 with arrow shaded left
number line with closed circle on point on negative 2 with arrow shaded right
number line with open circle on point on 2 with arrow shaded left
The graph that represents the number line is number line with closed circle on point on negative 2 with arrow shaded right
How to find the graph if the number lineInformation from the problem include
graph represents the solution to the inequality 1.5 is greater than or equal to the product of a number and −0.75
The word problem is solved first, let the number be x
1.5 ≥ -0.75x
1.5 / -0.75 ≥ -0.75x / -0.75
dividing both sides by negative 0.75 will make the less than or equal to sign change to greater than or equal to
-2 ≤ x
the solution of the inequality is -2 ≤ x
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suppose y′=f(x,y)=xycos(x)y′=f(x,y)=xycos(x).
The partial derivative of function f(x, y) = xy/cos(x) is ∂/∂y [xy/cos(x)] = x sec(x)
In this question we have been given a function y′ = f(x,y) = xy/cos(x)
We need to find the partial derivative of function f(x, y) with respect to y, ∂f/∂y
Consider the partial derivative of function
∂f/∂y = ∂/∂y [xy/cos(x)]
∂f/∂y = ∂/∂y [xy * 1/cos(x)]
we know that 1/cos(x) = sec(x)
∂f/∂y = ∂/∂y [xy * sec(x)]
∂f/∂y = x sec(x) ∂/∂y (y)
∂f/∂y = x sec(x) * 1
∂f/∂y = x sec(x)
Therefore, ∂/∂y [xy/cos(x)] = x sec(x)
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A retiree invests $6,000 in a savings plan that pays 6% per year. What will the account balance be at the end of the first year?
To find the account balance at the end of the first year, we need to calculate the amount of interest earned. The interest rate is 6%, or 0.06. The initial balance is $6,000, so the interest earned is 0.06*$6,000 = $360.
Adding the interest to the initial balance gives us the account balance at the end of the first year: $6,000 + $360 = $<<6000+360=6360>>6360.
Therefore, the account balance at the end of the first year will be $6360.
Mr. Harold invested $1,600 in an account
that paid him 3.25% simple interest. What
will be the balance of his account after
32 years, including interest?
A) $1,664.00
C) $16,640.00
B) $1,536.00
D) $3,264.00
Answer:
D) $3,264.00
Step-by-step explanation:
I = Prt
I = $1600 × 0.0325 × 32 = $1664
total = $1600 + $1664 = $3264
Put the following equation of a line into slope-intercept form, simplifying all fractions. 9z+ 3y = -9
Answer:
y = -3z - 3
Step-by-step explanation:
y=mz+b ==> slope-intercept form where m=slope
9z + 3y = -9
9z - 9z + 3y = -9z - 9 ==> solve for y
3y = -9z - 9
(3y = -9z - 9)/3 ==> divide equation by 3 to isolate y
y = -3z - 3
Help me asp thank you show your work please
Answer:
I believe the answer is y=3
Step-by-step explanation:
If you were to graph y=0, the line would be horizontal through the origin. Since the lines are parallel, you cannot have the answer being x=-3 or x=3 as they would intersect. Now that we have eliminated two answers, we have to choose between y=-3 and y=3. In the question, it says that the line passes through (-3,3). Because of the (x,y) coordinates, you can see that y does indeed equal 3.
I hope this helps!
Answer:
y = 3
Step-by-step explanation:
y = 0(x)
3 = 0(- 3)
y = 3
Chau reads a book at a rate of 26 chapters per hour how many chapters does he read in 2 hours
Answer: he reads 52 chapters in 2 hours.
Step-by-step explanation:
Since he reads 26 chapters per hour, multiply the number of chapters by the number of hours which is two.
26 * 2 = 52
he reads 52 chapters in 2 hours.
Answer:
52 chapters
Step-by-step explanation:
Because he reads 26 chapters in 1 hour and his rate is constant (never changing), multiply 26 by 2 to find how many chapter for 2 hours.
26 x 2 = 52
Solve for x in the image below. Note: figure not drawn to scale.
C
15
B
X
30.5
A
D
12.2
E
The value of x from the triangle CAE is x = 6
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔCAE
Now , the second triangle is ΔCBD
And , ΔCAE ≅ ΔCBD
So , Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
And ,
CE / CD = CA / CB
Substituting the values in the equation , we get
( 30.5 + 12.2 ) / 30.5 = ( 15 + x ) / 15
On simplifying the equation , we get
42.7 / 30.5 = ( 15 + x ) / 15
Multiply by 15 on both sides of the equation , we get
640.5 / 30.5 = 15 + x
15 + x = 21
Subtracting 15 on both sides of the equation , we get
x = 21 - 15
x = 6
Therefore , the value of x is 6
Hence , The value of x from the triangle CAE is x = 6
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9. Kenneth won a lottery prize of $2,000. He used
$500 to pay off his final car payment, spent $400
for a pair of tickets to a ball game, gave his
nephew a $50 gift card he bought from Target,
and put the rest in his bank account. After
completing his Income Statement, what is the item
that shows what Kenneth has left?
[A] Net Worth: $2,000
[B] Net Worth: $1,050
[C] Net Cash: $2,000
[D] Net Income: $2,050
[E] Net Income: $1,050
Answer:
The item that shows what Kenneth has left is [B] Net Worth: $1,050.
Net worth is a person's assets minus their liabilities. In this case, Kenneth's assets include the $2,000 lottery prize and the money he deposited in his bank account. His liabilities include the car payment he paid off and the gift card he bought for his nephew. Subtracting these liabilities from his assets gives us his net worth of $1,050.
Net cash is the amount of cash a person has available, which would not include any assets such as the money in Kenneth's bank account. Net income is the total amount of income a person has earned, which would not include the lottery prize in this case.