Answer: 35
Step-by-step explanation:
The rate of change of a graph is given by :-
[tex]k=\dfrac{\text{Change in y avlues}}{\text{Change in x values}}[/tex]
For points : (1, 35) and (2, 70)
The rate of change for the relationship in the graph is given by :-
[tex]k=\dfrac{70-35}{2-1}=35[/tex]
Hence, the rate of change for the relationship represented in the graph = 35.
The rate of change of the relationship shown in the graph is 35 miles per hour.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the elevator height after x seconds.
From the graph using points (0, 0) and (4, 140):
m = (140 - 0)/(4 - 0) = 35
The rate of change of the relationship shown in the graph is 35 miles per hour.
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Simplify 5(6x - (6 - 7y + 7x) + 6y)
-80x + 87y - 91
-5x + 65y - 30
-82x + 73y - 54
-60x + 9y - 17
None of the above
Can someone help me with this one real quick ? Thanks a lot! Please explain and show your work :)
Given the point (5, 6) and the slope of 5, find y when x = 21.
(04.02 LC)
The graph represents function 1 and the equation represents function 2:
Function 2
y = 3x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?
1
2
3
4
The rate of change of function 2 is 3 times greater than the rate of change of function 1.
Explanation:The rate of change of a function measures how much the output of the function changes when the input changes by 1 unit. In function 1, since the graph is a straight line, the rate of change is constant. We can find the rate of change of function 1 by finding the slope of the line, which represents the rate of change. In function 2, the equation is y = 3x + 1, so the rate of change is 3. Therefore, the rate of change of function 2 is 3 times greater than the rate of change of function 1.
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The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35
Evaluate the limit lim h → 0 (−5 + h)2 − 25 h
Write an equation for each translation of y=lxl
7 units up
you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years
An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.
A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units
Answer:
21 sq. units
Step-by-step explanation:
Find the product of 543.1187 and 100
Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}
Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.
A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.
The relations given by the following sets of ordered pairs is a function is,
d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
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Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm
Answer:
105.19 cm²
Step-by-step explanation:
The applicable area formula is ...
area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²
One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered pair?
To find the value of a in the ordered pair (a,b), we can solve the given equations. Substituting ab^4 with 12 in the second equation, we get a^5 (12)^5 = 7776. Solving for a gives a = 0.03125^(1/5) = 0.5.
Explanation:To find the value of a in the ordered pair (a,b), we can solve the given equations.
From the first equation, ab^4 = 12, we can substitute ab^4 with 12 in the second equation:
a^5 b^5 = 7776
This gives us:
a^5 (12)^5 = 7776
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832
Dividing both sides of the equation by (12^5) gives:
a^5 = 7776 / (12^5) = 7776 / 248,832 = 0.03125
Taking the fifth root of both sides gives:
a = 0.03125^(1/5) = 0.5
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The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.
area of a circle = pi x r^2
using 3.14 for pi
radius = 36/2 =18
area = 3.14 x 18^2 = 1017.36 square inches
1 sq ft = 144"
1017.36/144 = 7.065 sq ft
7.065*3.50 = $24.73 to the nearest dollar = $25
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A= Pe^rt, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
Answer:
Rate of interest = 6%
Step-by-step explanation:
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.
Use the formula,
[tex]A=Pe^{rt}[/tex]
[tex]P\rightarrow \$2000[/tex]
[tex]r\rightarrow ?[/tex]
[tex]A\rightarrow \$2543[/tex]
[tex]t\rightarrow 4\text{ years}[/tex]
Substitute the value into formula and solve r
[tex]2543=2000e^{4r}[/tex]
[tex]e^{4r}=1.2715[/tex]
Apply ln both sides
[tex]4r\ln(e)=\ln(1.2715)[/tex]
[tex]r=0.06[/tex]
Rate of interest = 6%
Hence, The rate of interest is 6%
if two triangles share a common side what else must be true for the SAS triangle congruence theorem to apply
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.
Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.
To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:
The two triangles share a common side.
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).
Thus,
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
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A stick 42 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two pieces ?
The answer is 14 inches and 28 inches:
Total length of stick = 42 inches.
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
What is the slope of the line on the graph below?
A. -1/2
B. 1/2
C. 1
D. 2
Answer:
d on edge
Step-by-step explanation:
What can you say about the function that generated the following table of values
best answer is b = it has exactly 1 x intercept
Answer:
B.
Step-by-step explanation:
We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.
As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.
Therefore, this function will have only one x-intercept.
Hence, option A, C, D are discarded and option B is correct.
Which is the best approximation for the value of √102?
A.10
B.11
C.50
D.51
Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).
a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19
Please select the best answer from the choices provided
A
B
C
D
Answer:
B
Step-by-step explanation:
Edge 2021
What is the value of
x/3y, when x = 18 and y = 3?
this has been asked at least 3 times so far today
18/3*3 = 18/9 = 2
answer is 2
HELPPPPPP make sure your right !:)
a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?
what is the vaule of 3.85+0.004+0.117 ?
what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7
Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.
Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.
It is given in the question that
[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]
And we have to find the value of
[tex]\frac{f(x)}{g(x)}[/tex]
Substituting the values of two functions, we will get
[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]
8x^3 is common in the numerator, and on taking it out, we will get
[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]
And that's the required answer .
-x+3+5(2x-6)+9(3x+11) will you answer with work shown and answer
How can x2 = x2 + 2x + 9 be set up as a system of equations?
Final answer:
To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.
Explanation:
To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:
Equation 1: x2 = x2 + 2x + 9
Equation 2: 0 = 2x + 9
By rearranging Equation 2, we can rewrite it as:
x = -4.5
Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.