18. Corky writes four equations to show each of the properties of equality. Which of Corky's equations is incorrect? Explain.
Answers
The last division operation of Corky is incorrect.
What is properties of equality?
The attributes of the equality connection, reflexivity, symmetry, transitivity, and the attributes of operations are employed to solve equations. These characteristics hold true in mathematical and algebraic expressions just as they do in propositional language.
Consider, each operation of Corky.
Addition:
3 + 4 = a, then
(3 + 4) + 2 = a + 2
This is the correct equality.
Subtraction:
3 + 4 = a, then
(3 + 4) - 2 = a - 2
This is the correct equality.
Multiplication:
3 + 4 = a, then
4(3 + 4) = 4a
This is the correct equality.
Division:
3 + 4 = a, then
(3 + 4)/2 = a/2
But in the properties 2/a is given.
Therefore, the division property of equality is incorrect.
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Related Questions
Select all the solutions to the inequality 2(7x + 1) < -26
_
A. -2
B. 9
C. -7
D. 4
Answers
Answer:X<-2
Step-by-step explanation:
7x+1<-13
7x<-13-1
7x<-14
Answer:
Step-by-step explanation:
the answer is A: x<-2
Find the slope of the line that passes through the following points: (−4, 3) and (5, 4).
Answers
Answer:
The slope would be 1/9.
Step-by-step explanation:
From 3 to 4 it would be 1. From -4 to 5 it would be 9, the equation for slope is y/x so it would be 1/9.
solution
slope M =(Y' - Y)/(x' - x)
Indicated by (-4, 3) and (5 , 4)
x = -4 , x' = 5 , y = 3 , y' = 4
M = (4 - 3)/( 5 + 4)
M = 1/9 Ans
Determine which set of side measurements could be used to form a right triangle.
6, 12, 60
4, 5, 7
square root of 27 comma square root of 35 comma 62
square root of 12 comma 3 comma square root of 21
Answers
Answer:
square root of 12, 3, square root of 21
Step-by-step explanation:
a
3.5 in
b
3 in
c (hypotenuse)
4.60977 in
Area
5.25
in²
The set of side measurements √12, 3, and √21 could be used to form a right triangle. which is the correct answer would be option (D).
What is Pythagoras's theorem?Pythagoras's theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
We have to apply Pythagoras's theorem in all the given options to find the right triangle.
As per option (A),
6, 12, 60
6² + 12² = 60²
36 + 144 = 3600
180 = 3600
This equation is not true.
As per option (B),
4, 5, 7
4² + 5² = 7²
16 + 25 = 49
41 = 49
This equation is not true.
As per option (C),
√27, √35, 62
(√27)² + (√35)² = 62²
27 + 35 = 3844
This equation is not true.
As per option (D),
√12, 3, √21
(√12)² + (3)² = (√21)²
12 + 9 = 21
21 = 21
The above equation is true and satisfies Pythagoras's theorem which means these measurements could be used to form a right triangle.
Hence, the correct answer would be an option (D).
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Find the maximum value of the function =z+8x3y subject to the following constraints.
≤+xy15≤+2xy18≥x0≥y0
Note that the ALEKS graphing calculator can be used to make computations easier.
Answers
The maximum value of the function z is 120
How to determine the maximum value of the function?The objective function is given as
z = 8x + 3y
While the constraints are given as
x + y ≤ 15
2x + y ≤ 18
x ≥ 0 and y ≥ 0
To determine the feasible region, we simply plot the graphs of x + y ≤ 15 and 2x + y ≤ 18
And we subset the graph to where x ≥ 0 and y ≥ 0
From the graph, we have the feasible coordinates to be
(x, y) = (0, 18), (3, 12) and (15, 0)
Substitute (x, y) = (0, 18), (3, 12) and (15, 0) in z = 8x + 3y
z = 8(0) + 3(18) = 54
z = 8(3) + 3(12) = 60
z = 8(15) + 3(0) = 120
Hence, the maximum value is 120
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A first number plus twice a second number is 10. Twice the first number plus the second totals 26. Find the numbers.
The smaller of the two numbers is what?
Answers
Step-by-step explanation:
let the first number be x &
the second number be y
x+2y=10×2
2x+y=26×1
2x+4y=20
2x+y=26
subtract
3y=6
divide both sides by 3
3y/3 = 6/3
y=2
put y=2 in x+2y=10
x+2(2)=10
x+4=10
x=10-4
x=6
the smallest number is 2
Find the matrix A of the linear transformation T from R2 to R2 that rotates any vector through an angle of 60∘ in the clockwise direction.
Answers
Any vector can be rotated via a 60 degree angle in the clockwise direction using the linear transformation from R2 to R2, and the corresponding matrix is
[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
What does a matrix for an angle alpha that is counter-clockwise mean?
An angle's matrix for counter clockwise rotation is
[tex]\left[\begin{array}{ccc}cos (alpha) &-sin (alpha) \\-sin (alpha)&cos (alpha)\end{array}\right][/tex]
Alpha angle matrix for a clockwise direction
Put alpha = -alpha in the matrix shown above.
The matrix above becomes
[tex]\left[\begin{array}{ccc}cos (alpha) &sin (alpha) \\sin (alpha)&cos (alpha)\end{array}\right][/tex]
if alpha = 60 degrees
The matrix above becomes
[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
Consequently, the matrix for the linear transformation from R2 to R2 that rotates any vector by 60∘ degrees in the clockwise direction.
is .[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]
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Mr. Harmon graded a Pre-Algebra test that he gave to his eighth-grade students. The results were 27 As, 54 Bs, 15 Cs, 3 Ds, and 1 F. What is the ratio of As to Ds in this class?
Answers
Work out the circumference of this circle.
Take pie T to be 3.142 and give your answer to 1 decimal place.
4 cm
Answers
Answer:
25.1 cm
Step-by-step explanation:
4 * 2 * 3.142 = 25.136 = 25.1 cm
The longest runway at an airport has the shape of a rectangle and an area of 2,304,700 square feet. This runway is 190 feet wide. How long is the runway?
Answers
The runway is 12,130 feet long.
To find are you have to times the two sides, in this case it's 190 X 12,130. To find the length of one of these sides you must divide the area by one known side, in this case 2,304,700/190, which means the answer is 12,130 feet
A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
Answers
The time taken for the rocket to reach its maximum height as determined from the given information is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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Can someone help me I have to verify the trig identities.
Answers
We have proved the given trigonometric equations by using trigonometric identities.
What are the trigonometric identities?
Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the most important trigonometric identities. We'll need to apply the sine and cosine rules to non-right-angled triangles.
For the first equation:
The given equation is
[tex]sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx=sec^2(x)[/tex]
Now simplifying the given equation, we can write
[tex]LHA= sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx\\\\LHS=sec^2(x)-sec(x)cos(x)+\frac{sin(x)}{sin(x)}+\frac{cos(x)}{sin(x)}-cot(x)\\\\LHS=sec^2(x)-1+1+cot(x)-cot(x)\\\\LHS=sec^2(x)[/tex]
LHS = RHS.
Hence proved.
For the second equation:
cos(π - Θ) + sin(π/2 + Θ) = 0
LHS = cos(π - Θ) + sin(π/2 + Θ)
= -cosΘ + cosΘ
= 0
LHS = RHS
Hence, we have proved the given trigonometric equations by using trigonometric identities.
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Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occur:
F(x)= - 3x² + 18x + 3
Select the correct choice below and fill in the answer boxes to complete your choice.
(Simplify your answers.)
The function has a maximum value of ___ at x=____.
The function has a minimum value of ____ at x=____.
Answers
The quadratic function has a maximum value of 0 at x = 3
Maximum and Minimum Value of Quadratic FunctionHere, the maximum value f(x) at x = 1 is called the absolute maximum value, global maximum or greatest value of the function f on the closed interval [0, 1]. Similarly, the minimum value of f(x) at x = 0 is called the absolute minimum value, global minimum or least value of the function f on the closed interval [0, 1].
In the function given f(x) = -3x² + 18x + 3
dy/dx = -6x + 18
For stationary values
0 = -6x + 18
6x = 18
x = 3
d²y/dx² = -6
for maximum or minimum value
d²y/dx² = -6x + 18
-6(3) + 18 = 0
The function has a maximum value of 0 at x = 3
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Please help me this is a chaos, im giving 20 points!!
Answers
The constant of proportionality that relates the quantities x and y is 2.25.
An equation that relates the quantities is, y = 2.25x.
What is constant of proportionality?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
1) From the given table,
4.5 / 2 = 2.25
11.25 / 5 = 2.25
15.75 / 7 = 2.25
2) The constant of proportionality that relates the quantities x and y is,
y / x = 2.25
3) An equation that relates the quantities is,
y = kx,
where, k is constant of proportionality.
Here, k = 2.25
Therefore,
y = 2.25x
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Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not.
1) Is this an experiment? If not, what kind of study is it?
2) Is it correct to conclude that shorter men are at higher risk of dying from a heart attack? Explain.
A. Yes, since the result is considered to be statistically significant.
B. No, since there may be confounding variables interfering with the treatment, such as patient age or weight.
C. No, since it cannot be determined which of the subjects will die from heart attacks in the future.
D. No, since there may be lurking variables, such as patient age or weight.
Answers
1. It is an experiment and the kind of study is the case - control study.
2. We can't conclude that shorter men are at higher risk of dying from a heart attack ad D. No, since there may be lurking variables, such as patient age or weight.
What is a case - control study?It should be noted that a case control study is an observational study where there are two groups that are compared based on certain attribute.
It should also be noted that it's an experiment as a research was made to get some needed information about heart attack.
Lastly, we can't conclude that shorter men are at higher risk of dying from a heart attack as some other variables are missing from the information provided.
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Which triangle congruence postulate or theorem proves that these triangles
are congruent?
Answers
The Angle-Side-Angle Postulate (ASA) asserts that two triangles are congruent if their two angles and included sides are congruent with each other.
What is Angle-Side-Angle Postulate ?According to the definition of an angle side angle, two triangles are congruent to one another if two angles from one triangle and the side between them are, respectively, equal to two angles from another triangle and the side between them. If two triangles are congruent, thenOne triangle's three sides will be equivalent to its three sides, respectively.The three angles of one triangle will be equivalent to the three angles of the other, respectively.But we don't always need to know information about all the sides and angles of a triangle to be sure that two triangles are congruent. Let's use an example to illustrate ASA.Let's use an example to illustrate ASA. Take into account the triangles ABC and DEF:We are given that,
BC = EF
∠B = ∠E
∠C = ∠F
We say that by ASA criterion: Δ ABC ≅ ΔDEF.
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Explain the five properties of multiplication.
Answers
What would the domain and range be for a problem like this. I can’t seem to recall how to determine them
Answers
The domain and range are [−4, 1] & [−4, 5].
What are the domain and range of a graph?
Graphs can also be used to determine the domain and range of functions. Because the domain refers to the set of possible input values, the domain of a graph includes all of the input values shown on the x-axis. The range is the set of possible output values shown on the y-axis.
We have given the graph,
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.
The range is the set of possible output values, which are shown on the y-axis.
We can observe that the graph extends horizontally from −4 to the right 1. so the domain of function h is [−4, 1].
The vertical extent of the graph is 0 to –4, so the range of function h is [−4, 5].
Therefore, the domain and range are [−4, 1] & [−4, 5].
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Consider the following scenario: P(E) = 0.4, P(F) = 0.5
a. Find P(E or F) if E and F are disjoint
b. Find P(E or F) if E and F are independent
Answers
Part (a)
The term "disjoint" is the same as "mutually exclusive".
If events E and F are disjoint, then we know that P(E and F) = 0. In other words, the two events have nothing in common. Therefore, it's impossible for them both to occur simultaneously.
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = 0.4 + 0.5 - 0
P(E or F) = 0.9
Answer: 0.9====================================================
Part (b)
If events E and F are independent, then P(E and F) = P(E)*P(F).
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = P(E) + P(F) - P(E)*P(F)
P(E or F) = 0.4 + 0.5 - 0.4*0.5
P(E or F) = 0.4 + 0.5 - 0.2
P(E or F) = 0.9 - 0.2
P(E or F) = 0.7
Answer: 0.7Which sequence of transformations can be used to show that triangle J is congruent to triangle P?
Answers
Answer:
it's answer D
Step-by-step explanation:
because it is the angle postulate theorem
Answer:
it's answer D
Step-by-step explanation:
Find the volume of a right circular cone-shaped building with a radius of 3cm and a height of 14 cm.
Answers
The volume of the right circular cone is, 131.95 cubic centimeter.
What is cone?
A cone is a smooth-tapering three-dimensional geometric object with a flat base and an apex or vertex. The base of a cone is made up of all the points on a plane other than the apex, and the apex is connected to all the other points on the base by a series of line segments, half-lines, or lines.
Here, the radius, r = 3 cm, and height h = 14 cm.
We have to find the volume of right circular cone.
Since,
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]V = \pi (3)^3(\frac{14}{3})\\ V = \pi (3)(14)\\V = 42\pi \\V = 131.95 cm^3[/tex]
Hence, the volume of the right circular cone is, 131.95 cubic centimeter.
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If f is a linear function for which f(4) = −13 and f(−4) = 19, find f(5). f(5) =
Answers
The value of the function f(5) is - 17.
How to solve linear function?A linear function is a function that represents a straight line on the coordinate plane.
A linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, for the linear function, f(4) = −13 and f(−4) = 19.
f(5) can be found as follows;
-13 = 4m + b
19 = -4m + b
2b = 6
b = 6 /2
b = 3
-13 - 3 = 4m
-16 = 4m
m = -4
Hence,
f(5) = -4(5) + 3
f(5) = -20 + 3
f(5) = - 17
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6. ΔABC ≅ ΔYWZ
x=___ AC= ____ T=____ WZ= ___ WY=____
AB=____ m
7. ΔABC ≅ Δ ZYW
X=___ YZ=____ T=____ WZ=___ WY=___
Answers
6) The missing angles and lengths are; x = 14, T = 14, AB = WY = 60
7) The missing angles and lengths are; X = 7, ∠A = ∠Z =31°, T = 9, YZ = AB = 28
How to interpret congruent triangles?6) We are told that;
ΔABC ≅ ΔYWZ
That means triangle ABC is congruent to triangle YWZ
Thus;
∠C ≅ ∠Z
5x - 4 = 66
5x = 70
x = 14
Similarly, AB = WY
5T - 10 = 4T + 4
5T - 4T = 10 + 4
T = 14
AB = 5(14) - 10
AB = 60 = WY
7) We are told that;
ΔABC ≅ ΔZYW
That means triangle ABC is congruent to triangle ZYW
Thus;
∠A ≅ ∠Z
5X - 4 = 3X + 10
2X = 14
X = 7
∠A = 5(7) - 4 = 31° = ∠Z
Similarly;
2T + 10 = 4T - 8
T = 18/2
T = 9
YZ = 4(9) - 8
YZ = 28 = AB
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What is 6/21 + 6/7? Please help with question
Answers
Answer: 8/7 Or In Mixed Number Form 1 1/7
Step-by-step explanation: Get the common denominator which is 21 because you get 6/7 and multiply the number and denominator by 3. You will get 18/21. Now you add. 18/21 + 6/21 = 24/21. Simplify them by the greatest common factor and so I divide by 3 and get 8/7.
Hoped This Helped!
Answer:
Step-by-step explanation:
6/21 + 6/7
6/21 + 18/21
24/21 = 1 1 / 7
6 x 3 18
____ = __
7 x 3 21
- You need common denominators to add fractions together!!
Which number is an integer?
2.3
0
-3/4
pi
Answers
0 is an integer number.
A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero.
i.e. the set of integers is
Z = {... -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...}
The integers do not contain any fraction or rational number.
Here,
2.3 is a fraction number so it is not an integer.
And -3/4 is a rational number and rational numbers are not integers.
And pi is irrational number
So,
This three numbers are not an integer
Now,
0 is an integer as per the definition of integers.
Hence,
0 is the integer number
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Solve the formula for t.
V=6πrt+7πr*2
t=
Answers
The unknown variable t has a value of t = (V - 7πr²)/6πr
How to determine the unknown variable?From the question, we have the following parameters that can be used in our computation:
Formula; V = 6πrt+7πr*2
Rewrite the formula properly
So, we have the following representation
V = 6πrt + 7πr²
Subtract the expression 7πr² from both sides of the equation
So, we have
V - 7πr² = 6πrt + 7πr² - 7πr²
Evaluate the difference
V - 7πr² = 6πrt
So, we have
6πrt/6πr = (V - 7πr²)/6πr
Evaluate
t = (V - 7πr²)/6πr
Hence, the value is t = (V - 7πr²)/6πr
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Answer:
[tex]t = \dfrac{V-7\pi r^2}{6\pi r}[/tex]
Step-by-step explanation:
V = 6πrt + 7πr²
Subtract the term without t from both sides.
V - 7πr² = 6πrt
Now you have a single term with t on the right side and two terms without t on the left side.
Switch sides.
6πrt = V - 7πr²
Divide both sides by 6πr.
[tex] t = \dfrac{V - 7\pi r^2}{6\pi r} [/tex]
help by the end of the week.
Answers
Answer:
1 ) Slope of the line
[tex]m = 2[/tex]
2 ) Equation of the line
[tex]y=2x-2[/tex]
3 ) Values of a and b
a = 5
b = 6
4 ) What is the y-coordinate when?
The y-coordinate is the vertical position of a point in terms of distance and direction along the y-axis.
In this graph, when x = 2 they y-coordinate is also 2 so it is 2 units from the y-axis.
Hope this helps! :)
1. Corey buys a Toyota Yaris for $15,000 at 4.1% interest rate for 6 years.
How much interest will Corey pay on his Yaris?
What is the total amount that will paid?
What is his monthly payment?
Answers
Answer:
a) $4089.55
b) $19089.55
c) $56.80
Step-by-step explanation:
a) (100 + 4.1)/100 = 1.041. So, 15000 × 1.041⁶ = 19089.55. Interest that will be paid: 19089.55 - 15000 = $4089.55 (2 dp).
b) $19089.55 (with interest and principal)
c) 4089.55/72 = $56.80
Dela made 21 peanut butter sandwiches with a 12-ounce jar of peanut butter.
How many ounces of peanut butter did Dela use on each sandwich? Use any strategy to solve this problem.
Answers
Answer:
Oh this is easy
Dela made 21
all of them is 12 ounce
so to know each of them
21/12
So the answer is 1.75ounce of peanut butter per sandwich
Step-by-step explanation:
I think i got it right
5. Rewrite the expression as a single logarithm. (1 point)
Answers
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
The given logarithmic expression can be expressed as
[tex]=\frac{1}{2}\ln}\left(x\right)+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\ln\left(x-1\right)-\frac{2\ln\left(x+1\right)}{3}[/tex]
By using the logarithmic properties, we get
[tex]=ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex]
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
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Using point-slope form, write the equation of the line that passes through the point (−1,4) and has a slope of −3.
step by step explanation will give 100 points pls answer fast
Answers
Answer:
y - 4 = - 3(x + 1)Step-by-step explanation:
Point- slope formy - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the point on the lineGivenm = - 3,(x₁, y₁) = ( - 1, 4).Plug in to get the equation of the liney - 4 = - 3(x - (-1)) ⇒ y - 4 = - 3(x + 1)Answer:
Answer:
y - 4 = - 3(x + 1)
Step-by-step explanation:
Point- slope form
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the point on the line
Step-by-step explanation:
