subtraction property of equality
multiplication property of equality
17
3
3
4
3
X-
Step
3
X=
17 3 17
7--7-x+5-77
3
5x.-
4
4
-2/x-12x X=
1 2
X= X-
2
X=-
4
5
-
-
X=
division property of equality
X+5
2
-/3/33
addition property of equality
2
3
8
15
-²333
x-²/3-1/2 x
-
17
4
5
3
given
simplification
Justification
The required justification for the solution to the equation is shown in the solution part.
As per the given equation, the required solution would be as follows:
Given:
17/3 - (3/4)x = 1(/2)x + 5
Subtraction property of equality:
17/3 - (3/4)x - 17/3 = 1(/2)x + 5 - 17/3
- (3/4)x = 1(/2)x - 2/3
Addition property of equality:
- (3/4)x - 1(/2)x = 1(/2)x - 2/3 - 1(/2)x
-(5/4)x = -2/3
Multiplication property of equality:
-(5/4)x × -4/5 = -2/3 × -4/5
Simplification:
x = 8/15
The required justification for the solution to the equation is shown in the solution part.
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Answer:
Answer shown in picture.
Evaluate the expression when a = 6 and x = -3.
-a+7x
A spinner with 12 equally sized slices is shown below. (The 12 slices are red.) The dial is spun and stops on a slice at random. What is the
probability that the dial stops on a red slice?
Write your answer as a fraction or a whole number.
Answer:
100/100
Step-by-step explanation:
XD
44+ 7/8r when r = -1/2
\(44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}\)
A tourist from Vermont won a jackpot worth 8,500,000 on a slot machine. The goverment gets 45% of his winning in taxes. How much of his winning does the tourist pay
The tourist has to pay the government $3,825,000.
make 45% into a decimal (0.45) and then multiply it by 8,500,000.
Replace ? with an expression that will make the equation valid.
Answer:
4x³
Step-by-step explanation:
d/dx ln(x⁴ + 7) = 1/(x⁴ + 7) × _?
To obtain the missing expression, let us simplify d/dx ln(x⁴ + 7). This can be obtained as follow:
Let y = ln (x⁴ + 7)
Let u = (x⁴ + 7)
Therefore,
ln(x⁴ + 7) = ln u
Thus,
y = ln u
dy/du = 1/u
Next, we shall determine du/dx. This is illustrated below:
u = (x⁴ + 7)
du/dx = 4x³
Finally, we shall determine dy/dx of ln (x⁴ + 7) as follow:
dy/dx = dy/du × du/dx
dy/du = 1/u
du/dx = 4x³
dy/dx = 1/u × 4x³
But:
u = (x⁴ + 7)
Therefore,
dy/dx = 1/(x⁴ + 7) × 4x³
Thus, the missing expression is 4x³
A loan of RM 5800 at 9% made on May 22 and due July 5.
Answer:
\(5800 \times 9 \times 5 \div 100\)
What is the inverse of a function?
A function for which the domain remains the same, and reciprocal values of the range are used
A function for which the values or the domain and the range are interchanged
A function for which the range remains the same, and reciprocal values of the domain are used
The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.
What is an inverse function?The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.
Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.
For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:
x = 2y + 3
2y = x - 3
y = (x - 3)/2
Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.
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solve the inequality for v.-4v < -12 simplify your answer as much as possible
Solve the inequality -4v<-12.
\(\begin{gathered} -4v<-12 \\ -\frac{4v}{4}<-\frac{12}{4} \\ -v<-3 \\ -v\cdot(-1)>-3\cdot(-1) \\ v>3 \end{gathered}\)So after simplification the inequality is v > 3.
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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Describe and correct the error in finding the perimeter or area of the polygon.
Answer:
Look at explanation.
Step-by-step explanation:
The error is that the length of the polygon is 5 not 4. The perimeter should be 16 units not 14 units.
The perimeter of the given polygon is 16 units.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
From the given figure, length =5 units and width =3 units.
We know that, the perimeter of a rectangle is perimeter =2(length+width)
P= 2l+2w
= 2(5)+2(3)
= 10+6
= 16 units
Therefore, the perimeter of the polygon is 16 units.
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Imagine your playing a game, you are currently level 5 and it takes 55 EXP to level up to level 6, each battle you fight you gain 3 EXP, how many battles would it take to level up? you don't have to show your work :).
Step-by-step explanation:
55 / 3 = 18.333.
Since it is a decimal, we round up to the nearest whole number.
It will take at least 19 battles to level up.
Answer:
Step-by-step explanation:
so divide 55 / 3 = 18.33333333 or 18 1/3 but.. you'll have to battle 19 times to level up
how many whole numbers are between 32 and 77
Answer:
45
Step-by-step explanation:
Simply subtract 32 from 77.
To find the numbers between any two numbers, we have to find the difference between them. The difference between 77 and 32 is 45.
45 whole numbers are there between 77 and 32.
We need to find whole numbers between 77 and 32
What is whole number?The complete set of natural numbers with zero is called as whole number
To find whole numbers between 32 and 77.
we need to find the difference.
seventy seven- thirty two = fourty five
77-32=45
Therefore 45 whole numbers are between 32 and 77
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what is -9.25 as a faction
Answer:
-37 / 4
Step-by-step explanation:
this is one of my homework questions and if possible please help, I do some of it to a certain point but then get stuck. if im correct, the right choice is sin with a degree but I need some guidance. Thank you!
Given the expression:
\(2\sin 67.5\degree\cos 67.5\degree\)The angle of the sine and the cosine is the same angle = 67.5°
The given expression is the same as the rule of the sine of the double angle
Where:
\(2\sin \theta\cos \theta=\sin (2\theta)\)so, we will use the sine double-angle to solve the question
So, the answer will be:
\(\sin (2\cdot67.5\degree)=\sin 135\degree\)So, the answer will be option B) sin 135°
In the figure below, two secants are drawn to a circle from exterior point V.
Suppose that VZ=30, VW=45, and VX=22.5. Find XY.
The value of secant XY is 37.5 units.
How to find the value of secant XY?The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".
Using the theorem above, we can say:
VZ * VW = VX * VY
30 * 45 = 22.5 * VY
22.5VY = 1350
VY = 1350/22.5
VY = 60 units
Since VY = VX + XY. We have:
60 = 22.5 + XY
XY = 60 - 22.5
XY = 37.5 units
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tristan bought an orange that weighs 1 8th of a pound
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
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Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
The area of a rectangular carpet is 54 square feet. The length is three feet more than the width. Find the length and the width of the carpet.
Sixty students are invited to an Hono Roll Pizza Party. There are 24
sodas in a package and 18 slices per pizza. What is the least number of
packages of soda and pizzas that can be bought if each person gets
one soda and one slice of pizza?
Answer:
2.5 boxes of soda or round it to 3
3.3 boxes of pizza or round it to 4
Dimitri has let out 40m of his kite string, which makes an angle of 72° with the horizontal ground. If the kite flies directly over Sarah's head, what is the distance between Dimitri and Sarah?
Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.
How to Apply the Cosine Ratio?The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.
Using the cosine ratio, we have:
Reference angle (∅) = 72 degrees
Hypotenuse length = 40 m
Adjacent length = distance between Dimitri and Sarah = x
Plug in the values:
cos 72 = x/40
x = cos 72 * 40
x ≈ 12.4 [to one decimal place]
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Write a word problem for the equation:
2,530/23=9
Solve your problem any way you choose.
Answer:
bob has 2530 apples and he has 23 friends. if he were to divide the apples evenly between his friends, how many apples would each friend receive?
this is one possible word problem.
A garden is 6 2/3 feet long and 2 2/3 Juan is putting a brick border around the garden each brick is 2/3 feet long how many bricks does Juan need
Answer:
Juan needs 28 bricks.
Step-by-step explanation:
Write the equation for a parabola with a focus at (-8,-1) and a directrix at y=-4
Answer:
y=(x+8)^2/6 - 5/2
Step-by-step explanation:
Khan Academy
which expression is equivalent to -3x(2x-8)+4x
Answer:
2x ( -3x + 14)
Step-by-step explanation:
What is Distribution Property?
Distribution property is used in a format like a ( b + c ). To simplify these kinds of expressions, we multiply the outside term by each of the inside terms. So in this instance, a ( b + c ) is equal to ab + ac.
Let's put this in the expression3x ( 2x - 8 ) + 4x
Let's use what we learned above, and multiply the outside term (-3x) by each of the inside terms.
-3x · 2x + (-3x) · (-8) +4x
Simplify by multiplication:
-6x² + 24x +4x
Finally, we add:
-6x² +28x
Now, to simplify further, we can look for terms that show up in numbers.
We can see that the variable x is present in each of the terms, so we can factor that out, removing it from the term as follows:
x ( -6x + 28)
We can look and see that 2 is also a common factor between the two terms, so we can take that out too.
2x ( -3x + 14)
This is the most simplified it can get.
If y equals -5 when X equals 2, find Y when X equals 8?
Answer:
4
Step-by-step explanation:
please help me thank you so much
Which of the following equation will produce the graph shown below
The quadratic equation in the given graph can be written in the vertex-form as:
y = -2(x - 1)² + 4
Which of the equations produce the given graph?We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
in the graph we can see that the vertex is (1, 4), replacing that we will get:
y = a*(x - 1)² + 4
In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:
2 = a*(0 - 1)² + 4
2 = a + 4
-2 = a
Then the quadratic is:
y = -2(x - 1)² + 4
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6. find the five-number summary
The solution to find the five number summary shown below.
What is five number summary?When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.
To find a five number summary we have follow:
Sort the numbers from smallest to largest in ascending order.The smallest number on the list is the minimum.The greatest number in the list is the maximum.The middle of the list is where you'll find the median.The median of the first half of the data makes up the lower quartile.Learn more about five number summary here:
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