Ivan and Javier manipulated the rational expression
6
x
+
4
12
x
+
4
12x+4
6x+4
start fraction, 6, x, plus, 4, divided by, 12, x, plus, 4, end fraction. Their responses are shown below.
Ivan Javier
3
x
+
2
6
x
+
2
6x+2
3x+2
start fraction, 3, x, plus, 2, divided by, 6, x, plus, 2, end fraction
6
x
12
x
12x
6x
start fraction, 6, x, divided by, 12, x, end fraction
Which student wrote an expression that is equivalent to the original expression?
Answers
Answer:only Ivan
Step-by-step explanation:
Related Questions
Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.
Answers
The given equation is
\(\sqrt[]{7t+5}=7\)Square both sides to cancel the square root
\(\begin{gathered} (\sqrt[]{7t+5})^2=(7)^2 \\ 7t+5=49 \end{gathered}\)Subtract 5 from both sides
\(\begin{gathered} 7t+5-5=49-5 \\ 7t=44 \end{gathered}\)Divide both sides by 7
\(\begin{gathered} \frac{7t}{7}=\frac{44}{7} \\ t=\frac{44}{7} \\ t=6\frac{2}{7} \end{gathered}\)The solution is t = 44/7 OR t = 6 2/7 (mixed number)
Please answer the question
Answers
Answer:
4.
a.octagon
b.squertagon
c.triangle
t.b
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
PLEASE HELP!! WILL GIVE BRAINLEST!!! :)))
Answers
Answer:
1.1892
Step-by-step explanation:
view the attached picture to see how i got that answer :)
Two parallel lines are crossed by a transversal.
What is the value of d?
Answers
The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.
What is a Transversal?In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.
The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.
Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°
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How many grams are in 7.4 x10 19 atoms of Copper? round the the thousandths place
Answers
There are 0.09779 grams in 7.4 x 10^19 Atoms of copper.
The number of grams in a given number of atoms of an element, we need to use the concept of molar mass and Avogadro's number.
The molar mass of an element represents the mass of one mole of that element. For copper (Cu), the molar mass is approximately 63.546 grams per mole.
Avogadro's number, denoted as N<sub>A</sub>, is the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms/molecules per mole.
To calculate the mass of a given number of atoms, we can use the following steps:
Step 1: Determine the number of moles of copper atoms.
Given: 7.4 x 10^19 atoms of copper
Number of moles = (Number of atoms) / (Avogadro's number)
Number of moles = (7.4 x 10^19) / (6.022 x 10^23)
Step 2: Calculate the mass using the molar mass of copper.
Mass = (Number of moles) x (Molar mass)
Mass = (7.4 x 10^19) / (6.022 x 10^23) x 63.546
Now, we can perform the calculations:
Mass ≈ 0.09779 grams
Therefore, there are approximately 0.09779 grams in 7.4 x 10^19 atoms of copper.
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Given f (x) = 3x - 6 and g (x) = 2x²
1. Find: f (g (x))
2. Evaluate: f ( g ( -2))
PLEASE HELP ASAP!
Answers
Answer:
1. 6x^2-6
2. 18
Step-by-step explanation:
1. f(g(x))= 3(2x^2)-6= 6x^2-6
2. f(g(-2))= 3 (2(-2)^2)-6= 3(2(4))-6= 3(8)-6=24-6=18
2. 18
Have a nice day / night! :)
What are the answers to question 1 and 3 PLZZ HURRRYYY
Answers
Step-by-step explanation:
1. Since ark MN is equal in length with ark PQ, line MN=PQ
So 4x+10=38
4x=38-10
4x=28
x=28/4
x=7
3. Same thing so we equate the two parameters
5x-7=3x+2
2x=9
x=9/2
x=4.5
57% is greater than, less than, or equal to 1
Answers
Answer:
Less than
Step-by-step explanation:
Answer:
57% is less than
Step-by-step explanation:
To convert from percentages to counting numbers, we move the decimal in the percentage two places behind its original point.
57.0% ---> .57
.57 < 1
Plot the image of point QQQ under the translation (x,y)\to(x+1,y+2)(x,y)→(x+1,y+2)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 1, comma, y, plus, 2, right parenthesis.
Answers
The coordinates of the image of the point Q is Q'(3, 6).
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
From the given graph, we have point Q(-4, 4).
Here the point is translated.
After translation, the original figure is shifted from a place to another place without affecting it's size.
The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).
So the given point is (-4, 4).
(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).
So the required point is (-3, 6).
Hence the image of point Q is (-3, 6).
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Your question is incomplete, Probably, the correct graph for the question is given below.
Five computer program modules are ranked as M1, M2, M3, M4, and M5 according to the ascending order of effort required to debug them, among which M1 requires the least amount of effort and M5 requires the most amount of effort. A software engineer must randomly select three program modules from the five modules. He (or she) does not know the amount of effort each module costs when selecting.
A) What is the sample space?
B) Let A be the event that one selected module requires the least amount of effort. List the outcomes in A, and calculate the probability of A.
C) Let B be the event that the one selected module requires the most effort. List the outcomes in B, and calculate the probability of B.
D) List the outcomes in the compound event AnB, and calculate the probability of it.
E) List the outcomes in the compound event AUB, and calculate the probability of it.
F) List the outcomes in the compound event AnB, and calculate the probability of it.
G) List the outcomes in the compound event AUB, and calculate the probability of it.
H) Are events A and B mutually exclusive? Explain why?
Answers
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Technician selects three out of 5 systems
In C(5,3)=10ways, this can be achieved
In part a:
Space sample chooses 3 of a 5 systems
\((M_1, \ M_2,\ M_3),\)\((M_1,M_2,M_4) \ (M_1,M_2,M_5) \ (M_1,M_3,M_4) \ (M_1,M_3,M_5),\)\((M_1,M_4,M_5) \ (M_2,M_3,M_4)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5)}\)
In point b:
A =MODULE WHICH INCLUDE M1 minimal amount of effort
Outcomes probable =
\((M_1,M_2,M_3),\ (M_1,M_2,M_4) \ (M_1,M_2,M_5)\ (M_1,M_3,M_4)\\\\(M_1,M_3,M_5),\ (M_1,M_4,M)5)\ =\ 6\)
\(\to p(A)=\frac{6}{10}\\\\\)
\(=0.6\)
In point c:
B = highest effort that is \(M_5\)
Potential result=
\((M_1,M_2,M_5) \ (M_1,M_3,M_5) \ (M_2,M_3,M_5)\(M_2,M_4,M_5) \\ (M_2,M_4,M_5), \ (M_3,M_4,M_5) \ =\ 6 \\\\\)
\(\to B= \frac{6}{10} \\\\\)
\(=0.6\)
\(\to P(B)=10\)
In point d:
\(\to \ A \ intersection \ B=(M_1,M_2,M_5), \ (M_1,M_3,M_5) \ ,(M_1,M_4,M_5)\)
\(\to A (A \ intersection \ B) = \frac{3}{10} \\\\\ \ \ \ \ \\)
\(=0.3\)
In point e:
\(\to (A \cup B) = (M_1,M_2,M_3),\ (M_1,M_2,M_4)\ (M_1,M_2,M_5)(M_1,M_3,M_4)\ (M_1,M_3,M_5), \\ (M_1,M_4,M_5)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5) \ = \ 9\)\(\to P(A \cap B)=\frac{9}{10}\)
\(= 0.9\)
In point f:
\(\to (A\cap B) = \frac{3}{10}\)
\(= 0.3\)
In point g:
\(\to (A \cup B) = \frac{7}{10}\)
\(=0.7\)
In point h:
\(\to p(A \cap B) = 0.3 \neq 0\)
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm
long. How many centimeters long was the actual tank?
cm
Answers
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.
To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.
Let's denote the length of the actual tank as "x".
According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.
So, we can set up the following proportion:
1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)
Cross-multiplying and solving for x, we get:
x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm
The actual tank is 1620 cm long.
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Julie thinks this will mean the prices will be reduced to $0 after the four reductions because 4 x
25% = 100%.
Explain why Julie is wrong
Answers
Answer:
4x25/100=1
Step-by-step explanation:
How I came up with it
4÷100=25
25÷25=1
Julie will only get a 1% discount
Hope it helps
The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4
Answers
An equation of the new graph is: A. y = ∣x - 4∣ - 9.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:
g(x) = f(x) + N
Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:
y = ∣x - 4∣ - 9
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
8 yd
10 yd
3 yd
Find the volume of the triangular prism.
A. 120 yd
B. 130 yd
C. 240 yd
D. 260 yd
Answers
Answer:
The answer for this question is 240 yd
Find the perimeter of the figure below. Round your answer to the nearest tenth.
Answers
The Perimeter is the sum of all edges so 8+12+13+20=53
the perimeter is 53
Select the correct answer. Simplify the following expression.
Answers
The simplified exponential expression for this problem is given as follows:
D. 1/49.
How to simplify the exponential expression?The exponential expression for this problem is defined as follows:
\(7^{-\frac{5}{6}} \times 7^{-\frac{7}{6}}\)
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.
Hence the exponent is given as follows:
-5/6 - 7/6 = -12/6 = -2.
The negative exponent is moved to the denominator, hence:
1/7² = 1/49.
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Find the length of the arc. Use 3.14 for the value of pi. Round to nearest tenth.
Answers
The arc length of the given arc is 7.85 km.
Any arc's length is given by the formula s = θr, where s is the arc's length, r is its radius, and θ is the angle's measurement in radians. Use the fact that equals to convert between degrees and radians that is \(\pi\) radians = 180 degrees. A subtended arc is the portion of the circle that is located in between the two rays that make up the center angle.
So, we have :
Arc Length, s = θr
Here, θ = 90 degrees = \(\frac{\pi }{4}\) radians
Radius of the circle, r = 10 km = 10*1000 m = 10000 m
Now, Calculating the Arc Length, s = θr
\(s =\frac{\pi }{4} *10000 = 7850 m\)
We have calculated the arc length in S.I. Units.
Hence, The arc length is 7850 m = 7.85 km.
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To solve 1/3÷9, James thinks of dividing a loaf of bread into 3 equal parts, dividing one of those parts into 9 equal slices, and then eating one of those slices.
What fraction of the loaf of bread is James thinking about eating?
(Answer as a fraction)
Answers
The equation of a parabola is 12y = (x-1)^2 - 48 . Identify the vertex, focus, and directrix of the parabola.show each step
Answers
Given: The equation of a parabola below
\(12y=(x-1)^2-48\)To Determine: The vertex, focus, and directrix of the parabola
Let us re-write the given equation
\(\begin{gathered} 12y=(x-1)^2-48 \\ (x-1)^2=12y+48 \\ (x-1)^2=12(y+4) \end{gathered}\)The general equation of the parabola with vertex (h, k) is of this form
\((x-h)^2=4p(y-k)\)\(\begin{gathered} focus=(h,k+p) \\ directrix=y=k-p \\ vertex=(h,k) \end{gathered}\)Let us compare the general equation with the given equation
\(\begin{gathered} (x-1)^2=12(y+4) \\ (x-h)^2=4p(y-k)_{} \\ h=1,k=-4 \end{gathered}\)Therefore
\(\begin{gathered} vertex=(h,k)=(1,-4) \\ vertex=(1,-4) \end{gathered}\)\(\begin{gathered} 4p=12 \\ p=\frac{12}{4}=3 \\ p=3 \end{gathered}\)\(\begin{gathered} focus=(h,k+p)=(1,-4+3)=(1,-1) \\ focus=(1,-1) \end{gathered}\)\(\begin{gathered} directrix=y=k-p,y=-4-3=-7 \\ directrix=y=-7 \end{gathered}\)Hence,
Vertex = (1, -4)
Focus = (1, -1)
Directrix, y = -7
A unit of electricity costs 13.2 pence. On average, Tanya uses 90 units of electricity per week. She pays for her bill in 12 weeks. How much will her electricity bill be then? £
Answers
Answer:
90*12=1080
1080*13.2=14256
14256:100=142,56pounds
The mean height of the students in a class is 152 cm. The mean height of boys is 158 cmwith a standard deviation of 5 cm. And the mean height of girls is 148 cm with a standarddeviation of 4 cm. Find the percentage of boys in the class and also the S.D of heights of allthe students in the class?
Answers
The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively
How to find the percentage of boys in the class?Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class
The given parameters that will help us to get the percentage are
Mean height of the class = 152 cm
Mean height of the boys = 158 cm
The standard deviation of the boys = 5 cm
Mean height of the girls = 148 cm
Standard deviation of the girls = 4 cm
(1) The percentage of boys in the class is
Total mean height = 158 +148 = 306
Percentage = 158/306 * 100 = 51.6%
Then the percentages 51.6/100 * 152 = 78%
(2) The total standard deviation of all the students
Boys + girls = 5+4 = 9 cm
Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively
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I will give brainliest out please help me answer the unsolved ones
Answers
For the given triangles:
(1) x = 5.4
(2) x = √23
(3) θ = 25.84 degree
(4) x = 9.5
(5) n = 41
(1) In the given triangle,
One angle = 16 degree
Perpendicular = x
Hypotenuse = 20
Since we know that
Sinθ = opposite side of θ/hypotenuse
Therefore,
⇒ sin 16 = x/20
⇒ 0.27 = x/20
⇒ x = 5.4
(2) In the given triangle,
Hypotenuse = 12 km
Base = 11 km
perpendicular = x
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (12)²= (x)² + (11)²
⇒ 144 = (x)² + 121
⇒ x² = 23
Taking square root both sides we get,
Hence,
⇒ x = √23
(3) In the given,
Base = 20
Perpendicular = 42
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (Hypotenuse)² = (42)² + (20)²
⇒ (Hypotenuse)² = 2164
Taking square root both sides,
⇒ (Hypotenuse) = 46.51
⇒ cosθ = Adjacent/hypotenuse
= 42/46.51
= 0.90
Taking inverse of cosθ,
⇒ θ = 25.84 degree
(4) In the given triangle,
One angle = 30 degree
Base = x
Hypotenuse = 11
Since we know that
cosθ = Adjacent/hypotenuse
Therefore,
⇒ cos 30 = x/11
⇒ √3/2 = x/11
⇒ x = 9.5
(4) In the given triangle,
Base = 40
Perpendicular = 9
Hypotenuse = n
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ n² = 9² + 40²
⇒ n² = 81 + 1600
⇒ n² = 1681
⇒ n = 41
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What is the value of cos theta given that (- 5, - 4) is a point on the terminal side of theta ?
Answers
Answer:I believe it's -5√41/41
Step-by-step explanation:
The value of \(cos\theta\) will be \(-0.7813\).
If the point \((-5.-4)\) were rotated around the origin, it would form a circle of radius \(r\). Also, if the point were projected to the x-axis, a right-angled triangle would be formed. Then, the value of \(cos\theta\), could be obtained by the formula
\(cos\theta=\dfrac{x}{r}\)
where
\(x=\text{the side of the triangle opposite the reference angle of }\theta\\r=\text{the radius of the circle}\)
From the point on the terminal side
\((x,y)=(-5,-4)\)
we can directly get the value of \(x\). But we need to calculate the value of \(r\).
To calculate the value of \(r\), make use of Pythagoras theorem
\(r=\sqrt{x^2+y^2}\\=\sqrt{(-5)^2+(-4)^2}\\=\sqrt{25+16}\\\approx6.4\)
We can now proceed to find the value of \(cos\theta\), since we have the values of \(x\), and \(r\). Therefore,
\(cos\theta=\dfrac{x}{r}\\\\=\dfrac{-5}{6.4}\approx-0.7813\)
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1+1+2+3+3+5+4+2=2+1+1
Answers
Answer:
21=4 ?????
Step-by-step explanation:
huh???????????
Answer:
False
Step-by-step explanation:
1+1+2+3+3+5+4+2= 21
2+1+1= 4
You put an equal sign right smack down in the middle. 21 is not equal to 4 so this inequality is false.
(-4 + 3i)(-12 + 6i)
Simplify expression
Answers
Answer:
=30−60i
Step-by-step explanation:
how much would $300 invested at 4% interest compounded monthly be worth after 8 years? round your answer to the nearest cent
Answers
Answer:
412.92
Step-by-step explanation:
\(A = P(1+\frac{r}{n} )^{nt}\)
A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years
We have P = 300
r = 4% = 0.04
n = 12 (compounded monthly)
t = 8
\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)
refer to exhibit 26-5. the data illustrate that the firm in question is a group of answer choices price taker (perfectly competitive firm). factor price taker. price searcher (monopolist, oligopolist, etc.). factor price searcher.
Answers
According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.
A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.
In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.
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The product of 4 and the difference of a number and 7.
Answers
Answer:
simplified: 4x−28
Step-by-step explanation:
The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
Answers
HELP!! URGENT!!
Find the perimeter of the triangle. Simplify your answer.
Answers
The expression that represent the perimeter of the triangle is 3d² - 4d + 1.
What is the perimeter of the given triangle?The perimeter of any two-dimensional figure is simply the distance around the figure.
Hence, the perimeter of the triangle is the sum of all its 3 side lengths.
From the diagram:
Side length 1 = ( d² + 3 )
Side length 2 = ( 4d² + 3d - 2 )
Side length 3 = ( -2d² - 7d )
Hence, the perimeter of the triangle will be:
Perimeter = side length 1 + side length 2 + side length 3
Plug in the expressions
Perimeter = ( d² + 3 ) + ( 4d² + 3d - 2 ) + ( -2d² - 7d )
Collect and add like terms:
Perimeter = d² + 3 + 4d² + 3d - 2 + -2d² - 7d
Perimeter = d² + 4d² - 2d² + 3d - 7d + 3 - 2
Perimeter = 3d² - 4d + 1
Therefore, the perimeter is 3d² - 4d + 1.
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