Answer:
option B
Step-by-step explanation:
Given :
\(y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\\)
Step 1 : simplify the equation :
\(3y = 2x + 9\\\\2y = 5x + 7\\\)
Step 2: Arrange the terms :
\(2x - 3y = - 9\\\\5x -2 y = -7\)
Step 3 : Solve for x and y :
2x - 3y = - 9 ------ ( 1 )
5x - 2y = - 7 --------- ( 2 )
_____________________
( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )
( 2) x 2 => 10x - 4y = - 14 ----------- (4 )
_______________________
( 3 ) - ( 4 ) => 0x - 11y = - 31
- 11 y = - 31
\(y = \frac{31}{11}\)
Substitute y in ( 1 ) :
2x - 3y = - 9
\(2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}\)
Therefore the solution to the sytem is \(( - \frac{3}{11} , \frac{31}{11})\)
The solution of the system of equation is a point which lies
on the both the lines.
Option A : False , It says the solution lies above one of the given line.
But the solution of the system of equation always lies on
both the line.
Option B : True , says the solution is a point on the coordinate plane.
Option C : False, because if the solution is on the x-axis , then
the y coordinate in the solution would be zero.
But it is not zero.
Option D : False , the solution is the point where both the lines intersect.
The expression (2a)4 is equivalent to
Answer:
2 is multiplied by -4 and then a4 is gone to the bottom
Answer:
4
Step-by-step explanation:
To make the exponent -4 put it over 1.
\(\frac{1}{(2a)^{4} }\)
\(\frac{1}{2^{4}a^{4} }\)
\(\frac{1}{2x2x2x2xaxaxaxa}\)
\(\frac{1}{16a^{4} }\)
(x+3)(x-8) Multiply and Simplify
Answer:
x^2-5x-24
Step-by-step explanation:
PLEASE HELP ME! Sally is paid a fixed amount of money to walk her neighbor's dog every day after school. When she is paid each month, she puts aside $20 to spend and saves the remaining amount. Write an expression that represents the amount Sally will save in 6 months if she earns m dollars each month.
Answer: 6($m - $20)
Step-by-step explanation:
From the question, we are told that Sally earns m dollars each month to walk her neighbor's dog every day after school and that when she is paid each month, she puts aside $20 to spend and saves the remaining amount. This means that Sally saves:
$m - $20.
The expression that represents the amount Sally will save in 6 months will be so multiplied by the amount saved every month. This will be:
= 6($m - $20)
Answer:
Ok first of all. You cant be in highschool with this question. because this is a 6th grade question. Second that person who gave you that asnwer is wrong because thats not even the answer now I advise you to listen for future refrences.
Step-by-step explanation:
she is paid $65 and she saves $20 so subtract those numbers then you get $45 so that means she saves $20 and had $45 to spend. that means 20 times 6(months) is... $120 so $120 is your answer. But, to be more professional "Sally has saved $120 in 6 (Months.)
can sombody help me fast ? !
Answer:
i think D
Step-by-step explanation:
A is the event that the student drives, and B is the event that the student went to the movies in the past month.
A Venn Diagram. One circle is labeled A (A and B Superscript C Baseline 0.06), another is labeled B (A Superscript C Baseline and B 0.22), and the shared area is labeled A and B (0.35). The area outside of the diagram is labeled A Superscript C Baseline and B superscript C Baseline 0.37.
Use the Venn diagram to answer the following questions.
What is the probability that a randomly selected student does not drive?
What is the probability that a randomly selected student went to the movies in the past month?
What is the probability that a randomly selected student drives or went to the movies in the past month?
If an event that "student-drives" is denoted by "A", and event "student go for movie" is denoted by B, then
(a) Probability that randomly selected student do not drive is 0.59,
(b) Probability for randomly selected student go for movie last-month is 0.57,
(c) Probability that randomly selected student "drives" or "go for movie past month" is 0.63.
(a) To find the probability that a randomly selected student does not drive, we can use the complement of event A, which is A'.
From the Venn-Diagram, We know that;
(A and \(B^{c}\)) = 0.06, (\(A^{c}\) and \(B^{c}\)) = 0.37, (A and B) = 0.35, (\(A^{c}\) and B) = 0.22,
We use the values of (A and \(B^{c}\)) and (A and B) to calculate P(A):
P(A) = (A and \(B^{c}\)) + (A and B) = 0.06 + 0.35 = 0.41;
So, P(\(A^{c}\)) = 1 - P(A) = 1 - 0.41 = 0.59,
The probability that randomly selected student do not drive is 0.59.
Part (b) : Probability that randomly selected student go for movies past month, is denoted by P(B).
So, P(B) = (A and B) + (\(A^{c}\) and B) = 0.35 + 0.22 = 0.57.
The probability that randomly selected student go for movies past month is 0.57.
Part (c) : Probability that randomly selected student drives or go for movies past month, is denoted by union of events A and B, and We know that, P(A U B) = P(A) + P(B) - P(A and B);
Substituting the values,
We get,
= 0.41 + 0.57 - 0.35
= 0.63.
So, probability that randomly selected student drives or go for movies past month is 0.63.
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Select all the polygons that have reflection symmetry.
A quadrilateral with two pairs of adjacent congruent sides, forming a kite.
A polygon is shaped like a composite figure made up of a rectangle with a small square on its top side and the same sized square on its right side.
A polygon shaped like a five-pointed star in which the left and right sides of the star are mirror images
A six-sided polygon that generally appears as a diagonally-oriented trapezoid attached to a shorter horizontally-oriented rectangle.
Assessment navigation
(added this for all^ my homies with k12 so its easier to find just ignore it)
Reflection Symmetry-
Line symmetry is also called as the reflection symmetry. If, at least one line that divides a figure into two halves such that one-half is the mirror image of the other half, exists, then the figure is said to be in reflection symmetry.
Analyzing all the 4 figures, it can be deduced that only 1st and 2nd figures have one symmetry line XX, as shown in the attachments.
3rd and 4th figures do not have any axisymmetric lines, so they are not in reflection symmetry.
The ratio is 2:5 red beads to blue beads. If you have a TOTAL of 21 beads, how many are red, and how many are blue beads?
Answer:
Number of red beads = 6
Number of blue beads = 15
Step-by-step explanation:
Number of total beads = 21
Ratio of red beads to the blue beads = 2 : 5
Therefore, number of red beads I have = \(\frac{2}{2+5}(\text{Total number of beads})\)
= \(\frac{2}{7}\times 21\)
= 6 beads
Number of blue beads = \(\frac{5}{2+5}\times (21)\)
= \(\frac{5}{7}\times 21\)
= 15 beads
Therefore, number of red beads = 6
And number of blue beads = 15
what is the ratio ηf/ηi, where ηf is the final surface charge density?
The ratio of the final surface charge density (ηf) to the initial surface charge density (ηi) is given by 3.68 * \(Q_i / (A_i \times A_i).\)
To understand the concept and solve this problem, we need to consider the relationship between surface charge density, area, and charge. Surface charge density (σ) is defined as the charge (Q) per unit area (A). Mathematically, we can express this relationship as σ = Q/A.
Let's assume the initial area of the irregular shape is \(A_i\), and the final area after each dimension is reduced is \(A_f\). Since each dimension (x and y) is reduced by a factor of 3.68, we can write the relationship between the initial and final areas as:
\(A_f = (1/3.68) \times A_i\)
Now, let's consider the relationship between charge and area. Since the charge remains constant for a given area, we can express it as \(Q_i = Q_f\), where \(Q_i\) is the initial charge and \(Q_f\) is the final charge.
Since the charge remains constant, the ratio of the surface charge densities can be expressed as:
ηf/ηi = \(\sigma _f/\sigma _i = Q_f/A_f / Q_i/A_i\)
Substituting the expressions for area into the equation, we have:
ηf/ηi = \(Q_f/A_f / Q_i/A_i = Q_f / (A_f * Q_i) * (A_i / Q_i)\)
Canceling out the \(Q_i\) terms, we get:
ηf/ηi = \(Q_f / (A_f * Q_i) * (A_i / Q_i) = Q_f / (A_f * A_i)\)
Since \(Q_i = Q_f\), we can simplify further:
ηf/ηi = \(Q_f / (A_f * A_i) = Q_i / (A_f * A_i)\)
Now, substituting the expressions for area into the equation, we have:
ηf/ηi = \(Q_i / (A_f * A_i) = Q_i / ((1/3.68) * A_i * A_i)\)
Simplifying, we find:
ηf/ηi = 3.68 x \(Q_i / (A_i \times A_i).\)
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Complete Question:
The irregularly shaped area of charge in the figure has surface charge density ηi. Each dimension (x and y) of the area is reduced by a factor of 3.68.
What is the ratio ηf/ηi where ηf is the final surface charge density?
Carlos and Diya perform the same transformations on the same pre-image, but in reverse order.
Carlos translates, then dilates.
Diya dilates, then translates.
Carlos claims the resulting images will always be the same. Diya disagrees.
Who is right? and why
Answer:Diya
Step-by-step explanation: she’s right because she is black and all black peoples is always right
The sides of a cube are measured in whole centimeters. Which of the following could not be the cube's volume?
100 cm^3
125 cm^3
64 cm^3
8 cm^3
Answer:
100cm^3
Step-by-step explanation:
It can be 125 because:
5 x 5 x 5 = 125
It can be 64 because:
4 x 4 x 4 = 64
It can be 8 because:
2 x 2 x 2 = 8
Therefore we only have one number remaining which is 100cm^3
Answer: 100cm 3
Step-by-step explanation: Since the sides of a cube are measured in whole centimeters, the answer can't be 100cm 3, but since it says "could NOT be the cube's volume" Then 100cm 3 would be your answer.
I also had this question and got it right. Have a good day! <3
the lateral surface area of cylinder R is 33π find the height of the cylinder
Answer:
1.7507
Step-by-step explanation:
See Image
I know how to do this, but for some reason got it wring on a Test. Can someone demonstrate how to do it so that I know what I'm doing wrong?
Answer:
Answer on a graph
7. call a positive integer an uphill integer if every digit is strictly greater than the previous digit. for example, 1357,89 , and 5 are all uphill integers, but 32,1240, and 466 are not. how many uphill integers are divisible by 15 ?
Answer:
6
Step-by-step explanation:
You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.
Divisible by 15An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.
An integer is divisible by 3 if the sum of its digits is divisible by 3
Uphill integersAn uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...
{5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}
Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.
The uphill integers that end in 5 are ...
5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345
Divisible by 3We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...
15, 45, 135, 345, 1245, 12345
There are 6 uphill integers divisible by 15.
please help!
fill in the blanks
(-2,1) m = -3
y - __ = __ ( x - __ ) ?
(3,-4) m = -1
y - __ = __ ( x - __ ) ?
(-2,-4) m = 1
y - __ = __ ( x - __ ) ?
Please show how you got the answer
rewrite in y = mx + b form:
y + 1 = 2/3(x - 6)
rewrite in Ax + By = C form:
y - 3 = -1/2(x - 4)
y + 1 = 2/3(x - 6)
Answer:
−3=−12(−4)+1=23(−6)
y-3=\frac{-1}{2}(x-4)y+1=\frac{2}{3}(x-6)
delroy is going to a dog adoption day at his local animal shelter. he wants to make 4 batches of dog biscuits for the dogs. it takes 1 3of a cup of margarine to make a batch. how many cups of margarine will he need?
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
What is a fraction in math?A fraction is a piece of the entire. The number is shown as a quotient in mathematics, in which the numerator and denominator are split. Both are integers in a straightforward fraction. The numerator, as well as the denominator of a complex fraction, as well as the denominator of a complex portion, is a fraction.
What is a whole number in math?Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of corresponding positive numbers, which are additive, are the negative numbers. The blackboard bold math b Z or boldface Z is a common way to represent the set of integers in mathematical terminology.
According to the given information:There are four batches of dog biscuits.
Making a batch requires 1/3 cup of margarine.
As we can see that for 1 batch of dog biscuits required 1/3 cup of margarine.
So to make 4 batches of dog biscuits:
= (1/3)*4
= 4/3
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
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You are going to make a large poster for a school project. To prepare, you make a scale drawing of the poster before creating the real thing. The dimensions of the scale drawing are 4 inches by 9 inches. The dimensions of the real poster will be 20 inches by 45 inches. What is the scale factor?
Answer:
5
Step-by-step explanation:
You are going to make a large poster for a school project. To prepare, you make a scale drawing of the poster before creating the real thing. The dimensions of the scale drawing are
The dimensions of the real poster will be 20 inches by 45 inches.
The dimensions of the scale Drawing
= 4 inches by 9 inches.
We can see the inches of the real poster increased from the one of the scale drawing
The scale factor is calculated as:
20 ÷ 4/45 ÷ 9
= 5/ 5
Hence, the scale factor is 5
Both the width and length of the scale drawing was multiplied by 5 to get the length of the real poster
How many pint are in 28 cups
Answer:
14 pints are in 28 cups
Step-by-step explanation:
Answer:
14 pints in 28 cup
Step-by-step explanation:
Diaz kindergarten class is no greater than 46 in let H the height in inches of a child in the class
Answer:
h < 46
--
hope it help
Inequalities are used to represent unequal expressions.
The inequality is:
⇒ H ≤ 46
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The height (h) is said to be no greater than 46 inches.
Here, The text "no greater than" means less than or equal to.
Hence, the inequality is:
⇒ H ≤ 46
Thus, The correct inequality is:
⇒ H ≤ 46
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I need help asap with this maths question
Answer:
\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)
Step-by-step explanation:
Suppose that
f(x) = 5 x^6 - 3 x^5.
(A) Find all critical numbers of f. If there are no critical numbers, enter 'NONE'.
Critical numbers =
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for \infty, '-INF' for -\infty, and use 'U' for the union symbol.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'.
x values of local maxima =
(E) Find the x-coordinates of all local minima of f. Note: If there are no local minima, enter 'NONE'.
x values of local minima =
(F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down:
(H) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'.
Vertical asymptotes x =
The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point
f(x) = 5x⁶ - 3x⁵
differentiation w.r.t x
=> f'(x) = 30x⁵ - 15x⁴
Putting f'(x) = 0
30x⁵ - 15x⁴ = 0
=> x⁴(30x - 15) =0
=> 30x - 15 = 0
=> x = 15/30
=> x = 0.5 , 0
Critical number is 0.5 , 0
(B) To find where f(x) is increasing
for x > 0.5 ,
(30x-15) > 0 => x⁴(30x - 15) > 0
Therefore , f(x) is increasing at ( 0.5 , ∞ )
(C)To find where f(x) is decreasing
for x < 0.5 ,
(30x-15) < 0 => x⁴(30x - 15) < 0
Therefore , f(x) is decreasing at ( -∞ , 0.5)
(D) Differentiation f'(x) again w.r.t to x
f'(x) = 30x⁵ - 15x⁴
f"(X) = 150x⁴ - 60x³
Substituting critical values of x
=> 150(0.5)⁴ - 60(0.5)³
=>9.375 - 7.5
=> -1.875 < 0 , Hence , x = 0.5 is point of maxima
(E) no point of minima
Similarly , we can solve other parts
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if 6 men plough a field in 10 hours how many hours will it taken4 men working at the same rate
Answer: 20/3
Step-by-step explanation:10*4/6=20/3
A rectangular steel structure is stabilized by 70 cm cables that connect opposite vertices. If the obtuse angle formed where the cables intersect is 140°, what are the dimensions of the rectangle?
In a rectangular steel structure stabilized by cables connecting opposite vertices, the cables act as diagonals of the rectangle. The dimensions of the rectangular steel structure are approximately 96.3 cm by 50 cm.
In a rectangular steel structure stabilized by cables connecting opposite vertices, the cables act as diagonals of the rectangle. We are given that the obtuse angle formed where the cables intersect is 140°.
Since the cables are diagonals, they divide the rectangle into four right triangles. In each right triangle, the acute angles are complementary to the obtuse angle of 140°.
Using trigonometry, we can determine the ratios of the sides in the right triangles. The tangent of an acute angle is equal to the ratio of the length of the opposite side to the adjacent side. In this case, the tangent of the acute angle is equal to the ratio of half the width to half the length of the rectangle.
Let's denote the length of the rectangle as "l" and the width as "w". From the given information, we have the equation:
tan(140°) = w/0.5l
By solving this equation, we can find the value of "w" in terms of "l". Substituting the value of "w" in the equation, we can determine the dimensions of the rectangle.
Calculating the values, we find that the approximate dimensions of the rectangular steel structure are 96.3 cm by 50 cm.
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What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 13 cm wide, and 9 cm tall?
The longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.
The right triangular face's hypotenuse is another name for this diagonal, which is also referred to as the space diagonal.
In this instance, the right triangle face with sides of 14, 13, and 9 cm can be taken into consideration. With the Pythagorean theorem in use,
we have:
14² + 13² + 9² = c²
196 + 169 + 81 = c²
446 = c²
c = \(\sqrt(446)\)
c = 21.2 cm (rounded to the nearest tenth)
So the longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.
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Choose an expression that is equivalent to negative four raised to the fourth power divided by negative four raised to the second power.
negative four raised to the second power divided by negative four raised to the fourth power
negative four raised to the fifth power divided by negative four
negative four raised to the sixth power divided by negative four raised to the fourth power
negative four divided by negative four raised to the fifth power
Answer:
C
Step-by-step explanation:
negative four raised to the sixth power divided by negative four raised to the fourth power
because negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power
negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power
The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.
Explanation:This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.
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Gear A makes 2 revolutions for every 5 revolutions gear B makes. If gear A makes 36 revolutions in 1 minute, then how many revolutions does gear B make in 1 minute?
Mountain mack spends his time carving fishing lures and duck decoys. if mountain mack spends all of his time carving fishing lures he can carve 30 lures in a week. if he spends all of his time carving duck decoys he can carve 25 decoys in a week. for every 5 duck decoys mountain mack carves he must give up 6 fishing lures.
Mountain Mack can carve 30 fishing lures and 36 duck decoys in a week.
Mountain Mack spends his time carving fishing lures and duck decoys. It is stated that if he spends all of his time carving fishing lures, he can carve 30 lures in a week. Similarly, if he spends all of his time carving duck decoys, he can carve 25 decoys in a week. Additionally, for every 5 duck decoys Mountain Mack carves, he must give up 6 fishing lures.
To determine the number of fishing lures and duck decoys Mountain Mack can carve in a week, we need to consider the trade-off between the two activities. Let's assume that Mountain Mack spends x amount of time carving fishing lures and y amount of time carving duck decoys in a week.
From the given information, we know that if Mountain Mack spends all of his time carving fishing lures, he can carve 30 lures in a week. Therefore, we can set up the equation:
x = 30
Similarly, if Mountain Mack spends all of his time carving duck decoys, he can carve 25 decoys in a week. Hence, we can set up another equation:
y = 25
Now, let's consider the trade-off between fishing lures and duck decoys. For every 5 duck decoys carved, Mountain Mack must give up 6 fishing lures. This means that for every 5 units of y (duck decoys), he loses 6 units of x (fishing lures). We can express this relationship as:
(5/6)y = x
Now we have a system of equations:
x = 30
y = 25
(5/6)y = x
To solve this system, we can substitute the value of x from the first equation into the third equation:
(5/6)y = 30
y = (6/5) * 30
y = 36
Now that we have the value of y, we can substitute it back into the second equation to find x:
x = 30
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What is the measurement?
Answer:180-124= answer
Step-by-step explanation:I don’t have a caclator srry
helllllpppppppp plzpzlzpzlz
Answer:
b
Step-by-step explanation:
my teacher went over the same on with me
i need help badly pls
Answer:
C. 840 Cubic Inches.
Step-by-step explanation:
write your answer as a fraction or as a whole or mixed number 4 4/5 times 2 1/5
Answer:
It would be 10 14/25
Step-by-step explanation:
You could use a calculator for this, but that’d be cheating so let me explain.
We make both of our fractions improper first
4 4/5 = 24/5
2 1/5 = 11/5
We won’t need to change the “bottom number“ since they’re already the same, so let’s multiply them now.
24 x 11 = 264
————
5 x 5 = 24
Ten 24s can fit into 264 so our final number is
10 14/25