Answer: a = [tex]\frac{2}{7}[/tex].
Step-by-step explanation:
10a - 2 = 4a - 1a
10a - 2 = 3a
10a -2 + 2 = 3a + 2
10a = 3a + 2
10a - 3a = 3a -3a + 2
7a = 2
a = [tex]\frac{2}{7}[/tex]
A rectangular corral of 117 square meters is to be fenced off and then divided by a fence into two sections, as shown in the figure to the right. If the cost of fencing for the boundary is $10 per meter and the dividing fence costs $6 per meter, find the dimensions of the corral that minimize the cost of the fencing.
Answer:
the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
Step-by-step explanation:
Let the length of the corral be x, and the width be y. We know that the area of the corral is 117, so:
xy = 117
We also know that the corral is divided by a fence into two sections. Let the length of one section be L, and the width be y. Then, the length of the other section will be x - L, and the width will still be y. The total fencing cost will be:
10(2x + 2y) + 6(L + 2y)
Simplifying this expression, we get:
20x + 32y + 6L
Using the area equation, we can rewrite this as:
20x + 32(117/x) + 6L
To minimize the cost, we need to take the derivative of this expression with respect to L, and set it equal to zero:
d/dL [20x + 32(117/x) + 6L] = 6 = 0
Solving for L, we get:
L = x/2
Therefore, the two sections of the corral will have equal length. Substituting this value of L into the expression for total fencing cost, we get:
20x + 32y + 3x
Simplifying this, we get:
23x + 32y
Using the area equation to substitute for y, we get:
23x + 32(117/x)
Taking the derivative of this expression with respect to x, and setting it equal to zero, we get:
23 - 3744/x^2 = 0
Solving for x, we get:
x = sqrt(3744/23) ≈ 17.91
Substituting this value of x into the area equation, we get:
y = 117/x ≈ 6.54
Therefore, the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
Prove the following: In a semigroup (written multiplicatively) multiplication of subsets is associative?
Therefore , the solution of the given problem of unitary method comes out to be x = (ab)c = a(bc) .
An unitary method is what?The job can be finished by multiplying the variable information obtained using this kind of nanosection alongside the results of the two people who used the unilateral approach. In essence, this mean that whenever a desired item happens, either the chosen entity is described or the tone of both commercial manufacturing is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.
Here,
We must demonstrate that the following formula holds for any subsets A, B, and C of S in order to demonstrate that multiplication of subsets is associative:
=> (AB)C = A(BC)
where AB and BC stand for the sets created by increasing all of the elements in A by all of the elements in B, and vice versa.
We must demonstrate that every element on the left-hand side is also an element on the right-hand side and vice versa in order to demonstrate that (AB)C = A(BC).
Let x represent any one of the (A*B)C elements. If a, b, and c are all in A, then x can be expressed as
=> x = (ab)*c by definition. * being associated with S gives us:
=> x = (ab)c = a(bc)
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Ron has an average of 83.5 on the first four mathematics tests this marking period. He needs an average of 85 to make the honor roll. If there is only one more test this marking period, what score will Ron need to earn on the last test to give him average of 85? Show your work and explain how you arrived at your answer.
Answer: 86.5
Step-by-step explanation:
(83.5 + x )/2= 85
2(85)= 83.5 + x
170-83.5 =x
x= 86.5
Jillian measures two line segments. Segment A is 12.4 centimeters long and segment B is
4 centimeters in length. Which best represents the ratio of the length of segment A to the length
of segment B?
4
1
3.1
3.1
3.1 best represents the ratio of the length of segment A to segment B.
What is ratio?
By comparing two amounts of the same unit and finding the ratio, one can determine how much of one quantity is included in the other.
We are given that Jillian measures two line segments.
The length of Segment A is measured as 12.4 centimeters and the length of Segment B is measured as 4 centimeters.
So, on comparing both the lengths, we get
⇒12.4 : 4
⇒124 : 40
⇒3.1
Hence, 3.1 best represents the ratio of the length of segment A to segment B.
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Sanjay attempts a 49-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.
Sanjay kicks the ball from the ground with an initial velocity of 73 feet per second, at an angle of 34° with the horizontal.
What is true of Sanjay's attempt?
Responses
The kick is not successful. The ball is approximately 5 feet too low.
The kick is not successful. The ball is approximately 8 feet too low.
The kick is not successful. The ball is approximately 2 feet too low
The kick is good! The football clears the crossbar by approximately 5 feet.
In the above prompt involving a trajectory calculation, the correct option is: "The kick is not successful. The ball is approximately 5 feet too low." (Option A)
What is the rationale for the above response?x component of trajectory = 73 cos 34 f/s
Now how long will it take to travel 49 yards (= 147 feet) ?
147 / (73 cos 34) = 2.43 seconds
Initial y component of trajectory = 73 sin 34 f/s = 40.82 f/s
but this velocity is acted upon by gravity
y = y0 + vot - 1/2 a t^2
y0 = 0
Now we need to know the y value at 2.43 seconds to see if it will clear the uprights.
y = 40.82 (2.43) - 1/2 (32.174)(2.43)2
= 4.2 Feet
Thus, it is correct to state that the "The kick is not successful. The ball is approximately 5 feet too low."
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-5/8 - -4/3 in simplest form
Answer:
To subtract two fractions, you need to have a common denominator. The common denominator for 8 and 3 is 24.
-5/8 = -15/24 (multiply both the numerator and denominator by 3)
-4/3 = -32/24 (multiply both the numerator and denominator by 8)
Now, we can subtract the two fractions by subtracting their numerators while keeping the common denominator.
-15/24 - (-32/24) = -15/24 + 32/24 = 17/24
Therefore, -5/8 - -4/3 = 17/24 in its simplest form.
How does the slope of the red triangle compare to the slope of the blue triangle 
A: the slope of the blue triangle is twice the slope of the red triangle
B: the slope of the red triangle steeper than the slope of the blue triangle
C: the slopes of the two triangles are the same
D: the slope of the red triangles have the slope of the blue triangle
Hence, in answering the stated question, we may say that C: the two graphs triangles' slopes are the same.
What is graphs?Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.
According to the image you gave, both the red and blue triangles have the same slope. As a result, the solution is:
C: the two triangles' slopes are the same.
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Need help my assignment is due in an hour. Please will be appreciated!
Answer:
a)g(x) = 2f(x+1)
B) the point (-1, 3) would end up at (-4, 1) on the new graph.
Step-by-step explanation:
Ramona has saved $63. She has saved 3 times has much
money as Luke. How much money has Luke saved?
Answer:
Luke has saved $21
Step-by-step explanation:
Answer:
According to the problem, Ramona has saved 3 times as much money as Luke, so:
Ramona's savings = 3x
Luke's savings = x
The problem tells us that Ramona has saved $63, so we can write an equation:
3x = 63
To solve for x, we can divide both sides by 3:
x = 21
Therefore, Luke has saved $21.
Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values.
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
(b). f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
(c). B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).
Are the functions equal in the domains?The first one is:
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.
b) f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
These are different, if x = 1 and y = -1
f(1, - 1) = |1 - 1| = 0
g(1, -1) = |1| + |-1| = 2
c) B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
This is clearly false, when x and y are 0 and 0 we have:
f(0, 0) = (1 - 0, 1 - 0) = (1, 1)
While g gives:
g(0, 0) = (0, 0)
These functions are different.
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PLEASE HELP QUICK 30 POINTS
What is the relationship between the radian measure of an angle and the length of the arc intercepted by that angle on the unit circle?
The radian measure of an angle is directly proportional to the length of the arc intercepted by that angle on the unit circle.
What is proportional?Proportional is a mathematical concept that describes the relationship between two or more values that have a constant ratio. It is commonly used to describe the relationship between two or more variables, such as the size of an object in relation to another or the amount of a certain item in relation to the total amount. In proportionality, the ratio of the amounts remains consistent, no matter what the size of the values.
This means that as the angle increases, so does the length of the arc. This is because the length of an arc is determined by the angle measure of the central angle created by the arc, and the radian measure of an angle is the ratio of the arc length to the radius of the circle. Therefore, if the angle measure increases, so does the arc length.
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What is the longest flagpole (in whole feet) that could be shipped in a box that measures 2 ft by 2 ft by 15 ft?
The longest flagopole that could fit in the box is 15.26 feet
What is the longest flagopole that could fit in the box?The longest flagopole would have a length equal to the diagonal of the box.
It goes, lengthwise, from one vertex to the opposite vertex, and if the dimensions of the box are x, y, z, then the diagonal is:
d = √(x² + y² + z²)
In this case the box is 2ft by 2 ft by 15ft, then the diagonal is:
d = √(2² + 2² + 15²) = 15.26
That is the maximum length that can fit in the box, 15.26ft
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Calculate the size of one exterior angle and one exterior angle of a regular ten-sided shape (decagon)
Answer:
36∘
Step-by-step explanation:
Decagon has ten sides and ten angles. All these sides and angles are equal to each other. Therefore, the measure of each exterior angle of a regular decagon is 36∘
(b). A competitive market has the demand schedule p=420-2q and the supply schedule p= 60+ 4q where p is measured in naira. (i) Find the equilibrium values of p and q. (ii) What will happen to these values if the government imposes a tax of N24 per unit on q?
1. The equilibrium quantity = 60, the equilibrium price = 300
2. If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
How to solve for equilibriumAt equilibrium we have P = Q
that is price is equal to quantity. Such that we would have:
420-2q = 60+ 4q
take the like terms
420 - 60 = 4q + 2q
360 = 6q
q = 360 / 6
q = 60
The equilibrium quantity = 60 then equilibrium price =
420-2q
420 - 2 * 60
300
The equilibrium price is 300
2. If the government imposes 24 dollar per unit
420-2q = 60+ 4q + 24
420 - 2q = 84 + 4q
420 - 84 = 4q + 2q
336 = 6q
56 = q
420-2 * 56
p = 308
If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
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I’s it yes or no because you have to justify the answer
Yes, both triangles are similar.
What is similar triangle?Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.
In ΔABC,
AC² = 36² +15²
AC² = 1521 = 39²
AC = 39
In ΔXYZ,
XY² = 24² +10²
XY² = 676 = 26²
XY = 26
If the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.
AB/XZ = BC/YZ = AC/XY
15/10 = 36/24 = 39/26
3/2 = 3/2 = 3/2
Here we can see that the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.
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Find the area of the triangle.
Easy points!
Answer:
53.06 ft^2
Step-by-step explanation:
Calculate semi perimeter and use Scalence triangle area formula
Semi perimeter: a+b+c/2
Area of Scalence triangle: √s(s-a)(s-b)(s-c). {where s=semi perimeter}
Answer: I don't know
There are rectangular cards divided into 4 equal cells with different shapes
, , , drawn in each cell. Cards can be placed side by side only if the
same shapes appear in adjacent cells on their common side. 9 cards are used
to form a rectangle as shown in the figure. Which of the following cards was
definitely NOT used to form this rectangle
The sοlutiοn οf the given prοblem οf rectangle cοmes οut tο be E is the answer.
A rectangle is what?In the Euclidean plane, a rectangle is a square with fοur perpendicular edges. It is alsο referred tο as an equiangular parallelοgram οr a seemingly equal-sided rectangle. The trapezοid can alsο have a straight edge. Fοur οf the sides οf a square are equal in length. Rectangular quadrilaterals have fοur equal sides and fοur 90° edges. Its name is sοmetimes "rectangular trapezοid" as a cοnsequence.
Here,
Due tο the shared suits οf the adjacent sectiοns.
Therefοre,
Case 1: Triangles and circles must be arranged in a series fοr hοrizοntal fitting.
Therefοre,
A, C, and D are excellent οptiοns. Sο they can't be the sοlutiοns.
Again,
Case 2.
Tο accοmmοdate vertically,
Rectangle and Triangle need tο be in the same cοlumn. And B is where that is happening.
sο that,
The οnly exceptiοn is:
"E" is the answer.
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Complete question:
Which equation represents the vertex form of the equation y = x2 + 6x + 5?
The vertex form is:y(x-3)2-4
:) Good luck
Use the method of completing the square to express in vertex form.
Given
[tex]y = x^2 - 6x + 11[/tex]
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
[tex]y = x^2 + 2(- 3)x + 9 - 9 + 11[/tex], then
[tex]y = (x - 3)^2 + 2[/tex]
[tex]\bold{y= (x - 3)2 + 2}[/tex]Please help me find the answer to this question pleaseeee
A five-pound bag of potatoes costs $2.95 in a particular store. What is the unit price of the potatoes per ounce?
Therefore, the unit price of the potatoes per ounce is $0.036875.
What is unitary method?The unitary method is a mathematical technique that involves finding a single unit value in order to solve a problem involving multiple units. In other words, the unitary method involves finding the value of one unit of a given quantity, and then using that value to calculate the value of another quantity that is related to it.
Here,
First, we need to convert pounds to ounces since the unit price is usually measured in terms of ounces. There are 16 ounces in one pound, so:
5 pounds = 5 x 16
= 80 ounces
The bag of potatoes costs $2.95 for 80 ounces, so the unit price per ounce can be found by dividing the total cost by the number of ounces:
Unit price per ounce = Total cost / Number of ounces
Unit price per ounce = $2.95 / 80
= $0.036875
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i don’t know how to do it
The total resistance of three resistors in parallel s 2 Ohms. Option A
What is resistance?Resistance can be defined as the measure of the opposition to current flow in an electrical circuit.
Resistance is measured in Ohms, using the Greek symbol for omega (Ω).
It is also described as the hindrance to the flow of electrons in material.
It is important to note that for resistors in parallel, the total resistance is the reciprocal of the sum of reciprocals of the individual resistors.
This is represented as;
1/Rt = 1/R₁ + 1/R₂ + 1/R₃ ...
Where the variables , 'R' represented the resistors
Now, substitute the values, we have;
1/Rt = 1/4 + 1/8 + 1/8
Find the lowest common multiple
1/Rt = 2 + 1 + 1/8
1/Rt = 4/8
Take the reciprocal of the values
Rt = 8/4 = 2 Ohms
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An integer is 17 more than 4 times another. If the product of the two integers is -15, then find the integers.
Let's use algebra to solve this problem.
Let x be one of the integers, and y be the other integer.
From the problem, we know that:
x = 4y + 17 (one integer is 17 more than 4 times the other)
xy = -15 (the product of the two integers is -15)
We can use substitution to solve for one of the variables. From the first equation, we can write:
y = (x - 17)/4
Substituting this expression for y into the second equation gives:
x(x - 17)/4 = -15
Multiplying both sides by 4 and expanding gives:
x^2 - 17x = -60
Rearranging gives:
x^2 - 17x + 60 = 0
This is a quadratic equation that can be factored as:
(x - 5)(x - 12) = 0
So the solutions are:
x = 5, y = (-12/4) = -3
x = 12, y = (-5/4) = -1.25
Since the problem states that the integers are both integers, the only valid solution is:
x = 5, y = -3
Therefore, the two integers are 5 and -3.
A flower bed is in the shape of a triangle, with a base of 15 feet and a height of 9 feet. What is the area of the flower bed? (4 points)
The area of the flower bed is 67.5 square feet.
An area in mathematics is what?The area of an object is the space that is enclosed by its boundaries. The number of unit squares on the surface of a closed figure determines its area.
The following formula provides the area of a triangle:
(1/2) * Base * Height = Area
Inputting the values provided yields:
Area equals (1/2) * 15 * 9
Dimensions: 67.5 square feet
The flower bed therefore has a 67.5 square foot space.
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Write and solve an equation to answer the question.
What number a is 24% of 25?
Answer:6
Step-by-step explanation:
24------100%
x--------25%
100x=25*24
x=25*24/100=24/4=6
12 1/2 4 7/10 = ? Select one answer. show your work A 7 6/8 B 7 8/10 C 8 6/8 D 8 8/10
According to the question the option C is the correct answer that is 8 6/8 or 8 ¾ calculated by simplifying the fraction.
what is fraction?To represent a whole, every number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of a numerator to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.
To add mixed numbers, we need to first convert any fractions to a common denominator. In this case, we can use 10 as the common denominator.
12 1/2 = 12 + 1/2 = 12 + 5/10 = 12 5/10
4 7/10 = 4 + 7/10
Now we can add the two mixed numbers:
12 5/10 + 4 7/10 = 16 12/10
Simplifying the fraction by dividing the numerator and denominator by their greatest common factor of 2, we get:
16 12/10 = 16 6/5
Therefore, the answer is C) 8 6/8 or 8 3/4.
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Point G' has coordinates (-5, 2). If it was reflected across the y-axis, what were the coordinates of its pre-image?
(-5, -2)
(5, 2)
(2, -5)
(5, -2)
Answer: Second answer, (5,2)
Step-by-step explanation:
To reflect across the y axis, it would be: (x,y) -> (-x,y)
So, (-5,2) reflected across the y axis would be (5,2)
What is the common difference in the arithmetic sequence 10, 8, 6, 4, ...?
1/2
-1/2
-2
2
Answer:
The common difference in an arithmetic sequence is the constant difference between any two consecutive terms. In this sequence, the difference between each pair of consecutive terms is -2, so the common difference is -2.
Therefore, the answer is -2.
please help me i really need help
Answer:
B. (-3, 4)
Step-by-step explanation:
x=0-3=-3
y=0+4=4
(-3, 4)
Answer:
(-3, 4)
Second answer choice
Step-by-step explanation:
The coordinates of A(0, 0) are shifted to the left by 3 units. A shift to the left means the new x- coordinate = old x-coordinate -3 = 0 -3
A shift up means the new y-coordinate = old y-coordinate + 4 + 0 + 4 = 4
Therefore the new coordinates of A are (-3, 4)
solve the system of equations graphed on the coordinate axes below
The solution to the system of equations on the graph is (0, 0)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
y = -2x and y = 4/3x represented on a graph
On the graph, we have two lines that intersect at a point
Using the above as a guide, we have the following:
The point of intersection of lines in a graph is the solution to the graph
In this case, they intersect at (0, 0)
So, the solution is (0. 0)
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Suppose the refills for a particular mechanical pencil
have a mean diameter of 0.5 mm and standard
deviation of 0.007 mm. Refills below 0.485 mm do not
stay in the pencil, while those above 0.520 mm do not
fit in the pencil at all.
What is the probability that a randomly chosen refill will
(Round all answers to nearest thousandths)
a) be too large?
b) be too small?
c) fit correctly?
回
Answer:
the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).
Step-by-step explanation:
We can use the standard normal distribution to solve this problem. We first need to calculate the z-scores for the given diameters.
a) To find the probability that a randomly chosen refill will be too large, we need to find the probability of getting a diameter greater than 0.520 mm.
z-score = (0.520 - 0.5) / 0.007 = 2.857
Using a standard normal table or calculator, we find that the probability of getting a z-score of 2.857 or greater is 0.0021.
Therefore, the probability that a randomly chosen refill will be too large is 0.0021 (rounded to three decimal places).
b) To find the probability that a randomly chosen refill will be too small, we need to find the probability of getting a diameter less than 0.485 mm.
z-score = (0.485 - 0.5) / 0.007 = -2.143
Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.143 or less is 0.0164.
Therefore, the probability that a randomly chosen refill will be too small is 0.0164 (rounded to three decimal places).
c) To find the probability that a randomly chosen refill will fit correctly, we need to find the probability of getting a diameter between 0.485 mm and 0.520 mm.
First, we find the z-scores for each diameter:
z-score for 0.485 mm = (0.485 - 0.5) / 0.007 = -2.143
z-score for 0.520 mm = (0.520 - 0.5) / 0.007 = 2.857
Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.143 and 2.857 is 0.9780.
Therefore, the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).