The opposite of the oppsite of 28,or (-28), is equivalent to the option (c) 28
How to determine the equivalent expressionThe opposite of a number is the number with the opposite sign.
For example, the opposite of 28 is -28, and the opposite of -28 is 28.
So, the opposite of the opposite of 28, or (-28), is the opposite of -28, which is 28.
This means that the answer is (c) 28.
To explain it further, think of the number line. 28 is a positive number, so its opposite is a negative number, which is -28.
Now, the opposite of -28 is a positive number, which is 28. So, the opposite of the opposite of 28 is 28.
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stal Find the Product (X+3÷x)²
the product of (x + 3/x)² is x² + 6 + 9/x².
Why it is and what is Algebra?
To find the product of (x + 3/x)², we can use the formula for squaring a binomial:
(a + b)² = a² + 2ab + b²
In this case, we have a = x and b = 3/x, so we can substitute these values into the formula and simplify:
(x + 3/x)² = x² + 2(x)(3/x) + (3/x)²
= x² + 6 + 9/x²
Therefore, the product of (x + 3/x)² is x² + 6 + 9/x².
Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent numbers and quantities in equations and expressions. The primary goal of algebra is to solve mathematical problems and equations using various operations such as addition, subtraction, multiplication, and division.
Algebraic concepts can be applied to a wide range of mathematical and real-world problems, including geometry, physics, engineering, economics, and statistics.
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Complete question:
Find the product of (x + 3/x)²2.
Please anyone help me with number 2 ? Thank you:))
Answer:
subtract 20; 80, 60, 40
The pattern is to subtract 20 from the previous term.
Next three terms: 20, 0, -20.
Therefore, the sequence continues as follows:
80, 60, 40, 20, 0, -20.
Prove the Converse of the Pythagorean Theorem
The Converse of the Pythagorean Theorem is proved below.
What is Pythagoras Theorem ?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.
To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.
Proof:
Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.
We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:
c² = a² + b² - 2ab cos(C)
Substituting a² + b² = c² into this equation, we get:
c² = c² - 2ab cos(C)
2ab cos(C) = 0
cos(C) = 0
Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.
Thus, this completes the proof of the converse of the Pythagorean theorem.
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I need help due tomorrow so please help I’ve been trying for a while so can I get some help?
Answer:
It will be same as angle x because they are on the same line and are alternative angles
So, measurement of angle u will be u=152
Step-by-step explanation:
Hope this helps:)
Good luck
SOLVE THIS BUT I DON'T WANT ANSWER I WANT SOLVING AND ANSWER
50PTS
WILL MARK AS BRAINLIEST
50/1.428
Answer:
Alright
Step-by-step explanation:
50/1.428
Multiply the numerator by the denominator to get 50000/1428
Set equation up in long division format
Divide 50000 by 1428 to get 3
Divide 7160 by 1428 to get 5
Divide 200 by 1428 to get 0
Divide 2000 by 1428 to get 1
Divide 5720 by 1428 to get 4
Divide 80 by 1428 to get 0
Divide 800 by 1428 to get 0
35.014
A charity organization has to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets they were still at a net loss of $800 (due to the production costs). They sold each tickets for $70.
the organization needs to sell at least 22 tickets to break even.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let C be the total production cost and n be the number of tickets sold.
From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:
10(70) - C = -800
Simplifying, we get:
C = 1500
This means that the total production cost was $1500.
The revenue from selling n tickets at $70 per ticket is given by:
R = 70n
Substituting the values of R and C, we get:
70n = 1500
Solving for n, we get:
n = 1500/70 = 21.43
Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.
Therefore, the organization needs to sell at least 22 tickets to break even.
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Jane made $143 for 11 hours of work. At the same rate, how many hours would she have to work to make $169 ?
13
First, we divide to figure out how much Jane makes an hour
143 ÷ 11 = 13
Second, we multiply multiply by 13 until we get 169
13 × 13 = 169
So Jane will make 169 dollars in 13 hours
Answer:
13 Hours
Step-by-step explanation:
$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169
$169 ÷ $13 = 13 hours
Extended sheet of paper in Europe is 21.0 CM wide and 29.7 cm long which has a greater area the standard sheet of paper with using stage or the standard sheet of paper in Europe explain and show your reasoning
the extended sheet in Europe has a greater area than the standard letter size paper. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.
What is area of rectangle ?area of rectangle = length * breath
The standard sheet of paper commonly used in the United States and Canada is known as "Letter" size paper, which measures 8.5 inches by 11 inches (21.59 cm x 27.94 cm). To compare the area of this paper to the extended sheet of paper used in Europe, we need to convert the dimensions to centimeters.
So, the area of the standard letter size paper in centimeters would be:
21.59 cm x 27.94 cm = 603.78 square cm
On the other hand, the extended sheet of paper in Europe measures 21.0 cm by 29.7 cm. Therefore, its area would be:
21.0 cm x 29.7 cm = 623.70 square cm
the extended sheet of paper in Europe has a greater area than the standard letter size paper used in the United States and Canada. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.
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Find the value of w and x in the following diagram zoom in
5
32⁰
W
6
to
Round your answers to the nearest hundredth.
The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.
How to determine the valueIt is important to note that there are different types of trigonometric identities are;
sinetangentcosinesecantcosecantcotangentFrom the image shown, we have;
Using the sine identity
sin θ = opposite/hypotenuse
sin 32 = w/5
find the value
w = 2. 649
To determine the value of angle x , we have;
Using the sine identity
sin x = w/6
sin x = 2. 649/6
sin x= 0. 4416
Take the sine inverse
x = 26. 206 degrees
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Provide a trigonometric equation. Considering only the space between = 0 and 2π the equation must only have solutions at x = 1 and x = 2. Explain your thought process and the work you did to create the equation. You may round decimal values to 3 places.
Therefore , the solution of the given problem of equation comes out to be f(x) = sin(/2 x) (when x = 1 or 2).
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.
Here,
The goal is to construct a trigonometric equation with only answers at
x = 1 and x = 2.
f(x) = A sin(Bx+C+D)
=> B + C + D + A = 0 (equation 1)
=> Equation 2: A sin(2B + C + D) = 0
=> B + C sin A = 0 (equation 3)
=> Sin(2B+C) = A = 0 (equation 4)
Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:
=> B + C = nπ (equation 5)
=> 2B + C = mπ (equation 6)
with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:
=> B = (m - n)π/2 (equation 7)
=> C = nπ - B (equation 8)
=> When x = 1, C = /2 - /2 = 0.
=> When x = 2, C = − /2 = 3/2.
Thus, the result is as follows:
when f(x) = sin(/2 x) (when x = 1 or 2)
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what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).
How to obtain the coordinates of point P?The coordinates of point P are obtained applying the proportions in the context of the problem.
P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:
P - A = 2/3(B - A)
Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:
x - 9 = 2/3(-6 - 9)
x - 9 = -10
x = -1.
The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:
y + 8 = 2/3(7 + 8)
y + 8 = 10
y = 2.
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a fourth grade class is hosting a pancake breakfast fundraiser adult tickets are $10 each and children tickets are$6 each the class sells a total of 105 the total amount raised is 870how many adult tickets and how many children tickets were sold
60 adult tickets and 45 children tickets were sold.
How to solve this problemLet's use algebra to solve the problem:
Let x be the number of adult tickets sold.
Let y be the number of children tickets sold.
From the problem, we know that:
x + y = 105 (total tickets sold)
10x + 6y = 870 (total amount raised)
We can solve this system of equations by using elimination:
Multiply the first equation by 6: 6x + 6y = 630
Subtract the second equation from the first: 4x = 240
Solve for x: x = 60
Now we can use x to find y:
x + y = 105
60 + y = 105
y = 45
Therefore, 60 adult tickets and 45 children tickets were sold.
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Mason’s pumpkin had a weight of 3 kg 250 g in August and 4 kg 125 g in October. What was the difference in weight from August to October?
dose 2+2=4?.............................
Answer:
[tex]yeah \: 2 + 2 = 4[/tex]
why is ÷ by five a step, there did this 5 come from if its not in the inequality?
Answer:
You divide by five because it's the common factor of 5 and 15 in the 4th line of work and the goal is to solve for x. The only way to get x alone in the inequality 5x>15 is to divide each side by 5. This would give you x and 3, hence the answer: x > 3
[tex]\frac{5x}{5} =x\\\\\frac{15}{5} =3[/tex]
PLEASE HELP ASAP ITS DUE IN AN HOUR
Answer:
[tex]3^2-5[/tex]
Step-by-step explanation:
Given equation:
( 3 - 2^2) + 5
3 - 4 + 5 (Simplify exponent)
-1 + 5 (Solve 3 - 4)
4 (Simplified)
Evaluation
2^2 + 5
4 + 5
9 (not the answer)
3^2 - 5
9-5
4 (answer)
Find the equation of the line containing the point
P(−2, 3)
and perpendicular to the graph of
3x + 9y = −2.
Answer:
Step-by-step explanation:
y = 3x + 9
A(-4,4) B(2,7) C(2,1) where is the orthocenter
Answer:
Step-by-step explanation:
(1\2, 4) = (0.5, 4)
How many 50ml can be filled from 5L
A cone has a volume of 300 in³ and a diameter of 10 in. What is the height and slant height of the cone?
The height and slant height of the cone is 7.64 inches and 9.38 inches respectively.
What is volume of cone ?
The volume of a cone is the amount of space occupied by the cone and is given by the formula:
[tex]Volume of a cone = (1/3) * pi * r^2 * h[/tex]
where pi is the mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.
The formula for the volume of a cone can be derived by using calculus or by dividing the cone into a series of infinitesimally thin circular disks, calculating the volume of each disk, and summing up the volumes to obtain the total volume of the cone
According to the question:
To solve this problem, we need to use the formulas for the volume and surface area of a cone:
[tex]Volume of a cone = (1/3) * pi * r^2 * h[/tex]
Surface area of a cone = [tex]pi * r * (r + \sqrt{h^2 + r^2})[/tex]
where r is the radius of the base, h is the height, and pi is a mathematical constant approximately equal to 3.14.
First, we need to find the radius of the cone. The diameter is 10 inches, so the radius is half of that, or 5 inches.
The volume of the cone is given as 300 cubic inches. We can plug in the values we know and solve for the height:
[tex]300 = (1/3) * pi * 5^2 * h[/tex]
[tex]h = 300 / ((1/3) * pi * 5^2)[/tex]
[tex]h \approx 7.64 inches[/tex]
So the height of the cone is approximately 7.64 inches.
Next, we can use the Pythagorean theorem to find the slant height of the cone.
[tex]slant height^2 = radius^2 + height^2[/tex]
[tex]slant height^2 = 5^2 + 7.64^2[/tex]
[tex]slant height \approx 9.38 inches[/tex]
So the slant height of the cone is approximately 9.38 inches.
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complete part A and B
The corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.
The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.
Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.
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A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
Out of 144 children who have school dinners, 1/3 chose pasta, 1/4 chose jacket potatoes and the rest chose curry. How many chose curry?
Answer:
A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us
Step-by-step explanation:
i may be wrong but I tried
21 20 18 15 11 ? WHAT COMES NEXT
Answer: 6
Step-by-step explanation:
21 - 1 = 20
20 - 2 = 18
18 - 3 = 15
15 - 4 = 11
11 - 5 = 6
What is the mode of Region A?
The mode for the region A is 2.6.
What exactly is mode?
In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.
To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.
The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.
Now,
As given Values for Region A are
2.3 2.5 2.6 2.6 2.6 2.7 2.7 2.8
Here 2.6 comes most times or frequency of 2.6 is highest of all.
Hence,
The mode for the region A is 2.6.
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Please help
Find the surface area (show work)
Answer:
148 cm²
Step-by-step explanation:
You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.
AreaThe formula is shown in your problem statement.
It can be made easier to compute using a little rearranging:
SA = 2LW +2LH +2WH
SA = 2(LW +LH +WH)
SA = 2(LW +H(L +W))
The choice of dimensions for L, W, and H doesn't matter.
SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²
The surface area is 148 cm².
Leo is drawing a map of the recess area at his school on a coordinate grid. If the scale of the map is 1 grid = 5 feet, what is the distance from the jungle gym to the four-square courts? Round your answer to the nearest tenth if necessary.
if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them. the four-square courts are approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
What are the coordinates of two points?The distance formula is:
[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.
For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:
[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]
[tex]= sqrt(6^2 + 4^2)[/tex]
[tex]= sqrt(36 + 16)[/tex]
[tex]= sqrt(52)[/tex]
[tex]\approx 7.2[/tex]
Therefore, the distance from the jungle gym to the four-square courts is approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
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2 logx 2 + logx 6 = 2
I really need this answer on properties of logarithms: practice
Answer:
Step-by-step explanation:
Simplify the expressionApply the logarithm power identityApply the logarithm product identitySimplify the expression2Exponentiate both sides
log10(4x8)=2log10(48)=2
48=102
x=258=258√
the sum of
44+45+46+47+...+131
Answer:313:)
Step-by-step explanation:
A particle has velocity function
v(t) = 1 - 2t cms-1
is initially 2 cm to the right of 0.
The formula for the displacement function (t).= s(t) = t - t^2 = 2 cm
Find the total distance travelled in the first second of motion.
answer = 1/2 cm but unsure how to solve
Please show procedure
Answer:
Step-by-step explanation:
To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.
The particle starts 2 cm to the right of 0, so its position function is given by:
s(t) = t - t^2 + 2
The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:
distance = |s(0.5) - s(0)|
We have:
s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm
s(0) = 0 - 0^2 + 2 = 2 cm
So, the distance traveled during the first half-second is:
|2.25 - 2| = 0.25 cm
To find the total distance traveled in the first second, we double this distance:
total distance = 2 * 0.25 = 0.5 cm
Therefore, the total distance traveled in the first second is 0.5 cm.