Given is square root of a negative real number, i.e. [tex] \sqrt{-0.25} [/tex]
When we find square root of positive real numbers, we get Real answers.
But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.
For square root of -1, we use english letter 'i' called Imaginary unit i.e. [tex] \sqrt{-1} = i [/tex]
Now we can use -0.25 = -1 x 0.25
[tex] \sqrt{-0.25} =\sqrt{-1*0.25} \\\\
\sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\
\sqrt{-0.25} =i*0.5 \\\\
\sqrt{-0.25} =0.5i [/tex]
Hence, "0.5i" is the final answer.
The square root of -0.25 is not a real number because the square root of a negative number is not defined within the set of real numbers.
The square root of a negative number is not a real number. In the case of √(-0.25), the expression is undefined within the set of real numbers because taking the square root of a negative number results in a complex number. The square root of a negative number is typically represented using the imaginary unit "i" in the complex number system. Therefore, √(-0.25) is not a real number.
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Please help! I don't get it! It is confusing me!
Create a function with roots x = 3 and x = 2 and x = -3
The average of their maximum speed was 260 KM per hour if double Malcolm’s maximum speed would be 80 KM per hour more than Robbins maximum speed what were Malcolm and Robbie’s maximum speed
For which intervals is the function positive?
If sin^2(x) - 2sin(x) = 2, then sin(x) = _____.
write parametric equations of the line with the equation 2x+3y=5
The question is asking to find the parametric equations of the line with the equation 2x+3y=5, which are x=t and y=(5-2t)/3 where t is a parameter.
Explanation:To obtain parametric equations for the line 2x + 3y = 5, first, solve for y, yielding y = (5 - 2x)/3. Introduce a parameter, often denoted as t, representing the 'time' a point travels on the line. When x = t, substitute it into the y equation, resulting in y = (5 - 2t)/3. Hence, the parametric equations for the line are x = t and y = (5 - 2t)/3. These equations express x and y in terms of the parameter t, allowing the representation of various points on the line as t varies, providing a concise and dynamic description of the line's behavior in a parametric form.
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Help me please l’m correct or wrong?
Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?
A. 25%
B. 33%
C. 67%
D. 75%
What is the range of f(x) = (3/4)^x – 4?
Answer:
answer is A bud
Step-by-step explanation:
i just took the test lol
Please answer! Confusing me. 20 points.
Solve each of the following equations. Show its solution set on a number line. Check your answers.
1/2 − x/3 = 5/6
The 1/2 and x/3 is in the absolute value lines.
To solve the equation with absolute value expressions, isolate the absolute value terms and solve two separate equations. The solutions are x = -1 and x = 1.
Explanation:To solve the equation 1/2 - x/3 = 5/6 with the absolute value expressions, we need to isolate the absolute value terms and solve two separate equations. First, rewrite the equation as |-x/3| = 5/6 - 1/2. Since the absolute value of a number is always positive, we can remove the absolute value symbols by considering the positive and negative cases separately.
For the positive case, we have -x/3 = 5/6 - 1/2. Simplifying, we get -x/3 = 1/3. Multiplying both sides by -3, we find x = -1. For the negative case, we have -(-x/3) = 5/6 - 1/2. Simplifying, we get x/3 = 5/6 - 1/2. Combining like terms, we have x/3 = 1/3. Multiplying both sides by 3, we find x = 1. Therefore, the solution set to the equation is {-1, 1}.
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A rectangle has an area of 180 cm22 and a perimeter of 58 cm. what are its dimensions?
To find the dimensions of a rectangle with a given area and perimeter, set up and solve a system of equations.
Explanation:Let's assume that the length of the rectangle is x cm and the width is y cm.
Given that the area of the rectangle is 180 cm², we have the equation x*y = 180.
Also, the perimeter of the rectangle is 58 cm, which gives us the equation 2x + 2y = 58.
By solving these two equations simultaneously, we can find the dimensions of the rectangle.
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A bird flies across your backyard at 4.0 feet per second. How many miles can the bird travel in 2.1 hours (rounded to the nearest tenth)?
A) 2.8 mi
B) 3.2 mi
C) 5.7 mi
D) 9.7 mi
The bird can travel approximately 5.7 miles in 2.1 hours.
Explanation:To find the number of miles the bird can travel in 2.1 hours, we need to convert the speed from feet per second to miles per hour. There are 5280 feet in a mile and 3600 seconds in an hour, so the bird's speed is 4.0 * 3600 / 5280 = 2.727 miles per hour. Multiplying this speed by 2.1 hours gives us a total distance of 2.727 * 2.1 = 5.7207 miles, rounded to the nearest tenth, which is 5.7 miles. Therefore, the answer is option C) 5.7 mi.
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What happens to the area of a circle when the radius is doubled? (1 point) it is doubled?
Find the SUM of the first 40 terms of the arithmetic series:
17 + 24 + 31 + 38 + ...
Hints:
1) find the 40th term using formula
2) find the sum of all 40 terms using formula
297
6147
6280
6140
What is the value of x in the proportion StartFraction 2 x plus 7 over 3 x minus 4 EndFraction equals 11 over 2?
A. 2
B. 58
C. eleven-twenty-ninths
D. two-fifths
Okay does anyone even know what this means LOL
Evaluate.
6! + 2! = [?]
Can you help me for question 8??? I really confused
1.) A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone? A.) 2cm B.) 3cm C.) 4cm D.) 5cm
2.) A cylinder with a radius of 1cm and a height of 21cm has the same volume as a cone with a height of 7cm. What is the radius of the cone? A.) 3cm B.) 5cm C.) 7cm D.) 9cm
Use the rules of significant figures to answer the following question: 43.5694•22.07
Answer:
961.6
Step-by-step explanation:
43.5694 22.07 = 961.6
The base of a soup can has an area of 9π in
2
and a height of 10
in. Find the area for the label needed to wrap around the can with
no overlaps.
soup can is in the shape of cylinder
given, base area = 9 pi
base area = area of circle = pi * r^2 = 9 * pi
r = 3
total surface area of cylinder = 2 *pi*r(h+r)
= 2*3(10+3) pi= 78 pi
area for the label needed to wrap around the can with
no overlaps 78 pi inches^2
how many liters will a quart (dry measure) hold?
Answer:
0.94635 Liters in a Quart
Step-by-step explanation:
A basketball coach is purchasing 12 shirts for her team, each with a different number. At the checkout counter, the clerk places 5 of the shirts in the first bag. How many different ways can a group of 5 shirts be placed in that first bag? A. 19,008
B. 60
C. 792
D. 95,040
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Total number of shirts purchased for her team = 12
Number of shirts places in the first bag = 5
We need to find the number of ways a group of 5 shirts be placed in that first bag.
We will use "Combination" to find the number of different ways :
As we know the formula for Combination.
[tex]^nC_r=\frac{n!}{r!\times (n-r)!}\\\\here, n=12\\\\r=5\\\\So,\ it\ becomes,\\\\^{12}C_5=\frac{12!}{5!\times 7!}\\\\=\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2}\\\\=792[/tex]
Hence, there are 792 ways to do so.
Therefore, Option 'C' is correct.
Delaney gave her hair stylist a $4.60 tip. The tip was 5% of the cost of the haircut. Write an equation to find b, the cost of the haircut.
The total cost of haircut is $92.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
We have,
Delaney gave her hair stylist a $4.60 tip.
The tip was 5% of the cost of the haircut.
let the cost of haircut be b.
So, 5% of b = 4.60
5/100 b = 4.6
b= 460 / 5
b = $92.
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What is the range
of this function?
-2 3
3 9
4 12
2
A. {3}
B. {3,9,12}
C. {-2,2,3,4}
D. {-2,2,3,4,9,12}
Answer: B
Step-by-step explanation:
Answer:
B. {3,9,12}
Step-by-step explanation:
test approved
Find the volume of the composite space figure to the nearest whole number.
The volume of the composite solid is approximately 438 mm³.
Given is a composite solid, composed of a half cylinder [cut vertically] as a roof and a rectangular prism of dimension 5 mm, 11 mm, 6 mm, as base.
We need to find the volume of the solid.
So, to find the volume of the whole solid we will just add the volume of the half cylinder and the rectangular prism.
Volume of a rectangular prism = length × width × height
Here, Length = 11 mm, Height = 6 mm and Width = 5 mm.
Volume of cylinder = π × radius² × height
Since here the cylinder is half so the volume = [π × radius² × height] ÷ 2
The diameter of the cylinder is the width of the prism, height is length of the prism,
Now, let calculate the volume,
Volume = [5 × 11 × 6] + [(3.14 × 2.5² × 11) ÷ 2]
Volume = 330 + 108
Volume = 438 mm³
Hence the volume of the composite solid is approximately 438 mm³.
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solve for 9(p-4)=-18
To solve the equation 9(p-4)=-18, distribute the 9, then add 36 to both sides, and finally, divide by 9 to isolate p, resulting in p = 2.
To solve the equation 9(p-4)=-18, we need to isolate the variable p. Here's a step-by-step solution:
First, let's distribute the 9 to both terms inside the parentheses: 9 times p - 9 times 4 = -18, which simplifies to 9p - 36 = -18.Next, we'll add 36 to both sides of the equation to move the constant term to the right side: 9p - 36 + 36 = -18 + 36, resulting in 9p = 18.Lastly, we'll divide both sides by 9 to get p by itself: 9p / 9 = 18 / 9, which gives us p = 2.The solution to the equation 9(p-4)=-18 is p = 2.
In ΔPQR, find the measure of ∡ P. (4 points)
Triangle PQR where angle Q is a right angle. PQ measures 33 point 8. PR measures 57 point 6. Measure of angle P is unknown
In a right triangle, use the Pythagorean theorem and the cosine function to find the measure of angle P.
Explanation:In triangle PQR, where angle Q is a right angle, we can use the Pythagorean theorem to find the measure of angle P. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, PR is the hypotenuse and PQ and QR are the other two sides.
Using the given measurements, PQ = 33.8 and PR = 57.6. To find the measure of angle P, we can use the cosine function. Cosine is the ratio of the adjacent side to the hypotenuse, so we have cos P = PQ / PR.
Plugging in the given values, we have cos P = 33.8 / 57.6. Using a calculator, we find that cos P ≈ 0.586. To find the measure of angle P, we can take the inverse cosine of this value, which is approximately 54.3 degrees.
Help me understand this
What is the value of x
PLEASE HELP NOW PLEASE
The area of a rectangle is 96 square feet. The ratio of the width to the length is 2:3. The width of the rectangle is ______ feet.
The width of a rectangle with an area of 96 square feet and a width to length ratio of 2:3 is 8 feet.
Explanation:In this mathematics problem, we are given the area of a rectangle (96 square feet) and the ratio between its width and length (2:3). The equation representing the area of a rectangle is Length x Width. Given that the area of the rectangle is 96 sq ft, and the ratio of width to length is 2:3. Let's assign the width to be 2x and the length to be 3x. Then, you would multiply these two together and set it equal to the area: (2x) * (3x) = 96 square feet. Simplifying this gives 6x2 = 96. Dividing both sides by 6 gives you x2 = 16. Taking the square root of both sides gives x = 4. Therefore, the width of the rectangle, which is 2x, is 2 * 4 = 8 feet.
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