To simplify negative 5 minus the square root of negative 44, you need to use imaginary numbers. The expression simplifies to -5 minus 2i√11. Hence, the correct answer is Option B.
To simplify
negative 5 minus the square root of negative 44, we need to work with imaginary numbers. Recall that the square root of -1 is defined as i, which is the imaginary unit. Using this, we can simplify the given expression step-by-step:
Recognize that
√-44 can be written as
√(-1 × 44).
Since
√(-1 × 44) = √(-1) × √44, and
√(-1) = i, we get
i × √44.
Now, we simplify
√44:
√44 = √(4×11) = 2√11.
Therefore,
i × √44 = 2i√11.
Putting it all together,
-5 - √-44 becomes
-5 - 2i√11.
Hence, the correct answer is
Option B. negative 5 minus 2 i times the square root of 11.
The fully simplified form of the expression is [tex]-25 - 14i \sqrt{11}[/tex]
To simplify the expression [tex]-5 - \sqrt{-44} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \cdot \sqrt{11} - 5 - 2 \cdot \sqrt{11} i[/tex], we will follow these steps:
Understanding Square Roots of Negative Numbers:
The square root of a negative number can be written using the imaginary unit [tex]i[/tex], where [tex]i = \sqrt{-1}[/tex].
Thus, we can rewrite [tex]\sqrt{-44}[/tex] as follows:
[tex]\sqrt{-44} = \sqrt{-1 \cdot 44} = \sqrt{-1} \cdot \sqrt{44} = i \cdot \sqrt{44}[/tex]
Note that [tex]\sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11}[/tex].
Thus,
[tex]\sqrt{-44} = 2i \sqrt{11}[/tex]
Now substituting this into the expression gives us:
[tex]-5 - 2i \sqrt{11} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \sqrt{11} - 5 - 2\sqrt{11} i[/tex]
Combining Like Terms:
Now combine all the real parts and the imaginary parts separately in the expression:
Real Part:
[tex]-5 - 5 - 5 - 5 - 5 = -25[/tex]
Imaginary Part:
[tex]-2i\sqrt{11} - 4i\sqrt{11} - 4i\sqrt{11} - 2i\sqrt{11} - 2i\sqrt{11}[/tex]
Combining these gives:
[tex]-2i \sqrt{11} - 4i \sqrt{11} - 4i \sqrt{11} - 2i \sqrt{11} - 2i \sqrt{11} = -14i\sqrt{11}[/tex]
Final Result:
Combining the real and imaginary parts, we get:
[tex]-25 - 14i \sqrt{11}[/tex]
In equilateral ΔABC, AD, BE, and CF are medians. If AC = 22, then BD
Answer:
11.
Step-by-step explanation:
Basically without calculus we have the answer. As ABC is a equilateral triangle we have that then medians cut each side at the half. So, as you can see in the picture, BD=x is a half of BC and ABC is equilateral so BC=AC=22. Then, BD=22/2=11.
A CD usually sells for $14.00. If the CD is 20% off, and sales tax is 8%, what is the total price of the CD, including tax?
Final answer:
To find the total cost of a CD with a 20% discount and 8% sales tax, calculate the discount on the original price, subtract it to find the discounted price, then add the sales tax to this discounted price. The total cost comes out to $12.10.
Explanation:
Calculating the Total Cost of a CD Including Discount and Sales Tax
Firstly, to determine the sale price of the CD that usually sells for $14.00 with a 20% discount, we apply the discount percentage to the original price. We convert 20% to its decimal form, which is 0.20, and multiply by $14.00 to find the amount discounted: $14.00 × 0.20 = $2.80. Subtracting this discount from the original price, $14.00 - $2.80, gives us the discounted price of the CD, which is $11.20.
Next, to calculate the total cost including a sales tax of 8%, we first convert the tax rate to its decimal form, 0.08, and multiply it by the discounted price: $11.20 ×0.08 = $0.896. Rounding to the nearest cent, the sales tax is approximately $0.90. Adding the sales tax to the discounted price, $11.20 + $0.90, gives us the total cost of the CD, which is $12.10.
Therefore, the total price of the CD, including the 20% discount and the 8% sales tax, is $12.10.
If the graph of y=cosθ has a change in amplitude and a vertical translation, the equation becomes y=acosθ+d, where a,d∈N and 0≤θ≤360∘. The graph of y=acosθ+d is shown below.
The amplitude and the downward vertical translation, respectively, are:
6 and 2
7 and 1
3 and 4
3 and 2
Answer:
The amplitude is 3 and the downward vertical translation is 4 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise some facts about the cosine function
- The Amplitude of cos(x) is the height from the center line to the
peak (or to the trough). Or we can measure the height from
highest to lowest points and divide that by 2.
- The Vertical Shift is how far the function is shifted vertically from
the usual position.
* Now lets solve the question
∵ y = cos(Ф)
- There is a change in amplitude, it becomes a
- There is a vertical translation by b units
∴ y = a cos(Ф) + d
* Now lets look to the graph to find a and d
- From the graph:
∵ The highest value is -1
∵ The lowest value is -7
∴ The amplitude a = (-1 - -7)/2 = (-1 + 7)/2 = 6/2 = 3
∵ The highest value of y = cos(Ф) is 1
∵ The amplitude is 3
∴ The highest value of y = acos(Ф) = 3
∵ The highest value of y = acos(Ф) + d is -1
∴ d = 3 - (-1) = 4 ⇒ means downward vertical translation by 4
∴ y = 3 cos(Ф) - 4
* The amplitude is 3 and the downward vertical translation is 4
Please answer I’ll rate brainlyest
Answer:
49.1%
Step-by-step explanation:
From the table, the number of male voters who are registered Democrats is given as 600. Moreover, the total number of male voters is given as 1222. Therefore, the probability that a randomly chosen male voter is a registered Democrat will be calculated as;
number of male voters who are registered Democrats / total number of male voters
600/1222 = 0.491
As a percentage this becomes;
0.491 * 100 = 49.1%
Randomly selecting a seventh grader from a school that has 256 sixth graders, 225 seventh graders ,and 275 eighth graders
Answer:
225/756
Step-by-step explanation:
275+256+225
=756
We want to know what are the odds of selecting a seventh grader which is:
225/756
Which box plot represents a set of data that has the greatest mean absolute deviation?
Answer:
i need a picture of the graph but im pretty sure its graph B
Step-by-step explanation:
Help with this trig math question
Answer:
8
Step-by-step explanation:
We want to evaluate the function f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16.
Note that 2^4 = 16, so (log to the base 2 of 16) is 4.
Also note that 1/16 = 1/(2^4), so (log to the base 2 of 1/(2^4 is -4.
In summary, f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16 is equal to 3(4) -4, or 8.
ABC is reflected about the line y= -x to give abc with vertices a (-1,1) b (-2,1) c (-1,0) what are the vertices of abc
Answer:
(-1, 1), (-1, 2), (0, 1)
Step-by-step explanation:
It appears as though letter designations have become confused. If not, your question answers itself, as a, b, c are given and you're asking for a, b, and c.
___
Reflecting the given points across the line y=-x transforms them like this:
(x, y) ⇒ (-y, -x)
That is, you swap the coordinates and negate them both. The result will be as shown above and in the attachment.
The vertices of the reflected triangle ABC are A'(-1, 1), B'(-1, 2), and C'(0, -1).
Explanation:Reflection of points involves transforming each point across a specified line or axis, resulting in a mirrored image. This geometric operation is fundamental in mathematics and is commonly used in various applications. To find the vertices of the reflected triangle ABC, we need to reflect each vertex across the line y=-x.
For vertex A (-1, 1), the reflection is (-1, 1).
Similarly, for vertex B (-2, 1), the reflection is (-1, 2).
And for vertex C (-1, 0), the reflection is (0, -1).
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What is the domain of the function y= radical x?
Answer: [tex]x\geq0[/tex] or [tex][0,\infty)[/tex]
Step-by-step explanation:
You have the function:
[tex]y=\sqrt{x}[/tex]
The domain of the function is the set of all the possible input values that the function can has.
We know that the square root of a negative number is not defined in the Real numbers. Therefore, "x" cannot be a negative number.
Then the domain of f(x) will be:
[tex]x\geq0[/tex] or [tex][0,\infty)[/tex]
Answer:
Step-by-step explanation:
Can you write this as y = √x?
The domain of the function y = √x is [0, ∞ ). In elementary algebra, before you encounter imaginary numbers, y = √x is not defined for negative x.
Question 14 Math Help please
ANSWER
(1,0) is a solution
EXPLANATION
The given inequality is
[tex]y \leqslant |x + 2|- 3[/tex]
We substitute the point to see which ones satisfy the inequality.
For (1,0)
[tex]0\leqslant|1+ 2|- 3[/tex]
[tex]0\leqslant 0[/tex]
This is true.
(1,0) is a solution.
For (-1-1)
[tex]- 1\leqslant | - 1 + 2|-3[/tex]
[tex]- 1\leqslant-2[/tex]
False
(-1,-1) is not a solution.
For (0,0)
[tex]0\leqslant|0+2|-3[/tex]
[tex]0\leqslant- 1[/tex]
False.
For (0,1)
[tex]1\leqslant|0+ 2|-3[/tex]
[tex]1\leqslant-1[/tex]
This is also false
Which descriptions from the list below accurately describe the relationship
between QRS and TUV? Check all that apply.
Answer:
There similar
Answer: Similar and Same shape
Step-by-step explanation:
I got it wrong and these were the correct answers ON G
Plot 5-5i and write the number in trig form
Answer:5√2(cos(−π/4)+ isin(−π/4)) is in trig form
Step-by-step explanation:
Please help me out :)
Answer:
818.4 in²
Step-by-step explanation:
shaded region = area of sector - area of triangle
area of sector = area of circle × fraction of circle
A = π × 27.8² × [tex]\frac{150}{360}[/tex] ≈ 1011.65 in²
area of triangle = 0.5 × 27.8 × 27.8 × sin150° ≈ 193.21 in²
shaded region = 1011.65 - 193.21 ≈ 818.4 in²
Which points are on a plane curve described by the following set of parametric equations?
Select all that apply
x= 3t+4 and y= 2t^2
(1,-2)
(1,2)
(1,7)
(2,10)
(7,2)
ANSWER
The points (1,2) and (7,2) lie on the given curve.
EXPLANATION
The given parametric equations are:
[tex]x = 3t + 4[/tex]
and
[tex]y = 2 {t}^{2} [/tex]
We make t the subject in the first equation to obtain:
[tex]t = \frac{x - 4}{3} [/tex]
We substitute this into the second equation to get:
[tex]y =2{(\frac{x - 4}{3} )}^{2} [/tex]
When x=1,
[tex]y = 2 {(\frac{1 - 4}{3} )}^{2} = 2[/tex]
When x=2
[tex]y =2{(\frac{2- 4}{3} )}^{2} = \frac{8}{9} [/tex]
When x=7,
[tex]y =2{(\frac{7 - 4}{3} )}^{2} = 2[/tex]
Therefore the points (1,2) and (7,2) lie on the given curve.
The points are on a plane curve described by the following set of parametric equations are:(1,2), (7,2).
What is Parametric equation?Given:
x= 3t+4 and y= 2t²
Hence:
x=3t +4 = t=(x-4)/3
y=2t² =y=2[(x-4)/3]
y=2[(x-4)/3]²
When x=1
y=2(1-4/3)²
y=2(-3/3)²
y=2(1)
y=2
When x=7
y=2(7-4/3)²
y=2(3/3)²
y=2(1)
y=2
Therefore the points are on a plane curve described by the following set of parametric equations are:(1,2), (7,2).
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Find the point where line A intersects line B.
Answer:
D.
Step-by-step explanation:
Use the equation m=y2-y1/x2-x1 to get the equation of both lines. Then, substitute numbers in to get the y-intercept. For example, for line A, you get y=4x+8. This is because 12-0/1--2 = 12/3 or 4. Then, do 12=4(1)+b. 12-4 = 8, so b equals 8. Do the same for the other line. Then, use the substitution method. This is where you take both equations and combine them without using y. For example, -2x+12=4x+8. You add 2x to 4x and get 6x. Then, you subtract 8 from 12 and get 4. We get x=4/6, which simplifies into 2/3. Then, you substitude that into one of the equations. 2/3 times 4 is 8/3 and add 8 to it. Multiply 8 by 3 to get that amount in thirds. You will get 8/3 plus 24/3 to get 32/3 as your y-value.
To find where two lines intersect, you set their equations equal to each other to solve for x, then substitute x into one equation to solve for y. The point of intersection in the example is (0.67, 4.34).
Explanation:To find the point where Line A intersects with Line B, you first need to write out the equations for both lines. Assuming you know the slope and y-intercept of each line, an equation for a line takes the form y = mx + b, where m is the slope and b is the y-intercept. For example, if Line A is y = 2x + 3 and Line B is y = -x + 5, you would set the two equations equal to each other, like this: 2x + 3 = -x + 5. Solving for x, you'd get x = 0.67. Then, you would substitute x into either line's equation for y (I'll use Line A): y = 2(0.67) + 3 = 4.34. So, the point of intersection would be (0.67, 4.34).
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The airport security randomly selected 24 suitcases from in the security like. Of these bags, they screened 7 suitcases. Based on this information, what is the most reasonable prediction for the number of suitcases they will screen in a group of 144?
Answer:
42 suitcases screened = x
Step-by-step explanation:
7/24 = x/144
7(144) = 24x
1,008 = 24x
42 = x
The most reasonable prediction for the number of suitcases should be 44.
Given information:The airport security randomly selected 24 suitcases from in the security like. Of these bags, they screened 7 suitcases.
Calculation of a number of suitcases:Here we assume that no of suitcases be x
So,
[tex]7\div 24 = x\div 144[/tex]
7(144) = 24x
1,008 = 24x
42 = x
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Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9).
a. y = (1/36)x^2
b. y= (1/9)x^2
c. y= 9x
d. y= 36x
Answer:
Answer is A
Step-by-step explanation:
Which function has a range of (−90°, 90°)?
Answer:
C) f(x) = tan^-1(x)
Step-by-step explanation:
The question is equivalent to asking which trig function passes the horizontal line test over the domain (-90°, 90°). Both the sine function and the tangent function are defined on that domain and pass the horizontal line test.
The inverse sine function has a range of [-90°, 90°] (with square brackets, signifying the end points are part of the range). The inverse tangent function does not have a range that includes ±90°, so is a better match for the range in the question.
Please Help
Write the equation of a parabola with vertex (-5,8) and directrix x=2. Show all of your work and put your equation in graphing/vertex form.
ANSWER
[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]
EXPLANATION
The given parabola has directrix x=2.
This implies that, the parabola is opens in the direction of the negative x-axis because it must open in a negative direction to the directrix.
The equation of such parabola is of the form:
[tex]( {y - k)}^{2} = 4p(x - h)[/tex]
where (h,k)=(-5,8) is the vertex.
[tex] |p| = | - 2 - 5| = 7[/tex]
[tex]p = \pm7[/tex]
But the parabola opens to the left.
p=-7
The equation now becomes
[tex]( {y - 8)}^{2} = 4( - 7)(x - - 5)[/tex]
[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]
Will someone please help me solve this !!
Answer:
∠H= 109º
∠F = 71º
∠G = 109º
Step-by-step explanation:
∠I = 71º
Interior opposite angles of parallel lines sums up to 180º.
∠H = 180 - 71 = 109º
Line IH is equal to Line FG.
∠F = ∠I
∠F = 71º
∠G = ∠H
∠G = 109º
A car salesperson sells a used car for $8,800 and earns 5% of the sale price as commission. How many dollars does the salesperson earn in commission?
Final answer:
To calculate the commission, multiply the sale price of $8,800 by the commission rate of 5% to get a commission of $440.
Explanation:
The question is asking to calculate the commission a salesperson earns from selling a used car. The salesperson earns a 5% commission on the sale price of the car, which is $8,800. To find the commission, we multiply the sale price by the commission rate:
Sale Price = $8,800
Commission Rate = 5% (or 0.05 in decimal form)
Commission = Sale Price × Commission Rate
Commission = $8,800 × 0.05
Commission = $440
Therefore, the salesperson earns a commission of $440.
Rewrite the following expression .
[tex]x\frac{9}{7}[/tex]
For this case we must rewrite the following expression:
[tex]x ^ {\frac {9} {7}}[/tex]
By definition of properties of powers and radicals we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, the expression can be rewritten as:
[tex]x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9}[/tex]
If we want to simplify:
[tex]\sqrt [7] {x ^ 9} = \sqrt [7] {x ^ 7 * x ^ 2} = x \sqrt [7] {x ^ 2}[/tex]
ANswer:
[tex]x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9} = x \sqrt [7] {x ^ 2}[/tex]
find the next two terms of the following sequence: 14,38,74,122,182,254
ANSWER
The next two terms are
338, 434
EXPLANATION
The given sequence is 14,38,74,122,182,254
Let us observe some pattern and use it to find the next two terms.
14+24=38
38+36=74
74+48=122
122+60=182
182+72=254
To get the next term we add 84 to 254
254+84=338
To get the next term,we add 96 to 338
338+96=434
Someone mind helping me out? :)
Answer:
Step-by-step explanation:
Area of a circle is A = πr², and diameter of a circle is d = 2r.
d = 2r
72 = 2r
r = 36
A = πr²
A = π(36)²
A = 1296π
A ≈ 4069
Math is right about the answer
What is the best next step in the construction of an equilateral triangle?
Answer:
option B
Step-by-step explanation:
Use a compass to draw a circle centered at B with a radius that is length of AB.
then draw a circle centered at A with a radius that is length of AB
join the point of intersection of two circles through straight lines to point A and point B.
!
Answer with explanation:
Given a circle having center A, and radius equal to AB.
One side of equilateral Triangle = AB
We have to draw two sides which have length equal to AB.
Draw a circle having center B and radius equal to AB.The Circle will pass through center A and cuts the Original circle at P.Join AP and BP.This is the equilateral triangle that we are interested in.
The Next in the construction of an equilateral triangle is:
Option B:→ Use a Compass to draw a circle centered at B with a radius that is equal to AB.
Doua carti costau impreuna 125 de lei. Stiind ca pretul uneia a crescut cu 10 la suta iar a celeillalte cu 20 la sutasi ca dupa cresterea peturilor ele costa impreuna 143,5 lei aflati pretul initial al fiecarei carti
Answer:
btw way you all this means
Step-by-step explanation:
Two books cost 125 MDL together. Knowing that the price has risen by 10% and the other by 20%, after the cost of the cars costs 143.5 lei together with the initial price of each book
A textbook has a length of 6 inches wide inches and a width of X inches if the length of diagonal of the front covers 8 inches the length of the diagonal of the width of 7 inches find the values of XY
Answer: x=7 y=8
Step-by-step explanation:width is x and the width is 7inches
height is y and the diagonal length 8inches
The circle graph shows the distribution of age groups of people living in a city. Identify the measure of arc PR. HELP ASAP!!
Answer:
100.8°
Step-by-step explanation:
∠POR = ∠POQ + ∠QOR
∠POQ is 20% of 360° ( measure of the angles in a circle )
= 0.2 × 360° = 72°
∠QOR is 8% of 360° = 0.08 × 360° = 28.8°
Hence
arc PR = ∠POR = 72° + 28.8° = 100.8°
i need help asapppppppp
Answer:
Question 1 - f(x) = | x | - 2
First, let's find the 5 values requested:
x = -2 ==> | x | - 2 = | - 2 | - 2 = 2 - 2 = 0
x = -1 ==> | x | - 2 = | - 1 | - 2 = 1 - 2 = -1
x = -0 ==> | x | - 2 = | 0 | - 2 = 0 - 2 = -2
x = 1 ==> | x | - 2 = | 1 | - 2 = 1 - 2 = -1
x = 2 ==> | x | - 2 = | 2 | - 2 = 0 - 2 = -2
You can see the plotted graph attached.
Question 1 - f(x) = | x - 1 | - 1
First, let's find the 5 values requested:
x = -2 ==> | x - 1 | - 1 = | - 2 - 1 | - 1 = | - 3 | - 1 = 3 - 1 = 2
x = -1 ==> | x - 1 | - 1 = | - 1 - 1 | - 1 = | - 2 | - 1 = 2 - 1 = 1
x = 0 ==> | x - 1 | - 1 = | 0 - 1 | - 1 = | - 1 | - 1 = 1 - 1 = 0
x = 1 ==> | x - 1 | - 1 = | 1 - 1 | - 1 = | 0 | - 1 = 0 - 1 = -1
x = 2 ==> | x - 1 | - 1 = | 2 - 1 | - 1 = | 1 | - 1 = 1 - 1 = 0
You can see the plotted graph attached.
Can someone help me out with this? I don’t know why I can’t get it??
Answer:
No hardly any difference
Step-by-step explanation:
Because they had about the same number of (ML) drank by the dogs and cats regardless of color