Answers
The given statement can be written as:
6+√-80
To solve √-80 re-write -80 as -1 * 80
Now √-80 =√-1 * 80
Now we can write it as:
6+ √-1 * √80
We know that √-1 = i
Thus it becomes:
6+ i√80
Now find the square root of 80
80 does not have a perfect square root
Its square root can be found as 80 = 4*4*5
Then,
6+i√4*4*5
Notice that 4 makes a pair.. So we will write it outside the square root
6+1*4√5
We will write it as:
6+4i√5
Thus the correct option is 6 plus 4 i times the square root of 5....
Related Questions
Select the correct answer.
A piece of gold has a mass of 14.12 grams and a volume of 4 cubic centimeters.
What is the density of the gold?
A. 3.53 g/cm^3
B. 0.28 g/cm^3
C. 1.77 g/cm^3
D. 0.57 g/cm^3
Answers
The density of the gold substance is 3.53 g/cm^3
What is the density of a substance?The density of a substance is the degree of compactness of a substance and it can be determined by the ratio of the mass of the substance to volume.
Mathematically, the density can be computed as:
[tex]\mathbf{Density = \dfrac{mass}{volume}}[/tex]
[tex]\mathbf{Density = \dfrac{14.12 \ g}{4 \ cm^3}}[/tex]
Density = 3.53 g/cm^3
Therefore, we can conclude from the above calculation that the density of the gold with a mass of 14.12 grams and a volume of 4 cubic centimeters is 3.53 g/cm^3.
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Answer:
A 3.53 g/cm^3 if it not a it still 3.53g/cm^3
Step-by-step explanation:
Please write the solution
Answers
Answer:
D.
Step-by-step explanation:
that is the answer to the question above
PLEASE HELP :))
Select the correct answer from each drop-down menu consider the given triangles
The length of side PR in PQR is____ and the measure of J in JKL is___
Answers
The measure of the side PR in PQR is 8.07 units and the measure of angle J in JKL is 35.30 degree.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
Applying cos law in the triangle PQR:
[tex]\rm PR = \sqrt{5^2+9^2-2(5)(9)cos63}[/tex]
PR = 8.07 units
Applying sin law in the triangle, JKL:
[tex]\rm Angle \ J = sin^{-1}[sin 52 \ (\dfrac{11}{15})][/tex]
Angle J = 35.30 degree
Thus, the measure of the side PR in PQR is 8.07 units and the measure of angle J in JKL is 35.30 degree.
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Answer: POR NADA
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
Can someone pls help me
Answers
Answer:
? what do u want me todo
Step-by-step explanation:
Write the equation of the circle given center (-13,-16) and point on the circle (-10,-16)
Answers
Answer:
Step-by-step explanation:
Why is 3 x 1/10 less than 3x 10
Answers
Answer:
Because 1/10 is less than 10
Step-by-step explanation:
10 is 100 times greater than 1/10
[tex]\frac{10}{1/10} =100[/tex]
Hope this helps
0.3<30
Someone please tell me if this is right or not!!
Answers
Answer:
close countess
Step-by-step explanation:
remember that the sign has to be postive so just change all the signs , then, you'll have a leading coefficient of +1, in front of the [tex]x^{2}[/tex], the 5 is in front of the 2nd term, they were just trying to trick you with that. the last answer is good :)
For the leading coefficient, I would see why you think it’s 5 since the highest number in front of x
but the definition of leading coefficient is the number of highest power of x
In this case it would be -x^2 is the higher power making -1 the leading coefficient
Hope this help, let me know if you have any question or concerns !
Find 1 + 3 + 5 + … + 389.
Answers
Answer:
The rule is +2
This is the 194th term
Step-by-step explanation:
This is an arithmetic sequence because 2 is added every time.
2x + 1 = 389
2x = 388
x = 194
194* 2 + 1 = 389
mark brainliest please!
Answer:
398 i think
Step-by-step explanation:
I NEED Help NOW FOR 10 POINTS
Answers
A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 5.5. what are the dimensions of such a cylinder which has maximum volume?
Answers
Check the picture below.
so hmm if we look at the cone straight from the front and check a cross-section of it, it'd look like the cross-section of the right-hand-side of the picture.
Now, with the cylinder having radius "r" and height "h", those two triangles we see in greenish color are similar, thus we can use proportions to correlate "h" and "r", so let's do that.
[tex]\cfrac{2.5-h}{r}~~ = ~~\cfrac{h}{5.5-r}\implies 13.75-5.5h-2.5r+rh=rh \\\\\\ 13.75-2.5r=5.5h\implies \boxed{\cfrac{13.75-2.5r}{5.5}=h}[/tex]
now, let's plug that in the volume of the cylinder's equation
[tex]V(r)=\pi r^2\cdot \cfrac{13.75-2.5r}{5.5}\implies V(r)=\cfrac{\pi }{5.5}(13.75r^2-2.5r^3) \\\\\\ \cfrac{dV}{dr}=\cfrac{\pi r(27.5-7.5r)}{5.5}\hspace{5em}0~~ < ~~r ~~ < ~~ 2.5[/tex]
now, our "r" variable can't be 0 or 2.5, as the cylinder tiptoes up and down, because if that ever happens, our cylinder's volume goes poof.
[tex]0=\cfrac{\pi r(27.5-7.5r)}{5.5}\implies 0=27.5-7.5r\implies 7.5r=27.5 \\\\\\ r=\cfrac{27.5}{7.5}\implies r=\cfrac{11}{3}[/tex]
the way I do region testing for the 1st derivative, is I usually grab the critical point and subtract hmm say 0.0000001 from it and put it in a variable in my calculator, then I add 0.0000001 to it and put it in another variable, then I use that variable in the 1st derivative calculation. Anyhow, doing so and running a 1st derivative test, we'd see that the region to the left of 11/3 is positive whilst the region to the right is negative, as you can see in the picture at the bottom, yielding a maximum extremum, r = 0 is another critical point but as we noticed the constraints is out of bounds, so not in consideration.
so V(r) is at a maximum when r = 11/3
[tex]\blacksquare~~ r=\cfrac{11}{3} ~~\blacksquare \hspace{5em} \cfrac{13.75-2.5\left( \frac{11}{3} \right)}{5.5}=h~\hfill \implies ~\hfill \blacksquare~~ \cfrac{5}{6}=h ~~\blacksquare[/tex]
Combine like terms to answer the question.
Answers
Answer:
3r + 5
Step-by-step explanation:
by "combining like terms", this means that if we have, for example,
1 * x + 5 * x, we can factor this out to be x*(1+5) = 6 * x and the like terms (1x and 5x) are combined
thus, we have
-5r + 8r + 5
the "like terms" here are -5r and 8r because they both have an r attached to it. thus, we can set out to only factor the r in these two numbers, resulting in
-5 * r + 8 * r + 5 = r * (-5 + 8) + 5 = r * 3 + 5 = 3r + 5
Solve the inequality. Graph the solution. Describe the graph in the area provided. Be sure to indicate where there is an open or closed circle and what direction the number line is shaded in.
Answers
To solve this problem, we can to simply plot using a graphing tool and the region under the area would be given. We would see there's no solution for this compound inequality
Graphing of InequalityThe given inequalities in this question are
x + 4 > 0.0132 ≤ - 4xWhen we plot this, we would see that no solution exists for this compound inequality problem.
Kindly check the attach image for more details.
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A parabola has vertex (−2, −1) and passes through the point (1, 26). Find its equation.
Answers
[tex]\text{Equation of parabola in vertex form,}\\\\~~~~~~~~~y = a(x-h)^2 +k\\\\\implies 26 = a(1+2)^2 -1~~~~~~~~;[(x,y) = (1,26)~ \text{and}~ (h,k) = (-2,-1)]\\\\\implies 26 = 9a -1\\\\\implies 9a = 26+1\\\\\implies 9a = 27\\\\\implies a = \dfrac{27} 9 \\\\\implies a = 3\\\\\text{Now,}\\\\~~~~~~~~y = 3(x+2)^2 -1~~~~~~~~~~;[\text{Vertex form.}]\\\\\implies y=3(x^2 +4x +4) -1\\\\\implies y = 3x^2 +12x +12 -1 \\\\\implies y=3x^2 +12x+11~~~~~~~~;[\text{Standard form.}][/tex]
can someone help me with this problem please? Thank you!
Answers
Answer:
50
Step-by-step explanation:
since the Pythagorean theorem is
[tex]c=[/tex] √[tex]a^2+b^2[/tex]
b is the bottom line (48)
a is the right line (14)
c is the top line (c)
plug that in
[tex]c =[/tex] √[tex]14^2 + 48^2[/tex]
then do the exponets
[tex]14^2[/tex] = 14 * 14 = 196
[tex]48^2[/tex] = 48 * 48 = 2304
then add them together
196 + 2304 = 2500
[tex]c =[/tex] √2500
the sqrt of 2500 is 50 (50 * 50 = 2500)
c = 50
your answer is 50
hope this helps:)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate the value of c using Pythagoras theorem ~
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = {14}^{2} + {48}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = \sqrt{196 + 2304} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = \sqrt{2500} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = 50 \: units[/tex]
what is the expression of the product for 17 and s?
Answers
Answer:
17s
Step-by-step explanation:
Note: an expression is NOT an equation
"Product" means the answer to a multiplication of two numbers.
You are asked to write the answer to 17 and s being multiplied together.
The product is therefore
17 x s = 17s
Which of the following can be found on a credit report?
A Personal Social Security Number
B Checking Account Balance
C Late Payments to Lenders
D Credit Card Balances
B and D Only
A Only
Not here
A, C, and D Only
Answers
Answer:
A, C, & D only
Step-by-step explanation:
All of the following are listed on your credit report except option B) your checking account balance.
is this the RIGHT answer
Answers
Answer:
Yes
Step-by-step explanation:
The horizontal line on a graph is the x axis and the "C" appears to be on the horizontal line therefore the answer would be x-axis
reasons its not the other answer choices
Y axis is the vertical line
Origin is where the two axis cross
Quadrant 1 may appear where C is however the C is pointing to the X axis
i cant figure this one out at all
Answers
Answer:
a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work
simplify- 4c^2-36/8c^2-24c/12c+36/2c^2-6c
pls help :)
Answers
[tex]\displaystyle \dfrac{\dfrac{4c^2-36}{8c^2-24c}}{\dfrac{12c+36}{2c^2 -6c}}\\\\\\=\left(\dfrac{4c^2 -36}{8c^2 -24c}\right) \cdot \left(\dfrac{2c^2 -6c}{12c+36}\right)\\\\\\=\left[\dfrac{4(c^2 -9)}{8(c^2-3)}\right]\cdot\left[\dfrac{2(c^2-3)}{12(c+3)}\right]\\\\\\=\dfrac{8(c^2-3^2)}{8 \cdot 12(c+3)}\\\\\\=\dfrac{(c+3)(c-3)}{12(c+3)}\\\\\\=\dfrac{c-3}{12}[/tex]
[tex]\text{Hence the answer is d.}[/tex]
Answer:
d
Step-by-step explanation:
separate the 2 divisions and simplify each , that is
[tex]\frac{4c^2-36}{8c^2-24c}[/tex] ← factor numerator/ denominator
= [tex]\frac{4(c^2-9)}{8c(c-3)}[/tex] ← factor difference of squares on numerator
= [tex]\frac{4(c-3)(c+3)}{8c(c-3)}[/tex] ← cancel (c - 3) and 4/8 on numerator/ denominator
= [tex]\frac{c+3}{2c}[/tex]
---------------------------------------------------
[tex]\frac{12c+36}{2c^2-6c}[/tex] ← factor numerator/ denominator
= [tex]\frac{12(c+3)}{2c(c-3)}[/tex] ← cancel 12 and 2 on numerator/ denominator
= [tex]\frac{6(c+3)}{c(c-3)}[/tex]
----------------------------------------------------------
to divide the top fraction by the lower fraction
leave top fraction, change division to multiplication, turn lower fraction upside down.
[tex]\frac{c+3}{2c}[/tex] × [tex]\frac{c(c-3)}{6(c+3)}[/tex] ← cancel (c + 3) and c on numerator/ denominator
= [tex]\frac{c-3}{2(6)}[/tex]
= [tex]\frac{c-3}{12}[/tex] → d
I need help asap !!!!! Olease
Answers
Answer:
[tex]\overline{BC}[/tex]
Step-by-step explanation:
[tex]\overline{BC}[/tex] does NOT intersect [tex]\overline{AG}[/tex]
Hope it helps you in your learning process.
Use >, <, or = to solve the following problems below.
(6^2)____(-6^2)
-5____ |-5|
0.372×1,000____37.2×100
(will mark brainliest)
Answers
(6^2)__>__(-6^2)
-5__=__ |-5|
0.372×1,000__<__37.2×100
how does the scatter plot show that age and time spent talking on the phone have a linear association?
Answers
Answer:
When the y variable tends to increase as the x variable increases we say there is a positive correlation between the variables
A watermelon has a mass of 6.45 kilograms. What is the mass of the watermelon in grams
Answers
6540 g
Calculations ↓Convert kilograms (kg) into grams (g) by multiplying the amount of kilograms (kg) by 1000 :
[tex]\boxed{\rm{6.45\:kg\:\:\:\:\:\:\:}}[/tex] times 1,000 --> [tex]\boxed{\rm{6540\:g\:\:\:\:}}[/tex]
So the mass of the watermelon is :[tex]\Large\text{6540\:g}[/tex]
[tex]\small\text{hope\:helpful~}[/tex]
The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
Answers
Area of three rectangles
3LB3(8)(6)24(6)144units²Area of two triangles
1/2(6)(4)3(4)12units²Total
144+12156units²please need help asap i will mark branliets
Choose the graph that correctly represents the equation 3x + 9y = −18. btw one of the graphs is the anwser
Answers
Lol I’m just talking nonsense but let me know if you want me to show work!
Answer:
Step-by-step explanation:
jfift
A textbook has 428 pages numbered in order starting with 1. You flip a random page in the book in a way that is equally likely to stop at any of the pages. (Type your answers as fractions).
What is the probability that you turn to page 45?
Answers
Answer:
1/428
Step-by-step explanation:
There are 428 pages,
Each page likely to be turned onto as equally as every other page,
and there is one possible correct page.
100 points please answer asap!!!!!!!!!!! this is algebra 1
part a: describe two types of transformations that can be used to transform f(x) to g(x).
part b: solve for k in each type of transformation.
part c: write an equation for each type of transformation that can be used to transform f(x) to g(x).
Answers
Answer:
f(x) has slope (10-0)/(10-5) = 10/5 = 2
and intercept y - mx = 0 - 5(2) = -10 so f(x) = 2x - 10
g(x) has slope (10-0)/(2+3) = 2 and intercept y - mx = 10 - 2*2 =6
so g(x) = 2x + 6
So to transform f to g, you move the graph 16 units up.
Step-by-step explanation:
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth if necessary. (Square units)
Answers
Answer:
389.1 units² (nearest tenth)
Step-by-step explanation:
Regular polygon: all side lengths are equal, all interior angles are equal.
Apothem: a line drawn from the center of any polygon to the midpoint of one of the sides
Radius: a line drawn from the center of the polygon to a vertex.
Therefore, we have been given the apothem of this regular dodecagon.
Formulae[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]
where:
n = number of sidesl = length of one sidea = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)[tex]\textsf{Length of apothem (a)}=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
l = length of one siden = number of sidesSolutionFirst, calculate the length of one side of the regular dodecagon by substituting a = 11 and n = 12 into the apothem formula:
[tex]\implies 11=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]
[tex]\implies l=11 \cdot 2 \tan\left(\frac{180^{\circ}}{12}\right)[/tex]
[tex]\implies l=44-22\sqrt{3}[/tex]
Now substitute n = 12, the found value of l, and a = 11 into the area formula:
[tex]\implies \textsf{Area}=\dfrac{12(44-22\sqrt{3})(11)}{2}[/tex]
[tex]\implies \textsf{Area}=389.0622274...[/tex]
[tex]\implies \textsf{Area}=389.1\: \sf units^2 \: (nearest\:tenth)[/tex]
Answer:
389.1 square units
Step-by-step explanation:
Area of the Dodecagon (12-sided polygon)
Area Formula
Area (A) = number of sides (n) x length of side (l) x apothem (a) x 1/2Finding the length (l)
Apothem Formula
a = l / 2tan(180/n)°11 = l / 2 tan15°l = 11 × 2tan(45 - 30)°l = 22 x (2 - √3)l = 44 - 22√3 unitsFinding Area
A = 12 × (44 - 22√3) x 11 x 1/2A = 66 x (44 - 22√3)A = 389.1 square units (approx.)For which system of equations is the graph below a solution?
A. y = x - 2
y = - x - 3
B. y = x + 2
y = - x - 3
C. y = x - 2
y = -x + 3
D. y = x + 2
y = -x + 3
Answers
Answer:
C
Step-by-step explanation:
Black line
slope = Δy / Δx = -3 / 3 = -1
Y intercept = 3
LINE equation ( y = slope times x + y intercept): y = -x +3
Blue line
slope = Δy / Δx = 2 / 2 = 1
Y intercept = -2
LINE equation ( y = slope times x + y intercept): y = x -2
Camile is packing seeds to send to her mother in law. She estimates that she needs a box with a volume of at least 6,856 cubic inches. Here are the boxes she has to choose from Option A Length: 13 inches, Width 12 inches, Height: 16 inches Option B Length: 18 inches, Width: 25 inches, Height: 16 inches Option C Length:12 inches, Width: 14 inches Height: 22 inches Option D Length: 20 inches, Width:22 inches, Height: 17 inches Which boxes con she choose?
Answers
Step-by-step explanation:
the volume of a box (or prism) is always
length × width × height
so, box A
13 × 12 × 16 = 2,496 in³
box B
18 × 25 × 16 = 7,200 in³
box C
12 × 14 × 22 = 3,696 in³
box D
20 × 22 × 17 = 7,480 in³
so, she can use B or D.
