Answer:
[tex] \rm - \dfrac{11}{2} [/tex]
Step-by-step explanation:
[tex] \rm Simplify \: the \: following: \\ \rm \longrightarrow - 5 + \dfrac{i}{2} i \\ \\ \rm Combine \: powers. \\ \rm \dfrac{i \times i}{2} = \dfrac{i^{1 + 1}}{2}: \\ \rm \longrightarrow - 5 + \dfrac{i^{1 + 1}}{2} \\ \\ \rm 1 + 1 = 2: \\ \rm \longrightarrow - 5 + \dfrac{i^2}{2} \\ \\ \rm i^2 = -1: \\ \rm \longrightarrow - 5 + \dfrac{( - 1)}{2} \\ \\ \rm \longrightarrow - 5 - \dfrac{1}{2} \\ \\ \rm Put \: - 5 - \dfrac{1}{2} \: over \: the \: common \: denominator \: 2. \\ \rm - 5 - \dfrac{1}{2} = \dfrac{2( - 5)}{2} - \dfrac{1}{2} : \\ \rm \longrightarrow \dfrac{ - 5 \times 2}{2} - \dfrac{1}{2} \\ \\ \rm 2 (-5) = -10: \\ \rm \longrightarrow \dfrac{ - 10}{2} - \dfrac{1}{2} \\ \\ \rm \dfrac{ - 10}{2} - \dfrac{1}{2} = \dfrac{ - 10 - 1}{2} : \\ \rm \longrightarrow \dfrac{ - 10 - 1}{2} \\ \\ \rm -10 - 1 = -11: \\ \rm \longrightarrow - \dfrac{11}{2} [/tex]
Solve the word problem using a proportion. Danny, who was 6 ft tall, cast a 15 ft shadow. The building he was standing next to cast a 35 ft shadow. How tall was the building? 30 ft, 70 ft, or 14 ft?
Answer: 14 feet
Step-by-step explanation:
Answer:
14 feet
Step-by-step explanation:
Can someone solve this equation for me? 34 + 12x = 3x - 22
Thanks. Any help is appreciated! :)
Answer: x= -56/9
Step-by-step explanation:
34+12x=3x-22
Subtract 12x from both sides
34=-9x-22
Add 22 to both sides
56=-9x
Divide -9 by both sides to get x alone
56/-9=x
So
x=-56/9
Styles
Because you want to prepare and serve the healthiest food possible, you monitor the fat
and calorie content of items on your menu. Some of the menu items are included in the
graph below
Answer:
Yes, my partner is correct because as the fat increases the calories increase. And when the points are rising from the left to the right, this indicates a positive correlation.
Step-by-step explanation:
WILL GIVE BRAINLIEST Katya is wanting to put artificial turf in her back yard. Her yard is 20 feet by 30 feet. She figures that she will need the drainage rock under the turf to be 1 foot deep. She goes to the home improvement store and sees the following signs for rock. What is the unit rate of brand B?
Write an equation in function notation for the relation shown in the picture below.
Answer:
y = -x + 2
Step-by-step explanation:
What is the y-intercept?
What is 8 divide 1/5?
What is 8 divide by 1/5
Answer:
40
Step-by-step explanation:
Factor by Grouping
2y2 + 7yz + 5z2
Find the slope of the line that passes
through these two points.
Answer:
1/5
Step-by-step explanation:
[tex]\frac{2-1}{3--2} = \frac{1}{5}[/tex]
Answer: 1/5
Step-by-step explanation: Following our hint,
let's start with the slope formula.
m = y₂ - y₁ / x₂ - x₁
We take the second y minus the first y over the second x minus the first x.
So we have m = 2 - 1 / 3 - (-2) or 1 / 5.
So our slope is 1/5.
Determine an expression for dy
dx given that x = sin3
(t)andy = cos3
(t)
Answer:
[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]
Step-by-step explanation:
Recall that using the chain rule we can state:
[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]
And similarly:
[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]
now notice that we can find [tex]cos(t) = \sqrt[3]{y}[/tex] from the expression for y,
and [tex]sin(t) = \sqrt[3]{x}[/tex] from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]
A bag of M & M’s has 4 red, 2 green, 3 blue, and 8 yellow M &M’s. What is the probability of randomly picking: a yellow, a blue or green, an orange? Round 4 decimal
Answer:
probability of picking a yellow =0.4706
a blue or green = 0.2941
an orange = 0 ( there is no orange bag)
What’s the answer to this? (2 * 198) - 1073 + 20/92 divided by 173/28
Answer:
if you have and piece of clothing that was left behind.
Step-by-step explanation:
Write an equivalent addition expression to : -10 – (-4)
Answer:
-6
Step-by-step explanation:
-10-(-4)=-1+4=-6
Hope this helps plz mark brainliest ;D
The pair of polygons is similar. Find the value of x.
A. 2.5 in.
B. 5 in.
C. 35 in.
D. 40 in.
Answer: 40
60÷15=4
10×4=40
I hope this is good enough:
Which expression is equivalent to 4x+6y-8x
Answer:The expression is 6y - 4x
Step-by-step explanation:
Answer:
-4x+6y
Step-by-step explanation:
4x+6y-8x4
(4x-8x)+6y
−4x+6y
Which values from the set make this inequality true?
4n<16 ; {1, 2, 3, 4}
Select each correct answer.
1
2
3
4
Answer:
1 2 3
Step-by-step explanation:
4 * 1 <16 4 is less than 16
4 * 2 <16 8 is less than 16
4 *3 <16 12 is less than 16
4 * 4 is not less than 16. 16 is not less than 16
Help and please show all your work I need this ASAP
How much would 7 bottles of water cost
Answer:
$5.25
Step-by-step explanation:
fill in the blanks thanks
Answer:
Um threre is no blanks or there is no question.
Step-by-step explanation:
The fifth grade students at East street decided to host a fundraiser for red ribbon week they planed to buy 240 inches of red ribbon how much will it cost them
Answer:
(Amount for 1 inch of red ribbon) x (240) = total cost
Step-by-step explanation:
After 10 years, the principal on this mortgage is $136,683. How much of the next payment will go towards interest
Answer:
26123 is the answer have a good day
Replace the with <, >, or = to make the statement true.
5 0-3
5>0-3
Step By Step- 5 is greater than 0-3 because 0-3 would equal a negative number, and all positive numbers are greater than negative numbers
Answer:
5>0-3
Step-by-step explanation:
1. Determine the intervals on which each function is increasing or
decreasing
(a) f(x) = x^3 - 11/2x^2 - 4x
Answer:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]
And we want to determine the intervals for which the function is increasing or decreasing.
We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.
To find the critical points, we need to find the first derivative and then solve for the x. So:
[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]
Differentiate:
[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]
Set the derivative equal to 0 and solve for x:
[tex]0=3x^2-11x-4[/tex]
Factor:
[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]
Zero Product Property:
[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]
Therefore, our critical points are -1/3 and 4.
We can thus sketch the following number line:
<————-(-1/3)——————————————(4)—————>
Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.
For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:
[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]
The result is positive.
Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).
For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:
[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]
The result is negative.
Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).
And finally, for greater than 4, we can use 5:
[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]
The result is positive.
Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.
Therefore:
[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]
In interval notation:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
Geometry
What is the range of possible values for x? The diagram is not to scale.
PLEASE HELP ILL GIVE AS MANY POINTS AS YOU WANT!!
Answer:
-2= y=-13, (x,y)= (-2,-13)
0= y= -3, (x,y)= (0,-3)
1= y= 2, (x,y)= (1,2).
Step-by-step explanation:
Please mark as brainliest. :)
Anyone know this or could help me out?
Juan's book has 248 pages this is 10 more pages than there are in Kevin's book how many pages are in Kevin's book
Answer:
238
Step-by-step explanation:
juans has 10 more than kevin's, so you just subtract 10 from 248, getting 238
Write the equation of a line parallel to the line y=2x
Answer:
to create an equation that is parallel to a line, you keep the slope or rate of change the same, all you do is change the y intercept. so you have to keep
y = 2x, but then you can add any number to the end.
Find the distance between E(5,3) and F(-4,3).
Answer:
3 - 3 = 0 units There is no distance, the points are in the same place.
Step-by-step explanation:
Write the equation in point-slope form of a line that has a slope of m=2 and the point (x, y) = (6,8).
(Remember: point-slope form is y-y1 = m(x -x1)
where (x1, y1) is a point and m is the slope.)
Answer:
y-8 = 2 (x-6)