Answer:
n(U) = n(AUB) + n(AUB)'
Step-by-step explanation:
The cardinality of the universal set will be to add the cardinalities of both the union of A and B i.e (A U B) and and the compliments of A and B i.e n(AUB)'
Help me with this one
9514 1404 393
Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
[tex]x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}[/tex]
_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
_____
* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).
Find the slope of the line given the two points below:
(5,-9) and (8,2)
Given f(x)=2x^2+3x-8 find (b+2)
Answer:
[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = 2x^2 + 3x - 8[/tex]
And we want to find:
[tex]\displaystyle f(b + 2)[/tex]
Substitute:
[tex]\displaystyle f(b+2) = 2(b+2)^2 + 3(b+2) - 8[/tex]
Expand and simplify:
[tex]\displaystyle \begin{aligned}f(b+2)&= 2(b^2+4b+4)+(3b+6)-8 \\ &= (2b^2+8b+8)+(3b+6)-8 \\ &= (2b^2) + (8b+3b)+ (8+6-8) \\ &= 2b^2 + 11b + 6 \end{aligned}[/tex]
In conclusion:
[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]
K-5+1-5k please I need help
Explanation:
The like terms k and -5k combine to -4k
The like terms -5 and 1 combine to -4
So overall, that's how we end up with -4k-4
Answer:
-4k - 4Step-by-step explanation:
1). (k - 5k) + (-5 + 1) {Collect like terms}
2). -4k - 4 {Simplify}
Like what is this and how do you do it please explain clearly and understandable
Answer:
1/4
Step-by-step explanation:
HT represent the probability of tossing a head then Tail.
There is 4 possible results and only 1 give us HT.
We call this theoretical probability. which is
[tex] \frac{x}{y} [/tex]
where x is favorable outcomes and y is total number of outcomes.
So there is a 1/4 probability of getting a head followed by a tail.
how do you solve 3-(-7)?
Answer:
10
Step-by-step explanation:
Subtracting a negative is like adding
3 +7
10
answer choices:
A. 182.3
B. 164.2
C. 288
D. 144
PLSSSS HELP
Answer:
288m^3
Step-by-step explanation:
the volume is base* height
to find the second side, use the Pythagorean theorem : [tex]\sqrt{10^2-8^2} = \sqrt{100-64}= \sqrt{36} = 6[/tex],
now find the area of the triangle: 6*8/2=24
now multiply it by the height and you get the volume: 24*12=288
-2u+(-1)=-13
---------------
Answer:
Solution given
-2u+(-1)=-13
open bracket
-2u-1=-13
add 1 on both side
-2u-1+1=-13+1
-2u=-12
divide both side by -2
-2u/-2=-12/-2
u=6
[tex]\huge\text{Hey there!}[/tex]
[tex]\textsf{-2u + (-1) = -13}\\\textsf{-2u - 1 = -13}\\\large\text{ADD 1 to BOTH SIDES}\\\textsf{-2u - 1 + 1 = -13 + 1}\\\large\text{CANCEL out: -1 + 1}\\\large\text{KEEP: -13 + 1}\\\rightarrow\textsf{-2u = -12}\\\large\text{DIVIDE -2 to BOTH SIDES}\\\mathsf{\dfrac{-2u}{-2}= \dfrac{-12}{-2}}\\\textsf{CANCEL out: }\mathsf{\dfrac{-2}{-2}}\\\textsf{KEEP: }\mathsf{\dfrac{-12}{-2}}\\\mathsf{u = \dfrac{-12}{-2}}\\\mathsf{u = \bf 6}\\\huge\boxed{\mathsf{Answer: u = 6}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]
28+12
—————
13-5
7th Grade Math Book (McGraw-Hill) page 9 exercise 26
Will someone help me please?
Answer:
Ok so
Step-by-step explanation:
Yes yes yes yes its C
What is the equation of a line with a y-intercept at (0, 6) and a slope of 3? y = 3x + 6 y = 6x + 3 y = 3x − 6 y = −6x − 3
Answer:
[tex]y=3x+6[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)
We're given that the slope of the line is 3. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=3x+b[/tex]
We're also given the point (0,6). Since the y-intercept occurs when x=0, the y-intercept is therefore 6. Plug this into [tex]y=3x+b[/tex] as b:
[tex]y=3x+6[/tex]
I hope this helps!
The measure of an angle is 87°. What is the measure of its supplementary angle?
Answer:
180-87 = 93
Step-by-step explanation:
supplementary angles add up to 180°
so (the other angle + 87)=180°
other angle =180-87=93°
Answer:
93 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:
[tex]87 + x = 180\\x=180-87\\x=93[/tex]
Have a nice day. Feel free to ask questions. Spread the love.
area of the shape...
Write -0.450 as a fraction in simplest form.
Answer:
-0.450 as a fraction is -9/20
Step-by-step explanation:
Since there 3 decimal places, divide it by 1000
-450/1000 and simplify it
1.1x + 1.2x -5.4 =-10
Show answer
I circled the answer and put an example hope it helps
Use the given graph to determine the limit, if it exists. A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1.5, a closed point at 3, 7, and a horizontal line starting at the open point 3, 2. Find limit as x approaches three from the left of f of x..
Explanation:
The given limit notation means we're approaching x = 3 from the left side. So start at say x = 0 and approach x = 3. We don't actually get to x = 3 itself, but instead just get closer and closer. Note how y gets closer to y = 1.5
Solve by using the quadratic formula: (3x + 3)^2 = 25
pls ans the question step by step
then i wil mark it as brainlist ans
Answer:
i hope it helped U
stay safe stay happy
in which figures is segment AB a median?
WILL RATE BRAINLIEST!!!
HELP
Answer:
B, D, H, I, J
Step-by-step explanation:
Median: A line segment that joins the vertex of a triangle to the midpoint of the opposite side.
-(-5.6g + 2h – 9)
Does anyone know this ?
Answer: 5.6g - 2h + 9
Explanation:
Flip the sign of each term inside the parenthesis.
The -5.6g becomes +5.6g or simply 5.6gThe +2h becomes -2hThe -9 becomes +9These sign flips occur because of the negative out front the parenthesis. It's the same as having -1 outside, and we distribute the -1 through.
It is midpoint please help
Step-by-step explanation:(2, -3)
[tex]thank \: you[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{5+8}{2},\dfrac{3.5+10}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{13}{2},\dfrac{13.5}{2}\right)[/tex]
Find the equation of the line that is perpendicular to y=1/6x+3 and contains the point (-3,23)
a different way of proving the angle sum of a triangle is to use diagram
a.yes
Step-by-step explanation:
a.angle BCD =b because angle BCD is alternate angle of angle ABC
b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line
multiply 3 by b, then multiply c by the result
Hi
Answer:
3bc
Step-by-step explanation:
3×b=3b
3b×c=3bc
4. Find the quotient. -7 ÷ 14/3
Order the numbers in each group from least to greatest 7/11, 0.63 and 0.636
7/11 , 0.636, and 0.63
Hope this helps
Answer:
Least to Greatest
7/11 , 0.636, 0.63
Step-by-step explanation:
7/11 = 0.6363636363636364
so this number is least
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a. What is the area of the pool cover?
b. What is the length of the rope?
You must show all of your work to receive credit
Answer:
The cover has diameter of:
20 feet + 2*12 inches = 20 feet + 2 feet = 22 feeta.
Area of the pool cover:
A = πd²/4 = 3.14*22²/4 = 379.94 ft²b.
The length of the rope:
C = πd = 3.14*22 = 69.08 ftAnswer:
346.19ft65.94ftStep-by-step explanation:
Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.
20 + 2 = 22ft
Part A:
The formula for the area of a circle is πr².
To find the radius just divide by two; 22 / 2 = 11ft
= π(11)²
= 121π
≈ 379.94ft
Part B:
We can use the circumference formula [ dπ ] to find how long the rope is.
= 22(3.14)
= 69.08ft
Best of Luck!
can someone help me with this question
Answer: The guage block height is 4.98 m
The base of the right triangle that is formed is 7.3784 m
The last angle in the triangle is 56 degrees
Step-by-step explanation:
Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base. Now we can use trig (SOHCAHTOA) to find the answaers.
Using sine, we can first find the gauge block height, O (Opposite). Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.
Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)
O = (8.9)*(0.5592)
O = 4.98 m, the height of the gauge block,
The base of the triangle, A, can be determined with cosine.
Cosine(34) = A/O, or A = Cosine(34)*O
A = (0.82904)*(8.9)
A = 7.3784 m
The sum of all angles in a triangle is 180 degrees.
180 = X + 34 + 90
X = 56 degrees
0.4141 rounded to the nearest thousandth
Answer:
0.4141 rounded to the nearest thousandth is 0.414.
Step-by-step explanation:
Since the number is 0.4141, and the number following the thousandths place is under 5, the thousandth place stays the same. If it were 5 or over, it would round up making it 0.415, but it's not so it is 0.414.
In the triangle above, the cosine of a is 0.8.What is sine of b?
Answer:
sin b = 0.8
Step-by-step explanation:
Since a and b are complementary angles , then
sin b = cos a = 0.8
The sine of angle b is 0.8
What is right triangle?"It is a triangle in which one of the angle measures 90° "
What is hypotenuse?"It is the longest side of the right triangle."
What is sine angle?"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle [tex]\theta[/tex] to the hypotenuse."
What is cosine angle?"In a right triangle, cosine of angle [tex]\theta[/tex] is the ratio of the adjacent side of angle [tex]\theta[/tex] to the hypotenuse."
What are complementary angles?"Two angles are complementary if the sum of their measures is equal to 90 degrees."
For given question,
We have been given a right triangle.
here,
∠a + ∠b = 90°
∠b = 90° - ∠a ................(i)
This means, a and b are complementary angles.
The cosine of a is 0.8
cos(a) = 0.8
We need to find the sine of angle b.
sin(b)
= sin(90 - a) .............(from (i))
= cos(a) .............(Since [tex]sin(90-\theta)=cos(\theta)[/tex])
= 0.8 ............(Given)
So, sin(b) = 0.8
Therefore, the sine of angle b is 0.8
Learn more about the sine angle here:
brainly.com/question/13256520
#SPJ2