By way of example, suppose A = {1, 2, 3} and B = {a, b, c}. Then the Cartesian product of A and B is
A × B = {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}
That is, each element in A gets a pairing with each element in B, and for each pairing you have n(A) choices for the first element and n(B) choices for the second element.
So if n(A) = p and n(B) = q, then n(A × B) = pq.
PLS TELL ME HOW TO FIND THIS ANGLE
Answer:
it is 80⁰
Step-by-step explanation:
cuz the it vertical angle
and to find a just get
180-80-70
Find the measure of the missing angle.
156°
a =
Answer:
Below!
Step-by-step explanation:
A straight line = 180 degrees, so all you need to do to find angle a is to subtract 156 from 180!
180 - 156 = 24 degrees
Hope this helped!
The graph shows the function f(x) = 2*
What is the value of x when f(x) = 8?
Ay
10-
A. 3
B. 2
C. 0
D. 1
Answer:
A
Step-by-step explanation:
Equate f(x) to 8 , that is
[tex]2^{x}[/tex] = 8 = 2³
Since bases on both sides are equal, both 2, then equate exponents
x = 3
The value of the x when the exponential function shown in the graph f(x) = 2ˣ is 8 is when x = 3, which is option A.
Here, given the graph of the function,
f(x) = 2ˣ
We have to find the value of x when f(x) = 8.
In order to find the value of x, when f(x) = 8, we have to write as,
f(x) = 8
2ˣ = 8
Now write 8 as an exponent with base 2.
2ˣ = 2³
Hence the value of x = 3
Learn more about Exponential Functions here :
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explanation would be appreciated. i don’t understand
Answer:
[tex]28\sqrt{3}[/tex]
Step-by-step explanation:
The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)
that ends up being [tex]\sqrt{108} = 36\sqrt{3}[/tex]
the small triangle are needs to be subtracted....
[tex]\frac{\left(4\cdot \:sin\left(90\right)\right)}{sin\left(30\right)}[/tex] that is the length of the unknown side...
1/2 B * h of that triangle get you to [tex]8\sqrt{3}[/tex]
just subtract the two areas
Answer:
(B) 28√3
Step-by-step explanation:
The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.
Area of triangle CDE:
Triangle ABC is equilateral. All sides have length 12.
AB = BC = AC = 12
BE = 8
BE + EC = BC
8 + EC = 12
EC = 4
In an equilateral triangle, all angles measure 60°.
m<C = 60°
m<CDE = 30°
Triangle CDE is a 30-60-90 triangle.
DE = EC√3
DE = 4√3
area of triangle CDE = bh/2
area of triangle CDE = (EC)(DE)/2
area of triangle CDE = (4)(4√3)/2
area of triangle CDE = 8√3
Area of triangle ABC:
Side AC is a base of triangle ABC.
AC = 12
(1/2)AC = 6
The altitude of triangle ABC from side AC to vertex B measures
h = 6√3
area of triangle ABC = bh/2
area of triangle ABC = (AC)(h)/2
area of triangle ABC = (12)(6√3)/2
area of triangle ABC = 36√3
area of quadrilateral ABED = area of triangle ABC - area of triangle CDE
area of quadrilateral ABED = 36√3 - 8√3
area of quadrilateral ABED = 28√3
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
O A. 12 feet
B. 13 feet
O C. 5 feet
O D. 17 feet
Answer:
13
Step-by-step explanation:
The diagonals of rectangle are equal in length.
The entrance ticket for a carnival costs $89.97, which includes a royal meal
that costs $10.85, 1 play station game, and 3 water rides (Each water ride
costs the same price). The cost of a water ride is twice as that of a play
station game. Find the cost of a water ride. Estimate to the nearest tenths.
Answer:
Cost of a play station game = $11.3
Cost of each water ride = $22.6
Step-by-step explanation:
Entrance tickets = $89.97
Royal meal = $10.85
Cost of a play station game = x
Cost of each water ride = 2x
Find the cost of a water ride
Entrance tickets = Royal meal + 1 play station game + 3 water rides
89.97 = 10.85 + 1(x) + 3(2x)
89.97 = 10.85 + x + 6x
89.97 = 10.85 + 7x
89.97 - 10.85 = 7x
79.12 = 7x
x = 79.12/7
x = 11.302857142857
Approximately to the nearest tenth
x = $11.3
Cost of a play station game = x = $11.3
Cost of each water ride = 2x
= 2(11.3)
= $22.6
If sec^2 teta (1+sin teta) (1-sin teta) = k, find k
Pls help no spamming
[tex]\boxed{\sf 1-sin^2\theta=cos^2theta}[/tex]
[tex]\boxed{\sf cos^2\theta=\dfrac{1}{sec^2\theta}}[/tex]
Solution:-
Let's do
[tex]\\ \sf\longmapsto k=sec^2\theta(1+sin\theta)(1-sin\theta)[/tex]
[tex]\\ \sf\longmapsto k=sec^2\theta(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto k= sec^2\theta(cos^2\theta)[/tex]
[tex]\\ \sf\longmapsto k=sec^2\theta\times \dfrac{1}{sec^2\theta}[/tex]
[tex]\\ \sf\longmapsto k=1[/tex]
[tex]\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]
[tex] \sec^{2} θ(1 + \sinθ)(1 - \sinθ) = k[/tex]
[tex] \sec^{2} θ \: (1 - { \sin}^{2} θ) = k[/tex]
[tex] { \sec }^{2} θ \cos^{2} θ = k[/tex]
[tex] \sec ^{2} θ. \frac{1}{ {sec}^{2}θ } = k[/tex]
[tex]1 = k[/tex]
Therefore:
[tex] \color{red}k = 1[/tex]
What is the range of f(x)?
{xl-2
{x|-2
{yl-5
{yl-5 sy<-1}
Answer:
-5≤y≤-1
Step-by-step explanation:
The range is the values that y takes
The smallest value of y is -5 and the largest value of y is -1
-5≤y≤-1
A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
(–1, 2)
(1, 3)
(8, 11)
(9, 12)
i really dont get this at all can someone help me and explain
Answer:
(8,11)
Step-by-step explanation:
1st line
y = x+ 3
We need to find the equation of the other line
We have two points (3, 1) and (4, 3)
Slope
m = (y2-y1)/(x2-x1)
= ( 3-1)/(4-3)
= 2/1 = 2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y =2x+b
Using the point (4,3)
3 = 2(4)+b
3 = 8+b
3-8=b
-5 =b
y = 2x-5
We have 2 lines
y =x+3 and y = 2x-5
Setting them equal to each other
x+3 = 2x-5
Subtract x from each side
x+3-x = 2x-5-x
3 = x-5
Add 5 to each side
3+5 =x-5+5
8=x
Now we can find y
y =x+3
y = 8+3
y=11
Answer:
c (8,11)
Step-by-step explanation:
multiply the monomials :
a) a³ , -6 a² b and 2 b³
b) 16 x⁶ , -10 xy² and 3/5 x² y²
c) -4 p² q² and 3/8 pq²
here we want to multiply different monomials, the particular important thing about this problem is learning how to simplify these multiplications.
Here we need to remember the property:
[tex]a^n*a^m = a^{n + m}[/tex]
Now we want to directly multiply the monomials:
a) a³ , -6 a² b and 2 b³
Here we just have:
[tex]a^3*(-6*a^2*b)*(2*b^3)[/tex]
Let's reorder that, so we can separate the variables and the coefficients, so then we can use the above property to solve this:
[tex]a^3*(-6*a^2*b)*(2*b^3) = (-6*2)*(a^3*a^2)*(b*b^3) = -12*a^5*b^4[/tex]
b) 16 x⁶ , -10 xy² and 3/5 x² y²
Like before, we want to simplify:
[tex](16*x^6)*(-10*x*y^2)*(\frac{3}{5}*x^2*y^2)[/tex]
Again, reordering that we get:
[tex](16*\frac{3}{5}*-10)*(x^6*x*x^2)*(y^2*y^2)[/tex]
Now solving each parenthesis:
[tex](16*\frac{3}{5}*-10)*(x^6*x*x^2)*(y^2*y^2) = -96*x^{6 +1 + 2}*y^{2 + 2}[/tex]
Simplifying the last expression we get:
[tex]-96*x^{6 +1 + 2}*y^{2 + 2} = -96*x^9*y^4[/tex]
c) -4 p² q² and 3/8 pq²
Here we want to simplify:
[tex](-4*p^2*q^2)*(\frac{3}{8}*p*q^2)[/tex]
Using the same approach as before, we will get:
[tex](-4*p^2*q^2)*(\frac{3}{8}*p*q^2) = (-4*\frac{3}{8})*(p^2*p)*(q^2*q^2) = \frac{-3}{2}*p^3*q^4[/tex]
If you want to learn more, you can read:
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What is the domain of g(x)
X is a real number
Answer:
The doing would be x
Step-by-step explanation:
since you are calculating domain for a specific value it would be the corresponding g(x) value which is the domain
3. What is the solution to the equation x3 = = 216
A. 72
B. 27
C. 8
D.6
Answer:
I assume that the question is [tex]x^{3} = 216[/tex]
6 * 6 = 36 35*6 = 216
in other words 6*6*6 = 216
Step-by-step explanation:
A random walk process for a single stock consists of the toss of a fair coin at the end of each day. If the outcome is heads, the stock price increases by 1.25 percent. If the outcome is tails, the stock price decreases by 0.75 percent. What is the drift of such a process
Answer:
+0.25
Step-by-step explanation:
Calculation to determine the drift of such a process
Using this formula
Drift=(Increases in stock price*50%)- (Decreases in stock price *50%)
Let plug in the formula
Drift = (0.5)(1.25) + (0.5)(-0.75)
Drift =0.625+ (0.375)
Drift = +0.25%
Therefore the drift of such a process is +0.25
In a function g(x), g(1) = 5. Which could be the function
of g(x)?
Answer:
Step-by-step explanation:
It could be almost anything.
g(x) = 5*x
g(x) = 5*(x)^2
g(x) = 2.5(2x)
g(x)= 4x *(5/3)
g(x) 10x / 2
Find the midpoint between two points on a number line if one of the points is at -7, and the other point is at 12.
A. 9.5
B. 5
C. -2
D. 2.5
Answer:
D
Step-by-step explanation:
The midpoint is the average of the 2 endpoints, that is
midpoint = [tex]\frac{-7+12}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 → D
resolve (5x+4) /( (x-4)( x+2))
Answer:
Step-by-step explanation:
Hello!
(5x+4) /( (x-4)( x+2))
(5x+4)/ (x² +2x -4x -8)=
(5x+4) /( x²-2x -8)
what is the area of the figure below?
Answer:
15x^9
Step-by-step explanation:
A=l x w
5x^4 times 3x^5 is basically 3*5*x^4*x^5
when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9
Jennifer is saving money to buy a bike. The bike costs $239. She has $127 saved, and each week she adds
$16 to her savings.
How long will it take her to save enough money to buy the bike?
It will take her
weeks to save for the bike.
Answer: 7 weeks
Step-by-step explanation:
16X + 127 = 239
16X = 239 - 127
16X = 112
X = 112/16
X = 7
Yesenia drove 45.3 miles on Monday and 3.8
miles more on Tuesday. How many miles did she
drive in all?
Answer:
49.1 milez
Step-by-step explanation:
Total miles driven=45.3+3.8=49.1 miles
Find the 5th term of each geometric sequence. 32,80, 200
Answer:
12.8
Step-by-step explanation:
factorise [tex]x^{2} - 121[/tex]
Answer:
(x+11)(x-11)
Step-by-step explanation:
Hello!
We are given the expression x²-121, and we want to factor it
The expression is a difference of squares expression.
The formula for the difference of squares is written as a²-b² can be factored as (a-b)(a+b)
121 is 11 squared, and x² is x squared
So that means that a=x, and b=11 in this case
Now substitute those values into the formula
a²-b²=x²-121=(x+11)(x-11)
Hope this helps!
Answer:
(x-11)(x+11)
Step-by-step explanation:
x^2 -121
x^2 -11^2
This is the difference of squares a^2 - b^2 = (a-b)(a+b)
(x-11)(x+11)
Help help help help help help help help help help help help
Answer:
$32.07
Step-by-step explanation:
I am not sure - are we seeing the full information about this problem ?
because the problem description is strangely vague and confusing, as it uses "total cost" two times for not the same thing ...
either total cost means including tax or not including tax. but it cannot mean both ...
I think the most likely understanding of this problem is that the first price is without tax, and now we need to calculate and add the extra 6% tax to get the really total price to be paid.
I will solve this now based on this assumption.
100% = $30.25
1% = 100%/100 = 30.25/100 = $0.3025
6% = 6×1% = 6×0.3025 = $1.815 ≈ $1.82
the total price is then calculated either by
100% + 6%
or by
106% = 100%×1.06 = 30.25×1.06 = $32.065 ≈ $32.07
in both cases we get the same result, of course.
Answer:
32.171
Step-by-step explanation:
Given m
11
n, find the value of x and y.
41°
וז.
20
n
yº
So I keep getting the wrong answer could someone help me pls
Answer:
x = 41°, y = 139°
Step-by-step explanation:
The given parameters are;
Line m is parallel to line n and lines m and n have a common transversal
The corresponding angles formed by the common transversal to the two parallel lines are 41° on line m and x° on line n
Therefore, x° = 41° by corresponding angles formed between on two parallel lines by a common transversal are equal
x° and y° are linear pair angles and they are, supplementary
∴ x° + y° = 180°
∴ x° + y° = 41° + y° = 180°
y° = 180° - 41° = 139°
y° = 139°.
Which graph represents the step function f(x)=⌊x+2⌋?
Answer:
biyotiptol graph by using pen
What is the estimate for 312+138+207
Answer:
657
Step-by-step explanation:
312 + 138 + 207
= 450 + 207
= 657
Answer:
600
Step-by-step explanation:
To round your answer, you check the tenths place to see if it is under 5 or above 5. If it is under 5, your answer will stay in the number the hundreds place is in currently. If it is above 5, you will add one to the hundreds place.
312: there is one in the tenths place, so it will stay as 300.
138: there is three in the tenths place, so it will stay as 100.
207: there is a zero in the tenths place, so it will stay as 200.
If you are doing it with the one's place, it is the same method. Either round up or down.
300 + 100 + 200 = 600
The answer is 600.
Which of the following correctly simplifies the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared.? (5 points) Select one: a. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 1 squared over 4 squared. = 1 over 6. b. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 0 over 4 squared. = 0 c. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 0 over 4 squared. = 0 d. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 1 squared over 4 squared. = 81 over 16.
Answer:
D
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The table shows certain values of a cubic function.
Answer:
7 and - infinity
Step-by-step explanation:
The function is decreasing in nature. The function has a maxima when x is near 7 and as the function is decreasing, the function will approach -infinity as x approaches positive infinity.
Help me solve for t please
Answer:
[tex]t = \frac{ v_{1} - v_{0}}{a} \\[/tex]
Step-by-step explanation:
[tex]a = \frac{v_{1} - v_{0}}{t} \\ a \times t = v_{1} - v_{0} \\ \frac{at}{a} = \frac{ v_{1} - v_{0} }{a} \\ t = \frac{ v_{1} - v_{0}}{a} \\ [/tex]
Which equation can be solved using the one-to-one property?
3X = 10
4In x = 2
log x = 5
4* = 47x+2
Answer:
3x=10
Step-by-step explanation:
x=10-3
x=7
i hope this answer will help u
Answer:
4x = 47x+2
Step-by-step explanation:
Using the one–to–one property, you can set x = 7x + 2.
Instructions: Find the missing side. Round your answer to the nearest tenth.
х
28°
25
Ans : 22
if my ans wrong im srry
Answer:
25 +28+x=180
53+x=180
x=180_53
x=127
