Answers
Answer:
10- I can't really help you with that one you have to just draw it on your own.
11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees,y=64 degrees,z=116 degrees
Step-by-step explanation:
11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.
Related Questions
Rodrick is visiting the local museum exhibit and has a maximum of $30 dollars to spend. The entry ticket cost $7. He can spend g dollars. Write an inequality that can find g and the amount of money Rodrick can spend at the gift shop.
Answers
Entry ticket = $7
Gift shop money = $g
Maximum to spend = $30
Inequality => 7+g ≤ 30
Hope it helps!
Divide 10000 among Irfan and asim in the ratio 2:3
Answers
Step-by-step explanation:
ratio of ifran and Asim= I:A
2:3
rule of equation= TOTAL ratio=total amount
=(addition of the two ratios which are 2 and 3=5) and 1000
=5=1000
ratio of ifran(2)=? cross multiplication
=2×1000÷5
=400
=5=1000
ratio of Asim(3)=? cross multiplication
=3×1000÷5
=600
Answer:
Step-by-step explanation:
Irfan and Asim's ratio is 2:3, which means Irfan gets 2 parts while Asim gets 3. There are 5 parts in total, and this equals 10000. Let parts be p. [tex]5p=10000\\\\p=2000[/tex]
This means Irfan gets 2p = 4000 and Asim gets 3p = 6000.
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Cedrick is going to meet his mother for dinner at a restaurant halfway between his house and hers. On a coordinate grip map, Cedrick’s house is at (–51, –26) and his mom lives at (2, –4).
Where is the best restaurant for them to meet?
Greek restaurant at (–25, –15)
French restaurant at (–27, –11)
Mediterranean restaurant at (–28, –12)
Thai restaurant at (–38, –1)
Answers
Using the mid-point concept, the best restaurant for them to meet is given by:
Greek restaurant at (–25, –15).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For the midpoint between his house and his mom's, the coordinates are given as follows:
x = (-51 + 2)/2 = -49/2 = -24.5.y = (-26 - 4)/2 = -30/2 = -15.Hence the Greek restaurant is the best option, as it is closest.
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Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
Answers
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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Find the value(s) of x in the function f(x) = |-2x – 3| when f(x) = 5. (Separate multiple answers with a comma.)
Answers
Answer:
x = -4, 1
Step-by-step explanation:
Since we have a absolute value function here, we can tell there is goning to be multiple values.
First we will find x with the original function since we know |5| = 5.
Given f(x) = 5 = -2x-3,
[tex]2x-3 = 5 \\
-2x-3+3 = 5 + 3 \\
-2x = 8 \\
x = \frac{8}{ - 2} \\ = - 4[/tex]
Now we also know that |-5| = 5 as well (absolute value)
Given |-2x-3| = |-5|,
[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]
You can verifiy these 2 values by substituting them into the equation.
f(-4) = |-2(-4)-3|
= |8-3|
= |5|
= 5
f(1) = |-2(1)-3|
= |-2-3|
= |-5|
= 5
A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.
What is a Modulus function?A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.
The function is given as,
f(x) = |-2x-3|
which implies that f(x) = -2x - 3 for x > 0 and f(x) = -(-2x - 3 )for x < 0
As per the question ,
Substitute the value of f(x) = 5, for both the cases to get the value of x as,
-2x - 3 = 5 and -(-2x - 3 ) = 5
=> x = -4 and x = 1.
Hence, the values of x obtained for the given condition are x =-4 and x = 1.
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A discount store had monthly sales of $86,600 and spent 14% of it on promotions. how much was spent on promotion?
Answers
The amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
The percent signifies the hundredth part of the whole.
When informed that the promotion is 14 percent of the monthly sales of $86,600.
Therefore, to calculate the total amount spent on promotion, we calculate 14 percent of 86600.
Therefore, the total amount on promotion = 14% of $86,600 = $ (14/100 * 86,000) = $ (14*866) = $12,124.
Therefore, the amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
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It is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring. True or False
Answers
It is a true statement that it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
What is a cubic equation?A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.
Thus, it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
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I want to fence in a square vegetable patch. The fencing for the east and west sides cost $7 per foot, and the fencing for the north and south sides cost $4 per foot. Find the total cost (I'm dollars) of the fencing as a function of the length (in feet) of a side x.
Answers
The total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
How to find the perimeter?The perimeter is made by adding the south, north, east, and west side.
Given that
The cost of fencing for the east and west sides is $7 per foot, and the cost of fencing for the north and south sides is only $5 per foot.
We have to find total cost of the fencing is a function of the length of a side x (feet).
The east and west fencing cost is $7/ft but the south and north fencing cost is $5/ft.
x = north and south fencing
y = the east and west sides, then you can get this equation.
Total cost= (south +north) × 5 + (east+ west) × 7
Total cost =(x + x) × 5 + (y+ y) × 7
Total cost = 5(2x) + 7(2y)
Total cost = 10x + 14y
Hence, the total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
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Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
The equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
How to determine the equations?The given parameters are:
Length = y
Width = y - 5
Area = 750
The area of a rectangle is:
Area = Length * Width
So, we have:
y * (y - 5) = 750
Expand
y^2 - 5y = 750
Rewrite as:
y^2 - 5y - 750 = 0
Factorize
(y + 25)(y – 30) = 0
Hence, the equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
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Complete question
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room?
Which of the following is NOT a factor of b3 +6b²?
63
062
Ob
(b + 6)
Answers
Answer:
b³
Step-by-step explanation:
The lowest common multiple of the expression is b². This because, taking out a factor of b, b ( b² + 6b ), taking out a factor of b², b² ( b + 6 ),
taking out a factor of ( b + 6 ), ( b + 6 ) b². As a result b² is only the option which is not a factor.
Dr. Silas studies a culture of bacteria under a microscope. The function b_1(t)=1200(1.8)^t represents the number of bacteria t hours after Dr. Silas begins her study.
The number of bacteria in a second study is modeled by the function b_2(t)=1000(1.8^t.
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?
The _ means the 1&2 is under the b
Answers
The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.
What are exponential Function ?Exponential functions are are written as y(x) = abˣ
Here
a is the initial population
b is the rate of growth or decrease
x is the time taken
The Given exponential function is
[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]
From the standard equation of Exponential function
(a) a = 1200 and 1000 is the initial population of the bacteria
(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies
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Brad bought an MP3 player on sale at a 20%
discount from its regular price of $120. If there
is a 5% sales tax that is calculated on the sale
price, how much did Brad pay?
Answers
Answer:
$100.8
Step-by-step explanation:
Discount=20% of 120 =24
Before tax: BP=120-24=96
After Tax BP=105% of 96=$100.8
Find the value of [tex]\frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}
Answers
Observe that the [tex]n[/tex]-th term in the sum is
[tex]\dfrac{n^2 + n(n+1) + (n+1)^2}{n^3(n+1)^3} = \dfrac{3n^2 + 3n + 1}{n^3 (n+1)^3} \\\\ ~~~~~~~~ = \dfrac{(n+1)^3 - n^3}{n^3(n+1)^3} \\\\ ~~~~~~~~ = \dfrac1{n^3} - \dfrac1{(n+1)^3}[/tex]
Then the sum telescopes, and we have
[tex]\displaystyle \sum_{n=1}^{9} \frac{n^2 + n(n+1) + (n+1)^2}{n^3 (n+1)^3} = \sum_{n=1}^{9} \left(\frac1{n^3} - \frac1{(n+1)^3}\right) \\\\ ~~~~~~~~ = \left(\frac1{1^3} - \frac1{2^3}\right) + \left(\frac1{2^3} - \frac1{3^3}\right) + \cdots + \left(\frac1{8^3} - \frac1{9^3}\right) + \left(\frac1{9^3} - \frac1{10^3}\right) \\\\ ~~~~~~~~ = \frac1{1^3} - \frac1{10^3} \\\\ ~~~~~~~~ = 1 - \frac1{1000} = \boxed{\frac{999}{1000}}[/tex]
The sum of the series is 999/1000 .
What is a Series ?A series is a sequence of expression in a certain pattern.
The series of n terms is given
[tex]\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}[/tex]
nth term of the series is given by
[tex]\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}[/tex]
On simplification it can be written as
[tex]\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}[/tex]
The sum of terms from 1 to 9 is given by
∑ ( [tex]\rm \frac{ 1}{n^3} - \frac{1}{(n+1)^3}[/tex])
= [tex]\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}[/tex]
= (1/1³) - (1/10³)
= 999/1000
Therefore the sum of the series given is 999/1000
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Check all of the functions that are odd. f(x)=x3-x2 f(x)=x5-3x3 2x f(x) = 4x 9 f (x) = startfraction 1 over x endfraction
Answers
The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
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Answer:
B.) f(x)=x5-3x3+2x is odd
D.) f (x) = 1/ x is odd
Step-by-step explanation:
just did it on edg
Evaluate the expression [tex]\sqrt[5]{3125{e}^{\frac{11 \pi }{2} i}}[/tex], leaving your answer in polar form.
Answers
[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]
Write the equation of the line that is parallel to the line y=−74x−2 through the point (4,-2).
Answers
Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.
Substituting into point-slope form,
[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]
Which is not a method for solving a system of equations?
A. Graphing
B. Substitution
C. Fundamental Theorem of Arithmetic
D. Linear combination
Answers
Fundamental Theorem of Arithmetic is not a method for solving a system of equations.
What are system of equation?A system of equations is a collection of two or more equations with a same set of unknowns.
The system of equation can be solved using the following method.
Graphing methodSubstitution methodLinear combinationThe graphing involves using graph to find the intersection of the system of equation.
Substitution method involves substituting one variable to another.
Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations
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Use clustering estimation to find the approximate total in the following question.
What is the estimated total of 674, 692, 724, and 739?
ill make you brainliest
Answers
The estimated total of 674, 692, 724, and 739 is: 2800.
Clustering estimation techniqueTo find the sum using clustering estimation technique first step is to round each number to the nearest 10s.
674 into 670
692 into 690
724 into 720
739 into 740
Second step is to add
Addition=670+690+720+740
Addition=2820
2820 to the nearest 100s is 2800.
Therefore the estimated total of 674, 692, 724, and 739 is: 2800.
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6. Construct the Truth Table and Determine whether each of the following compound
proposition is a Tautology, Contradiction or Contingency.
Answers
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
What is Truth table?A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.
What is Contingency?A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '
What is Contradiction?A statement is called a contradiction if the final column in its truth table contains only 0's.
What is Tautology?A tautology is a statement that is always true.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
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find the size of the angles marked with letters in each diagram
Answers
A construction company is building a drainage ditch that is shaped like a "V". The ditch will be 10 feet wide at ground level and 5 feet deep at its lowest point. The depth of the ditch increases at a rate of 1 vertical foot for every 1 horizontal foot out from the lowest point at the center of the ditch .If x is the horizontal distance from the left edge of the ditch, in feet, determine which absolve value function models the ditch's vertical depth below ground level, in feet.
A. f(x) = |x + 5| − 5
B. f(x) = -|x − 5| − 5
C. f(x) = -|x − 5| + 5
D. f(x) = |x − 5| − 5
Answers
The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5
How to illustrate the function?From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.
Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5
In conclusion, the correct option is B.
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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
Answers
Answer:
t=5.5
Step-by-step explanation:
The ball hits the ground when h = 0.
[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]
However, as the answer must be positive, t=5.5
Solve the equation on the
interval [0, 2π).
4(sin x)² - 2 = 0
Answers
The solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
What is the solution to the equation on the interval?Given that;
4(sin x)² - 2 = 0Interval = [ 0, 2π )4(sin x)² - 2 = 0
Add 2 to both sides and divide both sides 4
4(sin x)² - 2 + 2 = 0 + 2
4(sin x)² = 2
(4(sin x)²)/4 = 2/4
(sin x)² = 1/2
Square both sides
√((sin x)²) = ±√(1/2)
sin x = ±√(1/2)
sin x = ±(√2)/2
Next, we solve for x
Not that 180° = π
x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4
x = π/4
Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.
x = π - π/4
x = 3π/4
Now, we find the period of sin x
2π / |b|
We know that, the distance between a number and zero is 1
2π / 1
2π
Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.
Since sine function is negative in third and fourth quadrant,
x = 2π + π/4 + π
x = 5π/4
Now, add 2π to every negative angle to get a positive angle
x = 2π + ( - π/4 )
x = 2π×4/4 - π/4
x = ((2π × 8) - π ))/4
x = (8π - π)/4
x = 7π/4
Therefore, the solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
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Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x).
n=15, x=2, p=5
P(x)=
Answers
Using the binomial distribution, it is found that P(X = 2) = 0.0032.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 15, x = 2, p = 0.5.
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{15,2}.(0.5)^{2}.(0.5)^{13} = 0.0032[/tex]
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enter your answer in scientific notation
Answers
Answer:
[tex]1.7x10^{4}[/tex]
Step-by-step explanation:
To divide the scientific notation, divide 5.1 to 3 then subtract the exponents of your ten - following the quotient rule.
5.1/3 = 1.7, then 9-5 = 4
final answer is [tex]1.7x10^{4}[/tex]
A line is parallel to y = 5x + 3 and
intersects the point (3, 9).
What is the equation of this
parallel line?
y = 5x + [?]
Answers
Answer:
y = 5x - 6
Step-by-step explanation:
1. In a linear equation, it is represented by y = mx + b
2. A line parallel to another has the same slope (m) but a different y-intercept (b)
3. So we know that it is y = 5x as the first half. However, we need to find the new y-intercept.
4. Let's plug in the point we know into the equation, and see what amount we are missing (the y-intercept)
5. y = 5(3)
6. y = 15, however, we know that y = 9. That's a difference of -6.
This shows us that the y-intercept is -6 making the full equation:
y = 5x - 6
We can check by putting the point back into the equation:
y = 5(3) - 6
y = 15 - 6
y = 9
This correlates with the original point, we have solved the equation.
5. Ellie's street address is a prime number greater than 10 and less than 19. Which of the following could be Ellie's street address?
Answers
We want to find a prime number greater than 10 and less than 19.
* What is a prime number?
Prime number is a number that cannot be divided by any number other than 1 and itself
There are so many possibilities:
Ellie's street address could be 11, 13 or 17
Hope it helps!
keiko david and tony have a total of 106$ in their wallets. david has $6 less than keiko tony has 2 times what david has. how much do they have in their wallets? Please help
Answers
Keiko have $31 in her wallet.
David have $25 in his wallet.
Tony have $50 in his wallet.
Step-by-step explanation:Keiko
Let x = the amount in Keiko’s wallet.
David
David has $6 less than Keiko .
x - 6
Tony
Tony has has two times what David has.
2(x - 6)
The total sum of their money = 106
Keiko
x + x - 6 + 2(x - 6) = 106
2x - 6 + 2x - 12 = 106
4x - 18 = 106
4x = 106 + 18
4x /4 = 124/4
x = 31
Therefore Keiko have $31 in her wallet.
David
x - 6
31 - 6 = 25
Therefore David have $25 in his wallet.
Tony
2(x - 6)
2(31 - 6)
2(25) = 50
Therefore Tony have $50 in his wallet.
To check your work out
31 + 25 + 50 = 106
Please help!
P(A) = 1/3
P(B) = 2/9
P(A U B) = 4/9
Find P(A ∩ B).
A. 1
B. 1/3
C. 1/9
D. 20/18
Answers
Answer:
[tex]\sf C. \quad \dfrac{1}{9}[/tex]
Step-by-step explanation:
Addition Law for Probability
[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]
Given:
[tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]
[tex]\sf P(B)=\dfrac{2}{9}[/tex]
[tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]
Substitute the given values into the formula and solve for P(A ∩ B):
[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]
[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]
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Answers
The angle of X is 108°
Given,
XW ≅ YZ
∠Z = 72°
then ∠X = ?
Properties of trapezoid are:
The base sides are the only pair of sides that are parallel. Other than the base, the remaining sides are all non-parallel and equal in length. The length of the diagonals is constant. the same for the base angles.We know that from the figure that ∠Z = ∠V & ∠W = ∠U
∵ Isosceles trapezoid rule
And sum of all the angles in a trapezoid = 360°
Now, 2 × 72 = 144
∴ 360 ₋ 144 = 216°
Now sum of other two angles = 216°
one angle = 216/2
= 108°
Therefore the angle of ∠X is 108°
Learn more about "Quadrilateral" here-
brainly.com/question/16691874
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