The angle of Z is 63.2 degree.
Isosceles Triangle:The word isosceles comes from the Ancient Greek term isosceles which literally means "equal-legged." An isosceles triangle has two of its sides of equal length, which means that the angles opposite these sides would also be of equal measure.
In Triangle ΔXYZ,
∠Y = 83°, XY = 9 and XZ = 10
To find the angle of Z
Using Sine rule :- sine rule relates the sine of each angle to length of opposite side.
[tex]\frac{Sin A}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]
Where, A, B , C are the angles of the triangles and a, b, c are the side of the triangles
Then, Apply it:
[tex]\frac{Sin83}{10}=\frac{SinZ}{9}[/tex]
Using cross multiplication:-
Sin 83 × 9 = Sin Z × 10
Sin Z = (Sin 83 × 9)/10
Sin Z = 0.893
∠Z = [tex]Sin^-^1(0.893)[/tex]
∠Z = 63.2°
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The geometric mean of two numbers is 5√3. One of the numbers is 3. What is the other number?
The two numbers whose geometric mean is 5√3 is 3 and 25
Given data ,
Let the geometric mean of the numbers be A = 5√3
Now , the first number is a = 3
Let the second number be b
And , the equation for the geometric mean as:
√(b x 3) = 5√3
To solve for "b", we can square both sides of the equation
(√(b * 3))² = (5√3)²
b x 3 = 75 (since (√a)² = a)
Now, we can divide both sides of the equation by 3
b = 75 / 3
b = 25
Hence , the other number is 25
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Which of the following combinations of side lengths would NOT form a triangle with vertices X, Y, and Z?
OA. XY = 15 mm, YZ 10 mm, X
,
OB. XY = 18 mm, YZ = 10 mm, XZ = 25 mm
XY = 18 mm, Z= = 13 mm, XZ = 22 mm
XY 15 mm, YZ = 10 mm, XZ = 22 mm
C.
OD.
XZ = 28 mm
The combinations of side lengths that would not form a triangle with vertices X, Y, and Z is A. XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.
How can we determine combinations of side lengths that would not form a triangle?We shall us the triangle inequality theory for this problem.
According to this theory, the addition of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, for the sides XY, YZ, and XZ to form a triangle, we must have:
XY + YZ > XZ
YZ + XZ > XY
XZ + XY > YZ
We can check each option to see if it satisfies these conditions:
A. XY = 15 mm, YZ = 10 mm, XZ = 28 mm
15 + 10 > 28 (not satisfied)
10 + 28 > 15 (satisfied)
28 + 15 > 10 (satisfied)
Option A does not satisfy the condition XY + YZ > XZ, so it would not form a triangle.
B. XY = 18 mm, YZ = 10 mm, XZ = 25 mm
18 + 10 > 25 (satisfied)
10 + 25 > 18 (satisfied)
25 + 18 > 10 (satisfied)
Option B satisfies all the conditions, so it would form a triangle.
C. XY = 18 mm, YZ = 13 mm, XZ = 22 mm
18 + 13 > 22 (satisfied)
13 + 22 > 18 (satisfied)
22 + 18 > 13 (satisfied)
Option C satisfies all the conditions, so it would form a triangle.
D. XY = 15 mm, YZ = 10 mm, XZ = 22 mm
15 + 10 > 22 (satisfied)
10 + 22 > 15 (satisfied)
22 + 15 > 10 (satisfied)
Option D satisfies all the conditions, so it can form a triangle.
Therefore, the combinations that would not form a triangle is A, where XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.
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Katy is making 2-layer dip for a party and has 10 ingredients from which to choose. In how many ways can she pick out and layer 2 ingredients?
Answer:
45
Step-by-step explanation:
10!/(10-2)!*2!
10!=1*2*3*4*5*6*7*8*9*10=3628800
8!=1*2*3*4*5*6*7*8=40320
2!=1*2=2
3628800/40320*2
3628800/80640=45
College p has 32% less
The initial sum of the number of students in College P and College Q is 5040.
We have,
Let's assume that the number of students in college Q is represented by Q, and the number of students in college P is represented by P:
P = Q - 0.32Q = 0.68Q
We also know that if 960 more students enroll in college P, the two colleges will have the same number of students.
So, we can set up another equation:
P + 960 = Q
We can substitute the first equation into the second equation to eliminate P:
0.68Q + 960 = Q
Solving for Q, we get:
0.32Q = 960
Q = 3000
The initial number of students in college Q was 3000.
We can use this value to find the initial number of students in college P:
P = 0.68Q = 0.68(3000) = 2040
So, the initial sum of the number of students in College P and College Q is:
P + Q = 2040 + 3000 = 5040
Therefore,
The initial sum of the number of students in College P and College Q is 5040.
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The complete question.
College P has 32% less students then college Q if 960 more students college P , the two college will have the same number of student what is the sum of the number of student in college p and college Q initially?
1) 5880
2)5040
3)8400
4)6720
Prove:is tangent to circle C.
The tangent at any point of a circle is perpendicular to the radius through the point of contact by showing that line PQ coincides with the radius OP.
Let us assume that we have a circle with center O and radius r.
Let P be any point on the circle .
And let Q be the point of intersection of the tangent to the circle at P and the radius OP,
To prove that PQ is perpendicular to OP.
First, we observe that OP is a radius of the circle and therefore its length is r.
Since PQ is tangent to the circle at point P,
It is perpendicular to the radius drawn from the center of the circle to point P.
As the tangent to a circle is perpendicular to the radius drawn to the point of contact.
This implies, angle QOP is a right angle.
Next, triangle OPQ is a right triangle with right angle at Q.
By the Pythagorean Theorem, we have,
OP²= OQ² + PQ²
Substituting r for OP and noting that OQ = r since Q is on the radius. we have,
⇒ r² = r²+ PQ²
Subtracting r² from both sides, we get,
⇒ PQ² = 0
This implies that PQ = 0,
In other words, that point Q coincides with point P.
PQ is a line that coincides with the radius OP.
And since angle QOP is a right angle, we can conclude that PQ is perpendicular to OP.
Therefore, it is proved that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
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The above question is incomplete, the complete question is:
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Quadrilateral JKLM is an isosceles trapezoid. Write each length or angle measure. Trapezoid J K L M is divided into 4 triangles by its diagonals, which intersect at point R. Angle K M J is 27 degrees and angle L M K is 78 degrees. J R is 39 units and K R is 42 units.
m∠JKL =
m∠KJM =
JL =
m∠KRL =
JL = 4x = 12 units.
Step-by-step explanation:
Since JKLM is an isosceles trapezoid, we know that parallel sides JK and LM are congruent. Additionally, since the diagonals intersect at point R, we know that angles JRM and KRL are congruent.
To find m∠JKL, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees. We know that angle LMK is 78 degrees, angle KJM is 27 degrees, and JRM and KRL are congruent. So, m∠JKL = 360 - 78 - 27 - 2x, where x is the measure of angle KRL.
To find angle KRL, we can use the fact that JRL and KRM are congruent (since they are opposite angles formed by intersecting lines). We also know that JRL + KRL = 180 degrees (since they form a linear pair). Therefore, JRL = KRL = (180 - 27 - 78) / 2 = 37.5 degrees.
Plugging this into our equation for m∠JKL, we get:
m∠JKL = 360 - 78 - 27 - 2(37.5) = 197 degrees
To find m∠KJM, we can simply use the given measure:
m∠KJM = 27 degrees
To find JL, we can use the Pythagorean theorem on right triangles JRL and KRL. We know that JRL is a 3-4-5 right triangle (since 3, 4, 5 is a Pythagorean triple), so JR = 3x and RL = 4x for some value of x. Similarly, we know that KRL is a 7-24-25 right triangle (since 7, 24, 25 is another Pythagorean triple), so KR = 7y and RL = 24y for some value of y.
Since JR = 39 and KR = 42, we can set up two equations:
3x + 24y = 39
4x + 7y = 42
Solving for x and y using any method (substitution, elimination, etc.), we get:
x = 3, y = 2
Therefore, JL = 4x = 12 units.
If V=6i-j and w=-i+6j, What is v times w
The value of the product is -6i² + 37ij - 6j²
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of coefficients, their variables, constants, terms, and factors.
Also note that algebraic expressions are expressions that consists of mathematical or arithmetic operations.
These operations are listed thus;
ParenthesesBracketSubtractionMultiplicationDivisionAdditionFrom the information given, we have;
Then, the product is;
vw = (6i - j)(-i + 6j)
expand the bracket
= -6i² + 36ij + ij - 6j²
add the like terms
= -6i² + 37ij - 6j²
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What are the values of sin X and tab Y in the triangle below?
The value of the identities are;
sin X= 3/√34
tan Y = 3/5
Option A
How to determine the valueTo determine the value, we need to take note of the different trigonometric identities. These identities are;
sinetangentcotangentcosecantsecantcosineFrom the information given, we have that;
the hypotenuse side = √34
The opposite of X is 3
the opposite of Y is 5
Using the sine identity;
Substitute the opposite and the hypotenuse in the fraction order
sin X = 3/√34
Using the tangent identity, we have;
tan Y = 3/5
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Convert the fraction below into a decimal 23/40?
Answer:
Step-by-step explanation:
23/40 = 0.575
What is the measurement of the hypotenuse in the triangle?
07
08
0 ~/61
4
The length of the hypotenuse of the given right angled triangle is √113.
Three given side lengths of a triangle a, b and c are said to be the sides of the right angled triangle if -
a² = b² + c²
The above theorem is known as the Pythagoras theorem.
Now, we can write that -
(hypotenuse)² = (base)² + (perpendicular)²
(hypotenuse)² = (7 x 7) + (8 x 8)
(hypotenuse)² = 49 + 64
(hypotenuse)² = 113
(hypotenuse) = √113
So, the length of the hypotenuse of the given right angled triangle is √113.
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Look at the graph below. Is it a function or not a function? Explain your reasoning.
What is an expression equivalent to 2^3x − 4?
The equivalent expression to the given expression [tex]2^{3x}[/tex] - 4 is equal to 8ˣ - 4.
The expression is equal to,
[tex]2^{3x}[/tex] - 4
Simplify the expression using the law of exponent we get,
yᵃᵇ = (yᵃ)ᵇ
Here in the expression the value of y = 2,
Value of a = 3
and the value of b = x
Substitute the value in the formula we get,
= ( 2³ )ˣ - 4
value of the exponent 2³ = 2 × 2 × 2
= 8
This implies the equivalent expression is,
= 8ˣ - 4
Therefore, the value of the given expression is equivalent to 8ˣ - 4.
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A recent college graduate has a $2,400 balance on a credit card that charges 13.5% interest, compounded monthly. What monthly payment must be made to pay this balance in two years?
$116.46
$102.25
$114.66
$113.50
The monthly payment required to made for the balance on credit card of $2400 with 13.5% of compound interest is given by $114.66.
Balance on credit card = $2,400
Rate of interest = 13.5%
Time period = 2 years
Let us consider monthly payment be 'M' required to pay off a balance 'B'.
Time period of time 'n' with monthly interest rate 'r' .
Use the formula of monthly compounding is ,
M = r × B / (1 - (1+r)⁻ⁿ )
Here, the balance is B = $2,400,
The interest rate is r = 0.135/12 = 0.01125 since the interest is compounded monthly.
And the period of time is n = 2 years × 12 months/year
= 24 months.
Plugging in these values, we get,
M = 0.01125 × $2,400 / (1 - (1+0.01125)⁻²⁴)
Simplifying this expression, we get,
⇒ m = 27 /(1 - (1.01125)⁻²⁴)
⇒ m = 27 / ( 1- 0.7645 )
⇒ m = $114.66
Therefore, the monthly payment required to pay off the $2,400 balance with compound interest in two years is $114.66.
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Which situation could the probability distribution table represent?
X
A
B
C
P(X)
1
10
3
3
10
There are 50 cards. Each card is labeled A, B or C. Ten of the cards are labeled A, 30 of the cards are labeled B and 10 of
the cards are labeled C.
There are 20 cards. Each card is labeled A, B or C. Three of the cards are labeled A, 12 of the cards are labeled B and 5
of the cards are labeled C.
There are 40 cards. Each card is labeled A, B or C. Four of the cards are labeled A, 24 of the cards are labeled B and 12
of the cards are labeled C.
There are 60 cards. Each card is labeled A, B or C. Six of the cards are labeled A, 30 of the cards are labeled B and 24 of
the cards are labeled C.
The situation that could represent the probability distribution table is
There are 40 cards. Each card is labeled A, B or C. Four of the cards are labeled A, 24 of the cards are labeled B and 12 of the cards are labeled C; option is C.What is the probability distribution table?Considering the given probability distribution table:
X : P(X)
A = 1/10
B = 3/5
C = 3/10
Let there be 40 cards each labeled A, B, and C.
The probabilities are aclculated as follows:
Four of the cards are labeled A;
Hence, P(A) = 4/40 or 1/10
24 of the cards are labeled B;
Hence, P(B) = 24/40 or 3/5
12 of the cards are labeled C;
Hence, P(C) = 12/40 or 3/10
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What is the percentage of students who only answered one question?
75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . 50 is the percentage of students who only answered one question
A percentage is a quantity or ratio that is expressed as a fraction of 100. It is symbolised by the '%' percentage sign. 'pct' or 'pc' are the acronyms used to indicate the percentage. In sense, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.
Students answer Q.1 or Q.2 or both correctly = ( 100 - 20) = 80%
x% students answered both correctly
( 75 - x) + ( 55 - x) + x = 80
130 - x = 80
x = 50
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Your question is incomplete but most probably your full question was,
75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . What percent of students answered both question correctly ?
A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 13 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you seject an appetizer, an entrée, and a dessert?
To calculate the number of different meals available when selecting an appetizer, an entrée, and a dessert, we need to multiply the number of choices for each course.
Using the multiplication principle of counting, we can find the total number of meal options as follows:
Total number of meal options = number of appetizer choices x number of entrée choices x number of dessert choices
Total number of meal options = 5 x 13 x 4
Total number of meal options = 260
Therefore, there are 260 different meals available when you select an appetizer, an entrée, and a dessert from the given choices.
Solve the following differential equations:
The solution of the differential equation is y + e²ˣ = Ceˣ, if Ceˣ > 0
or -y - e²ˣ = Ceˣ, if Ceˣ < 0.
What is the solution of the differential equation?The solution of the differential equation is calculated as follows;
dy/dx = e²ˣ + y
Apply the method of separating viables;
dy/dx = e²ˣ + y
dy/(y + e²ˣ) = dx
Integrate both sides;
∫ dy/(y + e²ˣ) = ∫ dx
ln|y + e²ˣ| = x + C
To solve for y, we need to exponentiate both sides;
|y + e²ˣ| = e^(x+C) = Ceˣ
The final solution becomes;
y + e²ˣ = Ceˣ, if Ceˣ > 0
or
-y - e²ˣ = Ceˣ, if Ceˣ < 0
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i really need help with this
Answer:
(a) 15 students
(b) 3 minutes (by 4 students)
(c) 2 students
(d) 7 students
(e) Ordering this data from least to greatest:
0, 1, 2, 2, 3, 3, 3, 3, 5, 5, 7, 7, 9, 9, 11
The median number is 3.
The diagram shows a square.
(6x - 1) cm
Find the length of the side of the square.
Your final answer must say, side = . . . cm
(4x + 6) cm
Cm=?
+
The length of the side of the square is given as follows:
20 cm.
How to obtain the side length of the square?In the figure, there are two expressions used to give the side length to each square, as follows:
6x - 1.4x + 6.In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:
6x - 1 = 4x + 6
2x = 7
x = 3.5 cm.
Then the side length of the square is obtained as follows:
6(3.5) - 1 = 20 cm.
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Find the sum of the infinite series, if possible.
SOMEONE PLEASE PLEASE HELP!!
Expressing as single logarithm 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)
How to express the logarithm eqaution as a single logarithm?Since we have the logarithm expression
3/2㏑4x⁶ - 2/5㏑2y²⁵
To simplify, we proceed as follows
First, we use the power law of logarithm which states that
n㏑x = ㏑xⁿ
So, using this, we have that
3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑4x⁶ - 2/5㏑2y²⁵
[tex]= ln4x^{6\times\frac{3}{2} } - ln2y^{25\times\frac{2}{5} } = ln4x^{3\times3} } - ln2y^{5\times2 }[/tex]
= ㏑4x⁹ - ln2y¹⁰
Using the subtraction law of logarithm, which states that
㏑a - ㏑b = ㏑(a/b), we have that
㏑4x⁹ - ln2y¹⁰ = ㏑(4x⁹/2y¹⁰)
= ㏑(2x⁹/y¹⁰)
So, 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)
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Which Box And Whisker Plot Has GREATEST interguartile range? picture below
The box and whisker plot that has the greatest interquartile range is option 3..
What is the Interquartile Range of a data Displayed in a Box and Whisker Plot?The interquartile range of a data set can be found by finding the difference of the data at the beginning and end of the edges of the rectangular box in a box and whisker plot.
It is also the difference between the third and first quartile.
The box and whisker plot in option 3 has the greatest interquartile range because the difference of the Q3 and Q1 is close to 9, which is the highest compared to the other data.
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Find the value of each variable in the following parallelogram - show work
Answer: x=14 y=10
Step-by-step explanation:
Raymond applies the pearl guitar fret markers to his fret board as shown. Each fret marker is in the shape of a parallelogram. Each of the 3 bottom fret markers has a base that measures mm and a height of mm. What is the area of each of the bottom fret markers? please help me im in desperate need for this awnser
The area of each of the bottom fret markers using given dimensions is equal to 364 square millimeters.
Base of the fret marker = 45.5mm
Height of the fret marker = 8mm
Attached image.
The area of a parallelogram can be found by multiplying the base by the height.
Here, the base of each of the 3 bottom fret markers is 45.5mm and the height is 8mm.
So, the area of each fret marker is,
Area = base x height
Substitute the value of base and height we have,
⇒ Area = 45.5mm x 8mm
⇒ Area = 364 mm²
Therefore, the area of each of the 3 bottom fret markers is 364 square millimeters.
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The above question is incomplete, the complete question is:
Raymond applies the pearl guitar fret markers to his fret board as shown. Each fret marker is in the shape of a parallelogram. Each of the 3 bottom fret markers has a base that measures 45.5mm and a height of 8mm. What is the area of each of the bottom fret markers?
Attached image.
3x-6y=-30 in slope-intercept form
Answer:
y = 1/2x + 5
Step-by-step explanation:
hope this helps :)
Answer:
y= 1/2x +5
Step-by-step explanation:
3x-6y=-30
-3x -3x
-6y = -3x -30
/-6 /-6 /-6
y = 1/2 +5
The widget store manager points out that not all widget brands get equal purchase rates. A brand on premium shelf space has a 0.28 probability of being selected by each customer. He is willing to give you premium shelf space at the front of the store for a small fee. The additional fee, plus the original transportation costs, would raise the minimum number of widgets you would have to sell to 40 (to cover transportation costs and additional fee). Assuming 200 customers come into the store, use a binomial distribution to estimate the probability of at least covering the transportation costs and additional fee. Write your answer as a probability (not a percent) rounded to 4 decimals.
The probability of at least covering the transportation costs and additional fee is 0.9888.
To estimate the probability of at least covering the transportation costs and additional fee, we can use the binomial distribution.
The binomial distribution models the probability of success or failure in a fixed number of independent trials.
The probability of success is 0.28 (choosing a brand on premium shelf space), and we want to calculate the probability of at least 40 successes out of 200 trials (customers).
We can use the binomial probability formula to calculate this probability:
P(X ≥ 40) = 1 - P(X < 40)
Where:
P(X≥ 40) is the probability of at least 40 successes
P(X < 40) is the probability of less than 40 successes
P(X < 40) = sum of binomial probabilities for x = 0 to 39
P(X < 40) = sum [from x = 0 to 39] (200 C x) × (0.28ˣ)×(0.72²⁰⁰⁻ˣ)
P(X < 40) = 0.0112
Therefore,
P(X ≥ 40) = 1 - P(X < 40)
P(X ≥ 40) = 1 - 0.0112
P(X≥ 40) = 0.9888
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log 3 + log 6
this expression is equivalent to the log of what number?
The equivalent logarithmic value of the given expression log 3 + log 6 is equal to logarithm of 18.
The expression is equal to,
log 3 + log 6
By using the law of multiplication we have,
Log A + Log B = Log ( A × B )
Using the properties of logarithms, we can simplify the expression and get the equivalent logarithm number ,
Substitute the value of A = 3 and value of B = 6 in the formula we have,
log 3 + log 6
= log (3 × 6)
= log 18
Therefore, the expression log 3 + log 6 is equivalent to the logarithm of 18.
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at a particular school, 30% of children travel by bus. if it represents 360 children, how many students attend school?
If 30% children travelling by bus is represented by 360 children, then total number of students who attended the school are 1200.
The "Percent" is a way of expressing a fraction or proportion as a number out of 100. It is a unit of measurement used to represent the relative size or amount of something compared to the whole.
If 30% of the children at a particular school travel by bus and this represents 360 children, we use this data to find total number of children who attend the school.
Let "X" be = total number of children at the school.
We know that 30% of X represents 360 children, so we can write an equation:
⇒ 30% of X = 360,
⇒ 30% × X = 360,
⇒ 0.3 × X = 360, ...because 30% = 0.3,
⇒ X = 360/0.3 = 1200,
Therefore, there are 1200 students who attend the school.
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What’s the mean of 46,57,66,63,49,52,61,68
Answer:
Step-byHow do I calculate the mean?
The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value
-step explanation:
46+57+66+63+49+52+61+68= 462/8 the total number of observation
the answer 57
Help on 3 and 5…………..
Answer:
The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.
3) 56 + 2x = (1/2)(112 + x)
x = 0, so the measure of arc BCD is
360° - 112° = 248°.
5) 3 + 20x = (1/2)(43x - 3)
6 + 40x = 43x - 3
3x = 9, so x = 3
The measure of arc MLK is
360° - (43(3) - 3)° = 360° - 126° = 234°.