Answers
By using properties of right triangles, we will see that the value of x is 7.72
How to find the length of side x?In the image we have a set of right triangles, and we want to find the value of x.
Let's look at the large triangle in the left, we know that the hypotenuse measures 18 units and one angle measures 64°, with that information we can get the adjacent side (the dashed line, let's call it A) to that angle:
Cos(64°) = A/18
18*cos(64°) = A = 7.05
Now we know one of the cathetus of the smaller right triangle (the one we can see in the right side). Here we know one angle that measures 20° and the opposite to that angle measures 7.05
Then the value of x is given by the equation:
x = 7.05/sin(20°) = 7.72
We conclude that the value of x is 7.72
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Related Questions
W X Y Z is a square. If W T=3 , find each measure. m∠WTZ
Answers
Step-by-step explanation:
In this exercise we have to use the knowledge of quadrilaterals to calculate the measures of each side of the square, in this way we can say that it will be valid:
Given in the exercise that each the value of:
WT=3
The diagonals of a square are congruent, and bisect each other, that will help to find:
Write the equation of the line that is perpendicular to y = 2x+4 and passes through the
point (-4,-1).
y =____________ X+
Answers
Answer: (Likely) y = -2x
Step-by-step explanation:
1. We know the line y = 2x + 4, it intersects 4 and it's rate of change is 2. We also know the point it is passing, (-4,-1).
2. With this info, It is best to confirm the slope is likely -2, since it is likely that lines when perpendicular are likely to be congruent.
3. So, how about the y intercept? Well, it's simple as well, we will substitute x for 0, and 2 times 0 equals 0, and y = 0, so the perpendicular line is y = -2x
NEED HELP ASAP!!!!!!
Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?
A.
[tex]x > - 4[/tex]
B.
[tex]x \leqslant - 4[/tex]
C.
[tex]x \geqslant 8[/tex]
D.
[tex]x \leqslant 8[/tex]
THE ANSWER IS B.
Answers
Answer: Hope it helps!!
I believe it is B. as well
Desmos Graphing calculator is great for problems as well!
On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B?
Answers
1 x y = 20 x 4
Y = 80
Determine the total number of roots f(x) = (3x^4 + 1)^2
Answers
[tex]f(x) = (3 {x}^{4} + 1) {}^{2} \\ f(x) = 0 \\ (3 {x}^{4} + 1) {}^{2} = 0 \\ 3x {}^{4} + 1 = 0 \\ 3x {}^{4} = -1 \\ x {}^{4} = \frac{ - 1}{3} [/tex]
[tex]f(x) \: admits \: no \: real \: roots[/tex]
9. The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Targets hit
3
4 5 6
Score
8 16 24 32 40 48
0 1 2
0
Answers
The table shows relationship between the number of targets a person
hits in a game of laser tag and that score of that person. The table shows is a continuous graph.
What is a continuous function in a graph?As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil. In calculus, learning about a function's continuity is crucial since without it, a function cannot be differentiated.
If a function's graph is a continuous curve without any holes, gaps, or breaks, it is said to be continuous.
Now,
x-axis on the graph show "Target hit" and y-axis shows "Score"
Graph the points using a graphing calculator.
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The complete question is:
"The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Target hit 0 1 2 3 4 5 6
Score 0 8 16 24 32 40 48"
consider a little league team that has 13 players on its roster. a. how many ways are there to select 9 players for the starting lineup? b. how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters? c. suppose 6 of the 13 players are left-handed. how many ways are there to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players?
Answers
There are 715 ways to select 9 players for the starting lineup.
Permutation is used whenever there is arrangement or where order is important . denoted by [tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
n= no of item , r = no of items to be arranged.
Combination is used when there is selection . denoted by[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
n=no of item , r= no of item to be selected.
Part (a)
In the given question
we have to select 9 players out of 13 player , combination will be used
[tex]C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}[/tex]=715 ways.
Part(b)
In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.
Since the batting order is important , permutation will be used.
[tex]P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5[/tex]
=259459200 ways.
Part(c)
In this part we have to do selection of 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
Since order is not important Combination will be used.
To select 3 left handers from total 6 left handers = C(6,3)
& to select 6 positions of left handers from remaining 7 right handers=C(7,6)
No of ways of selection = C(6,3)*C(7,6)
[tex]=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\[/tex]
On solving further we get
[tex]= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways[/tex]
Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.
(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .
(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
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Find the midpoint of the segment with the given endpoints.
(-2,2) and (10,0)
Answers
Answer:
I think it’s (4,1)
The probability that Bob will make a free throw is 3/4 . What is the probability that Bob will make his next 2 free throws.
Answers
Answer:
9/16
Step-by-step explanation:
Number 13 and 9 please
Answers
Answer:
9.5>6 41.8>0
Step-by-step explanation:
what three numbers come next in the sequence 1458,486,162,54? and how do you get these numbers?
Answers
Answer:
18,6,2
Step-by-step explanation:
To get from the first term to the second term we divide by 3 .
To get from the second term to the third term we divide by 3 .
So we continue this pattern to find the next 3 terms :
So 54 ÷ 3 = 18
18 ÷ 3 = 6
6 ÷ 3 = 2
Hope this helped and have a good day
A sample of n=225 scores has =103 and s2 =16. what is the sample standard deviation?
Answers
Based on the calculations, the sample standard deviation is equal to 4.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
[tex]Z=\frac{\bar x\;-\;u}{\delta}[/tex]
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:
Note: Variance, δ² = 16
Taking the square root of the variance, we have:
Standard deviation, δ = √16
Standard deviation, δ = 4.
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Complete Question:
A sample of n=225 scores has [tex]\bar x[/tex] = 103 and δ² = 16. What is the sample standard deviation?
11. Put brackets into each of the following expressions to make it correct:
(a) 3+9/5-2x5=20
Answers
Answer:
(3+9)/(5-2)x5 = 20
Step-by-step explanation:
It's a rather tedious type of task, because there's no simple way to solve them, except kind of by brute force or by trial and error. Here we can start by noticing x5 at the end, so if we can force everything before to be 4 it's gonna be dandy:
can we add brackets to 3+9/5-2 to be equal to 4 (because 20 / 5)?
fortunately, 3+9 is 4 times more than 5-2, so (3+9)/(5-2) = 4
so (3+9)/(5-2)x5=20 is a correct solution
if <1 and <2 form a linear pair and m<1 is 18 degrees less than five times the measure of <2 find m<1
Answers
∠1 and ∠2 will have the values 33° and 147° respectively when they form a Linear Pair.
In the question, It is given that ∠1 and ∠2 form a Linear Pair.
So, ∠1 and ∠2 = 180°, Also it is stated that ∠1 is 18° lesser than 5 times ∠2.
Taking ∠2 = x we get ∠1 = 5x-18
Now for Linear Pair, we have ∠1 + ∠2 = 180°
putting values of ∠1 and ∠2 we get : (5x-18) + x = 180
Solving the equation => (5x-18) + x = 180 => 6x = 198
=> x = 33
Putting the value of x in both ∠1 and ∠2 we get :
∠2 = 33° and ∠1 = 5(33) - 18 => ∠1 = 147°
Hence, we get ∠1 and ∠2 measures 147° and 33° respectively.
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If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13
people?
Answers
Answer:
Step-by-step explanation:
2 pounds / 5 people
x pounds / 13 people
2/5 pounds per person so 2/5 * 13 = 26/5
5 1/5 i think
sorry if its wrong
Answer: The answer of the question is 2 and 3/5.
Step-by-step explanation: Every pound of meat serves one person, because 10 divided by 2 people is 5. Then, there are 3 pieces of meat left over, and since every person eats 5/5, or 1 whole, then there are 3/5 pieces left over. You then add 2 and 3/5 together, getting your answer 2 3/5.
Salome's house went from a valuation of 4.5 million ZAR (South African Rand) on 1st January
2011, to 6 million ZAR on 1st January 2020.
If the value of the house compounded monthly, what was the annual rate of increase?
Give your answer as a percentage, correct to 1 decimal place.
Answers
Using compound interest, it is found that the annual rate of increase was of 3.10%.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
t = 9, A(t) = 6, A(0) = 4.5, n = 12.
Hence we solve for r to find the interest rate as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]
[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]
[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]
[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]
1 + r/12 = 1.0026.
r/12 = 0.0026
r = 12 x 0.0026
r = 0.031.
The annual rate of increase was of 3.10%.
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Solve system of equations.
1/2x-y=-1
x-2 y=5
Answers
Answer:
No solution the lines are parallel
Step-by-step explanation:
see picture for reference.
richard cuts a $ 4\frac{1}{2} ~\text{ft} \times 7\frac{1}{2} ~\text{ft} \times 11\frac{1}{4}~ \text{ft}$ rectangular prism into congruent cubes without any part of the prism leftover. if he makes the cubes as large as possible, how many will he produce?
Answers
If he makes the cubes as large as possible, the maximum number of cubes is equal to 900 cubes.
How to determine the number of cubes?In order to determine the number of cubes that would be produced by Richard when the rectangular prism is cut into congruent cubes without any part of the rectangular prism leftover, we would make the edges of the cube 100 times larger and then evaluate:
Length of cube = 4 1/2 ft × 100 = 450 feet.Breadth of cube = 7 1/2 ft × 100 = 750 feet.Height of cube = 11 1/4 ft × 100 = 1125 feet.Note: The greatest common factor (GCF) of the dimensions above is 75.
Next, we would divide each of the dimension by 75:
Length of cube = = 450/75 = 6 feet.
Breadth of cube = 750/75 = 10 feet.
Height of cube = 1125/75 = 15 feet.
Therefore, the maximum number of cubes is given by:
Maximum number of cubes = 6 × 10 × 15
Maximum number of cubes = 900 cubes.
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Complete Question:
Richard cuts a 4 1/2 ft × 7 1/2 ft × 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?
As the degrees of freedom increase, the t distribution approaches the _____ distribution. a. exponential b. p c. normal d. uniform
Answers
As the degrees of freedom (DF) increase, the t distribution approaches the normal distribution. Therefore, the correct answer option is: C. normal distribution.
What is the degrees of freedom (DF)?The degrees of freedom (DF) in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses because they are the maximum number of logically independent numerical values (data points) in the final calculation of a statistical problem.
What is a normal distribution?A normal distribution is sometimes referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.
In this context, we can reasonably infer and logically deduce that the t-distribution generally approaches the normal distribution as the degrees of freedom (DF) increase.
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A triangle has an area of 15 square inches.
If the base is 5 inches, what is the height?
Draw the triangle and label its base and height with units
Answers
Answer:
The height is 5.
Step-by-step explanation:
Find this answer here in this link!
This is the correct answer
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16. SHORT RESPONSE The first story of a building is 24 feet high, and each
additional story is 18 feet high. Write an expression for the height to the top
of the nth story. Explain the meaning of each term in the expression
Answers
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
Height of first story of a building = 24 feet
Height of each additional story = 18 feet
Total number of stories in a building = n
The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.
The total number of additional stories = ( total number of stories in a building - 1) = (n-1)
The height of total additional stories = 18 (n-1)
Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
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A television transmitter tower is 600 ft high. If the angle between the guy wire (attached at the
top) and the tower is 55.4°, how long is the guy wire?
Answers
Using trigonometric relations, we can see that the length of the wire is 1,454.5 ft.
How can we find the length of the wire?
We can think of this as a right triangle, such that the height of the tower is one of the legs, and the wire is the hypotenuse.
In this case, we know that the angle between the tower and the wire measures 55.4°, and the height is the adjacent cathetus to this angle.
Then we can use the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Where:
a = 55.4°
adjacent cathetus = 600ft
hypotenuse = L = length of the wire.
Replacing that we get:
cos(55.4°) = 600ft/L
L = 600ft/cos(55.4°) = 1,454.5 ft
We conclude that the length of the wire is 1,454.5 ft.
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Find each quotient a7/12÷1/7b -0.05÷(5/8÷1/2) c6 1/4÷(-5/16) d-1÷-(10/13)
Answers
The quotient of the problem given are 49/12, -1/25, -20 and 13/10 respectively
These are the simple problems of fractions
A) 7/12 ÷ 1/7
7/12×7/1
49/12
B) -0.05 ÷(5/8 ÷ 1/2)
- 5/100 ÷ ( 5/8 ×2/1)
-5/100÷ (5/4)
-5/100 ×4/5
-1/25
C) 6 1/4 ÷(-5/16)
25/4 × (-16/5)
-20
D) -1 ÷(-10/13)
-1 ×(-13/10)
13/10
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The diagram shows three lines with some marked angle measures.
?
?
70°
?
?
53°
?
Find the missing angle
measures marked with
question marks.
Answers
The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
How to determine the measures of the missing angles of a geometric system
In this question we have a geometric system generated by three lines, where two lines pass through the first lines and four angles are generated on each intersection. The measures of the missing angles can be found by the following concepts:
Vertical angles - Two angles opposite to each other have the same measure.Supplementary angles - Two angles adjacent to each other that a total measure of 180°.The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
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I need help asap!!!!
Answers
Answer: The first one is correct.
Step-by-step explanation:
x = 3
y = -2
So: 2 x 3 + 2 x (-2) = 6 + (-12) = -6
2. Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).
Answers
Answer:
2 × [(3x² + x + 2) + (-x² – 5x + 1)] =Step-by-step explanation:
Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).
P = 2 × (L + W)
2 × [(3x² + x + 2) + (-x² – 5x + 1)] =
if you want the result:
4x²−8x+6
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
+
A.
B.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
N N
C.
D.
finance
SURPRISE!
Here's a $10
financet
Instant Cred
Answers
Answer:
b , d
Step-by-step explanation:
Solve system of equations.
x+y=-6
2 x-y=3
Answers
The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + y = -6 (equation 1)
2x - y = 3 (equation 2)
Express y in terms of x in one of the equations,
x + y = -6 (equation 1)
y = -x - 6
and then substitute it in the 2nd equation.
2x - y = 3 (equation 2)
2x - (-x - 6) = 3
2x + x + 6 = 3
3x = 3 - 6
3x = -3
x = -1
Substituting the value of x in the equation of y,
y = -x - 6
y = -(-1) - 6
y = 1 - 6
y = -5
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(1 + 2 × 3)² + 7
please helppppooppppppppp
Answers
Answer:
56
Step-by-step explanation:
(1+2*3)^2+7
(1+6)^2+7
7^2+7
49+7
56
Answer:
Step-by-step explanation:
Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.
use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Answers
We have proved that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length by using a vector.
What do you mean by vector?A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. A quantity or phenomenon that just exhibits magnitude and no specific direction is referred to as a scalar. (Weight is the force produced by the acceleration of gravity acting on a mass.) Scalars include things like velocity, mass, electrical resistance, and hard disk storage space.
In the triangle ABC, D is the midpoint of AB, and E is the midpoint of AC.
Now, using the triangle rule for triangle ADE,
AE+AD = ED
And for triangle ABC,
CA+AB = CB
2AE+2AD = CB [as AD = 1/2AB and AE=1/2AC]
=> 2(AE+AD) = CB
=> 2ED = CB
=> ED = CB/2
We can write two vectors equal to each other with only difference in magnitude only when they are parallel, i.e., the angle between ED and CB is 0.
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