Answers
Answer:
Step-by-step explanation:
a.
[tex]AC=\sqrt{AB^2-BC^2} =\sqrt{13^2-5^2} =\sqrt{169-25} =\sqrt{144} =12\\[/tex]
applying sine formula
AB=c
AC=b
BC=a
[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C} \\\\\frac{5}{sin A} =\frac{12}{sin B} =\frac{13}{sin 90} \\using~last~two\\\frac{12}{sin B}= \frac{13}{1} \\sin B=\frac{12}{13}\\ B=sin^{-1}(\frac{12}{13}) \approx 67.38 ^\circ[/tex]
b.
third angle ∠Y=180-(30+90)=180-120=60
using sine formula
[tex]\frac{xz}{sin Y} =\frac{xy}{sin Z} = \frac{yz}{sin X} \\\frac{30}{sin 60} =\frac{xy}{sin 90} =\frac{h}{sin 30} \\using ~first~and~last\\\frac{30}{\frac{\sqrt{3} }{2} } =\frac{h}{\frac{1}{2} } \\2h=\frac{60}{\sqrt{3} } \\h=\frac{30}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } =10\sqrt{3}[/tex]
Related Questions
I NEED HELP PLEASE !!!!
Answers
Answer:
See below
Step-by-step explanation:
So we have the following six values:
[tex]77.65488139\\\sqrt{0.156}\\368. 5468432...\\253,897,615.\bar3\\14.19274128...\\\\\sqrt{\frac{4}{9} }[/tex]
And we want to determine which are irrational.
Recall what irrational numbers, are they are numbers that do not repeat nor terminate. In other words, they never end, and their digits never repeat.
So, let's go through each one.
77.65488139 is rational. Yes, it has a lot of decimal places but notice there are no ellipses after it. Thus, it terminates and is rational.
√(0.156) is about (use a calculator) 0.39496835... It is not repeating nor does it end. Thus, √(0.156) is irrational.
368.5468432... has the ellipses. Thus, it doesn't repeat and doesn't terminate. It's irrational.
253,897,615.3 has a bar over the 3 at the end. This means that this repeats. Therefore, while it doesn't terminate, it is rational.
14.19274128... has an ellipses. It doesn't repeat nor terminate. It's irrational.
Lastly, the square root can be simplified to 2/3. This is approximately .6666... While this doesn't terminate, it repeats, so it's rational.
Edit: Grammar
The equation shows the relationship between the amount of money (y) remaining in Leigh's money box and the number of months (X)
Function 2
y = -9x + 60
Which statement explains which function shows a greater rate of change?
O Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.
O Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
O Function 2 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
O Function 2 shows a greater rate of change, because Morgan spends $50 each month and Leigh spends -$9 each month.
Answers
Answer:
A. The first choice.
Step-by-step explanation:
Look at function 1.
Month 1 -----> $50
Month 2 ----> $40
The difference between month 2 and moin th 1 is 1 month.
The difference between $40 and $50 is -$10. In other words, in function 1, the amount, y, went down $10 in a month. The rate of change of function 1 is -$10/month.
Function 2
y = -9x + 60
The rate of change is the slope. The slope of function 2 is -9. In function 2, the amount of money changes -$9/per month.
Answer: A. The first choice.
The ratio of the profit, material cost and production labour of an article is 5:7:13.
If the material cost is 840 more than that of labour , find the total cost of producing the article. Plsss help me.
Answers
Answer:
The cost of producing the article is -3500 (Negative cost)
Step-by-step explanation:
The given parameters are
The ratio of the profit to material cost to production labor = 5:7:13
The amount of the material cost = 840 + Labor cost
Let the total cost = X
Therefore, we have;
The fraction of the total cost that is material cost = 7/(5 + 7 + 13) = 7/25
Therefore, the material cost = 7/25 × X
The fraction of the total cost that is labor cost = 13/(5 + 7 + 13) = 13/25
Therefore, the labor cost = 13/25 × X
However, the amount of the material cost = 840 + Labor cost, which gives;
7/25 × X = 13/25 × X + 840
7/25 × X - 13/25 × X = 840
-6/25 × X= 840
X = 840/(-6/25) = 840×(-25/6) = -3500
The cost of producing the article = -3500.
-1 1/2+(-2 12/23)+5 7/46
Answers
Answer:
23/26 1 3/26
Step-by-step explanation:
you make to where all the denmanters are the same and add
10. Three oil tankers together contain 37 litres of oil. If two tankers have 11 litres and
12 litres of oil. Find the oil in the third tanker.
Answers
Answer:
Step-by-step explanation:
total quantity of oil = 37 litres
quantity of oil in first tank = 11 litres
quantity of oil in second tank = 12 litres
Total quantity of oil in first and second tanks = 11 + 12 = 23 litres
∴ quantity of oil in the third tank = 37 - 23
= 14 litres
Hope this helps
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Using the image as a reference, what is the csc of angle 90 - x?
Answers
Answer:
Option (F)
Step-by-step explanation:
Cosec of an angle is the ratio of Hypotenuse and Opposite side.
From the figure attached,
ΔABC is a right triangle.
m∠A + m∠B + m∠C = 180°
m∠A + 90 + x = 180
m∠A = 180° - (90 + x)°
= (90 - x)°
Now csc (90 - x)° = [tex]\frac{\text{Hypotenuse}}{\text{Opposite side}}[/tex]
= [tex]\frac{\text{AC}}{\text{BC}}[/tex]
= [tex]\frac{5}{3}[/tex]
= 1.67
Therefore, Option (F) will be the answer.
Find an equation of the line that passes through the given point and has the indicated slope m. Point Slope (−9, 6) m is undefined
Answers
Answer:
x = -9
Step-by-step explanation:
A line with "undefined" slope is a vertical line. Its equation is of the form ...
x = constant
If the line is to go through a point with an x-coordinate of -9, then that must be the value of the constant.
x = -9
Which of the following statements is true for 6.? Question 16 options: A) It's rational because 6. = 68∕33. B) It's irrational because 6. = 66∕25. C) It's rational because 6. = 66∕25. D) It's irrational because 6. = 68∕33.
Answers
Answer:
rational. I can't read the answer choices well.
The correct statement is: "It's rational because 6.24 repeated can be expressed as a fraction." Option A is true.
Here, we have,
To determine if 6.24 repeated is rational or irrational, we need to evaluate the options provided:
A) It's rational because 6.24 repeated = 68∕33.
To evaluate this option, we can convert 6.24 repeated into a fraction form.
Let x = 6.24 repeated.
We can multiply x by 100 to eliminate the repeating decimal:
100x = 624.24 repeated
Subtracting the original equation (x = 6.24 repeated) from the new equation (100x = 624.24 repeated), we can eliminate the repeating decimal:
100x - x = 624.24 repeated - 6.24 repeated
99x = 618
Simplifying:
x = 618/99
Now, let's check if 618/99 equals 6.24 repeated by calculating its decimal value.
Using a calculator, we find that 618/99 is approximately 6.242424..., which matches the repeating pattern.
Therefore, option A is true.
B) It's irrational because 6.24 repeated = 66∕25.
To evaluate this option, we can calculate the decimal value of 66/25 using a calculator. It turns out that 66/25 is approximately 2.64, which is not equal to 6.24 repeated. Therefore, option B is false.
C) It's rational because 6.24 repeated = 66∕25.
To evaluate this option, we can calculate the decimal value of 66/25 using a calculator. It turns out that 66/25 is approximately 2.64, which is not equal to 6.24 repeated. Therefore, option C is false.
D) It's irrational because 6.24 repeated = 68∕33.
To evaluate this option, we can convert 6.24 repeated into a fraction form. As we determined earlier, 6.24 repeated is rational. Therefore, option D is false.
The correct statement is: "It's rational because 6.24 repeated can be expressed as a fraction." Option A is true.
To learn more on multiplication click:
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complete question:
Which of the following statements is true for 6.24 repeated? Question 16 options: A) It's rational because 6. = 68∕33. B) It's irrational because 6. = 66∕25. C) It's rational because 6. = 66∕25. D) It's irrational because 6. = 68∕33.
FOR BRAINLIEST!!! ASAP SUPER EASY!!
One coin is randomly selected from a jar containing 20 pennies, 15 nickles, 3
dimes, and 12 quarters. Find the odds of a value greater than $0.10. *
6:19
3:47
12:50
08:12
Answers
Step-by-step explanation:
Total coins in the jar = 50. Number of coins with a value less than $0.05 = 20 (the pennies). ... Probability of picking a penny = 20/50 = 40%. ... 'Odds' = 3 to 2 against it.
Why do you only need a single counterexample to show that a conditional statement is false?
Answers
Answer:
A conditional statement is something like:
If (a condition is true) Then (something is also true.).
What this says is that ALWAYS that the condition is met, then "something" is also true.
For example:
If A > 3, then A > 2.
This is always true, because if A is larger than 3, then A is always also larger than 2.
Now, if we find a single counter-example, then the "always" is false.
This would mean that the condition is not enough, as we found a case that meets the condition, but the second part of the conditional statement is not true.
For example, if i told you that:
If a number is greater than 234, then the number is also greater than 235.
Now, there are a lot of numbers that are larger than 234 and also are larger than 235.
But here we have a counter-example.
235 is larger than 234, so the initial condition is true, but 235 is not larger than 235.
Then we find a number that makes the statement:
"If a number is greater than 234, then the number is also greater than 235."
false.
The perimeter of the square is equal to the perimeter of the triangle. What are the side lengths of each figure? square: ? units Question 2 triangle shorter side: ? units Question 3 triangle longer sides: ? units, ? units
Answers
Answer:
Square= 12 units
Triangle long sides= 19 units
Triamgle short side= 10 units
Step-by-step explanation:
It is a square, so all sides are the same. That means 3x+3 equals 4x. What number can be subsituted into x to equal 4? If x is 3, then 3x+3 would be 3(3)+3. It equals 12. 4 times 3 is also 12. It works! That also means the square's side is 12 units.
Square= 12 units
So, x=3
The triangle's longer sides are 7x-2. Subsitute x in, which is 3, and you get 7(3)-2. It equals 19. The two longer sides of the triangle are the same length, so both are 19 units.
Triangle long sides= 19 units
The triangles shorter side is 2x+4. Subsitute 3 in for x and you get 2(3)+4. It equals 10, so the shorter side is 10 units.
Triangle short side= 10 units
Answer:
Square: 12 unites
triangle shorter side: 10 units
triangle longer sides: 19 units, 19 units
Step-by-step explanation:
Hello!
First, we make the equations to find the perimeters of each shape by adding all the sides
Square: 4x + 4x + (3x+ 3) + (3x + 3)
Triangle: (7x - 2) + (7x - 2) + (2x + 4)
Since the perimeters are equal we can show that
4x + 4x + (3x+ 3) + (3x + 3) = (7x - 2) + (7x - 2) + (2x + 4)
Now we can solve for x.
Combine like terms
14x + 6 = 16x
Subtract 14x from both sides
6 = 2x
Divide both sides by 2
3 = x
Now we know what x is we can put that into the sides of the shapes
Square
4(x)
Put in x
4(3) = 12
The Square is 12 units
Triangle Short Side
2x + 4
Put in x
2(3) + 4
6 + 4
10
The shorter side of the triangle is 10 units
Triangle Longer Side
7x - 2
Put in x
7(3) - 2
21 - 2
19
The longer sides are 19 units
Hope This Helps!
The accepted value of the average distance between Earth and the moon is 384, 467 km. If a scientist measures that the moon is 384,476 km form the Earth, what is the measurement's percentage error?
Answers
Answer:
Percentage error is 0.0024 %
Step-by-step explanation:
Initial average distance between Earth and moon = 384467 km
Distance measure by the scientist = 384476 km
Total variation in the distance calculation = 384476 – 384467 = 9 km.
Now we can find the percentage by dividing the variation in distance from the initial measurement and then multiply with hundred.
Percentage error = ( 9 / 384467 ) × 100 = 0.0024 %
Find the measure of angle A. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answers
Answer:
20°
Step-by-step explanation:
The sum of angles in a ∆ = 180°
Therefore, [tex] (17x - 1) + (3x - 4) + 25 = 180 [/tex]
Use this expression to find the value of x, then find the measure of angle A.
[tex] 17x - 1 + 3x - 4 + 25 = 180 [/tex]
[tex] 17x + 3x - 1 - 4 + 25 = 180 [/tex]
[tex] 20x + 20 = 180 [/tex]
Subtract 20 from both sides
[tex] 20x + 20 - 20 = 180 - 20 [/tex]
[tex] 20x = 160 [/tex]
Divide both sides by 20
[tex] \frac{20x} = \frac{160}{20} [/tex]
[tex] x = 8 [/tex]
Find measure of angle A.
Angle A is given as [tex] 3x - 4 [/tex]
Plug in the value of x and solve
[tex] A = 3(8) - 4 = 24 - 4 = 20 [/tex]
Base 5
3213
3444
+ 3323
Answers
Answer:
21040
Step-by-step explanation:
As with base-10 addition, when the sum is equal to the base or more, a "carry" is generated into the next place value column. Useful equivalents here are ...
5₁₀ = 10₅
6₁₀ = 11₅
7₁₀ = 12₅
9₁₀ = 14₅
10₁₀ = 20₅
The addition is shown in the attachment. The sum is 21040₅.
_____
The equivalent decimal addition problem is 433+499+463=1395.
A suitcase has a lock on it consisting of four numbers. Each number could be any number 0-9. The only restriction is that the last slot has to be an even number.
Answers
Answer: We have 5000 possible combinations.
Step-by-step explanation:
I guess that we want to find the possible combinations for this lock.
We have 4 numbers, so we have 4 selections.
Now, let's count the number of options in each selection.
in the first selection, we have 10 options (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9)
in the second selection, we have 10 options (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9)
in the third selection, we have 10 options (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9)
in the last selection, we have 5 options (0, 2, 4, 6 and 8)
The total number of combinations is equal to the product of the number of options in each selection:
C = 10*10*10*5 = 5000 combinations.
Karla is in Group A, where 56 orange slices are shared equally among 7 people.
Jade is in Group B, where 54 orange slices are shared equally among 6 people
.
Who had the greater share of orange slices, Karla or Jade?
Answers
Answer:
Jade
Step-by-step explanation:
How many pennies could you have if:
When you break the pennies into groups of 2, you have 1 penny left over AND when you break the pennies into groups of 3, you have 1 penny left over?
Answers
Answer:
The number of pennies owned is 7 pennies
Step-by-step explanation:
The given parameters are;
The number of pennies left over when we break the pennies into groups of 2s = 1 penny
The number of pennies left over when we break the pennies into groups of 3s = 1 penny
Let the number of pennies owned = c
What we are given are as follows;
2 × a = c - 1
3 × b = c - 1
2 × a = 3 × b
a/b = 3/2
Therefore, if we multiply 2 by 3, and 3 by 2 we get 6
2 × 3 = 6, similarly 3 × 2 = 6
If we put 6 = c - 1, we get;
c = 6 + 1 = 7
c = 7
The number of pennies owned = 7 pennies.
How many real solutions exist for this system of equations?
A. Zero
B. One
C. Two
D. Infinite
Answers
A) zero as the value of determinant is imaginary
The number of real solutions of the equations y = x - 3 and y = x² - 6x + 10 will be zero. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y = x - 3
y = x² - 6x + 10
Compare both equations, then we have
x² - 6x + 10 = x - 3
Simplify the equation, then we have
x² - 7x + 13 = 0
The solution to the equation, then we have
x = [7 ± √(49 - 52)] / 2
x = 7/2 ± (√3/2)i
The number of real solutions of the equations y = x - 3 and y = x² - 6x + 10 will be zero. Then the correct option is A.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Which state comparing the function is true
Answers
Answer:
the slope of W is less than the slope of Z
Step-by-step explanation:
Function Z
find slope take two points (0,15.8) (1,15.76)
m=y2-y1/x2-x1
m=(15.76-15.8)/1-0
m=-0.04
the equation for function z : y=-0.04x+15.8
slope of W=-0.0625 which is less than -0.04
y intercept pf W=30, is greater than the y intercept of Z=15.8
Answer: The first statement is true.
Step-by-step explanation: The slope of function Z is -0.04 or - 1/25 The slope of function W is -0.0625 or -1/16.
Tricky! The absolute values of W are larger, but that makes the slope more negative.
Type the correct answer in each box. If necessary, use / for the fraction bar(s). John recorded the number of cars passing a traffic signal at intervals of 2 minutes. He plotted his data on this graph.
Answers
Answer:
Slope of the line is = [tex] \frac{5}{2} [/tex]
y-intercept = 5
Step-by-step explanation:
Slope (m) is can be calculated using the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinates of any two points located on the line. Let's use, (14, 40) and (10, 30).
Let,
[tex] (14, 40) = (x_1, y_1) [/tex]
[tex] (10, 30) = (x_2, y_2) [/tex]
Plug the above values into the formula to find the slope (m).
[tex] m = \frac{30 - 40}{10 - 14} [/tex]
[tex] m = \frac{-10}{-4} = \frac{5}{2} [/tex]
Slope of the line is = [tex] \frac{5}{2} [/tex]
Find y-intercept using y = mx + b
Where m = slope, and b = y-intercept
Use (10, 30) as (x, y).
30 = 5/2*10 + b
30 = 25 + b
30 - 25 = b
5 = b
b = 5
Triangle A B C is shown. Angle C A B is a right angle. Angle A B C is 30 degrees and angle B C A is 60 degrees. The length of A C is 9 and the length of hypotenuse C B is 18. Which trigonometric ratios are correct for triangle ABC? Select three options.
Answers
Answer:
SinB = 1/2, SinC = √3/2 and
TanC = √3
Step-by-step explanation:
The question lacks options. Find the complete question in the comment section.
Given triangle ABC, we will use the SOH, CAH, TOA trig identity to get the correct ratio.
Given the hypotenuse BC = 18 and one of the other two sides AC = 9, we can get the third side AB using Pythagoras theorem.
BC² = AC²+AB²
18² = 9²+AB²
2² = 1²+AB²
AB² = 4-1
AB² = 3.
AB = √3
Making <ABC as reference angle, AC will be opposite and AB will be the adjacent.
Sin<ABC = opp/hyp = AC/BC
Sin<ABC = 1/2
Cos<ABC = adj/hyp = AB/BC
Cos<ABC = √3/2
Tan<ABC = opp/adj = AC/AB
Tan<ABC = 1/√3
Making <BCA as reference angle, AB will be opposite and AC will be the adjacent.
Sin<BCA = opp/hyp = AB/BC
Sin<BCA = √3/2
Cos<BCA = adj/hyp = AC/BC
Cos<BCA = 1/2
Tan<BCA = opp/adj = AC/AB
Tan<BCA = √3
Frim the above calculation, the correct options are sin<ABC = 1/2, Sin<BCA = √3/2 and Tan<BCA = √3
Mean of 11,10,12,12,9,10,14,12,9 is
Answers
Answer: Hi!
To find the mean of a data set, you have to add the numbers in the set and then divide the sum by the number of values that are in the set.
11 + 10 + 12 + 12 + 9 + 10 + 14 + 12 + 9 = 99
There are 9 values in the data set, so we divide 99 by 9:
99 ÷ 9 = 11
The mean of this data set is 11.
Hope this helps!
Answer: 11
Order the Numbers
Before: 11,10,12,12,9,10,14,12,9
After: 9,9,10,10,11,12,12,12,14
Add
9+9+10+10+11+12+12+12+14=99
Divide
99÷9=11
52 times a number
Mathematics
Answers
Answer:
52x
Step-by-step explanation:
If we replace x with "a number", then the expression would be 52x.
Find mKNLˆ. A. 264 B. 196 C. 247 D. 184
Answers
Answer:
A. 264
Step-by-step explanation:
When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,
60° = 1/2[(18x - 6)° - (5x +17)°]
60° * 2 = (18x - 6 - 5x - 17)°
120° = (13x - 23)°
120 = 13x - 23
120 + 23 = 13x
143 = 13x
143/13 = x
11 = x
x = 11
(18x - 6)° = (18*11-6)°= (198 - 6)° = 192°
(5x +17)° = (5*11 +17)° =(55+17)° = 72°
m (arc KNL) = (18x - 6)° + (5x +17)° = 192° + 72°
m (arc KNL) = 264°
The indoor pool has a temperature of 24 The outdoor pool has a temperature of 23 Which pool has a higher temperature And which pool temperature has a greater absolute value
Answers
Answer:
The indoor pool has a higher temperature and also has the greatest absolute value.
Step-by-step explanation:
The indoor pool has a higher temperature becasue 24 is greater than 23. It also has a bigger absolute value because the absolute value how much a number is from 0.
So the absolute value of 24 is 24.
The absolute value of 23 is 23.
24 is greater so the indoor pool also has a bigger absolute value.
Eight less than three times x in a expression
Answers
Answer:
3x - 8
Step-by-step explanation:
I'd have to see a photo of the question, but eight less than three times x can be translated to 3x - 8.
The table shows the solution to the equation |2x - 4| - 3 = 3:
Step 1|2x - 4 = -3 + 3
Step 2|2x - 4 = 0
Step 32x - 4 = 0
Step 4 2x = 4
Step 5x = 2
which is the first incorrect step? (1 point)
Step 1
Step 2
Step 3
Solution is correct
Answers
Answer:
Step 1
Step-by-step explanation:
Step one is incorrect because you need to add 3 but it subtracted.
Simplify the expression by combining like terms:
k3+ m + m - k3 +Ka+ K2
Answers
Explanation:
k3 + m + m - k3 + Ka + K2
= 2m + Ka + K2
Twelve relatives always give gifts to one another. They have been doing it for eight years. How many exchanges have happened so far?
Answers
Answer:
660 exchanges
Step-by-step explanation:
Number of relatives = 12
Number of years = 5
Since each relative gives gift to one another each year:
Then each relative hands out 11 gifts (person giving out the gift will not be counted) to the others, and others also do the same.
Therefore, yearly exchange :
(Number of relatives * number of gifts given out per person)
(12 × 11) = 132
Number of exchanges after 5 years :
(Number of yearly exchanges × number of years)
(132 × 5) = 660
Plane H is shown. Plane H contains four points. Points A, C, and D form a diagonal line on the left. Point B is to the right of point C. Which points are coplanar and noncollinear? points A and D points C and D points A, C, and D points A, B, and D
Answers
Answer:
d
Step-by-step explanation:
edg 2021
Answer:
d
Step-by-step explanation: