The angles are: A =24.7° ; B = 40.6° ; C =114.7°.
What is Cosine law?
The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°
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ξ = {x:x is an integer, 2 ≤ x ≤ 14}
� = {x:x is a prime number}
� = {x:x is a multiple of 3}
Given that C ⊂ A, n(C)=3 and B ∩ C = ∅, list the members of a possible set C
The members of a possible set C are {6, 9, 12}
Set theoryThe universal set is the set that contains all other sets. Given the following sets
ξ = {x:x is an integer, 2 ≤ x ≤ 14}
B = {x:x is a prime number}
A = {x:x is a multiple of 3}
The sets B and A are:
B = {2, 3, 5, 7, 11}
A = {3, 6, 9, 12}
If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.
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Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0.
Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1.
Answer:
Perimeter of rectangle2 = k × perimeter of rectangle 1
area of rectangle 2 = k² × area of rectangle 1
Step-by-step explanation:
• rectangle 1 :
Length x
Width y
perimeter1 = 2×(x + y)
area1 = x × y
……………………
•• rectangle 2 :
Length kx
Width ky
Perimeter2 = 2×(Kx + ky)
area2 = kx × ky
……………………………………………
therefore,
Perimeter of rectangle 2
= 2×(Kx + ky)
= 2×k×(x + y)
= k×2×(x + y)
= k × perimeter of rectangle 1
On the other hand,
area of rectangle 2
= Kx × ky
= k×k×(x × y)
= k²×(x × y)
= k² × area of rectangle 1
rewrite the equation y-8=2 into slope form
Answer:
y=2x+16 is the slope intercept form
Step-by-step explanation:
sorry if its wrong tried!!!
The equation for the line of best fit for this situation is shown below.
Based on the line of best fit, complete the given statements.
The expected number of hot dogs sold when the temperature is 50° would be
hot dogs.
If the vendor sold 35 hot dogs, the temperature is expected to be
degrees.
Based on the line of best fit, for every 10-degree increase in temperature, she should sell
more hot dogs.
The expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.
Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
The question is incomplete.
The complete question is:
A hot dog vendor at the zoo recorded the average temperature in degrees, x, and the average number of hot dogs she sold, y.
The equation for the line of best fit for this situation is shown below.
[tex]\rm y=\dfrac{3}{10}x+8[/tex]
Based on the line of best fit, complete the given statements.
The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.If the vendor sold 35 hot dogs, the temperature is expected to be ___degrees.Based on the line of best fit, for every 10-degree increase in temperature, she should sell____more hot dogs.We have a line of best fits:
[tex]\rm y=\dfrac{3}{10}x+8[/tex]
Plug x = 50 in the line of best fit.
y = (3/10)50 + 8
y = 15+8
y = 23
Plug y = 35
35 = (3/10)x + 8
27 = (3/10)x
x = 90 degree
Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
Thus, the expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees, and based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
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Which expression is equivalent to...
Answer:
first option
Step-by-step explanation:
[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]
HELP DUE SOON A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
The farmer should purchase 2 bags of soil for his farm.
What is Area of parallelogram?A parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral, where opposite sides are equal and parallel. The area of a parallelogram is the space enclosed within its four sides. Area is equal to the product of length and height of the parallelogram.
The shape of the farm, according to the picture is a parallelogram. Therefore, the total area can be calculated as follows:
Area = base X height
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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look at the picture
thank you
The correct answer to this question is the first option
if cp=rs 400, loss=10% find sp
Answer:
cp = rs 400
loss = 10%
Then SP = 400 - 10% of 400
= 400 - 40
= 360
Therefore SP = Rs. 360
Simplify the following expression.
(4x + 7)2
Answer:
=8x+14 or
=16x²+56x+49
[tex]\bf{(4x+7)2 }[/tex]
[tex]\bf{=2(4x+7)}[/tex]
[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]
[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]
[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]
[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]
Multiply 2 x 4 = 8Multiply 2 x 7 = 14[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]
Pisces04An asset has a cost of $50,000, with a residual value of $10,000. It has a life of 5 years and was purchased on January 1. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?
The asset’s fourth full year of depreciation expense will be $6,666.67.
What is double-declining-balance?An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.
An asset has a cost of $50,000, with a residual value of $10,000.
It has a life of 5 years and was purchased on January 1.
Then the asset’s fourth full year of depreciation expense will be
Annual depreciation = (cost – salvage value)/ useful life
Annual depreciation = (50000 – 10000) / 5 = $8,000
Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.
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Solve for x:
5(1 – x) = 20
x = __
[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]
Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]
The value of x is -3! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] First multiply 5 times 1 and -x
[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]
[tex]\twoheadrightarrow\sf 5-5x=20[/tex]
[tex]\bullet[/tex] Now subtract 5 from both sides
[tex]\twoheadrightarrow\sf -5x=15[/tex]
[tex]\bullet[/tex] Now divide both sides by -5
[tex]\twoheadrightarrow\sf x=-3[/tex]
--
Hope that this helped! Best wishes.
--
Which statements about the system are true? Select two options.
y=-x-4
3y - x = -7
O The system has one solution.
O The system consists of parallel lines.
O Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The system of equation has one solution
How to determine the true statements?The equations are given as:
y = -x - 4
3y -x = -7
Rewrite the first equation as:
y + x = -4
Add y + x = -4 to the second equation to eliminate x
4y = -11
Divide by 4
y = -11/4
Substitute y = -11/4 in y + x = -4
-11/4 + x = -4
Make x the subject
x = -4 + 11/4
Evaluate
x = -5/4
The above means that the system of equation has one solution
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Option A and B. The system has one solution and the system consists of parallel lines.
Slope of the linesThe slope of the lines is calculated as follows;
y = -x - 4
slope = - 1
3y - x = -7
3y = x - 7
y = x/3 - 7/3
slope = 1/3
Solution of the equationsy = -x - 4 ----(1)
3y - x = -7 ----(2)
solve (1) and (2)
3(-x - 4) - x = -7
-3x -12 - x = -7
-4x = 5
x = -5/4
y = -5/4 - 4
y = -5.25
Thus, the system has one solution and the system consists of parallel lines.
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Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene 97degree
Answer:
Obtuse and the rest of the question is incomplete.
Step-by-step explanation:
I have a quick geometry question! Thank you!
Answer:
e4fodor8rsidididi2f2
Answer:
9
Step-by-step explanation:
3:4
AB:12
cross multiply giving
3×12:4AB
36: 4AB
divide both sides by 4,thus
AB=9
Question 10: Each tablet in a bottle of 30 costs the pharmacy $4.60. The pharmacy has additional costs including supplies and shipping of $1.40 per pill. If a 12% profit is desired, how much would the pharmacy charge for entire bottle?
The pharmacy must charge for $201.6 for the entire bottle.
Profit is the financial gain to the seller after selling some commodity
Revenue is the total sale of the seller after selling some commodity
Expenses is the expenditure to the seller before selling the commodity
Profit = Revenue - Expenses
Cost of the tablet = $4.60
Total cost of the bottle=$4.60x30
=$138
Additional cost=$1.40 x 30
= $42
Total expenses=$180
Profit %=125
Revenue= $180 x (1+12/100)
=$180 x (112/100)
=$201.6
Therefore, The pharmacy must charge for $201.6 for the entire bottle for a profit of 12%
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On May 6, Jim Ryan borrowed $14,000 from Lane Bank at 712% interest. Jim plans to repay the loan on March 11. Assume the loan is on ordinary interest. How much will Jim repay on March 11?
The amount to be repaid by Jim Ryan is $14,891.78.
Given that, Principal (P) =$14,000, the rate of interest (R) =7[tex]\frac{1}{2}[/tex]% and T=310 days.
What is ordinary interest?Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year.
Now, the interest=14,000×7.5 %×[tex]\frac{310}{365}[/tex].
=$891.78
The amount to be repaid=14,000+891.78=$14,891.78
Therefore, the amount to be repaid by Jim Ryan is $14,891.78.
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What does the ratio 6 to 8 represent in the situation?
Answer:
its 80
Step-by-step explanation:
the ratio is 80 hope this helps!
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. If you connect a 2 megohm resistor (2× 10^6 ohms) across a 2.4 kilovolt voltage source (2.4×10^3 volts),what would be the current in amps?
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.
What is Ohm's Law?Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.
The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)
= 1.2 × 10⁻³ amp
Hence, the current in the amp is 1.2 × 10⁻³.
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3 Three children share this chocolate equally.
What fraction does each child get?
Each child gets
CHALLENGE?
Answer: Each child gets 1/3
Step-by-step explanation: x/3
Please I need help on Fundametal Trigonometric Identities?
Fundamental Trigonometric Identities are listed below:
[tex]sin^{2}[/tex]Θ + [tex]cos^{2}[/tex]Θ = 1[tex]sec^{2}[/tex]Θ - [tex]tan^{2}[/tex]Θ = 1[tex]cosec^{2}[/tex]Θ - [tex]cot^{2}[/tex]Θ = 1sinΘ = 1 / cosec Θ cos Θ = 1 / sec Θ tan Θ = 1 / cot Θ tan Θ = sinΘ / cosΘ cotΘ = cosΘ / sinΘMeaning of Fundamental Trigonometric IdentitiesFundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.
In conclusion, A few Fundamental Trigonometric Identities are listed above.
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What is the solution to the equation below? Round your answer to two decimal places. 3e2x + 12 = 42
Answer:
X= 5.52
Step-by-step explanation:
1. Solve the equation:
e×2x + 12= 42
x=15/e
2. Round x=15/e to the required place
x=5.52
Answer:
X=1.15
Step-by-step explanation:
Prove that C(50,3) + C(50,4) = C(51,4)
By definition of the binomial coefficient,
[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]
so we have
[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]
as required.
On a coordinate plane, an absolute value graph has a vertex at (10, 6).
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing?
(–∞, 6)
(–∞, 10)
(6, ∞)
(10, ∞)
Answer: (10, ∞)
Step-by-step explanation:
See the graph in the attached image.
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Answer:
[tex]12(x - 4)[/tex]
Step-by-step explanation:
The question says, "twelve times the difference of a number and four"
Let's start with the first number, which is twelve = 12. Moving on, we have times = ×, then the difference which is minus(-). A number is unknown, any aphabet can be used to represent the number, so, we represent with 'x', and then four = 4.
Arranging them, we have:
[tex]12 \times x - 4[/tex]
in algebraic equations, times is always represented by bracket. Therefore, our final answer is:
[tex]12(x - 4)[/tex]
I hope this helps.
Sam wants to measure the height of a tree. She walks 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 33°. How tall is the tree? Round your answer to the nearest hundredth.
The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
To calculate the height of the tree , we use the formula below.
Formula:
tan∅ = H/B.............Equation 1Where:
∅ = Angle of elevation from the ground to the top of the treeH = Height of the treeB = Distance of the base of the tree to the point where Sam looks upFrom the question,
Given:
∅ = 33°B = 100 feetSubstitute these values into equation 1 and solve for H
tan33° = H/100H = tan33°×100H = 64.94 feetHence, the height of the tree is 64.94 feet.
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If Yang solves the inequality -4y> -40, then which of the following answers would be true for this claim?
Answer:
(a) 9, 8, 7, 6, 5, ...
Step-by-step explanation:
The solution to the inequality can be done a couple of ways. The solution is similar to that for a one-step linear equation.
__
reverse inequalityWe know that multiplying numbers by a negative value reverses their order. For example, 1 < 2, but -1 > -2. That is, multiplying by -1 requires a change in the comparison operator if it is to remain true.
For our inequality, we want to solve it by multiplying both sides by -1/4:
-4y > -40
(-1/4)(-4y) < (-1/4)(-40) . . . . . multiply both sides by -1/4 (reverses order)
y < 10 . . . . . . . . . . . simplify
The first few decreasing integer values that are part of this solution are ...
{9, 8, 7, 6, 5, ...}
__
make coefficients positiveWe can add 4y+40 to both sides of the inequality. The result will be an inequality with positive coefficients. This can be solved in one step.
-4y > -40 . . . . . given
(-4y) +(4y +40) > (-40) +(4y +40) . . . . . . add 4y+40 to both sides
40 > 4y . . . . . . . . . . . . . . . simplify
10 > y . . . . . . . . . . . . divide by 10 (order is unchanged)
y < 10 . . . . . . . . . rearrange to put y on the left
Integer solutions to this inequality are ...
{9, 8, 7, 6, 5, ...}
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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Below what price level would the firm go out of business in the long run?
A firm should go out of business in the long run when its price level is less than the average total cost.
When should a firm go out of business in the long run?The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.
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find the value of the hypotenuse for each of the following right triangles.
Answer:
I have done the 1st 2 sums in proper systematic manner. The remaining sums I'll be writing only the main formula and substitution. I hope you will write the missing sentences .
Step-by-step explanation:
Hope you will understand the sums..Also I would appreciate it if you could marke my answer as BRAINLIEST and THANK ME.｡◕‿◕｡
Answer:
Step-by-step explanation:
1. hypotenuse = 89
2. hypotenuse = 85
3. hypotenuse = 97
4. hypotenuse = 153
5. hypotenuse = 34
6. hypotenuse = 113
7. hypotenuse = 916
8. hypotenuse = 170
9. hypotenuse = 394
10. hypotenuse = 61
Express the radical using the imaginary unit, i sqrt{-27}
Answer:
27i
Step-by-step explanation:
Since we define i as [tex]\sqrt{-1}[/tex], [tex]\sqrt{-27} = 27i[/tex]
Answer:
Step-by-step explanation:
i [tex]i \sqrt{-27} =i\sqrt{-1 \times 27} =i\sqrt{27i^2} =i \times i\sqrt{27} =i^2\sqrt{9 \times 3} \\=-1\times 3\sqrt{3} \\=-3\sqrt{3}[/tex]
