Answers
Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:
Cosine Ratio
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Sine Ratio
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
Consider the angle of θ=30°, then we can write:
[tex]\displaystyle \cos 30^\circ=\frac{x}{12\sqrt{3}}[/tex]
Solving for x:
[tex]x=12\sqrt{3}\cos 30^\circ[/tex]
Since:
[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]
Then:
[tex]x=12\sqrt{3}\cdot \frac{\sqrt{3}}{2}[/tex]
[tex]x = 18[/tex]
Now apply the sine:
[tex]\displaystyle \sin 30^\circ=\frac{y}{12\sqrt{3}}[/tex]
Solving for y:
[tex]y=12\sqrt{3}\sin 30^\circ[/tex]
Since:
[tex]\sin 30^\circ=\frac{1}{2}[/tex]
Then:
[tex]y=12\sqrt{3}\cdot \frac{1}{2}[/tex]
[tex]y = 6\sqrt{3}[/tex]
Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
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Answer:
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Step-by-step explanation: (see picture :))
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Answer:
x=19
Step-by-step explanation:
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Answers
Answer:
Inequality Form:
x<7
Interval Notation:
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Step-by-step explanation:
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solve the following system of equation using elimination 2x+5y=12 -2x+3y=4
Answers
D'Angelo bought two shirts at a special sale. He paid the full price of $19.99 for one shirt and got a second shirt of the same price for half off. If the sales tax rate is 8.5%, how much sales tax did D'Angelo pay for the two shirts?
Answers
Answer: $2.55
Step-by-step explanation:
He bought the second shirt for half off the first shirt's price. He therefore bought it at:
= 19.99/2
= $10.00
Total paid for both shirts is therefore:
= 19.99 + 10
= $29.99
Sales tax is 8.5% so he paid:
= 29.99 * 8.5%
= 2.54915
= $2.55
A microscope was originally priced at $100 but went on sale for 10% off. If Adele bought the microscope and paid 10% sales tax, how much did she pay in total?
Answers
100x0.9%=90
90x1.1%=99
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Answers
Answer:
Statistica im pretty sure, i might be wrong tho, but if its right, cool
Step-by-step explanation:
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Answers
Answer:
y=2x+0
Slope:
2
y-intercept:
( 0, 0 )
Step-by-step explanation:
Slope intercept form: y=mx+b
Use the slope formula and the slope-intercept form to find the slope m and y-intercept b .
ou go to the store and buy jeans for $40, a shirt for $20, and a jacket for $60. You have a coupon for 35% off. What is the sale price?
Answers
Answer:
SAME AS THIS
Explanation:
County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$75 * 0.0725 = $5.4375
Add the original price and the sales tax.
$75 + $5.4375 = $80.4375
County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!
$70 * 0.08 = $5.6
Add the original price and the sales tax.
$70 + $5.6 = $75.6
Then take the difference.
80.4375 – 75.6 = 4.8375
Round to the nearest hundredth: $4.84
Answer:
the sale price would be $78
Step-by-step explanation:
add up all the prices to get 120
35% taken off of 120 is 78
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Answers
Answer:
lesser x = -4.73205, so -4.73
greater x = -1.26795, so -1.27
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Answers
Answer:
4x+4=5x-8
4x-5x+4=-8
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Step-by-step explanation:
Caroline ran 30 miles in 6 days. She ran the same distance each day. Enter and solve an equation to
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Help pls
Answers
Answer:
she ran 5 miles each day
Step-by-step explanation:
let the number of miles she ran each day = x
x = 30/6
x = 5 miles
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Answers
Answer:
-15
Step-by-step explanation:
jenny goes to the shop she buys
. three cups for £1.24 each
.three saucers for 95p each
. a teapot for £6.18
jenny has £20 to spend she also wants to but some plates, which are £1.57 each.
what is the greatest number of plates jenny she can buy
Answers
Answer:
5
Step-by-step explanation:
1.24 times 3 = 3.72
.95 (the value of pence to a pound in decimal form) = 2.85
6.18 for the teapot
2.72+2.85+6.18=11.75
She now has £8.25 left (20-11.75).
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BRAINLIEST
Like terms of 6ab^2
1. -3ab
2. 2ab^2
3.-6a^2 b^2
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Answers
Answer:
2nd option is the right answer
Greatest common factor of 4 and 19?
Answers
Answer:
The greatest common factor of 4 and 19 is 1
Step-by-step explanation:
Answer:
Greatest common factor of 4 and 19 is 1
[tex]8 \sqrt{72} [/tex]
how to solve ??
Answers
Answer:
[tex]8 \sqrt{72} = 8 \sqrt{3 \times 3 \times 2 \times 2 \times 2} \\ = 8 \times 3 \times 2 \times \sqrt{2} = 48 \sqrt{2} [/tex]
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Answer:
Area of gray region = [tex]8x^2+8x-7[/tex]
Step-by-step explanation:
The area covered by the furniture can be subtracted from the total area of the room to calculate the area of the gray region.
Total area of the room: [tex]13x^2+7x-2[/tex]
Area taken up by furniture: [tex]5x^2-x+5[/tex]
Area of gray region = total area of the room - area taken up by furniture
Area of gray region = [tex]13x^2+7x-2-(5x^2-x+5)[/tex]
Remember to distribute the negative sign:
Area of gray region = [tex]13x^2+7x-2-5x^2+x-5[/tex]
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Answer:
8x^2+6x+3
Step-by-step explanation:
13x^2+7x-2
- 5x^2- x+3
============
8x^2=6x=3
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3 in the thousands place
8 in the tenths place
5 in the hundredths place
0 in the ones place
Answers
Answer:
0.853
Step-by-step explanation:
8- 0.08
5- 0.005
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Answers
These are all your congruent parts and they are colour coded along with matching marks on the triangle to help you know that! :)
evaluate the following surds √2+√5
Answers
Answer:
The answer of the addition is;
√2+√5
Step-by-step explanation:
Here, we want to evaluate the given sure
Basically, we want to add the two surds together
In the case of this question, since they have nothing in common, the addition of both will give the same results
Thus;
√2+√5 = √2+√5
The total of two investments are $5,000. The average annual interest rate for one investment is 10% and 14% for the other. The total annual interest is $620. How much is invested at each rate.
Answers
Answer:
Step-by-step explanation:
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Answer:
1. x = 21°
2. x = 30°
3. x = 7°
5 x = 3
Step-by-step explanation:
Solving for x
1. 15+ 5x + 60° = 180°
75 + 5x = 180°
5x = 180 - 75
5x = 105
x = 105/5
x = 21°
2. These angle are vertical angles
Hence:
13x - 5 = 125°
13x = 125° + 5
13x = 130
x = 130/3
x = 30°
3. 8x - 1 = 55°
8x = 55 + 1
8x = 56
x = 56/8
x = 7°
5. These angles are angles in a straight line
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17x + 129° = 180°
17x = 180° - 129°
17x = 51
x = 51/17
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Answer:
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Step-by-step explanation:
It is true because the equation would be 1 is less than or equal to 3-(-4)
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[tex]\huge\boxed{\sf x = 8a}[/tex]
Step-by-step explanation:
[tex]\sf \frac{3}{a} x - 4 = 20\\\\Add \ 4 \ to \ both \ sides\\\\\frac{3}{a} x = 20+4\\\\\frac{3}{a} x = 24\\\\Multiply \ both \ sides \ by \ a\\\\3x = 24 * a\\\\Divide \ 3 \ to \ both \ sides\\\\x = 24a / 3\\\\x = 8a\\\\\rule[225]{225}{2}[/tex]
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Answers
Line m passes through points (1, 4) and (10, 9). Line n is parallel to line m. What is the slope
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Answers
#1: Solve the inequality below.
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Answers
Explanation: Just like any of your two-step equations,
in this inequality, start by isolating the x term which in this
case is -3x by subtracting 5 from both sides.
That leaves you with -3x < -24.
To get x by itself, divide both sides by -3 but watch out.
When you multiply or divide both sides of an inequality by a
negative number, you must switch the direction of the inequality sign.
So we have x < 8 and put your final answer in
set notation and it look like this → {x: x < 8}.