Answer:
[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
I'm assuming the angles are in degrees.
[tex]2x \tan(60\º)=10+\csc(30\º)[/tex]
[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\sin(30\º)} $[/tex]
[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\frac{1}{2} } $[/tex]
[tex]$2x\cdot \sqrt{3}=10+2} $[/tex]
[tex]$x=\frac{12}{2\sqrt{3}} $[/tex]
[tex]$x=\frac{6}{\sqrt{3}} =\frac{6\sqrt{3}} {3} }=2\sqrt{3} $[/tex]
20 points thanks :) im kinda stuck lol
1. (a) 0 = x² + 4x - 12 (Switch Sides)
x² + 4x - 12 = 0 (Factor Expression)
(x - 2)(x + 6) = 0 (Apply the Zero Factor Principle)
x = 2, and x = - 6
x - intercept : (2, 0) and ( - 6, 0)
(b) y = (0)² + 4(0) - 12 (Simplify)
y = 0 + 4 * 0 - 12 = 0 + 0 - 12 = - 12
y - intercept : (0, - 12)
(c) Our vertex belongs to an upward facing parabola, and hence it will be a minimum, of ( - 2, - 16).
2. Seth's solution is not accurate. He did the calculations accurately, and ended up with x = 3 and x = - 2. However he forgot to substitute those values back into the equations y = x² + 3x - 5 and y = 4x + 1, solving for the y values. Instead of being ( - 2, 0) and (3, 0) it should have been (3, 13), ( - 2, - 7)...
y = (3)² + 3(3) - 5 = 9 + 9 - 5 = 18 - 5 = 13,
y = 4( - 2) + 1 = - 8 + 1 = - 7
Hence we get the solutions (3, 13) and ( - 2, - 7).
the difference of 5 and y is at least 19
Answer:
-14
Step-by-step explanation:
5-y=19
collect all the like terms on one side
-y=19-5
when 5 moves over the the other side of the equation it becomes a negative
-y=14
divide both sides by a negative sign
y=-14
A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?
Answer:
son2: 5
son1: 10
Step-by-step explanation:
2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59
3x = 15
x = 5
The age of each boy at present will be 2 years and 3 years.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the age of the sons will be x and y.
A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be
x = 2y
In 3 years, the sum of all their ages will be 59 years. Then the equation will be
x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59
Simplify the equation, we have
3x + 3y + 41 = 59
6y + 3y = 59 – 41
9y = 18
y = 2
Then the value of x will be
x = 2y
x = 2(2)
x = 4
Thus, the age of each boy at present will be 2 years and 3 years.
More about the linear system link is given below.
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PLZ HELP ASAP!!!!!!!!!
WILL MARK BRAINLIST!!
meagan worked 24 hours and earned $84 what is her rate pay
Answer: 3.50 Per hour
Step-by-step explanation:
Divide 84 by 24
given a right-angled triangle with area 30 square centimeters and one of the legs of the right-angled triangle has 5cm, of the sum of the altitudes of the triangle can be expressed as a/b where gcd(a,b)=1. find a+b.geometry
Answer:
See explanation
Step-by-step explanation:
If A = 30 = 1/2ab = 1/2(5)(b)
60 = 5b
b = 12
a/b = 5/12
a + b = 5 + 12 = 17
Answer:
See explanation
Step-by-step explanation:
If A = 30 = 1/2ab = 1/2(5)(b)
60 = 5b
b = 12
a/b = 5/12
a + b = 5 + 12 = 17
Kent has 20 pieces of 50 sen and 20 sen coins.The total value of the coins is RM6.10.
How many 50 sen coins does he have?
Answer:
Number of 50sen coins = 13
Step-by-step explanation:
Let the number of 50sen coins be = x
Let the number of 20sen coins be = y
Total coins = 20
x + y = 20 ----------------------(i)
Value of 50sen coins = 0.50*x = 0.50x
Value of 20sen coins = 0.20 *y = 0.20y
Total value = RM 6.10
0.5x + 0.2y = 6.10 -------------------(ii)
Multiply (i) by (-0.5) and then add the equations. So, x will be eliminated and we can find the value of y
(i) * (-0.5) -0.5x - 0.5y = -10
(ii) 0.5x + 0.2y = 6.10 { add and now x will be eliminated}
- 0.3y = -3.90
Divide both sides by (-0.3)
y = -3.90/-0.3
y = 13
Plug in the value of y in equation (i)
x + 13 = 20
Subtract 13 from both sides
x = 20 -13
x = 7
Number of 50sen coins = 13
Answer:
the number of 50sen coins:
x = 7
Step-by-step explanation:
Taking the number of 50sen coins as x
50(x)
∴ the number of 20sen coins is 20-x (as total no. of coins are 20)
20(20-x)
total amount = 6.10RM = 610sen
equating:
50x + 20(20-x) = 610
50x + 400-20x = 610
50x - 20x = 610-400
30x = 210
x = 210/30 = 7
Therefore, the number of 50sen coins is 7
20sen coins is 20-7= 13.
verification=
50*7 + 20*13 = 610
310 + 260 = 610
610sen = 610sen
6.10RM = 6.10RM
L.H.S = R.H.S
hence, verified.
Mrs kanja ,miss kanene and Mrs nyaga have to mark a form three contest for 160students .They take 5mins ,4mins and 12mins respectively to mark a script .If they all start to mark at 9.00am non-stop ,what is the shortest time they ca n take to complete the marking?
Answer:
300 minutes
2:00 p.m
Step-by-step explanation:
Given the following:
Time taken to mark a script :
Mrs Kanja = 5mins
Miss Kanene = 4mins
Mrs Nyaga = 12 mins
Number of scripts = 160
Start time = 9:00 a.m
Rate at which each of them mark:
Mrs Kanja = t / 5
Miss Kanene = t/4
Mrs Nyaga = t/12
Combined rate :
t/5 + t/4 + t/12 = 160
(12t + 15t + 5t) / 60 = 160
32t / 60 = 160
32t = 160 * 60
32t = 9600
t = 9600 / 32
t = 300 minutes
300 minutes = 300/60 = 5hrs
9:00 a.m + 5 hours = 2:00 p.m
Write and equation of the line that passes through the pair of points (4,6) and (-1,1)
Answer:
y = x + 2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Find slope m
m = (1 - 6)/(-1 - 4)
m = -5/-5
m = 1
y = x + b
Step 2: Find y-int b
y = x + b
1 = -1 + b
b = 2
Step 3: Rewrite equation
y = x + 2
The equation of C is (x - 2)^2 + (y - 1)^2 = 25. Of the points P(0,5), Q(2,2) R(5,-2), and S(6,6), which point is located outside the circle?
Answer:
( 6,6) is outside
Step-by-step explanation:
(x - 2)^2 + (y - 1)^2 = 25
This is of the form
(x - h)^2 + (y - k)^2 = r^2
where ( h,k) is the center and r is the radius
(x - 2)^2 + (y - 1)^2 = 5^2
The center is at ( 2,1) and the radius is 5
P(0,5), Q(2,2) R(5,-2), and S(6,6)
Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)
( 6,6) is outside the circle
Please answer. I need this to be done, Thanks. Will give brainliest
Answer:
The answer is s^26/pq59
Step-by-step explanation:
Answer:
p^ -1 q ^ -59 s ^26
or without negative exponents
s^ 26 /(p q^ 59)
Step-by-step explanation:
When multiplying , we can add the exponents when the bases are the same
p^0 q ^ -60 r^-1 s^25 * p^-1 qrs
When there is no exponent written, there is an implied 1
p^ (0+-1) q^(-60+1) r ^( -1 +1) s ^ ( 25+1)
p^ -1 q ^ -59 r ^0 s ^26
r^0 = 1
p^ -1 q ^ -59 s ^26
If you need the negative exponents written as positive
a^-b = 1/ a^b
s^ 26 /(p q^ 59)
Please help!! What is the volume of four cubes with a side length of fraction 1 over 4 foot? V = s3, where s is the side length. fraction 1 over 4 ft3 fraction 1 over 3 ft3 fraction 1 over 12 ft3 fraction 1 over 16 ft3
Answer:
1/16 is the answer!!Hope this helps. sorry for no explanation but i already did this flvs quiz and i don't remember how to f=do it
Step-by-step explanation:
The area of a triangle is 30
square inches. The height is
5 in. Find the base.
Answer:
12 inches
Step-by-step explanation:
A=1/2bh
30=1/2b5
(30*2)/5=b
B=12
Which of the following steps can be performed so that the square root property may easily be applied to 2x2 = 16? (1 point)
1. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is 16, so divide both sides by 2 before applying the square root property.
2. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.
3. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 16 before applying the square root property.
4. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is 16, so divide both sides by 16 before applying the square root property.
Answer:
[tex]\Large \boxed{\mathrm{Option \ 2}}[/tex]
Step-by-step explanation:
[tex]2x^2 =16[/tex]
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.
The x variable should be isolated on one side of the equation. The x variable is squared so before performing the square root property where we take the square root of both sides, we divide both sides by 2, then take the square root of both sides.
Dividing both sides by 2.
[tex]\displaystyle \frac{2x^2 }{2} =\frac{16}{2}[/tex]
[tex]x^2 =8[/tex]
Taking the square root of both sides.
[tex]\sqrt{x^2 } =\pm \sqrt{8}[/tex]
[tex]x=\pm 2\sqrt{2}[/tex]
Answer:
Option 2
Step-by-step explanation:
2x² = 16
Since x is completely squared and and 2 isn't , so we need to divide both sides by 2. As to find x , we need to "isolate" x first so that is why we need to get rid of 2 with the x². We'll divide both sides by 2 in order to get rid of 2.
Dividing both sides by 2
=> x² = 8
Now , that is the x is isolated so we'll take square root on both sides
=> x = ±2√2
Factor :2x^(5)-9x^(4)+6x^(3)+22x^(2)-20x-25
Answer:
(x+1)(x+1)(2x−5)(x^2−4x+5)
Step-by-step explanation:
2x^5−9x^4+6x^3+22x^2−20x−25
2x^5−9x^4+6x^3+22x^2−20x−25
=(x+1)(x+1)(2x−5)(x2−4x+5)
SOMEBODY HELP PLEASE! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Answer:
Kindly check explanation
Step-by-step explanation:
SMALL SIZE :
AMOUNT OF LIQUID = 250 milliliters
Sales price = $4.50
Cost per milliliter :
Sales price / amount of liquid
$4.50 / 250 = $0.018
MEDIUM SIZE :
AMOUNT OF LIQUID = 500 milliliters
Sales price = $9.95
Cost per milliliter :
Sales price / amount of liquid
$9.95 / 500 = $0.0199
= $0.020 ( 3 decimal places)
LARGE SIZE :
AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters
Sales price = $16.95
Cost per milliliter :
Sales price / amount of liquid
$16.95 / 500 = $0.0199
= $0.01695
= $0.017 ( 3 decimal places)
A) LARGE < SMALL < MEDIUM
B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
1 large size + 2 small sizes
$16.95 + 2($4.50)
$16.95 + $9.00
= $25.95
C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
3 medium sizes
3 * ($9.95)
$29.85
5a - 2b for a = -2 and b = 5
Answer:
-20
Step-by-step explanation:
5a - 2b a=-2 b=5
5(-2)-2(5)
-10-10=-20
Answer:
The answer is - 20Step-by-step explanation:
5a - 2b
To find the value of the expression when
a = -2 and b = 5
Substitute the values of a and b into the expression
That's
5(-2) - 2(5)
-10 - 10
-20
We have the final answer as -20
Hope this helps you
PLS HELP. i really need this fast ill give brainliest too
Answer:
24 square units
Step-by-step explanation:
Use the formula for area of a parallelogram to solve. The base is 6 units, and the height is 4 units.
A = bh
A = (6)(4)
A = 24 square units
The area of the parallelogram is 24 square units.
A dwarf planet is discovered with a radius that is 1/100 the radius of planet c. Write the diameter of the dwarf planet as power. The diameter of the dwarf planet is meter
Answer:
1^-100
Step-by-step explanation:
in the negative powers the negative sign stands for the fraction line symbol and the power stands for the bottom number.
true or false the ratio of the circumfernce of a circle to its diameter is called pi
That's true. Pi is known to be defined as the ratio of the circumference of a circle to its diameter.
is 11-2x the same as 2x-11
No they are not the same.
We can plug in x = 0 to get
11-2x = 11-2(0) = 11-0 = 11
2x-11 = 2(0)-11 = 0-11 = -11
We get the results 11 and -11 for the expressions 11-2x and 2x-11 respectively. Since we got different outputs, this is enough to show that the expressions are not the same. They would need to produce the same outputs for any given x value.
On a graph, y = 11-2x and y = 2x-11 are two different lines to show they are not the same expression.
note: if you plug in x = 11/2 = 5.5, then both outputs are the same; otherwise, you'll get different outputs.
The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could be
The length of the side can be both 5 and 9.
What is an Isosceles Triangle?An Isosceles Triangle is a triangle that has two equal sides.
The length of the sides of an isosceles triangle is given as 5 and 9
To determine the third side, the property of Triangle Inequality will be used
According to the property, the sum of any pair of a triangle’s sides is always greater than the third side.
If the third side is 5 then
5+5 > 9
10 >9
true
if the third side is 9 then
5+9 > 9
14>9
Therefore, the length of the side can be both 5 and 9.
To know more about Isosceles Triangle
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is 16 a perfect cube
Answer:
No
Step-by-step explanation:
No, 16 is not a perfect cube. Perfect cubes are numbers that are the cube of an integer and can also be written in the form x³ where x is an integer. Since 16 cannot be written like that, it is not a perfect cube.
Please answer answer question
Answer:
156.6 m²
Step-by-step explanation:
To find the surface area of this pyramid, we need to find the area of the base and the sides.
The base triangle has a length of 9 and a height of 7.8. So:
[tex]\frac{bh}{2} = \frac{9\cdot7.8}{2} = \frac{70.2}{2} = 35.1[/tex]
Now, the length of the sides are 9 and the height is 9. So:
[tex]\frac{9\cdot9}{2} = \frac{81}{2} = 40.5[/tex]
Since there are 3 identical sides:
[tex]40.5\cdot3=121.5[/tex]
Add the values:
[tex]121.5+35.1=156.6[/tex]
Hope this helped!
The statement "a is not more than b" is the same as a > b.
True
False
Answer:
False
Step-by-step explanation:
A > B means A is greater than B, so A is not more than B is false.
Solve for x. 3:12 = x:16
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
We can represent each ratio as a fraction, then use the cross products property to find the value of x.
[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]
Hope this helped!
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer: 280 tons
Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons
Answer: 10 ships
Step-by-step explanation:
Help, i just need the answers and no need for explanations.
Answer:
The equation of the quadratic function shown is;
x^2+ 2x -3
Step-by-step explanation:
Here in this question, we need to know the quadratic equation whose graph was shown.
The key to answering this lies in knowing the roots of the equation.
The roots of the equation are the solution to the quadratic equation and can be seen from the graph at the point where the quadratic equation crosses the x-axis.
The graph crosses the x-axis at two points.
These are at the points x = -3 and x = 1
So what we have are;
x + 3 and x -1
Multiplying both will give us the quadratic equation we are looking for.
(x + 3)(x-1) = x(x -1) + 3(x-1)
= x^2 -x + 3x -3 = x^2 + 2x -3
HELP! BRAINLIEST! AHJHHHHHH
Answer:
129.5 Square feet is the correct answer.
Step-by-step explanation:
I am a 100% SURE of that.
Hope this helps....
Have a nice day!!!!
The formula for the area (A) of a circle is A = π • r2, where r is the radius of the circle. Ronisha wants to find the area of a sector of a circle that has a central angle of π6 radians. Enter the number that Ronisha should multiply by to find the area of the sector of the circle. Round your answer to the nearest hundredth.
Greetings from Brasil...
Here we will apply rule of 3...
This formula, A = πR², its for the whole circle, that is, 360° (2π)
We want the area of only a part, that is, a circular sector whose angle π/6
sector area
2π ----- πR²
π/6 ----- X
2πX = (π/6).πR²
2πX = π²R²/6
X = π²R²/12π
X = πR²/12If Ronisha multiply the area by 1/12 she will get the area of sector with angle of π/6
