Answer:
Hello,
Step-by-step explanation:
AB=DC=b, AD=BC=a
p=BD, q=AC
angle ABC=x
[tex]AB^4+AD^4+AB^2*AD^2=AC^2*BD^2\\\\b^4+a^4+b^2a^2=(a^2+b^2+2abcos(X))(a^2+b^2-2abcos(X)\\\\(a^2+b^2+2a^2b^2)-a^2b^2=((a^2+b^2)^2-4a^2b^2*cos^2(X))\\\\\\4a^2b^2cos^2(X)=a^2b^2\\\\\\cos^2(X)=\dfrac{1}{4} \\\\(cos(X)-\dfrac{1}{2} )(cos(X)+\dfrac{1}{2} )=0\\cos(x)=\frac{1}{2} \ or\ cos(X)=\dfrac{-1}{2} \\\\\\X=60^o =\dfrac{\pi}{3} rad \ or \ X=120^o=\dfrac{4\pi}{3} rad\\\\\\\\Product=\dfrac{\pi}{3}*\dfrac{4\pi}{3} =\boxed{\dfrac{4\pi^2}{9}}\\[/tex]
radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?
9514 1404 393
Answer:
(18 1/48)π ≈ 56.61 units
Step-by-step explanation:
Arc length is the product of radius and intercepted arc in radians:
s = rθ
s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units
|a-7| - |a-9| if a<7
Step-by-step explanation:
[tex] - |a - 7| - ( - |a - 9| ) = - a + 7 + a - 9 = - 2[/tex]
Solve the following system of equations for x: y = 4 -x^2
X - y =
2
Answer:
B. x=2, x=-3
Step-by-step explanation:
Hello,
We are given this system of equations:
y=4-x²
x-y=2
And we want to solve it for x.
There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.
But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.
In x-y=2, subtract x from both sides.
-y=-x+2
Multiply both sides by -1.
y=x-2
Substitute y as x-2 in y=4-x².
x-2=4-x²
Add x² to both sides.
x²+x-2=4
Subtract 4 from both sides.
x²+x-6=0
Now factor using FOIL.
1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.
Two numbers that add up to 1 but multiply to get -6 are -2 and 3.
So now factor:
(x-2)(x+3)=0
Split and solve:
x-2=0
x=2
x+3=0
x=-3
The solutions for x are x=2 and x=-3, which means the answer is B.
Hope this helps!
A block of wood has a density of 0.6g/cm^3 and a volume of 1.2cm^3.What is the mass of the block of wood?
Answer:
Below
Step-by-step explanation:
You can use this formula to calculate the mass of an object
Mass = Volume x Density
Plugging everything in....
Mass = ( 1.2cm^3 ) ( 0.6g/cm^2 )
= 0.72 g
Hope this helps!
Find the sum end difference between the numbers 473 and the number obtained by reversing the digits
Answer:
Step-by-step explanation:
The given number is 473
The reverse number is 374
The sum is (473 + 274) = 847
The difference is (473 - 274) = 99
Find the measure of a.
A. 20
B. 70
C. 80
D. 40
A circle is a curve sketched out by a point moving in a plane. The measure of a is 70°. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the given circle, the line AC is the diameter of the circle, therefore, the measure of ∠ABC will be 90°.
∠ABC = 90°
This is because a triangle formed on the diameter of the circle such that all the vertices of the triangle intersect the circle, then the angle opposite to the diameter is a right angle.
Now, in ΔABC, the sum of all the angles of the triangle can be written as,
∠ABC + ∠BCA + ∠BAC = 180°
90° + a + 20° = 180°
110° + a = 180°
a = 180° - 110°
a = 70°
Hence, the measure of a is 70°.
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Plz help a beggar I don’t get it
Answer: 3
happy learning
Answer:
B.
Step-by-step explanation:
From the point (-1,0) the next point on the graph is up 3, right 1, making the slope a positive 3.
Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.
Answer:
[tex]\frac{(x-3)^2}{4^2} +\frac{(y-1)^2}{6^2} =1[/tex]
Step-by-step explanation:
[tex]9x^{2}+4y^{2} -54x-8y-59=0[/tex]
[tex]9x^{2}-54x+4y^{2} -8y=59[/tex]
Factor 9 and 4 out
[tex]9(x^2-6x)+4(y^2-2y)=59[/tex]
Complete the square, don't forget to add the 2 extra numbers
[tex]9(x-3)^2+4(y-1)^2=59+81+4[/tex]
[tex]9(x-3)^2+4(y-1)^2=144\\[/tex]
Divide everything by 144
[tex]\frac{(x-3)^2}{16} +\frac{(y-1)^2}{36} =1[/tex]
Answer:
Step-by-step explanation:
it's D
the surface area of a prism
Answer:
surface area of a prism is
48 km^2
pLEASE help best and right answer gets brainliest
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
Find the volume of the following figure round your answer to the nearest tenth and if necessary use pi
Answer:
1526.04
Step-by-step explanation:
the formula for calculating the volume of cone is
V=πr^2(h/3)
Thus,
V = (3.14)(9)^2(18/3)
V = (3.14)(81)(6)
V = 1536.04 yd^3
Rounding off to the nearest tenth, we get
V = 1536 yd^3
Biểu diễn 1 ràng buộc trên mặt phẳng tọa độ Oxy là
Step-by-step explanation:
yah kaun se language mein likha hai aapane
If f(x) = 3x-1 and g(x)= x+2 find (f-g) (x)
Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x)= x+2
(f-g) (x) = 3x-1 - (x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x -1-2
=2x -3
what is sixth root of -2i
Answer: 1.08421508 - 0.290514556 i
Step-by-step explanation:
The 6th root of a number is the number that would have to be multiplied by itself 6 times to get the original number
(-(2×i)) = 1.08421508 - 0.290514556 i
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Multiple Choice: Read the Math Notes box in this
lesson and then examine the diagram at right.
Which angle below is another name for ZABC?
The top of the picture
Answer:
not now but i will answer
Another name for the angle ABC based on the diagram Given is the angle named FBG.
Using the three letter angle naming convention, the middle letter refers to the vertex which is the exact angle being referred to.
Given the angle ABC, the angle being referred to is B;
Therefore, whenever, B remains in the the middle of the 3 letter angle naming convention, the angle being referred to is the angle B.
Hence, another name for the angle ABC based on the diagram Given is the angle named FBG, as the vertex of both is B.
The angle EBC does not mean the same as ABC because they are opposite.
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the area of an equilateral triangle of side 8cm is
pls i need answer ASAP
I'll mark brainliest for anyone who can help me
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}a^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}(8)^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{64\sqrt{3}}{4}[/tex]
[tex]\\ \sf\longmapsto Area=16\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto Area=16\times 1.732[/tex]
[tex]\\ \sf\longmapsto Area=27.7cm^2[/tex]
Name the property of real numbers illustrated by the equation
Answer:
A. Commutative property
Step-by-step explanation:
The commutative property states that multiplication can be performed in any order. This means that a*b=b*a. Therefore, it does not matter whether [tex]\sqrt{2}[/tex] or 3 is first in the multiplication problem. So, the first answer is correct.
27. Which statement is true about the system x+3y=11 y=r-7 a. (8,-1) is a solution to both equations, so it is a solution to the system b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system d. (8,-1) is not a solution to either equation, so it is not a solution to the system
Answer:b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
Step-by-step explanation:
27. Which statement is true about the system
x+3y=11
y=r-7
a. (8,-1) is a solution to both equations, so it is a solution to the system
b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system
d. (8,-1) is not a solution to either equation, so it is not a solution to the system
by how much is 90125 more than 58478
Hey there!
First, we should subtract them.
90125 - 58478 = 31,647
90125 is 31647 more than 58478.
Hope this helps!
Have a great day!
How far apart are the 2 cities? See picture.
Show steps
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Answer:
373 miles
Step-by-step explanation:
The difference in latitude is ...
39.1° -33.7° = 5.4° = 0.54°(π/180°) radians = 0.03π radians
The arc length is given by ...
s = rθ, where θ is the angle in radians
The length of the arc along the longitude line is ...
s = (3960 mi)(0.03π) ≈ 373 mi
The distance from Atlanta to Cincinnati is about 373 miles.
Rebecca is comparing prices on toilet paper. Charmin has 18 rolls, each with 200 sheets, for $12.97. Angel Soft has 24 rolls, each with 425 sheets, for $19.98. Which is the better value?
The product that provides the better value per sheet is Angel Soft toilet paper.
Each sheet of Angel Soft costs $0.20 whereas each sheet of Charmin costs $0.36.
Data and Calculations:
Charmin has 18 rolls, each with 200 sheets, for $12.97
Angel Soft has 24 rolls, each with 425 sheets, for $19.98
Product Rolls Sheets Total Sheets Total Cost Cost per Sheet
in a Roll (rolls x sheet) (Total cost/No. Sheets)
Charmin 18 200 3,600 (18 x 200) $12.97 $0.36 ($12.97/3,600)
Angel Soft 24 425 10,200 (24 x 425) $19.98 $0.20 ($19.98/10,200)
Thus, Rebecca should go for Angel Soft toilet paper because it provides a better value per sheet than Charmin toilet paper.
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Can any one solve this.Please
Answer:
True
Step-by-step explanation:
The first derivative tells you the slope of the graph at a specific point. If f'(c) =0, then that means that at f(c), the slope of the graph is 0. It is neither going up nor down
The second derivative tells you the slope of the slope of the graph. If f''(c) < 0, this means that the slope is decreasing. This means that going from the left to f(c), the slope is greater than the slope at f(c), and going from f(c) to the right, the slope is less than the slope at f(c).
Therefore, since the slope at f(c) is 0, the slope is positive to the left of f(c) and negative to the right of f(c). This means that the graph is going up until it hits f(c) and then goes down. Because f(c) is greater than the values to the left of it (because it is going up until it hits f(c)) and the values to the right of it (because it is going down past f(c)), f(c) is a local maximum
Solving the quadratic equation 3x^2+12x=-14 by quadratic formula
9514 1404 393
Answer:
x = -2 ±i(√6)/3
Step-by-step explanation:
The formula for the solution of ax²+bx+c=0 is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
When your equation is written in standard form, it is ...
3x² +12x +14 = 0
so the values needed in the formula are a=3, b=12, c=14.
[tex]x=\dfrac{-12\pm\sqrt{12^2-4(3)(14)}}{2(3)}=\dfrac{-12\pm\sqrt{-24}}{6}=\dfrac{-12\pm2i\sqrt{6}}{6}\\\\\boxed{x=-2\pm\dfrac{\sqrt{6}}{3}i}[/tex]
which of the following equations has both 1 and -3 as a solution?
A). x^2-2x-3=0
B). x^2+2x-3=0
C). x^2-4x+3=0
D). x^2+4x+3=0
Solve this inequality: 14 <-7x
Answer:
-2 > x
Step-by-step explanation:
14 <-7x
Divide each side by -7, remembering to flip the inequality
14/ -7 > -7x/-7
-2 > x
Write the following as an inequality: The sum of x and y is no greater than 2.
the answer is x+y≤2
The sum of x and y is greater than or equal to 2
Answer:
x+y<_2
Step-by-step explanation:
8/9 - Evaluating Algebraic Expressions
5. Which is equivalent to 4x - (y + x) + 2, if x = 5 and y=-3?
O 20
-20
-15
O 15
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Answer:
(a) 20
Step-by-step explanation:
Put the numbers in place of the corresponding letters and do the arithmetic.
4(5) -((-3) +5) +2 = 20 -2 +2 = 20
What temperature is 10 degrees les then 6 degrees Celsius
Answer:
-4
Step-by-step explanation:
you say 6-10
which is -4
What is the temperature if 10°C less than 6°C
Answer:-10°C less than 6°C is -4°C
Explanation:
So, if we start with 6°C, and we want a temperature 10°C less than that, then we can just subtract 10 from 6.
6-10 = -4
```````````````````````````````````````````````````````````Each time Kristine gets paid, she spends $20 and saves the rest. If the amount Kristine earns is represented by x and the amount she saves is represented by y, which graph models her savings?
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (5, 100) and (10, 200).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 1) and (40, 2).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (0, 20) and (10, 30).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Answer:
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Step-by-step explanation:
If Kristine spends $20 and saves the rest when she gets paid, the amount she saves should always be 20 less than the amount she earned.
The points (20, 0) and (25, 5) accurately represent this, where x is how much she earns and y is how much she saves.
(20, 0) represents her earning $20 and saving $0, because she spends $20 every time she gets paid.
(25, 5) represents her earning $25 and saving $5, because she spent $20.
So, the correct graph is A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Answer:
d
Step-by-step explanation:
4. Manuel swims at a speed of 1 yard per second. How many feet per minute does he swim?
Answer:
180 Feet Per Minute
Step-by-step explanation:
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