Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
Since the triangle is a right triangle with a 60 degree angle, the triangle is what can be referred to as a 30-60-90 triangle. In this type of triangle, the larger leg (the one opposite the 60 degree angle) is [tex]\sqrt{3}[/tex] times larger than the smaller leg (the one opposite the 30 degree angle). Also, the hypotenuse (the side opposite the right angle) is twice larger than the smaller leg. Since the smaller leg is 8/2=4 units long, x is [tex]\sqrt{3}[/tex] larger than that or just [tex]4\sqrt{3}[/tex]. Hope this helps!
Answer:
4√3
Step-by-step explanation:
We can use trig functions since this is a right triangle
The side opposite the right angle is 8, that is the hypotenuse
We know the opposite side is x
sin theta = opp/ hyp
sin 60 = x/8
Multiply each side by 8
8 sin 60 =x
sin 60 = sqrt(3)/2
8 (sqrt(3)/2 =x
4 sqrt(3) =x
ITS AN EMERGENCY!! PLEASE HELPP!! I WILL MARK YOU BRAINLIEST IF CORRECT
Answer: A, C, E
Step-by-step explanation:
Since it was only translated and reflected, nothing changed except for its location.
Therefore, I chose answers A, C, and E.
Hope this helps! :)
Suppose a parabola has vertex (-8, -7) and also passes through the point (-7,-4). Write the equation of the parabola invertex form
Answer:
y = 3 (x+8)^2 -7
Step-by-step explanation:
The vertex form of the equation is
y = a(x-h)^2 +k
where (h,k) is the vertex
y = a (x- -8)^2 + -7
y = a (x+8)^2 -7
Now substitute the point into the equation to determine a
-4 = a (-7+8)^2 -7
-4 = a (1^2) -7
-4 = a -7
Add 7 to each side
-4+7 = a-7+7
3 =a
y = 3 (x+8)^2 -7
Answer:
y = 3(x + 8)² - 7
Step-by-step explanation:
y = a(x - -8)² - 7
y = a(x + 8)² - 7
-4 = a(-7 + 8)² - 7
3 = a
y = 3(x + 8)² - 7
F (1) = -16. f(n)=-29-f(n-1) f2=
Step-by-step explanation:
f(n) = - 29 - f( n - 1 )
f(1) = - 16
Now
f(2) = - 29 - f ( 2 - 1 )
= - 29 - f ( 1)
= -29 - ( - 16)
= - 29 + 16
= - 13
100 students in the gym 25 are wearing a hat, 25 are wearing a T- shirt, 25 are wearing a hoodie and 25 are wearing a yankee T-shirt. If one student is randomly selected what is the probability that student is wearing a hat.
Answer:
1/4 or 25%
Step-by-step explanation:
So there are 1/4 of the students wearing each of the items. 1/4=25% if you are asked for it. I hope this helps.
If sin = O =5/6, what are the values of cos O and tan O? (2 points)
Answer:
[tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and [tex]tan(\alpha )=\frac{5\sqrt{11} }{11}[/tex]
Step-by-step explanation:
First we would need to solve for the missing leg in order to figure out the remaining answers.
To do this we can use the Pythagorean Theorem a² + b² = c²
Our missing leg in this case is a, so solving for a gives us [tex]a=\sqrt{c^{2} -b^{2} }[/tex]
Here our b is 5 and our c is 6. So plugging in these values we get [tex]a=\sqrt{(6)^{2}-(5)^{2} } =\sqrt{36-25} =\sqrt{11}[/tex]
With this missing leg being solved, we can use trig identities to solve for cos and tan
I used the trig identity [tex]sin(\alpha )=\frac{opposite}{hypotenuse}[/tex] to set up the triangle in the attached image. We can use the trig identity [tex]cos(\alpha)=\frac{adjacent}{hypotenuse}[/tex] which would give us [tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and we can use the trig identity [tex]tan(\alpha ) = \frac{opposite}{adjacent}[/tex] which would give us [tex]tan(\alpha )=\frac{5}{\sqrt{11} } =\frac{5\sqrt{11} }{11}[/tex]
Answer:
As trigonometry property:
(sinO)^2 + (cosO)^2 = 1
tanO = sinO/cosO
Then, if sinO = 5/6 = 0.83
=> (5/6)^2 + (cosO)^2 = 1
=> cosO = +/- sqrt(1 - (5/6)^2) = +/- 0.55
=>tanO = +/- 0.83/0.55 = +/- 1.51
Hope this helps!
:)
Find the value of x.
x =
Answer:
4
Step-by-step explanation:
The bottom half needs to be equal due to it's symmetrical sides.
Answer:
3
Step-by-step explanation:
^^
Brooklyn is starting a running plan to train for a race . In the first week of her running plan , Brooklyn will run 8 miles . The plan calls for Brooklyn to increase her weekly mileage by 1.5 miles every week . If Brooklyn sticks to the plan , how many miles would she be expected to run during her 19th week of training plan ?
Answer:
36.5 miles
Step-by-step explanation:
Answer:
write out the first three terms (ex. the first term was 8 miles for the first week)
find out the arithmetic sequence or d. (d= 1.5)
plug into explicit formula.
answer: 35
Express sqrt-72 in its simplest form.
Answer:
[tex]\sqrt{72}[/tex] = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{72}\\\sqrt{(4)(18)}\\[/tex]
2[tex]\sqrt{(2)(9)}[/tex]
(2)(3)[tex]\sqrt{2}[/tex]
6[tex]\sqrt{2}[/tex]
Answer:
6√2
Step-by-step explanation:
hello :
√72 = √(36×2) =√36×√2 =6√2 because :√36=6
select all the pairs that are alternate interior angles
Answer:
- ∠3 & ∠5
- ∠2 & ∠8
----------------------------------------------------------------------
Interior Angles - Angles that appear INSIDE the transversal
Transversal - The shape you see with two parallel lines intersecting it.
Alternate - Opposite of each other, on the other side as well.
The alternate interior angles are the pair of ∠2,∠8 and ∠3,∠5.
What is alternating interior angle?Alternate interior angles are the angles which are formed when two parallel lines cut by a transversal line.
Hence, the pair ∠2,∠8 and ∠3,∠5 are alternating interior angle.
Learn more about angles here:
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A circle has the equation (x−13)2+(y−1)2=4.
A: What is the center of the circle?
B: What is the radius of the circle?
Select two answers: one for question A, and one for question B.
A: (13,1)
B: 4
A: (−13,−1)
A: (−13,1)
A: (13,−1)
B: 2
B: 2–√
Final answer:
The center of the given circle is at (13, 1), and the radius of the circle is 2.
Explanation:
The equation of a circle is generally given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Looking at the given equation (x - 13)^2 + (y - 1)^2 = 4, we can see that it is already in this standard form.
To answer the questions:
The center of the circle is (13, 1), which comes from the terms within the parentheses being subtracted from x and y.
The radius of the circle is not simply 4, as one might surmise by a quick glance. Instead, the equation gives us the radius squared, r^2 = 4. Taking the square root of both sides, we find that the radius, r, is 2.
If the mean of the data set is 158 thousand dollars, find the revenue for the Granton location. 121,189,147,?
Answer:
175
Step-by-step explanation:
Since the mean is 158
(121+189+147+x)/4=158
121+189+147+x=632
x=175
Answer:
[tex]175[/tex] (thousand dollars) - written in [tex]2/22/2021[/tex]
Step-by-step explanation
In order to know the answer in the question, we should need to solve for the [tex]x[/tex] (Granton). It is other way around in solving for the mean because in here the mean is given. After using this formula, [tex]\frac{121+189+147+x}{4}=158[/tex] we derived at our answer that Granton has a revenue of [tex]175[/tex] (thousand dollars).
Can someone check to see if this is correct?
Answer:
yes
Step-by-step explanation:
Answer:
yes it is correct good job
Step-by-step explanation:
find the measurement of the angle
Answer:
∠ 1 = 120°
Step-by-step explanation:
Note that ∠ Q and ∠ R are congruent, that is both 30°, thus
∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°
If x = 4 and y = 6 , evaluate the following expression:
20+2(3y-4x)
By applying the PEMDAS rule, the solution to the given expression is equal to 24.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
20 + 2(3y - 4x)
20 + 2(3(6) - 4(4))
20 + 2(18 - 16)
20 + 2(2)
20 + 4 = 24
Read more on expression here: brainly.com/question/16729936
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How does the graph of the circle described by x2+(y−7)2=49 change when its equation is changed to (x+5)2+(y−4)2=64?
Select each correct answer.
The Circle's radius decreases
The circle's radius increases
The circle moves up
The circle moves down
The circle moves left
The circle moves right
Please help, I will give Brainliest and 30 points.
The circle moves down
the circle moves left
the circle's radius increases
I took the test
The circle radius increases , the circle moves down and the circle moves left.
What is circle?A circle is special kind of "ellipse in which eccentricity is zero and the two foci are coincident".
According to the question,
The circle x² + (y-7)² = 49. When the given circle changes (x+5)² + (y-4)² = 64
Equation of the circle = (x-a)² + (y-b)² = r²
x² + (y-7)² = 49
(x-0)² + (y-7)² = (7)²
The circle has center (0,7) and radius is 7.
Circle changes (x+5)² + (y-4)² = 64
(x+5)² + (y-4)² = (8)²
The circle has center (5,4) and the radius 8.
Below diagram clearly shows the circle radius increases , the circle moves down and the circle moves left.
Learn more about Circle here
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Translate the algebraic expression and simplify if possible.
The quotient of -2 and the sum of a and b
Please help me!
a snail travel 1/5 of inch in an hr how long will it take to travel 5 inches
Answer:
25 hours
Step-by-step explanation:
5/.2=25
Answer:
25 hours
Step-by-step explanation:
If it travels 1/5 of an inch in an hour, then it travels 1 inch every 5 hours. We want 5 inches, so 5 hours x 5 is 25 hours. :)
find the exact length of the third side
find the valu of x.
Answer:
Easy! X is going to be 58° degree's as well, because of the Vertical Angles Theorem!
Answer:
58 degrees
Step-by-step explanation:
It is symmetrical to the other side, which is 58 degrees.
A circle has the equation x2+y2+16y−30x=0.
What is the equation of the circle in standard form, the coordinates of its center, and the length of its radius?
The equation of the circle is (x+15)2+(y−8)2=289; the center is at (−15,8), and the radius is 17 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (−15,8), and the radius is 289 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (15,−8), and the radius is 17 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (15,−8), and the radius is 289 units.
Answer:
Step-by-step explanation:
hello :
x2+y2+16y−30x=0 means : (x²-30x)+(y²+16y) =0
(x²-30x+15²)-15²+(y²+16y+8²) -8²=0
(x-15)²-225+(y+8)²-64=0
(x-15)²+(y+8)²=289=17²......standard form when the center is (15,- 8)
and radius 17
Final answer:
To transform x^2+y^2+16y-30x=0 into the standard form of a circle equation, we must complete the square to obtain (x-15)^2+(y+8)^2=289. The circle's center is at (15, -8) and has a radius of 17 units.
Explanation:
To rewrite the given equation of the circle x^2+y^2+16y−30x=0 into standard form, we must complete the square for both x and y terms. First, rearrange the equation to group x and y terms together: x^2−30x + y^2+16y = 0. To complete the square, take half of the coefficient of x, which is −15, square it to get 225, and add it to both sides. Similarly, take half of the coefficient of y, which is 8, square it to get 64, and add it to both sides as well.
After adding these values, the equation becomes x^2−30x+225 + y^2+16y+64 = 225+64. Now it can be written as (x−15)^2 + (y+8)^2 = 289.
The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Thus, from our equation (x−15)^2 + (y+8)^2 = 289, the center is at (15, −8) and the radius is √289 which is 17 units.
Therefore, the correct statement is: 'The equation of the circle is (x−15)^2+ (y+8)^2=289; the center is at (15, −8), and the radius is 17 units.'
a. A game uses spinner A below. If a player spins a 1, he or she wins
a prize. Explain How to find the theoretical probability of winning
a prize.
Spinner A
Answer:
1/4
Step-by-step explanation:
There are 4 slot, he/she need 1 slot to win, so 1/4
John has an account balance of -$30.00 and Steve has an account balance of
-$50.00. Who has more debt?
A. Steve
B. John
Answer:
A. Steve
Step-by-step explanation:
Steve has to pay $50. So he has more debt than John
Please help will give brainliest!!! I need help ASAP
Answer:
Area = 54.1 ft²
Perimeter = 25.5 ft
Step-by-step explanation:
Area:
The formula for the area of a circle is (A = πr²). The radius is r, and r is half of the diameter, or d. So, it would be:
A = (3)(4.25)²
A = (3)18.0625
A = 54.1
Perimeter:
The perimeter, of circumference, formula for a circle is (C = πd), where C is the circumference and d is the diameter.
C = (3)(8.5)
C = 25.5
Hope this helps! Sorry it is a bit late! Have a great day! :)
Which best describes how to subtract 6.45 from 81.3?
Answer:
simple just subtract and you get-74.85
Step-by-step explanation:
A scale drawing of a square object has a scale of 1 in. : 5 mm. The scale drawing has a length of 2.5 inches. Find the perimeter and the area of the object in the scale drawing. Then find the perimeter and area of the actual object.
Answer:
Perimeter and area of drawing
Perimeter= 10 In
Area = 6.25 In²
Perimeter and area of object
Perimeter = 51.836 mm
Area = 167.936 mm²
Step-by-step explanation:
We are dealing with a square object, so let's talk about the drawing first.
The length of one side = 2.5 In
Perimeter of square= 4L
Perimeter = 4*2.5
Perimeter= 10 In
Area = L*L
Area = 2.5*2.5
Area = 6.25 In²
Letd note that 1 inch =
25.4 millimetres
So 2.5 Inch = 2.5 * 25.4
2.5 In = 63.5 mm.
25.4 mm is to 5mm
63.5 mm is to (63.5*5)/24.5
63.5mm is to 12.959 mm
So the length of actual object is 12.959mm
The perimeter = 4*12.959
Perimeter = 51.836 mm
Area = 12.959²
Area = 167.936 mm²
Answer:
The perimeter of the actual object is 50 mm.
The area of the actual object is 156.25 mm square
Step-by-step explanation:
Given
Shape: Square
Scale: 1 in : 5 mm
Length of Scale Drawing = 2.5 in
Required:
- Perimeter of Actual Object
- Area of Actual Object
Calculating the perimeter of the actual object
Provided that the shape is a square;
The perimeter of the actual object is calculated by
Perimeter = 4 * Length
Recall that the scale is 1 in : 5 mm
This means 1 in on the scale represents 5 mm of the actual measurements of the object.
So, if 1 in ≈ 5 mm, then
2.5 in ≈ 2.5 * 5 mm
2.5 in = 12.5 mm
So, Length = 12.5mm
Now, the perimeter of the actual object can be calculated.
P = 4 * 12.5mm
P = 50mm
Hence, the perimeter of the actual measurements is 50 mm.
Calculating the area of the actual object
The area of the actual object is calculated by
Area = Length * Length
Recall that Length = 12.5 mm as calculated above
So,
Area = 12.5 * 12.5
Area = 156.25 mm square
Hence, the area of the actual object is 156.25 mm square
A football player tosses the ball through the air to a teammate. Could the path of the ball be described by the equation y = 0.5x2 + 0.3x + 2?
Answer:
Step-by-step explanation:
No; the graph for the path of a ball must be a parabola that opens downward, so if the equation is in the form y = ax2 + bx + c, a must be negative.
Compare the two fractions using <, >, or =. 6/12 ___ 1/2
Answer:
6/12=1/2
Step-by-step explanation:
6/12_1/12
Reduce 6/12 into lowest form
6/12=1/2
We get,
1/2_1/2
Both are equal,therefore
6/12=1/2
Step-by-step explanation:
6. and 1
12. 2
=1. = 1
2. 2
i simplified 6 and 12
which gave me
1 over 2
Convert this decimal into a percentage: 1.125
Answer:
112.5 percent
Step-by-step explanation:
Answer:
112.5%
Step-by-step explanation:
Look at answer
The bar of the square pyramid shown has and area of 576 units. If the slant height of the pyramid is 29 units, what is the height of the pyramid?
Answer:
[tex]\sqrt{697}[/tex]
Step-by-step explanation:
If the base of the square pyramid has an area of 576 units, then the side length must have a length of [tex]\sqrt{576}=24[/tex]. 24/2=12, and using the pythagorean theorem you can find that the height of the pyramid is [tex]\sqrt{29^2-12^2}=\sqrt{697}[/tex]. Hope this helps!
Dorian has two bags. Each bag has the letters A, B, and C written on little pieces of paper inside of it. He draws one letter from each bag. What is the probability that he draws out a vowel and a consonant? A. B. C. D.