The formula for surface area of a sphere is: A = 4 x PI x r^2
Replace r with the given radius and calculate the area:
Area = 4 x PI x 100^2
Area = 4 x PI x 10,000
Area = 40,000PI
Which equation can be used to determine the reference angle, r, if 0=7 pi/12?
Answer:
[tex]r=180-\frac{7\pi }{12}[/tex]
Step-by-step explanation:
To find the reference angle of a given angle, first of all, the quadrant of the given angle is determined.
So for 7pi/12
The quadrant is 2nd.
For the angle belonging to 2nd quadrant the equation for reference angle will be:
r=180 - theeta
[tex]r=180-\frac{7\pi }{12}[/tex]
Rationalize the denominator- 12x/√x-10
ANSWER
[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]
EXPLANATION
The given function is
[tex] \frac{ - 12x}{ \sqrt{x} - 10 } [/tex]
In the denominator we have
[tex] \sqrt{x} - 10[/tex]
The conjugate of this surd is
[tex] \sqrt{x} + 10[/tex]
To rationalize this function, we multiply both the numerator and the denominator by the conjugate surd.
[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x} - 10)(\sqrt{x} + 1)} [/tex]
We apply the identity
[tex] (a + b)(a - b) = {a}^{2} - {b}^{2}[/tex]
in the denominator.
This implies that,
[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x})^{2} - {10}^{2} } [/tex]
[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]
Which linear inequality is represented by the graph?
Answer:
Step-by-step explanation:
In this question we will find the equation of the dotted line first.
Since this line passes through two pints (0, 2) and (-3, -7)
So slope of the line will be m = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{-7-2}{-3-0}[/tex]
= [tex]\frac{-9}{-3}[/tex]
= 3
y-intercept of the line is c = 2
Now we will put these values in the standard form of the equation
y = mx + c
y = 3x + 2
Now we will check the inequality shown by shaded region
we take a point from shaded region and plug in the value of x and y.
For point ( -2, 0) y = (-2)(2)+2
= -4 + 2 = -2 and 0>-2
So there should be the sign of greater than.
Therefore, inequality will be y > 3x + 2
Linear inequality represented by the graph is y > 3x +2 and this can be determine by using the slope intercept form.
Given :
Two points - (0 , 2) and (-3 , -7)
Slope of the line can be calculated as follows:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-7-2}{-3-0}=3[/tex]
y intercept is 2.
Now we know that the slope intercept form is given by:
y = mx + c
y = 3x + 2 --- (1)
To check the inequality we take a point from the shaded region and plug in the value of x and y.
At Point (-3,0), equation (1) can be given by:
y = -9 + 2 = -7 < 0
Than inequality must be y > 3x + 2.
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What is the solution to the following equation?
x2 + 3x + 4 = 0
Answer:
No real solutions
Step-by-step explanation:
Using the quadratic formula, you will end up with a square root of a negative number in the numerator. Hence there is no real solution.
see attached.
The solution to the equation x^2 + 3x + 4 = 0 can't be computed using real numbers, because the formula we use (the quadratic formula) results in the square root of a negative number. Therefore, the solutions will be in the form of complex numbers.
Explanation:The subject question falls under Mathematics, specifically algebra. The equation given is a standard form of a quadratic equation. The general form of a quadratic equation is ax2 + bx + c = 0.
To find the solution for the equation x2 + 3x + 4 = 0, we usually use the quadratic formula x = [-b ± sqrt(b2 - 4ac)] / 2a. Applying this formula, we can put a = 1, b = 3 and c = 4. However, when we compute b2 - 4ac, which is 9 - 16, we receive a negative result (-7). This implies that the equation has no real solutions, because square roots of negative numbers are not real numbers, they are complex numbers.
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A number cube with the numbers 1 to 6 is rolled. What is the theoretical probability of rolling the number 3?
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:There are 6 possible options: [tex]\text{1, 2, 3, 4, 5, 6}[/tex]
There is 1 option out of those 6 that we are finding: [tex]\text{3}[/tex]
Therefore, the probability is [tex]\frac{1}{6}[/tex].
Answer:
1/6
Step-by-step explanation:
When we roll a die, we can get the numbers 1,2,3,4,5,6
Each is equally likely
P(3) = How many times 3 occurs/ total
3 occurs 1 time in on the die and there are 6 possible numbers
P(3) = 1/6
pls help asap i’m timed!!!
This is ed right? If so the answer would be c
ANSWER
[tex]g(x) = - \sqrt{x + 3} + 8[/tex]
EXPLANATION
The given function is
[tex]f(x) = - 2 \sqrt{x - 3} + 8[/tex]
The vertex of this function is (3,8)
This function opens downwards so its range is
[tex]y \leqslant 8[/tex]
The function
[tex]g(x) = - \sqrt{x + 3} + 8[/tex]
also has vertex (-3,8)
This function is also reflected in the x-axis. Its range is;
[tex]y \leqslant 8[/tex]
The correct answer is C
How many more website hits were there on Friday than on Thursday? Horizontal bar graph with number of website hits per day of week contains the following data: Sunday 1900, Saturday 2000, Friday 1000, Thursday 800, Wednesday 1200, Tuesday 1900, and Monday 1300. 100 50 200 150
Answer:
200 more on Friday than thursday
10) Jane has 68 stickers. She sticks 3 stickers on each page of her
album.
a) How many pages does she use in all?
pages
b) How many stickers will the last used page have?
stickers
c) The sticker album has 50 pages.
How many more stickers does Jane need to fill all the pages?
stickers
Answer:
Step-by-step explanation:
a) She uses 23 pages (but the last page has 2)
b) 2
c)Jane needs 82 more stickers because
50pages-23=27
27x3(stickers, befcuaase 3 stickers per page)=81
81+1=82 because on 23 page theres only 2 sticker
Hope this helps
If you double a number and add 1 you get 11 what is the number
Answer:
Should be 5, hopes this helps
Step-by-step explanation:
That's it.
Final answer:
To find the original number, we use the equation 2x + 1 = 11; solving for x gives us the number 5.
Explanation:
To find the number that when doubled and added to 1 gives 11, we can set up a simple algebraic equation to solve for the unknown number. Let's call the unknown number x. According to the problem, if we double the number (2x) and then add 1, the result is 11. So, our equation is 2x + 1 = 11.
Next, we can solve for x by subtracting 1 from both sides of the equation, giving us 2x = 10. Finally, we divide both sides by 2 to isolate x, resulting in x = 5. Thus, the number we're looking for is 5.
Select the correct answer. If f(x)=x^1/2-x and g(x)=2x^3-x^1/2-x, find f(x) − g(x).
Answer:
2( √x - x³ )
Step-by-step explanation:
see attached.
Answer:
(f-g)(x) = 2√x - 2x³
Step-by-step explanation:
Write out the terms of f(x) as they are and then the negatives of all the terms of g. We get:
(f-g)(x) = √x - x - 2x³ + √x + x
Combining like terms, we get:
(f-g)(x) = 2√x - 2x³
What is the value of y?
y + 30
you can't solve this nor find the value of y because its not a full equation
Answer:
You cant solve for y without knowing the end number.
Step-by-step explanation:
maybe your equation y + 30 = 32 then we would know y is = to 2
Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no solution?
Answer:
3(x-2)+x=4x+6
Step-by-step explanation:
case 1) we have
3(x-2)+x=4x-6
Solve for x
3x-6+x=4x-6
4x-6=4x-6
0=0 ----> is true for any value of x
therefore
The equation has infinite solutions
case 2) we have
3(x-2)+x=2x-6
3x-6+x=2x-6
4x-2x=-6+6
2x=0
x=0
case 3) we have
3(x-2)+x=3x-3
3x-6+x=3x-3
4x-3x=-3+6
x=3
case 4) we have
3(x-2)+x=4x+6
3x-6+x=4x+6
4x-4x=6+6
0=12 ------> is not true
therefore
The equation has no solution
Answer:
3(x-2)+x=4x+6Step-by-step explanation:
The first equation is the one that doesn't have solution. Let's demonstrate this:
[tex]3(x-2)+x=4x+6\\3x-6+x=4x+6\\4x-6=4x+6\\4x-4x=6+6\\0=12[/tex]
As you can observe, the equation doesn't have any solutions, because it result in a false statement.
If we solve the other equations, we would have:
[tex]3(x-2)+x=2x-6\\3x-6+x=2x-6\\4x-6=2x-6\\4x-2x=-6+6\\2x=0\\x=0[/tex]
[tex]3(x-2)+x=3x-3\\3x-6+x=3x-3\\4x-3x=-3+6\\x=3[/tex]
[tex]3(x-2)+x=4x-6\\3x-6+x=4x-6\\4x-6=4x+6\\6=6[/tex]
The last equation has infinite solutions.
Therefore, the only one that doesn't have any solutions is
3(x-2)+x=4x+6using the prime factor method, find the lcm of 32 and 44
Answer:
lcm = 352
Step-by-step explanation:
32 = 2 × 2 × 2 × 2 × 2 = [tex]2^{5}[/tex] ← product of prime factors
44 = 2 × 2 × 11 = 2² × 11 ← product of prime factors
lowest common multiple (lcm) = [tex]2^{5}[/tex] × 11 = 352
32 = 2*2*2*2*2 = 2^5
44 = 2*2*11 = 2^2*11
We take common and non-common numbers with the highest exponent and we multiply them.
2^5*11 = 32*11 = 352.
If 3 x − 6 < 12 , then x could be
Answer:
3x - 6 < 12
3x < 18
x < 6
X could be numbers that's less than 6
[tex]3 x - 6 < 12 \\3x<18\\x<6[/tex]
If f(x) = 3x^2 and g(x) = 4x^3 + 1, what is the degree of (fg)(x)?
i think this question already been solved:
https://brainly.com/question/4342896
Answer:
degree 5
Step-by-step explanation:
(fg)(x) = f(x) × g(x)
f(x) × g(x) = 3x²(4x³ + 1) = 12[tex]x^{5}[/tex] + 3x²
The degree of the polynomial is determined by the value of the largest exponent, that is
12[tex]x^{5}[/tex] ← largest exponent of 5
Hence (fg)(x) is of degree 5
Which represents the solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)?
Answer:
1. Simplify the inequality 5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4):
15.3+11.22x>-14.25-10.2x-24 10;15.3+11.22x>-10.2x-38.75.
2. Separate terms with x and without x in different sides:
11.22x+10.2x>-38.75-15.3.
3. Add similar terms:
21.42x>-54.05.
4. Divide by 21.42:
x>-54.05/21.42
x>-2.5
Step-by-step explanation:
if ln2=0.693, what is the value of ln32
Answer:
3.4657359...
Step-by-step explanation:
just put into your phone calculator 32 then hit In.
The value of ln 32 is 3.468 .
What is Logarithm ?Logarithm is an inverse of Exponentiation , The power to which a number must be raised in order to obtain another number is known as a logarithm.
It is given that
ln 2 = 0.693
ln 32 = ?
32 = 2⁵
ln 32 = ln 2⁵
ln aⁿ = n ln a
ln 32 = 5 ln 2
ln 32 = 5 * 0.6936
ln 32 = 3.468
Therefore the value of ln 32 is 3.468 .
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Choose a pair of corresponding angles.
22 and 25
_1 and 26
7/8
48 and 410
10 and
4
_9 and 43
Answer:
∠10 and ∠4
Step-by-step explanation:
we know that
When two lines are crossed by another line (called the transversal), the angles in matching corners are called Corresponding Angles
In this problem
∠10 and ∠4 are corresponding angles
Distance traveled 342 miles with an average speed of 40 mph. What is the travel time of the trip?
Answer:
The travel time of the trip is 8.55 hours
Step-by-step explanation:
The average speed of an object is calculated using the following formula:
[tex]s=\frac{d_2 -d_1}{t}[/tex]
Where [tex]d_2 - d_1[/tex] is the total distance traveled by the object and t is the time it took the object to travel that distance.
So we know that:
[tex]d_2 - d_1=342\ miles[/tex]
[tex]s=40\ mph[/tex]
Therefore:
[tex]40=\frac{342}{t}[/tex]
[tex]t=\frac{342}{40}[/tex]
[tex]t=8.55\ hours[/tex]
Answer: 8 hours and 33 minutes
Step-by-step explanation:
you can set up a ratio, cross multiply, and divide.
Can somebody help me solve this?
"The measures of two complementary angles are 6y + 3 and 4y - 13. Find the measures of the angles."
Answer:
The measures of two complementary angles are 63° , 27°
Step-by-step explanation:
The measures of two complementary angles are 6y + 3 and 4y - 13.
Sum of complementary angles = 90°
6y + 3 + 4y - 13 = 90°
10y - 10 = 90°
10y = 90 + 10 = 100
10 y = 100
y = 100/10 = 10
One angle = 6y + 3 = 6 * 10 + 3 = 60 + 3 = 63
other angle = 4y - 13 = 4 * 10 - 13 = 40 - 13 = 27
The angles are 63° , 27°
What is the probably of getting heads when poing a coin and getting a number greater than or equal to 5 when rolling a single die
A) 1/6
B) 1/3
C) 1/4
D) 1/12
Answer:
1/6
Step-by-step explanation:
1/2 (the coin chance) * 2/6 (the dice chance) = 2/12 = 1/6
Answer:
A. 1/6
Step-by-step explanation:
Probability of getting heads: 1/2
Probability of rolling a number >or equal to 5: 2/6
(1/2)(1/3)=1/6
Is 8 a solution to the equation below? Yes or No?
3(x - 2) + 4 = 22
To see if 8 is the solution to the equation, 3 (x - 2) + 4 = 22, you must replace x with 8 and solve using the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction) REMEMBER: IF NOT APPLICABLE TO THE EQUATION YOU MAY SKIP THAT STEP IN PEMDAS . If the sides are equal to each other then 8 IS a solution.
3(8 - 2) + 4 = 22
Parentheses...
3(8 - 2) + 4 = 22
8 - 2 <<<In the parentheses so you must solve first
6
so...
3(6) + 4 = 22
Multiplication...
3(6) + 4 = 22
3 * 6
18
so..
18 + 4 = 22
Addition...
18 + 4 = 22
18 + 4
22
so...
22 = 22
Are they equal to each other? YES!!!
8 is a solution to the equation 3 (x - 2) + 4 = 22
Hope this helped!
~Just a girl in love with Shawn Mendes
Use the graph below to determine the number of solutions the system has.
x=4
y=-x-1
Answer:
The system x = 4 and y = -x - 1 has one solution
Step-by-step explanation:
x = 4 and y = -x - 1 intersects only once on the graph
Answer:
The line x = 4 and y = - x - 1 has only one solution.
Step-by-step explanation:
Consider the provided graph.
The system of equation has the solution at the point where the line intersects.
Now consider the graph of the equation x = 4 and y = - x - 1
The graph of x = 4 is a vertical line.
From the graph it is clear that the line x = 4 and y = - x - 1 intersect at a point.
Now to calculate the number of solutions simply count the number of intersecting points.
By observing the graph it can be concluded that the graph of x = 4 and y = - x - 1 intersect only at one point i.e (4,-5).
Hence, the line x = 4 and y = - x - 1 has only one solution.
Given the function f(x)=8+2x2, calculate the following values:
f(a)=
f(a+h)=
f(a+h)−f(a/)h=
f(x) = 3x - 12, what is (2)?
Answer:
f(2) = -6
Step-by-step explanation:
f(x) = 3x - 12
Plug in 2 for x & solve:
f(2) = 3(2) - 12
Remember to follow PEMDAS. First multiply, then subtract:
f(2) = 3(2) - 12
f(2) = 6 - 12
f(2) = -6
f(2) = -6 is your answer.
~
Which of the following polygons is not a regular polygon?
Answer: the rectangular
Step-by-step explanation:
All the sides are equal for a regular polygon
Answer:
The Rectangle Is Not A Regular Polygon, Option 2
Step-by-step explanation:
For a polygon to be regular all sides and angles have to be the same! A square is an example of a regular polygon, since all sides and angles are even, a rectangle is not.
Find the area of the kite
Answer:
30 sq. units
Step-by-step explanation:
Multiply the length of the two diagonals together and divide by two
[tex]\frac{d1 * d2}{2}[/tex]
10 * 6 = 60
60/2 = 30
The area of the kite is 30 sq. units
Answer: B
Step-by-step explanation:
How to get the area of a rhombus
( diagonal x the other diagonal )1/2
(6*10)1/2
60*1/2
30
Which comparison is correct?
-5 > -4
-8 > -9
5 < 4
-8 > 5
How do you solve this?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-6)^2+(y+5)^2=16\implies [x-\stackrel{h}{6}]^2+[y-(\stackrel{k}{-5})]^2=\stackrel{r}{4^2}~\hfill \begin{cases} \stackrel{center}{(6,-5)}\\ \stackrel{radius}{4} \end{cases}[/tex]
Check the picture below.
The equation of a circle is:
(x - h)² + (y - k)² = radius²
Note:
h = x coordinate for the centre of the circle
k = y coordinate for the centre of the circle
The equation for the circle in the question is:
(x - 6)² + (y - 5)² = 16
So the coordinates for the centre of the circle is:
(6, 5)
------------------------
Since PQ is the diameter of the circle, that means the coordinates for the midpoint of PQ would also be the coordinates for the centre of the circle
That means:
( (x coords of P and Q) / 2 , (y coords of P and Q) / 2 )= (6 , 5)
So x-coords of Q:
[tex]\frac{10 + x}{2} = 6[/tex]
10 + x = 12
x = 2
y-coords of Q
[tex]\frac{-5+ x}{2} = -5[/tex]
-5 + x = - 10
x = 5
So the coordinates for Q are:
(2, -5)
---------------------------------------------
Answer:
Option A) (2, - 5)
A triangular playground has angles with measures in the ratio 8 : 6 : 4. What is the measure of the smallest angle?
Answer:
20°
Step-by-step explanation:
One way of doing this is to find the constant of proportionality, k:
8k + 6k + 4k = 90° Then 18k = 90°, and k turns out to be 90/18, or 5.
Then the angles are 8(5), 6(5) and 4(5). The smallest of these angles is thus 20°
let's recall that the sum of all interior angles in a triangle is 180°.
we know the angles are in a 8:6:4 ratio, so we simply divide 180 by (8+6+4) and then distribute accordingly.
[tex]\bf 8:6:4\qquad \qquad \left( 8\cdot \cfrac{180}{8+6+4} \right) : \left( 6\cdot \cfrac{180}{8+6+4} \right) : \left( 4\cdot \cfrac{180}{8+6+4} \right) \\\\\\ (8\cdot 10):(6\cdot 10):(4\cdot 10)\implies 80~:~60~:~\stackrel{\textit{smallest}}{40}[/tex]