Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does Avery need to reach the river?
Factor completely 36x2− 121.
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.
Approximately what percentage of scores falls below the mean in a standard normal distribution
A cone has a volume of about 28 cubic inches. Which are possible dimensions for the cone?
a) radius 6 inches, height 3 inches
b) diameter 6 inches, height 3 inches
c) diameter 4 inches, height 6 inches
d) diameter 6 inches, height 6 inches
Now you can probe those options to see which leads to an approximate volume of 28 cubic inches.
a) radius 6 in, height 3 in
=> V = (1/3)*3.14*(6in)^2 * 3in = 113.04 in^3 => not possible
Find all complex solutions of 3x^2+3x+4=0.
(If there is more than one solution, separate them with commas.)
The complex solutions to the equation[tex]3x^2+3x+4=0 are x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
Explanation:To find all complex solutions of the quadratic equation [tex]3x^2+3x+4=0[/tex]e the quadratic formula:
[tex]x = \((-b \pm \sqrt{b^2-4ac})/(2a)\).[/tex]
Here, a = 3, b = 3, and c = 4. Plugging these values into the formula, we get:
[tex]x = \((-3 \pm \sqrt{3^2-4 \cdot 3 \cdot 4})/(2 \cdot 3)\).[/tex]
This simplifies to:
[tex]x = \((-3 \pm \sqrt{-39})/6\).[/tex]
Since the discriminant (under the square root sign) is negative, we know that the solutions will be complex. Using i to represent the square root of -1, we can write the solutions as:
[tex]x = \((-3 \pm i\sqrt{39})/6\).[/tex]
So, the complex solutions are [tex]x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
A quadratic equation has a discriminant of 0. which describes the number and type of solutions of the equation?
Discriminant 0 in quadratic equation means 1 real solution—a repeated root where parabola touches x-axis once.
When the discriminant of a quadratic equation is 0, it means that the quadratic equation has exactly one real solution. This solution is considered a "double root" or "repeated root," meaning that the parabola defined by the quadratic equation touches the x-axis at exactly one point. Mathematically, this occurs when the quadratic equation has two identical roots.
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], and the discriminant, denoted by [tex]\(b^2 - 4ac\),[/tex] helps determine the nature of the roots.
When the discriminant is zero [tex](\(b^2 - 4ac = 0\))[/tex], the quadratic equation has one real root. This happens when the parabola defined by the equation just touches the x-axis at one point. The solution is given by:
[tex]\[x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{{2a}}\][/tex]
The following conditions are:
D < 0 ; there are two non-real or imaginary roots which are complex conjugates
D = 0 ; there is one real root and one imaginary (non-real)
D > 0 ; there are two real distinct roots
Therefore the answer to this question is:
The solution has one real root and one imaginary root.
What kind of transformation is illustrated in this figure ?
Which expression is equivalent to (cos x)(tan(–x))?
A. -sin x
B. sin x
C. -csc x
D. csc x
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.
Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?
To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.
Explanation:The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.
Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.
Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.
Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.
Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.
How do I solve this
Need help with this please
Answer please math isn't my forte
During one year about 163 million adults over 18 years old in the United States spent a total of about 93 billion hours online at home. On average, how many hours per day did each adult spent online at home?
1. How do you write each number in scientific notation?
2 How do you convert the units to hours per day.
Final answer:
To write each number in scientific notation, express it as a product between 1 and 10 and a power of 10. Each adult spent an average of 570.55 hours per day online at home.
Explanation:
To write each number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.
163 million can be written as 1.63 x 10⁸
93 billion can be written as 9.3 x 10¹⁰
To convert the units to hours per day, we need to divide the total number of hours by the number of adults.
So, each adult spent an average of (93 x 10¹⁰) / (163 x 10⁸) = 570.55 hours per day online at home. Scientific notation simplifies large numbers, facilitating computations and providing a concise representation of quantities in mathematical contexts.
It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?
What is the factored form of the expression k^2 - 9h^2
ANSWER ASAP Find the value of x. A. sqrt 3 B. 3 sqrt 2/2 C. 3 sqrt 2 D. 3 sqrt 3
Answer:
B.
Step-by-step explanation:
Four less than a number is greater than -28
What value of x makes the denominator of the function equal zero? y= 6/4x-40
The value of x makes the denominator of the function equal zero is 10
what is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given that:
y = [tex]\frac{6}{4x-40}[/tex]
Now the denominator is: 4x - 40
So, 4x =40
x =40/4
x =10
So, make the denominator 0, put x= 10.
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Rationalize the denominator
Answer:
[tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex]
Step-by-step explanation:
Hello!
To rationalize the denominator, we have to remove any root operations from the denominator.
We can do that by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate simply means the same terms with different operations.
Rationalize[tex]\frac{6 - \sqrt10}{10 + \sqrt3}[/tex][tex]\frac{6 - \sqrt10}{10 + \sqrt3} * \frac{10 - \sqrt3}{10 - \sqrt3}[/tex][tex]\frac{(6 - \sqrt10)(10 - \sqrt3)}{100 - 3}[/tex][tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex]The answer is [tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex].
Find the probability of at least 2 girls in births. Assume that male and female births are equally likely and that the births are independent events. Round to three decimal places.
Solve the following system by graphing.
x - y = 4
x + y = 2
What is the solution of the system?
(3, -1)
(3, 1)
(-1, 3)
The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
x - y = 4 (1)
And x + y = 2 (2)
To find the solution of the equations,
Add both the equations,
x - y + x + y = 4 + 2
2x = 6
x = 3,
Substitute the value of x = 3 in equation (1),
3 - y = 4
y = -1
The values of x and y are 3 and -1 respectively.
Hence, option (A) is correct.
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what is the slope of a line that passes through (-4,-13) and (19,11)
Answer:
24/23
Step-by-step explanation:
- vs - = + after -24,-23 =
Answer = 24, 23
Write 11•47 using the distributive property. Then simplify.
Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?
52% = 0.52
78/0.52 =150
150 students voted
Write 5000 = 12 as an order pair
How many three digit numbers can be made from the digits 1,\ldots,9 if repetitions of digits are not allowed?
There are 84 three digit numbers can be made from the digits 1, ..., 9
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
The numbers are,
⇒ 1, 2, ..., 9
Now,
All the three digit numbers can be made from the digits 1, ..., 9 are;
⇒ [tex]^{9} C_{3}[/tex]
⇒ 9! / 3! 6!
⇒ 9 × 8 × 7 / 6
⇒ 84
Thus, There are 84 three digit numbers can be made from the digits
1, ..., 9.
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If XYZ measures 75, what is the measure of XWZ ? A. 285 B. 210 C. 75 D. 150
(Its a circle, and its saying that the arc is 775 and wants to know what the rest of the circle is)
The measure of XWZ is 285
what is arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Given:
<XYZ = 75
As, we know central angle of 360
So, arc(XWZ) + <XYZ = 360
arc (XWZ) = 360 - 75
arc(XWZ) = 285
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in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
Answer:
There are [tex]26[/tex] alternative schools in the country
Step-by-step explanation:
Let
x------> the number of charter schools
y-----> the number of alternative schools
we know that
[tex]x=48[/tex]
[tex]x=2y-4[/tex] -----> equation A
substitute the value of x in the equation A and solve for y
[tex]48=2y-4[/tex]
[tex]2y=48+4[/tex]
[tex]2y=52[/tex]
[tex]y=26[/tex]