Answer:
b
Step-by-step explanation:
There are 18 skaters competing in the competition. How many ways can they win the gold, silver, and bronze medal?
Only one person can win gold, silver, and bronze. The order of the winner does matter. So it’ll be 18 times 17 times 16.
Answer: 4,896
Stwhiep-by-step explanation:
Given, There are 18 skaters competing in the competition.
To find : The number of ways in which they can win gold, silver, and bronze medal.
Since, in distribution of medals(gold, silver, and bronze) we require 3 winners in a particular order, so for this we use Permutations.
According to permutation , number of ways of selecting r things out of n = [tex]\dfrac{n!}{(n-r)!}[/tex]
Then, The number of ways in which 18 skaters can win 3 medals= [tex]\dfrac{18!}{(18-3)!}=\dfrac{18\times17\times16\times15!}{15!}=4,896[/tex]
Hence, the required number of ways =4,896
Given the system of contstraints: y ≥ 2x x + y ≤ 14 y ≥ 1 5x + y ≥ 14 x + y ≥ 9 Which region represents the graph of the feasible region for the given constraints?
Answer:
Region A is the region represents the graph of the feasible region
for the given constraints
Step-by-step explanation:
* Lets look to the graph to answer the question
# y ≥ 2x represented by the orange line
∵ The sign of inequality is greater than, then the shaded part will
be over the line
∴ The solution is in A region
# x + y ≤ 14 represented by the purple line
∵ The sign of inequality is smaller than, then the shaded part will
be under the line
∴ The solution is in A or B or C regions
# y ≥ 1 represented by the pink line
∵ The sign of inequality is greater than, then the shaded part will
be over the line
∴ The solution is in A or B or C regions
# 5x + y ≥ 14 represented by the blue line
∵ The sign of inequality is greater than, then the shaded part will
be over the line
∴ The solution is in A or B or C regions
# x + y ≥ 9 represented by the green line
∵ The sign of inequality is greater than, then the shaded part will
be over the line
∴ The solution is in A or B regions
* From all above The common region in the five inequalities is A
∴ Region A is the region represents the graph of the feasible region
for the given constraints
Answer:
A. Region A
Step-by-step explanation:
Si 4x= 5/6y entonces 5y=
Answer:
[tex]5y=24x[/tex]
Step-by-step explanation:
The question in English is
If 4x= 5/6y then 5y=
we have
[tex]4x=\frac{5}{6}y[/tex]
Solve for 5y
Multiply both sides by 6
[tex]6*4x=(6)*\frac{5}{6}y[/tex]
Simplify
[tex]24x=5y[/tex]
Rewrite
[tex]5y=24x[/tex]
If f(x)= -x^2+3x+5 and g(x) =x^+2, which graph of (f+g)(x)
Answer:
See explanation
Step-by-step explanation:
If
[tex]f(x)=-x^2 +3x+5[/tex]
and
[tex]g(x)=x^2 +2,[/tex]
then
[tex](f+g)(x)=-x^2+3x+5+x^2+2=3x+7[/tex]
This is the linear function. To plot the graph of this function, find x- and y- intercepts:
x-intercept:
[tex]y=0\Rightarrow 3x+7=0\\ \\3x=-7\\ \\x=-\dfrac{7}{3}[/tex]
y-intercept:
[tex]x=0\Rightarrow y=3\cdot 0+7\\ \\y=7[/tex]
Plot these two points on the coordinate plane and connect them with a straight line.
Determine whether the function f(x) = 3(x - 1)^4 is even or odd
Answer:
The function is neither even nor odd.
Step-by-step explanation:
the function is even if f(-x) = f(x)
The function is odd if f(-x) = -f(x)
We are given the function:
f(x) = 3(x-1)^4
Solving
f(x) = 3(x^4 -4x^3+6x^2-4x+1)
f(x) = 3x^4-12x^3+18x^2-12x+3
Now putting -x instead of x i,e f(-x)
f(-x) = 3(-x)^4-12(-x)^3+18(-x)^2-12(-x)+3
Solving
f(-x) =3x^4+12x^3+18x^2+12x+3
so, f(-x) ≠ f(x) The function is not even
and f(-x) ≠ -f(x) The function is not odd
Hence the function is neither even nor odd.
Freshman Algebra, I need to simplify it
[tex] \frac{ - 1}{4} (v {q}^{4} )( - 8 {v}^{3} q {)}^{2} [/tex]
[tex]\bf -\cfrac{1}{4}(vq^4)(-8v^3q)^2\implies -\cfrac{1}{4}(vq^4)\stackrel{\textit{distributing the exponent}}{[(-8)^2v^{2\cdot 3}q^2]}\implies -\cfrac{1}{4}(vq^4)(64v^6q^2) \\\\\\ -\cfrac{1}{4}(vq^4 64v^6q^2)\implies -\cfrac{64}{4}(v v^6 q^4q^2)\implies -16v^{1+6}q^{4+2}\implies -16v^7q^6[/tex]
Solve The Equation
4x×9y=7
4x-9y=9
Answer:
[tex]\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2[/tex]
[tex](4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}[/tex]
[tex]4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}[/tex]
After a rotation, A(–3, 4) maps to A'(4, 3), B(4, –5) maps to B'(–5, –4), and C(1, 6) maps to C'(6, –1). Which rule describes the rotation?
Answer:
R0, 270°Step-by-step explanation:
Answer:
The correct answer is R0, 270°
8. What is the solution to the system of equations?
1 x-35-2=-9
-2x+ y + 2z = 3
| 2x + y + 3z = 8
(1,3,1)
(1,3,-1)
(1, -3,1)
(-1,3,1)
Answer: (-1,3,1)
Step-by-step explanation:
What is the y-value of the solution to the system of equations?
3x + 5y = 1
7x + 4y = −13
−3
−1
2
5
The answer is y=2 !!!!!!!!!!!!!!
Answer:
y = 2
Step-by-step explanation:
3x + 5y = 1
7x + 4y = −13
We will use the elimination method to eliminate the x variable. Then we will solve for y. We need the coefficients of the x-terms in the two equations to be additive inverses, so they will add to zero, eliminating x.
Multiply both sides of the first equation by -7, and multiply both sides of the second equation by 3.
-21x - 35y = -7
21x + 12y = -39
Now add the equations to eliminate x.
-23y = -46
Divide both sides by -23.
y = 2
the points (4, -6) and (9, -6) represent the location of two towns on coordinate grid, where one unit is equal to one mile. what is the distance, in miles, between the two towns? Is it 5 miles the difference, can anyone explain please!
Answer:
It is 5 miles difference . GOOD JOB!!!!!!!!!!!!!!!
Step-by-step explanation:
Answer:
Yes, the distance is 5 miles
Step-by-step explanation:
Since the y-coordinates are the same, we can ignore the y-distance and treat the total distance like a number line.
So, the distance is |9 - 4| = 5 units
Since each unit is a mile, that translates the distance to 5 miles.
find the circumference of the circle. use 3.14 for round to the nearest unit
21 cm
A. 24
B.66
C.125
D.69
Answer:
66 (B.)
Step-by-step explanation:
I hust got an 100% on the unit test
Final answer:
Using the formula C = πd with pi (3.14) and the given diameter 21 cm, the circumference is calculated to be 65.94 cm, which rounds to 66 cm, making the correct answer B. 66.
Explanation:
The circumference (C) of a circle is calculated by the formula C = πd, where π (pi) is a constant approximately equal to 3.14, and d is the diameter of the circle.
Given the diameter of 21 cm for the circle, we calculate the circumference as follows:
Circumference = π × diameterCircumference = 3.14 × 21 cmCircumference = 65.94 cmWhen rounded to the nearest whole number, the circumference is 66 cm.
Therefore, the correct answer is choice B. 66.
find the x and y intercepts of the following function.
g(x)=x^2-5x-84
Answer:
see explanation
Step-by-step explanation:
To find the y- intercept let x = 0 in the function
g(0) = 0 - 0 - 84 = - 84 ← y- intercept
To find the x- intercepts let y = 0, that is
x² - 5x - 84 = 0
To factor the quadratic
Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term
The factors are - 12 and + 7, since
- 12 × 7 = - 84 and - 12 + 7 = - 5, thus
(x - 12)(x + 7) = 0
Equate each factor to zero and solve for x
x - 12 = 0 ⇒ x = 12
x + 7 = 0 ⇒ x = - 7
x- intercepts are x = - 7 and x = 12
PLEASE HELP! I don’t understand. 8 POINTS!
Answer:
Step-by-step explanation:
3√2 sec(x) + 2 = 2√2 sec(x) Subtract 2√2 sec(x) from both sides
√2 sec(x) + 2 = 0 Subtract 2 from both sides.
√2 sec(x) = - 2
The secant is related to the cosine. sec(x) = 1/cos(x). The statement tells you that wherever the cos(x) < 0 , the secant will be as will. That means your answer will be in quad 2 and quad 3 and you are to use the appropriate rules for theta in those two quads.
It turns out that you could do this by using the reciprocal of 2
cos-1(- 0.5) = 120 degres. In terms of pi (which is 180 degrees)
120/180 * pi = (2/3) * pi
In quad three you would get pi + pi/3 = 4/3 pi
So your answers are
2/3 pi and 4/3 pi
Haley constructed this 10-sided polygon using triangles,
What is the minimum number of triangles required to construct this figure?
A.5
B.8
C.10
D.12
Answer:
its 8 i just finished the test
Step-by-step explanation:
At a cost of $200, your club bought 175 frisbees to sell at the pep rally. You plan on selling them for $5 each. Which of the following represents the profit function, P, after selling a certain number of frisbees, f.
This prompt involves calculating total revenue, marginal revenue, total cost, and marginal cost for a competitive firm and finding the profit maximizing quantity of dog coats sold. The analysis is done by constructing a table and graphing relevant curves to identify where marginal revenue equals marginal cost.
Explanation:The question regards the calculation of total revenue, marginal revenue, total cost, and marginal cost for a perfectly competitive firm, Doggies Paradise Inc., and the identification of the profit maximizing quantity of dog coats sold. To find these values, a table must be constructed with output levels from one to five units. The price per unit is $72, and fixed costs are $100, with variable costs increasing with each additional unit produced. The total revenue (TR) is the price multiplied by the quantity sold, while the marginal revenue (MR) is the additional revenue from selling one more unit. Total cost (TC) is the sum of fixed costs and variable costs at each output level, and marginal cost (MC) is the change in total costs when production is increased by one unit. The profit maximizing quantity is determined where MR equals MC or where the additional cost of producing one more unit no longer yields an additional profit.
Total Revenue and Total Cost Curves
Sketching these curves will show the relationship between the cost of producing dog coats and the revenue generated from sales at different production levels. The TR curve shows a steady increase as more units are sold, while the TC curve reflects the fixed costs and the upward slope as variable costs increase with higher output.
Marginal Revenue and Marginal Cost Curves
Graphing MR against MC allows for visual determination of the profit maximizing output, which is the point where the two curves intersect. This indicates that producing any more units beyond this point will not increase profit.
Starla bought cloth napkins at an outlet store for $3.50 each, and she also used a $15 off coupon. In the equation below, x represents the number of napkins, and y represents the cost before tax. y = $3.50x - $15 If Starla paid $55.00 before tax, how many napkins did she buy? A. 20 B. 2 C. 16 D. 21
A. 20
Begin by substituting the known value. I have removed the symbols for now just to make the equation easier to read. 55 = 3.5x - 15
Add 15 on both sides of the equation to cancel out the subtraction. 70 = 3.5x
Finally, divide both sides by 3.5 to cancel out the subtraction. 20 = x
So, Starla bought 20 napkins.
how to find the scale factor of two
similar shapes
Answer:
In two similar geometric figures, the ratio of their corresponding sides is called the scale factor. To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other
Step-by-step explanation:
Find the product (8/6n-4)(9n^2-4)
Answer:
4(3n+2) or 12n+8
Step-by-step explanation:
Given expression is:
[tex](\frac{8}{6n-4})(9n^{2}-4)[/tex]
The numerator of the fraction will be multiplied with 9n^2- 4
So, Multiplication will give us:
[tex]=\frac{8(9n^2-4)}{6n-4}[/tex]
We can simplify the expression before multiplication.
The numerator will be broken down using the formula:
[tex]a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}[/tex]
We can take 2 as common factor from denominator
[tex]=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)[/tex]
Hence the product is 4(3n+2) or 12n+8 ..
Answer: 1 and the second part is 12n+8
Step-by-step explanation:Edgen2020
Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots sqrt 5 and 2
Answer:
f(x) = 3x² -21x + 30
Step-by-step explanation:
Polynomial function of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:
P(x) = c (x - a) (x - b)
Given: Leading coefficient = 3, Roots = sqrt 5 and 2
P(x) = 3 (x - 5) (x - 2)
= 3 ( x² - 2x - 5x +10)
= 3 ( x² - 7x +10)
= 3x² - 21x + 30
Which is an equation of the line through (-1, -4) and parallel to the line 3x + y = 5?
A. y= 3x - 1
B. y= -3x + 7
C. y = -3x - 7
D. y = 3x + 1
The answer is C. y = -3x - 7
The equation of the line that is parallel to the line 3x + y = 5 and passing through (-1, -4) will be 3x + y + 7 = 0.
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.
The equation of the line that is parallel to the line 3x + y = 5 and passing through (-1, -4).
We know the equation of a parallel line is given as 3x + y = C
The equation is passing through (-1, -4).
Then we have
C = 3 × (-1) + (-4)
C = - 3 - 4 C = -7
Then the equation of the parallel line will be
3x + y = -7
3x + y + 7 = 0
More about the linear system link is given below.
https://brainly.com/question/20379472
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Which number is addition property?
B. 6
C. 4
D. 7
E. 1
F. 2
G. 6
Hope this helps :)
It took me a min to understand how they were doing the numbers corresponding to the letters lol
Answer with explanation:
a → 3
b → 5
c→ 4
d →7
e→ 1
f→2
g→6
Solve |3x - 4| = 15
a) {-19/3, 19/3}
b) {11/3, 19/3}
c) {-11/3, 19/3}
Answer:
option C
{-11/3 , 19/3}
Step-by-step explanation:
Given in the question an equation
|3x-4| = 15
To solve the absolute equation we need to add ± on right side of equation.
3x-4 = ±15
3x - 4 = 15 or 3x - 4 = -153x = 15+4 or 3x = -15 + 4
3x = 19 or 3x = -11
x = 19/3 or x = -11/3
The solution of |3x-4| = 15 is {-11/3 , 19/3}
Answer:
The solution of I3x - 4I = 15 is {-11/3 , 19/3}
Step-by-step explanation:
* Lets explain the meaning of I I (absolute value)
- The absolute value of any number is the magnitude of the number
means the value of the number without its sign, we ignore the sign
of the number
- The absolute never equal a negative value
- If IxI = a, then x = a or x = -a
* Now lets solve the problem
∵ I3x - 4I = 15
∴ 3x - 4 = 15 OR 3x - 4 = -15
* Lets solve the two equation
∵ 3x - 4 = 15 ⇒ add 4 to both sides
∴ 3x = 19 ⇒ divide both sides by 3
∴ x = 19/3
∵ 3x - 4 = -15 ⇒ add 4 to both sides
∴ 3x = -11 ⇒ divide each side by 3
∴ x = -11/3
* The solution of I3x - 4I = 15 is {-11/3 , 19/3}
Find the product of -7-i and its complex conjugate
Answer:
50Step-by-step explanation:
[tex]-7-i\\\\\text{complex conjugate:}\ -7+i\\\\(-7-i)(-7+i)\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(-7)^2-(i)^2\qquad\ i=\sqrt{-1}\to i^2=-1\\\\=49-(-1)\\\\=49+1\\\\=50[/tex]
What is the quotient of -8(^6)/4x(^-3)
For this case we must find the quotient of the following expression:
[tex]\frac {-8x ^ 6} {4x ^ {- 3}} =[/tex]
By definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Rewriting the expression we have:
[tex]\frac{-8}{4}*x^6*x^3[/tex]
By definition of multiplication of powers of the same base we have to put the same base and add the exponents:
[tex]-2x^{6+3}[/tex]
Answer:
[tex]-2x ^ 9[/tex]
thirty less than one half the value of x
Answer:
[tex]30 < \frac{1}{2}x[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase " thirty less than one half the value of x" is equal to
[tex]30 < \frac{1}{2}x[/tex]
solve for x
Multiply by 2 both sides
[tex]2*30 < x[/tex]
[tex]60 < x[/tex]
Rewrite
[tex]x > 60[/tex]
The solution is the interval ----> (60,∞)
All real numbers greater than 60
The phrase 'thirty less than one half the value of x' can be interpreted as a mathematical statement and translated into the algebraic equation 0.5x - 30.
Explanation:The question 'thirty less than one half the value of x' asks us to express a mathematical concept in an algebraic equation. We can do this by firstly taking half the value of x, represented as 0.5x. Following the phrase 'thirty less than', we subtract 30 from this half-value of x, giving the equation "0.5x - 30". So, when someone says 'thirty less than one half the value of x', they are referring to this mathematical equation.
Learn more about Algebraic Translation here:https://brainly.com/question/28612373
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Write the expression as single natural logarithm
3 in 3 + 2 in x ? Help needed 10 points.
Answer:
ln 27x²
Step-by-step explanation:
Using the rules of logarithms
• log[tex]x^{n}[/tex] ⇔ nlogx
• logx + logy ⇒ logxy
Given
3 ln 3 + 2 ln x, then
= ln 3³ + lnx²
= ln 27 + lnx² = ln 27x²
What is the equation of a circle centered at the origin with raduis 15? Please show work
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~\stackrel{origin}{(\stackrel{0}{ h},\stackrel{0}{ k})}\qquad \qquad radius=\stackrel{15}{ r} \\\\\\ (x-0)^2+(y-0)^2=15^2\implies x^2+y^2=225[/tex]
The graph below represents which system of inequalities?
graph of two infinite lines that intersect at a point. One line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.
Answer:
The system of inequalities is
[tex]y\leq x+3[/tex]
[tex]y\leq -2x+3[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid line that goes through the points negative 3, 0, negative 4, negative 1
Let
A(-3,0),B(-4,-1)
Find the slope
m=(-1-0)/(-4+3)
m=-1/-1=1
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=1
point A(-3,0)
substitute
y-0=(1)(x+3)
y=x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
[tex]y\leq x+3[/tex]
step 2
Find the equation of the solid line that goes through the points 1, 1, 2, negative 1
Let
C(1,1),D(2,-1)
Find the slope
m=(-1-1)/(2-1)
m=-2/1=-2
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=-2
point C(1,1)
substitute
y-1=(-2)(x-1)
y=-2x+2+1
y=-2x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
[tex]y\leq -2x+3[/tex]
therefore
The system of inequalities is
[tex]y\leq x+3[/tex]
[tex]y\leq -2x+3[/tex]
In triangle ABC, sinA= 0.3, sinB=0.4 and a=12. Find b
Answer:
b = 16Step-by-step explanation:
Use the formula of an area of a triangle:
[tex]A=\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B=\dfrac{1}{2}ab\sin C[/tex]
Therefore we have the equation:
[tex]\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B[/tex] multiply both sides by 2
[tex]bc\sin A=ac\sin B[/tex] divide both sides by c
[tex]b\sin A=a\sin B[/tex] divide both sides by sin A
[tex]b=\dfrac{a\sin B}{\sin A}[/tex]
We have
[tex]\sin A=0.3,\ \sin B=0.4,\ a=12[/tex]
Substitute:
[tex]b=\dfrac{(12)(0.4)}{0.3}=\dfrac{4.8}{0.3}=\dfrac{48}{3}=16[/tex]
Using the Law of Sines and given values sinA, sinB, and side a, we can determine that the length of side b in the triangle is 16 units.
To find the length of side b in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:
a / sin A = b / sin B = c / sin C
Given that sinA = 0.3, sinB = 0.4, and a (side opposite angle A) is 12, we can write
12 / 0.3 = b / 0.4
Multiplying both sides of the equation by 0.4 and solving for b gives us:
b = (12 / 0.3) * 0.4
b = 40 * 0.4
b = 16
Therefore, the length of side b is 16 units.