given
[tex]\begin{gathered} s-65=13 \\ s=78 \end{gathered}[/tex]So speed of son of beast is 78 mph
Using the system of equations are these two equations independent or dependent. -4x-2y=10 and y=-2x-5
Answer:
Independent equations
Explanation:
We were given that:
[tex]\begin{gathered} -4x-2y=10----------1 \\ y=-2x-5-----------2 \end{gathered}[/tex]We will proceed to solve simultaneously, we have:
[tex]\begin{gathered} -4x-2y=10----------1 \\ \begin{equation*} y=-2x-5-----------2 \end{equation*} \\ \text{We will substitute equation 2 into 1, we have:} \\ -4x-2(-2x-5)=10 \\ \text{Expanding, we have:} \\ -4x+4x+10=10 \\ 10=10 \\ \end{gathered}[/tex]The system of equation has just one solution, hence, ithese are independent equations
Pick one question: Explain why each statement is not a good definition, 10. Supplementary angles are angles that form a straight line. 11. Vertical angles are angles that are congruent. *
Here, we want to explain why the definition given about supplementary angles that form a straight line
When we talk of supplementary angles, we are refeering to angles that add up to 180
So an angle is a supplement of the other if they add up to 180
However, coincidentally, angles on a straight line are angles that add up to 180
While all angles forming a straight line are supplementary, all supplementary angles do not form a straight line
What we are saying here is that two angles may be supplementary and may not be angles that form a staright line
The definition that is given in the question is too general to work and did not consider cases where we might have angles that are strai
Determine which one of the answer choices is equivalent to the given equation. 10x + y = -7
Determine the equivalent equation;
[tex]\begin{gathered} 10x+y=-7 \\ We\text{ move 10x to the other side of the equation where it becomes negative} \\ \text{Therefore, the equivalent expression becomes} \\ y=-10x-7 \end{gathered}[/tex]The third option is the correct answer
List the sequence of transformations. You must use the sequence from our notes.()=−2(−3)^4+1
The transformed function is given as,
[tex]f(x)=-2(x-3)^4+1[/tex]The function is a transformation of the parent function,
[tex]g(x)=x^4[/tex]Consider that the horizontal translation by right by 'c' units is given by,
[tex]g(x)\rightarrow g(x-c)[/tex]Applying the definition, it seems that the first transformation is a translation of the function right by 3 units.
After this first transformation, the function will become,
[tex]g(x)=(x-3)^4[/tex]Now, consider the next transformation, that is, vertical stretch (|a|>0),
[tex]g(x)\rightarrow a\cdot g(x)[/tex]Applying the definition to the function,
[tex](x-3)^4\rightarrow2(x-3)^4[/tex]Thus, the second transformation will be the vertical stretch.
Now, consider the reflection of the function about the x-axis, is characterized by,
[tex]g(x)\rightarrow-g(x)[/tex]Applying the definition to the definition,
[tex]2(x-3)^4\rightarrow-2(x-3)^4[/tex]Thus, the third transformation will be a reflection about the x-axis.
Now, consider that the transformation of vertical translation up by 'd' units, is characterized as,
[tex]g(x)\rightarrow g(x)+d[/tex]Applying the definition,
[tex]-2(x-3)^4\rightarrow-2(x-3)^4+1[/tex]This represents the vertical translation of the function by 1 unit.
Thus, the fourth transformation will be the vertical translation by 1 unit.
And finally, the transformed function is obtained.
Thus, it can be concluded that the parent function undergoes the following transformation sequence to be the given function,
1. Translation right by 3 units.
2. Vertical stretch by a factor of 2.
3. Reflection about the x-axis.
4. Vertical translation by 1 unit.
the house was originally on the market for $358,000 and sold for $202,000 what was the percent of decrease in price
Answer:
43.6%
Explanation:
Initial Price of the house = $358,000
Final price of the house = $202,000
The percent of decrease can be obtained using the formula:
[tex]\text{Percent Decrease =}\frac{Initial\text{ Price-Final Price}}{\text{Initial Price}}\times100[/tex]Therefore:
[tex]\begin{gathered} \%\text{ decrease=}\frac{358,000-202,000}{358,000}\times100 \\ =\frac{156,000}{358,000}\times100 \\ =43.6\% \end{gathered}[/tex]The percent of decrease in price is 43.6%.
Express the area A of the triangle as a function of x. a(x)=
..
Given:
[tex]y=x^2[/tex]The area of the right angle triangle is
[tex]A_{\text{triangle}}=\frac{1}{2}\times width\times height[/tex]From the right triangle in the curve given, the dimension of the width and height is
[tex]\begin{gathered} width=x \\ height=y \end{gathered}[/tex]Therefore, the area becomes
[tex]A_{\text{triangle}}=\frac{1}{2}\times x\times y[/tex][tex]\begin{gathered} \text{Note} \\ y=x^2 \\ \text{Therefore,} \\ A_{\text{triangle}}=\frac{1}{2}\times x\times x^2 \\ A_{\text{triangle}}=\frac{1}{2}\times x^3 \end{gathered}[/tex]Hence:
A(x) = x³/2
The international rules of basketball state the rim of the net should be 3.05 meters above the ground. If your life of sight to the rim is 34 degrees an you are 1.7 meters tall what is distance from you to the rim
From the given information, draw a figure.
By using trigonometric ratio,
[tex]\tan 34^o=\frac{Opposite\text{ side}}{Adja\text{cent side}}[/tex]Plug the given values.
[tex]\begin{gathered} \tan 34^o=\frac{\text{1}.35}{l} \\ l=\frac{1.35}{\tan 34^o} \\ \approx2.0015 \end{gathered}[/tex]The distance from the person to the rim is approximately 2 meters.
What is the vertex of (3,-3)
Question:
Solution:
Note that the standard quadratic form of a quadratic polynomial is given by the following equation:
[tex]ax^2+bx+c\text{ = }y[/tex]so that, the vertex form of a quadratic equation is
[tex]y\text{ = a(}x-h)^2+k[/tex]where (h,k) is the so-called vertex. Thus, according to this, we can say that the equation that represents a vertex (h,k)=(3,-3) is
[tex]y\text{ = 5(}x-3)^2\text{-}3[/tex]then, we can conclude that the correct answer is:
[tex]y\text{ = 5(}x-3)^2\text{-}3[/tex]Write an equation for a line perpendicular to y = − 4 x − 5 and passing through the point (-4,-4)
Answer:
[tex]y = \frac{1}{4}x - 3[/tex]
Step-by-step explanation:
the line perpendicular to another line has the opposite reciprocal slope of the original
the opposite reciprocal of -4 is 1/4
so
put that in the equation
[tex]y = \frac{1}{4}x + b[/tex]
now plug in the points for (-4, -4)
[tex]-4 = \frac{1}{4}(-4) + b[/tex]
-4 = -1 + b
b = -3
now plug that into the equation
[tex]y = \frac{1}{4}x - 3[/tex]
thats your answer
what expression can be used to suntract 2/3 - 4/9
From the options, we have that:
[tex]\frac{2}{3}\cdot\frac{3}{3}=\frac{6}{9}[/tex]Then, 6/9 is an equivalent fraction to 2/3. Therefore, the expression that can be used to subtract 2/3 - 4/9 is:
[tex]\frac{6}{9}-\frac{4}{9}[/tex]That is. the answer is option C.
Young's rule find dosage for child. Adult dosage is 75mg. And the age of the child is 12. Calcuate child dosage in my.C=ad________ (a+12)
Given:
The adult dosage is 75mg and the age of the child is 12.
The formula to find the child's dosage is
[tex]C=\frac{ad}{a+12}[/tex]where a is the child's age, d is the usual adult's dosage and C is the child's dosage.
Required:
We need to find the child's dosage.
Explanation:
Consider the formula to find the child's dosage.
[tex]C=\frac{ad}{a+12}[/tex]Substitute a =12 and d =75 in the formula.
[tex]C=\frac{12\times75}{12+12}[/tex][tex]C=\frac{900}{24}=37.5\text{ mg.}[/tex]Final answer:
The child's dosage is 37.5mg.
18x^4y^5________6x^2yFully simplify using only positive exponents Dividing powers
Solution
[tex]\frac{18x^4y^5}{6x^2y}[/tex][tex]\begin{gathered} \frac{3x^{4-2}y^{5-1}}{1} \\ \\ 3x^2y4 \end{gathered}[/tex]f(t) = t - 4 g(t) = -2t-3 Find (fog)(t) Find (gof)(t)
The graph of 2x-3y=4 is shown. What is the domain ofthis function?
The graph of the function is
As you can see in the graph, the function is linear, that is, it is a line that continues indefinitely in each direction.
By definition, The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
Regarding the domain of a linear function, any real number can be substituted for x and get a meaningful output.
As for the range of a linear function, for any real number, you can always find an x value that gives you that number for the output.
Therefore, the domain and range of this function are all real numbers.
[tex]\begin{gathered} D_f=\R \\ R_f=\R \end{gathered}[/tex]= Initial Knowledge Check Divide 4 ? - 6 2- 23 Simplify your answer as much as p
The given expression is
[tex]\frac{4z^7-6z^5}{2z^3}[/tex]First, we factor out the third power of z, and factor 2.
[tex]\frac{2z^3(2z^4-3z^2)}{2z^3}[/tex]Now, we simplify to get the final expression
[tex]2z^4-3z^2[/tex]The divisions made were
[tex]\begin{gathered} \frac{4z^7}{2z^3}=2z^4 \\ \frac{6z^5}{2z^3}=3z^2 \end{gathered}[/tex]find the rate of change of the radius of a sphere at the point in time when the radius is 6ft if the volume is increasing at the rate of 8 pie cubic feet per second.
Answer:
Explanation:
The volume of a sphere is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]taking the derivative of both sides gives
[tex]\frac{dV}{dt}=\frac{d(\frac{4}{3}\pi r^3)}{dt}[/tex][tex]\frac{dV}{dt}=\frac{4}{3}\pi\frac{d(r^3)}{dt}[/tex]using the product rule gives
[tex]\frac{d(r^3)}{dt}=r^2\frac{dr}{dt}+r\frac{dr^2}{dt}[/tex][tex]=r^2\frac{dr}{dt}+2r^2\frac{dr}{dt}[/tex][tex]=3r^2\frac{dr}{dt}[/tex]Thus, the rate of change of volume is
[tex]\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]Now we know that at a certain time, r = 6 ft and dV/dt = 8; therefore,
[tex]undefined[/tex]opposite value of -2.
The opposite value of a number can be found by switching the signal of the value.
So, to find the opposite value of -2, we need to switch the negative signal by a positive signal.
Therefore the opposite value of -2 is equal to 2.
Find decimal notation for 800%.800% =
In mathematics, a percentage is a number or ratio expressed as a fraction of 100
For example
A% is
[tex]A\text{ \%=}\frac{\text{ A}}{100}[/tex]The question was given to figure out
[tex]800\text{ \%}[/tex]Therefore,
[tex]\begin{gathered} 800\text{ \%= }\frac{\text{800}}{100} \\ 800\text{ \%= 8} \end{gathered}[/tex]Hence,
800 % = 8
Is either x=9 or = 15 a solution to ×-3= 12
Is either x=9 or = 15 a solution to ×-3= 12
x-3 = 12
x= 12+3
x= 15
______________
Answer
x= 15
_______________
x=9
×-3= 12
9-3 = 12
6 ≠ 12
What is the area watered by the sprinkler? I can’t figure it out.
We are asked to determine the area of a circular sector. To do that we will use the following formula:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
[tex]\begin{gathered} r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]Now, we convert the angle of 85° to radians using the following conversion factor:
[tex]1\pi=180\text{degrees}[/tex]Now, we multiply by the conversion factor:
[tex]\theta=85\times\frac{\pi}{180}=\frac{17\pi}{36}[/tex]Now, we substitute in the formula for the area:
[tex]A=\frac{(5m)^2(\frac{17\pi}{36})^2}{2}[/tex]Substituting the value of pi for 3.14
[tex]A=\frac{(5m)^2(\frac{17(3.14)}{36})^2}{2}[/tex]Solving the operations:
[tex]A=18.5m^2[/tex]Therefore, the area is 18.5 square meters.
The vertex of this parabola is at (-2, 5). Which of the following could be itsequation?4111-5(-2,5)10O A. y=3(x+ 2)² +5OB. y= 3(x-2)²-5OC. y= 3(x-2)² +5OD. y=3(x+2)²-5015
Given:
The vertex of this parabola is at (-2, 5).
Required:
Find the equation of the parabola.
Explanation:
The equation of the parabola in vertex form is:
[tex]y=a(x-h)^2+k[/tex]We can observe from the options that the value of a = 3 and vertex (h,k) is given (-2,5).
So the equation of the parabola will be:
[tex]y=3(x+2)^2+5[/tex]y = - (x + 3)² + 5 Step 3: Identify the axis of symmetry: x = h x=3 x= -3 y = 5 y = -3
In the given equation:
[tex]\text{ y = -(x + 3)}^2\text{ + 5}[/tex]The equation already in vertex form,
[tex]\text{ y = a(}x-h)^2\text{ + k}[/tex]The axis of symmetry is h.
From the equation,
[tex]\text{ y = -(x + 3)}^2\text{ + 5}[/tex]The axis of symmetry is therefore,
[tex]\text{ x + 3 = 0 }\rightarrow\text{ x }=\text{ -3}[/tex]I need help with unions, intersections, and complements involving 2 sets
Here, we want to get the set resulting from the given set operations
a) This set is the complement of the intersection of the subsets C and D
The intersection refers to that set that has its members as the elements present in both subsets
The intersection here is;
[tex]\mleft\lbrace8\mright\rbrace[/tex]Now, the complement here are the other elemnts present in the universal set
We have this as;
[tex]\mleft\lbrace1,2,4,7\mright\rbrace[/tex]b) Here, we want to get a union
The complement of set C are the elements that not present in set C but are in the universal set
So, the union here is are the list of elements in both set, without no repetitions
[tex]\begin{gathered} C^{\prime}\text{ = }\mleft\lbrace2,4\mright\rbrace \\ D\text{ = }\mleft\lbrace2,8\mright\rbrace \\ C^{\prime}\text{ U D = }\mleft\lbrace2,4,8\mright\rbrace \end{gathered}[/tex]A plumber charges a flat fee of $76 to visit home and examine a clogged drain the plumber charges an additional $28 per hour spent fixing the drain the total cost C in dollars for fixing the drain that takes H hours is given by the following: C = 76 + 28hquestion 1 : total cost for fixing a drain that takes 7 hoursquestions 2 : if the plumber charged a total of $384 how many hours did he spend fixing the drain
Answer:
1. $ 272
2. 11 hours
Explanation:
Given the below equation;
[tex]C=28h+76[/tex]where C = the total cost
h = hours spent
1. If h = 7 hours, let's go ahead and find C;
[tex]\begin{gathered} C=28(7)+76 \\ =196+76 \\ \therefore C=272 \end{gathered}[/tex]So if it takes 7hours to fix the drain, the total cost will be $272.
2. If C = $384, let's go ahead and find h;
[tex]\begin{gathered} 384=28h+76 \\ 28h=384-76 \\ 28h=308 \\ h=\frac{308}{28} \\ \therefore h=11 \end{gathered}[/tex]So if the plumber charged $384 to fix the drain, it means that he'd spent 11 hours to fix the drain.
Hello! Was able to figure out everything on this problem besides the slant asymptotes and types of discontinuities. Thanks for your help!
Answer:
• The slant asymptote is y=x-3.
,• The function g(x) has a removable discontinuity at x=-1.
,• The function g(x) has a non-removable discontinuity at x=2.
Explanation:
Given that the function, f(x) has zeros of 8, -1, and -3.
Then, by the factor theorem:
[tex]f(x)=(x-8)(x+1)(x+3)[/tex]If we divide the f(x) by x²-x-2:
[tex]\begin{gathered} g(x)=\frac{f(x)}{x^2-x-2}=\frac{(x-8)(x+1)(x+3)}{x^2-2x+x-2} \\ =\frac{(x-8)(x+1)(x+3)}{x(x-2)+1(x-2)} \\ =\frac{(x-8)(x+1)(x+3)}{(x+1)(x-2)} \\ =\frac{(x-8)(x+3)}{x-2} \end{gathered}[/tex]Therefore, the rational function, g(x) in simplest form is:
[tex]g(x)=\frac{(x-8)(x+3)}{x-2}[/tex]Since the degree of the numerator is one degree greater than the degree of the denominator, a slant asymptote exists. To find this, divide the numerator by the denominator:
[tex]g(x)=\frac{x^2+3x-8x-24}{x-2}=\frac{x^2-5x-24}{x-2}[/tex]The quotient of the division is x-3 with a remainder of 18.
The slant asymptote is y=x-3.
Given g(x) in the form below:
[tex]g(x)=\frac{(x-8)(x+1)(x+3)}{(x+1)(x-2)}[/tex]Set the denominator equal to 0 to find the point of discontinuities.
[tex]\begin{gathered} (x+1)(x-2)=0 \\ x+1=0\text{ or }x-2=0 \\ x=-1,x=2 \end{gathered}[/tex]The function is discontinuous at x=-1 and x=2.
However, notice that there is a common factor in the numerator and the denominator, x+1. The zero for this factor is x = -1 . Therefore:
• The function g(x) has a removable discontinuity at x=-1.
• The function g(x) has a non-removable discontinuity at x=2.
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function bewritten using function notation?
If x is the independent variable, we have that y is the dependent variable.
Using function notation, let's say that y is our function, that is, y = f(x).
So we need to isolate the variable y in the equation:
[tex]\begin{gathered} 9x+3y=12 \\ 3y=12-9x \\ y=\frac{12-9x}{3} \\ y=4-3x \end{gathered}[/tex]So our function is:
[tex]f(x)=-3x+4[/tex]I'm not understanding this equations I'm doing how I was taught but does answer still isn't right..so the math equation is f(x)=2x[tex]f{x} =2(x)^{3} - 3(x)^{2} + 7[/tex]f(-1)=
The given equation is
[tex]f(x)=2x^3-3x^2+7[/tex]We need to find f(-1)
That means substitute x by -1 in the given function
[tex]f(-1)=2(-1)^3-3(-1)^2+7[/tex]since (-1)^3 = -1 ------- (-1)(-1)(-1) = -1
Since (-1)^2 = 1 -------- (-1)(-1) = 1, then
[tex]\begin{gathered} f(-1)=2(-1)-3(1)+7 \\ f(-1)=-2-3+7 \\ f(-1)=-5+7 \\ f(-1)=2 \end{gathered}[/tex]Then f(-1) = 2
8a-4b=20 5a-8b=62What is a? What is b?
The given system of equations is:
8a - 4b = 20...............(1)
5a - 8b = 62...............(2)
Multiply equation (1) by 2
16a - 8b = 40........................(3)
Subtract equation (2) from equation (3)
11a = -22
a = -22/11
a = -2
Substitute a = -2 into equation (1)
8a - 4b = 20
8(-2) - 4b = 20
-16 - 4b = 20
4b = -16-20
4b = -36
b = -36/4
b = -9
Therefore the solution to the system of equations is:
a = -2 and b = -9
For how many integers x is the equation 22x+1 = 3x - 3 true?
REmember that
the speed is equal to divide the distance by the time
so
speed=d/t
in this problem we have
speed=3.6x10^4 miles/hour
d=7.2x10^8 miles
substitute in the formula
[tex]3.6\cdot10^4=\frac{7.2\cdot10^8}{t}[/tex]solve for t
[tex]\begin{gathered} 3.6\cdot10^4=\frac{7.2\cdot10^8}{t} \\ t=\frac{7.2\cdot10^8}{3.6\cdot10^4} \\ t=2.0\cdot10^4\text{ hours} \end{gathered}[/tex]therefore
answer is option DIn a large school it was found that 70% of students are taken to math class 80% of students are taken in English class and 66% of students are taken both find the probability that a randomly selected student is taking a math class or an English or at class rightly answer as destiny run into 2 decimal places
The answer is:
P{neither Maths nor English) = 0.13
The question tells us that in a school, the proportion of students doing maths is 78%
The proportion of students doing english is 80%
The proportion of students doing both subjects is 66%.
We are then asked to find the probability of students that did neither English nor Maths.
In order to get this value, we must remove the probability of those doing maths and english and also those that are doing both from 1. In other words, we subtract the probability of getting a student in Math or English class from 1.
Let us put this into mathematical expressions:
[tex]\begin{gathered} P(\text{Math)}=\frac{73}{100} \\ P(\text{English)}=\frac{80}{100} \\ \\ P(\text{Math and English) = }\frac{66}{100} \end{gathered}[/tex]Therefore, we can find the probability of getting a student in either Math or English using the OR probability formula.
The OR probability formula states:
[tex]\begin{gathered} \text{if A and B are independent events,} \\ P(A\text{ OR B) = P(A)+ P(B) - P(A n B)} \\ \text{where,} \\ P(A)=\text{probability that event A occurs} \\ P(B)=\text{probability that event B occurs} \\ P(A\cap B)=\text{probability that both A and B occur} \end{gathered}[/tex]Using P(Math) and P(English) as P(A) and P(B) respectively, we can easily compute the probability that a student is in Math or English class using the above formula.
This is done below:
[tex]\begin{gathered} P(\text{Math or English) = P(Math) +P(English) - P(Math n English)} \\ P(\text{Math)}=\frac{73}{100} \\ P(\text{English)}=\frac{80}{100} \\ P(\text{Math}\cap\text{English)}=\frac{66}{100} \\ \\ \therefore P(\text{Math or English) =}\frac{73}{100}+\frac{80}{100}-\frac{66}{100} \\ \\ P(\text{Math or English) =}\frac{87}{100}=0.87 \end{gathered}[/tex]Therefore, to find the probability of a student studying neither Maths nor English,
we simply subtract P(Math or English) from 1.
This is done below:
[tex]\begin{gathered} P(\text{neither Maths nor English) = 1 - P(Maths or English)} \\ P(\text{neither Maths nor English)=1 - 0.87} \\ \\ \therefore P(\text{neither Maths nor English)}=0.13 \end{gathered}[/tex]Therefore, the final answer is:
P{neither Maths nor English) = 0.13