Answer:
y=-5,y=1
Step-by-step explanation:
To solve this, we need to solve a quadratic equation, using the bhaskara formula.
Initially, let's place the equation in the standard format. So
[tex]2y^2-10y+44=(y-7)^2[/tex][tex]2y^2-10y+44=y^2-14y+49[/tex][tex]2y^2-y^2-10y+14y+44-49=0[/tex][tex]y^2+4y-5=0[/tex]Now we apply the bhaskara formula:
[tex]y=\frac{-(4)\pm\sqrt{4^2-4\ast1\ast-5}}{2\ast1}[/tex]Then
[tex]y=\frac{-4\pm6}{2}[/tex]So two solutions:
[tex]y^{^{\prime}}=\frac{-4+6}{2}=1,y^{^{\prime}^{\prime}}=\frac{-4-6}{2}=-5[/tex]The solution are y=-5,y=1
The local bike shop rents bikes for $18 plus $6per hour. Bill paid $36 to rent a bike. For howmany hours did he rent the bike for?
we have:
h = hour
the equation is
[tex]\begin{gathered} 18+6h=36 \\ 18+6h-18=36-18 \\ 6h=18 \\ \frac{6h}{6}=\frac{18}{6} \\ h=3 \end{gathered}[/tex]answer: 3 hours
The following table is a function.х15725354 9у-3 27-4 5971 0
a For any relation to be a function, an independent variable x cannot produce different dependent varible y
From the table,
when x = 5, y = 2
Also, when x = 5, y = 5
and when x = 5, y = 7
We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function
Hence, the table is not a function
The answer is False
I need help ASAP please can you help you help
OPTION C
A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.
From our question, it was easy to
What is the LCM of 10 and 4?
One way to find the least common multiple of two numbers is to first list the prime factors of each number.
[tex]\begin{gathered} 10=2\cdot5 \\ 4=2\cdot2 \end{gathered}[/tex]Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.
[tex]undefined[/tex]Write each equation in slope intercept form. Then graph .
ANSWER
EXPLANATION
Given;
[tex]y=-\frac{5}{6}x+4[/tex]Recall, the general formula for slope - intercept form is;
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]comparing the given equation with the standard slope intercept form formula;
[tex]\begin{gathered} y=mx+c \\ y=-\frac{5}{6}x+4 \\ m=-\frac{5}{6} \\ c=4 \end{gathered}[/tex]Hence, the graph of the given equation is;
Which of the following represents the factorization of the trinomial below?x2 – X-20A. (x-4)(x-5)B. (X + 4)(x-5)oC. (x-2)(x-10)0D. (x+2)(x-10)
Answer:
(x+4)(x-5)
Step-by-step explanation:
Second order polynomial in the following format:
ax² + bx + c = 0
Has roots x¹ and x².
Can be factored as:
(x - x¹)(x - x²)
So, we have to find the roots.
Finding the roots:
Bhaskara formula, which is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In the polynomial given in this question:
a = 1, b = -1, c = -20
So
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]The roots are:
[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]The factored form is:
(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)
the corporate team building event will cost $30 if it has 6 attendees. How many attendees can there be, at most, if the budget for the corporate team building event is $50? Assume the relationship is directly proportional.
Let the number of attendees be a.
ak=c , where k=constant of variation.
6k=30
k=30/6
k=5
Find a when c=$50
5a=50
a=50/5
a=10
There will be 10 attendees for a bu
Multiply the pair conjugates using the Product of Conjugates Pattern (simplify) (rs-2/5)(rs+2/5)
In order to calculate the product of a pair of conjugate terms, we can use the pattern below:
[tex](a+b)(a-b)=a^2-b^2[/tex]So we have:
[tex]\begin{gathered} (rs-\frac{2}{5})(rs+\frac{2}{5}) \\ =(rs)^2-(\frac{2}{5})^2 \\ =r^2s^2-\frac{4}{25} \end{gathered}[/tex]please help. due today! will mark as brainliest!
Answer:
which question you want to be answered
Answer:
[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]
[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]
Step-by-step explanation:
Question 13The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:
[tex]\boxed{P=0.5 \pi d+d}[/tex]
Part (a)
To express d in terms of P, rearrange the equation to isolate d.
Factor out the common term d from the right side of the equation:
[tex]\implies P=d(0.5 \pi +1)[/tex]
Divide both sides by (0.5π + 1):
[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]
[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]
[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]
Part (b)
Given:
Perimeter = 36 in[tex]\pi \approx \dfrac{22}{7}[/tex]Substitute the given values into the equation derived in part (a) and solve for d:
[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]
[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]
[tex]\implies d=36 \times \dfrac{7}{18}[/tex]
[tex]\implies d=\dfrac{252}{18}[/tex]
[tex]\implies d=14[/tex]
Therefore, the diameter is 14 inches.
how would I graph 3x + 4y = -4
Answer:
To graph a line you have to find two points on the line, one way of doing this is first setting x=0 and solving for y, as follows:
[tex]\begin{gathered} 3(0)+4y=-4, \\ 4y=-4, \\ y=-1. \end{gathered}[/tex]With the above calculations, we got that the point (0,-1) is on the line.
Now, to find another point on the line we set y=0 and solve for x:
[tex]\begin{gathered} 3x+4(0)=-4, \\ 3x=-4, \\ x=-\frac{4}{3}\text{.} \end{gathered}[/tex]With the above calculations, we got that the point (-4/3,0) is on the line.
Once we have those points we draw the line that passes through those points.
The graph of the given equation is:
Find the derivative of the trigonometric function using the Chain Rule.[tex]y = \cos \sqrt{x} [/tex]
Giving a test to a group of students, the grades and gender are summarized below A B C TotalMale214 4 20Female1018 13 41Total1232 17 61If one student is chosen at random,Find the probability that the student did NOT get an "C". Round your answer to 3 decimal places_____.
Given:
⇒There are 61 students in total.
⇒12 of them got an A while 32 of them got a B.
⇒In total, 44 students did not get a C.
⇒So, 44 out of 61 students did not get a C.
Convert 44/61 into decimal form.
[tex]\frac{44}{61}=44\div61=0.721311\approx0.721[/tex]Answer:
The probability that a randomly chosen student did not get a C is 0.721 approximately.
Find the area of the shaded sector of the circle. Leave your answers in terms of pi
Answer:
D. 8pi yd^2
Explanation:
Area of a sector is expressed as;
[tex]A\text{ = }\frac{\theta}{360}\times\pi r^2[/tex]r is the radius of the circle
theta is the angle substended at the centre
Given the following
r = 9yd
theta = 360-200
theta = 160degrees
Substitute
A = 160/360 * pi(9)^2
A = 4/9*18pi
A = 72pi/9
A = 8pi yd2
Hence the area of the shaded sector is 8pi yd2
What is the probability of rolling a die (ordinary, 6-sided die with numbers 1, 2,3, 4, 5, 6) and getting a 7?
Let:
A = Getting a 7
a = Number of sides with 7
N = Number of sides
so:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{0}{6} \\ P(A)=0 \end{gathered}[/tex]Can you pls help with 7 I need to do 8 more packets like these by tomoghy
The daily rate can be found by dividing the total number of books over the number of calendar days.
15,260 / 28 = 545
545 books per day
I need the answer but i also need to check my answer after
we have the following:
[tex]\begin{gathered} 7=\frac{x-8}{3} \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} x-8=7\cdot3 \\ x=21-8 \\ x=13 \end{gathered}[/tex]"The distributive Property"
Using the distributive property, the maximum number of players that can be in the NBA is; 450 players
How to use distributive property?The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;
a(b + c) = ab + ac
Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;
Number of players on each team = (12 + 3)
Now, for the 30 teams;
Total number of players for the teams = 30(12 + 3)
Applying distributive property, we have;
(30*12 + 30*3) = 450
Read more about distributive property at; https://brainly.com/question/2807928
#SPJ1
I need to write and simplify an algebraic expression for the perimeter of each shape.please help!
For the square, we have that each side's length is 2p, since the perimeter is the sum of the length of all sides of a geometric figure, this means that we have to add all the lengths of the square like this:
[tex]\begin{gathered} P=2p+2p+2p+2p_{} \\ \Rightarrow P=8p \end{gathered}[/tex]And we can do the same with the 3 sides of the triangle:
[tex]\begin{gathered} P=2x+2x+3x+1 \\ \Rightarrow P=7x+1 \end{gathered}[/tex]is rational or irrational v2
The square root of 2 is irrational
Here, we want to check if the square root of 2 is rational or not
When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers
Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd
which is the best description of the data in the scatter plot
Types of correlation:
Based on the types of correlation, we can see that the best description of the data given is a positive correlation.
Answer: A positive correlation.
What is the multiplicity of each of the roots of this graph?2
SOLUTIONS
What is the multiplicity of each of the roots of this graph?
[tex]f(x)=2x^4+12x^3+16x^2-12x-18[/tex]Factorise f(x) by the options
(a) According to the option we have -3 is a root of so x+3 is a factor
[tex]\frac{2x^4+12x^3+16x^2-12x-18}{x+3}=2x^3+6x^2-2x-6[/tex](b) 1 is a root too so x - 1 is a factor
[tex]\frac{2x^3+6x^2-2x-6}{x-1}=2x^2+8x+6[/tex][tex]\begin{gathered} 2x^2+8x+6=2(x+3)(x+1) \\ f(x)=2(x+3)^2(x+1)(x-1) \end{gathered}[/tex]Therefore the correct answer = Option A
(x² + 5x - 2)-(3x²-x+4)
Given: (x² + 5x - 2)-(3x²-x+4)
Remove the parentheses:
[tex]=x^2+5x-2-3x^2+x-4[/tex]Add like terms:
[tex]\begin{gathered} =x^2-3x^2+5x+x-2-4 \\ =-2x^2+6x-6 \end{gathered}[/tex]Answer:
[tex]\begin{equation*} -2x^2+6x-6 \end{equation*}[/tex]3 batteries cost $5r and 8 folders cost $2r. Jason bought6 batteries and 4 folders. How much does he pay?Give your answer in terms of the
We are asked to determine the total amount paid for 6 batteries and 4 folders. To do that we need to determine the unit price of each item. We do that by dividing the amount spent by the number of items that were bought. That is:
[tex]\begin{gathered} n_b=\frac{5\text{ dollars}}{3\text{ batteries}} \\ \\ n_f=\frac{2\text{ dollars}}{8\text{ folders}} \end{gathered}[/tex]Now we multiply the desired number of items by each of the corresponding unit prices:
[tex]N=\frac{5}{3}\times6+\frac{2}{8}\times4[/tex]Solving the operations:
[tex]\begin{gathered} N=10+1 \\ N=11 \end{gathered}[/tex]Therefore, the total amount paid is $11.
A hose for the hot tub at a rate of 3.61 gallons per minute. How many hours will it take to fill a 345 gallon hot tub?
We have a 345 gallon hot tub that fills at a rate of 3.61 gallons/min.
To calculate filling time, we need to divide as it follows:
[tex]t=\frac{345\text{gal}}{3.61\frac{\text{gal}}{\min }}[/tex]in that way we can find how much time does it take in minutes
[tex]t=\frac{345}{3.61}=95.56786[/tex]now, if we want to determine time in hours, we must divide by 60, because there are 60 min. in one hour.
[tex]t=\frac{345}{3.61}\cdot\frac{1}{60}=1.59279[/tex]Then, it would take approximately 1.59 hours to fill the hot tub.
(7 x 10^-5) x (5 * 10^-8)= ?x 10^
1) Let's calculate that. Start by multiplying the factors 7, and 5.
[tex]\begin{gathered} 7\cdot10^{-5}\text{ x 5 }\cdot10^{-8}= \\ 35\cdot10^{-13} \end{gathered}[/tex]After that, we use the property of the exponents when multiplying. Repeat the base and then add the exponents -8 + (-5) = -8 -5 = -13.
I need help finding the angle measurements of 1 and 2
To find the angles 1 and 2:
In the above triangle, the angles opposite to the equal sides are equal.
Let us take,
[tex]\angle1=\angle2=x[/tex]So, using the angle sum property of a triangle
[tex]\begin{gathered} 55+x+x=180 \\ 2x=180-55 \\ 2x=125 \\ x=62.5^{\circ} \end{gathered}[/tex]Hence, the angles are
[tex]\begin{gathered} \angle1=62.5^{\circ} \\ \angle2=62.5^{\circ} \end{gathered}[/tex]Where x is the horizontal distance in feet from the point at which the ball is thrown.How far from the child does the ball strike the ground?
To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:
[tex]\begin{gathered} y=-\frac{1}{14}x^2+4x+3 \\ \Rightarrow y^{\prime}=-\frac{2}{14}x+4=-\frac{1}{7}x+4 \\ \Rightarrow y^{\doubleprime}=-\frac{1}{7} \end{gathered}[/tex]Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow-\frac{1}{7}x+4=0 \\ \Rightarrow\frac{1}{7}x=4 \\ \Rightarrow x=7\cdot4=28 \\ x=28 \end{gathered}[/tex]Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:
[tex]\begin{gathered} y=-\frac{1}{14}(28)^2+4(28)+3 \\ \Rightarrow y=-\frac{1}{14}(784)+112+3 \\ \Rightarrow y=-56+112+3=59 \\ y=59 \end{gathered}[/tex]Finally, we have that the ball will go 59 feet from the child
Enter an algebrak expression for the word expression. twice a number, minus 19 The expression is ?
x is an unknown number
twice a number means: 2x
and twice a number minus 19 means: 2x - 19
I need help with part b please
we have that
interval (-infinite,0) ------> f(x)=5x+4
interval [0, infinite) ------> f(x)=x+7
Part B
f(0)
For x=0 ------> belong to the interval [0, infinite)
so
f(x)=x+7
substitute
f(0)=0+7
f(0)=7Part C
f(3)
For x=3 ---> belong to the interval [0, infinite)
so
f(x)=x+7
substitute
f(3)=3+7
f(3)=1011.Solve the given equation over the interval [0, 271): 2 sin x++3 = 0.117and x=64757X=- and x=332лx= -- and x=3T57x= -- and x=6and x3
Question:
Solution:
Let the following trigonometric equation:
[tex]2\sin (x)+\sqrt[]{3}=\text{ 0}[/tex]Subtract the root of 3 from both sides of the equation:
[tex]2\sin (x)=-\sqrt[]{3}[/tex]solve for sin(x):
[tex]\sin (x)=\text{ -}\frac{\sqrt[]{3}}{2}[/tex]Applying the trigonometric circle on the given interval, we obtain that the correct answer is:
[tex]x\text{ = }\frac{4\pi}{3}\text{ , x = }\frac{5\pi}{3}[/tex]