The quadratic functions are given as below:-
x = 3y² - 6y + 5
y = 2x² + 2
y = 2x² -8x + 6
y = 5x² + 45x -8
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
As we know that the function which will have the highest power of the variable equal to 2 will be called a quadratic polynomial.
So from the given expressions following equations has a degree of 2.
x = 3y² - 6y + 5
y = 2x² + 2
y = 2x² -8x + 6
y = 5x² + 45x -8
Therefore the above equations are quadratic functions.
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Chester scored 84, 88, and 80 on his first 3 math tests. How can you find Chester's mean, or average, score on these tests?
Answer:
Add and Divide.
Mean = 84
Step-by-step explanation:
Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.
Here we add:
(80 + 84 + 88)
then divide by 3, because there's 3 numbers in this list.
(80 + 84 + 88)/3
= 252/3
= 84
The mean, or average is 84.
7. Write the equation -3x +2y = 7 in slope-intercept form.
Answer:
y = 3/2x + 7/2
Step-by-step explanation:
Slope-intercept form is when y is the subject. So we make y the subject:
Add 3x to both sides :
2y = 3x + 7
Now we divide both sides by 2 :
y = 3/2x + 7/2
This is our final answer.
Hope this helped and brainliest please
Hi student, let me help you out! :)
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We are asked to write the equation -3x+2y=7 in slope-intercept form.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The equation for slope-intercept form is y=mx+b, where m= slope (gradient) of the line, b=y-intercept of the lineSo let's write this equation, -3x+2y=7, in slope-intercept form...
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\
First, we add -3x to both sides of the equal sign:
[tex]\large\pmb{2y=7+3x}[/tex]
We can switch the order of the terms:
[tex]\large\pmb{2y=3x+7}[/tex]
This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:
[tex]\large\pmb{y=(3x+7)\div2}[/tex]
Which simplifies to...
[tex]\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}[/tex]
That's the equation in slope-intercept form.
Hope this helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
i need help with these two questions ASAP and preferably shown work.. Thank you!
Answer:
1: sin B, cos B, and tan B = 36.87°
2: x = 11.7
Step-by-step explanation:
Question 1: As toy can see they all have the same angle answer just different methods of finding it
Question 2:
adjacent is the closest side to the angle
opposite is the side across from the angle
hypotenuse is always the longest side
x = 11.7025
Hope it helps :)
If you have any questions or anymore help lmk, happy to help with any school work!!
Have a nice day, you’ll make it thru <3
DONT BE AFRAID TO ASK IF YOU CANT READ MY HANDWRITTING
What is the range of the function [tex]y=\sqrt[3]{x+8}[/tex]?
A. -∞ < y < ∞
B. -8 < y < ∞
C. 0 ≤ y < ∞
D. 2 ≤ y < ∞
Answer:
-∞ < y ∞
The range is all real numbers.
What is the value of ax² + bx + c at x = a ?
[tex]a\cdot a^2+b\cdot a+c=a^3+ab+c[/tex]
I need the x axis to solve this
Answer:
As a fraction:
x | y
________
|
7/3 | 2
3 | 4
11/3 | 6
13/3 | 8
As a mixed fraction:
x | y
________
|
2 ⅓ | 2
3 | 4
3 ⅔ | 6
4 ⅓ | 8
As a decimal:
x | y
___________
|
2.33.. | 2
3 | 4
3.66.. | 6
4.33.. | 8
You should start with x values since the y values will be easier to plot. x's will not be easy to represent.
For example:
x | y
________
|
0 | -5
1 | -2
2 | 1
3 | 4
4 | 7
5 | 10
Which are the solutions of x2 = –7x – 8?
StartFraction 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction negative 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction negative 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction 7 + StartRoot 17 EndRoot Over 2 EndFraction
StartFraction negative 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction negative 7 + StartRoot 17 EndRoot Over 2 EndFraction
The solution to the system of equation is x = -7+√17/2 and -7-√17/2
Equations and expressionsEquations are expressions separated by an equal sign
Given the equation
x^2 = –7x – 8
Equate to zero
x^2+7x+8 = 0
Factorize
x = -7±√49-4(8)/2
x = -7±√17/2
x = -7+√17/2 and -7-√17/2
Hence the solution to the system of equation is x = -7+√17/2 and -7-√17/2
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Answer:
Option 4
Step-by-step explanation:
The answer above is correct.
The equation of the line with slope = 3, going through point (2, 4) is:
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]
What is the summation notation for the geometric series 1/2+2+8+32+128?
Answer ( k=1 ∑ 5 ) 1/2(4)^k-1
The summation notation is ∑ [tex](4^{n} -1)\\[/tex]/2.
What is geometric progression?The common ratio multiplied here to each term to get the next term is a non-zero number.
Given: 1/2+2+8+32+128
Using,
[tex]a_n= a_1r^{n-1}[/tex]
We have,
a1 =1/2 and r= 4
notation is : An= ∑ [tex](4^{n} -1)\\[/tex]/2
Hence, the notation is An= ∑ [tex](4^{n} -1)\\[/tex]/2.
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What is the equivalent to 1 tablespoon?
Answer:
3 teaspoons
Step-by-step explanation:
Three teaspoons are equivalent to one tablespoon
The model represents x2 – 9x + 14.
An algebra tile configuration showing only the Product spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled negative x, and 14 are labeled +.
Which is a factor of x2 – 9x + 14?
x – 9
x – 2
x + 5
x + 7
the awnser is B x-2
What is the product?
The correct answer is option C which is [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
What is a matrix?Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.
The multiplication of the matrix will be calculated as:-
M = [tex]\dfrac{1}{2}\left[\begin{array}{cc}12&64&\\78&30&\\\end{array}\right][/tex]
M = [tex]\left[\begin{array}{cc}\dfrac{12}{2}&\dfrac{64}{2}&\\\dfrac{78}{2}&\dfrac{30}{2}&\\\end{array}\right][/tex]
M = [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
Therefore the correct answer is option C which is [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
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Please help me, I really appreciate it! Thanks!
Answer: See the attached images below.
The steps and explanations are on those screenshots, so there's not much for me to mention right here on this main page. The decimal results are approximate to 6 decimal places. Make sure your calculator is in degree mode.
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder
as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3,14 as an approximation of "pl.)
Answer:
Given:
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
HURRY GIVING BRAINLIEST
Answer:
12 or 7??
Step-by-step explanation:
it depends if they are being spinned at the same time because then you can get for eg. 'A,1' 'A2' etc.
Find the slope of the line graphed below.
to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]
(05.05 mc)
~
a a food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the to
questions:
likes hamburgers does not like hamburgers total
likes burritos
29
41
does not like burritos
54
135
total
110
205
part a: what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
How to find the percentage?A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%
B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;
MRF = 134/205 = 0.65
C) Let us first find the ratio of all the four data with the total;
Ratio of those who like Hamburgers and burritos = 39/134 = 0.29
Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71
Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53
Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47
Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
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A philanthropist pledges to donate 10% of a fund each year. If the fund initially has $450,000 how much will
the fund have after 7 years?
Fund Balance = $
After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. [tex]\rm y = a^x[/tex]
where a is a constant and a>1
We have:
A philanthropist pledges to donate 10% of a fund each year.
We can find the amount left after 7 years as follows:
A = 450000(1 - 0.1)⁷
10% of a fund each year.
Rate r = 10% = 0.1
A = 450000(0.9)⁷
A = $2152336.05
Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
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HURRY for 100 points
If p is true and ~ q is false, then p -> ~ q is ____ false.
-sometimes
-always
-never
Find the quotient. Simplify your answer.
s + 1/
s²1
÷
s^2/
6s²
Enter the correct answer.
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]
[tex]\\ \rm\Rrightarrow 5s[/tex]
Solve for h
-8 = - 2 (h - 6)
H=
The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that. Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.
The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.
Distribute
[tex]-8 = - 2 (h - 6)[/tex][tex]-8 = (- 2 * h) + (-2 * - 6)[/tex][tex]-8 = (- 2h) + (12)[/tex]After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.
Subtract 12 from both sides
[tex]-8 = - 2h + 12[/tex][tex]-8 - 12 = - 2h + 12 - 12[/tex][tex]-20 = - 2h[/tex]The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h. Then we will simplify the expression and that will give us our final answer.
Divide both sides by -2
[tex]-20 = - 2h[/tex][tex]\frac{-20}{-2} = \frac{- 2h}{-2}[/tex][tex]\frac{-20}{-2} = h[/tex]Simplify the expression
[tex]\frac{-20/-2}{-2/-2} = h[/tex][tex]\frac{10}{1} = h[/tex][tex]10= h[/tex]We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.
Evaluate this function at the given value using the remainder theorem.
F(x)=x^4+5x^3-18x+1 at x=-4
Please show work , I give brainliest. :)
Answer:
9
Step-by-step explanation:
[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]
Give the domain and range.
X
-2
0
2
y
-1
0
1
a.
b.
domain: (2, 0, 2), range: (1, 0, 1)
domain: {-2, 0, 2), range: {-1, 0, 1)
domain: {-1, 0, 1), range: (-2, 0, 2}
d. domain: {1, 0, 1), range: {2, 0, 2)
C.
DI
at the host answer from the choices provided
1
2
3
4
5
Answer:
(b) domain: {-2, 0, 2}, range: {-1, 0, 1}
Step-by-step explanation:
For the function defined by the table ...
[tex]\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}[/tex]
we want the function's domain and range.
__
domainThe domain is the list of x-values for which the function is defined. Here, that list is ...
domain = {-2, 0, 2}
__
rangeThe range is the list of y-values the function produces. Here, that list is ...
range = {-1, 0, 1}
_____
The domain and range sets are most conveniently listed in order, with duplicates removed.
find the height of the trapezoid
Answer:
h = 19
Step-by-step explanation:
The are is given so we can use the area to find the height because the area of a trapezoid is calculated by the following formula:
1/2 * (a+b)*h (a: base, b: base, h: height)
We already know the bases; 37 and 51
1/2*(37+51)*h = 836 first multiply both sides by 2
(37+51)*h = 1672 now divide both sides by 88 (sum of bases)
h = 19
x^k=1/x^-1
Someone help me please
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]
What is the (LCD) of 3/5 and 5/6
Answer: 30
Step-by-step explanation:
A LCD, or least common denominator, is the lowest common multiple of both denominators.
Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...
Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...
We can see the LCD of 3/5 and 5/6 is:
30
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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal. In this case, the problem is asking us to determine the LCD or least common denominator of two numbers. We are provided with two fractions that we will use to help determine our solution. However, before solving for the LCD let us first define what LCD means.
Least Common Denominator ⇒ LCD is a term that is used to help describe a number that can be used in the bottom of the fraction (also known as a denominator) that is common between two numbers. For example, the LCD between 2 and 5 is 10 because that is a time where both of them can be equal to.Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.
Multiples of 5 ⇒ 5, 10, 15, 20, 25, 30Multiples of 6 ⇒ 6, 12, 18, 24, 30Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.
What are the exact values of x and y?
x =
y =
Answer:
[tex]x = 2\\y = 2\sqrt{3}[/tex]
Step-by-step explanation:
**Look at the picture
What are the solutions to the following system of equations? x + y = 3 y = x2 − 9 (3, 0) and (1, 2) (−3, 0) and (1, 2) (3, 0) and (−4, 7) (−3, 0) and (−4, 7)\
The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
Simultaneous linear and quadratic equationsFrom the question, we are to determine the solutions to the given system of equations
The given system of equations are
x + y = 3 ----------- (1)
y = x² - 9 ----------- (2)
From equation (1)
x + y = 3
We can write that
y = 3 - x -------- (3)
Substitute this into equation (2)
y = x² - 9
3 - x = x² - 9
x² +x -3 - 9 = 0
x² +x -12 = 0
Solve quadratically
x² +x -12 = 0
x² +4x -3x -12 = 0
x(x +4) -3(x +4) = 0
(x -3)(x +4) = 0
∴ x -3 = 0 OR x +4 = 0
x = 3 OR x = -4
Now, using equation (3)
When x = 3
y = 3 - x
y = 3 - 3
y = 0
When x = -4
y = 3 - -4
y = 3+4
y = 7
∴ When x = 3, y = 0; and when x = -4, y = 7
Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
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Using the digits 0 to 9
Supplementary Angles:
[tex]\boxed{100°} and \boxed{80°}[/tex]
Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.
Complementary Angles:
[tex]\boxed{45°} and \boxed{45°}[/tex]
Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.
A certain 300-term geometric sequence has first term 1337 and common ratio $-\frac12$. How many terms of this sequence are greater than 1
There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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