What is the location of the vertex on the parabola defined by f(x) = 2x2 + 14x + 11 and in what direction does the parabola open?
Answers
Vertex of a parabola
The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved.
The given function is,
[tex]f(x)=2x^2+14x+11[/tex]We will apply graphical method to obtain the solution to the vertex of the parabola
From the graph above, the vertex of the parabola is (- 3.5, - 13.5) which can also be represented into fraction as
[tex](-\frac{7}{2},-\frac{27}{2})[/tex]And finally, the parabola opens upward.
Hence, the correct option is Option 2.
Related Questions
A rectangular prism is shown below.A formula for the volume of a rectangular prism V = Bh. The volume, V, of this prism is 600 cm³. Which expression can be used to find x, the width of the prism in centimeters? A: 600/15B: 600/8C: 600/(8)(15)D: (8)(8)(15)(15)/600
Answers
Volume of a rectangular prism = base length x width x heigth
Where;
Volume = 600 cm3
base length = 15
width = x
height = 8
Replacing:
600 = (15) (x) (8)
Isolate x
600/ (15)(8) = x
x = 600/ (8)(15)
option C
describe and correct the error solution error a student made when graphing a linear equation y equals -3 / 4 x - 6
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we have two points (0, 6) and (4, 3)
this can be represented as (x, y)
the equation of a straight line is
y = mx + c
slope = m = y2 - y1/ x2 - x1
x1 = 0, y1 = 6, x2 = 4 and y2 = 3
slope = 3 - 6 / 4 - 0
slope = -3/4
slope = -3/4
from the equation of a straight line
(y - y1) = m(x - x1)
y1 = 6 and x1 = 0
y - 6= -3/4(x - 0)
y - 6 = -3/4x + 0
y = -3/4x + 6
the error he made was that he used - 6 instead of +6 in the final answer
Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
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Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]Simplify: 7a + 2a - a + 6b - 5b
Answers
We must simplify the following expression:
[tex]7a+2a-a+6b-5b[/tex]From the expression, we see that we have terms with variable a and terms with variable b. In order to simplify the expression, we add the terms with a together (which sums up 8a), and we do the same for the terms with b (which sums up 1b):
[tex]\begin{gathered} 7a+2a-a+6b-5b \\ =(7a+2a-a)+(6b-5b) \\ =8a+b \end{gathered}[/tex]The solution is: 8a+b
Evaluate 10y-15 for y=5
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10 y - 15
y = 5
We replace 5 in the expression
10 * 5 - 15 =
50 - 15 = 35
____________________
Answer
35
Which is the graph of the solution set of -2x + 5y > 15?10 1310 138896421OT810x2468 10622-4Ox681010 138642X246810
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To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:
[tex]-2x+5y=15.[/tex]Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):
[tex]-2(0)+5(0)=0<15,[/tex]therefore, the origin is not a point of the solution set.
Answer:Question 5 of 15, Step 1 of 14/15CorrectIfy is inversely proportional to x and y = -71 when x = 16, find yifx = 7. (Round off your answer to the nearest hundredth.)
Answers
Answer:
[tex]y=-31.06[/tex]Step-by-step explanation:
Since y and x are inversely proportional, we'll have that:
[tex]y=\beta x[/tex]For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:
[tex]\begin{gathered} y=\beta x\rightarrow-71=\beta\times16\rightarrow\beta=-\frac{71}{16} \\ \end{gathered}[/tex]This way, our formula would be:
[tex]y=-\frac{71}{16}x[/tex]Plugging in x = 7,
[tex]\begin{gathered} y=-\frac{71}{16}x\rightarrow y=-\frac{71}{16}(7)\rightarrow y=-\frac{497}{16} \\ \\ \Rightarrow y=-31.06 \end{gathered}[/tex]A support cable runs from the top of a telephone pole to a point on the ground 42.7 feet from its base. Suppose the cable makes an angle of 29.6 with the ground (as shown in the following figure).(a) Find the height of the pole. (Round the answer to the nearest tenth.) feet (b) Find the length of the cable. (Round the answer to the nearest tenth.) feet
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We will draw a sketch to see the position of the cable
From the figure, we can use the tangent ratio to find the height
[tex]\frac{h}{42.7}=tan(29.6)[/tex]By using the cross-multiplication
[tex]\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}[/tex]a) The height of the pole is 24.3 feet to the nearest tenth
To find the length of the cable we will use the cosine ratio
[tex]cos(29.6)=\frac{42.7}{L}[/tex]Switch L and cos(29.6)
[tex]\begin{gathered} L=\frac{42.7}{cos(29.6)} \\ \\ L=49.1\text{ feet} \end{gathered}[/tex]b) The length of the cable is 49.1 feet to the nearest tenth
Measure the dimensions of all the walls of the bedroom in your home, in feet. Find the dimensions of any windows or doorways as well.
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Explanation
we can fill up the dimensions as follow
Solve on the interval [0,27): RCŨsx+c05X +1 = ] T O 3 A. X= 27,x = x=57 4. 4 O B. X = 27,X = O c. X= 7T,X = 1 47T 3 T D. X= ET 6 6 NAMAN
Answers
ANSWER:
C.
[tex]x=\pi,x=\frac{2\pi}{3},x=\frac{4\pi}{3}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]2cos^2x+3cosx\: +1\: =\: 0[/tex]Using the substitution method, we can calculate the value of x, like this:
[tex]\begin{gathered} u=\cos x \\ \text{ therefore:} \\ 2u^2+3u+1=0 \\ 3u=2u+u \\ 2u^2+2u+u+1=0 \\ 2u(u+1)+u+1=0 \\ (u+1)(2u+1)=0 \\ u+1=0\rightarrow u=-1 \\ 2u+1=0\rightarrow2u=-1\rightarrow u=-\frac{1}{2} \\ \text{ replacing:} \\ \cos x=-1\rightarrow x=\cos ^{-1}(-1)\rightarrow x=\pi \\ \cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})\rightarrow x=\frac{2\pi}{3},\frac{4\pi}{3} \end{gathered}[/tex]Estimate the product by adjusting the larger factor to the compatible number 25 and then multiply. 27 x 8 = Think about counting by 25s.
Answers
You have the following product:
27 x 8
To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.
Then, you have:
25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25
25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50
25 x 8 = 100 + 100 each pair of 50's add up 100
25 x 8 = 200
Hence, an estimation of the given product is 200, by considering 27 rounded to 25.
Pleaee help me draw this. Construct a tangent to the circle from point R.
Answers
solution
For this case the tangent line to the circle and the point should be:
The reason is because the tangent line and the point needs to touch the circle just one time
what expression is equivalent to 2y+7
Answers
The expression which is equivalent to the given expression (3y - 4) (2y + 7) + 11y - 9 is 6 y²+ 24y- 37
Define an expression.A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
Presented expression = (3y - 4) (2y + 7) + 11y - 9
Solving the expression we get= 6y²+21y-8y-28+11y-9
= 6y²+24y-37
There for the correct response is that the given expression is equivalent to = 6y²+24y-37
To know more about expressions, visit:
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I need to know which point is the solution and I need a check for it to make sure it’s correct and the line on the graph
Answers
The system of equations are given as
[tex]\begin{gathered} y-2x=-4 \\ y=-x-1 \end{gathered}[/tex]The graph of the system of equations is
The point which is the solution is
[tex](1,-2)[/tex](linear approximation calc !) The radius of a disc is 24 cm if the radius has a maximum error of 0.2 cm. estimate the relative percentage air in the calculated area the area of a circle = pi r ^2
Answers
Given:
The radius of the circular disk is 24cm.
The radius has a maximum error of 0.2 cm.
To find:
The area
Explanation:
Using the area of the circle,
[tex]A=\pi r^2[/tex]The area of the disk is,
[tex]\begin{gathered} A=\pi\times24^2 \\ =576\pi cm^2 \end{gathered}[/tex]If the radius is increased from 24 by 0.02, then the radius becomes, r = 0.02
The change in the calculated area will be,
[tex]\begin{gathered} \Delta A=Area\text{ of the cirlce with radius of 24.02-Area of the circle with radius of 24} \\ =\pi\times24.02^2-\pi\times24^2 \\ =576.96\pi-576\pi \\ =0.96\pi cm^2 \end{gathered}[/tex]The relative percentage of area is,
[tex]\begin{gathered} \frac{\Delta A}{A}\times100=\frac{0.96\pi}{576\pi}\times100 \\ =0.0017\times100 \\ =0.17\text{ \%} \end{gathered}[/tex]Final answer:
The maximum error in area is,
[tex]0.96\pi cm^2[/tex]The relative percentage error in the area is 0.17%.
use the functions f (×) and g (×) to complete the comparison statements using <,>,or =.F(x)= -×-5
Answers
First Question:
f(3) = (-3)-5 (Replacing x in the equation)
f(3) = -8 (Operating integers)
From the table we see that g(3) = 8, therefore, f(3)< g(3)
Second Question:
The slope of f is the coefficient of x in the equation, so, the slope of f is -1.
Using the slope formula for g(x) with points (0,2) and (3,8) we find that:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]The slope of g is 2.
Therefore, the slope of f is less (<) than the slope of g
Third Question:
The y-intercept of f is the value next to the term -x, so, it is equal to -5
The y-intercept of g can be found with the point (0,2), when x=0, y is equal to 2, then the y-intercept is 2.
Therefore, the y-intercept of f is less(<) than the y-intercept of g.
find the value of f (4)
Answers
we know that
f(4) is the value of the function f(x) when the value of x is equal to 4
so
For x=4
Look at the graph
The value of the function f(x) is equal to 3
therefore
f(4)=3Find the probability of the event.If a single die is tossed once, find the probability of the following event. Rollinga 3 or a 5
Answers
ANSWER
1/3
EXPLANATION
If we have a fair die, the probability of rolling any of the numbers is the same. In this case, we want to know the probability of rolling a 3 or a 5, which is the sum of the probabilities of rolling each of these values,
[tex]P(3)=P(5)=\frac{1}{6}[/tex]So,
[tex]P(3or5)=P(3)+P(5)=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}[/tex]Hence, the probability of rolling a 3 or a 5 is 1/3
Use the expressions from the previous questions to determine Mary’s age.
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The age of Mary is 15 years old.
To solve this, we have three expressions:
[tex]\begin{gathered} M=J+5 \\ J=T-28 \\ T=3H-1 \end{gathered}[/tex]Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry
Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:
[tex]\begin{gathered} \begin{cases}H=13 \\ T=3H-1\end{cases} \\ \text{Then:} \\ T=3\cdot13-1=39-1=38 \\ T=38 \end{gathered}[/tex]Now we can replace T in the second equation:
[tex]\begin{gathered} \begin{cases}T=38 \\ J=T-28\end{cases} \\ \text{Then:} \\ J=38-28=10 \\ J=10 \end{gathered}[/tex]Finally, we can replace J in the first equation to get the age of Mary:
[tex]\begin{gathered} \begin{cases}J=10 \\ M=J+5\end{cases} \\ \text{Then:} \\ M=10+5=15 \end{gathered}[/tex]Thus, the age of Mary is 15 years old.
Hello may you please check me work for number 5
Answers
Surface area of a rectangular prism:
[tex]SA=2(wl+hl+hw)[/tex]Substitute 1.2 for all of the variables in the formula:
[tex]SA=2[(1.2)(1.2)+(1.2)(1.2)+(1.2)(1.2)][/tex]Using a calculator, you should get an answer of:
[tex]SA=8.64\text{ }yd[/tex]The answer is that the surface area of this shape is 8.64 yards.
Which expression represents the distance between point (0, a) and point (a,0) on a coordinate grid?
2a
Ο Ο Ο Ο
2a
O
Answers
Answer:
Explanation:
To determine the distance between two points on a coordinate grid, use the formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]the odds against (E) are 23:77 Find the probability of (not E) :
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We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.
The number 23:77 is a ratio and is it equivalent to:
[tex]\frac{23}{77}[/tex]To get the probability of the event not-E, we can proceed as follows:
[tex]1-\frac{23}{77}=\frac{77}{77}-\frac{23}{77}=\frac{53}{77}\approx0.7013[/tex]So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).
The edge of a cube measures 11 m. Find the surface area.
Answers
In order to determine the surface area of the cube, use the following formula:
[tex]S=6a^2[/tex]where a is the length of the side of a cube a = 11 m.
Replace the value of a into the formula for S:
[tex]S=6(11m)^2=726m^2[/tex]Hence, the surface area of the given cube is 726m^2
3. By elimination 2x - 3y =- 55x + 2y =16
Answers
By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get
[tex]5\cdot(2x-3y)=5\cdot-5\text{ = 10x-15y = -25}[/tex]Now, lets multiply by 2 the second equation
[tex]2\cdot(5x+2y)\text{ = 16}\cdot2\text{ = 10x+4y=32}[/tex]With this two equations, lets subtract the second equation from the first equation
[tex]10x+4y-(10x-15y)\text{ = 32-(-25)}[/tex]We get
[tex]19y\text{ = 57}[/tex]If we divide y by 19 we get
[tex]y=\frac{57}{19}=3[/tex]Now, using this value in the second equation we get
[tex]5x+2\cdot3\text{ = 16 }=5x+6[/tex]If we subtract 6 on both sides, we get
[tex]16-6\text{ = 5x = 10}[/tex]Finally, we divide by 5 on both sides and we get
[tex]x=\frac{10}{5}=2[/tex]can you please help me with the work sheet and get all the answers and thank you
Answers
ANSWER
[tex](x+2)(x-4)[/tex]EXPLANATION
7) Given;
[tex]f(x)=x^2-2x-8[/tex]Using factors of 2 and -4;
[tex]\begin{gathered} \lparen x^2+2x-4x-8) \\ \left(x^2+2x\right)+\left(-4x-8\right) \\ \end{gathered}[/tex]Factorise;
[tex]\begin{gathered} x\left(x+2\right)-4\left(x+2\right) \\ \end{gathered}[/tex]Factor out the common term;
[tex]\begin{gathered} x(x+2)-4(x+2) \\ (x+2)(x-4) \end{gathered}[/tex]The graphical solution is attached.
The entire graph of the function h is shown in the figure below.Write the domain and range of h using interval notion.(a) domain=(b) range=
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The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,
[tex]\lbrack-2,3)[/tex]The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,
[tex](-2,3\rbrack[/tex]I do not understand the problem on how to to write an equation.
Answers
Given a line passes through the point (-4,6) and has a slope of 3
We will write the equation of the line in point-slope from
The formula of the point-slope form will be as follows:
[tex]y-k=m(x-h)[/tex]Where (h, k) is the point that lies on the line and (m) is the slope
From the given:
m = 3
h = -4
k = 6
Substitute into the formula
so, the answer will be:
[tex]y-6=3(x+4)[/tex]Factor 64x3 + 27.(4x – 3)(16x2 – 12x + 9)(4x + 3)(16x2 - 12x + 9)(4x + 3)(16x2 + 12x + 9)(4x - 3)(16x2 + 12x + 9)
Answers
Answer
Option B is correct.
64x³ + 27 = (4x + 3) (16x² - 12x + 9)
Explanation
We are told to factorize
64x³ + 27
To do this, we use the factorization of (x³ + y³) as a guide. First of,
(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)
(x + y)³ = x³ + y³ + 3x²y + 3xy²
So, we can write
x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)
= (x + y) [(x + y)² - 3xy]
= (x + y) (x² + y² + 2xy - 3xy)
= (x + y) (x² - xy + y²)
So, comparing (64x³ + 27) with (x³ + y³), we can see that
64x³ = (4x)³
27 = (3)³
(64x³ + 27) = (4x)³ + 3³
x³ + y³ = (x + y) (x² - xy + y²)
(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]
= (4x + 3) (16x² - 12x + 9)
Hope this Helps!!!
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
Answers
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
4. Write the equation of the line in SLOPE-INTERCEPT FORM that passes through the given points(4,2) and (0,6)
Answers
The slope intercept form equation is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
slope, m = (y2 - y1)/(x2 - x1)
From the information given,
y2 = 6, y1 = 2
x2 = 0, x1 = 4
Slope, m = (6 - 2)/(0 - 4) = 4/- 4
m = - 1
We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes
6 = - 1 * 0 + c
6 = c
c = 6
The equation would be
y = - x + 6