Find a quadratic function to model the values in the table.x | y-1 -80 -23 -81. y =-2x^2 + 4x - 22. y=x^2+2x-23. y=-2x^2-4x-24. y=-x^2-2x+2
Answers
Step 1
When x=0, y=-2
[tex]\text{The general equation of a quadratic function is y=ax}^2+bx+c[/tex]Substitute for x=0,y=-2
[tex]\begin{gathered} -2=a(0)^2+b(0)+c \\ -2=c \\ c=-2 \end{gathered}[/tex]Step 2
When x=-1,y=-8
[tex]\begin{gathered} -8=a(-1)^2+b(-1)+c \\ -8=a-b+c \\ -8=a-b-2 \\ a-b=-8+2 \\ a-b=-6--(1) \end{gathered}[/tex]When x=3,y=-8
[tex]\begin{gathered} -8=a(3)^2+b(3)+c \\ -8=9a+3b-2 \\ 9a+3b=-8+2 \\ 9a+3b=-6---(2) \end{gathered}[/tex]Step 3
From 1;
[tex]\begin{gathered} a=-6+b \\ \text{Substituting for a in equation gives; 9(-6+b)+3b=-6} \\ -54+9b+3b=-6 \\ 12b=54-6 \\ 12b=48 \\ \frac{12b}{12}=\frac{48}{12} \\ b=4 \end{gathered}[/tex]From equation 1;
[tex]\begin{gathered} a-b=-6 \\ a-4=-6 \\ a=-6+4 \\ a=-2 \end{gathered}[/tex]Therefore, the equation will be;
[tex]y=-2x^2+4x-2[/tex]Related Questions
A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. How long does it take the projectile to reach the highest point in its trajectory?
Answers
We have a projectile that is fired with a initial speed of 35 m/s and an angle of 55 degrees above the horizontal. We want to calculate how long does it take to reach the highest point.
As we are only interested in the vertical trajectory, we will be working with the y-axis.
The vertical speed is equal to the initial speed less the effect of the gravity force. This force is an acceleration that goes against the direction of the vertical initial speed.
We can write this as:
[tex]\begin{gathered} v_y(t)=v_{y0}-g\cdot t \\ v_y(t)=v_o\cdot\sin (\alpha)-g\cdot t \\ v_0=35\text{ m/s} \\ \alpha=55\text{ deg} \\ g=9.8\text{ m/s\textasciicircum 2} \end{gathered}[/tex]The maximum height is reached when the vertical speed is 0. That means that from that time on, the projectile will go downwards.
So we can use the previous formula to solve that for time t:
[tex]\begin{gathered} v_y(t)=0=v_0\cdot\sin (\alpha)-g\cdot t \\ v_0\cdot\sin (\alpha)=g\cdot t \\ t=\frac{v_0\cdot\sin (\alpha)}{g}=\frac{35\cdot\sin (55)}{9.8}=\frac{35\text{ m/s}\cdot0.82}{9.8\text{ m/s\textasciicircum 2}}=2.92\text{ s} \end{gathered}[/tex]It takes 2.92 seconds for the projectile to reach the maximum height.
The slope of the line is?I came up with 2 over 8 2/8. Do you reduce? Would it be 1 over 4?
Answers
The slope m of a line can be found by dividing the difference between two y-values by the difference between the respective x-values:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]We can use, for example, the first two points of the table. So we have:
x₁ = 1
x₂ = 3
y₁ = 2
y₂ = 10
Now, using those values in the above formula, we obtain:
[tex]m=\frac{10-2}{3-1}=\frac{8}{2}=4[/tex]Therefore, the slope of the line is 4.
3x-6=4(2-3x)-8xwhat does x equal?
Answers
x = 14/23
Explanations:The given equation is:
3x - 6 = 4(2 - 3x) - 8x
Open the parenthesis by expanding the equation
3x - 6 = 8 - 12x - 8x
3x - 6 = 8 - 20x
Collect like terms
3x + 20x = 8 + 6
23x = 14
Divide both sides by 23
23x / 23 = 14/23
x = 14/23
Which of the following correctly shows the re-grouping strategy for solving 57 x 18?50 x 10; 7 x 10; 50 x 8; 7 x 850 x 10; 7 x 50; 50 x 8; 7 x 850 x 10; 7 x 10; 10 x 8; 7 x 810 x 8; 7 x 10; 50 x 8; 7 x 8
Answers
the question wnats us to find the correct regrouping strategy for solving 57 x 18
in othe r to get the correct re-grouping strategy, we must first know what it entails.
57 x 18 = 1026
so, the correct regrouping strategy will be the one that will be equal to 1026 when summed up
so,
50x10; 7x10; 50x8; 7x8
= 500 + 70 + 400 + 56
= 1026
therefore the correct option is A
Susan has a jar of jellybeans. She has 10 yellow, 5 green, 3 red, and 2 black jellybeans. What is the probability thatshe will get a yellow jellybean on her first grab, replace it, and then grab a black jellybean on her second grab?Write your answer in simplest form.оO 20O 30о3
Answers
The probability formula is given by:
[tex]\text{ P(E) =}\frac{\text{ N(Required outcome)}}{\text{ N(Total outcome)}}[/tex]Number of yellow jellybeans, n(Y) = 10
Number of green jellybeans, n(G) = 5
Number of red jellybeans, n(R) = 3
Number of black jellybeans, n(B) = 2
Total number of balls = 10 + 5 + 3 + 2 = 20 balls
P( she gets a yellow jellybean first, replaces it, and grabs a black jellybean)
[tex]\begin{gathered} \text{ P(gets a yellow jellybean) =}\frac{10}{20} \\ \text{ P(grabs a black jellybean) =}\frac{2}{20} \end{gathered}[/tex][tex]\text{ P( yellow first, black second with replacement) =}\frac{10}{20}\times\frac{2}{20}\text{ =}\frac{1}{20}[/tex]Therefore, the answer to the probability that susan gets a yellow jellybean on her first grab, replaces it, and grabs a black jellybean is 1/20
Find the slope of a line parallel to the line that passes through the points (4,9) and (22,3).
Answers
The formula used to calculate the slope of a line is given to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The points that the line passes through are:
[tex]\begin{gathered} (x_1,y_1)=(4,9) \\ (x_2,y_2)=(22,3) \end{gathered}[/tex]Therefore, the slope of the line is given to be:
[tex]\begin{gathered} m=\frac{3-9}{22-4}=\frac{-6}{18} \\ m=-\frac{1}{3} \end{gathered}[/tex]Recall that the slopes of parallel lines are equal.
Therefore, the slope of the parallel line is -1/3.
9) Solve and graph each inequality on a number line.e. x + 9 < -6
Answers
we have the next inequality
[tex]x+9<-6[/tex]we need to clear x
[tex]\begin{gathered} x+9<-6 \\ x<-9-6 \\ x<-15 \end{gathered}[/tex]the graph is
according to the US Bureau of Labor Statistics there were one hundred thousand four hundred Chef head cook employed in the United States in 2010 and 320700 Food Service managers those number were projected to decrease to 96900 and 310000 by 20 20 which job was facing the largest percent decrease
Answers
Answer
The percentage decrease is 3.49%
Step-by-step explanation:
According to the data given:
The initial data for chef/head cooks = 100,400
It is expected to decrease to 96,900 by 2020
Percentage decrease in chefs and head cooks can be calculated as follows
Percentage change = new - old / old * 100%
Percentage change = 96,900 - 100,400 / 100, 400 * 100%
Percentage change = -3500 / 100400 *100%
Percentage change = -0.0349 * 100%
Percentage change = -3.49%
Hence, the percentage decrease in chefs and head cooks is 3.49%
Solve 36q = 18 in decimal form
Answers
Let's solve the equation 36*q=18
The answer is q=0.5
find the distance of the diagonal and compare it to walking along the streets.
Answers
Given data:
The given image of the park.
The lenght of the diagonal is,
[tex]\begin{gathered} d^2=40^2+30^2 \\ d^2=1600+900 \\ d^2=2500 \\ d=50\text{ yards} \end{gathered}[/tex]The distance covered w
Answer:
20 yards
Step-by-step explanation:
If you walked along the streets it would be 30 yards + 40 yards = 70 yards.
However, to calculate the length across the diagonal, we have to use the Pythagorean Theorem, [tex]a^{2}+b^{2} =c^{2}[/tex], where: [tex]a, b[/tex] are sides, and [tex]c[/tex] is the hypotenuse.
In this case, [tex]a=30[/tex], [tex]b=40[/tex], and [tex]c[/tex] is the hypotenuse, which is the length we have to calculate.
So:
[tex]30^{2} + 40^{2} =c^{2}[/tex]
[tex]900+1600=c^{2}[/tex]
[tex]2500=c^{2}[/tex]
[tex]50=c[/tex]
Finally, we subtract the 2 lengths, [tex]70-50=20[/tex], which gives us the difference, which is the amount of yards Carla will save.
i dont understand this question and please need help especially since its more than one answer
Answers
Answer
For the graph given, the statements that are true are:
A. The domain is the set of all real numbers
D. The range is the set of all real numbers greater than or equal to zero.
Explanation
The domain of the curve is (-∞, ∞). Hence this implies the domain is the set of all real numbers.
The range of the curve is [0, ∞). This implies the range is the set of all real numbers greater than or equal to zero.
there are 6 women and 7 men signed up to join a salsa dance class. in how many ways can the instructor choose 5 of the people to join if 4 or more must be men?
Answers
Data:
• 6 women
,• 7 men
,• Total = 6 + 7 = 13
Steps:
0. We have to calculate the option where we 5 five men only:
Formula:
[tex]C_{n,x}=\frac{7!}{5!\cdot(7-5)!}=21[/tex]2. Then, we have to make the calculations for the option in which we choose one woman
[tex]C_{n,x}=\frac{7!}{4!\cdot(7-4)!}=35[/tex]3. We multiply the last result times 6 because that is the number of groups we could make:
[tex]\text{Total}=35\cdot6+21=231[/tex]Answer: 231
consider the right triangle inside the circle with a center at point E(1,1). which equation can be used to show how he pythagorean theorem can lead to an equation for the circle?
Answers
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
(h, k) is the center
r is the radius
Since the center is (1, 1), we can write:
[tex](x-1)^2+(y-1)^2=r^2[/tex]EG (hypotenuse of the right triangle) is the radius of the circle. Thus, we can say >>>
[tex](x-1)^2+(y-1)^2=(LengthOfEG)^2[/tex]The correct answer is
BCan you please help me with this question what should you set as the speed limit (i.e., initial velocity of the car) so that the braking distance is 17 feet or less (round to the nearest foot per second)? feet per second
Answers
ANSWER
31 feet per second
EXPLANATION
The equation for the braking distance is,
[tex]d=0.018268\cdot V^2_o[/tex]In this problem, we have to find the maximum initial velocity Vo, for d = 17 feet.
Solving the equation above for Vo,
[tex]V_o=\sqrt[]{\frac{d}{0.018268}}=\sqrt[]{\frac{17}{0.018268}}=30.505557ft/s\approx31ft/s[/tex]Hence, the speed limit should be 31 feet per second.
A right circular cylinder is shown in the figure below with dimensions given in feet. What is the surface area, in square feet, of this cylinder?
Answers
The surface area of a regular cylinder is given by the following formula.
[tex]A_{\text{surface}}=2(r^2\pi)+(2r\pi)h[/tex]Where r is the radius and h is the height of the cylinder. In our case,
[tex]\begin{gathered} r=4 \\ h=3 \\ \Rightarrow A_{\text{surface}}=2(16\pi)+2(4\pi)\cdot3=32\pi+24\pi=56\pi \\ \Rightarrow A_{\text{surface}}=56\pi \end{gathered}[/tex]The answer is 56pi ft^2
Find the first derivative and the second derivative of each of the following functions.
Answers
To find the first derivative and second derivative of the following functions.
Now,
a)
[tex]y=4x^7+5x^3[/tex]The first derivative is given by,
[tex]\begin{gathered} y^{\prime}=\frac{d}{dx}(4x^7+5x^3) \\ =4\times7x^{7-1}+5\times3x^{3-1} \\ =28x^6+15x^2 \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} y^{\prime\prime}=\frac{d^{}}{dx^{}}(28x^6+15x^2) \\ =28\times6x^{6-1}+15\times2x^{2-1} \\ =168x^5+30x \end{gathered}[/tex]b)
[tex]y=\frac{2}{x^4}[/tex]The first derivative is,
[tex]\begin{gathered} y^{\prime}=\frac{d}{dx}(\frac{2}{x^4}) \\ =\frac{d}{dx}(2x^{-4}) \\ =2\times-4x^{-4-1} \\ =-8x^{-5} \\ =-\frac{8}{x^5} \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} y^{\prime\prime}=\frac{d}{dx}(-\frac{8}{x^5}) \\ =\frac{d}{dx}(-8x^{-5}) \\ =-8\times-5x^{-5-1} \\ =40x^{-6} \\ =\frac{40}{x^6} \end{gathered}[/tex]c)
[tex]x=36\sqrt[3]{t}[/tex]The first derivative is,
[tex]\begin{gathered} x^{\prime}=\frac{d}{dt}(36\sqrt[3]{t}) \\ =\frac{d}{dt}(36\times t^{\frac{1}{3}}) \\ =36\times\frac{1}{3}\times t^{\frac{1}{3}-1} \\ =12\times t^{\frac{1-3}{3}} \\ =12\times t^{-\frac{2}{3}} \\ =\frac{12}{\sqrt[3]{t^2}} \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} x^{\prime\prime}=\frac{d}{dt}(\frac{12}{\sqrt[3]{t^2}}) \\ =\frac{d}{dt}(12\times t^{-\frac{2}{3}}) \\ =12\times-\frac{2}{3}\times t^{-\frac{2}{3}-1} \\ =-8t^{-\frac{5}{3}} \\ =-\frac{8}{t\sqrt[3]{t^2}} \end{gathered}[/tex]d)
[tex]x=4e^{5t+3}[/tex]The first derivative is,
[tex]\begin{gathered} x^{\prime}=\frac{d}{dt}(4e^{5t+3}) \\ =4\times e^{5t+3}\times(5+0) \\ =20e^{5t+3} \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} x^{\prime\prime}=\frac{d}{dt}(20e^{5t+3}) \\ =20\times e^{5t+3}\times(5+0)_{} \\ =100e^{5t+3} \end{gathered}[/tex]e)
[tex]y=16\ln (2x)[/tex]The first derivative is,
[tex]\begin{gathered} y^{\prime}=\frac{d}{dt}(16\ln (2x)) \\ =16\times\frac{1}{2x}\times2 \\ =\frac{16}{x} \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} y^{\prime\prime}=\frac{d}{dt}(\frac{16}{x}) \\ =\frac{d}{dt}(16x^{-1}) \\ =16\times-1x^{-1-1} \\ =-16x^{-2} \\ =-\frac{16}{x^2} \end{gathered}[/tex]f)
[tex]x=4\sin (3\theta-1)+5\cos (2\theta+7)[/tex]The first derivate is,
[tex]\begin{gathered} x^{\prime}=\frac{d}{d\theta}(4\sin (3\theta-1)+5\cos (2\theta+7)) \\ =4\times\cos (3\theta-1)\times(3-0)+5\times-\sin (2\theta+7)\times(2+0) \\ =12\cos (3\theta-1)-10\sin (2\theta+7) \end{gathered}[/tex]The second derivative is,
[tex]\begin{gathered} x^{\prime\prime}=\frac{d}{d\theta}(12\cos (3\theta-1)-10\sin (2\theta+7)) \\ =12\times-\sin (3\theta-1)\times(3-0)-10\times\cos (2\theta+7)\times(2+0) \\ =-36\sin (3\theta-1)-20\cos (2\theta+7) \end{gathered}[/tex]all you need is in the photo please answer fast please helpppppp
Answers
2.5%
[tex]2536(1.025)^{12t}[/tex]Becomes 2536(1.025) after 1 year
So the increase in 1 year = 2536(1.025) - 2536= 0.025 x 2536 =
what ratio is equivalent to 7:4 if the question is 84:(blank) i need to know the answer for blank
Answers
ANSWER
48
EXPLANATION
Two ratios are equivalent if they both simplify to the same ratio.
If we have ratio 7:4 - which is already simplified - and we want to know what's the equivalent ratio that starts with 84:__ we have to see by what number should we multiply 7 to get 84. Then, to fill in the blank, we have to multiply 4 by that number.
To find this number we just have to divide 84 by 7:
[tex]\begin{gathered} 7x=84 \\ x=\frac{84}{7} \\ x=12 \end{gathered}[/tex]If 7 times 12 is 84, then the number that's missing is 4 times 12:
[tex]4\cdot12=48[/tex]The equivalent ratio is 84:48
In the trapezoid below, if < BAC = x - 2 degrees and the measure of < DCA is 4x - 3 degrees, find x.
Answers
Assuming an isosceles trapezoid
the sum of the inner angles of a trapezoid is 360°
then
[tex]360=2(BAC)+2(DCA)[/tex][tex]360=2(BAC+DCA)[/tex][tex]180=(BAC+DCA)[/tex][tex]180=(x-2)+(4x-3)[/tex][tex]180=5x-5[/tex][tex]180+5=5x[/tex][tex]185=5x[/tex][tex]\frac{185}{5}=x[/tex][tex]x=37[/tex]x=37
correct answer
Option D
Which choice is equivalent to the quotient shown here for acceptable values of x? sqrt25(x-1)÷sqrt5(x-1)^2
Answers
We have
[tex]\frac{\sqrt[]{25(x-1)}}{\sqrt[]{5(x-1)^2}}[/tex]we will use the next rules
[tex]\sqrt[]{n\cdot m}=\sqrt[]{n}\sqrt[]{m}[/tex][tex]\sqrt[]{m}=m^{\frac{1}{2}}[/tex]with these in mind we can find the equivalent quotient.
[tex]\frac{\sqrt[]{25(x-1)}}{\sqrt[]{5(x-1)^2}}=\frac{\sqrt[]{25}\sqrt[]{x-1}}{\sqrt[]{5}\sqrt[]{(x-1)^2}}=\frac{5(x-1)^{\frac{1}{2}}}{5^{\frac{1}{2}}(x-1)}[/tex]then we will use
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]so we continue simplifying
[tex]\frac{5(x-1)^{\frac{1}{2}}}{5^{\frac{1}{2}}(x-1)}=5^{1-\frac{1}{2}}(x-1)^{\frac{1}{2}-1}=5^{\frac{1}{2}}(x-1)^{-\frac{1}{2}}=\frac{\sqrt[]{5}}{\sqrt[]{x-1}}=\sqrt[]{\frac{5}{x-1}}[/tex]the answer is B.
For Exercises 2 and 3, give the coordinates of each image. 2. r (90°, 0) (MN) for M(3, -5), N(2, 4) 3. (180°, 0) (AABC) for A(1, 1), B(3,5), C(5, 2)
Answers
2.
This is a 90 degree anticlockwise rotation.
If a point X(x,y) is rotated 90 degree anticlockwise with respect to the origin, the new point X' would be X'(-y,x).
M' would be M'(5,3)
N' would be N'(-4,2)
3.
This is 180 degree rotation with respect to the origin.
If a point A(x,y) is rotated 180 degrees with respect to the origin, the new point A' would be A'(-x,-y).
A' would be (-1,-1).
B' would be (-3,-5).
C' would be (-5,-2).
y varies directly as x and inversely as z can be modeled by the equation ______
Answers
Direct variation is a relationship between two variables. In this case, y is directly proportional to x. We say y varies directly with x if:
[tex]\begin{gathered} y=kx \\ \text{ Where k is a constant} \end{gathered}[/tex]On the other hand, inverse variation is another relationship between two variables. In this case, y is inversely proportional to x. We say y varies inversely with x if:
[tex]y=\frac{k}{x}[/tex]Now, if we combine the two previous definitions, we have:
[tex]\begin{gathered} y=kx\Rightarrow\text{ Because y varies directly with x} \\ y=\frac{kx}{z}\Rightarrow\text{ Because y varies inversely with z} \end{gathered}[/tex]Therefore, y varies directly as x and inversely as z can be modeled by the equation
[tex]$$\boldsymbol{y=\frac{kx}{z}}$$[/tex]Find the surface area of the cylinder Formula: SA= 2 * 3.14 * r * h +2 * 3.14 * r^2
Answers
Surface area of a cylinder :
A = 2rh + 2h^2 ; where r = 2 yd and h = 7yd
A = 2 (2x 7) + 2(7x7)
= 126yd ^2
=395.84 yd ^2
what are two examples of numbers that would be natural, whole, and integer
Answers
i need help finding the other pointsDilate the Rhombus with a scale factor of k= 3/2
Answers
Step 1: Define dilation
To dilate a figure in the coordinate plane, multiply the coordinate of each vertex by the scale factor, k. This is called mapping. For any dilation the mapping will be (x,y)→(kx,ky) . The center of dilation will always be the origin unless otherwise stated or given
Step 2: Write out the coordinates of the vertices of the Rhombus
[tex]W(2,-4),X(6,-2),Y(10,-4),Z(6,-6)[/tex]Step 2: Write out the mapping for dilation with constant k = 3/2 = 1.5
The mapping, D, is defined as
[tex]D\colon(x,y)\to(1.5x,1.5y)[/tex]Step 3: Find the coordinates of W', X', Y', Z'
[tex]\text{Coordinates of W' }=(1.5(2),1.5(-4))=(3,-6)[/tex][tex]\text{Coordinates of X' }=(1.5(6),1.5(-2))=(9,-3)[/tex][tex]\text{Coordinates of Y' }=(1.5(10),1.5(-4))=(15,-6)[/tex][tex]\text{Coordinates of Z' }=(1.5(6),1.5(-6))=(9,-9)[/tex]Hence, the coordinates of the vertices Rhombus after dilation are:
W'(3, -6)
X'(9, -3)
Y'(15, -6)
Z'(9, -9)
You are taking a true-false test has 10 questions. Assuming your answer every question, in how many different ways can the test be completed?
Answers
there are
[tex]2^{10}[/tex]forms of completing the test
A system of linear equations has been graft in the diagram determine a reasonable solution for a system of equations,A. (2,1)B. (-2,1)C. (2,-1)D. (3,-1)
Answers
Solution
The solution of the system of the linear equation is the point where the linear graphs (lines) intersect.
by observation, the point of intersection is to the right of the origin zero on the x-axis and above the line y=0 ( x-axis line).
This implies that the x and y values of the coordinate are positive for both
Hence, the solution for the system of the linear equations is
[tex](2,1)[/tex]Option A is the answer
evaluate. show all work. properties of expoenents/ super helpful property.
Answers
Okay, here we have this:
We need to evaluate the following:
[tex]\begin{gathered} a32^{\frac{3}{5}} \\ =a(2^5)^{\frac{3}{5}} \\ =a2^{5\cdot\frac{3}{5}} \\ =a2^3 \\ =8a \end{gathered}[/tex]Finally we obtain that the answer is 8a.
1)) Look at this set of ordered pairs:(9, -7)(5, 11)(15, 3)(9, 13)(1) Is this relation a function?
Answers
In order to check if the set of points represent a function, every value of x can only have one corresponding value of y.
Looking at the set, we have two points with x = 9 that have different values of y, therefore this set can't be a function.
So this set of ordered pairs is a relation.
the cost to rent a boat is 250 per day plus $3.50 per gallon of gas used which expression represents renting a boat for one day and using X gallons of gas
Answers
Answer:
The expression that represents renting a boat for one day and using X gallons of gas is;
[tex]T=250+3.50X[/tex]Explanation:
The cost to rent a boat is $250 per day plus $3.50 per gallon of gas used.
the fixed cost is $250
the variable cost is $3.50 multiplied by the number of gallons of gas used (given as X).
Total cost of renting the boat is the sum of the fixed and the variable cost;
let T represent the total cost of renting the boat for one day;
[tex]T=250+3.50X[/tex]The expression that represents renting a boat for one day and using X gallons of gas is;
[tex]T=250+3.50X[/tex]