Which of the following are possible equations of a parabola that has no real solutions and opens downward?y > = -(x + 4)2 - 2y > = -(x + 4)2 + 2y > = -x2 - 2y > = (x - 4)2 + 2y > = -(x - 4)2 - 2
Answers
We have to identify the parabola that:
a) has no real solutions (it has complex roots).
b) opens downward.
The equations are in vertex form, so to have no real solutions and be downward, the vertex should have a value of y that is less than 0:
If the vertex had a value of y greater than 0, if it opens downward, there should be two values of x so that f(x) = 0. Then, this would be the real solutions.
The vertex form can be written as:
[tex]y=a(x-h)^2+k[/tex]where (h,k) are the coordinates of the vertex.
Then, we need k <= 0.
The equations that satisfy this are:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
The second condition is that the parabola opens downward. This means a quadratic coefficient "a" with negative value.
All this three equations satisfy this condition.
We can graph them and check if the conditions are satisfied:
Answer:
There are 3 equations that satisfy the two conditions:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
Related Questions
For this problem, write the numbers in standard form.
19. 1.49 x 102 (1 point)
14.9
149
0 1,490
Answers
Answer:
1.49 × 101.
100+40+9
1.49 × 103.
Step-by-step explanation:
is this Right?
Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer.
What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters?
Answers
If he initially had 30 liters of fuel, and his car's fuel efficiency is cubic centimeters per kilometer. The calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters is: 30- 100/1000×120
How to determine the estimated volume?Given data:
Distance = 120 kilometers
Liters of fuel = 30 liters
Using this formula to find the remaining volume
Remaining volume = I - E × D
Where:
I = Initial volume
E = Fuel efficiency
D = Distance
First step is to formula an equation that will be use to find the remaining volume
Equation = 30- 100/1000 ×120
Now let use the formulated equation to find the remaining volume
Remaining volume = 30- 100/1000 × 120
Remaining volume = 30- 12
Remaining volume = 18
Therefore 30- 100/1000×120 can be used to determine the remaining volume.
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2.Make a table & Graph the function f(x) = 2)*х-1012y
Answers
We are given the function
f(x) = 2(1/2)^1
Firstly, let f(x) = y
Then, y = 2(1/2)^x
To find y, substitute the value of x into the function.
y = 2(1/2)^x
Find y, when x = -1
y = 2(1/2)^-1
y = 2 ( 1/ 1/2)
y = 2(2 x 1 / 1)
y = 2 x 2
y= 4
When x = -1 , y = 4
find y, when x = 0
y = 2(1/2)^0
In mathematics, anything raise to the power of zero is 1
Therefore, (1/2)^0 = 1
y = 2 x 1
y = 2
When x = 0 , y = 2
find y, when x = 1
y = 2(1/2)^1
y = 2 * 1/2
y = 2/2
y = 1
when x = 1, y= 1
find y, when x = 2
y = 2(1/2)^2
(1/2)^2 = (1/4)
y = 2(1/4)
y = 2x 1/4
y = 2/4
y = 1/2 or 0.5
When x = 2, y= 1/2 or 0.5
The new table becomes
x y
-1 4
0 2
1 1
2 1/2
jon drove an average of 250 miles a day for three days he drove 400 miles on the first dat 125 miles on the second day
Answers
Answer:
225 miles on 3rd day
Step-by-step explanation:
400 + 125 + x /3 = 250
multiply each by 3 to get 400 +125 +x = 750
subtract 525 each to get x = 225
PeriodNameDateUsing Tables to Graph Quadratic Functions1. Match the four graphs to the corresponding table.AB10TO105СD105-10D351055-10х-1х-2-101y47014у34.30-5NOХ-3-2-101у-3-4-3AWN-TOXo/w/tw/okalow2
Answers
In order to match each plot with its corresponding table, consider the positive and negative values of y respect to the positive or negative values of x.
For example, in the first case (plot A), all values of y-coordinate are positive. The only table with all positive y values if the first one.
Hence, plot A matches with the first table.
For plot B, you can notice that for x=0, y=4. The only table in which you have this result is the second one.
Hence, plot B matches with the second table.
For plot C, you can observe that x=0 for y=0. Moreover, if y=0, x = 4. The only table with this result is the fourth table.
Hence, plot C matches with the fourth table.
Finally, plot D matches with the third table.
The yearbook club washes cars to raise at least$600. The club charges $3 for each car (c) thatthey wash. What is inequalities of this situation?
Answers
Abdoul, this is the solution to the problem:
Goal of the club : raise at least $ 600
Price of each car : $3
Let c the number of cars that the club has to wash
In consequence, the inequality that represents this situatiion is:
Total money raised ≥ 600
Total money raised = 3c
Thus,
3c ≥ 600
(We use higher and equal symbol because the statement says "at least 600". If the statement would say, "more than 600", we shoould use >)
4. 5.26 x 1031.37 x 10-1Which of the following pairs of numbers are between the two numbers shown?A. 294 and 0.0294B. 7,338 and 0.7388C. 5,007 and 0.5007D. 6,152 and 0.06152
Answers
Answer:
C. 5,007 and 0.5007
Explanation:
Given the two numbers:
[tex]\begin{gathered} 5.26\times10^3=5260 \\ 1.37\times10^{-1}=0.137 \end{gathered}[/tex]From the given options:
[tex]5260>5007>0.5007>0.137[/tex]All other options do not satisfy the condition.
The correct choice is C.
(08.01 LC)A cylinder has a height of 2 meters and a diameter that is 5 timesthe measure of the height. Using 3.14 for pi, which of the followingcan be used to calculate the volume? (6 points)
Answers
Let's begin by identifying key information given to us:
This figure is a cylinder. The formula for its volume is:
[tex]V=\pi r^2h[/tex]Height (h) = 2 m,
Diameter (d) = 5 × h = 5 × 2 = 10 m; radius (r) = d/2 = 10/2 = 5 m
pi = 3.14
The volume of the cylinder is calculated as shown below:
[tex]\begin{gathered} V=3.14\times5^2\times2 \\ V=3.14\times25\times2=157 \\ V=157m^3 \end{gathered}[/tex]x 1 2 3 y 16 32 48 Write an equation that represents the proportional relationship. y = 16x y = 2x y equals 1 over 16 times x y equals 1 over 2 times x Question 6(Multiple Choice Worth 2 point
Please HELP ME I WILL GIVE BRAINLYNEST
Answers
The equation which represents the proportionality relationship is:
y=16x.
Given, we have the pairs as:
(1,16),(2,32) and (3,48)
calculate the value of y/x for the ordered pairs:
For (1,16), the value of y/x is = 16/1 = 16
For (2,32), the value of y/x is = 32/2 = 16
For (3,48), the value of y/x is = 48/3 = 16
now, compare ratios:
for each ordered pair, y/x = 16
Since, k=y/x, you know that the constant of proportionality , k is 16.
Substitute 16 for k in the equation for a proportional relationship.
y = kx
y = 16x
Hence we get the equation as y=16x.
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Which of the following would be enough information to know that ABC~MNP?
Answers
Answer:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are the same size and the corresponding sides are in the same ratio.
Therefore, if triangle ABC is similar to triangle MNP then their corresponding angles are congruent:
m∠A = m∠Mm∠B = m∠Nm∠C = m∠PSimilarly, if triangle ABC is similar to triangle MNP then their corresponding sides are in the same ratio:
[tex]\implies \dfrac{AB}{MN}=\dfrac{BC}{NP}=\dfrac{AC}{MP}[/tex]
SAS Triangle Similarity
If two sides of one triangle are in the same ratio to the corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar.
∠A is the included angle of sides AB and AC.
∠M is the included angle of sides MN and MP.
Therefore, the only statement that shows that two corresponding sides are in the same ratio and their included angles are congruent is:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
Describe the key features of the graph of the quadratic functionf(x) = -5x^2+5.A. Does the parabola open up or down?B. Is the vertex a minimum or a maximum?C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
Answers
The graph of the function will be something like this.
To make the graph correctly we can give values to x to find points in the plane
[tex]\begin{gathered} f(x)=-5x^2+5 \\ x\text{ | f(x)} \\ -2|-5(-2)^2+5=-15 \\ -1|-5(-1)^2+5=0 \\ 0|-5(0)^2+5=5 \\ 1|-5(1)^2+5=0 \\ 2|-5(2)^2+5=15 \end{gathered}[/tex]Then the graph passes by the points
[tex]\begin{gathered} (-2,15) \\ (-1,0) \\ (0,5) \\ (1,0) \\ (2,15) \end{gathered}[/tex]From this, you can draw the points in a cartesian plane.
Once we have the graph we can answer the question.
The parabola open down.
the vertex of the parabola is a maximun since all the other points are below it.
Finally, we see that the axis of symmetry is the y axis. Since the left part of the the graph is the reflection of the right part.
the vertex of the parabola is the point (0,5).
the y intercept of the parabola is 5. we see that from the point (0,5).
Point J is on line segment IK. Given IK=15 and IJ=13, determine the length of segment JK.
Answers
Line segment IK includes Point J. The length of the segment IK=15 and IJ=13. The length of the segment JK is 2.
Given that,
Line segment IK includes Point J.
We have to determine the length of segment JK.
We have length of the segment IK=15 and IJ=13.
Two unique points on a line define the boundaries of a line segment. A line segment is also known as a part of a line that connects two locations. A line and a line segment vary in that a line has no ends and can continue indefinitely in any direction.
We can write as,
IK=IJ+JK
15=13+JK
JK=15-13
JK=2
Therefore, The length of the segment JK is 2.
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6 Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff didnot spend more than $14 on the hot dogs and the bottle of water. Which inequality canbe used to find h, the number of hot dogs that Jeff could have bought?F 3h - 2 s 14G 3h + 2 S 14H h - 2 2 14J 3h + 2 2 14
Answers
SOLUTION
Step1: Write out the parameters in the question
Let the number of hot dogs be h
The cost of a hot dog is $3
The cost of the bottle of water is $2
The total amount spent by jeff is $ 14
Step2: Write the inequality
The total amount spend should be less than or equal to the total amount
then
The cost of the hot dog is
[tex]3\times h=3h[/tex]The inequality will be the sum of the cost of the hot dog and the bottle of water
[tex]3h+2\leq14[/tex]Hence option G is the correct op
A cash register contains $20 bills and $100 bills with a total value of $1260. If there are 23 bills total, then how many of each does the register contain?
$20 bill answer
$100 bill answer
Answers
According to the solving Each register held eight $20 bills, thirteen $100 bills.
What is a linear equation?A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
What makes an equation linear?A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from.
According to the given data:x=number of $20bills
y=number of $100 bills
20x+100y
=1460 20x+100(-x+21)
=1460 20x-100x+2100
=1460 -80x
=-640 x
=8
-8+21 =13
y=13
20x+y=21 --&g t;
y=-x+21
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The graph below describes the distance from home over a period of time. What is the rate of change from 70 seconds to 100 seconds?
Answers
According to the given graph, after 70 seconds it ran 40 units of distance, after 100 seconds it ran 160 units of distance. So, the points we are going to use to find the rate of change are: (70, 40) and (100, 160).
Now, we use the following formula.-
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]r=\frac{160-40}{100-70}=\frac{120}{30}=4[/tex]Therefore, the rate of change from 70 seconds to 100 seconds is 4.how many liters of paint must you buy to paint the walls of a rectangular prism shaped room that is 20m x 15m, with a ceiling height of 8m.. if 1 Liter of paint covers 40m^2? the amount of paint needed is ____ liters. (Round up to the nearest integer as needed)
Answers
For this question, we compute the superficial area of a rectangular prism without including the ceiling area nor the floor area. We will use the following formula:
[tex]A=\text{ }(\text{rectangle perimeter)}\cdot\text{ height}[/tex]The rectangle perimeter is 2*(20m+15m)=70m. Substituting in the equation above we get:
[tex]A=\text{ 70m}\cdot8m=560m^2[/tex]Therefore, the amount of paint needed is
[tex]\frac{560}{40}\text{liters}=14\text{liters}[/tex]Answer: 14 liters.
Answer: 14
Step-by-step explanation:
Write the vector v in terms of i and j whose magnitude and direction angle are given.
Answers
The magnitude, r, of the vector, v , is given to be 4/5.
The direction angle is given to be 114 degrees.
A vector component is written in the form of:
[tex]V=ai+bj[/tex]We are going to use the given magnitude and direction angle to obtain the values of a and b.
Thus, we have:
[tex]\begin{gathered} \text{The magnitude, r, of a vector with i and j component is given as:} \\ r=\sqrt[]{a^2+b^2} \\ \frac{4}{5}=\sqrt[]{a^2+b^2} \\ \text{square both sides;} \\ (\frac{4}{5})^2=a^2+b^2 \\ \frac{16}{25}=a^2+b^2 \\ \frac{16}{25}-b^2=a^2 \\ a^2=\frac{16}{25}-b^2 \\ a=\sqrt[]{\frac{16}{25}-b^2}\text{ ----eqn i)} \end{gathered}[/tex][tex]\begin{gathered} \text{The direction angle, }\theta,\text{ of a vector is given as;} \\ \text{Tan }\theta=\frac{b}{a} \\ \text{Tan 114=}\frac{b}{a} \\ -2.2460=\frac{b}{a} \\ b=-2.2460a\text{ -----eqn }ii) \end{gathered}[/tex]Substitute for b into eqn i); thus we have:
[tex]\begin{gathered} From\text{ eqn i)} \\ a=\sqrt[]{\frac{16}{25}-b^2} \\ \text{Put b=-2.2460a into the equation, we have:} \\ a=\sqrt[]{\frac{16}{25}-(-2.2460a)^2} \\ a=\sqrt[]{\frac{16}{25}-(5.0447a^2)} \\ \text{square both sides;} \\ a^2=\frac{16}{25}-5.0447a^2 \\ a^2+5.0447a^2=\frac{16}{25} \\ 6.0447a^2=0.64 \\ a^2=\frac{0.64}{6.0447} \\ a^2=0.1058 \\ a=\sqrt[]{0.1058} \\ a=0.325 \end{gathered}[/tex]Substitute for a= 0.325 into any of the equations, we have:
[tex]\begin{gathered} \text{From eqn }ii) \\ b=-2.2460a \\ b=-2.2460(0.325) \\ b=-0.729 \end{gathered}[/tex]Hence, the vector, v, in terms of i and j is:
[tex]\begin{gathered} v=0.325i-0.729j \\ \text{This can also be written as:} \\ v=\frac{13}{40}i-\frac{729}{1000}j \end{gathered}[/tex]In the year 2016, Ethan was single and had a total income of $58,000. He took a deduction of $9,000 and had a tax credit of $1,500. Calculate the tax owed by Ethan. (Refer to the 2016 Tax Table for Singles for tax rates.)
Answers
The tax owed by Ethan is $6,521.25.
Ethan's total income was $58,000. There was a deduction of $9,000. Ethan's net income is $49,000. The tax table is attached below. Now we will calculate the tax as per the table.
From $0 to $9,275, the tax is 10%, i.e., $9,27.5.
From $9,276 to $37,650, the tax is 15%, i.e., $4,256.25.
From $37,651 to $49,000, the tax is 25%, i.e., $2,837.5.
The payable tax is the sum of the above calculated taxes. The payable tax is $8,021.25. There is a tax credit of $1,500. The tax owed is the difference between the payable tax and the tax credit. The tax owed is $8,021.25-$1,500 = $6,521.25.
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At soccer practice, 35 minutes are spent playing and 5 minutes are spent on a water break. What percentage of practice time is spent playing?
Answers
Answer: 87.5%
Step-by-step explanation:
35/40 = x/100
40 times 2.5 gives you 100 so to find what x is you multiply 35 by 2.5.
Use algebra to solve each problem. If a diagram is not given, you MUST sketch one.Show your calculations for each question. Place your answer in the space provided.Yis between X and Z on segment XZ. XY = x + 7, XZ - 152, and YZ - 2XY. Find x to thenearest tenth.xX
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |XY|=x+7 \\ |XZ|=152 \\ |YZ|=2|XY|\Rightarrow|XZ|=|XY|+|YZ| \\ But\colon|YZ|=2|XY|\Rightarrow|XZ|=|XY|+2|XY|\Rightarrow|XZ|=3|XY| \\ |XZ|=3|XY| \\ But\colon|XY|=x+7,|XZ|=152 \\ 152=3(x+7)\Rightarrow152=3\cdot x+3\cdot7\Rightarrow152=3x+21 \\ 152=3x+21 \\ \text{Subtract 21 from each side, we have:} \\ 152-21=3x+21-21\Rightarrow131=3x\Rightarrow3x=131 \\ 3x=131 \\ \text{Divide each side by 3, we have:} \\ \frac{3x}{3}=\frac{131}{3}\Rightarrow x=43\frac{2}{3}\approx43.667\cong43.7 \\ x=43.7(ToNearestTenth) \end{gathered}[/tex]Given the following table of values for f(x), find f(9).x−5−42489f(x)4124058
Answers
We have a table of values which contains different x-values and their related f(x).
We are searching for f(9), then we have to observe the value of the function f(x) when x=9.
In the table of values we can observe when x=9, then f(x)=8.
So f(9)=8
Step-by-step explanation:
please write the question properly
Not good at math at all so I rlly don’t know much of anything, could really use the help.
Answers
Given
Stack of 39 pennies is exactly as tall as 31 pennies
Find
the correct options
Explanation
No the two stacks will have different volume.
The two stacks will have same height but the area of cross section of the penny stack is smaller than that of nickel stack
Final Answer
option (b) is correct
Drag each set of coordinates to the correct location on the table.
Calculate the distance between the pairs of coordinates, and classify them according to the distance between them.
Answers
The required set of coordinates with the match is shown.
Distance between points can be evaluated from the distance formula,
(3, 4) and (2, 1)
= √[(3-2)² + (4-1)²]
= √ 10
Similarly,
The points whose distance between them is √10 are,
(3, 4) and (2, 1)
(-2, 3) and (1, 2)
(-4, -2) and (-3, 1)
The points whose distance between them is √29 are,
(3, 7) and (5, 2)
(5,-2) and (3, 3)
(4, -1) and (-1, 1)
Thus, the required set of coordinates with the match is shown.
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Help me please help me out please please
Answers
Answer:
The answer is it is true.hope the day is saved
Study the function defined by:f(x)= [tex]x \sqrt{ \frac{x - 1}{x + 1} } [/tex]
Answers
So, we have the following function:
To calculate the derivative then, we have to make the following calculation:
So, the result of the equation would be as follows:
The graph of the function would be as follows:
A tennis racket at Sport City costs $180and is discounted 15%. The same modelracket costs $200 at Tennis World and is onsale for 20% off. Which store is offering thebetter deal? Explain.
Answers
We can find the discounted price of the tennis racket at Sport City by finding the 100% - 15% = 85% of the total price. We can do this by multiplying the total price by the decimal form of 85%:
[tex]180(85\%)=180(0.85)=153[/tex]then, we have that the price of the racket at Sport City is $153
Doing the same but with the price at Tennis World, we get:
[tex]\begin{gathered} 100\%-20\%=80\% \\ \Rightarrow200(80\%)=200(0.80)=160 \end{gathered}[/tex]since the price of the tennis racket is $160 at Tennis world, we can clearly see that Sport City offers a better deal (since 153 < 160)
Find the perimeter and area of a triangle with a base of 9 cm, height of 9.3 cm, and sides of 12
cm and 19 cm. Round to the nearest hundredth when necessary.
Answers
Answer:
P(perimeter) = 40 cm A(area) = 41.85 ≈ 41.9 cm
Step-by-step explanation:
To find the perimeter of any shape, you just add the length of the sides together. Therefore, you would add the base, 9 cm, with the sides, 12 and 19 cm. 9 + 12 = 21 + 19 = 40 cm, so the perimeter is 40 cm.
To find the area, you need to use the formula for the area of triangles, which is [tex]\frac{1}{2} bh[/tex], where b = base and h = height. So, you would plug the numbers in to get [tex]\frac{1}{2} (9)(9.3)[/tex]. This equals [tex]\frac{1}{2} (83.7)[/tex], which equals 41.85 cm. Since the question says to round to the nearest hundredth, the final answer would be 41.85 ≈ 41.9 cm.
Suppose sin(A) = 1/4 Use the trig identity sin^2(A)+cos^2(A)=1 to find the cosine in quadrant II. round to ten-thousandth.0.1397-0.9682-0.85720.4630
Answers
To find the value f rthe cosine function we will us the identity:
[tex]\sin^2A+\cos^2A=1[/tex]We know that the sine of A i 1/4 then we have:
[tex]\begin{gathered} (\frac{1}{4})^2+\cos^2A=1 \\ \cos^2A=1-\frac{1}{16} \\ \cos A=\pm\sqrt{\frac{15}{16}} \\ \cos A=\pm0.9682 \end{gathered}[/tex]Now, we need to determine which sign to choose. Since the sinA lies in th second quadrant thismeans that tehe coosine als lies in the quadrant; furthermore, we know that the cosine is negative in the second and thirsd quadrants whichmeans that we need to use the negative sign. Therefoore:
[tex]\cos A=-0.9682[/tex]IlusComplete the squareto find the vertexof this parabola.2.yº+4 x - 2y +21=0+([?], []).Enter
Answers
Answer
The vertex of the parabola is (-5, 1)
Given the following equation:
y^2 + 4x - 2y + 21 = 0
Explanation:
[tex]\begin{gathered} y^2\text{ + 4x - 2y + 21 = 0} \\ \text{Step 1:} \\ \text{Isolate 4x} \\ 4x=-21+2y-y^2 \\ \operatorname{Re}-\text{arranging the equation} \\ -y^2\text{ + 2y - 21 = 4x} \\ -y^2\text{ +2y - 21 = 4x} \\ -y^2\text{ - }\frac{2}{2}y\text{ -21 = 4x} \\ -(y-1)^2\text{ -21 + 1 = 4x} \\ -(y^{}-1)^2\text{ - 20 = 4x} \\ \text{Divide all through by 4} \\ x\text{ = -}\frac{1}{4}(y-1)^2\text{ - 5} \\ U\sin g\text{ the equation} \\ x\text{ = }a(y\text{ }-k)^2\text{ + h} \\ \text{a = -}\frac{1}{4} \\ \text{h = -5} \\ \text{k = 1} \end{gathered}[/tex]Vertex is (h, k)
Therefore, the vertex is (-5, 1)
4-(-3/5) is equivalent to
Answers
Subtracting a negative number is the same as adding that number. In this case,
[tex]4-(-\frac{3}{5})=4+\frac{3}{5}[/tex]