The equation y=3x^2=3 is graphed below on Graph A. What is the equation graphed on Graph B?
Answers
Answer:
Equation given in graph B → y = -3x² + 4
Step-by-step explanation:
Equation of the graph A,
y = 3x² - 3
We have to find the equation of the graph (parabola) given in graph (B).
Parabola given in graph B is the inverted form of graph A with vertex at (0, 4)
Therefore, equation of the parabola given in graph B will be,
y = -a(x - h)² + k
where negative notation of the coefficient a shows the inverted form of the parabola given in graph A and (h, k) will be the vertex.
y = -3(x - 0)² + 4
y = -3x² + 4
Answer:
[tex]y = -3x^2 + 4[/tex]
Step-by-step explanation:
Hello!
The equation of a parabola is written as [tex]y = ax^2 + bx + c[/tex].
Y-interceptThe [tex]c[/tex] value of the equation determines the y-intercept, or where the graph hits the y-axis (x = 0).
In Graph A we can see that the graph hits the y-axis at -3, showing the y-intercept is also -3. We can use the same logic to determine the y-intercept of Graph B. We can see that it hits the y-axis at 4, so the y-intercept is 4.
A-value
The [tex]a[/tex] value determines the direction and width of the graph. If it is positive, it opens up. If it's negative, it opens down.
Since Graph B opens down, we can simply add a negative sign to indicate that it is a negative graph.
EquationWe can plug in the values that we solved for [tex]a[/tex] and [tex]c[/tex].
Equation: [tex]y = -3x^2 + 4[/tex]
Related Questions
Probability of Tournament Winners
Try it
Which statements are true? Check all that apply.
A local chess tournament gives medals for first, second,
and third place. There are five students from Midland
High, three students from Leasburg High, and six
students from Cassville High competing in the
tournament.
Order matters in this scenario.
There are 2,184 ways to select a first-place,
second-place, and third-place winner.
The probability that all three winners are from
Midland High is 0.0275.
The probability that all three winners are from
Leasburg High is 0.0046.
The probability that all three winners are from
Cassville High is 0.0549
Answers
Answer:
The answer is A B C and E
Step-by-step explanation:
I just took it
The statements are true A, B, C, and E.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The given data in the problem is;
No of the students from Midland High = 5
No of the students from Leasburg High= 3
No the students from Cassville High = 6
The statements that are true will be;
A.Order matters in this scenario.
B.There are 2,184 ways to select a first-place,second-place, and third-place winner.
C.The probability that all three winners are from Midland High is 0.0275.
E.The probability that all three winners are from Cassville High is 0.0549
Hence the statements are true A, B, C, and E.
To learn more about the probability refer to the link;
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A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select all that apply.
A. a reflection over the y–axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2 B. a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5 2 C. a dilation about the origin by a scale factor of 2 3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left D. a dilation about the origin by a scale factor of 5 7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3 4
Answers
Answer:
C, D
Step-by-step explanation:
Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4
Answer:
c and something is not d
Step-by-step explanation:
I WILL MAKE YOU THE BRAINLLEST
Which description matches the graph of the inequality y ≤ 2x – 1?
A.a shaded region below a solid boundary line
B.a shaded region above a dashed boundary line
C.a shaded region below a dashed boundary line
D.a shaded region above a solid boundary line
Answers
Answer:
The correct option is;
A. a shaded region below a solid boundary line
Step-by-step explanation:
The parameters given are;
The equation, y ≤ 2x - 1
We compare the above equation with the equation for a straight line, y = m·x + c to get
The slope m = 2
The y-intercept c = -1
Therefore, we have;
The graph of an inequality of a y value which is less than or equal to a function is represented by a solid line having the shaded region, which shows the area that satisfies the inequality, shaded below the line
Which gives the correct option as A. A shaded region below a solid boundary line.
anyone know how to do this?
Answers
Answer:
12.1 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 30 = x/14
14 cos 30 = x
12.12435565 =x
12.1 =x
A circular pond has a radius of 6 feet. What is the area of that pond?
Answers
Answer:
radius x radius x pi = area of circle
6 x 6 = 36
36 x 3.14 = 113.04
113.04
Hope this helps
Step-by-step explanation:
Alexi thinks of a number. he multiplies his number by 10 and then divides the answer by 100. he then multiples this answer by 1000 and gets a final answer of 67. What number does Alexi thinks of first ? please tell fast
Answers
Answer:
The number Alexis thinks of first is 6.7.
Step-by-step explanation:
Let the number Alexis thinks of be x and the first answer he got be y.
Since he multiplies the number by x and divides the answer by 100, the equation is
10x = y
10x = [tex]\frac{y}{100}[/tex]
Then, he multiplies this answer, [tex]\frac{y}{100}[/tex], by 1000 and gets a final answer of 67. The equation is
[tex]\frac{y}{100}[/tex] × 1000 = 67
To find y, you divide 1000y by 100 which gives 10y.
i.e. [tex]\frac{1000y}{1000} = 67[/tex]
10y = 67
Divide both sides of the equation by the coefficient of y (which is 10)
[tex]\frac{10y}{10} = \frac{67}{10}[/tex]
y = 6.7
Substituting 6.7 for y in 10x = y
10x = 6.7
Divide both sides of the equation by the coefficient of x (which is 10)
[tex]\frac{10x}{10} = \frac{6.7}{10}[/tex]
x = 0.67
∴ The number Alexis thinks of first is 0.67.
Hope this helps!!! :))
Answer:
0.67
Step-by-step explanation:
Solution 1
We can work out the initial number by going backwards from the end:
67/1000= 0.067
0.067*100= 6.7
6.7/10= 0.67
Solution 2
(x*10/100)*1000= 67
x/10*1000= 67
100x= 67
x=67/100
x=0.67
The points (0, 1), (7, 1), and (2, -3) represent the vertices of a triangle. What is the area, in square units, of the triangle?
Answers
Answer:
14 [tex]u^2[/tex]
Step-by-step explanation:
The attached image shows the diagram of the triangle drawn on the Cartesian plane.
We can see that it has the following measures:
base: [tex]b=7u[/tex]
height: [tex]h=4u[/tex]
the area of a triangle is given by the formula:
[tex]A=\frac{b*h}{2}[/tex]
substituting the values:
[tex]A=\frac{(7u)(4u)}{2}\\ \\A=\frac{28u^2}{2} \\\\A=14u^2[/tex]
the area, in square units, of the triangle is 14
Circle O is shown. Line segments A O and B O are radii. The length of O B is 16 inches. Angle A O B has a measure of StartFraction pi Over 4 EndFraction
In circle O, angle AOB measures radians.
What is the length of arc AB?
π in.
Answers
If you know the angle in radians, then the length of the arc is
(measure of the angle in radians) x (radius of the circle) .
In this circle, we know the angle and we know the radius.
Arc AB = ( π/4) x (16")
Arc AB = 4π inches
Arc AB = about 12.566... inches
Answer:
6 pie correct on edge
Step-by-step explanation:
Simplify
(y + 1)
(y + 1)
Answers
Answer:
That is already at its simplest form.
Step-by-step explanation:
(y + 1)(y + 1) or (y + 1)² is the factored form of y² + 2y + 1. You cannot break it down any further after you reached binomials after you factor unless you are solving for x.
A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?
Answers
Answer:
Height of building is 57.12 m.
Step-by-step explanation:
Let us try to understand the given dimensions as per the attached diagram.
Please refer to attached image (Right angled [tex]\triangle OBT[/tex])
with [tex]\angle B =90^\circ[/tex]
Let O be the point where the Surveyor is standing.
B be the point of the base of building.
T be the point of top of building.
As per question statement,
[tex]\angle O = 55^\circ[/tex]
Side OB = 40 m
To find: Side BT = ?
Using tangent trigonometric identity:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]
So, height of building is 57.12 m.
f(x) = 4x^2 – 4x
Find f(-7)
Answers
Answer:
f(-7)=224
Step-by-step explanation:
[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]
Find the volume of this square
based pyramid.
10 in
12 in
[ ? ]
Answers
Answer:
480 in.^3
Step-by-step explanation:
volume of pyramid = (1/3) * (area of base) * height
Since this pyramid has a square for the base, the area of the base is
A = s^2, where s = length of the side of the square
volume = (1/3) * s^2 * h
volume = (1/3)(12 in.)^2 * (10 in.)
volume = (1/3)(144)(10) in.^3
volume = 480 in.^3
The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.
To find the volume of a square-based pyramid, we can use the formula:
Volume = (1/3) x base area x height.
In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.
First, we calculate the base area of the pyramid, which is the area of the square base:
Base area = side length x side length
= 12 in x 12 in
= 144 square inches.
Now, we can substitute the values into the volume formula:
[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].
Multiplying these values, we get:
[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]
Simplifying the expression, we have:
[tex]Volume = 480\ in^3[/tex].
To learn more about the pyramid;
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Can someone please help me I’m stuck with this question I don’t know what’s the answer please help
Answers
Answer:
the SSS similarity theoremPlease see the attached picture...
Hope it helps...
Good luck on your assignment....
The measures of both
Answers
Answer:
m<EAD=29°
m<CAB=119°
Solution,
< CAE+<EAD+90°=180°( angles on a straight line)
61+<EAD+90°=180°
<EAD=180-(90+61)
=180-151
=29°
<CAB+<FAB=180°( Linear pair)
<CAB+61°=180°
<CAB=180°-61°
<CAB=119°
hope this helps ..
Good luck on your assignment..
Find the height of a cylinder of volume 200cm^3 and radius 4
Answers
Answer:
3.98 cm
Step-by-step explanation:
V= πr²h
V= 200 cm³, r= 4 cm, h=?
h= V/(πr²)= 200/(3.14*4²)= 3.98 cm
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. The point (8, -2) is on the circle. What is the equation of the line that is tangent to the circle at (8, -2)?
Answers
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.
please mark me as brainliest :)
Owen’s grandmother put some money into his savings account on the day he was born. Today, Owen turns 18 years old, and he’s discovered that he has earned $225 in simple interest on his grandmother’s money. If the yearly interest rate was 5%, how much money did his grandmother deposit at the time of his birth?
Answers
Answer:
Step-by-step explanation:
The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.
For us,
p = ??,
r = .05,
t = 18, and
I = 225.
Filling in:
p(.05)(18) = 225 and
.9p = 225 so
p = 250
Answer:
The answer is $250.
Step-by-step explanation:
First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.
Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.
Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.
Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.
Sandy borrowed 6709 R.O from a bank to buy a piece of land. If the bank charges 12 1/3 % compounded each two months, what amount will she have to pay after 2 years and half? Also find the interest paid by her.
Answers
Answer:
she is paying back 9112.5 R.O
Interest paid back is 2,403.95
Step-by-step explanation:
To find the amount, we use the compound interest formula.
This is given as;
A = I( 1 + r/n)^nt
where A is the amount we are trying to calculate
I is money borrowed = 6709
r is the interest rate = 12 1/3% = 37/3 = 12.33% which is same as 12.33/100 = 0.1233
n is the number of times interest is compounded. We have 15 2 months in 2 and a half years
t is the number of years = 2.5
Plugging these values, we have;
A = 6709(1 + 0.1233/15)^(15)(2.5)
A = 6709(1.0082)^(37.5)
A = 9112.95 R.O
Interest is amount - principal( money borrowed)
9112.95 - 6709 = 2403.95
please help me for the brainliest answer
Answers
Answer:
3, 12, 27 and 300
Step-by-step explanation:
Plug n as 1, 2, 3 and 10.
3(1)² = 3
3(2)² = 12
3(3)² = 27
3(10)² = 300
The mean mass of a squad of 19 hockey players is 82 kg. A player of mass 93 kg joins the squad. work out the mean mass of the squad now
Answers
Answer:
82.55kg
Step-by-step explanation:
Calculate the total weight of the 19 hockey players: 19*82=1558kg.
Calculate the total weight of new players: 1558+93=1651kg.
The total number of players added is 19+1=20. Calculate the average weight: 1651/20=82.55kg.
What is the slope-intercept equation of this line
Answers
Answer:
y = -3x + 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope = y2 - y1/x2 - x1
-2 - 4/2-0 = slope
slope = -6/2 or -3
Equation:
y = -3x + 4
Answer:
[tex]y = 4x-3[/tex]
Step-by-step explanation:
y-intercept = b = 4 (because x becomes zero here)
Now, Finding the slope:
Slope = m = [tex]\frac{rise}{run}[/tex]
Slope = [tex]\frac{-2-4}{2-0}[/tex]
Slope = [tex]\frac{-6}{2}[/tex]
Slope = -3
Now putting m and b in the slope intercept equation to get the required form:
=> [tex]y = mx+b[/tex]
=> [tex]y = 4x-3[/tex]
A family needs to build fencing around their rectangular home and square swimming pool, depicted below. A rectangle labeled home has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.
Answers
Answer:
1) 38
2) 160
3) 40
Step-by-step explanation:
Answer:
23, 42, 12
Step-by-step explanation:
Which expression is equivalent to the following complex fraction? StartFraction x Over x minus 3 EndFraction divided by StartFraction x squared Over x squared minus 9 EndFraction StartFraction x minus 3 Over x EndFraction StartFraction x + 3 Over 1 EndFraction StartFraction x + 3 Over x EndFraction StartFraction x Over x + 3 EndFraction
Answers
Answer:
[tex](C) \dfrac{x+3}{x}[/tex]
Step-by-step explanation:
We want to determine an equivalent expression to:
[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]
Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.
[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]
Step 2: Change the division sign to multiplication
[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]
Step 3: Cancel out common terms and simplify
[tex]= \dfrac{x+3}{x}[/tex]
The correct option is C.
The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
Given expression is,
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]
Use factorization, [tex]x^{2} -9=(x-3)(x+3)[/tex]
Now simplify the given expression.
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]
Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
Learn more:
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Which inequality is represented by this graph?
Answers
Answer:
C. y < -1/5x + 1
Step-by-step explanation:
We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.
Pavel and Katie share some sweets in the ratio 3: 8.
Katie gets 32 sweets.
How many sweets does Pavel get?
Answers
Answer:
Step-by-step explanation:
Katie gets 32/8 = 4 lots of sweets
Pavel gets 4 lots x 3 = 12 sweets
9. If y = kx, where k is a constant, and y = -3
when x = 6, what is the value of x when y = 12?
Answers
Hey there! :)
Answer:
x = -24.
Step-by-step explanation:
Plug in the values to find the value of 'k':
-3 = k(6)
Divide both sides by 6 to solve for 'k':
-3/6 = k
k = -1/2
Plug this into the equation to solve for the value of x when y= 12:
12 = -1/2(x)
Divide both sides by -1/2:
-24 = x
x = -24.
Answer:
x would be -24
Step-by-step explanation:
since k is a constant, we have to find out what k is from the equation
. -3=6(k) divide both sides by 6 to get that k is -0.5/-1/2.
then, solve for what x is when y is 12 by setting up the equation 12=(-0.5)x. this would result in x being -24
The numbers x, y and z are successive terms of the arithmetic sequence with a common difference of d=4. What is the sum of these numbers, if the numbers x, y and z+8 are successive terms of the geometric sequence?
Answers
Answer: The sum of the numbers is 3x + 12
Step-by-step explanation: A brief explanation of an arithmetic progression would be useful for a start.
An arithmetic progression (also known as arithmetic sequence) is series of consecutive numbers in which every term in the entire series is determined by adding a common difference to the previous term. In other words, if x and y are two successive numbers in an arithmetic term, y can be determined by adding the common difference to x. Similarly, the term that comes after y is determined by adding the same common difference to y.
As stated in the question, the numbers x, y and z are successive terms of an arithmetic progression, and the common difference is given as 4. This simply means;
y = x + 4
z = y + 4
z = (x + 4) + 4
z = x + 8
The terms x, y and z can now be re-written as follows,
x, x + 4, and x + 8
The sum of these numbers therefore is derived as,
Sum = x + x + 4 + x + 8
Sum = 3x + 12
What is the domain of the step function f(x) = ⌈2x⌉ – 1?
Answers
Answer:
believe its 2x cause 1 was wrong
A car made a trip of 352 miles on 16.8 gallons of gasoline. Which is closest to the number of miles per gallon the car got on that trip?
Answers
Answer: divide both numbers
Step-by-step explanation:
20.95
Find the slope of a line passing through the points (-4,2) and (5,6)
Answers
Step-by-step explanation:
I hope you understand what I did