what is y= - 2 (x-5) ^ 2 + 3 vertex, axis of symmetry, direction of opening, max or min and y intercept
Answers
Answer:
vertex: (5, 3)axis of symmetry: x = 5direction of opening: downwardmax: y = 3y-intercept: -47Step-by-step explanation:
Most of the questions can be answered by comparing the given equation to vertex form.
Vertex formThe vertex form of the equation for a parabola is ...
y = a(x -h)² +k
where 'a' is a vertical scale factor, and (h, k) is the vertex. The sign of 'a' determines whether the parabola opens upward or downward.
Parameter valuesWhen we compare the given equation to the vertex form, we can easily see the values of 'a' and (h, k).
y = -2(x -5)² +3 . . . . . . . given equation
y = a(x -h)² +k . . . . . . . vertex form
The parameters are ...
a = -2, (h, k) = (5, 3)
We notice ...
the sign of 'a' is negativethe vertex is (5, 3)Axis of symmetryThe axis of symmetry is the vertical line through the vertex. It has the equation ...
x = h
x = 5 . . . . equation of the axis of symmetry
Direction of opening, maxThe sign of 'a' is negative. This means that large x-values will result in large negative y-values. The parabola opens downward.
When the curve opens downward, it means the vertex is the highest point on the curve. The maximum is the y-value of the vertex: k. There is no minimum.
The maximum is y = 3.
Y-interceptThe y-intercept is where the graph crosses the y-axis. It can be found by setting x=0, and computing the value of y:
y = -2(0 -5)² +3
y = -2(25) +3 = -50 +3
y = -47 . . . . the y-intercept.
The ordered pair for the point there is (0, -47).
__
We show the graph so you can see how these features relate to the shape of the graph and points on it.
Related Questions
Given: A, C, and F are collinear
Prove: measure of angle s= measure of angle x+measure of angle y
Answers
m∠x+m∠r+m∠y=180° (angles in a triangle add to 180°)
m∠r+m∠s=180° (angles that form a linear pair add to 180°)
m∠x+m∠r+m∠y=m∠r+m∠s (Transitive property of equality)
m∠x+m∠y=m∠s (subtraction property of equality)
m∠s=m∠x+m∠y (symmetric property of equality)
On a coordinate plane, parallelogram A B C D, parallelogram A prime B prime C prime D prime, and parallelogram A double prime, B double prime, C double prime, D double prime are on the graph.
In the pre-image of the parallelogram, the slope of AD is −3 and the slope of BC is −3. The image is translated down 7 units and then reflected over the y−axis.
The slope of A"D" is
.
The slope of B"C" is
.
What can you determine about the line segments A"D" and B"C"?
Answers
Using translation concepts, we have that:
The slope of A"D" is of 3.The slope of B"C" is 3.The lines are parallel.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
When the function is translated down, the slope remains constant, while when the function is reflected over the y-axis, the slope is multiplied by -1, hence both lines will have a slope of 3, and since they have the same slope, they are parallel.
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in triangle abc and triangle def angle a=angle d and angle b= angle e and ab=ef. will the 2 triangles be congruent ? justify your answer
Answers
Answer:
Step-by-step explanation:
no, you don't have the measure of at least one side, so having the same angles is similar but not congruent
Write a proof
given: angle 1 and angle 3 are supplementary
prove: m is parallel to n
Answers
sorry just wanted to see if the bold thing works
Sam is installing a walkway around a rectangular flower patch in his garden. The flower patch is 12 feet long and 6 feet wide. The width of the walkway is x feet. Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width. What does represent in this function
Answers
In the function, the thing that is represented is the area of the walkway along the length of the flower patch.
How to illustrate the function?From the information given, Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width.
Therefore, the thing that is represented is the area of the walkway along the length of the flower patch.
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look at the pic below an help pls
Answers
Answer:
y=2/3(x-3)^2+1
Step-by-step explanation:
The parent function of a parabola is y=x^2:
The transformation of this graph shows the parabola is shifted to the right 3 and up 1 so we apply that to our equation y=(x-3)^2+1
to solve the stretch factor:
y=a(x-3)^2+1
we can see when x=0 y=7 so we use this set
7=a(0-3)^2+1
7=a(-3)^2+1
-1 -1
6=9a
divide by 9
a=2/3
Evaluate the following expressions by substituting s = 20 and t = 6
s - 0.2t2
12.5
10.8
12.8
18.8
Answers
Answer:
The answer will be the 3rd option, 12.8
Step-by-step explanation:
I'm gonna assume that since you copy and pasted the question, the equation is actually s - 0.2t^2
Now we just need to substitute the values with their respective ones.
20 - 0.2(6)^2
Now we just have to solve :)
20 - 0.2(6)^2
= 12.8
So the answer will be the 3rd option, 12.8
Hope this helped! :D
What is the approximate total length of iron edging needed to create the square frame and the two diagonals? 43.5 inches 50.9 inches 54.0 inches 61.5 inches
Answers
Total length of iron edging needed to create the square frame is 43.5 inches
Important properties of square:
All four interior angles are equal to 90°
All four sides of the square are congruent or equal to each other.
The opposite sides of the square are parallel to each other.
The diagonals of the square bisect each other at 90°
The two diagonals of the square are equal to each other.
Diagonal of square = [tex]\sqrt{2}[/tex]a
9 = [tex]\sqrt{2}[/tex]a
a = [tex]\frac{9}{\sqrt{2}}[/tex]
a = 6.36 inches
Iron edging needed to create the square frame = 4*6.36 = 25.44 inches
iron edging needed to create two diagonals = 2*9 = 18 inches
total length = 18 + 25.44
= 43.44 ~ 43.5 inches
Thus, Total length required is 43.5 inches
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If you vertically stretch the exponential function f(x) = 2* by a factor of 4, what
is the equation of the new function?
A. g(x) = 2.4*
OB. g(x) = 24x
OC. g(x)=1.2*
OD. g(x)=4-2*
Answers
If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x
Vertical stretch of a functionExponential function is written in standard form as y= ab^x
where
a is the base
x is the exponent
Given the following exponential function f(x) = 2^x. If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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What is the L.C.M of: 6(a+b)+3
Answers
Answer:
I hope this is the right answer
We used these functions to represent the two sides of the equation:
f(x) = 3x
g(x) = 4x + 1
Graph the functions y = f(x) and y = g(x) on the same coordinate plane.
Answers
The solution to the system of equation graphed is (-1, -3)
Solution to system of equationGiven the system of equations graphed on the plane expressed as:
f(x) = 3x
g(x) = 4x + 1
Equate
f(x) = g(x)
3x = 4x + 1
3x - 4x = 1
-x = 1
x = -1
Determine the value of y
y = 3x
y = 3(-1)
y = -3
Hence the solution to the system of equation graphed is (-1, -3)
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is 7.666 a rational number
Answers
Answer:
Yes, it's a rational number
Step-by-step explanation:
I need help pls WILL GIVE BRAINLIEST
Answers
Answer: (3,-2)
Step-by-step explanation:
[tex]-3x-7y=5\\15x+6y=33[/tex]
[tex]5(-3x-7y)=5(5)\\-15x-35y=25[/tex]
new system:
[tex]-15x-35y=25\\15x+6y=33[/tex]
add.
[tex]-29y=58\\y=-2[/tex]
plug in -2 for y
[tex]-3x-7(-2)=5\\-3x+14=5\\-3x=-9\\x=3[/tex]
system:
[tex](3,-2)[/tex]
Answer:
(3, - 2 )
Step-by-step explanation:
- 3x - 7y = 5 → (1)
15x + 6y = 33 → (2)
multiplying (1) by 5 and adding to (2) will eliminate x
- 15x - 35y = 25 → (3)
add (2) and (3) term by term to eliminate x
0 - 29y = 58
- 29y = 58 ( divide both sides by - 29 )
y = - 2
substitute y = - 2 into either of the 2 equations and solve for x
substituting into (2)
15x + 6(- 2) = 33
15x - 12 = 33 ( add 12 to both sides )
15x = 45 ( divide both sides by 15 )
x = 3
solution is (3, - 2 )
I need answer quickly
Answers
Answer:
4.47
Step-by-step explanation:
4^2+b^2=6^2
16+b^2=36
-16. -16
√b^2=√20
b=4.47
Simplify
50(x^2+7x+6)
Answers
Distribute [tex]50[/tex] to every term inside the parentheses.
[tex]50\cdotx^2+50\cdot7x+50\cdot6[/tex]
Simplify with multiplication.
[tex]\huge\boxed{50^2+350x+300}[/tex]
You can't simplify further by adding, so leave the answer as-is.
Answer:
50x^2 + 350x + 300
Step-by-step explanation:
Original Equation:
50(x^2+7x+6)
Distribute 50 to all 3 #'s:
50x^2 + 350x + 300
Simplify the radical. What is the number under the radical sign when it is simplified? Do not rationalize the denominator. ∛-27/81. Please help asap^^
Answers
Answer:
[tex]-\frac{1}{\sqrt[3]{3}}[/tex]
Step-by-step explanation:
To do this we can ask ourselves "What number multiplied three times by itself is _____?" In this case we have -27 and 81. We see that -3*-3*-3=-27. We also see that 3*3*3*3=81. This means that [tex]\sqrt[3]{-27}=-3,[/tex] and [tex]\sqrt[3]{81} = 3\sqrt[3]{3}.[/tex]
The fraction we get is [tex]\frac{-3}{3\sqrt[3]{3} }[/tex], and we can simplify to get [tex]-\frac{1}{\sqrt[3]{3}}[/tex].
Taseem’s loose change consists of dimes and quarters. When you ask her how many of each type of coin she has, she gives you the following clues: 0.1x+0.25y=19.9 and x+y=100 What can you conclude? Select all that apply.
Answers
The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
0.1x + 0.25y = 19.9 and
x + y = 100
Let x = number of dimes
y = number of quarters
After solving the above system of equations by substitution method.
[tex]\rm \dfrac{398-5y}{2}+y=100[/tex]
y = 66
[tex]\rm x=\dfrac{398-5\cdot \:66}{2}[/tex]
x = 34
Thus, the statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
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There are two conditions under which we can assume that the sample means follow a normal distribution. What are they
Answers
Two conditions under which we can assume that the sample means follow a normal distribution are as follows:
1). If the sample size is large enough, n greater than or equals 30, the sampling distribution is approximately normal regardless of the shape of the population.
2). In order to be considered a normal distribution, a data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean.
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Can someone help out on this please I’m having trouble
Answers
Answer:
Step-by-step explanation:
Find the product of (x − 5)2. (1 point) Group of answer choices x2 + 10x + 25 x2 − 10x + 25 x2 − 25 x2 + 25
Answers
Answer:
[tex]x^2 - 10x + 25[/tex]
Step-by-step explanation:
Hello!
Expand the square using the Distributive Property.
Expand[tex](x - 5)^2[/tex][tex](x - 5)(x-5)[/tex]Distributive x - 5 to each factor
[tex]x(x - 5) -5 (x - 5)[/tex][tex]x^2 - 5x - 5x+25[/tex][tex]x^2 - 10x + 25[/tex]The answer is [tex]x^2 - 10x + 25[/tex].
We can also use a special binomial product formula.
Formula: [tex](a - b)^2 = a^2 - 2ab + b^2[/tex]
[tex](x - 5)^2 = x^2 - 2(x)(5) + 5^2[/tex][tex](x - 5)^2 = x^2 - 10x + 25[/tex]We get the same answer both ways.
solve the inequality
8x - 3 ≥6x + 4
Answers
Answer:
Hello! The answer is x ≥ [tex]\frac{7}{2}[/tex].
Step-by-step explanation:
To solve this inequality, we have to get x by itself. To do so, we will rearrange the inequality. To do so, we will subtract 6x from both sides and add 3 to both sides:
8x - 3 ≥ 6x + 4
-6x +3 -6x +3
----------------------
2x ≥ 7
Now, we have to get x by itself and divide both sides by 2 to do so:
2x ≥ 7
-- --
2 2
This leaves us with:
x ≥ [tex]\frac{7}{2}[/tex]
The required solution to the inequality 8x - 3 ≥6x + 4 is x ≥ 3.5.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To solve the inequality, we want to isolate the variable x on one side of the inequality symbol.
8x - 3 ≥ 6x + 4
Subtract 6x from both sides:
2x - 3 ≥ 4
Add 3 to both sides:
2x ≥ 7
Divide both sides by 2:
x ≥ 7/2
Therefore, the solution to the inequality is x ≥ 3.5.
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The sum of two numbers is 79. Three times the first number added to 5 times the second number is 283. What are the two numbers?
Answers
Answer:
The two numbers are 56 and 23.
Step-by-step explanation:
Let the two numbers be A and B.
We are told that:
A+B = 79, and
2) 3A + 5B = 283
Rearrange the first expression to isolate A:
A = 79-B
Now use this value of B in the second expression:
3A + 5B = 283
3(79-B) + 5B = 283
237-3B + 5B = 283
2B = 46
B = 23
If B=23, we can find A from (1):
A+B = 79
A+23 = 79
A = 56
CHECK:
Does A+B = 79?
56 + 23 = 79? YES
Does 3A + 5B = 283?
3(56) + 5(23) = 283?
168 + 115 = 283? YES
Write an expression for cotA
Answers
Answer:
[tex]cotA=\frac{2x}{5}[/tex]
Step-by-step explanation:
Answer:
[tex]\text{cotA} =\frac{2x}{5}[/tex]
Step-by-step explanation:
cotA = (Adjacent side) ÷ (Opposite side)
The measure of the Adjacent side = 2x
The measure of the Opposite side = 5
Then
[tex]\text{cotA} =\frac{2x}{5}[/tex]
Pls help solve i will mark branliest
Answers
Answer:
1.875 liters
Step-by-step explanation:
x=1.25×32=3.752=1.875 liters
2. On Friday, the Lee family had dinner at a
restaurant. They ordered 12 cheeseburgers and
4 chili bowls for $19.40. The following Friday,
the Lee family went back to the same restaurant.
They ordered 8 cheeseburgers and 6 chili bowls
for $16.60. How much does a cheeseburger
cost?
Answers
Answer:
cheeseburger costs $1.25
Step-by-step explanation:
let x be the cost of a cheeseburger and y the cost of chilli and set up 2 simultaneous equations, that is
12x + 4y = 19.4 → (1)
8x + 6y = 16.6 → (2)
multiplying (1) by 6 and (2) by - 4 and adding the result will eliminate y
72x + 24y = 116.4 → (3)
- 32x - 24y = - 66.4 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 50
40x = 50 ( divide both sides by 40 )
x = 1.25
the cost of a cheeseburger is $1.25
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
Answers
The percentage given shows that the amount is decreasing by 8%.
How to illustrate the information?From the information given, the function is f(x) = 9,628(0.92)x. This illustrates that the amount is decreasing by 8% she compared to the previous year. This was computed as:
= 1 - 0.92
= 0.08
= 8%
For part B, the percentage change will be:
= (8,972 - 8,074.80)/8972 × 10
= 10%
Therefore, the account recorded a greater percentage change in amount of money over the previous year is account B as 20% is lore than 8%.
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Is this a function?
yes
no
Answers
help me please i dont understand this
Answers
Answer:
It is not a function
Step-by-step explanation:
A function refers to a set of points/lines with this characteristic:
Each Y value has only one corresponding X value.
Meaning one X value cannot have multiple Y Values.
In this case, the X value of 2 has 2 different Y values, making it not a function.
2. A person takes a loan of Rs 100 000 at an interest rate of 4.2% compounded annually and deposits it in a bank that pays 8% interest compounded annually. What is the profit of his investment after 2 years?
Answers
The profit of his investment after 2 years is $8,063.60.
What is the profit of his investment?The profit earned is the difference between the amount he earned from the deposit at the bank and the interest paid on the loan.
Total value of the loan in 2 years : 100,000 x (1.042²) = 108,576.40
Total value of the amount deposited in 2 years : 100,000 x (1.08²) = 116,640
Difference = 116,640 - 108,576.40 = $8,063.60
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