The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution to the equation is x = -5,7/1. Similarly , the vertex for the given equation [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].
What is parabola?The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).
What is vertex of a parabola?A parabola's vertex is the location where its symmetry line and parabola intersect.
The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:
[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]
For the first equation: [tex]y = x^2 + 5x - 7[/tex]
The vertex would be:
[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]
So the vertex is [tex](-2.5,-4.25)[/tex]
For the second equation:[tex]y = -x^2 + 3x + 8[/tex]
The vertex would be:
[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]
So the vertex is [tex](-3/2,1/4)[/tex]
To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.
[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]
Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4
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A rope is fixed between two trees that are 10 metres apart. When a child hangs on to the centre of the rope, it sags so that the centre is 2 metres below the level of the ends. Find the lenth of the rope.
The length of the rope is 2√29 meters.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Given that the distance between two trees is 2 meters. A boy hangs on a rope tied to the trees in the middle of the rope.
it sags so that the center is 2 meters below the level of the ends.
Thus it forms an isosceles triangle. △ACD and △BCD are two right triangles.
Since △ABD is isosceles triangle and AD = BD.
In △ACD, Hypotenouse = AD, Base = AC = 10/2 = 5 cm, Height = CD = 2 meters
Apply Pythagorean theorem on △ACD:
AD² = AC² + CD²
AD² = 5² + 2²
AD² = 29
AD = √29
Therefore, BD = √29
The length of the rope is AD + BD = 2√29 meters.
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p(d+z)=2z+3 solve for d
Answer:
D= 2z/p + 3/p = -z
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ME THIS QUESTION
PLEASE
ILL GIVE BRAINLIEST IF ITS RIGHT
Answer:
142 degrees
Step-by-step explanation:
d-c is 90 degree angle so you add that to the 52 degree
Which graph represents the solution to the inequality 3 < 2- x/3 <7/2
Answer:
C
Step-by-step explanation:
Please Help!
I need this for an important Test
You will be deeply appreciated
Steve wants to open a savings account. Bank A will increase the interest rate on the savings account by
1/5% after the first year he is a customer. Bank B offers an interest rate increase of 0.25% after the first year he is a customer. Which bank has the higher interest rate increase? Explain how you were able to compare the rates. i need help asap please help
Answer:
Bank A
Step-by-step explanation:
Get them wrong then push try agian and remember it hope it helps?
thats my trick sometimes!
Find the value of the expression below for r= 4 and t = 2.
2-r+20=r
09
072
06
040
Answer: 8-4+5
Step-by-step explanation: Best I could do
HELP DUE IN 15 MINS!
Assume that any lines that appear to be tangent are tangent.
x=??
Answer:
x = 156
Step-by-step explanation:
Yes. The comment was correct.
The central angle and the Arc measurement are the same amount (in degrees)
So The entire circle is 360 degrees.
Answer = 360 - the two central angles.
Answer = 360 - 65 - 139
Answer = 360 - 204
Answer = 156
Ben Nevis has a height of approximately 1300 metres above sea level.
Assuming that temperature decreases by 1°C for every 100 metres above
sea level, work out the temperature at the summit of Ben Nevis when the
sea level temperature is 5°C.
The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
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work out the size of angle x
Answer:
[tex]13^{\circ}[/tex]
Step-by-step explanation:
Consider the smaller of the two triangles with angle [tex]x[/tex].
Using vertically opposite angles, one of the angles of this triangle is [tex]85^{\circ}[/tex].
Using corresponding angles combined with angles on a straight line, one of the angles is [tex]82^{\circ}[/tex].
Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]x=13[/tex].
3. Geese and Pigs: A farmer raises only geese and pigs. She wants to raise no more than
16 animals total including no more than 10 geese. She spends $5 to raise a goose and $15 to raise a pig, and has $180 available for this project. Find the maximum profit she can make if each goose produces a profit of $6 and each pig a profit of $20.
The maximum profit she can make if each goose produces a profit of $6 and each pig a profit of $20.
How can you determine the table's maximum profit?Making the Most of Total Revenue and Total Cost Data. Just multiply the price by the quantity at each quantity to find the company's total revenue. Next, deduct the company's total cost at each quantity, which is provided in the table.
Let the number of geese be x and the number of pigs be y
From the given information, we can form the following inequalities:
x ≤ 10
y ≥ 05
x + 15y ≤ 180
Maximize 6x + 20y.
We want to find the intersection points of the first three equations since x and y are bounded within the area under these
These points are (0,0), ( 10,0), (0,12), (10,65/3).
At (0,0) , the profit is $0
At ( 10,0), the profit is $60
At (0,12) , the profit is $240
At (10,65/3) , the profit is $499.33
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What is the inverse of f(x) = -6(x-2)?
please help <3
Answer:
The answer is number 2. f^-1(x)= 2- x/6
Step-by-step explanation:
Just is
Help!?!?!?!??!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Answer d) looks good
D. [tex] \frac{21 \: b}{10} - 48[/tex] ✅
Step-by-step explanation:
[tex] - 6( \frac{1}{4} b+ 10) + 4( \frac{9}{10}b + 3) \\ = \frac{ - 6 \: b}{4} - 60 + \frac{36 \: b}{10} + 12 \\ = \frac{ - 3 \: b}{2} + \frac{18 \: b}{5} - 60 + 12 \\ = \frac{ - 3 \: b \times 5}{2 \times 5} + \frac{18 \: b \times 2}{5 \times 2} - 48 \\ = \frac{ - 15 \: b + 36 \: b}{10} - 48 \\ = \frac{21 \: b}{10} - 48[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
-1, 0, 4
Step-by-step explanation:
2f - 8 ≤ 6f + 4
-4f ≤ 12
f ≥ 12/-4 **flip the inequality when you divide by a negative number
f≥ -3
Check all the answers that are ≥ -3
find the value of x .
9514 1404 393
Answer:
x = (23 1/3)°
Step-by-step explanation:
The sum of angles in a triangle is 180°.
40° +2x +4x = 180°
6x = 140° . . . . . . . . . . . subtract 40°
x = 140°/6 = (23 1/3)° . . . . divide by the coefficient of x
_____
This makes the angles be 40°, 46.67°, and 93.33° (rounded to hundredths).
SOMEBODY PLEASE GIVE ME THE ANSWERS! I AM GIVING AWAY A LOT OF POINTS!
Answer:
nice to see you again
Step-by-step explanation:
14.) 20
15) 16
16) true
Answer:
20, 16, true
Step-by-step explanation:
The input is the number of rides, or the x-coordinate. The output is the dollars remaining on card, or the y-coordinate. We know this because the number of rides dictates how much money is on the card.
14. The question is asking for the output when the input is ten. Thus, we need to find the y-coordinate on the line when the x-coordinate is 10. We see that (10,20) is on the line, so then our output (or y-coordinate) is 20.
15. The question is asking for the input when the output is five. Thus, we need to find the x-coordinate on the line when the y-coordinate is 5. We see that (16,5) is on the line, so then our input (or x-coordinate) is 16.
16. 7 rides is the x-coordinate, and 27.50 is the cost, or the y-coordinate. However, this is true because even though the y-coordinate is NOT the cost of the rides, but the amount of money remaining on the card AFTER the rides are cashed in, 27.50 is half of 45 dollars, so then if 27.50 is spent on the rides, there will still be 27.50 left over on the card. Thus, it is true.
Use the Distributive Property to simplify the expression 9(2n+1)
Answer:
18n+9
Step-by-step explanation:
9 times 2n is 18n.
9 times 1 is 9.
There's your answer.
Answer:
[tex]\huge\boxed{\bold{18n+9}}[/tex]
Step-by-step explanation:
Hi there!
Let's simplify this expression!
All we should do is "distribute" 9:
[tex]\bold{9(2n+1)}[/tex]
[tex]\bold{18n+9}[/tex]
Hope it helps!
[tex]\rm{Have~A~nice~day![/tex]
~Just a teenage girl willing to help
[tex]\bold{Besties4Ever}[/tex]
Which expression is equivalent to (-3) × (-3)²?
Answer:
[tex] \sf \: (-3) × {( - 3)}^{2} = - 27[/tex]
Step-by-step explanation:
Given expression,
→ (-3) × (-3)²
Let's simplify the expression,
→ (-3) × (-3)²
→ (-3) × ((-3) × (-3))
→ (-3) × 9
→ (-3 × 9) = -27
Hence, the answer is -27.
Given: 2x−43=2
Prove: x = 5
Select from the drop-down menus to correctly complete the proof.
Statement Reason
2x−43=2 Given
2x−4=6
Choose...
2x = 10
Choose...
x = 5
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Given : 2x-4=6
To prove x =5
Thus,
We have to find the value of x
=> 2x =10
=> x =10/2
=> x =5
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
18x - 9 = 72 and x = 4.5 represents the same value as 3/5(30x - 15) =72.
What is equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions
The sign that connects these two expressions is “=”.
Given
x = 4.5
And equation
3/5(30x - 15) =72
Simplifying
90x/5 - 45/5 = 72
18x - 9 = 72 -----------(a)
18x = 81
x = 81/18
x = 4.5 ------------(b)
Equation (a) and (b) are among the equations given in the options.
Hence, from the above calculation equations 18x - 9 = 72 and x = 4.5 express the same value of x as 3/5(30x - 15) =72 .
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Need help with math triangle question in image. Thank you
What must be added to the polynomial 2x³ 3x² 8x so that it leaves a remainder 10 when divided by 2x 1?
To find the remainder 10 when dividing 2x³ 3x² 8x by 2x 1, the polynomial must be augmented with -12.
What is polynomial?A polynomial is an expression that consists of variables, exponents, and coefficients. It is a mathematical function composed of two or more terms, each of which is a number or a variable multiplied by an exponent. It can be used to represent a variety of relationships in mathematics, including equations, linear functions, quadratic functions, and more.
Therefore, the polynomial that will leave a remainder 10 when divided by 2x 1 is 2x³ 3x² 8x -12.
This is because if we divide the polynomial by 2x 1, the remainder will be the last term of the resulting polynomial, which is -12.
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In order to visit the Museum of Mathematics, Ascend requires `2` chaperons for every `5` students. If the school has `210` people going in total, how many students are going to the Museum?
Answer:
150
Step-by-step explanation
What are the two types of angles?
The two types of Angles of the triangle are Acute Angle ( angle that are less than 90 degree) and Obtuse Angle ( angle between 90 and 180 degree ).
What are Angles ?
The Angle is defined as the geometrical shape that is constructed by joining two rays to each other at their end points.
The two types of angles of the triangle are Acute Angle and Obtuse Angle :
(i) Acute Angle :
An angle can be called as Acute if the measure of the angle is less than 90 degree .
(ii) Obtuse Angle :
an angle can be called as Obtuse if the measurement of the angle is greater than 90 degree and less than 180 degree .
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A rectangular patio has a volume of 360 cubic feet. If the width is 8 feet and the length is 15 feet, what is the height of the patio stones?
Answer:
3 feet
Step-by-step explanation:
Volume of a rectangular object = length x width x height
360 = 8 x 15 x height
360 = 120 x height
height = 360 / 120
height = 3ft
[tex]{x}^{2} + x - 2[/tex]
solve this with first X last method
Answer:
[tex]x=-2,1[/tex]
Step-by-step explanation:
[tex]x^2+x-2=0\\(x+2)(x-1)=0\\x_1=-2,x_2=1[/tex]
How do you find the sides of a 45 45 90 triangle when given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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How can you differentiate best time worst time and average time of an algorithm?
You can differentiate best time, worst time and average time of an algorithm like this:
Best time = fastest completion time with optimal inputs.
Worst time = slowest completion time, with pessimistic inputs.
Average time = arithmetic mean
What is Average case?The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.
There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.
Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.
Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.
What is average case complexity
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How to do log2 in Excel?
The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.
For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
Next, since we have the multiplication sign, we use the addition law:
The power of the number becomes the product of the log, so we have:
When you have the same base and number, the result is always 1.
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What are 3 completed examples for functions?