When the completing the square is applied, the rewritten function is (x + 2)^2 = 4
How to complete the square?The equation is given as:
x^2 + 4x = 0
The above equation is a quadratic equation and the coefficient of x in the above equation is 4.
So, we have:
k = 4
Divide the variable k by 2
k/2 = 4/2
k/2 = 2
Square the above result
(k/2)^2 = 4
Next, we add 4 to both sides of x^2 + 4x = 0
x^2 + 4x + 4 = 4
Expand the equation by expressing 4x as 2x + 2x
This gives
x^2 + 2x + 2x + 4 = 4
Factorize the above equation
x(x + 2) + 2(x + 2) = 4
Factor out x + 2 from the above equation
(x + 2)(x + 2) = 4
Rewrite the equation as a perfect square of (x + 2)
(x + 2)^2 = 4
Hence, the rewritten function after completing the square is (x + 2)^2 = 4
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Select the correct answer.
What is the zero of the function represented by this graph?
x = 5
x= -6
x=-5
x=6
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the explanation ~
Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.
That is :
The point where it cuts the x - axis, it has an x - coordinate = -6
Therefore, we can conclude that The zero of given function is -6
Answer:
x = -6.
Step-by-step explanation:
It is where the graph cuts the x-axis (where the function is zero).
That is -6.
Help me please, I'm stuck
Answer:
Gradient: 5
y-intercept: (0, 15)
Step-by-step explanation:
The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.
One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
Shawn graphed the points listed below.
(0, 0) (1, -1) (3, 0) (4, 4) (4, 5) (5, 4) (6, -2)
Which pair of points could be used to show that the points Shawn graphed do not represent a function?
A. (4, 4) and (4, 5)
B. (4, 4) and (5, 4)
C. (0, 0) and (3, 0)
D. (1, -1) and (6, -2)
Answer: A. (4, 4) and (4, 5)
Step-by-step explanation:
The same x value maps onto more than one y value.
Can the sides of a triangle have lengths 2, 4, and 7?
Answer:
No, they can't
Step-by-step explanation:
According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.
2+4= 6<7
As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.
2+7=9>4
4+7=11>2
A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
A possible critical point of the function f(x) is given by: (0,-2)
What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the function can change from decreasing to increasing, or vice-versa.
For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).
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percentage of 67 of 98
The percentages of 67 of 98 is 68.36%
Percentages and fractionsFractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.
Fraction of 67 of 98 = 67/98
Percentage = 67/98 * 100
Percentages = 6700/98
Percentages = 68.37%
Hence the percentages of 67 of 98 is 68.36%
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increase $32 in the ratio 2:5
decrease 54 litter in the ratio 5:1
Answer:
Step-by-step explanation:
32 = 2 : 5
32/7 = 4
2 x 4 : 4 x 5
8 : 20
What is the explicit formula for this sequence?
-9,-3,3,9,15
Answer: A
Step-by-step explanation:
Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.
In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A
which whole number is equal to the fraction 42/6
Answer:
7.
Step-by-step explanation:
Think of 42/6 as a division question.
42 ÷ 6.
The answer to this equation is 7.
Ed wants to buy a new video game system which costs $250. he has
saved $135. ed charges $9 for each lawn he mows. which equation could
be used to find the number of lawns, x, ed must mow to have more than
the amount he needs to buy the video game system?
The required equation is 135 + 9x > 250.
The number of lawns Ed must mow is assumed to be x.
The amount Ed charges for each lawn he mows is $9.
Thus, the total amount Ed earns by mowing x lawns = $9x.
The savings which Ed has is $135.
Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).
The cost of the video game is given to be $250.
We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.
This can be shown as the equation:
Total amount Ed has > Cost of the video game,
or, 135 + 9x > 250.
Thus, the required equation is 135 + 9x > 250.
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need help with the y value
Answer: 12x
Step-by-step explanation:
The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.
For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.
Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,
[tex]y=12x[/tex]
If we use any x on the left, it's corresponding height will be the y.
Please help em fast I really need help
lf ƒ(x) = 2(x + 1)² and g(x) = 3x- 2 determine f[g(2)]
Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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the area of a rectangle is (16x^2 - 9y^2) square units
Determine the slope of the line.
The slope of the line is - 3 / 2 .
How to find slope?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, using (0, 6)(4, 0)
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
slope = 0 - 6 / 4 - 0
slope = -6 / 4
slope = - 3 / 2
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WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
B
Step-by-step explanation:
Let t and d be their ages now.
2 years ago, their ages were t - 2 and d 2.
Now, Tyler is 3 years older than David: t = d + 3
2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)
The system of equations is:
t = d + 3
t - 2 = 4(d - 2)
Answer: B
Answer:
D
Step-by-step explanation:
Answer this please !
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
If my mother has 5 boys and my father has 4 girls, what is the probability of one being a boy?
Answer:
5/9
Step-by-step explanation:
4+5=9 and there are 5 boys
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
the following 3 equations are equivalent :
• x + 1 = 4
• 2 + x = 5
• -5 + x = -2
Step-by-step explanation:
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
-5 + x = - 2
Let’s take this equation :
x + 1 = 4
=======
By Adding 1 to both sides of the equation we get :
x + 1 + 1 = 4 + 1
⇔ x + 2 = 5
⇔ 2 + x = 5
Then the equations x + 1 = 4 and 2 + x = 5 are equivalent.
…………………………………………………………………
On the other hand ,if we subtract 6 from both sides
of the equation x + 1 = 4 we get :
x + 1 - 6 = 4 - 6
⇔ x - 5 = -2
⇔ -5 + x = -2
Then the equations x + 1 = 4 and -5 + x = -2 are equivalent.
Answer:
A. 2 + x = 5
B. x + 1 = 4
E. -5 + x = -2
Step-by-step explanation:
right on edg, hope it helps ya'll.
Factorize the expressions 8a⁶ + 5a³ + 1.
Use a³+b³ +c³ - 3abc
Here a = 2a²
b= -a
And c = 1
Answer:
Step-by-step explanation:
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
the graph below could be the graph of which exponential function?
The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.
How to interpret the graph?Mathematically, the standard form of an exponential function is given by:
F(x) = ab^x
Where:
a is the initial value of an exponential function.b is the growth rate.As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)
By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).
F(x) = 3.(1.2)^x
Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.
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The number of visitors to the homepage of an online magazine can be modeled by the equation y = 1100.74x − 1976.47, where x = 5 represents the year 2005 and y represent the total number of visitors.
FIRST ONE GETS BRAINLIEST OR 5 STARS
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Let y represent the total number of visitors x years since 2000. Hence:
y = 1100.74x - 1976.47
In the year 2005 (x = 5):
y = 1100.74(5) - 1976.47 = 3527.23
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
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the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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Draw a line segment of length 6.4 cm and divide it in to 4 equal parts.
Write the length of each part.
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The line segment has a length of 6.4 cm. Hence:
Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
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Please help and explain how to solve
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
Point Y is the circumcenter of ΔDEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. The length of F Y is 3 x + 7 and the length of Y E is 5 x minus 3.
Find FY.
5
11
17
22
The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.
What is the Circumcenter of a Triangle?The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.
Based on the definition of the circumcenter, and Y is the circumcenter, therefore:
YE = FY
Plug in the values
5x - 3 = 3x + 7
5x - 3x = 3 + 7
2x = 10
x = 5
FY = 3x + 7 = 3(5) + 7
FY = 22 units.
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Answer:
D
Step-by-step explanation:
PLEASE ANSWER QUICKLY
Answer:
Option (4)
Step-by-step explanation:
See attached image.
can someone please help me
Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.
How to find the value of a trigonometric functionHerein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:
[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]
[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]
sin θ ≈ - √731 / 30
Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.
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