The vertex form of the Quadratic equation is y = [tex](x-3)^{2}[/tex] +5. The vertex is (3, 5), which is a maximum point.
what is a quadratic equation?A quadratic equation is an algebraic equation with the power of its variable 2.
it can be written in standard form which is called vertex form or in the general form.
Analysis:
y = [tex]x^{2}[/tex] -6x +14
y = [tex]x^{2}[/tex] -6x +9 +5
Simplifying this perfect square expression y = [tex]x^{2}[/tex] -6x +9
y = [tex]x^{2}[/tex] -3x -3x +9
y = x(x-3) -3(x-3) + 5
y = (x-3)(x-3) +5
y = [tex](x-3)^{2}[/tex] + 5
In conclusion, the Vertex form of the equation is y = [tex](x-3)^{2}[/tex] + 5
Learn more about quadratic equation: brainly.com/question/1214333
#SPJ1
One-quarter of the counters in a tub are red. The rest of the counters are green. If there are 48 green counters, how many red counters are there?
There are 16 red counters there.
Fractions and proportionsIf one-quarter of the counters in a tub are red and the rest are green, then there are three-quarter of the counter in the tub.
Let the total counter be x such that
3/4x = 48
3x = 4 * 48
x = 4 * 16
x = 64
Determine the amount of red counter
Red counter = 64 - 48
Red counter = 16
Hence there are 16 red counters there.
Learn more on proportion here; https://brainly.com/question/1496357
#SPJ1
When doing his homework, a student uses the addition property of equality to solve for c below. Which statement BEST applies to the sample? 6 + c = 10 6 + (–6) + c = 10 + (–6) c = 4 A. The student failed to keep both sides of the equation balanced. B. The student’s final answer does not have the variable c isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have used the subtraction property of equality.
Answer:
The answer would be C
NOTE: Angles not necessarily drawn to scale.
Answer:
60
Step-by-step explanation:
I'm assuming that ED is an exactly straight line, that would mean the angle is 180 degrees. So the sum of the angles in between should also equal 180. This gives you the equation
100 + 20 + x = 180
120 + x = 180
60 = x
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Using the triangle midsegment theorem, x = 5; BC = 10 units.
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, ED = 1/2(BA).
Given the following:
ED = x + 2
BA = 4x - 6
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BC = 2(BE)
BC = 2(x)
BC = 2(5)
BC = 10 units
Learn more about the triangle midsegment theorem on:
https://brainly.com/question/12234706
#SPJ1
Answer:
D
Triangle Midsegment
5
10
Step-by-step explanation:
E2020 Geometry B!!:3
question on the image
Let [tex]x,y[/tex] be the legs of the triangle, with [tex]x[tex]\mathrm{area}_{\rm square} = y^2[/tex]
[tex]\mathrm{area}_{\rm triangle} = \dfrac12 xy[/tex]
The square has 3 times the area of the triangle, so
[tex]y^2 = \dfrac32 xy[/tex]
Meanwhile, in the triangle we have
[tex]\tan(\theta) = \dfrac xy[/tex]
Now,
[tex]y^2 = \dfrac32 xy \implies \dfrac23 = \dfrac xy \implies \boxed{\tan(\theta) = \dfrac23}[/tex]
Solve the equation
(6x18) (3x + 2) = 0
Answer:
[tex] - \frac{2}{3} [/tex]
Step-by-step explanation:
Given (6x18)(3x+2) = 0
[tex]108(3x + 2) = 0 \\ 324x + 216 = 0 \\ 324x = - 216 \\ x = \frac{ - 216}{324} \\ = - \frac{2}{3} [/tex]
Which of the following represents a function
Answer:
(2,3),(4,3),(-2,-3),(-4,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.
A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.
In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
Consider the function f(x)=1/3(6)x. What is the value of the growth factor of the function?
Answer:
F = 2
Step-by-step explanation:
Answer:6
Step-by-step explanation:i did the quiz
Lily is 22 years old. Monica is 3 years older than Lily and 2 years younger than Christine. How old is Christine
Answer:
she would be 20 years old if lily is 22
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.
Answer:
a
Step-by-step explanation:
this is the anser on e2020
Find the area of a triangle with points (-8,8) , (10,-2), and (-8,-8)
Answer:
144
Step-by-step explanation:
Base:16
Height: 18
Triangle area formula: (bxh)/2
16x18=288
288/2=144
Solve for y
:
V=−4y+4x
[tex] - 4y = v - 4x \\ y = \frac{ - v}{4} + x[/tex]
[tex]\\ \rm\dashrightarrow V=-4y+4x[/tex]
[tex]\\ \rm\dashrightarrow -4y=V-4x[/tex]
[tex]\\ \rm\dashrightarrow y=\dfrac{V-4x}{-4}[/tex]
[tex]\\ \rm\dashrightarrow y=x-\dfrac{V}{4}[/tex]
A solid right pyramid has a square base with an edge length of s units and a height of h units.
Which expression represents the volume of the pyramid?
One-fourth s^2h units^3
One-third s^2h units^3
s^2h units^3
3^s2h units^3
The volume of the square pyramid is: B. One-third s^2h units^3.
What is the Volume of a Square Pyramid?An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.
A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.
Given the following parameters for a square pyramid:
The length of the edge of the square base (a) = s units
The height of the square pyramid = h units.
Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:
Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)
Volume of the square pyramid = 1/3s²h units ³.
The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.
Learn more about square pyramid on:
https://brainly.com/question/3688277
#SPJ1
Solve for x
[tex]\ \textless \ br /\ \textgreater \ x = \dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x} } } \: \: \: , (x \neq 2)[/tex]
Help me with this!
Answer:
[tex]x= \dfrac{3-2x}{4-3x}[/tex]
Step-by-step explanation:
Given:
[tex]x=\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x}}}}[/tex]
Simplify:
[tex]\begin{aligned}2-\dfrac{1}{2-x} & =\dfrac{2(2-x)-1}{2-x}\\\\ & =\dfrac{3-2x}{2-x}\end{alilgned}[/tex]
Therefore:
[tex]x=\dfrac{1}{2-\dfrac{1}{\dfrac{3-2x}{2-x}}}[/tex]
Simplify:
[tex]\begin{aligned}2-\dfrac{1}{\dfrac{3-2x}{2-x}} & =2-\dfrac{2-x}{3-2x}\\\\ & =\dfrac{2(3-2x)-(2-x)}{3-2x}\\\\ & = \dfrac{6-4x-2+x}{3-2x}\\\\ & = \dfrac{4-3x}{3-2x}\end{aligned}[/tex]
Therefore:
[tex]x & =\dfrac{1}{\dfrac{4-3x}{3-2x}}[/tex]
[tex]\textsf{Apply the fraction rule}: \quad \dfrac{1}{\frac{b}{c}}=\dfrac{c}{b}[/tex]
[tex]\implies x& = \dfrac{3-2x}{4-3x}[/tex]
A space shuttle can orbit the earth at 330 mi above sea level. The average commercial airplane can fly at 5.7 mi above sea level. What is the distance between the two aircraft?
Answer:
324.3mi
Step-by-step explanation:
Given Space Shuttle height above ground = 330mi
Airplane height above ground = 5.7mi
Difference between two aircrafts = Space Shuttle height - airplane height above ground
= 330 - 5.7
= 324.3mi
What is the area of the sector
shown in the diagram below?
OA. 11.1 cm²
OB. 2.5 cm²
OC. 39.3 cm²
OD. 50 cm²
Answer:
OC. 39.3 cm²
Step-by-step explanation:
Area of a circle = πr² (π ≈ 3.14)
45 degrees = 1/8 of a full circle
Area of the full circle : 3.14 × 10² =
3.14 × 100 = 314 cm²
Area of the sector : 314 × 1/8 = 39.25 cm² ≈ 39.3 cm²
73. Real-World Applications
A city's population in the year 1960 was 287,500 . In 1989 the population was 275,900 . Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
Answer:
The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.
Step-by-step explanation:
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.
Step 1 of 1
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
To find the rate of growth of population and make a statement about the population rate of change in people per year.
Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]
Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for then,
[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]
The rate of growth of population -400, so there is a drop in the population by 400 per city.
In a binomial experiement, what does it mean to say that each trial is independent of the other trials?.
In a binomial experiment to say that each trial is independent of the other trials means that the outcome of one trial does not affect the other trial.
An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.
To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.
This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.
For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.
Learn more about binomial experiments at
https://brainly.com/question/24756209
#SPJ4
Calculate the residuals for the scatter plot (image provided)
From the given graph, and using the scatter plot function of a graphing calculator, the residuals are;
-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578
Which method can be used to find the residuals?From the diagram, the given points are;
(14, 4), (15, 4), (16.5, 3.5), (18, 4), (18, 3.9), (19.5, 3.85), (20, 4), (26.8, 3.8)
Utilizing a graphing calculator, using the scatter plot function we have the following predicted values;
Best fit line; y = 5.032 - 0.0676•x
Residuals = Actual - Predicted from equation
The residuals are;
y1 = 4 - 4.08693 = -0.08693
y2 = 4 - 4.019376 = -0.019376
y3 = 3.5 - 3.918 = -0.518
y4 = 4 - 3.817 = -0.183
y5 = 3.9 - 3.817 = -0.083
y6 = 3.85 - 3.715 = 0.135
y7 = 4 - 3.682 = 0.318
y8 = 3.8 - 3.222 = 0.578
The residuals are therefore;
The residuals are;
-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578Learn more about finding the residuals of a scatter plot here:
https://brainly.com/question/16511034
#SPJ1
20) Find the surface area of the solid shown. 16 dm 17 dm 30 dm
Answer:
680π dm² = 2136.28 dm²
Step-by-step explanation:
Recall:
lateral area of cone = πrs; where s = slant height = 17 dm
area of circle = πr²
lateral area of cylinder = πdh
Lateral area of cone: (3.14159)(8 dm)(17 dm) = 427.26 dm²
Area of base of cylinder: (3.14159)(8 dm)² = 201.06 dm²
Lateral area of cylinder: (3.14159)(16 dm)(30 dm) = 1507.96 dm²
Total surface area = 427.26 dm² + 201.06 dm² + 1507.96 dm²
Total surface area = 680π dm² = 2136.28 dm²
approximately how high to the nearest tenth of a metre is emma's kite above ground
How far does judy travel in 2 3/4 hours if she travels at the rate of 5 1/2 miles per hour
Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Given:
Speed = 5 1/2 miles per hour Time = 2 3/4 hoursSubstituting it in the relationship we get,
Distance = Speed x Time
Distance = 5 1/2 miles per hour x 2 3/4 hours
Distance = [tex]\frac{11}{2} X \frac{11}{4}[/tex] miles
Distance = [tex]\frac{121}{8}[/tex] miles or 15[tex]\frac{1}{8}[/tex] miles
Thus Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours
Learn more about time related questions here :
https://brainly.com/question/16403317
#SPJ4
16 percent of what number is 17
Work Shown:
16% of x = 17
0.16x = 17
x = 17/(0.16)
x = 106.25
HELPP!!!
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Answer:
15/17
Step-by-step explanation:
he coordinate grid shows the graph of four equations: A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6. Which set of equations has (5, 0) as its solution? A and B C and D B and D A and D
The set of equation that is known to have 5 and 0 as solutions is A and B.
How to solve for the system of equations.From the graph that we have here in this question, we are supposed to identify the equations that have this point.
We can do this by tracing the lines in order to locate 5 and 0 on the grid.
When we trace the bine that has 5 and 0, We would find out that it is traceable to A and B.
Read more on graphs here:
https://brainly.com/question/10465970
#SPJ1
please help me out somebody!
Answer:
Step-by-step explanation:
His friends all drive more expensive cars, and Tony is now starting to desire these same expensive products. Which factor is Tony experiencing
E
What is the solution to the system of equations?
y = 0x + 3
x = −2
O [--]
O
[22]
[2
O
[-2]
Answer:
-2
Step-by-step explanation:
The solution to the system of equations is (x, y) = (-2, 1).
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The second equation tells us that x = -2.
Substituting this value into the first equation, we get:
y = -2 + 3
Simplifying, we get:
y = 1
Therefore,
The solution to the system of equations is (x, y) = (-2, 1).
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
For the following exercises, solve each inequality and write the solution in interval notation.
29. | x − 2 | > 10
Answer:
The solution to the inequality |x-2|>10 in interval notation is given by -8<x<12
Step-by-step explanation:
An absolute value inequality |x-2|>10 is given.
It is required to solve the inequality and write the solution in interval form.
To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.
Step 1 of 2
The given absolute value inequality is $|x-2|>10$.
The inequality can be written as
x-2<10 and x-2>-10
First solve the inequality, x-2<10.
Add 2 on both sides,
x-2<10
x-2+2<10+2
x<12
Step 2 of 2
Solve the inequality x-2>-10.
Add 2 on both sides,
x-2>-10
x-2+2>-10+2
x>-8
The solution of the inequality in interval notation is given by -8<x<12.
37. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
37. x-intercept at (-5, 0) and y-intercept at (0, 4)
Answer:
The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).
It is asked to find a linear equation satisfying the given condition.
To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
[tex]$$y=m x+b$$[/tex]
The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.
So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,
[tex]$y=\frac{4}{5} x+4$$[/tex]
This is the required linear equation.