Write three quadratic equations that are NOT equivalent, each forming a graph with vertex
(−2,3).
Please explain it
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
The vertex of a quadratic equation:
a[tex]x^{2}[/tex]+bx + c = y
is located at :
x = -b/2a.
In this case, x = -2
Then,
-b/2a = -2
And we also have that:
a[tex](-2)^2[/tex] -2b + c = 3
Then we have two equations:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + c = 3
We have only equations and 3 variables, So we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0 ,Our equations are:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + 0 = 3
In the first equation we can isolate b and get :
b = 4a
Now we can replace this in the other equation and solve this for a.
4a + 4a x -2 = 3
-4a = 3
a = -3/4
then:
b = 4a = 4 x -3/4 = -3
The first quadratic equation is:
(-3/4)[tex]x^{2}[/tex] - 3x = y
Now, To find the second let's use a different value of c.
c = 1
b = 4a
a[tex](-2)^2[/tex] -2b + 1 = 3
Let's solve in the same way as before:
4a + 4a x -2 + 1= 3
-4a = 2
a = 2/-4 = 1/-2
b = 4 x -1/2 = -2
Then our equation is :
(-1/2)[tex]x^{2}[/tex] -2x + 1 = y
For the last equation, let's use c = 2
then our equation are:
b = 4a
a(-2)^2 - 2b +2 = 3
Same as before, replace the first equation in the second
4a + 4a x-2 +2 = 3
-4a +2 = 3
-4a = 1
a = -1/4
Then:
b = 4 x (-1/4) = -1
Our third equation is :
(-1/4)x^2 - x + 2 = y
Now, Below you can see all of them graphed.
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
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Each night Liz spends at least 45 minutes and no more than 120 minutes on her phone.
Choose which double inequality describes how long Liz spends on her phone each night.
"n" will be used as your variable.
pls help me its due today
Using the given information, we can write the compound inequality for the variable n:
45 ≤ n ≤ 120
How to write the inequalities?
Here we know that Liz spends at least 45 minutes and no more than 120 minutes on her phone.
So if we define the variable n as:
n = number of minutes that Liz spends on her phone.
We know that n must be larger than or equal to 45, so we can write the first inequality:
45 ≤ n
And we also know that it must be smaller than or equal to 120, then the other inequality is:
n ≤ 120
Combining the two we can write the compound inequality:
45 ≤ n ≤ 120
That is what we wanted to get.
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6:3(3+3)= can anyone answer this
Name the Inequalities
Find the value of x. Then find the measure of each labeled angle.
(x - 58)° =
(x-58)
Answer:
x° = 119°(x-58)° = 61°Step-by-step explanation:
You want the measures of supplementary angles x° and (x-58)°.
Supplementary anglesConsecutive interior angles where a transversal crosses parallel lines are supplementary.
x° +(x -58)° = 180°
2x = 238
x = 119
x -58 = 61
The two angles are ...
x° = 119°(x-58)° = 61°<95141404393>
what is the value of sin 78^
The exact value of the sine of angle 78° sin(78°) is presented as follows;
[tex]sin(78^{\circ}) = \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]
What is the sine of an angle?The sine of an angle is found by taking the ratio of the opposite side to the hypotenuse side of a right triangle that has the specified angle.
The sine of angle 78° is found from the sine of the sum of two angles (60° + 18°) as follows;
sin(78°) = sin(60° + 18°)
sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)
Therefore, sin(78°) = sin(60° + 18°) = sin(60)·cos(18°) + cos(60°)·sin(18°)
Where, 18° = A, we have;
5·A = 90°
2·A = 90° - 3·A
sin(2·A) = sin(90° - 3·A) = cos(3·A)
2·sin(A)·cos(A) = 4·cos³(A) - 3·cos(A)
2·sin(A)·cos(A) - (4·cos³(A) - 3·cos(A)) = 0
2·sin(A) - (4·cos²(A) - 3) = 0
2·sin(A) - (4·(1 - sin²(A)) - 3) = 0
4·sin²(A) - 2·sin(A) - 1 = 0
Which gives;
[tex]sin(A) = \dfrac{-1\pm \sqrt{5} }{4}[/tex]
[tex]sin(18^{\circ}) = \dfrac{\sqrt{5} -1 }{4}[/tex]cos²(18°) = 1 - sin²(18°)
cos(18°) = √(1 - sin²(18°))
[tex]cos(18^{\circ}) =\sqrt{1 - \left( \dfrac{\sqrt{5} -1 }{4}\right)^2} = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]
[tex]cos(18^{\circ}) = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]
Therefore;
[tex]sin(78^{\circ})=\dfrac{\sqrt{3} }{2} \cdot \left( \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }\right) +\dfrac{1}{2} \cdot \left( \dfrac{\sqrt{5} -1 }{4}\right)= \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]
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26% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answer:
a) p(X =2) = 0.261
b) P(x>2) = 0.566
c) P(2<x<5) = 0.334
Step-by-step explanation:
Given 24% of U.S. adults say they are more likely to make purchases during a sales tax holiday
Probability 0f U.S. adults say they are more likely to make purchases during a sales tax holiday (p) = 0.24
n = 10
By using Poisson distribution
mean number of make purchases during a sales tax holiday
λ = np = 10 X 0.24 = 2.4
a)
The probability of getting exactly '2'
The probability
b) The probability of getting more than '2'
= 0.090 + 0.2177+0.261 = 0.566
P(x>2) = 0.566
c) The probability of getting between two and five
P( 2<x<5) = P(x=3)+p(x=4) =P(2<x<5) = 0.2090 + 0.125 = 0.334
hope this helps
Determine the intercepts of the line.
Do not round your answers.
y=-2x - 21
x-intercept:
y-intercept:
The x intercept of y = -2x - 21 is [tex]\frac{-21}{2}[/tex]
The y intercept of y = -2x - 21 is -21
What is x - intercept and y - intercept of a line?
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given equation of line is
y = -2x - 21
For x intercept, we have to put y = 0
[tex]-2x - 21 = 0\\2x = -21\\x = \frac{-21}{2}[/tex]
So the x intercept is [tex]\frac{-21}{2}[/tex]
For y intercept, we put x = 0
[tex]y = -2\times 0 -21\\y = -21[/tex]
The y intercept is -21
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Quill works for a newspaper. He was hired
five years ago. When he was hired, he was
given three vacation days. For each year he
works with the company, he earns two
additional vacation days up to a maximum
of 20 days. How many paid vacation days
does he now get at the end of five years of
employment. If his annual salary is
$64,480, how much does he make during his
vacation?
He got 11 vacation days in five years. If his annual salary is $64,480 he earned during his vacation days $2277
How much vacation time should employee get?The average nationwide is 10, however it varies a little by industry and area. These days off—generally regarded as vacation time—usually get longer the longer an employee works. For the majority of businesses, an employee can receive an additional three to four days per year every five years based on longevity.
The normal recommendation is to wait three to six months. However, the organization and its culture have a big impact. He continued by saying that many businesses make it very clear what their vacation policy is. Some employers allow you to accumulate additional vacation time the longer you work
64,480/12 =5373.33
5373.33/26 = 207
207 x 11 =2277
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He got 11 vacation days in five years. If his annual salary is $64,480 he earned during his vacation days $2277
How much vacation time should employee get?The average across the country is 10, but it varies slightly by region and industry. The length of these vacation days typically increases with an employee's length of service. Based on longevity, most companies allow employees to get an extra three to four days per year every five years.
The usual advice is to hold off for three to six months. The organization and its culture, however, play a significant role. He went on to remark that a lot of companies are quite explicit about their vacation policies. The longer you work for some employers, the more vacation time you can accrue.
64,480/12 =5373.33
5373.33/26 = 207
207 x 11 =2277
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35 lbs of bananas
cost $280. How
much would 42 lbs
cost?
Answer:
$336
Step-by-step explanation:
[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]
Write an inequality in slope intercept form from the linear inequality graphed below.
The inequality represented by the graph in slope intercept form is
y ≤ 2x - 4How to find the inequality the graph representsA graph is a pictorial representation of data and the graph presented represents inequality data
The graph shows a linear function written in the slope intercept form form as
y = mx + c
where slope, m calculated as
c = intercept
x = input variables
y = output variables
calculation of slope
The points used for the slope is gotten from the graph as (2. 0) (0, -4)
m = (y₂ - y₁) / (x₂ - x₁)
substituting the values
= ( -4 - 0 ) / ( 0 - 2 )
= -4 / -2
= 2
y intercept, c
this is a point where the graph cuts the y axis
c = -4
The graph contains
a solid line as result there will be "equal to" attached to the inequality symbol usedshading below the line means less thanthis gives the idea to use less than or equal to written with the symbol ≤
hence the equation is written using y = mx + c and substituting the values
y ≤ 2x - 4
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While volunteering in her community, Janicka picked up 5 2/5 lb of trash. If 2/3 of what she collected was able to be recycled, how many pounds of trash did Janicka recycle?
The pounds of trash that Janicka recycle is 3 3/5 pounds.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
In this situation, Janicka picked up 5 2/5 lb of trash and 2/3 of what she collected was able to be recycled.
The amount to be recycled will be:
= 2/3 × 5 2/5
= 2/3 × 27/5
= 54 / 15
= 3 9/15
= 3 3/5
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At 12 noon it was discovered that a driver has travelled 3/8 of the distance from Kano to lagos ,while another driver had travelled 3/10 of that distance from lagos,travelling at the same rate .if the two drivers are 390km apart .find the distance from Kano to lagos
The distance from Kano to Lagos is 1200 km
How to determine the distance from Kano to LagosThe problem involves addition of fractions
The fraction required are:
let the distance form kano to Lagos be x
it was discovered that a driver has travelled 3/8 = 3x/8
another driver had travelled 3/10 of that distance = 3x/10
The drivers are still 390 km apart
total distance, x
x = 390 + 3x/8 + 3x/10
x - 3x/8 - 3x/10 = 390
0.325x = 390
x = 390 / 0.325
x = 1200 km
From the driving distance information 1200 km is the distance from Kano to Lagos
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Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. At this rate, when will Cassidy and Calvin have the same amount of money? How much will they each have?
Cassidy and Calvin have the same amount of money in 11 months.
The amount is $370.
How to illustrate the equation?Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:
= 425 - 5m
Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:
= 95 + 25m
where m = number of months
The equation will be:
425 - 5m = 95 + 25m
Collect like terms
425 - 95 = 25m + 5m
330 = 30m
Divide
m= 330/30
m = 11
The number of months is 11.
The amount will be:
= 425 - 5m
= 425 - 5(11)
= 425 - 55.
= 370
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Solve the equation in the image below correct to 2 decimal places. in Logarithm Terms
The solution to the given equation is 5.630.
What is a logarithmic equation?
An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Here, we have
2^(x+1) = 3^(2x-5)
Taking logarithms on both sides, we get
(x+1)log2 = (2x - 5)log3
xlog2 + log2 = 2xlog3 - 5log3
log2 + log3⁵ = 2xlog3 - xlog2
log 2* 243 = x(log6 - log2)
log486 = x(log6/2)
log486 = xlog3
x = log486/log3
x = 5.630
Hence, the solution to the given logarithmic equation is 5.630.
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Which function has the following domain and range?
Domain: {-5, -3, 0, 3, 11)
Range: {4, 0, 2}
O {(-5, 4), (3, 0), (0, 2), (3, 5), (10, -1)}
{(-4,-3), (2, 11), (0, 3), (-4,-5), (0, 0))
O {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}
O ((-5, 11), (-4,2}
-
The function which have Domain:{-5, -3, 0, 3, 11} and Range:{4, 0, 2} is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}.
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
What is domain?
The domain of a function is the set of values that we are allowed to plug into our function.
What is range?
The collection of potential output values for a function is known as its range. For instance, the range is the non-negative real numbers for the function fn(x)=x2 on the domain of all real numbers (x ∈ R), which may be represented as fn(x)≥0 (or [0,∞] using interval notation).
Given:
Domain: {-5, -3, 0, 3, 11)
Range: {4, 0, 2}
If the input of function is a and output is b then it is defined by (a, b).
a always belong to domain and b from range of function.
∴ By using given domain and range set of our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}
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Answer:our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}
Step-by-step explanation:
What does the Big Bang Theory explain?
Answer:
The big bang is how astronomers explain the way the universe began. It is the idea that the universe began as just a single point, then expanded and stretched to grow as large as it is right now—and it is still stretching!
Step-by-step explanation:
In 1927, an astronomer named Georges Lemaître had a big idea. He said that a very long time ago, the universe started as just a single point. He said the universe stretched and expanded to get as big as it is now, and that it could keep on stretching The universe is a very big place, and it’s been around for a very long time. Thinking about how it all started is hard to imagine. Some More Information
Just two years later, an astronomer named Edwin Hubble noticed that other galaxies were moving away from us. And that’s not all. The farthest galaxies were moving faster than the ones close to us. This meant that the universe was still expanding, just like Lemaître thought. If things were moving apart, it meant that long ago, everything had been close together.
Everything we can see in our universe today—stars, planets, comets, asteroids—they weren't there at the beginning. Where did they come from?
A Tiny, Hot Beginning
When the universe began, it was just hot, tiny particles mixed with light and energy. It was nothing like what we see now. As everything expanded and took up more space, it cooled down.
The tiny particles grouped together. They formed atoms. Then those atoms grouped together. Over lots of time, atoms came together to form stars and galaxies.
The first stars created bigger atoms and groups of atoms. That led to more stars being born. At the same time, galaxies were crashing and grouping together. As new stars were being born and dying, then things like asteroids, comets, planets, and black holes formed!
write -(1/4x1/4x1/4x1/4) using exponents
The solution to the mathematical expression -(1/4x1/4x1/4x1/4) in exponent form is [tex]\mathbf{-4^{-4}}[/tex]
Writing mathematical expressions in exponents formNumber multiplication is a basic and common operation. However, the product of multiplication can be stated differently at times, whether to reduce the equation or to explain the mathematics required. Many numbers can be expressed exponentially.
The concept of exponential form is a method of expressing a number that has been multiplied by itself several times. The fundamental formula is [tex]\mathbf{y=b^x}[/tex]
Exponential expressions are simply a shorthand way of writing powers. The exponent specifies how many times the base has been utilized as a factor.
From the information given
:= -(1/4*1/4*1/4*1/4)[tex]
=-(4^{-1}\times4^{-1}\times4^{-1}\times4^{-1})[/tex][tex]=-(4^{(-1+(-1)+(-1)+(-1))})[/tex][tex]=-(4^{(-1-1-1-1)})[/tex][tex]=-(4^{(-4)})[/tex][tex]\mathbf{=-4^{-4}}[/tex]
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Christina buys coffee for her office mates everyday. Normally she buys just three coffees for $5.55. on special days there are five people in the office who drink coffee. How much will five cost?
Answer:
5 coffees will cost $9.25
Step-by-step explanation:
If you divide $5.55 by the 3 coffees, you get $1.85 which is the price per coffee. Multiply $1.85 by 5 to get $9.25 which is the cost for 5 coffees
determine between which two consecutive integers the square root lies.
Step-by-step explanation:
we know the square numbers of the basic integer numbers :
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
so, we see when we square the inequality, the closest numbers are
81 < 91 < 100
and therefore
9 < sqrt(91) < 10
1.You need to earn at least $90. You earn $7 for each hour you work.
Which inequality represents the number of hours h that you need to
work?
(Look at the picture for options for the answer)
2. Write a graph that represents the solution
Answer:
Inequality:
Graph choice:
Step-by-step explanation:
Inequality
It says at least 90, which means we have to use the greater than or equal to sign
Our inequality so far: 90≥______
Now it says you earn 7 dollars per hour, which means 7 times the number of hours you work or 7h. Our inequality now looks like this:
90≥7h
The answer choice that matches is A (90≥7h = 7h≤90)
For the second question on the bottom, I added an image.
(Answer is B)
A CFL football player has an annual salary of $305 000. The player donates 1/8 of his salary to charity . What amount is this ?
Answer: $38,125
Step-by-step explanation:
1/8*305000
For a circle with a radius = 4.3, find the following:
(Use π = 3.14 for all answers. Do not round!)
Circumference =
Area =
Answer: Circumference equals = 27.004
Area equals = 58.0586
We can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.
What is a two - dimensional figure?A two - dimensional figure is a collection of two - dimensional points enclosed by a single dimensional entity. For example, triangle, circle, trapezium etc all represent a two - dimensional figure. The points inside these figures can be expressed as (x, y).Given is that a circle with a radius of 4.3.
We can write the area of the given circle as -
Area = πr²
Area = π x 4.3 x 4.3
Area = 18.49π square units
We can write the circumferance of the given circle as -
circumferance = 2πr
circumferance = 2 x π x 4.3
circumferance = 8.6π units
Therefore, we can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.
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Show, by shading on the grid, the region defined by all three of the inequalities
x ≤ 5 y ≥ 3 y ≤ x
Answer:
See below
Step-by-step explanation:
The area (triangle) marked 'x' in the diagram below
HELP!! WILL MARK BRAINLIEST!!
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
rise/run you can count it but it doesn't always work
If you want to know the mathematical way of doing it it's:
m(slope) = y2-y1/x2-x1 Choose any two points I chose (-4,5) & (0,6)
m = 6-5/0-(-4) Then subtract 6 - 5 and 0-(-4)
m = 1/4
A hotel has a budget of $63,750 to repaint the lobby and some hotel rooms. The hotel spent $26,700 on painting the lobby. Each room costs $4,250 to paint. The inequality 26,700 + 4,250n ≤ $63,750 can be used to determine the number of rooms (n) the hotel can repaint.
Which statement about the number of rooms that can be painted is true?
A.
The hotel can repaint 9 rooms.
B.
The minimum number of rooms that can be repainted is 2.
C.
The maximum number of rooms that can be repainted is 2.
D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
The statement that is true about the number of rooms that can be painted using inequality is; D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
How to solve Inequality Word problems?We are given;
Budget of hotel to repaint the lobby and some hotel rooms; $63750
Amount spent on painting the lobby = $26700
Cost to paint each room = $4250
Thus, the inequality to represent the given situation is;
26,700 + 4,250n ≤ $63,750
where;
n is number of rooms the hotel can repaint
Subtract 26700 from both sides of the inequality to get;
4250n ≤ 37050
n ≤ 37050/4250
n ≤ 8.717
Since we can't paint only a portion, we leave it as a maximum of 8 rooms
Looking at the given options, the only correct one is option D.
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Which table represents a function?
Answer:
C (the one which starts with x = -2 and y = -1)
Step-by-step explanation:
because for every x value there is only an y value
Mrs Ali baked some cookies.
She gave away 250 cookies and packed the remaining cookies into bags of 12.
Each bag of cookies was sold for $8.
She received $2016 from the sale of all bags of cookies.
How many cookies did she bake at first?
Answer: 3274 cookies
Step-by-step explanation:
She sold : 2016 ÷ 8 = 252 ( bags )
The remaining cookies : 12 × 252 = 3024 ( cookies )
She baked : 3024 + 250 = 3274 ( cookies )
Name the points. I give you brainiac or whatever.
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Which value of a makes the following equation true?
(³) = 125
a = 1
No value of a will work.
a=3
a = 2
Answer:
No value of a will work.
Step-by-step explanation:
let me explain,
given values of a are1,2,3
checking these values of a ,
(1)³=125
1=125 (not true)
(2)³=125
8=125 (not true)
(3)³=125
27=125 (not true)
the correct value of a which makes this equation true is 5. let me make you clear,
(5)³=125
125=125 (true).