The set X is convex.
In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.
b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.
c)set X is not a closed set as the compliment of the set is not an open set.
d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.
To learn more about convex sets:
https://brainly.com/question/12577430
#SPJ9
which is the graph of the function y=4x^2-8x+7
If anyone can help me to solve this!!
Answer:
[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]
[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]
[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]
[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
Step-by-step explanation:
Question 1Method: Extracting the Square Root
[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]
Question 2Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]
Question 3Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]
Question 4Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x-4=-2x^2[/tex]
Rearrange into standard form by adding 2x² to both sides:
[tex]\implies 2x^2+5x-4=0[/tex]
Therefore:
[tex]a=2, \quad b=5, \quad c=-4[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
Question 5Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x^2-7x-13=0[/tex]
Therefore:
[tex]a=5, \quad b=-7, \quad c=-13[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
PLEASE HELP DUE TOMORROWW
Consider the function f,g:[tex]\mathbb{R} \to\mathbb{R}[/tex] defined by
[tex] \rm f(x) = {x}^{2} + \frac{5}{12} \: and \: g(x) = \begin{cases}2 \bigg( \rm 1 - \dfrac{4 |x| }{3} \bigg), \: \: \: \: |x| \leq \dfrac{3}{4}, \\ \\ 0, \: \: \: \: \: \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |x| > \dfrac{3}{4} .\end{cases} [/tex]
If [tex]\alpha[/tex] is the area of the region
[tex] \rm \bigg \{(x,y) \in \mathbb{R} \times \mathbb R : |x| \leq \dfrac{3}{4} ,0 \leq y \leq min \{f(x),g(x) \} \bigg \}[/tex]
then the value of 9[tex]\alpha[/tex]
Suppose [tex]x>0[/tex]; then the curves meet when
[tex]x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12[/tex]
By symmetry, they intersect at [tex]x=\pm\frac12[/tex].
We also see that [tex]\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}[/tex] and [tex]\max\left\{g(x):|x|\le\frac34\right\} = 2[/tex] at [tex]x=0[/tex]. [tex]f[/tex] and [tex]g[/tex] are continuous, so it follows that
[tex]\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}[/tex]
Compute the area [tex]\alpha[/tex]. Taking advantage of symmetry again, we have
[tex]\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23[/tex]
and it follows that [tex]9\alpha = \boxed{6}[/tex].
Robert spends $30.45, before tax, at the bookstore. If the sales Tax rate in his city is 7.25%, and Robert started with $40, how much does Robert have left?
The amount of money Robert has left given the amount he started with and after deducting tax is approximately $7.34
How much does Robert have left after deducting tax?Tax can be defined as the compulsory levy paid by citizens of a particular country on their income, goods and be services.
Amount Robert started with = $40Amount Robert spent before tax = $30.45Tax rate = 7.25%Amount of tax = Tax rate × Amount Robert spent before tax
= 7.25% × $30.45
= 7.25/100 × 30.45
= 0.0725 × 30.45
= $2.207625
Total amount Robert spent = Amount Robert spent before tax + Amount of tax
= $30.45 + $2.207625
= $32.657625
Amount Robert has left = Amount Robert started with - Total amount Robert spent
= $40 - $32.657625
= $7.342375
Approximately,
$7.34
Therefore, the amount Robert has left after deducting tax is $7.34
Read more about tax:
https://brainly.com/question/9437038
#SPJ1
Which of the following phrases could be translated to an expression y + 5
Answer:five more than y
Step-by-step explanation:
carla wrote this number:815,247 travis wrote this number: 638.571 the digit 8 in carlas number represents how many times what the digit 8 represents in travis number?(55 points)
The 8 in Carla's number is 100 times the 8 in Travis' number.
How many times what the digit 8 represents in Travis number?Here you need to understand the concept of place value. For any number, each digit is always a order of magnitude of 10 larger than the digit in the left.
For example, in 88
The first 8 is 10 times larger than the second one.
There comes the concept of place value, the first digit at the left of the decimal point represents the units, the second represents the tens, the third one the hundresd, and so on.
So, in the two given numbers:
815,247 Here the 8 represents the hundreds of thousands.
638,571 Here the 8 is in the thousands place value.
Then the relation between the first 8 and the second one is:
100,000/1,000 = 100
The 8 in Carla's number is 100 times the 8 in Travis' number.
If you want to learn more about place value:
https://brainly.com/question/12386995
#SPJ1
Solve.
c = kny, for y
The solution of the equation c = kny, for y is y = c/kn
How to solve the equation c = kny, for y?The equation is given as
c = kny
Divide both sides of the given equation by k
So, we have
c/k = kny/k
Evaluate the quotient on both sides of the above equation
So, we have
c/k = ny
Divide both sides of the above equation by n
So, we have
c/kn = ny/n
Evaluate the quotient on both sides of the above equation
So, we have
c/kn = y
Rewrite as
y = c/kn
Hence, the solution of the equation c = kny, for y is y = c/kn
Read more about subject of formula at:
https://brainly.com/question/10643782
#SPJ1
Can I please get help?
Answer:
a) 9
b)3
c)22
Step-by-step explanation:
a)13+14/8-5 =27/3 =9
b) 9+9/4+2= 18/6 = 3
c) 12+16-6=22
Answer:
A- 9
B-3
C-22
Step-by-step explanation:
A-13+7*2/8-(3+2)
13+14/8-5
27/3
9.
B-9+3^2/2^2+2
9+9/4+2
18/6
3.
C-(10+2)+(4^2-6)
(12)+(16-6)
12+10
22
I need help with this
Answer: last one
Step-by-step explanation:
I think it's the last one because the value of 8 is negative and the value of 1 is positive. however, rita changes the negative and positive numbers and thats why she is wrong.
Need help with this was will off 30 points
The solution of the simultaneous equations is given by: x=0.60 and
y = 0.80 .
A system of equations or simultaneous equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.
The elimination approach, which involves taking one of the unknowns out of each equation, is the most popular technique for solving simultaneous equations. The final step is to calculate the remaining unknown. If the coefficient of one of the letters is the same, regardless of sign, this is possible.The given pair of simultaneous equations are:
6 x + 8 y = 10
9 x + 6 y = 10.20
Now let us multiply the first equation by 6 and the second equation by 8 and subtract it from the first.
36 x + 48 y = 60
72 x + 48 y = 81.60
⇒ 36 x = 21.60
⇒ x = 21.60 ÷ 36
⇒ x = 0.60
Substituting the value in the first equation we get:
y= 0.80.
Hence the solution of the simultaneous equation is x=0.60 and
y = 0.80 .
To learn more about simultaneous equation visit:
https://brainly.com/question/16763389
#SPJ9
Solve the formula of the indicated variable C=xw+x, for w
The larger room is twice as wide as the smaller room which is 29 3/4’. How wide is the
larger room?
Based on the fact that the larger room is twice as wide as the smaller room, the width of the larger room is 59¹/₂ inches.
How wide is the larger room?The larger room is twice the width of the smaller room.
If the smaller room is 29³/₄ inches therefore, the width of the larger room will be:
= Width of smaller room x 2
Solving for the width of the larger room gives:
= 29³/₄ x 2
= 29.75 x 2
= 59.50
= 59¹/₂ inches
Find out more on the width of a room at https://brainly.com/question/2082460
#SPJ1
Jane and Jim spend the same amount of money today. If Jim spent 5.25 on food and rode the train three times and Jane spent 12.45 on food and rode the roller coaster twice, then how much does a token cost?
The cost of a Token from the question is; $7.2
How to solve Algebra Word Problems?
We are told that Jane and Jim spend the same amount of money today.
Now, Jim spent 5.25 dollars on food and rode the train 3 times, and Jane spent 12.45 dollars on food and rode the roller coaster twice.
Assuming cost of a token is T, the the algebraic expression formed is;
5.25 + 3T = 12.45 + 2T.
3T - 2T = 12.45 - 5.25
T = $7.2
Thus, we conclude that the cost of a Token is; $7.2
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
Evaluate the left hand side to find the value of a in the equation in simplest form.
The value of a in the equation in the simplest form will be 17 / 6.
We are given an equation:
x³ / x^(1/6) = x^(a)
We need to evaluate the left hand side to find the value of a in the equation in simplest form.
We know that:
x^ (a) / x^ (b) = x^ ( a - b)
Using this, we get that:
x^ (3 - 1/6) = x^ (a)
x^ (17/6) = x^ (a)
By comparing the bases, we get the value of a as:
a = 17 / 6.
Therefore, the value of a in the equation in the simplest form will be 17 / 6.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ9
192 students in 4 buses
________ in each bus
Answer:
48
Step-by-step explanation:
use a calculator
To two decimal places,
√70
must lie between ____
and _____.
To two decimal places,
√70
must lie between 8.3
and 8.4
What is the linear speed in miles per hour of the tip of a lawnmower blade spinning at 2800 revolutions per minute in a lawnmower that cuts a path that is 26 inches wide?
What is the angular speed in degrees per hour?
The linear speed in miles per hour of the tip of a lawnmower blade spinning is 0.0601509076 miles per hour and angular velocity is 293.276 rad/hr.
What is linear speed?The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an item along a straight line. It is the distance traveled along a linear path in the allotted amount of time.
2800 rotations per minute on a lawnmower blade.
Specifically, the frequency of the blade is 2800 revolutions per hour,
f = 2800 / 60, or 46.66.
The angular velocity is
ω = 2πf
where f = frequency
ω = 2 × 3.14 × 46.7
ω = 293.276 rad/hr
The diameter of the circle centered at the blade's middle determines the path's breadth.
26 inches in diameter
radius = 26 / 2 = 13
13 inch = 0.0002051 miles
Velocity is given by -
V = ωR
V = 293.276 × 0.0002051
Velocity = 0.0601509076 miles per hour
To learn more about linear velocity from given link
https://brainly.com/question/2612576
#SPJ9
_____= 240 mL
Group of answer choices
4 oz
4 pints
1 cup
8 drams
The volume 240 ml to oz is 8 oz.
How to find volume in different units?The volume is in millilitres. Therefore, we have to convert to other units.
1 ml = 0.033814 oz
1 ml = 0.00175975 pints
1 ml = 0.00422675 cup
1 ml = 0.57 grams
Hence, lets convert the volume to the various units.
1 ml = 0.033814 oz
240 ml = ?
cross multiply
volume = 240 × 0.033814 = 8.11536 oz = 8 oz
1 ml = 0.00175975 pints
240ml = ?
volume = 0.00175975 × 240 = 0.42216 = 0.4 pints
1 ml = 0.00422675 cup
240 ml = ?
volume = 0.00422675 × 240 = 10.1442 cups
1 ml = 0.57 grams
240 ml = ?
volume = 0.57 × 240 = 136.8 grams
learn more on volume in ml here: https://brainly.com/question/27122947
#SPJ1
Watch help video
Given g(x) = 2x + 3, find g(0).
Answer:
g(0) = 3
Step-by-step explanation:
Hello!
Substitute 0 for x in the equation.
Evaluateg(x) = 2x + 3g(0) = 2(0) + 3g(0) = 0 + 3g(0) = 3g(0) is 3.
Simplify 2.67 + (−8.9).
Answer:
-6.23 is the answer
HOPE IT'S HELPS YOUAnswer:
-6.23
Step-by-step explanation:
The solution will be,
→ 2.67 + (−8.9)
→ 2.67 - 8.9
→ -6.23
So, the answer is -6.23.
Point B is between points A and C. AC-10x+6, AB=5x, and BC-4x+12, Find AB.
The value of AB that is 5x is equal to 30.
It is given that the points A, B and C are collinear. Collinear points may be defined as three or more points which lie on a straight line.
Here B lies between A and C and the three points A, B and C are collinear. Thus, according to property of collinear points:
AB+BC=AC
Now, according to question AB=5x, BC= 4x+12 and AC= 10x+6.
So, 5x+4x+12=10x+6
Taking the like terms on one side;
12-6 = 10x+9x
=> x=6
Now, AB=5x, thus AB= 5×5=30
Therefore, the value of AB is 30.
Learn more about question at:
brainly.com/question/14240601
#SPJ1
Complete question:
Three points A, B and C are collinear. Point B is between points A and C. AC=10x+6, AB=5x, and BC=4x+12, Find AB.
According to a survey conducted by a city’s chamber of commerce, approximately 41.5% of city residents prefer local businesses over national chains. The survey had a margin of error of ±3.8%. Round to the nearest tenth, if necessary.
The values in percentages will be 37.7% and the maximum will be: 45.3%
How to illustrate the information?From the information, approximately 41.5% of city residents prefer local businesses over national chains and the survey had a margin of error of ±3.8%.
Therefore, the minimum number will be:
= 41.5% - 3.8%
= 37.7%
The maximum will be:
= 41.5% + 3.8%
= 45.3%
Learn more about percentages on:
brainly.com/question/19247356
#SPJ1
rita had 300$. she spent 1/3 of her money on notebook and 1/4 on stationary items how much money is left with her?
with statement and explanation pls.
Rita is left with $25
How to calculate the amount of money left ?Rita has $300
She spent 1/3 of the money on notebook
= 1/3 × 300
= 100
Rita also spent 1/4 of the money on stationary item
1/4 × 100
= 25
Hence Rita is left with $25
Read more here
https://brainly.com/question/16204763?referrer=searchResults
#SPJ1
Over the last baseball season, Billy averaged 28 hits per 100 turns to bat, while Carl averaged one hit for every 2.5 turns. At these rates, which player would have more hits in 500 turns to bat, and how many more?
Using proportions, it is found that Carl would have 60 more hits in 500 turns.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Billy's proportion is of 28/100, hence his amount of hits in 500 turns is:
500 x 28/100 = 140 hits.
Carl's proportion is of 1/2.5, hence his amount of hits in 500 turns is:
500 x 1/2.5 = 200 hits.
The difference is:
200 - 140 = 60 hits.
Carl would have 60 more hits in 500 turns.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Which of the expressions are equivalent to the one below? Check all that
apply.
(6.1)-8
A. 6-(1-8)
B. (1-8) (6-8)
C. 8- (1.6)
D. (1.6)-8
Answer:
C. & D.
Step-by-step explanation:
I believe it is C & D because, They both are in the same order just switched around, combine like like terms on both sides of the equation then if they are identical then they're equivalent.
b) Express 8.423 hours in hours, minutes, and seconds.
Hello!
[tex]8.423 \texttt{ hours in hours, minutes, seconds}[/tex]
[tex]8.423=08:25:22[/tex]
Hope this helps!
refer to the image pls!! Will give brainliest
Step-by-step explanation:
hmmm, it is all there, you only need to write it up.
so, please, let me know what you don't understand about such equations and variables.
(a)
2x + 5y = 45
8x + 3y = 44
(b)
to solve this we try to use either one equation to express one variable by the other. and solve for that remaining variable (and then drive the second one from that), or to combine both equations directly to eliminate one variable and solve.
I think the second option is best here.
so, we multiply the 1st equation by -4, and then we add both equations :
-8x - 20y = -180
8x + 3y = 44
-------------------------
0 - 17y = -136
-17y = -136
17y = 136
y = 8
2x + 5y = 45
2x + 5×8 = 45
2x + 40 = 45
2x = 5
x = 2.5
to rent a chair costs $2.50.
to rent a table costs $8.00.
Exit This table reflects the result of a survey conducted in a town to find out the number of cars of a particular color. Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Graph? A. 10 to 20 B. 20 to 100 C. 0 to 50 D. 0 to 30
The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.
Bar graph :
Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data
The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.
because
it is not possible to have zero number of cars that have a particular color,
in That way, we can eliminate options C and D .
in option A the range is too small which is not possible.
the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.
this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.
For more details :brainly.com/question/13298277
#SPJ9
The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.
Bar graph :
Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data
The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.
because
it is not possible to have zero number of cars that have a particular color,
in That way, we can eliminate options C and D .
in option A the range is too small which is not possible.
the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.
this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.
r = 10 units and h = 7 units, then what is the volume of the cylinder shown above?
Answer:
radious:10
height:7
volume:?
we know that
volume of cylinder:2pie×r²×h
=22/7×10²×7
=2200unit³