Answer:
a function is a rule or correspondence by which each element x is associated with a unique element y.
hope this was helpful!
Daniel works at least 30 hours a week. He works as a math tutor and as a teacher. The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x). •Write a set of inequalities that represents the constraints of the situation and state a point (x,y) that is the feasible region.
The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
How to write the set of inequalities that represents the constraints of the situation and state a point (x, y) that is the feasible region.The given parameters are:
Number of hours = at least 30 hours a week
This means that
x + y ≥ 30
Also, we have:
The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).
This means that
y ≤ 2x
Substitute y ≤ 2x in x + y ≥ 30
x + 2x ≥ 30
This gives
3x ≥ 30
Divide
x ≥ 10
Substitute x ≥ 10 in y ≤ 2x
y ≤ 2 x 10
Evaluate
y ≤ 20
Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
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8.a) A tree of 14m height is broken by the wind so that its touch touches the ground and makes an angle of 60 with ground. Find the length ot broken part of tree .please help for brainliest.
Answer:6.5m
Step-by-step explanation:
1.which expression is equivalent to x² 10x 24?(x 1)(x 24)(x 4)(x 6)(x 2)(x 12)(x 3)(x 8)
x2 − 10x − 24 x 2 - 10 x - 24 this expression is equivalent to x² 10x 24 (x 1)(x 24) (x 4)(x 6)(x 2)(x 12)(x 3)(x 8).
What are algebraic expressions?A logarithmic articulation is a numerical expression that incorporates factors, constants, coefficients, and mathematical tasks. To increase two logarithmic articulations, we duplicate each term of the main articulation with each term of the subsequent articulation and join every one of the items. In a mathematical articulation, a term might comprise of a steady, one variable, a result of at least two factors, a result of both the variable and consistent part. Moreover, the mathematical terms can be both positive and negative. There are significantly three sorts of mathematical articulations.
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What is the square root of 23 to the nearest integer?
Answer:
5
Step-by-step explanation:
If you put this in a calculator it comes back with 4.79583... decimals forever. Rounding to the nearest integer gives 5.
Answer:
5
Step-by-step explanation:
√23 : 4.795831523 whose nearest integer is 5 .
Hence, the nearest number is 5.
Find each sum or difference. Write the result in standard form.
(2.7m^2 - 3.1n) - (4n^2 + 5.1m)
The difference of the algebraic expression is 2. 7m² - 4n² - 8. 2m
How to determine the difference
To represent the difference in standard form is leave in the power or exponent of a variable or number.
Given the expression
(2.7m^2 - 3.1n) - (4n^2 + 5.1m)
First, expand the brackets
2. 7m² - 3.1 m - 4n² - 5. 1m
Then, collect like terms
2. 7m² - 4n² - 3.1m - 5. 1m
Subtract like terms, we have
2. 7m² - 4n² - 8. 2m
The difference of the algebraic expression gives 2. 7m² - 4n² - 8. 2m
Thus, the difference of the algebraic expression is 2. 7m² - 4n² - 8. 2m
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Evaluate 4+2(x+6)^2 for x=-3
= (-54)
Step-by-step explanation:
ATQ
4+2(x+6)^2
6(x^2+12x+216)=0 [ {a+b}^2 = a^2+2ab+b^2 ]
6x^2 +72x+216=0
Put the value of x=(-3)
So ,
6x^2 +72x+36=0
6(-3)^2+72(-3)+216=0
6×(-9)+72×(-3)+216=0
(-54)+(-216)+216=0
= -54
Hence, the solution is -54 at x=(-3).
Thank You
The cost of 20 cans of dog food at Store B is $18.40?
Calculate the price for 11 cans of dog food.
The cost of 11 cans of dog food will be equal to $10.12.
What is unitary method ?
The unitary method is a method in which , you first determine the value of a single unit before determining the value of the required quantity of units.
It is given that the cost of 20 cans of dog food at store B is $18.40.
We need to find cost of 1 can of dog food and that can be calculated by dividing the cost of cans of dog food by total no. of cans.
i.e.,
Cost of 1 can of dog food = $ 18.40 ÷ 20
So ,
The cost of 1 can of dog food will be :
= $0.92
Now , the cost of 11 cans of dog of food will be calculated by multiplying cost of 1 can of food to 11 cans of dog food which will be :
= 11 × $ 0.92
= $10.12
Therefore , the cost of 11 cans of dog food will be equal to $10.12 .
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(-2,-13), (-8,0)
A) 6/13
B) 13/6
C) -6/13
D) -13/6
Answer:
D
Step-by-step explanation:
It looks line you are asking for the slope. The slope is the change in y over the change in x
Ordered pairs are writing in the from (x,y) The first number is the x value and the second number is the y value.
[tex]\frac{0 - (-13)}{-8 - (-2)}[/tex] I am subtracting the y's on the top and the x's on the bottom.
[tex]\frac{0 + 13}{-8 + 2}[/tex] Subtracting a negative is the same as adding a positive.
[tex]\frac{13}{-6}[/tex] The fraction is negative, so the negative sign can go on the top or the bottom.
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of
x
x that support your conclusion.
−5x=35
what is the equation?
Can anyone help with solving this?
Answer:
A=l×b
A=20×14
A=280
tan(90)=14/aq
aq×tan(90)=14/aq×as
aqtan(90)=14
aqtan(90)/tan(90)=14/tan(90)
aq=0.16
convert 3.7, which is drawn from a population with a mean of 2.8 and a standard deviation of 1.3, to a standard normal variable.
The standard normal variable for 3.7 is 0.67.
we are advised that the quantity is to be converted to a widespread everyday variable.The range (x) is 3.7.A facts set's suggest (average) is calculated by way of summing all the numbers in the set and then dividing through the range of values inside the set.imply (µ) is two.8.The rectangular root of the variance of a random variable, sample, statistical populace, data series, or possibility distribution is its general deviationthe usual deviation (σ) is 1.three.A typically disbursed random variable with a median (µ) of zero and a widespread deviation (σ) of 1 is referred to as a trendy ordinary random variable. The letter Z will continually be used to symbolize it.permit the usual regular variable be "z".z = (x-µ)/σz = (3.7-2.8)/1.3x = 0.9/1.3x = 0.69To learn more about standard normal variable, visit :
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Write an equation of the line that is parallel to y = 16 and passes through point (-7, 43).
The required equation of the line is y = 43 which is parallel to line y = 16 and passes through the point at (-7, 43).
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
First, we have to determine the slope of the line y = 16 by placing it into a slope-intercept form:
y = 16
Therefore, the slope of the line is m = 0
Since the required line passes through the point at (-7, 43).
Let the line (y - y₁) = m(x -x₁ )
Here x₁ = -7, y₁ = 43
Substitute the values in the equation,
So, y - (43) = 0(x-(-7))
⇒ y - 43 = 0
⇒ y = 43
Hence, the required equation of the line is y = 43 which is parallel to line y = 16 and passes through the point at (-7, 43).
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 42 N acts on a certain object, the acceleration of the object is 7 m/s^2. If the acceleration of the object becomes 2 m/s^2, what is the force?
The force on the object will be 12 N.
We have a moving object.
We have to determine the force on object when the acceleration of the object becomes 2 m/s².
What is the need of Force in real Life? How is it calculated ?Force is necessary to bring around a change in the state of the body. Either from rest to motion or motion to rest. It can be calculated using the formula-
Force (F) = mass (m) x acceleration (a)
According to the question -
When a force of 42 N acts on the object, then using the formula of force -
F = m x a
42 = m x 7
m(Object) = 6 Kg
When the acceleration of the object becomes 2 m/s², then -
F = m(object) x a
F = 6 x 2 = 12 N
Hence, the force on the object will be 12 N.
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f(x) = 4/5x - 2
Find f(3)
Answer:
[tex]f(3) = \frac{2}{5} [/tex]
Step-by-step explanation:
f(x) = 4/5x - 2
f(3)=4/5(3)−2
f(3)=4/5(3)−2
f(3)=12/5+−2
f(3)=(12/5+−2)(Combine Like Terms)
f(3)=2/5
1. true or false?
2.true or false?
3.true or false?
4.true or false?
(don’t mind the circled answers)
Answer:
1. true
2. false
3. false
4. true
Step-by-step explanation:
PLEASE HELP I'LL GIVE BRAINLIEST
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answer: the first table with all 2s as its y values
Step-by-step explanation: the first table shows that no matter what the x value is, the graph is staying still at y=2. Its rise/run is 0 since it is not rising at all.
Answer:
The first column of the first chart due to the repetition of the numbers! hope this helps!
The length of a rectangle is 3 more than twice the width. the perimeter is 36 inches. what is the area?
If the length of a rectangle is 3 more than twice the width and the perimeter is 36 inches, then the area of the rectangle is equal to 65 in².
The length and width of the rectangle can be determined by using the formula for the perimeter of the rectangle,
P = ( L + W ) × 2
P = 2L + 2W
Here L is equal to the length of the rectangle and W is the width of the rectangle.
As the length is 3 more than twice the width, we can write the length of the rectangle as,
L = 3 + 2W
Putting L = 3 + 2W in the equation of perimeter,
P = 2L + 2W
As P = 36
36 = 2( 3 + 2W) + 2W
36 = 6 + 4W + 2W
6W = 30
W = 30 ÷ 6
W = 5
The length of the rectangle can be found by putting W = 5 in the equation,
L = 3 + 2W
L = 3 + 2(5)
L= 3 + 10
L = 13
Therefore, the length and width of the rectangle are equal to 13 and 5 respectively
As, area = width × length
area = 5 × 13
area = 65
Hence, the area of the rectangle is equal to 65 square inches.
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he temperature t, in degrees f, of a cold yam placed in a hot oven is given by , where t is the time in minutes since the yam was put in the oven.
a) Positive b) Degree per minute c) Interpretation of f'(20)=2
So as we have we are given in the question: T = f(t)
where T is the temperature in degrees Fahrenheit of a cold yam placed in a hot oven and t is the time in minutes since the yam was put in the oven .f'(t) will represent the rate of change in temperature.
f'(t) will represent the change in temperature of yam when 1 minute has passed since it was kept in oven.
Since the temperature will always increase in oven, f'(t) will have a positive sign. units of f'(20)Since, f'(t) represent the rate of change in temperature. the unit will be degrees Fahrenheit per minute .f'(20)=2f'(20) will tell the change in temperature when 20 minutes have passed after the yam has been kept in oven .Thus, the given statement means that 20 minutes after the yam was kept for in the oven, the temperature of yam was increasing by 2 degree Fahrenheit per minute.
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i really need help with this someone pls help
Answer: D=(8,10) Y=(-2,6) N=(2,-6) U=(-8,-5) G=(8,-11) O=(4,-5)
Step-by-step explanation:
On the coordinate plane, left or down means decreasing in value and right or up means increasing in value.
if you take a point and it's at (1,2) and translate it 3 to the left and 4 upwards, your new point would be (-2,6). This is because you subtracted(cause you were going left) 3 from 1 (cause it's your x value), and added(cause you were going up) 4 to 2 (cause it's your y value.)
4 1/7 times - 2 1/8 what is the answer
Answer: -8 45/56
Step-by-step explanation:
What is n and m? In the angle
In the given triangle , ∠n = 50° and ∠m = 35°
What is an angle ?In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.
Some common terms related to angles :
Endpoint : It is the point where the rays met to each other.Ray : Ray is the side or line segment on which angle is formed.Curve : It is a line but not straight i.e. a bended line.Tangent : A line which touches the surface of curve.In the given question mark the triangle as ABC and the mid line as point D.
that means,
∠A = ∠n
∠B = ∠m
and, in ΔABC
∠C = 60 + 35 =95
now, as ΔCDB is isosceles triangle therefore,
∠m = ∠C = 35°
Also, as sum of all angle of triangle is 180
Therefore, ∠A + ∠B + ∠C = 180
=> ∠n + ∠m + 95 = 180
=> ∠n + 35 + 95 = 180
=> ∠n = 180- 130
=>∠n = 50
Hence in the triangle given , ∠n = 50 and ∠m = 35
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quadrilateral \(abcd\) has vertices \(a(1,0)\), \(b(5,0)\), \(c(7,2)\), and \(d(3,2)\). use slope to prove that \(abcd\) is a parallelogram. show all of your work.
Since, the sides ab || dc, ad || bc, and ad || bc . hence, the given quadrilateral abc is a prallelogram.
According to the given question.
We have the vertices of a quadrilateral abcd such that a(1, 0), b(5, 0), c(7, 2) and d(3, 2).
As we know that, a parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.
Since, we have to prove that the given quadrilateral is a parallelogram by using slope. From the definition of the parallelogram we can say that, the opposite sides of the parallelogram are parallel to each other.
Now,
slope of side ab = 0-0/(5 -1) = 0
slope of side dc = 2 -2/(3-7) = 0
slope of the side ad = 2 -0/(3 -1) = 1
slope of the side bc = 2 -0/(7 -5) = 1
Here, the slopes of the opposite sides ab and dc, and ad and bc are equals and we know that when the slope of two line are equals then the lines are parallel to each other.
Therefore, the sides ab || dc, ad || bc, and ad || bc . hence, the given quadrilateral abc is a prallelogram.
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Given f(x) = 5x? + 2 and g(x) = 8 - 3x, find the following.
12. Find g[f(-2)].
11. Find flg(x)).
Value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:
a. g(f(-2)) =32
b. f(g(x)) =42 -15x
As given in the question,
Given function:
f(x) = 5x + 2
g(x) = 8 - 3x
Value of the function for the following condition:
a. g(f(-2))
f(x) = 5x + 2
⇒f(-2) = 5(-2) + 2
⇒f(-2) = -8
g(f(-2))= g(-8)
= 8 - 3(-8)
= 32
b. f(g(x)) = f(8-3x)
= 5(8 -3x) + 2
=42 -15x
Therefore, value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:
a. g(f(-2)) =32
b. f(g(x)) =42 -15x
The complete question is :
Given function f(x) = 5x + 2 and g(x) = 8 - 3x, find the following value.
a. Find g[f(-2)].
b. Find f(g(x)).
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Ali and habib play a computer game to score points ali scores 43,901 points habib scores 5,089 points the winner is the first player to get 40,000 points more than the other player a. estimate the difference between their scores b.is the estimate enough to find the winner
Based on the points obtained from Ali and Habib in the game we can say that:
a. The difference between their scores is: 38.812
b. The estimate is not enough to find the winner
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Ali's points = 43,901Habib's points = 5,089Difference between their scores =?To calculate the difference between their scores we must perform the following subtraction:
Difference between their scores = Al's points - Habib's points
Difference between their scores = 43.901 - 5.089
Difference between their scores =38.812
Due to the difference between their scores is less than 40,000 points, it is not yet possible to define a winner.
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Sascha sells 80 printed placemats and earns a profit of $12. She plans to sell 500 placemats at the fair. How much profit will she earn if she sells 500 placemats?
Answer:
75
Step-by-step explanation:
Each placemat is .15 cents
500 x .15
The company you work for requires you to use your own car while traveling to work. They will pay you $25 a day plus an additional $0.35 per mile. Let the distance driven be x miles and let the total cost for using your car for one day be y dollars. Which of the equations below represents how much your company would need to pay you for driving your own car?
A. y=0.35x+25
B. y=35x+25
C. y=25x+0.35
D. y=25x+35
E. y=25x+0.35x
The use of electricity in the US in 1902 was 6. 03 x 10^9 kilowatt-hours.
The use of electricity in the US in 1950 was 4. 3 x 10^11 kilowatt-hours.
What was the total kilowatt-hours of electricity used during these two years?
O a
Ob
Oc
Od
(6. 03 x 10^9) + (4. 3 x 10^11)= 10. 33 x 10^20 = 1. 033 x 10^19
(6. 03 x 10^9)+(4. 3 x 10^11) = (0. 0603 x 10^11) + (4. 3 x 10^11)=4. 3603 x 10^11
(6. 03 x 10^9) x (4. 3 x 10^11) = 25. 929 x 10^20= 2. 6 x 10^19
(6. 03 x 10^9) x (4. 3 x 10^11) = 25. 929 x 10^2=2. 6 x 10^1
The total kilowatt-hours of electricity used during these two years is (6.03 x 10^9)+(4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11 using arithmetic operations.
What is addition and multiplication?Addition is the sum of two or more numbers or values to get a new number. The addition symbol is the plus sign (+).
Multiplication is the repeated addition of a number. If we multiply m by n, that means m is repeatedly added to itself for n times. The symbol for multiplication is ‘×’.
Given that the use of electricity in the US in 1902 was 6. 03 x 10^9 kilowatt-hours and in 1950, it was 4. 3 x 10^11 kilowatt-hours.
To find the total kilowatt-hours of electricity used during these two years, we must add the kilowatt-hours of electricity used in 1902 and 1950.
6. 03 x 10^9 kilowatt-hours can also be written as 0.0603 x 10^11 kilowatt-hours.
This implies, (6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11)
= (0.0603+4)10^11
= 4.3603 x 10^11 kilowatt-hours
Therefore, the total kilowatt-hours of electricity used during these two years is 4.3603 x 10^11.
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The temperature today was 82° last year on this day the temperature was 71 what was the change in temperature
The change in the temperature is 11°.
What is temperature ?Temperature is the physical quantity which describes, how much hot is something? Or we can say it is the quantity which measures the hotness and coldness of something. There are two main quantity values to measure the temperature which are Celsius and Fahrenheit.
Mathematically we can write :
1° Celsius = 32 Fahrenheit
How to find temperature change ?Suppose if we have temperature of two difference time space then we can easily find the difference between the two by simply subtracting them.
For the given question,
last year temperature = 82 degree
temperature today = 71 degree
therefore the change in the temperature in one year is :
82 - 71 = 11 degree.
Thus , the change in temperature is 11 degree.
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One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
The quadratic equation with a repeated root is:
8*x^2 - 32*x +32
And the repeated root is x = 2
What is the repeated root?For a quadratic equation:
0 = a*x^2 + b*x + c
We define the discriminant as:
D = b^2 - 4ac
If D = 0, we have only one real root (or two repeated roots). Then we just need to see which of the given quadratic equations has a discriminant of zero.
1) -x^2 + 18x + 81
The discriminant is:
D = 18^2 - 4*(-1)*81 = 648
2) 3x^2 - 6x + 9
The discriminant is:
D = (-6)^2 - 4*3*9 = -72
3) 8*x^2 - 32*x +32
The discriminant is:
D = (-32)^2 - 4*8*32 = 0
So this is the one with a discriminant of zero.
The roots are given by:
8*x^2 - 32*x +32 = 0
Using Bhaskara's formula we will get:
x = (- (-32) ± √( (-32)^2 - 4*8*32))/(2*8)
x = (32/16) = 2
The repeated root is x = 2
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