The minimum value of the expression is -9
From the question, we have
the expression is 4cosx–3sinx−4.
minimum value of the expression =[tex]c- \sqrt{a^{2} +b^{2} }[/tex]
[tex]=-4- \sqrt{4^{2} +(-3)^{2} }\\=-4-5\\=-9[/tex]
Subtraction:
The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4.
Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.
The minuend, from which we subtract another number, is the first number in a subtraction process.
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Sal has already finished startfraction 5 over 9 endfraction of the 45 math problems he was assigned. If each math problem took him three-fifths of a minute to finish and this pace continues, which expression can be used to determine the amount of time it will take him to finish his remaining homework? 45 times startfraction 5 over 9 endfraction times three-fifths 45 times startfraction 5 over 9 endfraction divided by three-fifths 45 times startfraction 4 over 9 endfraction times three-fifths 45 times startfraction 4 over 9 endfraction divided by three-fifths.
The correct expression to determine the amount of time is 45 times startfraction 4 over 9 endfraction times three-fifths.
Sal has finished = 5/9 of 45 maths problems
So, the remaining number of maths problems = 1 - 5/9
The remaining number of maths problem = (9 - 5)/9
The remaining number of maths problem = 4/9 of 45
Amount of time to solve 1 problem = 3/5 of a minute
Amount of time to solve 4/9 problems = 45×4/9 × 3/5 of a minute.
Hence, 45 times startfraction 4 over 9 endfraction times three-fifths is the correct expression to find the time.
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the population of the world in 2010 was 7 billion and the annual growth rate was estimated at 1.2 percent per year. assuming that the world population follows an exponential growth model, find the projected world population in 2044. round your answer to one decimal place.
With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion
The formula for the exponential growth model is:
X(t) = Xo (1 + r)^t
Where:
X(t) = value of X at time t
Xo = initial value
t = time interval
r = growth rate
Parameters given:
Xo = 7 billion = 7 x 10⁹
t = 2044 - 2010 = 34
r = 1.2% = 0.012
Hence,
X(t) = 7 x 10⁹ (1 + 0.012)³⁴
X(t) = 10.5 x 10⁹ = 10.5 billion
Therefore,
The projected world population in 2044 = 10.5 billion
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Find the length of the third side. If necessary, write in simplest radical form.
Suppose you are able to download 1 free song to your tablet daily and each additional download costs $0. 59. If your monthly bill is $15. 34, how many songs did you download if you downloaded 28 free songs? write an equation and solve for the unknown variable.
For the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
As given in the question,
Total free download songs is equal to 28
Let us consider variable 'x' to represent the number of downloaded songs at the rate of $0.59
Total monthly bill of downloaded songs = $15.34
Equation formed :
0.59x = $15.34
⇒ x = 15.34 / 0.59
⇒ x = 26 songs
Total number of downloaded songs including 28 free songs
= 26 + 28
= 54 songs
Therefore, for the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
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A farmer bought a number of pigs for $168. However, 7 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $36. How many pigs did he originally buy?
Answer:
15$
Step-by-step explanation:
The U.S. Bureau of the Census
predicted that the population of
Florida would be about 17.4 million in
2010 and then would increase by
about 0.22 million per year until 2015.
Which of the following linear models
predicts the population, y, of Florida
(in millions) in terms of x, the number
of years since 2010.
A. y = 17.4x + 0.22
B. y = -0.22x + 17.4
C. y = 0.22x + 17.4
D. y = -17.4x + 0.22
The linear model that predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010 is y = 17.4+0.22x.
According to the question,
We have the following information:
The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015.
Now, y is the population.
So, we will have the total population in 2010 and 0.22 times the number of years.
So, the expression will be:
y = 17.4+0.22x
Hence, the correct option is C.
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Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
The value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
First, let us understand the equation:
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given the system of equations;
3x − 4y + z = 2 ...........equation 1
−9x + 12y − 3z = − 6 ...........equation 2
4x − 2y − z = -16 ...........equation 3
Add equation 1 to equation 3, we will get;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 ...........equation 4
Multiply equation 3 by 3 and subtract from equation 2, we will get;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42 ...........equation 5
Multiply equation 4 by 3 and add it to equation 4, we will get;
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Put z = 1 in equation 5, we will get;
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
x = -2/3
y = -1/2
Thus, the value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
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Radius: 6 mm
Diameter: 12 mm
Area:
Answer:
The area of the circle would be 113.04
Step-by-step explanation:
If you plug the radius into the formula for finding the area of a circle (π·r²), or (3.14 · r²) then you'll get 113.04
Hope this helps! :D
Please mark brainliest!! <3
a number increased by 6 is 30
Answer:
the number is 24 good luck :)
Answer:
24
Step-by-step explanation:
1) Break down the question
We are told that a number increased by 6 is 30 meaning a number added to 6 will get 30.
2) Work you way backwards to get your answer
To find the answer to this question we have to subtract 30 from 6.
This is because we are told that a number is added to get 30 so we should subtract to find our number!
30 - 6 = 243) Check you answer
Every question that you may be unsure of or had been struggling with should always be checked.
To check our answer we have to go backwards and see if the numbers match
24 + 6 = 30As we can see the numbers match together and are correct in our equation
Hope this helps, have a great day!
five and five-sixths minus three and three-fourths plus two and one-half equals blank line.
Answer:
4 7/12
Step-by-step explanation:
Solve: 9l5n - 8l - 3 < 15
Answer:
9l^5n-8l-3<15
Step-by-step explanation:
Find the distance between the points ( – 9.3,3) and ( – 9.3, – 7.5).
We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]
When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]
The distance between the points ( – 9.3,3) and ( – 9.3, – 7.5) is 10.5WHAT DOES Y EQUAL PLS HELP ASAP
The standard form of quadratic function is f(x) = 1(x-2)2 - 6
A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).
Given points (5,3) and (2,-6)
We know that the General form of a quadratic function is
f(x) = ax2+bx+c
Standard form = a(x-h)2 + k
Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)
y = a(x-h)2 + k
3 = a(5-2)2 – 6
3 = a(3)2 – 6
3 + 6 =9a2
9= 9a2
a2 = 9/9
a2=1
a=1
Now substitute a value in standard form
f(x) = 1(x-2)2 – 6
Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
11r+2
Step-by-step explanation:
combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2
Determine the measure of each missing angle:
Angle f= 69
Angle g= 69
Angle h= ??
I found G and F but I’m stuck on H please help me!!
Answer:
Angle f = 69°Angle g = 69°Angle h = 125°Step-by-step explanation:
Angles f and g are congruent as opposite sides are congruent. Therefore:
g = f = (180° - 42°)/2 = 138°/2 = 69°Angles h, 76°, g and the right angle all together form 360°:
h + 76 + g + 90 = 360h + 166 + 69 = 360h + 235 = 360h = 360 - 235h = 125What is the value of 43?
Responses
The Answer is : 64
I took the test and it showed this is the correct answer, hope this helped :)
QUESTION 8/10 HELP ASAPP
Answer:
y = - 2x - 4=================
The slope- intercept form:
y = mx + bUse two points on the graph to find the slope:
(-2, 0) and (0, - 4)Find the slope:
m = (- 4 - 0)/(0 - (-2)) = - 4/2 = - 2The y-intercept is b = - 4.
The equation is:
y = -2x - 4List the first 5 multiples
4:
3:
9:
12:
Answer:
Step-by-step explanation:
3 * 4 = 12 3 * 5 = 15 List of the First 5 Multiples of 3: 3, 6, 9, 12, 15 Notes: The listed multiples are the First 5 Multiples of 3 that are positive (greater than 0) The sum of the digits in Multiples of 3 are divisible by 3
Graph the solution of the inequality 2x - (3-x) > x + 1 on the number line.
Ο Α.
-5 -4 -3 -2 -1 0 1
OB.T
0 с.
2
+
-5 -4 -3 -2 -1 0 1 2
F
OD. |▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
+ +
3
10Ø|||
-5 -4 -3 -2 -1 0 1 2 3
-5 -4 -3 -2 -1 0 1 2
+43
3
4 5
14
4 5
++
4 5
+
4 5
The solution of the inequality is x>2 and the graph is attached below.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. When two values are compared, an inequality shows whether one is higher, lower, or simply not equal to the other.
The given inequality is 2x - (3-x) > x + 1,
Now, solving the inequality by opening the bracket,
2x - (3-x) > x + 1
[tex]2x - 3 + x > x + 1[/tex]
3x - 3 > x + 1
Subtracting x from both sides and adding 3 on both sides,
2x > 4
x > 2
So, the graph is attached below and Option D is correct.
Therefore, after solving the given inequality, we get x > 2 and the graph is attached below.
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use your knowledge of angle relationship to solve for X in the diagram below. By your solution by name in the geometric relationship.
Answer:
Solution
Here ,
5x +7 = 9x-63 (Corresponding angle)
or, 5x-9x =-63-7
or, -4x =-70
or, X=17.5
Hence the value of X is 17.5 degree.
Challenge In basketball, some baskets are worth two points. Others are worth three points. In one game, the ratio of three-point baskets to three-point tries for one team was 2:5. If the team scored 24 points from three-point baskets, how many three-point tries did the team have?
Answer:
20
Step-by-step explanation:
3-point shots made : 3-point shots attempted = 2 : 5
If the team made 24 points out of 3-point baskets, then since 24/3 = 8, it made 8 3-point baskets.
Proportion:
8 made is to 2 as x attempted is to 5
8/2 = x/5
2x = 40
x = 20
Write ap text-style pseudocode for a linear search that searches through a list to find an item x. It should display found if the x is equal to an item in the list.
list <- value, value, value, value
x<-value
FOR EACH item IN the list
{
IF item=x
display "found"
}
Pseudocode is an informal manner of programming description that does not require any strict programming language syntax or underlying era concerns. it is used for growing an outline or a rough draft of a program. Pseudocode summarizes an application's flow but excludes underlying info.
Pseudocode is a synthetic and casual language that facilitates programmers' to increase algorithms. Pseudocode is a "text-primarily based totally" element (algorithmic) layout device. The policies of Pseudocode are fairly straightforward. All statements showing "dependency" are to be indented. the Python pseudocode is a syntax-loose representation of code. So, the Python pseudocode no longer involves any code in it. The Python pseudocode should be a very near illustration of algorithmic good judgment.
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Find slope intercept form
Answer: y=x+4
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b where
m is the slope and b is the y-intercept.
Formula for working out the slope: y2-y1/x2-x1
Put the values in the equation: 4-3/0-(-1). Answer is 1/1 which is 1.
y-intercept: put one of the x and y values from the graph into the equation y=mx+b. Here, I'm going to choose the point (0,4).
The equation is now 4=1(0) + b
Working out for equation:
4=0+b
4=b
The final equation is y=x+4.
You can also use the graph to help you find the y-intercept! First, look at the y-axis. Then the point that passes it is your y-intercept!(Remember it's the y value not the x)
What constant would be added to the expression x^2+8/3x in order to make it a perfect square
Answer:
Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer
Step-by-step explanation:
only if your answers are
A) 3/2
B) 9/4
C) 6
D) 9
HELP ME PLS!!!!!!!!!
Answer:
It's a positive correlation.
Step-by-step explanation:
It's gradually going up, even if there's a few points that are a bit uncorrelated.
Simplify your answer as much as possible please.
Answer:
3/5=w
Step-by-step explanation:
the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.
Answer:
16/5
Step-by-step explanation:
10x3/5=10x w-2/2
The table below shows the number of hours the Carrera family has been driving and the number of miles they’ve driven. Which of the following equations best represents this relationship?
*
Captionless Image
y = 84x
y = 56x
y = 1.5x
Not here
The equation that best represents this relationship given in the table is y = 56x.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a table below that shows the number of hours the Carrera family has been driving and the number of miles they’ve driven.
We can find the slope of the line from the table as follows -
m = (168 - 84)/(3 - 1.5)
m = 56
Now, we can write -
y = 56x + c
84 = 56 x 1.5 + c
c = 0
So, the equation would be -
y = 56x
Therefore, the equation that best represents this relationship given in the table is y = 56x.
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Half of A's money plus one, fifth of B's makes #100. Two
Thirds of A's money plus two-fifth of B's makes # 150.
How much money has each?
The money A has is #150 and the money B has is #125.
According to the question,
We have the following information:
Half of A's money plus one-fifth of B's makes #100. Two-thirds of A's money plus two-fifth of B's makes # 150.
So, we will convert these verbal phrases into expression.
Now, let's take the amount of A to be #x and the amount of B to be #y.
x/2 + y/5 = 100
Using the least common factor of 2 and 5:
5x+2y = 1000
5x = 1000-2y ...(1)
2x/3 + 2y/5 = 150
Adding the fractions using the least common multiple of 3 and 5:
(10x+6y)/15 = 150
Using the cross multiplication method:
10x+6y = 2250
Now, putting the value of 5x from equation 1:
2(1000-2y)+6y = 2250
2000-4y+6y = 2250
2y = 2250-2000
2y = 250
y = 250/2
y = #125
Now, putting this value of y in equation 1:
5x = 1000-2y
5x = 1000-2*125
5x = 1000-250
5x = 750
x = 750/5
x = #150
Hence, the money A has is #150 and the money B has is #125.
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Here is a scatterplot showing the relationship between the number of turnovers and the number of points scored for players in a recent NBA season. The correlation for these data is r = 0.92.
Interpret the correlation
Yes.There is a strong , positive association,so an increase in turnovers causes an increase in points for NBA players..
Given that,
This scatterplot illustrates the correlation between a player's turnover rate and their points scored during a recent NBA season. 3000 2500 2000 Points 1500 and r= 0.92
r = 0.92 A strong positive (upward sloping) linear relationship
While a correlation of 0.10 would be a modest positive correlation, a correlation of 0.97 is a significant negative correlation.
Hence, Yes. Because there is a significant positive correlation, more turnovers result in more points for NBA players.
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v/7 + 7.1 = -4.1 solve for v