f(3) = -9 for the function [tex]\( y = f(x) = -3x \) when \( x \) is 3.[/tex]
To find f(x) when ( x ) is 3 for the given function [tex]\( y = f(x) = -3x \),[/tex] you substitute 3 for ( x ) in the function: [tex]\[ f(3) = -3 \times 3 \][/tex]
Now, calculate the value: [tex]\[ f(3) = -9 \][/tex]
Therefore, when ( x ) is 3, f(x) is -9 for the function [tex]\( y = f(x) = -3x \).[/tex]
In more detail, this means that if you plug ( x = 3 ) into the function, it will result in ( y = -9 ). The function ( y = -3x ) represents a linear relationship where the coefficient of ( x ) is -3. This indicates that for each unit increase in ( x ), ( y ) decreases by 3 units. In the specific case of ( x = 3 ), substituting this value into the function gives [tex]\( y = -3 \times 3 = -9 \).[/tex]
This kind of analysis is fundamental in understanding the behavior of linear functions. It provides insight into how the function's output (y) changes in response to changes in the input ( x ). In this case, when ( x ) increases by 1, ( y ) decreases by 3, leading to the slope of -3 in the function ( y = -3x ).
A selection of staff wages is collected and shown below. £254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700 What is the mode of staff wages? £ and £
the mode is the amount/s which occurs most frequently.
In this data set there are 2 values which occur twice
the mode is £254 and £180
The mode of staff wages is:
£ 180 and £ 254
Step-by-step explanation:The mode of a data set is a data value that exist or occur in the set most frequently (i.e. most of the times)
We are given data points as:
£254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700
On arranging these data points along with their frequency we get:
Data point Frequency
£90 1
£116 1
£165 1
£180 2
£221 1
£239 1
£243 1
£254 2
£276 1
£310 1
£312 1
£350 1
£536 1
£700 1
Two data points has highest frequency
£180 and £254
( since both have frequency 2)
The solution to w/-7=-21 is 3 true or false
false , w = 147
multiply both sides by - 7 to eliminate the fraction
w = - 7 × - 21 = 147
The solution to the equation w/-7=-21 is not 3 but 147. Therefore, the original statement is false.
Explanation:The equation in question is w/-7 = -21. To solve this equation, we multiply both sides by -7.
When we do this, the equation simplifies to w = -(-21)*7. As -(-21) turns to 21, and 21*7 is equal to 147, we find that the solution to the equation w/-7=-21 is w=147, and not w=3.
Therefore, the statement 'The solution to w/-7=-21 is 3' is false.
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It was -8 degrees in the morning, but by 5pm the temperature decreased 10 degrees. What was the temperature then?
Select all the proper fractions
5/3
6/7
12/17
9/5
11/4
6/25
6/7 and 12/17 all the other have to be reduced
These are the proper fractions
6/7
12/17
6/25
These are improper fraction
5/3
9/5
11/4
X(x+3)-x=5 is a quadratic equation?
True
False
The given equation can be simplified to ...
... x² +2x = 5
This is a quadratic equation. The highest-degree term has degree 2. (TRUE)
In City A, the temperature rises 4
degrees
°F from 8 A.M. to 9 A.M. Then the temperature drops 7
degrees
°F from 9 A.M. to 10 A.M. In City B, the temperature drops 6
degrees
°F from 8 A.M. to 9 A.M. Then the temperature drops 2
degrees
°F from 9 A.M. to 10 A.M. Write an expression that represents the change in temperature from 8 A.M. to 10 A.M. for each city. Simplify and interpret each sum.
Use pencil and paper. Which city has the greater change in temperature?
The general expression for the change in temperature between 8am and 10am
[tex]\delta_{8-10}= \delta_{8-9} + \delta_{9-10}[/tex] where [tex]\delta[/tex] stands for change in the subscripted time interval.
For city A:
[tex]\delta_{8-10} = 4 - 7 = -3\enspace ^\circ F[/tex]
For city B:
[tex]\delta_{8-10} = -6 - 2 = -8\enspace ^\circ F[/tex]
In city A, there is an overall drop of 3 degrees (negative value). In city B, the temp drops 8 degrees.
Among A and B, city B has a greater change in temperature (8 vs. 3)
If VUW is equiangular, find k and t.
A.
k = 62, t = 74
B.
k = 64, t = 52
C.
k = 68, t = 52
D.
k = 72, t = 64
Answer:
C. k=68, t=52
Step-by-step explanation:
Let u, v, y represent the measures of the unmarked angles at the respective vertices. The angles of the equiangular triangle are all 180°/3 = 60°, so we have the relations ...
y=vy+v+k = 180v+64+60 = 180u=64u+64+t = 180From these relations, we know that
... v = 180 -124 = 56 . . . . . 3rd equation above
... 56 +56 +k = 180 . . . . . . 2nd equation above, with y=v=56
... k = 180 -112 = 68 . . . . . above with 112 subtracted
... t = 180 -128 = 52 . . . . . 5th equation above with u=64 and 128 subtracted
Need help on this please
1/2divide by 5 =1 blank of 1/2
Answer:
i am pretty sure that it is .2,
Step-by-step explanation:
first, you would do .5 divided by 5 which is 0.1. Then you would do 0.1 divided by 0.5 and you would get 0.2
For the following system of inequalities, which point lies in the solution set?
4x + 2y > 12
x − y > 5
Select one:
A. (1,1)
B. (8,4)
C. (3,9)
D. (9,1)
D
Substitute the coordinates of the given points into the inequalities and if both are true then the point is a solution to the system.
A(1, 1 ) : 4 + 2 = 6 and 1 - 1 = 0 not a solution
B(8, 4 ) : 32 + 8 = 40 and 8 - 4 = - 4 not a solution
C(3, 9 ) : 12 + 18 = 30 and 3 - 9 = - 6 not a solution
D(9, 1 ) : 36 + 2 = 38 and 9 - 1 = 8 is a solution
the point (9, 1 ) is the only point that makes both inequalities true
In figure, MN : NP = 9:1. If MP = 2. Find the distance from M to point K that is 1/4 the distance from M to N?
(A) 1 (B) 1 1/3 (C) 9/20 (D) 1 8/10
The distance MN is 9/(9+1) = 9/10 of the distance MP, so is
... MN = (9/10)×MP = (9/10)×2 = 9/5
The distance MK is 1/4 that, so is ...
... MK = (1/4)×(9/5) = 9/20 . . . . . matches selection (C)
Answer:
C
Step-by-step explanation:
the answer is C. give the person the brainly :) ignore this answer
solve 0.7cos(x)-sin(x)=r for x
where r is a real number
show all steps (if you don't show steps, I'll report the answer)
Try this solution (see the attachment), note:
1. the word 'ctgx' means 'cotangens x'; 2. this equation has roots not for all the real number 'r', it is shown in the 2-d line of the answer; 3. the answer is marked with red colour.
Answer "and" Explanation:
You know that [tex]sin^{2} + cos^{2} x = 1[/tex], so with the given information, you can write
[tex](\frac{7}{10} cos/x-r)^{2} + cos^{2} x= 1[/tex]
that becomes
[tex]\frac{149}{100} cos^{2} / x- \frac{7}{5} r / cos /x + r^{2} - 1 = 0[/tex]
or as well
[tex]149cos^{2} / x -140r / cos / x + 100(r^{2} - 1) = 0[/tex]
The condition for this equation to have real roots is
[tex]70^{2} r^{2} - 149 x 100^{2} (r^{2} - 1) \geq 0[/tex]
hence [tex]r^{2} \leq 149/ 100[/tex]
The roots of the quadratic equation [tex]149t^{2} - 140rt + 100(r^{2} - 1) = 0[/tex] are in the interval [- 1, 1], because with the limitation [tex]|r| \leq \sqrt{149/100}[/tex], the point of a minimum of the polynomial lies between - 1 and 1. Moreover, the polynomial evaluated at - 1 and 1 is > 0 for every r.
Solve for cos x and find the value of sin x.
Find a gradient of a line that is parallel and perpendicular to this line with this gradient of -2
a gradient of a line that is parallel and perpendicular to this line with this gradient of -2
Gradient is the slope
So slope of the line =-2
Slope of parallel line is equal to the slope of the line
So slope of parallel line = -2
Slope of perpendicular line is equal to negative reciprocal of slope of the line
We know slope of line = -2
Negative reciprocal = [tex]\frac{1}{2}[/tex]
So , Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 16 cups in a gallon.
× ×
× ×
× ×
× ×
Answer:
Expression Katrina drinks of water in 7 day = 8 *7 cups .
Step-by-step explanation:
Given : Katrina drinks 0.5 gallons of water per day and There are 16 cups in a gallon.
To find : Which expression shows how to find the number of cups of water she drinks in a week.
Solution : We have given that
Katrina drinks of water per day = 0.5 galoons.
1 gallon = 16 cup .
So, Katrina drinks of water per day = 0.5 * 16 cups.
Katrina drinks of water per day = 8 cups.
1 week = 7 days .
Katrina drinks of water in 7 day = 8 *7 cups.
Katrina drinks of water in 7 day = 56 cups.
Therefore, Expression Katrina drinks of water in 7 day = 8 *7 cups .
Need help with this please
Stanley wants to know how many students in his school enjoy watching talk shows on TV. He asks this question to all 24 students in his history class and finds that 55% of his classmates enjoy watching talk shows on TV. He claims that 55% of the school's student population would be expected to enjoy watching talk shows on TV. Is Stanley making a valid inference about his population? No, it is not a valid inference because he asked all 24 students in his history class instead of taking a sample from his math class No, it is not a valid inference because his classmates do not make up a random sample of the students in the school Yes, it is a valid inference because his classmates make up a random sample of the students in the school Yes, it is a valid inference because he asked all 24 students in his history class
Answer:
The Answer is;
No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.
Step-by-step explanation:
You cannot make a valid inference of the preference of watching TV talk shows by only considering students in one class. You have to randomly select people from the whole population (i.e the total number of students in the school) and then make an inference.
Answer:
No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.
Dad, Anna, and Todd are walking in a city park together. While dad made 3 steps, Anna made 5 steps. For every 3 of Anna's steps, Todd made 5 steps. Anna and Todd calculated that they did 400 steps together. How many steps did dad make during that period?
Answer:
Dad made 90 steps during that period.
Step-by-step explanation:
Let x,y,z be the steps made by dad,Anna and Todd.
Given that while dad made 3 steps, Anna made 5 steps.
That is [tex]\frac{x}{y}= \frac{3}{5}[/tex]
[tex]y=\frac{5x}{3}[/tex]
And for every 3 steps Anna made, Todd made 5 steps.
That is [tex]\frac{y}{z}= \frac{3}{5}[/tex]
[tex]z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}[/tex]
It is also given that total number of steps made by Anna and Todd is 400.
That is y+z=400
let us plugin y and z in terms of x.
[tex]\frac{5x}{3} +\frac{25x}{9} =400[/tex]
[tex]\frac{15x}{9} +\frac{25x}{9}=400[/tex]
[tex]\frac{40x}{9}=400[/tex]
[tex]x=400X\frac{9}{40} =90steps[/tex]
Hence Dad made 90 steps during that period.
Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
How do you write 300450390 in expanded form
300000000+400000+50000+300+90= 300450390
Hope this helped! :)
How do you write 300450390 in expanded form ?
300000000+ 400000+ 50000+ 300+ 90= 300450390
Hope this helps. If it does, please mark me brainiest! <3
An Uber fare in Columbus is $3.50 for the first ½ mile and additional mileage charged at a rate of $0.30 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $15? Please show or explain your calculations.
If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.
After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel
... $11.00/$0.30 = 36 2/3 . . . . tenth-miles
The trip is measured in whole tenths, so you can ride ...
... 36 × 1/10 = 3.6 miles
_____
If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...
... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00
... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses
... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4
... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3
... x ≤ 3.6 . . . . . rounded down to the tenth
The table below shows two equations:
Equation 1 |4x − 3|− 5 = 4
Equation 2 |2x + 3| + 8 = 3
Which statement is true about the solution to the two equations?
Equation 1 and equation 2 have no solutions.
Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.
Answer:
The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
Step-by-step explanation:
Rearranging the two equations, you get ...
|4x -3| = 9 . . . . . has two solutions|2x +3| = -5 . . . . has no solutions (an absolute value cannot be negative)The above-listed answer is the only one that matches these solution counts.
_____
Testing the above values of x reveals they are, indeed, solutions to Equation 1.
(1) has solutions x = 3, x= - 1.5 and (2) has no solution
solving each equation
(1)
add 5 to both sides
|4x - 3 | = 9 ( remove bars from absolute value )
4x - 3 = 9 or 4x - 3 = - 9 ( by definition )
4x = 9 + 3 = 12 or 4x = - 9 + 3 = - 6
x = 3 or x = - 1.5
(2)
subtract 8 from both sides
|2x + 3 | = - 5
the absolute value cannot be equal to a negative quantity
thus |2x + 3 | = - 5 has no solution
it takes Jupiter 11.9 years to orbit,or go around the sun. Saturn takes 17.6 more years than Jupiter to orbit the sun. About how long does it take Saturn to orbit the sun?
Saturn takes 17.6 more years than Jupiter, so 17.6 + 11.9 will get you how long Saturn will take to orbit the sun, which would give you 29.5 years.
The time it takes Saturn to orbit the sun can be calculated by adding Jupiter's orbit time to the additional time Saturn takes after Jupiter. Saturn takes approximately 29.5 years to complete one orbit around the sun.
To find out how long it takes Saturn to orbit the sun, we know that Jupiter takes 11.9 years and Saturn takes 17.6 more years than Jupiter. So, Saturn takes 11.9 + 17.6 = 29.5 years to orbit the sun.
on an incoming field trip, 60 sixth graders and 48 seventh graders, will be traveling by vans to the museum. Each van will be carry the same number of students and carry only sixth graders on only seventh graders. If vans are to carry the greatest possible number of students, how many vans will be needed?
The greatest common factor of 60 and 48 is 12. If 12-student vans are used for transport, then (60+48)/12 = 9 vans will be needed.
_____
5 vans are needed for the 6th graders; 4 vans are needed for the 7th graders.
City A and city B each have 10 parks. The table shows the number of acres for each park in the two cities. City A 6 9 10 7 10 10 2 5 8 8 City B 5 10 8 11 7 12 6 5 4 5 Select from the drop-down menus to correctly complete each statement. The mean number of acres for each park for the two cities is . The range for the number of acres for parks for the two cities is .
Answer:
The mean number of acres for each park for the two cities is:
City A: 7.5
City B: 7.3
The range for the number of acres for parks for the two cities is : 8
Step-by-step explanation:
The table shows the number of acres for each park in the two cities.
City A: 6 9 10 7 10 10 2 5 8 8
City B : 5 10 8 11 7 12 6 5 4 5
City A:
Minimum acre of park=2
Maximum acre of park=10
Range=Maximum-Minimum
Range=10-2
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{6+9+10+7+10+10+2+5+8+8}{10}\\\\\\Mean=\dfrac{75}{10}\\\\Mean=7.5[/tex]
City B:
Minimum acre of park=4
Maximum acre of park=12
Range=Maximum-Minimum
Range=12-4
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{5+10+8+11+7+12+6+5+4+5}{10}\\\\\\Mean=\dfrac{73}{10}\\\\Mean=7.3[/tex]
Answer:
1. about the same
2. the same
Step-by-step explanation:
If f is a polynomial function and xminus−5 is a factor of f, then f(5)equals=_______.
if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0
Answer:
[tex]f(5) = 0[/tex]
Step-by-step explanation:
A function [tex]f[/tex] can be simplified by it's roots.
For example, a second order function expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0.[/tex]
Can be expressed in function of it's roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex].
Is [tex]x-5[/tex] is a factor of f, this means that f can be expressed in function of [tex]x - 5[/tex], that is, x = 5 is a root of the equation.
This means that:
[tex]f(5) = 0[/tex]
PLEASE HELP QUICK
Mike was in charge of collecting contributions for the Food Bank. He received contributions of $13, $34, $26, $31, and $28 from five co-workers. Find the median value of these contributions.
median = $28
the median is the middle value of the data arranged in ascending order
rearrange the data in ascending order
13 26 28 31 34
the middle entry is 28
hence median = $28
The median is the middle value so put the numbers in order from smallest to largest.
13,26,28,31,34
The middle value is 28, so the median value is 28
What is the slope of the line passing through the points (2, 4) and (5, 6)?
2/3 is the slope of (2,4) and (5,6)
slope = [tex]\frac{2}{3}[/tex]
calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = ( 2, 4 ) and (x₂, y₂ ) = (5, 6 )
m = [tex]\frac{6-4}{5-2}[/tex] = [tex]\frac{2}{3}[/tex]
Suppose that you are asked if there would be a strong or weak correlation between the number of people shopping in malls and the approach of the Holiday Season. Explain whether there would be a strong or weak correlation and the difference between the two.
There could be a strong correlation between the proximity of the holiday season and the number of people who buy in the shopping centers.
It is known that when there are vacations people tend to frequent shopping centers more often than when they are busy with work or school.
Therefore, the proximity in the holiday season is related to the increase in the number of people who buy in the shopping centers.
This means that there is a strong correlation between both variables, since when one increases the other also does. This type of correlation is called positive. When, on the contrary, the increase of one variable causes the decrease of another variable, it is said that there is a negative correlation.
There are several coefficients that measure the degree of correlation (strong or weak), adapted to the nature of the data. The best known is the 'r' coefficient of Pearson correlation
A correlation is strong when the change in a variable x produces a significant change in a variable 'y'. In this case, the correlation coefficient r approaches | 1 |.
When the correlation between two variables is weak, the change of one causes a very slight and difficult to perceive change in the other variable. In this case, the correlation coefficient approaches zero
Most likely, there would be a strong correlation between the two.
A correlation is a measurement of the relationship between two variables. When two variables are strongly correlated, this means that a change in one variable has a strong impact on the other one. On the other hand, when the correlation between variables is weak, this means that the two variables are not strongly connected. In this example, the two situations are likely to be strongly correlated because the number of people is very likely to go up as the holiday season approaches.
Please Answer The Following Questions.
Answer:
4. 73
5. 40°
Step-by-step explanation:
The sum of the angles in a triangle is 180°. The sum of angles in a linear pair is 180°.
4. 45° +62° + k° = 180°
... 107 +k = 180 . . . . . collect terms, divide by °
... k = 180 -107 = 73 . . . . . subtract 107
_____
5. ∠STR = ∠SRT = 20°
... ∠STR +∠STU = 180°
... 20° + 4x = 180°
... 4x = 160° . . . . . . . . subtract 20°
... x = 40° . . . . . . . . . . divide by the coefficient of x
Which expression is equivalent to the expression -2 4/5+6/7: 2 4/5-6/7: -2 4/5-6/7: -(2 4/5+6/7): -(2 4/5 - 6/7)
When you factor out -1, you get ...
... -(2 4/5 - 6/7)