Answer:
f(x) = - [tex]\frac{1}{2}[/tex] x
Step-by-step explanation:
The standard form for a linear function is
f(x) = ax + b
Using the given values f(- 4) = 2 and f(6) = 3 , then
- 4a + b = 2 → (1)
6a + b = - 3 → (2)
Subtract (2) from (1) term by term to eliminate b
- 10a = 5 ( divide both sides by - 10 )
a = - [tex]\frac{1}{2}[/tex]
Substitute a = - [tex]\frac{1}{2}[/tex] into either of the 2 equations and solve for b
Substituting into (1)
2 + b = 2 ( subtract 2 from both sides )
b = 0
Thus the linear function is
f(x) = - [tex]\frac{1}{2}[/tex] x
The linear function is f(x) = -0.5x
For f(-4) = 2
x₁ = -4, y₁ = 2
For f(6) = -3
x₂ = 6, y₂ = -3
The slope(m) is found using the formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (-3-2)/(6-(-4))
m = -5/10
m = -0.5
Substitute m = -0.5, x₁= -4, and y₁ = 2 into the equation below:
y - y₁ = m(x - x₁)
y - 2 = -0.5(x - (-4))
y - 2 = -0.5(x + 4)
y - 2 = -0.5x - 2
y = -0.5x - 2 + 2
y = -0.5x
Therefore, the linear function is f(x) = -0.5x
Learn more here: https://brainly.com/question/17003809
a rectangular tank is 76cm long, 50cm wide and 40cm high, how many litres of water can it hold?
Answer:
Volume of a cuboid or rectangular tank = side × side × side
or
volume of a cuboid or rectangular tank = length× width × height
volume of the rectangular tank = 76 × 50 × 40
volume of the rectangular tank = 152000cm³
Therefore the rectangular tank can hold 152000cm³ litres of water
Composite functions
g(d) = 2d - 5
h(d) = -4d +3
Find (hºg)(d)
Answer:
[tex](h\circ g)(d)=-8d +23[/tex]
Step-by-step explanation:
Composite Function
Given g(d) and h(d) real functions, the composite function named (hog)(d) is defined as:
[tex](h\circ g)(d)=h(g(x))[/tex]
For practical purposes, it can be found by substituting g into h.
The functions g and h are given as:
[tex]g(d) = 2d - 5[/tex]
[tex]h(d) = -4d +3[/tex]
Substituting g into h:
[tex](h\circ g)(d)=-4(2d - 5) +3[/tex]
Operating:
[tex](h\circ g)(d)=-8d +20 +3[/tex]
[tex]\boxed{(h\circ g)(d)=-8d +23}[/tex]
The 7th grade class experienced a 15% decrease in enrollment.Last year,the 7th grade class had 280 students. How many how many students are enrolled in the 7th grade this year?
Answer: 238
Step-by-step explanation: 10% of 280 is 28. 1% of 280 is 2.8. Multiply 2.8 times 5 and you get 14. Add 10% and 5% (28+14) and you get 15% which is 42. Subtract 42 from 280 and you get 238.
Answer:
232 students are enrolled this year.
Step-by-step explanation:
Since 15% of the enrollment of the previous year is gone, you must take 15% of the total number of students and subtract that from the total number of students.
[tex]280*0.15=42[/tex]
This tells us that the 15% decrease means there are 42 fewer students enrolled this year. Now you would just subtract 42 from 280.
280 - 42 = 232
How do horizontal and vertical translations each affect the coordinates of the points on a figure.
Answer:
Hi there!
Your answer is:
Perform the translation:
x-10
y-3
Step-by-step explanation:
A translation is how many units X moved left/right and how many units Y moved up/down!
In your case, X went left and Y went down! This means there was a DECREASE in both of these values!
We can determine this by choosing one point and counting how many units it moved.
Lets use the point on figure 1 at (2,5)
Where did it move on figure 2? (-8, 2)
How many units left did it go? 10!
How many units down did it go? 3!
Rigid transformations is preservative of the distance between pairs of points on the figure. Horizontal and vertical translations are rigid motion transformation such that the shape and size of the figure do not change;
The sequence of translation used to move Figure 1 onto Figure 2 is T₍₋₁₀, ₋₃₎
Translate Figure 1, ten units left and three units down to move Figure 1 onto Figure 2
The reason the above sequence is correct is as follows:
Given that translations are rigid motion, we have;
The sequence of translation that will move a point on Figure 1 to the corresponding point on Figure 2 is the same as the sequence of translation used to move Figure 1 to Figure 2
The coordinates of the point on the top right corner of Figure 1 is (6, 8)
The coordinates of the corresponding point in Figure 2 is (-4, 5)
The sequence of translation, T, is given by the difference of the coordinates as follows;
The sequence of translation is T₍₍₍₋₄₎ ₋ ₆₎, ₍₅ ₋ ₈₎₎ = T₍₋₁₀, ₋₃₎
Therefore, the sequence of translation are;
1) Shift Figure 1, 10 units to the left then 2) Shift Figure 1, 3 units down to move Figure 1 to Figure 2
Learn more about rigid transformations here:
https://brainly.com/question/23461633
i rlly need help im stuck can someone help me out. What the total price?
Part E
After how many years will the investment have a value of less than $2,000?
Answer:
At year 3 and beyond, The investment will have a value less than $2,000.
t=3.
Step-by-step explanation:
Write a system of linear equations that has (-4, 8) as the solution. Once you have made your system of equations, solve it algebraically to show that you do indeed get the solution (-4, 8).
Answer:
See below
Step-by-step explanation:
(-4, 8) has to be the solution.
1st equation: -4x+8y = 1
2nd equation: 8x - 4y = 1
These should work. Do the matrix-substitution combo method to see:
-4 8 1
.8 -4 -1
Reduce and and matrix-substitution combo:
1 0 -4
0 1 8
The reduced eckerd form of the matrix shows that the solutions are (-4, 8)
Therefore it -4x + 8u = 1 and 8x - 4y = 1 are the two equations for the system.
Pick < ,< or = to make the statement true. 11 ..... 52/9
Answer:
11>52/9
Step-by-step explanation:
52/9 = 5.7777....
11> 5.77777....
Whats the primer and área?
Answer:
perimeter = 32
area = 60
Given the absolute value function y =| x - 3| +1, describe the transformations . type your answer...
Answer:
parent funiction y=|x|
hozonital shift right 3 units
vertical shift up 1 units
reficlation none
vertical none
Step-by-step explanation:
Courtni is multiplying 3.2 x 30. Explain how Courtni can use expanded form
and properties of multiplication to solve this problem mentally. What is the
product of 3.2 x 30?
If we multiply 3.2 x 30, the answer is 96.
Jacob's job pays him $12.50 per hour. Which equation can be used to find Jacob's salary,
y, if he works for x hours? *
(5 Points)
A. y = x/12.50
B.y = 12.50 + x
.
C.y = 12.50 - x
D.y = 12.50x
Answer:
D
Step-by-step explanation:
BECAUSE the number of hrs he works his salary multiplies
hope this helps..
A concentrated cleaning solution must be mixed with water in a container that allows users to spray onto the surfaces they need to clean. Pam’s mom asked her to add 30 ounces of cleaning concentrate into the sprayer and then add water to fill the sprayer. Her father told her that the sprayer must contain 20% cleaning concentrate and 80% water.
a. How many ounces does the sprayer hold?
ounces
b. How much water was added to the sprayer?
ounces
Answer: The sprayer can hold 150 ounces, and Pam needs to add 120 ounces of water.
Step-by-step explanation:
The data that we know is:
We must use 30 oz of cleaning concentrate.
The end product must be 80% water and 20% cleaning concentrate.
This means that:
Mass of water/total mass in the sprayer = 0.8
mass of cleaning concentrate/total mass in the sprayer = 0.2
Then, let's define the variables:
X = ounces that the sprayer can hold.
Y = ounces of water added.
Then we have the equations:
30oz + X = Y.
30oz/Y = 0.20
X/Y = 0.80
From the second equation we can find the value of Y.
30oz = 0.20*Y
30oz/0.20 = Y = 150oz.
Then the sprayer can hold 150 ounces.
Now from the third equation we have:
X/Y = 0.8
We know that Y = 150oz
Then:
X/150oz = 0.8
X = 0.8*150oz = 120 oz.
Then the water that must be added is 120 ounces.
Una empresa comercial vende automóviles cuyo precio es de S/. 60 000, con una cuota inicial del 20%, para cancelar el saldo en 30 meses de plazo.calcula la cuota fija mensual que se pagará seda empresa cobra una tasa de interés simple del 12% semestralmente
Responder:
2560
Explicación paso a paso:
Dado lo siguiente:
Precio del automóvil = 60000
Cuota inicial = 20% del precio = (0.2 * 60000 = 12,000
Saldo = (60000 - 12000) = 48000
La empresa cobra un interés simple del 12% cada 6 meses
Periodo de pago = 30 meses / 6 = 5 periodos
Interés simple: p * r * t
= 48000 * 0,12 * 5 = 28800
Por lo tanto, monto total a reembolsar, incluidos los intereses:
Balance + 28800; 48000 + 28800 = 76800
El reembolso mensual es fijo;
Por lo tanto,
76800/30 = 2560
What is the value of the expression below when w = 2?
Answer:57
Step-by-step explanation:
Rewrite the following equation in slope-intercept form. 6x - 3y = 19
Answer:
y= 2x - 19/3
Step-by-step explanation:
6x-3y=19
3y=6x-19
y=2x- 19/3
slope: 2
y-intercept: -19/3
Zahmiere and Brayden are playing basketball. Yesterday, Zahmiere made 3 shots in 5 attempts, while Brayden made 4 shots in 6 attempts. If they continue at those rates, who will make more shots in 30 attempts? Plsss answer
Brayden would make the most shots in 30 attempts.
how do you work out 7.62 + 5.97 + 3.6 =?
Answer:
17.19
Step-by-step explanation:
First, you add 7.62 and 5.97. This leaves you with 13.59 + 3.6, and you add these together to get 17.19. That is your answer :)
i need help on this
Which expression is equivalent to 6(x-4)?
how do you simplify this?
Answer:
tan x
Step-by-step explanation:
(tan-x)[sec(pi/2)-x] (sin-x)
We know that tan (-x) = - tan (x) and sin (-x) = - sin (x)
-(tanx)[sec(pi/2)-x] -(sinx)
(tanx)[sec(pi/2)-x] (sinx)
Using the identity sec = 1/ cos
sec ( pi/2 -x) =1/cos ( pi /2 -x)
We know that cos (s-t)=cos (s) cos(t) + sin (s) sin (t)
1/ ( cos pi/2 cos x + sin pi/2 sin x) = 1/(0 cos x - 1 sinx) = 1 / sinx
Replacing into the equation
(tanx)[1/ sinx] (sinx)
tan x
Please help!
Jill's father is a pilot. The airplane he flies can carry 396 passengers. If each passenger is allowed to take 60 pounds of luggage, how many total pounds can the plane carry in luggage?
Answer:
23760 pounds
Step-by-step explanation:
396 passengers
60 pounds for each passenger
total pounds plane can carry=passengers × pounds
= 396×60
= 23760 pounds
....
SORRY I NEED HELP AGAIN! 5 cans of soda cost $3.75. At this rate, how much do 3 cans of soda cost?
Type your answer here..
Answer:
So if 5 soda cost $3.75 per can, multiply 3 times $3.75 and that would be your answer: $11.25
Step-by-step explanation:
What is 11/12 - 5/12
And plz explain step by step.
Answer:
6/12 or 1/2
Step-by-step explanation:
Since 11/12 and 5/12 have the same denominator (12), I didn't need to worry about anything pertaining to it. And because I didn't need to do anything that had to do with the denominator (12), I just did 11-5 (6), and made it 6/12, which is equivalent to 1/2. Hope this helped!
Answer:6/12
Step-by-step explanation: Step 1
Since our denominators match, we can subtract the numerators.
11 − 5 = 6
So the answer is:
6
12
Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 45 of the number of part 1 questions. Part 2: She got 16 questions correct, which was 23 of the number of part 2 questions. What was the total number of questions on Stephanie's exam?
Given :
Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions. Part 2: She got 16 questions correct, which was 2/3 of the number of part 2 questions.
To Find :
The total number of questions on Stephanie's exam.
Solution :
Let, number of questions in Part 1 is x :
[tex]16=\dfrac{4}{5}x\\\\x=20[/tex]
Let, number of questions in Part 2 is y :
[tex]16=\dfrac{2}{3}y\\\\y=24[/tex]
Therefore, total number of questions on Stephanie's exam are 20 + 40 = 60.
Hence, this is the required solution.
What is the greatest common factor of 16 and 13
Answer:
1
Step-by-step explanation:
The only factor they have in common is 1
1
The price of a video game was reduced from $60 to $45. By what percentage
was the price of the video game reduced?
А
15%
B
75%
C
25%
D
40%
Answer:
C, 25%
Step-by-step explanation:
25% = 1/4
1/4 of 60 = 15
60 - 15 = 45
What’s the common difference for this arithmetic sequence: 23,__,__,50...
9514 1404 393
Answer:
9
Step-by-step explanation:
The 4th term is the sum of the first term and 3 times the common difference.
50 = 23 + 3d
27 = 3d
9 = d
The common difference is 9.
__
The first few terms are ...
23, 32, 41, 50, 59, 68, ...
Pls help im in the test i’ll give 50 points
Answer:
I think it's A
Step-by-step explanation:
the point is touches the y axis is 2
Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)? Select two
options
y=-3/4x+1
3x - 4y = -4
4x - 3y = -3
y-2 = -3/4(x - 4)
y+2 =3/4(x + 4)
Answer:
y = 3/ 4 x + 1
Step-by-step explanation:
