Step-by-step explanation:
For y = 2^x:
f(-3) = 2^-3. f(-2) = 2^-2. f(-1) = 2^-1
= 1/8 = 1/4. =1/2
f(0) = 2^0 f(1) = 2^1. f(2) = 2^2
= 1 = 2. =4
f(3) = 2^3
=8
For 3y = 7x + 3, y= (7x+3)/3
f(-3) = [7(-3)+3] / 3. f(-2) = [7(-2)+3] / 3
= -6. = -11/3
f(-1) = [7(-1)+3] / 3. f(0) = [7(0)+3] / 3
= -4/3 = 1
f(1) = [7(1)+3] / 3. f(2) = [7(2)+3] / 3
= 10/3 = 17/3
f(3) = [7(3)+3] / 3.
= 8
point of intersection, where y=2^x and 3y = 7x + 3 has the same x and y coordinate
Answer: (0,1) and (3,8)
3353 8. A survey showed that 1/3 of the students in the class liked blue 1/4 of the remainder liked red. The remaining 24 students liked yellow. How many students were in the class?
Answer: there are 48 students in the class
Step-by-step explanation:
let x = the total number of students in the class
1 - 1/3 = 2/3
1/4 * 2/3 = 2/12 = 1/6
1/3x + 1/6x + 24 = x
2/6x + 1/6x + 24 = x
3/6x + 24 = x
1/2x + 24 = x
24 = x - 1/2x
24 = 1/2x
24 * 2 = x
x = 48
there are 48 students in the class
I need help finding the intercept , slope and equation please help!
Answer:
Step-by-step explanation:
if they are saying approximately then y = 3 for the y intercept, and
the slope, m , is 3/4 ( rise / run)
then the equation for this line is
y = [tex]\frac{3}{4}[/tex] * x + 3
y = 3x/4 + 3
if f (x)=x^2+1 and g(x) =x-4 which value is equivalent to f x g
Answer:
A value of [tex]x^3 - 4x^2 + x - 4[/tex] is equivalent to [tex]f \times g[/tex]
Step-by-step explanation:
We are given the following functions:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = x - 4[/tex]
Which value is equivalent to f x g?
We multiply these functions, applying the distributive property. So
[tex]f \times g = (x^2+1)(x-4) = x^3 - 4x^2 + x - 4[/tex]
A value of [tex]x^3 - 4x^2 + x - 4[/tex] is equivalent to [tex]f \times g[/tex]
HELP ME W MY MATH IM BEGGINGM
Answer:
Year 1: 164.87
Year 2: 169.88
Year 5: 185.86
Step-by-step explanation:
She is earning 3% interest per year that compounds once yearly.
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Question 4
10
Answer:
um what
Step-by-step explanation:
how do you solve simple linear equations?
9514 1404 393
Explanation:
The rules of equality tell you that you can do anything you like to an equation, as long as you do the same thing to both sides of the equal sign. This is the essence of Algebra, so is worth remembering. My teacher summarized it as "keep the equal sign sacred."
__
"Simple linear equations" come in several varieties. They are sometimes called "one-step", or "two-step", or "three step" linear equations, depending on how many steps are required to solve them. In what follows, we're using "x" as the variable, and the letters a, b, c, d as constants.
One-step
In general, the "one step" will be either an addition or a multiplication.
x + a = b . . . . an addition equation
ax = b . . . . . . a multiplication equation
The key in any case is to look at what is done to the variable and use an inverse operation to "undo" it. The opposite of addition is addition of the additive inverse (add the opposite). This is also called subtraction. For the addition equation, this looks like ...
x + a - a = b - a . . . . . . add (-a) to both sides (or subtract 'a')
x = b - a . . . . . . . . . . . the solution
The opposite of multiplication is multiplication by the multiplicative inverse (the reciprocal) This is also called division. For the multiplication equation, this looks like ...
ax(1/a) = b(1/a) . . . . . multiply by (1/a) on both sides (or divide by 'a')
x = b/a . . . . . . . . . . . the solution
__
Two-step
As with one-step linear equations, two-step equations come in some different forms.
ax +b = c
ax +b = cx
a(x +b) = c
In general, the two steps are an addition step and a multiplication step, not necessarily in that order. You will notice that the first step can transform the equation to a "one-step" equation. As before, inverse operations are involved, and whatever is done is done to both sides of the equal sign.
ax +b = c ⇒ ax = (c -b) . . . . subtract b to get a multiplication equation
In this next, we have the variable on both sides of the equal sign. we can put the variable on one side of the equal sign by adding the opposite of the term we don't want where it is. Leaving the constant alone, we can add (-ax) to both sides to get ...
ax +b = cx ⇒ b = cx -ax ⇒ b = (c -a)x
When you have numbers, you can go directly to (c-a)x by "combining terms". This is now the one-step multiplication equation.
Finally, another 2-step form is ...
a(x +b) = c ⇒ x +b = c/a . . . . . divide by 'a' to get an addition equation
This last equation can also be solved by using the distributive property first.
ax +ab = c . . . . . still a 2-step equation, now of the first type
__
Three-step
The most typical "3-step" linear equation is of the form ...
ax +b = cx +d
where both variables and constants are on both sides of the equal sign. As you may have noticed above, we prefer to have variables on one side and constants on the other side. So, add the opposite of the term you don't want where it is (to both sides, of course).
If we want variables on the left and constants on the right, we can add -cx and -b. The "3 steps" assume you do these as separate operations.
ax +b -cx = cx +d -cx ⇒ (a-c)x +b = d . . . a two-step equation
(a-c)x +b -b = d -b ⇒ (a-c)x = d-b . . . . a one-step multiplication equation
_____
Additional comments
There are some choices you can make that will tend to reduce errors. One of them involves selection of the variable term you want to eliminate (add the opposite of). Generally, if you choose the term with the lowest (most negative, left-most on the number line) coefficient, adding its opposite will result in a positive coefficient for the remaining variable term. Then when you divide by that coefficient, you're dividing by a positive number. Most folks perform arithmetic with fewer errors when they're working with positive numbers.
The general approach to any "solve for" situation is to look at what is done to the variable you're solving for. The Order of Operations is a useful lens for looking at this. When you list the operations, your "undo" sequence will start with the last operation on the list, and work backward.
Further note: your total comfort with doing arithmetic with any kind of numbers (integers, fractions, mixed-numbers, decimals, scientific notation, positive or negative) will aid you immensely. Always be careful with minus signs. They tend to get lost, forgotten, ignored, Be sure they don't.
Rewrite the function f(x)=2(x-2)^2+6 in the form f(x)=ax^2+bx+c.
Answer:
To write a polynomial in standard form, simplify and then arrange the terms in descending order.
f(x)=ax²+bx+c
Simplify each term.
f(x)=2x²−8x+8+6
Add 8 and 6.
f(x)=2x²−8x+14
Step-by-step explanation:
What is an equation of the line that passes through the points (4, -1) and
(-8. – 7)?
Answer:
[tex]y = \frac{1}{2} x - 3[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the gradient formula above,
gradient of line
[tex] = \frac{ - 1 - ( - 7)}{4 - ( - 8)} [/tex]
[tex] = \frac{ - 1 + 7}{4 + 8} [/tex]
[tex] = \frac{6}{12} [/tex]
[tex] = \frac{1}{2} [/tex]
Substitute m= ½ into the equation:
y= ½x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= -1,
[tex] - 1 = \frac{1}{2} (4) + c[/tex]
-1= 2 +c
c= -1 -2 (-2 on both sides)
c= -3
∴ The equation of the line is y= ½x -3.
1+2+3+4+5+6+7+8+9+10=
im bor*ed...pls ch*at with me???
6 friends share 10 pizzas equally plz help
Answer:
6/10 of the pizza.
The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set
Answer: Your question has some missing data attached below is the missing data
Answer : Mean value is Greater
Step-by-step explanation:
The relative value of the mean for original data set is greater
Relative value of median for original data set is lesser
This is simply because the The distribution is generally skewed to the right ( Right skewed )
Find the 14th term of the arithmetic sequence x-4, 7x-9, 13x-14, ...
Answer:
14x-9
Step-by-step explanation:
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
It is:
B.Divide the area of the triangle by the base and multiply the result by 2.
Is this correct? the question is asking if the triangle would have a right, acute, or obtuse angle.
Answer:
Acute
Step-by-step explanation:
All triangles have to have a acute or it would be to big
Answer:
yes it is because its a triangle and its acute
I can believe my teachers think i can do this
Answer:
Is that actually your hw-?
Step-by-step explanation:
Answer:
Well dang
Step-by-step explanation:
Help which one
A . (1/2)(4)(3)
B . (1/2)(4)(11)
C . (1/2)(4)(8)
D . (1/2)(8)(4)
9514 1404 393
Answer:
B. (1/2)(4)(11)
Step-by-step explanation:
The length of the base is the sum of the lengths that make it up:
3 + 8 = 11 . . . . feet
The height is 4 ft, so the area is ...
A = 1/2bh
A = 1/2(11)(4) . . . . . equivalent to choice B
Can someone help me please
Answer:
It's 2/15
Step-by-step explanation:
please help school is literally about to end
Answer:
192 is the answer
Step-by-step explanation:
Answer:
SA = 272 sq in
Step-by-step explanation:
SA = 2(8 x 2) + 2(8 x 12) + 2(2 x 12)
= 2(16) + 2(96) + 2(24)
= 32 + 192 + 48
= 272 sq in
IVE BEEN ASKING FOR AN HOUR PLEASE HELP!! PLEASE ANYONE!! solve for x
Answer:
[tex]\sqrt{3}[/tex] sqrt(3)
Step-by-step explanation:
Pythagroean theorem shows that x^2+sqrt(2)^2=sqrt(5)^2
In other words,
x^2+2=5
x^2=3
x=sqrt(3)
what is quartile 1 and 3
Answer:
Q1 = 2
Q3 = 3
I think that's the answer
Hope this helps! (°◡°♡).:。
Answer:
Q1 is 2 Q2 is 3
Just cut the list of number into quarters
ANSWERRRRRRRRRRRRRRRRRRRR PLZZZZZZZZZZZZZZzz
Answer:
-1/3
Step-by-step explanation:
Find two points on the line (0,2) and (3,1)
Using the slope formula
m = (y2-y1)/(x2-x1)
= (1-2)/(3-0)
= -1/3
Answer:
A
Step-by-step explanation:
1) take two points of the line
A(0,2) ; B(3,1)
2) use this formula for find the slope
(y2-y1)/(x2-x1)
(1-2)/(3-0)
slope = -1/3
each pack of sugar free gum at a store cost $0.89 including tax if Evan pays $10.00 and receives $0.21 in change how many packs of gum did he buy
Answer:
12
Step-by-step explanation:
how do you find the answer?5y+8=-6
Answer:
Step-by-step explanation:
5y+8=-6
-8
5y=-14/5
y=-2.8
Answer:
y = - 2.8
[tex]y=-2\frac{4}{5}[/tex]
Step-by-step explanation:
5y + 8 = - 6
5y + 8 - 8 = - 6 - 8
5y = - 14
5y ÷ 5 = - 14 ÷ 5
y = - 2.8
A quantity with an initial value of 760 grows exponentially at a rate of 90% every week. What is the value of the quantity after 49 days, to the nearest hundredth?
Answer: ≈67934.25
Step-by-step explanation:
-2,6,-18,54 find the 12th term
Answer:
354294
Step-by-step explanation:
-2,6,-18,54,-162,486,-1458,4374,-13122,39366,-118098,354294
multiply each number by -3
The U.S. federal government conducts a survey of high school seniors concerning their plans for future education and employment. One question asks whether they are planning to attend a four-year college or university in the following year. Fifty percent answer yes to this question; that fifty percent is a: Question 2 options: parameter statistic variable data
Answer:
statistic
Step-by-step explanation:
Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Answer:
The answer is 15 ounces
Step-by-step explanation:
33/4 ÷ 4 pounds.
(4 × 3 + 3)/4 ÷ 4 pounds.
15/4 ÷ 4 pounds.
15/4 × 1/4 pounds.
15/16 pounds.
Now we know that, 1 pound = 16 ounces.
So, 15/16 pounds = 15/16 × 16 ounces = 15 ounces.
Thus, The answer is 15 ounces
An equation is modeled. What value of x makes the equation true? Explain.
A) x = 7
B) x = -1
C) x = 1
D) x = -5
Answer:
B: x=-1
Step-by-step explanation:
5x+6=1
5x+6-6=1-6
simplify
divide by 5 on both sides
x=-1
Unit 3: Parallel & Perpendicular Lines Homework 5: Linear Equations Slope-Intercept & Standard Form
Directions: Determine if the equations are parallel, perpendicular, or neither.
11. y = -3x + 6 and y = 1/3 x -8
12. y = 5/4 x + 1 and y = 5/4 x - 7
13. 3x + 2y = 6 and y = -3/2 x + 5
14. 3y = 4x + 15 and 9x + 12y = 12
15. 10x - 2y = 16 and x + 5y = -20
16. 5x + 3y = 3 and 3x + 5y = -25
17. -9y = -3x + 18 and 2x -6y = 30
18. x-y = 5 and x + y = -10
11. y = -3x + 6 and y = 1/3 x -8 (perpendicular)
12. y = 5/4 x + 1 and y = 5/4 x - 7 (parallel)
13. 3x + 2y = 6 and y = -3/2 x + 5 (parallel)
14. 3y = 4x + 15 and 9x + 12y = 12 (perpendicular)
15. 10x - 2y = 16 and x + 5y = -20 (perpendicular)
For two equations to be parallel, the slope has to be the same
For two equations to be perpendicular, the product of their slopes must be equal to -1
The equation of a line is the slope-intercept form is:
y = mx + c
where m is the slope and c is the intercept
11) y = -3x + 6 and y = 1/3 x -8
The equations are perpendicular because -3 x 1/3 = -1
12) y = 5/4 x + 1 and y = 5/4 x - 7
The two lines are parallel because they both have a slope of 5/4
13) 3x + 2y = 6 and y = -3/2 x + 5
The equation 3x + 2y = 6 can be re-written as y = -3/2 x + 3
Therefore, the two equations are parallel since they have the same slope of -3/2
14) 3y = 4x + 15 and 9x + 12y = 12
3y = 4x + 15 can be re-written as y = 4/3 x + 5
9x + 12y = 12 can be re-written as y = -3/4 x + 1
The two lines are perpendicular because -3/4 x 4/3 = -1
15) 10x - 2y = 16 and x + 5y = -20
10x - 2y = 16 can be re-written as y = 5x - 8
x + 5y = -20 can be re-written as y = -1/5 x - 4
Both equations are perpendicular since -1/5 x 5 = -1
Learn more here: https://brainly.com/question/11482954
Answer:
Step-by-step explanation:
two pipes with lengths of 42 inches and 54 inches respectively are to be cut in pieces of equal lengths. what is the greatest possible length of these pieces so that no part of either pipe is left over in inches
Answer: 6
Step-by-step explanation:
Since we are informed that two pipes with lengths of 42 inches and 54 inches respectively are to be cut in pieces of equal lengths and we want to know the number of pieces that they can be cut into.
This question simply means that we need to find the factors of both 42 and 54 and choose the highest.
42 = 1, 2, 3, 6, 7, 14, 21, and 42.
54 = 1, 2, 3, 6, 9, 18, 27, and 54.
Therefore, the highest common factor is 6. Therefore, the greatest possible length will be 6 inches