[tex]f(x)[/tex] passes through origin, i.e. $(0,0)$
if you move 5 units up, it should pass through $(0,5)$
so you'll add 5 to $y$ i.e. $y+5=x^2$ this satisfies $(0,5)$
and to move right, it should pass through $(7,0)$ so you'll subtract $7$ from $x$ i.e. $y=(x-7)^2$
now combine both translations
$g(x)=(x-7)^2-5=x^2-14x+45$
561
Worksheet
1. Assume that your kidneys can filter out 25% of medicine in your blood every 4 hours. You take one
1000-milligram dose of the medicine. Fill in the table showing the amount of the medicine in your
blood as a function of time. The first three data points are already completed.
At first you will have decimals. Round each value to the nearest milligram so there are no
decimals in your answers.
Time since taking the medicine (in hours)
Amount of medicine in blood (in milligrams)
0
1000
4
1000 - (1000 x 0.25) = 750
8
750 - (750 x 0.25) = 562.5 563
12
16
20
24
28
32
36
40 44 48 52 56
Answer:
12
563 - (563x0.25) = 422.25 -> 422
16
422 -(422x0.25) = 316.5 -> 317
20
317 - (317x0.25) = 237.75 -> 238
24
238 - (238x0.25) = 178.5 -> 179
28 (continue the step by step process)
134.25 -> 134
32
100.5 -> 101
36
75.75 -> 76
40
57
44
42.75 -> 43
48
32.25 -> 32
52
24
56
18
Step-by-step explanation:
the time interval has to keep skipping by four hours because the medicine is filtered in that amount of time.
The multiplying by 0.25 part must be done first in order to show how much the kidney has filtered.
after this, you need to subtract that from how many milligrams of medicine are left in your system
note that if you do not subtract, you will only be showing how much the kidney has filtered. the question asks for how much is left in the SYSTEM overall, so subtracting is quite necessary to completely answer the question.
I hope this helped.
(x-5)(3x-8)=(4-3x)(6-x)+13
Answer:
x = 3
Step-by-step explanation:
Use FOIL method
(x - 5)(3x - 8) = x*3x + x*(-8) + (-5)*(3x) + (-5)*(-8)
= 3x² - 8x - 15x + 40 {Combine like terms}
= 3x² - 23x + 40
(4 - 3x)( 6 - x) = 4*6 + 4 *(-x) + (-3x)*6 + (-3x)*(-x)
= 24 - 4x - 18x + 3x² {Combine like terms}
= 3x² - 22x + 24
(x - 5)(3x - 8) = (4 - 3x)( 6 - x) + 13
3x² - 23x + 40 = 3x² -22x + 24 + 13
3x² - 23x + 40 - 3x² + 22x - 24 - 13 = 0
3x² - 3x² - 23x + 22x + 40 - 24 - 13 = 0 {Combine like terms}
0 - x = 0
-x +3= 0
3 = x
x =3
Why the answer question now correct
Answer:
461.58 in²
Step-by-step explanation:
The surface area (A) is calculated as
A = area of base + area of curved surface
= πr² + πrl ( r is the radius of base and l is slant height )
= 3.14 × 7² + 3.14 × 7 × 14
= 3.14 × 49 + 3.14 × 98
= 3.14(49 + 98)
= 3.14 ×147
= 461.58 in²
solving polinomial(2x+8)(2x-1)
Answer:
4x²+14x-8 ( multiplying)
x=-4 , x=1/2 ( find solution)
Step-by-step explanation:
(2x+8)(2x-1)
start :
2x*2x=4x²
2x*-1 = -2x
8*2x=16x
8*-1=-8
add the results : 4x²-2x+16x-8 = 4x²+14x-8
If you mean find the solution :(2x+8)(2x-1)=0
2x+8=0
x=-8/2=-4
OR 2x-1=0
then x=1/2
Answer:
=4x2+14x−8
Step-by-step explanation:
(2x+8)(2x−1)
=(2x+8)(2x+−1)
=(2x)(2x)+(2x)(−1)+(8)(2x)+(8)(−1)
=4x2−2x+16x−8
=4x2+14x−8
I hope this helps! :]
Evaluate ∫4x cos(2-3x)dx
Answer:
[tex]{ \sf{ \int 4x \cos(2 - 3x) dx = {4x}^{2} \cos(2 - 3x) + c }}[/tex]
Step-by-step explanation:
From integration by parts:
[tex]{ \boxed{ \bf{ \int u \: \frac{dv}{dx} = uv - \int v \: \frac{du}{dx} }}}[/tex]
let u be cos(2-3x) and let dv/dx be 4x:
[tex]{ \sf{ \frac{du}{dx} = 3 \sin(2 - 3x) }} \\ \\ { \sf{ v = \int 4x = 2 {x}^{2} }}[/tex]
Substitute in formular box:
[tex]{ \sf{ = (2 {x}^{2} \times \cos(2 - 3x)) - \int 2 {x}^{2} .3 \sin(2 - 3x) dx}} \\ = { \sf{2 {x}^{2} ( \cos(2 - 3x) - 3 \int \sin(2 - 3x)dx }} \\ { \sf{ = 2 {x}^{2} ( \cos(2 - 3x) - 3( - \frac{1}{3} \cos(2 - 3x) ) + c}} \\ { \sf{ = {4x}^{2} \cos(2 - 3x) + c}}[/tex]
Which of the binomials below is a factor of this trinomial?
X^2 + 5x + 6
Answer:
(x + 2) , (x + 3) are factors
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 2 and + 3, since
2 × 3 = 6 and 2 + 3 = 5 , thus
x² + 5x + 6 = (x + 2)(x + 3)
372 to the nearest 100
Answer: 400
Explanation: To round 372 to the nearest hundred, we first find the digit in the rounding place which in this case is the 3 in the hundreds place.
To decide whether to round up or down, we look
at the digit to the right of the 3, which is 7.
According to the rules of rounding, if the digit to the right of the
rounding place is greater than or equal to 5, we round up.
So in this problem, since 7 is greater than or equal to 5, we round up.
This means that we add 1 to the 3 in the rounding place
to get 4 and all digits to the right of 4 become 0.
So 372 rounded to the nearest hundred is 400.
Find the product of 0.3×0.23
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
Write a function rule for the table
х
f(x)
0
3
1
4
2
5
3
6
Answer:
f(x) = x +3
Step-by-step explanation:
The first differences for adjacent x-values are all 1, so this is a linear function. Because those differences are all 1, it is a linear function with a slope of 1. We observe that f(0) = 3, so that is the y-intercept.
__
The slope-intercept form of a linear function is ...
y = mx + b . . . . . where m is the slope (1) and b is the y-intercept (3).
A suitable function rule is ...
f(x) = x +3
What transformation of the parent function f(x) is made to get f(3x)?
Answer: Vertically shifting it by 3
The transformation of a function is horizontally shrink by a factor of 3 .
What is a horizontal shrink?We can apply horizontal shrink to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1.Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.
Below is a graph of the data.As we have expected, the graph stretches by a factor of 2 and 3. This is true for all horizontal stretches. The graph only stretches away from the y-axis when we horizontally stretch a graph.Horizontal stretch on other functions will exhibit similar properties. Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|.How do you horizontally shrink by a factor of 3 ?
If g(x) = 3f (x): For any given input, the output of g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.Learn more about Transformation on :
brainly.com/question/10644134
#SPJ2
Determine algebraically whether the function is even, odd, or neither even nor odd.
A. Neither
B. Even
C. Odd
9514 1404 393
Answer:
B. even
Step-by-step explanation:
Functions are classed according to what happens when x is replaced by -x.
f(-x) = f(x) . . . even
f(-x) = -f(x) . . . odd
__
Here, we have ...
f(-x) = 2/(-x)^2 = 2/x^2 = f(x) . . . . an even function
Given the equation 4x−8y=32, a second equation that forms a system with no solution is: 1. x−2y=8 2. x−2y=32 3. x+2y=8 4. 2x−y=32
Answer:
2. x−2y=32.3
Step-by-step explanation:
Given 4x - 8y = 32, a second equation that forms a system with no solution is most easily found by reducing the given equation to x - 2y = 8; we can then easily compare this x - 2y = 8 to x - 2y = 32.3. These two lines are parallel and thus do not intercept, and thus the system has no solution.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Larry is going on a road trip for work. He is recording how many miles he drives, and how many gallons of gas he uses for his expense report. Which is the independent variable?
A. the amount of gasoline Larry uses
B. the type of car Larry drives
C. the type of roads Larry drives on
D. the amount of miles Larry drives
Answer: option A the amount of gasoline larry uses
Step-by-step explanation:
This is because a independent variable is not changed by other variables.
please click thanks and mark brainliest if you like :)
Aug 10,9:55:10 AM
Find the length of the third side. If necessary, round to the nearest tenth.
16
10
Submit Answer
Answer:
attempt 1 out of 2
The distance between two points on a number line can be found by taking the blank of the blank of the coordinates.
absolute
value
sum
quotient
difference
product
Answer:
The correct options are;
Absolute value
Difference
Step-by-step explanation:
The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates such that the result will always have a positive value
The distance between two, points a and b on the number line is defined as [tex]\left | a - b \right |[/tex] that is the distance is found by taking finding the absolute value of the difference of the two numbers.
how do you solve 2m-10=44+8m
Answer:
m = -9
Step-by-step explanation:
2m-10=44+8m
Subtract 2m from each side
2m-2m-10=44+8m-2m
-10 = 44+6m
Subtract 44 from each side
-10-44 = 44-44+6m
-54 = 6m
Divide by 6
-54/6 = 6m/6
-9 = m
Answer:
solve by solving the salvation for equation don't be a slave get educated from what's gave
Please please please please help
Answer:
m = 9
Step-by-step explanation:
8/12 = 6/m
8m = 72
m = 9
will mark brainliest! determine if this is a one solution, no solution, or infinite solution equation
Find X
A. 3
B. sqrt6
C. 3sqrt3
D. 3sqrt2/2
Answer:
B. sqrt 6 is the answer.maja
Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$. [tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]
Answer:
[tex]x =-5\ - \sqrt{8}[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 10x + 25 = 8[/tex]
Required
Find the smallest value of x
[tex]x^2 + 10x + 25 = 8[/tex]
Expand the expression on the right hand side
[tex]x^2 + 5x + 5x + 25 = 8[/tex]
Factorize
[tex]x(x+5)+5(x+5) = 8[/tex]
[tex](x+5)(x+5) = 8[/tex]
[tex](x+5)^2 = 8[/tex]
Take Square root of both sides
[tex]\sqrt{(x+5)^2} = \±\sqrt{8}[/tex]
[tex](x+5) = \±\sqrt{8}[/tex]
Remove bracket
[tex]x+5 = \±\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5 =-5\± \sqrt{8}[/tex]
[tex]x =-5\± \sqrt{8}[/tex]
[tex]x =-5\ + \sqrt{8}[/tex] or [tex]x =-5\ - \sqrt{8}[/tex]
Comparing both values of x;
The smallest value of x is
[tex]x =-5\ - \sqrt{8}[/tex]
help me with guys plzzzzz
Answer:
C
Step-by-step explanation:
So the lion weighs more than the ant right?
And we wish to figure out how much greater the lion's weight is compared to the ant's weight.
So only thing we have to do is divide.
[tex]\frac{1 * 10^5}{2*10^-3} = \frac{10^5}{2*10^-3} = \frac{10^8}{2} = 50000000 = 5 * 10^7[/tex]
Answer:
5×10^7
Step-by-step explanation:
2×10^-3 1×10^5
(1×10^5)/(2×10^-3)=
5×10^7
to scheck :(2*10^-3)(5*10^7)=(1*10^5)
which is odd one out 4:10 12:25 20:50 8:20
Answer:
All of them except 12:25 simply to 2:5. So 12:25 is the odd one out.
For a company picnic, Jacob ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 68 cookies, and 75% of them were gingerbread. How many gingerbread cookies did Jacob get?
Answer:
51 gingerbread cookies
Step-by-step explanation:
Find how many gingerbread cookies he got by finding 75% of 68:
68(0.75)
= 51
So, Jacob got 51 gingerbread cookies.
Will Mark Brainlest Help pls
Answer:
can you snap it again it's not clear
yesterday the temperature was 1 degree farenheit. today the temperature is 0 degree farhenheit. what is the change in tempeature from yesterday to today
Answer:
It is one degrees colder
A taxi charges a flat rate of $8 plus $2 per mile travelled. Write an equation to represent the total cost of a journey. (Let d miles = distance travelled)
Answer:
Y = 8 + 2d
Step-by-step explanation:
Y = 8 + 2d where d is miles traveled
Answer:
y = 2d + 8
Brainliest, please!
Step-by-step explanation:
y = mx + b
m = slope, b = y-intercept
The flat rate of $8 is the y-intercept, and the slope is $2.
y = 2x + 8
We can change x to d to match the context of this problem.
y = 2d + 8
find the area of parallelogram and round to the nearest tenth.
Answer:
A = 152.9 ~ 153
Step-by-step explanation:
A = bh
= 13.9 * 11
= 152.9 ~ 153
Yivgeny's gymnastics scores were 1.5, 1.7, 5.5, and 9.1. In order to calculate his total score, you pick the two top scores and add them. What is his total score?
Answer:
14.6
Step-by-step explanation:
In the question, we are told that:
Yivgeny's gymnastics scores were 1.5, 1.7, 5.5, and 9.1.
In the question, we are also told that to calculate his total score, we add his top two scores.
Yivgeny's top two gymnastics scores are:
5.5 and 9.1.
Hence, his total scores = 5.5 + 9.1
= 14.6
Yivgeny's total scores = 14.7
this graph shows the solution to which inequality (3 3) (-3 -1)
Answer:
B
Step-by-step explanation:
since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer
y>2/3 x +1 is your answer (B)
Answer:
[tex] \boxed{y > \frac{2}{3} x + 1}[/tex]Option B is the correct option.
Step-by-step explanation:
point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1
point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3
Now, let's find the slope:
Slope ( m ) = [tex] = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{3 - ( - 1)}{3 - ( - 3)} [/tex]
[tex] = \frac{3 + 1}{3 + 3} [/tex]
[tex] = \frac{4}{6} [/tex]
[tex] = \frac{2}{3} [/tex]
At ( 3 , - 1 )
y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis
[tex] - 1 = \frac{2}{3} \times ( - 3) + c[/tex]
Solve for c
[tex] - 1 + 2 = c[/tex]
[tex]c = 1[/tex]
Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.
The answer would be:
[tex]y > \frac{2}{3} x + 1[/tex]
Hope I helped!
Best regards!
2x+6y=7draw graph and check x=1,y=2 is solution of this equation
Answer:
The solution in the photo
I hope it helps ^_^