if f(x)=x-6 and g(x)=x^1/2(x+3), find g(x) X f(x)
Answer:
[tex]\bold{f(x)\cdot g(x)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12}[/tex]
Step-by-step explanation:
[tex]f(x)=x-6\ ,\qquad g(x)=\big x^\frac12(x+3)\\\\\\f(x)\cdot g(x)=(x-6)\cdot\big x^\frac12(x+3)=\big x^\frac12(x^2-3x-18)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12[/tex]
A baby weighs 100 ounces. Find the baby's weight in pounds and ounces.
Work Shown:
1 pound = 16 ounces
100/16 = 6.25
100 ounces = 6.25 pounds
100 ounces = 6 pounds + 0.25 pounds
-------
1 pound = 16 ounces
0.25*1 pound = 0.25*16 ounces
0.25 pounds = 4 ounces
------
100 ounces = 6 pounds + 0.25 pounds
100 ounces = 6 pounds + 4 ounces
100 ounces = 6 pounds, 4 ounces
PLEASE HELP
You have to create 3 functions to make hills on a grap
Requirements are in the photo.
(ignore graphs)
4. Write equations for three hills that do meet the requirements. Sketch them on one axis. (For the
purposes of this exercise, this is a sketch, so the steepness and minimums and maximums of the
graphs do not need to be exact). (6 points: 1 point for each equation, 1 point for each sketched curve)
Answer:
Hill 1: F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 2: F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 3: F(x) = 4(x - 2)(x + 5)
Step-by-step explanation:
Hill 1
You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.
Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.
One possibility is
F(x) = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)
Hill 2
Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.
Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.
The transformed function should be
F(x) = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)
Hill 3
To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.
The zeroes of your picture run from -4 to +7.
One of the zeros of your parabola is +5 (2 less than 7).
Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.
The function could be
F(x) = ¼(x - 2)(x + 5).
In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.
WILL GIVE BRAINLY PLEASE HELP!!!!!!!
Describe the type of correlation between two variables on the scatterplot. How do you know? Does the correlation between the variables imply causation? Explain
contains points:
(0.7,1.11)
(21.9,3.69)
(18,4)
(16.7,3.21)
(18,3.7)
(13.8,1.42)
(18,4)
(13.8,1.42)
(15.5,3.92)
(16.7,3.21)
Answer:
r² = 0.5652 < 0.7 therefore, the correlation between the variables does not imply causation
Step-by-step explanation:
The data points are;
X, Y
0.7, 1.11
21.9, 3.69
18, 4
16.7, 3.21
18, 3.7
13.8, 1.42
18, 4
13.8, 1.42
15.5, 3.92
16.7, 3.21
The correlation between the values is given by the relation
Y = b·X + a
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where;
N = 10
∑XY = 499.354
∑X = 153.1
∑Y = 29.68
∑Y² = 100.546
∑X² = 2631.01
(∑ X)² = 23439.6
(∑ Y)² = 880.902
From which we have;
[tex]b = \dfrac{10 \times 499.354 -153.1 \times 29.68}{10 \times 2631.01 - 23439.6} = 0.1566[/tex]
[tex]a = \dfrac{29.68 - 0.1566 \times 153.1}{10} = 0.5704[/tex]
[tex]r = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{\sqrt{\left [N\sum X^{2} - \left (\sum X \right )^{2} \right ]\times \left [N\sum Y^{2} - \left (\sum Y \right )^{2} \right ]}}[/tex]
[tex]r = \dfrac{10 \times 499.354 -153.1 \times 29.68}{\sqrt{\left (10 \times 2631.01 - 23439.6 \right )\times \left (10 \times 100.546- 880.902\right )} } = 0.7518[/tex]
r² = 0.5652 which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.
If f(x) = 3х2 +1 and g(x) = 1-х, what is the value of (f-g)(2)?
12
14
оооо
36
38
Answer:
( f - g)(2) = 14Step-by-step explanation:
f(x) = 3x² + 1
g(x) = 1 - x
To find (f - g)(2) first find (f - g)(x)
To find (f - g)(x) subtract g(x) from f(x)
That's
(f - g)(x) = 3x² + 1 - ( 1 - x)
(f - g)(x) = 3x² + 1 - 1 + x
(f - g)(x) = 3x² + x
To find ( f - g)(2) substitute 2 into (f - g(x)
That's
( f - g)(2) = 3(2)² + 2
( f - g)(2) = 3(4) + 2
( f - g)(2) = 12 + 2
We have the final answer as
( f - g)(2) = 14Hope this helps you
in 2003 the toyota camry was the top selling passenger vehicle in the united states followed by the honda accord there was 35,000 fewer honda accords than toyota camrys sold in the us in 2003 total sales for the two models together equaled 833,000 that year how many of
Answer:
the amount of camry sold in 2003 = 434000
Step-by-step explanation:
let the number of camry sold be X
then the number of honda accord will be x - 35000
the total will be:
x + x-35000 = 833000
2x = 868000
x = 434000
The amount of Camry sold in 2003 is 434000
How to find the amount of Camry sold in 2003?Let the number of Camry sold be X
Then the number of honda accord will be x - 35000
The total will be:
x + x-35000 = 833000
2x = 868000
x = 434000
Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
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Simplify 6 to the second power
Answer:
36Step-by-step explanation:
[tex]6^2 =6\times 6\\\\= 36[/tex]
Ten years ago. Phukan is 18 years younger than Namwan.Currently, the sum of their ages is 100 years. Find their current ages.
WRITE AS AN EQUATION
Step-by-step explanation:
phukan = x
Nanwan = y
let this be a simultaneous equation.
x - y = 18.... equation i
x + y = 100.... equation ii
subtract equation i from equation ii
= 2y = 118
y = 59
substitute y = 59 in equation ii to get x
x + 59 = 100
x = 100- 59
x = 41
Nanwan = 59, Phukan = 41
Answer:
Nawman = 59 years
Phukan = 41 years
Step-by-step explanation:
P = N - 18
P + N = 100
(N - 18) + N = 100
2N = 100 + 18
2N = 118
N = 118 : 2
N = 59 years
P = (59 - 18) years
P = 41 years
-k^2-(7k-5n)+9n
k= -1
n= -2
Answer:
-k² - (7k - 5n) + 9n
-(-1)² - [7(-1) - 5(-2)] + 9(-2)
-1 - [-7 - (-10)] - 18
-1 - 3 - 18
= -22
the circumference of a circle is 20 pi. what is the radius of this circle?
Work Shown:
C = circumference = 20pi
d = diameter
C = pi*d
pi*d = 20pi
d = 20 after dividing both sides by pi
The radius is half the diameter, so r = d/2 = 20/2 = 10.
As an alternative, you can use the formula C = 2*pi*r
Using the circumference of the circle formula to solve the problem. Then the radius of the circle is 10 units.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Given
The circumference of a circle is 20π.
We know that the circumference of the circle is given by
[tex]\rm Circumference\ of\ the\ circle = 2\pi r[/tex]
Where r is the radius of the circle.
Then the radius of the circle will be
[tex]\begin{aligned} 20 \pi &= 2 * \pi * r \\r &= 10\end{aligned}[/tex]
Thus, the radius of the circle is 10 units.
More about the circle link is given below.
https://brainly.com/question/11833983
solve equation show all steps what is 2x-3x+5=18
Answer:
x = -13
Step-by-step explanation:
2x-3x+5=18
Combine like terms
-x +5 = 18
Subtract 5 from each side
-x +5-5 = 18-5
-x = 13
Multiply each side by -1
x = -13
Answer:
[tex]\huge \boxed{{x=-13}}[/tex]
Step-by-step explanation:
[tex]2x-3x+5=18[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-1x+5=18[/tex]
[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]
[tex]-1x+5-5=18-5[/tex]
[tex]-1x=13[/tex]
[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]
[tex]-1x \times (-1)=13 \times (-1)[/tex]
[tex]x=-13[/tex]
What are the zeros of this function?
A. X= 2 and x = -6
B. x= 0 and x = -6
C. X= 0 and x = 5
D. X = 0 and x= -5
Answer:
I think its C because if I remember correctly zero of the function is just the x intercept
Represent 1/3 and 5/2 on the same number line. Please Draw it
Answer:
[tex]\Huge{\fbox{\red{Attachment}}}[/tex]
#Be Brainly
Find m∠WVT. A. 40 B. 45 C. 53 D. 50
Using the formula for the angle of a secant and tangent line
Angle V = (TW - UW)/2
Write the formula with the given information:
3x+4 = (14x+7 - 7x+11)/2
Simplify:
3x+ 4 = (7x -4)/2
Multiply both sides by 2:
6x + 8 = 7x-4
Add 4 to both sides:
6x+12 = 7x
Subtract 6x from both sides:
X = 12
Now replace x with 12 in angle v:
3(12) +4 = 35 + 4 = 40
The answer is A) 40
9=m/3=4 please help!!
Answer:
Step-by-step explanation:
9 = m/3 + 4
5 = m/3
m = 15
Answer: m=15
Step-by-step explanation:
[tex]9=\frac{m}{3}+4[/tex]
subtract 4 on both sides
[tex]\frac{m}{3}+4-4=9-4[/tex]
[tex]\frac{m}{3}=5[/tex]
multiply 3 on both sides
[tex]\frac{3m}{3}=5\cdot \:3[/tex]
[tex]m=15[/tex]
Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes. Which graph represents Sondra's earnings?
Answer: I know this is a bit late but for anyone looking the answer to this question, i got it right here :D.
Step-by-step explanation: I guessed and got it correct.
The graph representing Sondra's weekly earnings is plotted and attached.
What is a expression? What is a mathematical equation? What is Equation modelling ?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes.
Assume that her weekly earnings is $y. Assume she does [x] extra chores in a week. Then, we can model her earnings by the equation -
y = 5x + 10.
Refer to the graph attached.
Therefore, the graph representing Sondra's weekly earnings is plotted and attached.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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Part of the population of 6,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 6 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
====================================================
Explanation:
6 in the sample of 50 are infected, so 6/50 = 12/100 = 12% are infected in the sample. We expect this percentage to carry over to the entire population assuming we picked a representative random sample that isn't biased.
12% of 6250 = 0.12*650 = 750 is the expected number of infected individuals in the population.
----------
Here's an alternative way you can solve through a proportion
(number infected)/(total) = (number infected)/(total)
6/50 = x/6250
6*6250 = 50x ... cross multiply
37500 = 50x
50x = 37500
x = 37500/50 ... divide both sides by 50
x = 750
The sum of Rhonda and her daughter Tenica’s age is 64. The difference in their ages is 28. How old is each person?
Answer:
The mother (Rhoda) is 46 years old.
The daughter (Tenica) is 18 years old
Step-by-step explanation:
Let the age of the mother (Rhoda) be m
Let the age of the daughter (Tenica) be d.
The sum of Rhonda and her daughter Tenica’s age is 64. This can be written as:
m + d = 64 ... (1)
The difference in their ages is 28. This can be written as:
m – d = 28 ... (2)
From the above illustrations, the equation obtained are:
m + d = 64 ... (1)
m – d = 28 ... (2)
Solving by elimination method:
Add equation 1 and 2 together
. m + d = 64
+ m – d = 28
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
2m = 92
Divide both side by 2
m = 92/2
m = 46
Substitute the value of m into any of the equation to obtain the value of d. Here, we shall use equation 1
m + d = 64
m = 46
46 + d = 64
Collect like terms
d = 64 – 46
d = 18
Therefore, the mother (Rhoda) is 46 years old and the daughter (Tenica) is 18 years old.
Jolene bought 3 plants at a greenhouse. Each plant cost $2.50. To calculate the total cost of the plants, Jolene added (3(2)) + (3(0.50)). What property of multiplication did she use?*
A.Distributive Property
B.Associative Property
C.Commutative Property
D.Identity Property
Answer:
The answer is A.Distributive PropertyStep-by-step explanation:
Distributive property of multiplication has to do with the multiplication of numbers by the sum of that number
say in our given example $2.05.
When we decide to multiply 3 property with $2 and $0.5 which when added together will still give $2.05, we are using distributive property of multiplication.
Hence according to distributive property 3*$2.05 is the same as
3*$2 + 3*$0.5
Simplify 3(2x - 5). 1)-6x - 15 2) 6x - 15 3) 6x - 8 4) 5x - 2
Answer:
[tex] \boxed{ \bold{ \: 6x - 15}}[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathsf{3(2x - 5)}[/tex]
Distribute 3 through the parentheses
⇒[tex] \mathsf{3 \times 2x - 3 \times 5}[/tex]
Calculate the product
⇒[tex]6x - 15[/tex]
Hope I helped!
Best regards!!
look at picture and solve
ANSWER ASAP THANK youuu
Answer:
A
Step-by-step explanation:
● -7x > 21
Divide both sides by 7
● -7x/7 > 21/7
● -x > 3
Multiply both sides by -1 and switch the sign since you have multiplied by a negative number.
● x < -3
The representation is A since -3 is represented by an empty dot ○ wich means it's out the solutions
The solution to the given inequality -7x/7 > 21/7 is x < -3 which is the correct answer that would be option (A).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question
⇒ -7x > 21
Divide both sides by 7 both sides of the above inequality
⇒ -7x/7 > 21/7
⇒ -x > 3
Multiply both sides by -1 and because we multiplied by a negative quantity, flip the sign.
⇒ x < -3
The representation is A because -3 is represented by an empty dot which shows the solution of the graph.
The required graph has been attached which represents the solution to the given inequality -7x/7 > 21/7 is x < -3
Hence, the correct answer would be an option (A).
Learn more about the inequalities here:
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solve equation show all steps 3/8x=36
Answer:
x = 96
Step-by-step explanation:
3/8x = 36
You have to multiply both sides of the equation by the inverse of the fraction to cancel it out.
(8/3)(3/8x) = (36)(8/3)
x = 96
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Hi my lil bunny!
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Let's solve your equation step-by-step.
[tex]\frac{3}{8}x=36[/tex]
Step 1: Multiply both sides by 8/3.
[tex]( \frac{8}{3} ) * ( \frac{3}{8}x) = ( \frac{8}{3} ) * ( 36)\\x = 96[/tex]
Answer : [tex]\boxed {x = 96}[/tex]
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If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
Let's see what it would take to win that trip to Hawaii.
Remember that you think you'll respond to 12 questions and hope to score 600 points to win,
although it's possible to score even more points or many fewer (including negative scores!) on
the show.
Here are the equations you wrote to model your winning scenario:
x+y=12
100x - 200y = 600
Are the boundaries of the first equation viable in the second equation? What does this
suggest about your plan to score 600 points?
Select the two correct statements.
Answer:
A and D choices (Plato)
Step-by-step explanation:
The upper boundary of the first equation is at x = 12, y = 0. With these values, this is the second equation:
100(12) − 200(0) = 1,200.
The lower boundary of the first equation is at x = 0, y = 12. With these values, this is the second equation:
100(0) − 200(12) = -2,400.
Both of these scores are possible in the game, so they are both viable.
Because the upper boundary is greater than 600, it suggests that you can still score 600 points and win the game even if you get one or two of the questions incorrect.
In fact, you could give 10 correct and 2 incorrect answers to score 600 points and still beat the champion, Kimberly, assuming she answers 15 correct and 5 incorrect to score 500 points.
help me with this problem im slow
Answer:
Option D
Step-by-step explanation:
Option D's equation is in slope-intercept form. Slope-intercept form equations are used for linear functions.
Nonlinear functions would have an exponent (that is higher than 1), 'x' as an denominator in a function, or a square/cube root symbol in it's equation.
Option D should be the correct answer.
Hope this helps.
A sequence of transformations is described below. A reflection over a line \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point PPP Another reflection over \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point QQQ Which of the following must be preserved under this sequence of transformations? Choose 1 answer: Choose 1 answer: (Choice A) A Angle measures only (Choice B) B Segment lengths only (Choice C) C Both angle measures and segment lengths (Choice D) D Neither angle measures nor segment lengths
Answer:
The correct option is;
(Choice C) Both angle measures and segment lengths
Step-by-step explanation:
The given transformations are;
The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;
The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions
Therefore, the correct option is, both angle measures and segment lengths.
(Choice C) C Both angle measures and segment lengths
Which item is more economical?
Answer:
what are the items
Step-by-step explanation:
Can someone please help me
Answer:
a = 84°
Step-by-step explanation:
∠ QPR and ∠ TPR are adjacent and supplementary, thus
∠TPR = 180° - 123° = 57°
Given there are parallel lines , then
∠ PTR = 27° ( alternate angle )
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ TRS is an external angle , thus
∠ TRS = a = 57° + 27° = 84°
Answer:
84 degrees.
Step-by-step explanation:
m < R + m < T = 123 (External angle of a triangle theorem)
m < T = 27 degrees (alternate angle to 27 degrees).
So m < R = 123 - 27 = 96 degrees.
Finally m < a = 180 - 96 = 84 degrees ( as it is adjacent to < R)
plz help me f(x) = 2x – 2 , find f(– 1)
Answer:
-4
Step-by-step explanation:
f(-1) = 2(-1) - 2 = -4
What is the simplest form of this expression? 3x(-x2 + 2x + 12)
Answer:
-3x³ + 6x² + 36x
Step-by-step explanation:
3x(-x² + 2x + 12)
3x*-x² + 3x*2x + 3x*12)
-3x³ +6x² + 36x
