Answer:
The answer is given below
Step-by-step explanation:
The slope of a line is the gradient of the line and is the ratio of the vertical change (change in y) to horizontal change (change in x) between two points. The slope of a line determines its steepness and direction.
A positive slope means the line slants from the right downward while a negative slope means the line slant upwards to the left. The greater the slope of for a positive slope the greater the steepness while for a negative slope the lesser the slope the greater the steepness.
Line f has a slope of −63, and line g has a slope of −84. Since both lines have negative slope, the line slant upwards to the left. The slope of line g is smaller than that of line f, therefore line g is more steeper than line f.
T_T I need big help
Answer:
D. The volume is the product of the area of the base, (2x - 1)(x - 3), and the height x + 4.
Step-by-step explanation:
Volume of a Rectangular Block: V = lwh
Since we are given variables l, w, and h, we simply plug them in:
V = (2x - 1)(x -3)(x + 4)
We can see that we would need to multiply all 3 to find our volume. Therefore, our answer is D.
what are the values of a and b?
I hope this helps you
Step-by-step explanation:
By using cosine rules:
6/sin45° = b/sin90°
b = 6× sin45°/sin90°
b = 9.124(3d.p)
Also,
using Pythagoras theorm of right-triangle
b² = 6² + a²
9.124² = 6² + a²
83.247376 = 36 + a²
83.247376-36 = a²
47.247376 = a²
√47.247376 = a
6.874 = a
solve the following: x+5=11 x-6=8 3+x=7 12=x+5
Answer:
1) x = 6
2) x = 14
3) x = 4
4) x = 7
Step-by-step explanation:
1) x+5=11
x = 11-5
x =6
2) x-6=8
x = 8+6
x = 14
3) 3+x=7
x = 7-3
x = 4
4) 12=x+5
12-5 = x
7 = x
Determine if the coordinate (6, 8) lies on the circle x^2 + y^2 = 100.
Answer:
x² + y² = 100
6² + 8² = 100
36 + 64 = 100
100 = 100
Because this is a true statement, the answer is yes, it does lie on the circle.
Marco is investigating some of the business models of SureSpin, one of Faster Fidget's top competitors. He has learned that they model their cost of production for one type of spinner with the function C(x) = 13,450 + 1.28x, where x is the number of spinners produced. Interpret the model to complete the statement. Type the correct answer in each box. Use numerals instead of words. Based on the model, the fixed cost of production is $
Answer:
$13,450
Step-by-step explanation:
The fixed costs of production, are the costs incurred that are independent from the production volume, that is, regardless of how many spinners the company produces, those costs will remain the same. If 'x' is the number of spinners produced, interpreting the cost function, we can see that it costs $1.28 to produce each spinner and that there is a cost that does not rely on production of $13,450. Therefore, the fixed cost of production is $13,450.
I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful
Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let [tex]f(x)=\sqrt{x}[/tex] and [tex]g(x)=7x^2+4x+1[/tex]. Then, the given equation is essentially [tex]f(g(x))=\sqrt{7x^2+4x+1}[/tex]. Thus, we can use the chain rule.
Recall the chain rule: [tex]\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)[/tex]. So, let's find the derivative of each function:
[tex]f(x)=\sqrt{x}=x^\frac{1}{2}[/tex]
We can use the Power Rule here:
[tex]f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}[/tex]
Now:
[tex]g(x)=7x^2+4x+1[/tex]
Again, use the Power Rule and Sum Rule
[tex]g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4[/tex]
Now, we can put them together:
[tex]y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)[/tex]
[tex]y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }[/tex]
A student wants to estimate the mean score of all college students for a particular exam. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible scores range from 300 to 2200. Use technology and the estimated standard deviation to determine the sample size corresponding to a 90% confidence level and a margin of error of 100 points. What isn't quite right with this exercise? The range. rule of thumb.estimate for the standard deviation. nothing.
Answer:
See explanation below
Step-by-step explanation:
range = 2200 - 300 = 1900
To find standard deviation, we have:
standard deviation = range/4 = [tex] \frac{1900}{4} [/tex] = 475
The range rule of thumb estimate for the standard deviation is 475
Given:
Standard deviation,[tex] \sigma[/tex] = 475
Margin of Error, ME = 100
[tex] \alpha [/tex] = 1 - 0.90 = 0.10
Za/2 = Z0.05 = 1.64
Find sample size, n:
n ≥ [tex] [Z_\alpha_/_2 * (\frac{\sigma}{ME})]^2 [/tex]
n ≥ [tex][1.64 * (\frac{475}{100})]^2[/tex]
n ≥ 60.68
≈ 61
Minimun sample size,n = 61
The equations of four lines are given. Identfy which lines are parallel. Line 1: y = -9x + 6 Line 2: x + (1/3)y = -6 Line 3: y = -3x - 8 Line 4: y + 7 = (-1/9)(x + 4)
Answer:
line 2 and line 3
Step-by-step explanation:
line1=y=-9x+6. gradient 1= -9
line2=x+⅓y=-6
⅓y=-6-x. gradient2= -3
y=-18-3x
line3=y=-3x-8. gradient3= -3
line4=y+7=-1/9x-4/9
y=-1/9x-4/9-7. gradient4= -1/9
y=-1/9x-7⁴/9
parallel lines have the same gradient
please help ASAP: Factorise the following:
Answer:
hope u will understand it....
Answer:
Hello!
___________________
A)Factor x^2 - 12x + 32 using the AC method. ( x - 8 ) ( x - 4)
B) Factor x^2 - 14x + 48 using the AC method. ( x - 8) ( x - 6)
C) Factor x^2 - 3x + 2 using the AC method. ( x - 2) ( x - 1)
Step-by-step explanation: Always factor by x^2 while using the AC method.
Hope this helped you! :D
20 POINTS!! WILL GIVE BRAINLIEST!! ANSWER SOON PLEASE!!
You own a restaurant and want to “carpet” the floor with coins. What kind of coin would you use and why? How much would it cost to cover the floor with the coin you chose? Explain your reasoning. Include calculations in your reasoning.
Answer: I would use pennies. It is the lowest cost per unit of area.
The cost of the "penny carpet" would be about $ 5,319
Step-by-step explanation:
Each penny is 19.05mm or 1.905cm in diameter 100 centimeters per meter, so 100/1.905 = 52.493 pennies per meter in width, Squared to find number per square meter: 52.493² = 2755.5
The total area of the floor is 23 × 12 in the main area and 3×3 in the entrance,
184 m² + 9 m² = 193 m² . Multiplied by the cost per square meter, $27.56
Total cost: $5,919
The closest comparison would be the nickel. At 2.121 cm, it would take slightly fewer coins per m² , about 2223, but at $0.05 each, the cost per m² is about $111.15. The nickel carpet would cost 4 times as much as the penny carpet.
Which of the following expressions is a factor of the polynomial x 2 +3/2x-1
Answer:
[tex]\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's solve
[tex]x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\[/tex]
[tex]\Delta=b^2-4ac=9+4*2*2=9+16=25[/tex]
There are two solutions
[tex]x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}[/tex]
And
[tex]x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}[/tex]
So we can write
[tex]x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
please help me out with these questions. It's trigonometry
Step-by-step explanation:
LOOK AT THE PICTURE
In ΔABC:
[tex]\sin\alpha=\dfrac{x}{y+p}\\\\\cos\alpha=\dfrac{q}{y+p}\\\\\tan\alpha=\dfrac{x}{q}[/tex]
In ΔADC
[tex]\sin\alpha=\dfrac{y}{x}\\\\\cos\alpha=\dfrac{z}{x}\\\\\tan\alpha=\dfrac{y}{z}[/tex]
In ΔBCD
[tex]\sin\alpha=\dfrac{z}{q}\\\\\cos\alpha=\dfrac{p}{q}\\\\\tan\alpha=\dfrac{z}{p}[/tex]
If f(x)=-5squared -4 and g(x) = -3x-2find (f+g)(x)
Answer:
-3x + 19
Step-by-step explanation:
f(x) = -5² - 4
f(x) = 25 - 4
f(x) = 21
(f+g)(x) = f(x) + g(x)
21 + -3x - 2
-3x + 19
The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. What are the dimensions of Sally’s garden
Answer:
Width=8
Length=28
Step-by-step explanation:
Width=x
Length=3x+4
perimeter is 2 lengths and 2 widths
2x + 2(3x+4)=72
2x+6x+8=72
8x=72-8
8x=64
x=8, so the width is 8
the length Is 3(8)+4 = 28
In circle o, the length of radius OL is 6 cm and the length
of arc LM is 6.3 cm. The measure of angle MON is 75º.
Rounded to the nearest tenth of a centimeter, what is the
length of arc LMN?
L
0 7.9 cm
6.3 cm
O 10.2 cm
6 cm
M
0 12.6 cm
0 14.2 cm
0 75
N
Answer:
14.2cm
Step-by-step explanation:
The diagram representing the circle and its attributes has been attached to this response.
As shown in the diagram;
The circle is centered at o,
The length of radius OL = 6cm
The length of the arc LM = 6.3cm
The angle MON = 75°
The angle LOM = θ
Remember that;
The length, L, of an arc is given by;
L = (θ / 360) x (2πr) -------------(i)
Where;
θ is the angle subtended by the arc
r = radius of the circle.
Using the formula in equation (i), let's calculate the angle θ subtended by arc LM as follows;
L = (θ / 360) x (2πr)
Where;
L = length of arc LM = 6.3cm
r = radius of the circle = length of radius OL = 6cm
Substitute these values into the equation to get;
6.3 = (θ / 360) x (2 x π x 6)
6.3 = (θ / 360) x (12 x π)
6.3 = (θ / 30) x (π) [Take π = 22/7]
6.3 = (θ / 30) x (22 / 7)
θ = [tex]\frac{6.3*30*7}{22}[/tex]
θ = 60.14°
Therefore, the angle subtended by arc LM is 60.14°
Now, from the diagram,
The angle subtended by arc LMN is;
θ + 75° = 60.14° + 75° = 135.14°
Let's now calculate the length of arc LMN using the same equation (i)
L = (θ / 360) x (2πr)
Where;
L = length of arc LMN
θ = angle subtended by LMN = 135.14°
r = radius of the circle = length of radius OL = 6cm
Substitute these values into the equation;
L = (135.14° / 360°) x (2 x π x 6) [Take π = 22/7]
L = 14.15cm
Therefore, the length of arc LMN is 14.2cm to the nearest tenth.
Answer:
14.2
Step-by-step explanation:
Edge
Robyn saves up $204 and spends $32.50 on books. She wants to purchase more books from a sale where they cost $8.15 each. Which answer gives the best estimate for the number of books Robyn can buy?
Answer: 21 books
Step-by-step explanation:
I am estimating $32.50 to $33.
Remaining amount= 204 - 33 = $171
$8.15 = $8
$171 ÷ $8 = 21.375
Estimated answer = 21 books.
By reading the question it feels like there are options to choose from for the final answer. If it is, then choose the one which seems as close as possible to what I have got above.
Hope this helps :)
MATH HELP ASAP PLSSSS
Answer:
(30,0)
Step-by-step explanation:
y=0
-2/5 *x +12=0
2x/5=12
2x=12*5
2x=60
x=60/2
x=30
Hey there! :)
Answer:
(30, 0).
Step-by-step explanation:
Solve for the x-intercept, or zero of the equation by setting the equation equal to 0:
y = -2/5x + 12 becomes:
0 = -2/5x + 12
Subtract both sides by 12:
-12 = -2/5x
Divide both sides by -2/5:
-12 (-5/2) = -2/5x (-5/2)
30 = x.
Therefore, the x-intercept is at (30, 0).
simplify -13 + 25 - 36 + -2
Answer:
-26
Step-by-step explanation:
-13 + 25 - 36 + -2
12 - 36 - 2
-24 - 2
-26
Answer:
-13 + 25 - 36 + -2
12 - 36 + -2
12 - 38
-26
Which of the following is the equation of a line in slope-intercept form for a
line with slope = 5 and y-intercept at (0, -3)?
O A. y = 5x - 3
O B. y = 5x + 3
O C. y=-3x + 5
D. x = 3y-5
Answer:
The answer is option A
y = 5x + 3Step-by-step explanation:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
From the question
Slope or m = 5
y intercept is ( 0 , - 3) which is - 3
So the equation of the line is
y = 5x - 3
Hope this helps you
You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded quarterly
Which investment as the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
the investment with simple? or compound?
interest earns $___ more in interest.
(Round to the nearest cant as needed.)
Answer:
Step-by-step explanation:
the simple interest formula= principal* interest rate*time
simple interest : 100000*%2*2 years
simple interest= 4000 dollars
compound quarterly : A=principal(1+r/4)^t
since it is quarterly and have 4 quarters in a year, and 8 in two years.
compound quarterly: 100000(1+0.03/4)^8=106159.88
it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.
the difference between the interest: 6159.88-4000=2159.88
Ronnie can paint 8 rocks in 5 minutes. How long will it take him to paint 54 rocks
Answer:
33 minutes and 45 seconds.
Step-by-step explanation:
We can easily set up a proportion...
He can paint 8 rocks in 5 minutes. He can paint 54 rocks in x minutes.
[tex]\frac{8}{5} =\frac{54}{x}[/tex]
8 * x = 54 * 5
8x = 270
4x = 135
x = 33.75
So, it will take Ronnie 33 minutes and 45 seconds to paint 54 rocks.
Hope this helps!
Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply. Which expression is equivalent to 2(a+2b)-a-2b
Answer:
1 and 3
Step-by-step explanation:
The equation can be arranged to form equations 1 and 3.
Hope this helps!!! Please mark brainliest and thanks!!
Please please please someone help me
what is the domain represented by the graph
Answer:
All real numbers.
Step-by-step explanation:
Since the graph is a linear function, and the line doesn't have any holes or asymptotes, the graph can input any x-value and output any y-value. Therefore, our domain is all real numbers (any x-value can work).
Answer: All real numbers
Step-by-step explanation:
It is a infinite line, therefore all x values and all y values can be put in and will read a value :)
It takes me 10 minutes to swim 2 laps. How long will it take
me to swim 5 laps?
Answer:
25 minutes
Step-by-step explanation:
10 ÷ 2 = 5
1 lap = 5 minutes
5/1 × 5 = 25
25 minutes
Hope this helped! :)
Answer:
25 minutes
Step-by-step explanation:
Let's set up a proportion using the following setup:
minutes/laps=minutes/laps
It takes 10 minutes to swim 2 laps.
10 minutes / 2 laps = minutes/laps
We don't know how long it will take to swim 5 laps. Therefore, we can say it takes x minutes to swim 5 laps.
10 minutes/ 2 laps= x minutes / 5 laps
10/2= x/5
We want to find out what x is. Therefore, we need to get x by itself.
x is being divided by 5. The inverse of division is multiplication. Multiply both sides by 5.
5*(10/2)=(x/5)*5
5*10/2=x
5*5=x
25=x
It takes 25 minutes to swim 5 laps.
What do I do next please help
Answer:
13
Step-by-step explanation:
Since a point on the line is (0, 13) we know that the y-intercept is 13. The answer is already written in slope-intercept form so the answer is 13.
Answer:
13
Step-by-step explanation:
Let the missing value be c.
y = -3x + c
Put x as 0, and y as 13.
13 = -3(0) + c
13 = 0 + c
13 = c
For what value of k will k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.?
Answer:
18
Step-by-step explanation:
Since, k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.
Therefore, their common differences would be same.
Hence,
(2k - 1) - (k + 9) = (2k + 7) - (2k - 1)
2k - 1 - k - 9 = 2k + 7 - 2k + 1
k - 10 = 8
k = 8 + 10
k = 18
In 2008 a newspaper sold 120 thousand papers, and had 60 thousands people reading online. Their online readership has been increasing by 8 thousand people each year, while their physical paper sales have decreased by 6 thousand papers a year. In what year does online readership exceed physical sales?
Answer:
t = 5 years
online readership will exceed physical sales in 5 years
Step-by-step explanation:
The number of physical readership can be represented by the equation;
P(t) = 120 - 6t
The number of Online readership can be represented by the equation;
K(t) = 60 + 8t
For online readership to exceed physical sales
K(t) > P(t)
60 + 8t > 120 - 6t
Collecting the like terms;
8t+6t > 120-60
14t>60
t > 60/14
t > 4.29
To the nearest year greater than 4.29.
t = 5 years
online readership will exceed physical sales in 5 years
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Step-by-step explanation:
Part A
A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.
Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.
It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.
Part B
Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.
The axis of symmetry will serve as a ladder through the coaster at x = -3.
Part C and D will use the math above to create the coaster and ad campaign.
What is the solution to the equation
?
1/x=x+3/2x2
Answer:
x = 0 , 3
Step-by-step explanation:
[tex]\frac{1}{x}=\frac{x+3}{2x^{2}}\\\\1*2x^{2}=x*(x+3)\\\\2x^{2}=x*x+x*3\\\\2x^{2}=x^{2}+3x\\\\2x^{2}-x^{2}-3x = 0\\\\x^{2}-3x =0\\\\x(x-3)=0[/tex]
x = 0 ; x - 3 = 0
x = 0 ; x = 3