Answer:
The answer is 10m + 7n - 14
Step-by-step explanation:
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
[Q - R] + [S - T] is
[ 7m + 3n - (11 - 2m) ] + [ n + 5 - ( - m - 3n+8)]
Solve the terms in the bracket first
That's
( 7m + 3n - 11 + 2m ) + ( n + 5 + m + 3n - 8)
( 9m + 3n - 11 ) + ( m + 4n - 3)
Remove the brackets
That's
9m + 3n - 11 + m + 4n - 3
Group like terms
9m + m + 3n + 4n - 11 - 3
The final answer is
10m + 7n - 14Hope this helps you
Find the lateral area of the cone in terms of pi.
To find the lateral area of a cone, use this formula:
[tex]\pi r\sqrt{h^2+r^2}[/tex]
where r is the radius (in this case, 11) and h is the height (in this case, 26)
Try plugging the values in. If you need additional help, feel free to ask!
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
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
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
Any point on the parabola can be labeled (x,y), as shown. What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers.
distance to the focus: (x+3)2+(y−3)2−−−−−−−−−−−−−−−√
distance to the focus: (x−2)2+(y+3)2−−−−−−−−−−−−−−−√
distance to the focus: (x+3)2+(y−2)2−−−−−−−−−−−−−−−√
distance to the directrix: |x−4|
distance to the directrix: |y−4|
distance to the directrix: |y+4|
Answer:
Step-by-step explanation:
Standard form of the equation:
y = [tex]-\frac{1}{4} (x+3)^2+3[/tex]
Directrix: y=4
Focus: (-3,2)
Points on the parabola (x,y):
(-5,2) (-3,3) (-1,2)
Distance from points to focus:
(-5,2) = (-3,2)
Answer choices: (x+3)^2+(y−3)^2, (x−2)2+(y+3)2, (x+3)2+(y−2)2
(-5+3)^2+(2-3)^2=5
(-5-2)^2+(2+3)^2=74
(-5+3)^2+(2-2)^2=4
(-1,2)
use the elimination method to solve the system of equations. choose the correct ordered pair x+y=3 y=8
Answer:
(-5, 8)
Step-by-step explanation:
Step 1: Multiply 2nd equation by -1
x + y = 3
-y = -8
Step 2: Elimination
x = -5
Step 3: Find y
y = 8
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.
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
Helppp!!!! please!!!
Answer:
[tex]\boxed{Area = 32.5 mm^2}[/tex]
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]
Where base = 13 mm, Height = 5 mm
Area = 1/2 (13)(5)
=> Area = 1/2 (65)
=> Area = 32.5 mm^2
Answer:
c. 32.5 mm²
Step-by-step explanation:
The equation for the area of a triangle is a=1/2bh. In this equation you basically multiply the length of the base of the triangle times the height of the triangle and divide that by 2 to get the area. So, you would take 13, the base, and multiply it by 5, the height to get 65. Then, you would divide that by 2 to get 32.5 mm².
Write the answer using scientific notation.
(2 x 10^13)^-2
Answer:
2.5 * 10^-27.
Step-by-step explanation:
(2 x 10^13)^-2
= 2^-2 x 10^-26
= 1/2^2 x 10^-26
= 0.25 x 10^-26
= 2.5 * 10^-27.
━━━━━━━☆☆━━━━━━━
▹ Answer
2.5 x 10⁻²⁷
▹ Step-by-Step Explanation
(2 x 10¹³)⁻²
2⁻²(10¹³)⁻²
0.25 x (10¹³)⁻²
0.25 x 10⁻²⁶
2.5 x 10⁻²⁷
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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.
If A=2+i, O=-4, P=-i, and S=2+4i, find A-O+P+S.
==================================================
Work Shown:
A = 2+i
O = -4, this is the letter 'oh' not to be confused with the number zero
P = -i
S = 2+4i
A-O+P+S = (2+i) - (-4) + (-i) + (2+4i)
A-O+P+S = (2+i) + 4 + (-i) + (2+4i)
A-O+P+S = (2+4+2) + (i-i+4i)
A-O+P+S = 8+4i
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
Simplify 5x5^2 leaving answers in index form
Answer:
5^3
Step-by-step explanation:
5*5^2
We are multiplying when the bases are the same
5^1 * 5^2
Add the exponents
5^(1+2)
5^3
Answer:5^3
Step-by-step explanation:Its a fact
Two ships are located 200 m and 300 m respectively from a lighthouse. If the angle formed by their paths to the lighthouse is 96°. What is the distance between the two ships?
Answer:its from applications of trignometry
The distance between the two ships is 377.54 m.
Given that, two ships are located 200 m and 300 m respectively from a lighthouse and the angle formed by their paths to the lighthouse is 96°.
We need to find the distance between the two ships.
What is the cosine rule to find the side?The cosine rule is c²=a²+b²-2abcosC
Now, c²=200²+300²-2×200×300cos96°
⇒c²=40000+90000-1,20,000×(-0.1045)
⇒c²=40000+90000+12,540
⇒c=377.54 m
Therefore, the distance between the two ships is 377.54 m.
To learn more about trigonometry application visit:
https://brainly.com/question/11687813.
#SPJ2
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.
como resuelvo este ejercicio de matematica x +824 = 6 789 en propiedad uniforme
Please answer it in two minutes
Answer:
p = 3
Step-by-step explanation:
We have a right triangle with both legs equal, whose hypotenuse is 3 times the root of 2.
We know both legs are equal because we have identical opposite angles in this right rectangle.
If we apply the Pythagorean theorem, we obtain:
[tex]p^2+p^2=(3\sqrt{2})^2=9\cdot 2=18\\\\2p^2=18\\\\p^2=18/2=9\\\\p=\sqrt{9}\\\\p=3[/tex]
Stephanie wants to buy 's' tomato plants, and Diego wants to by 'd' tomato plants. Each plant costs $7. Stephanie will use a coupon that will give them $25 off the total cost of all their plants. Which expression represents the total cost of all the plants with the discount? *
Answer:
7·(s + d) - 25
Step-by-step explanation:
if each plant cost $7
and there are two plants so its 7 times (s+d)
and then the discount so its -25
hope this helps
HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Step-by-step explanation:
Equation 2: -[tex]x^{2}[/tex] + 3x - 6
Equation 2 should represent a parabola that opens down and has a negative y-intercept.
Parabola that opens down = a<0
Ax^2 + Bx + C
-[tex]x^{2}[/tex] + 3x - 6
Negative y-intercept: -(0)^2 +3(0) -6 = y= -6
Strategy to solve: Quadratic formula
Why? - This equation doesn't factor cleanly.
Show your work:
a= -1 b= 3 c= -6
Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Show step, solve.
x= 1.5 + 1.9365i
Equation 3:
Sorry, I can't do this.
Equation 4 :[tex]x^{2} -1[/tex]
You decide.
Alright, easy parabola.
1. Does parabola open up or down. UP
2. Is there a vertical stretch or compression? NO
3. What is the y-intercept- (0,-1)
[tex]x^{2} -1[/tex]
Strategy: Simple factoring patterns (Difference of squares) -
(x+1)(x-1)
x = + 1
Show work: x^2 is square of x,
Equation 5: [tex]x^{2} -3x+15[/tex]
x^2−3x+15
a=1 b= -3 c=15
([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.
Find the following information using the given image.
Answer:2.9
3
Step-by-step explanation:
Solve this a² ÷ a⁴ × a²
Step-by-step explanation:
a^4 - a^4 = (a^2 +a^2)(a^2-a^2)
a^4 - a^4 = (a^2 + a^2)(a+a)(a-a)
there is no need of this solution, because it equal to 0 because a^4 - a^4 will be equal then it will be 0
i hope this will help you
Answer:
Hello There!
~~~~~~~~~~~~~~~
a² ÷ a⁴ × a² =
1
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice!
☆_____________❤︎______________☆
If i make $8.00 per hour and work 6 hours a day 5 days per week how much would my check be bi-weekly?
Answer:
480$
Step-by-step explanation:
Bi-weekly means every other week. So it is 6 times 5, because u work 30 hours a week. Than 30 (hours) times 8 (money per hour). This is 240 a week. So 240 times 2 is 480.
The probability of pulling out a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math
THIS IS THE COMPLETE QUESTION BELOW;
The probability of pulling a green marble out of a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math
Answer:
We would approximately pick a green marble 240 times
Step-by-step explanation:
Given from the question the probability of pulling a green marble out of a bag of colored marbles is 2:5
Let us denote the number of trials as X
Now the approximately number of times a green marble can be selected would be
=2/5 times
From the question we are given 600 trials
which implies our x=600
Therefore, the number of times we would pick a green marble is:
2/5 × 600 times
≈ 240 times
Therefore, we would approximately pick a green marble 240 times
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
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.
If n is the term, what is the first integer value of n where the sequence 2n² is greater than 50?
Answer:
The 6th term is first integer value of n greater then 50 in the 2n^2 sequence.
Step-by-step explanation:
2n^2 sequence:
2,8,18,32,50,72
Jessica and Barry squeezed oranges for juice. Jessica squeezed 23 5 cups of juice. Barry made 1 4 cup less than Jessica. Barry estimated that Jessica squeezed about 21 2 cups of juice. Which is the best estimate for the amount of juice Barry made? 2 1/4 cups How much juice did Barry actually make? 2 and three-fifths minus one-fourth = StartFraction 13 over 5 EndFraction minus one-fourth = StartFraction 52 over 20 EndFraction minus StartFraction 5 over 20 EndFraction
Answer:
1. 2 1/4 cups
2. 2 7/20 cups
Answer:
2 1/4 and 2 7/20
Step-by-step explanation:
Please solve part h you have to find thr value of x
Answer:
x=301
Step-by-step explanation:
first thing you must know the sum of angle
for this question the polygon has 6 sides (if you connect B and D)
so based on formula (n-2)×180; n is number of side
(6-2)×180=720
so the sum of angle in the polygon is 720
to find x you just need to subtract 720 with all the angle given in the diagram. (and don't forget the 90 degree that made from connected line B and D)
x=720-118-87-34-90-90
x=301
What is the equation of a horizontal line that passes
through the point (-4, -5)?
Answer: y=-5
Step-by-step explanation:
A horizontal line appears on the graph if it goes through the y-axis. Knowing this, the coordinate tells us that the y-coordinate is -5. This tells us that the equation of the line is y=-5.