Consider that we need to find [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Given:
The functions are:
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
To find:
The function operations [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Solution:
We have,
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
Now,
[tex](a+b)(x)=a(x)+b(x)[/tex]
[tex](a+b)(x)=4x+9+3x-5[/tex]
[tex](a+b)(x)=7x+4[/tex]
Similarly,
[tex](a-b)(x)=a(x)-b(x)[/tex]
[tex](a-b)(x)=4x+9-(3x-5)[/tex]
[tex](a-b)(x)=4x+9-3x+5[/tex]
[tex](a-b)(x)=x+14[/tex]
And,
[tex](ab)(x)=a(x)b(x)[/tex]
[tex](ab)(x)=(4x+9)(3x-5)[/tex]
[tex](ab)(x)=12x^2-20x+27x-45[/tex]
[tex](ab)(x)=12x^2+7x-45[/tex]
And,
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}[/tex]
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex]
Therefore, the required functions are [tex](a+b)(x)=7x+4[/tex], [tex](a-b)(x)=x+14[/tex], [tex](ab)(x)=12x^2+7x-45[/tex] and [tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex].
Please answer 8,9, and 10!!
Answer:
260,
43.73,
34.28
Step-by-step explanation:
8. Triangle's base is 10, height 4.
10 * 4 = 40
40/2 = 20
24 * 10 = 240
240 + 20
= 260
9. Radius 3.
πr²
9π
12 * 6 = 72
72 - 9π
≈43.73
10. Semicircle has a radius of 2.
2²π
4π
4π/2 = 2π
≈6.28
6.28 + 28 = 34.28
≈34.28
8. It has Triangle embedded to a Rectangle
Area of Figure =Area of Triangle + Area of Rectangle
Area of Triangle = ½ base x height
= ½ x 10 x 8 =40
Area of Rectangle= 24 x 10 =240
TOTAL AREA OF FIGURE = 240 + 40 = 280
9.
Its a rectangle with a Circle in the Middle
Area of Shaded Region would be
Area of Rectangle – Area of circle
Area of Rectangle = 12 x 6 =72
Area of Circle = πr² = π x 3² = 28.27
AREA OF SHADED REGION= 72 - 28.27
=43.73in².
10.
The shape contains a semicircle on a rectangle
Area of the shape = Total Surface Area of semicircle + Area of a Rectangle
Total Surface Area of a semi circle=2πr²
Diameter was given = 4cm
Radius = Diameter/2 = 4/2 = 2cm
= 2 x π x 2² = 25.13cm²
Area of rectangular part = 4 x 7 =28cm²
AREA OF FIGURE = 25.13 + 28 =53.13cm².
Pls notify me if there are any Mistakes.
Have a great day!
Solve for the class width if R = 40 and I = 7.
A. 5
B. 6
C. 8
D. 7
Answer:
A.5
Step-by-step explanation:
divide 40 by 7 which is equal to 5
Please help!!
A diameter is 22 feet. What is the radius?
Answer:
11, take 22 and divide by 2 because radius is half
Step-by-step explanation:
hope this helps
Answer:
r = 11 ft
Step-by-step explanation:
The radius is 1/2 of the diameter
r = 1/2 (d)
r= 1/2 (22)
r = 11 ft
Which dot plot shows 3 students purchased 4 books at the book fair? A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 0 dots, 3 has 3 dots, 4 has 4 dots, and 5 has 2 dots. A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 1 dot, 2 has 3 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 2 dots. A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 2 dots, 3 has 3 dots, 4 has 3 dots, and 5 has 1 dot.
Answer:
A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 2 dots, 3 has 3 dots, 4 has 3 dots, and 5 has 1 dot.
Step-by-step explanation:
The title given to a boxplot will be the values labeled on the horizontal axis, hence since the title of the plot is the number of books purchased at a book fair, If 3 students purchased 4 books, then the Horizontal label at 4 (number of books purchased) will have 3 dots (which corresponds to the number of students who purchased 4 books).
A rectangle has a perimeter of 54 cm. It has a length of 15 cm. What is its area? *
the area is 180 cm. to find the perimeter you would do 15+15+14+14 to get 54 cm. So for area you do (l×w) which is 15×14=180.
si alguien me ayuda en esta doy coronita
Answer: yuh Step-by-step explanation: yuh
Answer:
11/8, 7/4, 8/2
someone reported me
Find all solutions to the equation in the interval [0, 2pie] Enter the solutions in increasing order.
sin 2x = sin x
=============================================
Work Shown:
sin(2x) = sin(x)
sin(2x) - sin(x) = 0
2*sin(x)*cos(x) - sin(x) = 0
sin(x)*(2cos(x) - 1) = 0
sin(x) = 0 or 2cos(x)-1 = 0
sin(x) = 0 or cos(x) = 1/2
Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi
Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3
So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.
All solutions to the equation in the interval [0, 2[tex]\pi[/tex]] is {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.
What is solution to an equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
As sin2x = 2 sinx cosx,
sin2x = sinx is equivalent to
2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or
sinx (2cosx − 1) = 0 i.e.
either sinx = 0 and x = 0, π, 2π
or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}
Learn more about solution to an equation here
https://brainly.com/question/14603559
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This is another one same thing but not the same problem
#1 is a. 11.25
#2 is h. 375
#3 is B 82.50
What is the product of 4xy and y^2 + 2x
Answer:
C
Step-by-step explanation:
4xy(y^2 + 2x) Remove the brackets (distributive law)
4xy^3 + 8x^2y
You have to turn the two terms around to see the correct answer. That's perfectly alright when dealing with addition of pluses.
8x^2y + 4xy^3
A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.8%. How much interest will the customer earn in 10 years? b. What will the account balance be after 10 years?
Answer: See explanation
Step-by-step explanation:
The Simple Interest will be calculated as:
= P × R × T
= $3000 × 1.8% × 10.
= $3000 × 0.018 × 10
= $540
The interest that the customer earn in 10 years is $540.
Then, the account balance after 10 years will be:
= Principal + Interest
= $3000 + $540
= $3540
Therefore, the account balance will be $3540
Please help.............
Answer:
...........
2(x + 2) + 2x = 20
Answer:
x(x+2) = 20
Step-by-step explanation:
Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)
A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey... -Goes up three feet -But, slips down two feet How long will it take the monkey to get to the top of the tree?
Answer:
58 Minute
Step-by-step explanation:
According to the Question,
Given, A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey Goes up three feet But, slips down two feet.Therefore, he climbs (3-2)1 Foot in 1 minute. Now at 57minute, he scales 57feet.
Now, at the 58th minute, he climbs 3 feet MoreThus 57 feet + 3 feet = 60feet( Reached the Top of the tree Now he Never Fall again)
the monkey will take total 58 minutes to get to the top of the tree.Please answer these graph questions for the following! (✿◡‿◡)
a) how far did he go before stopping?
b) which part of the journey is the traveling the fastest a, b, c, or d?
c)what was his speed on the last section of his journey (d)?
Answer:
60
a
30
Step-by-step explanation:
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Anthony worked to earn $25.00. Joyce worked for $8.00 per hour. If he earns $5.00 per hour, how many hours did Anthony work?
Answer:
5 hours
divide 25 by 5 you get 5
A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides length of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf
Answer: The value of x is 5.970.
Step-by-step explanation:
Given: The square has sides length of X cm.
Let r be the radius of the circle.
The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.
Then diagonal of square = diameter of circle
i.e. [tex]\sqrt{2}x= 2r[/tex] [Diagonal of square = [tex]\sqrt{2}[/tex](side)]
i.e. [tex]r=\dfrac{x}{\sqrt{2}}[/tex]
area of circle =[tex]\pi r^2[/tex]
i.e. [tex]56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2[/tex]
[tex]56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970[/tex]
Hence, the value of x is 5.970.
Helppppppppppp:)))))))))
Hi there!
We are given the set of ordered pairs below:
[tex] \large \boxed{(3, - 1),(2, - 2),(0,2),(2,1)}[/tex]
1. What is the domain?
Domain is a set of all x-values in one set of ordered pairs. So what are the x-values that I am talking about? In ordered pairs, we define x and y which both have relation to each others which we can write as (x,y). That's right, the domain is set of all x-values from ordered pairs.Therefore, we gather only x-values from (x,y). Hence, the domain is {3,2,0,2}. Whoops! Something is not right. As we learn in Set Theory that we don't write the same or repetitive in a set. Hence, the actual domain is {0,2,3}
2. What is the range?
Because domain is set of all x-values. Then what do you think the range is? That's right! The range is set of all y-values. If you got this right before looking up the underlined words then a handclap for you! So how do we find range? Simple, we just do like finding the domain in the Q1, except we gather the y-values in (x,y) instead and make sure that we don't write same number!Therefore, gather y-values from the ordered pairs. Hence, the range is {-2,-1,1,2}
3. Is the relation a function?
All functions are relations but not all relations are functions. Function is a set of ordered pairs where domain is not repetitive or in a set, there cannot be more than one same value. Consider the following relation: (1,1),(1,2) - Oh, looks like in a set of ordered pairs, there are two same domains which make it only a relation, and not a function. On the other hand, (1,1),(2,2) - Looking good! No same or repetitive domain, making it indeed a function.Consider the domain from Q1 and see if there are two same values of x in a set. Looks like the relation is not a function since there are same x-values which are 2 in a set, making it only a relation. Hence, the relation is not a function.
These are all 3 answers along with an explanation. Let me know if you have any doubts regarding Relations and Functions.
From the Q1's answer, there are two bold texts, please choose the second bold text to answer (the one with underline) and not the first one (the one with same 2's).
Good luck on your assignment, have a nice day!
Edgar has a business painting Lines on the Highway. His workers can pay online 1/6 of my along every 10 minutes. At the end of an eight-hour workday, how many miles of wine will his workers have painted.
Answer:
8 miles
Step-by-step explanation:
In every 10 minutes, the workers paint 1/6 miles
Total number of minutes in 8 hours = 8 *60 = 480
Number of ten minutes in 480 minutes = 48
total miles of wine painted = 1/6 * 48 = 8 miles
what is the measure of ABD
Answer:
39
Step-by-step explanation:
Factors of polynomial 3xsquare +x-4
Answer:
(3x + 4)(x - 1)
Step-by-step explanation:
3x^2 + x - 4
use middle term break method
we need two number which gives 12 when multiplied and 1 when subtracted
3x^2 + (4 - 3)x - 4
3x^2 + 4x - 3x - 4
x(3x + 4) -1(3x + 4)
(3x + 4)(x - 1)
Answer:
(x - 1)(3x + 4)
Step-by-step explanation:
Given
3x² + x - 4
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 4 = -12 and sum = + 1
The factors are - 3 and + 4
Use these factors to split the x- term
3x² - 3x + 4x - 4 ( factor the first/second and third/fourth terms )
= 3x(x - 1) + 4(x - 1) ← factor out (x - 1) from each term
= (x - 1)(3x + 4) ← in factored form
Seven-ninths of the students surveyed like to participate in extra curricular activities after school. Which decimal is equivalent to the fraction of students
who like to participate in activities after school?
O 0.7
0.7
0.78
O 0.79
Answer:
0.7
Step-by-step explanation:
7/9 = 0.7
Answer:
0.7 (with the repeating sign on the 7)
Step-by-step explanation:
Please help me solve my problem!!!
Write the equation of a line passing through (4,1) and parallel to y = 3/2x + 3.
Answer:
y = 3/2x - 5
Step-by-step explanation:
y = 3/2x + b
1 = 3/2(4) + b
1 = 6 + b
-5 = b
ramu swims a distance of 3 km each upstream and downstream. The total time taken is one hour. if the speed of the stream is 4km/h, then find the speed of ramu in still water.
(a) 12km/h
(b) 8km/h
(c) 9km/h
(d) 6km/h
please answer :)
Answer:
:5 or 6km per hour is your answer.
21. Glass Vase You are taking a glass-blowing class and have created a vase in the
shape of a sphere. The vase will have a hole in the top so you can put flowers in it
and it will sit on a stand. The radius of your vase is 21 inches. Use the formula
= ar to write an expression for the volume of your vase.
V
Answer:
V = 12,348·π
Step-by-step explanation:
The given parameters of the glass Vase are;
The shape of the glass vase = A sphere
The radius of the vase, r = 21 inches
The given formula for finding the volume of a sphere is [tex]V = \dfrac{4}{3} \cdot \pi \cdot r^3[/tex]
Therefore, when r = 21 inches, we get;
[tex]V = \dfrac{4}{3} \cdot \pi \cdot 21^3 = {12,348 \cdot \pi}[/tex]
Therefore, the expression for finding the equation of the spherical glass vase, V = 12,348·π
10.)A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet and a height of 12 inches. The pool is filled with water to 2/3 of its height. Determine and state the volume of the water in the pool, to the nearest cubic foot. One cubic foot equals 7.48 gallons of water. Determine and state, to the nearest gallon, the number of gallons of water in the pool.
Answer:
165.47≈165 Gallons of Water
Step-by-step explanation:
According To the Question,
Given, A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet (or) 6.5 feet (radius is 3.25 feet) and a height of 12 inches(1 feet).The pool is filled with water to 2/3 of its height (H= 2/3 feet) .
Volume of Cylinder = π×R²×H , now put values, we get
Volume = 3.14×3.25²×2/3
Volume = 22.122 foot³ .
And, One cubic foot equals 7.48 gallons of water
Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .
GUYS HELP please i dont know what to answer
Answer:
2nd one : y = -4/x
3rd one : y + x/2 = 9
4th one
5th one : y = x^2
6th : 5.8x - y = 2.3
Step-by-step explanation:
Not sure about these. You might want to wait for another person to answer
Have a nice day!
Determine the location and values of the absolute maximum and absolute minimum for given function : f(x)=(‐x+2)4,where 0<×<3
Answer:
Where 0 < x < 3
The location of the local minimum, is (2, 0)
The location of the local maximum is at (0, 16)
Step-by-step explanation:
The given function is f(x) = (x + 2)⁴
The range of the minimum = 0 < x < 3
At a local minimum/maximum values, we have;
[tex]f'(x) = \dfrac{(-x + 2)^4}{dx} = -4 \cdot (-x + 2)^3 = 0[/tex]
∴ (-x + 2)³ = 0
x = 2
[tex]f''(x) = \dfrac{ -4 \cdot (-x + 2)^3}{dx} = -12 \cdot (-x + 2)^2[/tex]
When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2
We have, f(2) = (-2 + 2)⁴ = 0
The location of the local minimum, is (2, 0)
Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3
When x = 0, -x + 2 = 0 + 2 = 2
Similarly, we have;
-x + 2 = 1, when x = 1
-x + 2 = 0, when x = 2
-x + 2 = -1, when x = 3
Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16
The location of the local maximum is at (0, 16).
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy
Answer:
15
Step-by-step explanation:
u add up that then u get the answet
contruct triangle LMN with LM=6cm,MM=9cm and LN =5cm
Answer:
LNM are quations the answer
Step-by-step explanation:
L=5x3 5,8 M=9x8x3+40-9 N=23-90)+90
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
Complete Question
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
a) Determine the total amount they will pay for their house
b) How much of the cost will be interest?
c) How much of the first payment on the mortgage is applied to the principal?
Answer:
a) [tex]X=\$289800[/tex]
b) [tex]I=\$169800[/tex]
c) [tex]Y=\$116[/tex]
Step-by-step explanation:
From the question we are told that:
Time [tex]T=25years =>300 months[/tex]
Initial Mortgage [tex]N=140,000[/tex]
Mortgage [tex]N'=120,000[/tex]
Rate [tex]r=8.5\%=>0.085[/tex]
Monthly Mortgage payment P=\%966
a)
The total amount Payable X is mathematically given as
[tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]
[tex]X=966*300[/tex]
[tex]X=\$289800[/tex]
b)
Generally the equation for Interest I is mathematically given by
[tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]
[tex]I=289800-120000[/tex]
[tex]I=\$169800[/tex]
c)
Generally the equation for Interest I is mathematically given by
[tex]I=Ptr[/tex]
Where
[tex]t= Month +.1month=>1/12[/tex]
Therefore
[tex]I=120000*1/12*0.085[/tex]
[tex]I=850[/tex]
Therefore the first payment on the mortgage is applied to the principal is
[tex]Y=\$966-850[/tex]
[tex]Y=\$116[/tex]
