The domain restriction for (f/g)(x) is x=7
What are the functions in mathematics?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.
What does a domain math example mean?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
Given,
f(x) = 6x+2
g(x) = x-7
So,
(f/g)(x) = 6x+2/x-7
Remember that the denominator can not be equal to zero
Find the domain restriction
x-7=0
x=7
Therefore, the domain is all real numbers except the number 7
(-∞,7)∪(7,∞)
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Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=
Find out the division
3x^4-6x^3-8x+16 : (x-2)
3x^3-8
-3x^4+6x^3
-----------------------
-8x+16
8x-16
------------
0
The remainder is zero
that means
The expression (x-2) is a factor of the polynomial
so
3x^4-6x^3-8x+16=(x-2)(3x^3-8)
Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!
ANSWER
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]EXPLANATION
To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,
[tex]du=-\sin (x)dx[/tex]Thus, dx is,
[tex]dx=\frac{du}{-\sin (x)}[/tex]Replace the function and the differential in the integral,
[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]The sin(x) cancels out,
[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,
[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,
[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]Finally, we have to replace u with the function we substituted before,
[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]Hence, the result of the integral is,
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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Show that the points (3, 6), (0, -2), (-7, -5) and (-4, 3) are thevertices of a parallelogram.
Let
A(3,6) B(0,-2) C(-7,-5) D(-4,3)
Remember that
A parallelogram has opposite sides congruent and parallel
so
step 1
Find out the length of the side AB
using the formula to calculate the distance between two points
[tex]\begin{gathered} AB=\sqrt{(-2-6)^2+(0-3)^2} \\ AB=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side AB
[tex]m_{AB}=\frac{-2-6}{0-3}=\frac{8}{3}[/tex]step 2
Find out the length of the side BC
[tex]\begin{gathered} BC=\sqrt{(-5+2)^2+(-7-0)} \\ BC=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side BC
[tex]m_{BC}=\frac{-5+2}{-7-0}=\frac{3}{7}[/tex]step 3
Find out the length of the side CD
[tex]\begin{gathered} CD=\sqrt{(3+5)^2+(-4+7)^2} \\ CD=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side CD
[tex]m_{CD}=\frac{3+5}{-4+7}=\frac{8}{3}[/tex]step 4
Find out the length of the side AD
[tex]\begin{gathered} AD=\sqrt{(3-6)^2+(-4-3)^2} \\ AD=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side AD
[tex]m_{AD}=\frac{3-6}{-4-3}=\frac{3}{7}[/tex]step 5
Compare the length of the sides
we have that
AB=CD
BC=AD
that means ----> opposite sides are congruent
Compare their slopes
mAB=mCD
mBC=mAD
that means ----> opposite sides are parallel
therefore
The given figure is a parallelogramI'll send you the pic a
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]Dee, Sarah, Brett, and Betsy are splitting their dinner bill. After the tip, the total is $30.08. How muchdoes each owe if they split the bill four ways?
The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;
[tex]\begin{gathered} \text{Per person=}\frac{Total}{4} \\ \text{Per person=}\frac{30.08}{4} \\ \text{Per person=7.52} \end{gathered}[/tex]This shows that when paying the bill, each of the four individuals will have to pay $7.52
A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?
Answer: $111 is earn by shoe salesman as commission .
Step-by-step explanation:
As given the statement in the question be as follow.
Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.
Total cost of the pair of shoes = 3 × 70 + 2 × 80
= 210 + 160
= $ 370
As given
shoe salesman earns a commission of 30% of all shoe sales made.
30% is written is decimal form
= 0.30
Commission earns = 0.30 × Total cost of the pair of shoes .
= 0.30 × 370
= $ 111
Therefore $111 is earn by shoe salesman as commission .
Which of the following are solutions to the inequality below? Select all that apply.
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
whats the simplest term of 9m-2(3m-1)
Answer:
[tex]3m+2[/tex]
Step-by-step explanation:
I'm assuming you mean: [tex]9m-2(3m-1)[/tex] and not: [tex](9m-2)(3m-1)[/tex]
So you simply need to know the Distributive Property, which allows you to expand out values being multiplied within parenthesis without adding the values first as such: [tex]A(B+C)=AB+AC[/tex]
Applying this to distribute the -2, we get: [tex]9m-6m+2[/tex]
Adding like terms we get: [tex]3m+2[/tex]
What is the mean for the data shown in the dot plot?
We will determine the mean as follows:
[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]So, the mean will be 6.
Pedro can't decide which size pizza to order. The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza, the total price will be divided among 3people. If he chooses the 12-inch pizza, then the total price will be divided among 4 people. Which is the better buy? How much will each person pay? (Use 3.14 for r.)A. 10-inch pizza; $1.50B. 12-inch pizza; $1.50C. 10-inch pizza; $1.66 D. 12-inch pizza; $1.66
Answer: The better buy is the the 12-inch deluxe for $5.99.
B. 12-inch pizza; $1.50
Explanation:
From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as
Area = πr^2
where
π = 3.14
r is the radius of the circle
For the 10-inch cheese and sausage pizza,
diameter = 10
r = 10/2 = 5
Area = 3.14 x 5^2 = 78.5
If it is divided among 3 people,
each person gets 78.5/3 = 26.2 in^2
Amount that each person pays = 4.99/3 = $1.66
This means that each person pays $1.66 for 26.2 in^2
For the 12-inch cheese and sausage pizza,
diameter = 12
r = 12/2 = 6
Area = 3.14 x 6^2 = 113.04
If it is divided among 4 people,
each person gets 113.04/4 = 28.26 in^2
Amount that each person pays = 5.99/4 = $1.5
This means that each person pays $1.5 for 28.26 in^2
Thus, the better buy is the the 12-inch deluxe for $5.99.
The amount that each person pays is
B. 12-inch pizza; $1.50
what is 2^-3 as a fraction
Answer:
Solution below.
Step-by-step explanation:
The question tests on the concept of indices.
We know the following indices rule:
[tex] {x}^{ - y} \\ = \frac{1}{ {x}^{y} } [/tex]
Which means by inversing the power, we will multiply the power by -1.
So in the case of this question, we can:
[tex] {2}^{ - 3} = \frac{1}{ {2}^{3} } \\ = \frac{1}{8} [/tex]
Which ordered pair is a solution to the equation? y=7x-3 O only (14) O neither only (-1,-) both (1, 4) and (-1,-4)
The givenn equation can be written as
[tex]\begin{gathered} 7x-y=3 \\ On\text{ substituting (1,4) in the left hand side of the equation we get:-} \\ 7-4=3 \\ \text{which is equal to RHS} \end{gathered}[/tex][tex]\begin{gathered} \text{Now substitute (-1,-4) in LHS of the equation} \\ -7+4=-3 \\ \text{which is not equal to RHS.} \end{gathered}[/tex]Hence only (1,4) satisfies the given equation.
So the correct option is the first one (1,4).
x+y=22x+7y=9can u help me solve this equation
Keeping Od, this is the solution:
x + y = 2
2x + 7y = 9
___________
Step 1: Let's isolate x in equation 1, as follows:
x + y = 2
x = 2 - y
__________________
Step 2: Let's substitute x and solve for y in equation 2, this way:
2x + 7y = 9
2 (2 - y) + 7y = 9
4 - 2y + 7y = 9
4 + 5y = 9
Subtracting 4 at both sides:
4 + 5y - 4 = 9 - 4
5y = 5
Dividing by 5 at both sides:
5y/5 = 5/5
y = 1
_______________________
Step 3: Let's substitute y and solve for x in the first equation, as follows:
x + y = 2
x + 1 = 2
Subtracting 1 at both sides:
x + 1 - 1 = 2 - 1
x = 1
_____________________
Step 4: Let's write the solution as an ordered pair, this way:
(1, 1)
4) Using the number line to help you, decide which fraction is larger or if they are equal: one/twos or three/fifths. Label each fraction on the number line.
Explanation:
The number line is between 0 to 1. There are 10 smaller lines in between
Each of the small lines represent 1/10 or 0.1
one/twos is the same as 1/2 = 0.5
three/fifths is the same as 3/5 = 0.6
From the above, 0.6 is greater than 0.5
Showing both numbers on the number line:
In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.
Solution
We will equate the two values
[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]The answer is
Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%
14.select the correct answerwhat is the sum of [tex]9.72 \times {10}^{8 \: and} 1.93 \times {10}^{7} [/tex]Answer options[tex]9.913 \times {10}^{7} [/tex][tex]9.913 \times 10 {}^{8} [/tex][tex]1.165 \times {10}^{8} [/tex][tex]1.165 \times {10}^{9} [/tex]
9.72 x 10⁸ + 1.93 x 10⁷
= 972 000000 + 193 00000
=991 300 000
= 9.913 x 10⁸
If a number with two places to the right of the decimal place is added to a number with three places to the right of thedecimal place then the answer should be reported as having how many numbers to the right of the decimal place
Let the number with two places to the right of the decimal place be represented as 20.45 and the number with three places to the right of the decimal place be 20.456
Required:
When we add the two numbers, how many numbers to the right of the decimal place is it going to have?
We can know this by adding the two fictitious numbers:
[tex]20.45\text{ + 20.456 = 40.906}[/tex]Here we can see that
Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to
if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175
And when she found two $5 bills, it is like she received 2 times 5 = $10
Normally, expenses are negative numbers and earning are positive numbers, in this case
-$175 + $10 = - $165
Sothe answer is -165
Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.
Let
A₁ be the area of the parallelogram
A₂ be the area of the trapezoid
Solving for the area of the parallelogram
Given the following dimensions
b = 23 cm
h = 14 cm
The area is solved using
[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]The area of the parallelogram therefore is 322 square centimeters.
Solving for the area of the trapezoid.
Given the following dimensions
b₁ = 15 cm
b₂ = 34 cm
h = 19 cm
The area is solved using
[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]The area of the trapezoid is 465.5 square centimeters.
Solving for the area of the composite figure.
Get the sum of the two areas to get the area of the composite figure, we have
[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the composite figure is 787.5 square centimeters.
Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
it takes a rat 65 seconds to run from its food source to its home. If the rat has to run 28 meters which is going faster: the rat, or a child on a bike moving at 2 m/s?
Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
r
please when I send u this math explain it for me I'm only 12 and stuff is kinda hard to comprehend
First, we have to get rid of the parenthesis, to do that, we just multiply signs to get
[tex]-14-42[/tex]Now, we sum these numbers since they have the same signs
[tex]-14-42=-56[/tex]Therefore, the answer to (a) is -56.
The second operation is [tex]34+(-24)[/tex]We get rid of the parenthesis
[tex]34-24[/tex]Then, we subtract these numbers since they have different signs
[tex]34-24=10[/tex]Therefore, the answer to (b) is 10.
The third operation is[tex]-7+10[/tex]We just subtract these numbers since they have different signs
[tex]-7+10=3[/tex]Therefore, the answer to (c) is 3.
The fourth operation is[tex]-50+45[/tex]We just subtract
[tex]-50+45=-5[/tex]Therefore, the answer to (d) is -5.
The last operation is[tex]8+88[/tex]We just sum
[tex]8+88=96[/tex]Therefore, the answer to (e) is 96.
.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
the vertices of ABC and the endpoints of DE have coordinates that are integers. Determine the coordinates of point F so That ABC≈DEFOPTIONS:(-7, 1)(-5, 3)(-7, -8)(-2, -8)
We want figure EDF≈ABC.
We can see that if we rotate figure ABC we will obtain the following:
If we rotate it we can see that the segment AB is exactly as the segment ED.
We can now find the answer if we look how far is the point C, we see it is three unities up from B and 5 unities to its left. Then F must be 3 unities up from E and 5 unities to its left.
Since E is located :
at y = -2 if we go up 3 unities
-2 + 3 = 1
at x = -2 if we go at its left 5 unities then
-2 - 5 = -7
Then, F must be at x = -7 and y = 1.
Answer: (-7, 1)Please help with the question below (please try to answer in maximum 10/15 minutes).
Solution:
Given the dimensions of the composite figure below
[tex]\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}[/tex]To find the surface area, SA, of the composite figure, the formula
[tex]SA=2(lh)+2(wh)+(lw)+2(\frac{1}{2}lh)+(bc)+(ah)[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left(\frac{1}{2}\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area, SA, is
[tex]276\text{ cm}^2[/tex]