ANSWER
[tex]4y+20=[/tex]EXPLANATION
We want to expand the expression:
[tex]4(y+5)[/tex]To do this, we apply the distributive property:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Therefore, we have:
[tex]\begin{gathered} (4\cdot y)+(4\cdot5) \\ 4y+20 \end{gathered}[/tex]That is the answer.
15. Which of the following is the equation of the graph below? (2 points) y - - 3 2 -10 1 2 3 4 5 (A) y = -2x + 4 (B) y = 2x + 4 (C) y = -x - 2 (D y = -2x - 2
Mr.Foltz has a box for gym class. In the box are 5 basketballs, 9 softballs, 12 volleyballs, and 23 soccer balls. what is the ratio of the vollyballs to basketballs?
Show that the function g(x)=x-2/5 is the inverse of f(x)=5x+2Step 1: the function notation f(x) can be written as a variable in an equation. Is that variable x or y?Write f(x)=5x+2 as an equation with the variable you chose above.Step 2: switch the variables in the equation from Step 1. Then solve for y. Show your work.Step 3: Find the inverse of g(x)= x-2/5. What does this tell you about the relationship between f(x)=5x+2 and g(x)? Show your work.
Given that :
[tex]f(x)\text{ = 5x + 2}[/tex]We can prove that :
[tex]g(x)\text{ = }\frac{x\text{ -2}}{5}[/tex]is it's inverse doing the following:
Step 1. Set y = f(x):
[tex]y\text{ = 5x + 2}[/tex]Step 2. Switch the variables:
[tex]x\text{ = 5y + 2}[/tex]Then we solve for y:
[tex]\begin{gathered} 5y\text{ = x - 2} \\ \text{Divide both sides by 5} \\ y\text{ = }\frac{x\text{ -2}}{5} \end{gathered}[/tex]Step 3. The inverse of :
[tex]g(x)\text{ = }\frac{x-2}{5}[/tex]can be found in a similar way.
[tex]\begin{gathered} y\text{ = }\frac{x-2}{5} \\ x\text{ = }\frac{y-2}{5} \\ \text{Cross}-\text{Multiply} \\ 5x\text{ = y -2} \\ y\text{ = 5x + 2} \end{gathered}[/tex]This tells us that f(x) and g(x) are one to one functions are f(x) is the mirror image of g(x)
Solve each system by substitution.8). -7x-2y=-13x-2y=11
We have the following:
[tex]\begin{gathered} -7x-2y=-13 \\ x-2y=11 \end{gathered}[/tex]solving by substitution:
[tex]\begin{gathered} x-2y=11\Rightarrow x=11+2y \\ \text{replacing} \\ -7\cdot(11+2y)-2y=-13 \\ -77-14y-2y=-13 \\ -16y=-13+77 \\ y=\frac{64}{-16} \\ y=-4 \end{gathered}[/tex]now, for x
[tex]\begin{gathered} x=11+2\cdot-4 \\ x=11-8 \\ x=3 \end{gathered}[/tex]The solution is
[tex](3,-4)[/tex]What is the value of the expression below? 64 + 16 A. 4 C. - 4 B. 1 D. 8
We want to find the value of the expression:
[tex]\frac{64}{16}[/tex]Since 2 is a common factor of both numerator and denominator, we divide by 2s:
[tex]\frac{64}{16}=\frac{32}{8}=\frac{16}{4}=\frac{8}{2}=\frac{4}{1}=\text{ 4}[/tex]The answer is 4. (Option A)
Two-thirds of the people on a hike are adults. If there are 36 adults, what isthe total number of people on the hike?
You have the following information:
- Two-thirds (which means 2/3) of the people on a hike are adults.
- There are 36 adults
In order to calculate the number of people, you consider that 36 is 2/3 of the total people. If you name x as the total people, the number of adults is 2/3x. Thus, you can write the following algebriac expression:
2/3 x = 36
you solve the previoues equation for x. First, you multiply both sides by 3 and you divide both sides by 2.
x = 36(3/2) = 108/2 = 54
Hence, the number of people on the hike is 54
DO ev ew 1 A local business is installing a ramp to the back door of t the ramp is 80 inches while the vertical height of the ran What is the approximate degree measure of the angle of 2
Using the given information, let's make a diagram
To find x, we just have to use the sine function which is equivalent to the ratio between the opposite leg and the hypotenuse.
[tex]\begin{gathered} \sin x=\frac{20}{80}=\frac{1}{4} \\ x=\sin ^{-1}(\frac{1}{4}) \\ x\approx14 \end{gathered}[/tex]Hence, the angle of elevation is 14°.Rewrite the expression using the distributed Property and for the final answer cant have Double signs/operations
Distributive Property
The distributive property of the product with respect to the sum states that if a product and a sum are to be operated like follows:
x* ( y + z )
Then the result is the product of x by each term separately:
x* ( y + z ) = x*y + x*z
Now, we have the expression:
8 ( 2m + 1 )
Applying the distributive property:
8 * 2m + 8 * 1
16m + 8
5. What is the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each?6. 20,000 people voted in each county, and there are 7 counties. What is the order of magnitude for the total number of people who voted?
An order of magnitude is the class of scale of any amount in which each class contains values of a fixed ratio to the class preceding it. Usually, the amount scaled is 10, and the scale is the exponent applied to this amount.
Question 5
The weight of each car is 3,000 pounds. There are 5 cars in total. Therefore, the total weight is given to be:
[tex]\Rightarrow3000\times5=15000\text{ pounds}[/tex]Writing the calculated weight in standard form, scaling to 10, we have:
[tex]15000=1.5\times10^4[/tex]Therefore, the order of magnitude is 4.
Question 6
The number of people that voted per county is 20,000. There are 7 counties in total. Therefore, the total number of people that voted is:
[tex]\Rightarrow20000\times7=140000[/tex]Writing the calculated number in standard form, scaling to 10, we have:
[tex]140000=1.4\times10^5[/tex]Therefore, the order of magnitude is 5.
how to determine maximum or maximum point without using a graph
you could calculate the derivative and equalize it to zero,then you can evaluate the function in the boundary points of the domainand compare them to the ones found in the last step to find the maximum of a given function.
I need to do the “use vocabulary in writing part” But if I can get help with all that would be much appreciated
• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.
And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.
1) As congruent triangles have three congruent angles and sides in order, then we state that, using this specific vocabulary:
2) Δ ABC is congruent to ΔDEF, because
• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.
And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.
3) Hence, that's the answer.
The area of the triangle below is 24.75 square centimeters. What is the length of the base?
Okay, here we have this:
Considering the provided figure and information, we are going to calculate the requested measure, so we obtain the following:
So to calculate the length of the base, we will solve in the formula for the area of the triangle, we have:
Triangle Area=(Base*height)/2
Triangle Area*2=Base*height
Base=(Triangle Area*2)/height
Let's replace:
[tex]\begin{gathered} Base=(24.75cm^2\cdot2)\frac{\placeholder{⬚}}{5.5cm} \\ =\frac{49.5cm^2}{5.5cm} \\ =9cm \end{gathered}[/tex]Finally we obtain that the length of the base of triangle is 9 cm.
if you walk 200 meters in 1 minute, 400 meters in 4 minutes and 800 meters in 10 minutes find your average velocity for the whole walk
First, calculate each velocity:
[tex]v=\frac{distance}{time}[/tex]so:
[tex]v1=\frac{200m}{1min}[/tex][tex]v2=\frac{400m}{4min}=\frac{100m}{min}[/tex][tex]v3=\frac{800m}{10min}=\frac{80m}{min}[/tex]Now calculate the average between the 3 velocities:
[tex]av\text{ }v=\frac{200+100+80}{3}=\frac{126.67m}{min}[/tex]The answer is 126.67 m per minute.
1+1 I dont know what's the answer
We are given the following operation
[tex]1+1[/tex]The result of this operation is the addition of one and another one that is by definition 2, we represent it like thio
On election day the polls open at 7:30 am and closes at 9pm. Marlene worked all day exceptfor a break at lunch 10:30 am to 12 pm and dthen break for dinner at 5:30 pm to 7 pm. Marleneworked What fraction of the time that the polls were open?(a) 4/7(b) *(C) ?(d)?(e) ?
ANSWER;
The fraction of the time she worked was 7/9 of the time the polls were opened
EXPLANATION;
Here, we want to get the fraction of the time in which Marlene worked
What we have to do here is to calculate the total time the pool was opened, then calculate the total time in which she went for break. Then we divide the break time by the total opening time
We proceed as follows;
From 7 : 30 am to 9pm
7:30 am to 9:30 pm is 14 hours
Kindly note that we are to subtract 30 minutes, so we have the total time as 13 hours and 30 minutes
For ease of calculations, we shall have all the time in minute
Recall, 60 minutes are in an hour
So, in 13 hours, we have 13(60) = 780 minutes
Added to the 30, we have a total of 780 minutes + 30 minutes = 810 minutes
Break Times
The first break is 10; 30 am to 12 pm; that is a total time of 1 hour 30 minutes
The second break is from 5:30 pm to 7 pm; that is another 1 hour 30 minutes
Total time spent on breaks is 3 hours
Converting to minutes, we simply multiply by 60 and that will give 3(60) = 180 minutes
Thus, we can now proceed to divide;
[tex]\frac{180}{810}\text{ = }\frac{6}{27}\text{ = }\frac{2}{9}[/tex]The above is the fraction spent on breaks. To get the farction worked, we simply subtract the above fraction from 1
We have this as;
[tex]1\text{ - }\frac{2}{9}\text{ = }\frac{7}{9}[/tex]The length of a rectangle is 2 meters less than 3 times the width. The perimeter is 60 meters. Find the width.The width ismeters.
Step 1
Let x= the width
[tex]3x-2=length[/tex](because the length is 2 meters less than 3 times the width)
Step 2
The perimeter of a rectangle is given as;
[tex]\begin{gathered} P=2length+2width \\ P=2(3x-2)+2x \\ P=60 \end{gathered}[/tex][tex]\begin{gathered} 60=6x-4+2x \\ 60=8x-4 \\ 60+4=8x \\ x=8m \end{gathered}[/tex]Answer;
[tex]Width=8m[/tex]In how many ways can a committee of three men and two women be formed from a group of eight men and seven women?
By counting principle rule, we have
[tex]\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}[/tex]Then the ways a committee of three men and two women can be formed is
[tex]\binom{8}{3}\cdot\binom{7}{2}=1176[/tex]Therefore, there are 1176 possible ways.
ze space below the questo8. Each of the 10 floors in the largebuildings has 8 windows on the front andon the back and 4 windows on each ofthe 2 sides. A cleaning contractor willwash the windows for $6 each. What isthe cost of washing all the windows inthe 22 large buildings?
Step 1
Find the number of windows on each floor
In a large building, there are 10 floors, each floor has the following;
[tex]\begin{gathered} 8\text{ windows }in\text{ the front} \\ 8\text{ windows in the back} \\ 4\text{ windows on the side to the right} \\ \text{and} \\ 4\text{ windows to the side on the left} \\ \text{Therefore, each floor has 24 windows} \end{gathered}[/tex]Step 2
Find the number of windows in a large building
[tex]\begin{gathered} \text{There are 10 floors,} \\ \text{Number of windows in each large building = 10 }\times24\text{ = 240 windows} \end{gathered}[/tex]Step 3
Find the cost the cleaning contractor will take to clean the windows in each building.
[tex]\text{\$}6\text{ }\times240\text{ = \$}1440[/tex]Step 4
Find the cost of cleaning all the windows in 22 large buildings
[tex]22\times\text{ \$}1440=\text{ \$}31,680[/tex]Hence, the cost of washing all windows in the 22 large buildings = $31,680
What is the value of x?
SOLUTION
The principle behind the Exterior Angle Theorem is that:
the sum of two interior angles is equal to one exterior angle.
In this question, we have that :
X + ( X - 48 ) = X + 50
Collecting like terms, we have that:
2 X - 48 = X + 50
2X - X = 50 + 48
X = 98 Degrees.
CONCLUSION: The value of X = 98 Degrees.
How would I solve this. Since I’m not sure what formula I could be using to solve this or how?
Answer:
[tex]\begin{gathered} a)\text{ 23 \%} \\ b)\text{ w\lparen t\rparen= 90e}^{0.23t} \end{gathered}[/tex]Explanation:
a)We have the general representation as follows:
[tex]w(t)\text{ = ae}^{kt}[/tex]when t = 3, we have the value doubling
Thus: w(t) = 2 * 90 thousand = 180 thousand megawatts
Thus:
[tex]\begin{gathered} 180\text{ = 90e}^{3k} \\ e^{3k}\text{ = 2} \\ k\text{ = }\frac{ln\text{ 2}}{3}\text{ = 0.231} \end{gathered}[/tex]This means we have the continuous growth rate at 23%
b) Writing w as a function of t, we have it that:
[tex]w(t)\text{ = 90e}^{0.23t}[/tex]1 14 แ li ! 14 badute Value ineguanten NM แจls แทนเจ 1 ปี 58 หมอยอด | |44| |14 นางอ 24.122 (Mitr 5.1 \\\\\ย - 5 \\
This implies that
[tex]\begin{gathered} 10b\text{ +7 }>\text{ 37} \\ or \\ 10b\text{ +7 <-37} \end{gathered}[/tex][tex]\begin{gathered} \text{if 10b + 7>37} \\ \text{then 10b >37-7} \\ 10b\text{ >30} \\ b\text{ >}\frac{30}{10} \\ b\text{ >3} \end{gathered}[/tex][tex]\begin{gathered} \text{if 10b + 7<-37} \\ 10b\text{ <-37-7} \\ 10b<-44 \\ b<\frac{-44}{10} \\ b<-4.4 \end{gathered}[/tex]Combining them we have
-4.4
Now to the graph
A shirt retails for $22.40. A 10% tax is then applied to the original. What is the final price after tax? $20.16 $24.64 $22.50 $32.40 $22.30
To solve this question, follow the steps below.
Step 01: Find the value of the tax.
If a tax of 10% is applied, then the tax is:
[tex]\begin{gathered} tax=\frac{10}{100}*22.40 \\ tax=2.24 \end{gathered}[/tex]Step 02: Find the final price.
The final price is the original price + tax.
Then, the final price is:
[tex]\begin{gathered} final\text{ }price=22.40+2.24 \\ final\text{ }price=24.64 \end{gathered}[/tex]Answer: $24.64.
the first square is 3 cm by blank centimeters in the other square 13 .5 them by 9 cm what is the scale factor going from the smallest rectangle to the largest one. ans what is the missing side.
Answer:
Step-by-step explanation:
Question 10How many area codes of the form (XYZ)are possible if the digit 'X' and 'Y' can beany number 1 through 9 and the digit 'Z'can be any number 2 through 9?
Name Samantha cebolos Date 3/8/202 Kuta Software - Infinite Algebra 2 Absolute Value Inequalities Solse each inequality and graph its solution. 2) Ip+4158 1 onls 18 -12 -10 - - - belzaalila -8LPtube -2 -1 0 1 2 8 -BHL PLO
Let's begin by identifying key information given to us:
[tex]\begin{gathered} |5x|\le10 \\ \Rightarrow5x\le10 \\ =\frac{5}{5}x\le\frac{10}{5} \\ =x\le2 \\ \\ OR \\ |5x|\le10 \\ \Rightarrow-5x\le10 \\ =\frac{-5}{-5}x\le\frac{10}{-5} \\ =x\le-2 \\ \\ \therefore x\le\pm2 \end{gathered}[/tex]x is lesser than or equal to plus or minus 2
We will proceed to plot the graph
Hello, is it possible to help me understand this question a little better?
1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:
As we can see in each step the aim is to cancel the leading coefficient.
2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:
[tex]\frac{3x^3-4x^2+5x-2}{3x+2}=\quad x^2-2x+3-\frac{8}{3x+2}[/tex]Note that the remainder is written above the divisor on the final answer.
What are the domain and range of the function f(x)=2x+1?domain: (0.00)range: (-0.00domain: (-0.00)range: (0.co)domain: (-0.00)range: (2.00)domain: (0.00)range: (2.0)
The given function is expressed as
f(x) = 2^(x + 1)
The domain of a function is the set of all the possible values of x that would satisfy the function.
The range of a function is the set of all the possible values of y that would satisfy the function.
Since the fuction has no denominator or even root, the values of can be all real numbers. This means that the domain would be between - infinity and infinity
For the range, no matter how small the value of x that we input into the function, the value of f(x) or y would never be lesser than zero. Also, there is no limit to the value of f(x) even if we input very large values of x. Thus, the range is between 0 and infinity. Thus,
the correct option is the second one
Find the surface areaDo not round pleaseFormula: SA= 2 * 3.14 * r * h + 2 * 3.14 * r^2
Given:
The radius of cylinder is r = 2 yd.
The height of cylinder is h = 7.
Explanation:
The formula for the surface area of cylinder is,
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values in the formula to determine the surface area.
[tex]\begin{gathered} S=2\cdot3.14\cdot2\cdot7+2\cdot3.14\cdot(2)^2_{} \\ =87.92+25.12 \\ =113.04 \end{gathered}[/tex]Answer: 113.04
Of 100 students in a club,23 are freshman. What percent of the students are freshman ?
Answer
Percentage of students that are freshman = 23%
Explanation
Total number of students in a club = 100
Number of freshman = 23
Percentage of students that are freshman = [(Number of freshman)/(Total number of students in a club)] x 100
Percentage of students that are freshman = (23/100) x 100
Percentage of students that are freshman = 23%
There are 15 pieces of the same size candy in a bag. Four are banana flavored, three strawberry flavored, and two orange flavored. What would be the probability of picking an orange or a cherry flavored candy from the bag? Write your answer as percent rounded to the nearest tenth.
Given:
Total number of candy in a bag is 15.
Number of orange flavored candy is 2
Number of cherry flavored candy is 6
Let A be the event of picking an orange or a cherry flavored candy from the bag.
[tex]\begin{gathered} n(A)=2+6 \\ n(A)=8 \end{gathered}[/tex][tex]P(A)=\frac{8}{15}[/tex][tex]\begin{gathered} \text{Percentage}=\frac{8}{15}\times100 \\ \text{Percentage}=53.3\text{ \%} \end{gathered}[/tex]