y=12
Explanation
The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same,
in order to know the y value, we have to isolate y, then
Step 1
subtract 6 in both sides
[tex]\begin{gathered} 6+y=18 \\ 6+y-6=18-6 \\ \end{gathered}[/tex]Step 2
add like terms
[tex]\begin{gathered} 6+y-6=18-6 \\ y=12 \end{gathered}[/tex]therefore, the answer is
[tex]y=12[/tex]I hope this helps you
solve the polynomials in standard form1) y=4x^4+7x^3-2x^3+5x^52) y=(x-3)^2-3(x-4)
The standard form of a polynomial contains no like terms and the exponents are in descending order (largest to smallest).
[tex]\begin{gathered} y=4x^4+7x^3-2x^3+5x^5 \\ \text{Std Form:} \\ y=5x^5+4x^4+7x^3-2x^3 \end{gathered}[/tex]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 tree diagram below represents the relationships between the sets and subsets of real numbers. Real Numbers Rational Numbers {..., V2, e, , ...) ? Non-integer Rational Numbers {0, 1, 2, 3, ---) Whole Number Opposites Which group of numbers could replace the question mark in the tree diagram
The diagram starts with Real Numbers which comprehend all numbers except for complex numbers.
The second level is formed by rational numbers and irrational numbers.
The third level is formed by subsets of rational numbers non-integers rational numbers and integers rational numbers.
Therefore, the right answer is C. -7, 8, -4, since these numbers are rational and integers.A data set of monthly expediture rounded to the nearest dollar and cure at coffee shop by a sample of 700 household has a minimum value of 4 and a maximum value of 210 suppose we want to group these data into 6 classes of equal with assuming we take the lower limit of the 1st class as one and the upper limit of the sick class as 210 determine the class limit boundaries and midpoint for a group quantitive data table
EXPLANATION
Number of households = 700
Minimum value = $4
Maximum value = $210
Dividing this by the upper limit by by the needed number of classes: 210/ 6 = 35
The width of each class is 35.
Class width = 35
Class Limits Lower Boundary Upper Boundary Class midpoint
1 to 35 0.5 35.5 36/2 = 18
36 to 70 35.5 70.5 106/2= 53
71 to 105 70.5 105.5 176/2= 88
106 to 140 105.5 140.5 246/2= 123
141 to 175 140.5 175.5 316/2= 158
176 to 210 175.5 210.5 386/2= 193
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]Question 3 of 5Select the correct answer from each drop-down menu.The graph of function p represents the profit, in dollars, from concert ticket sales when the tickets are sold for x dollars each.
In order for the concert to make money, the graph must be above the x-axis, because they y-axis represents the profit. This happens in the interval:
[tex](20,120)[/tex]For the concert to lose money, the graph must be below the x-axis. This happens in two intervals:
[tex](0,20)\cup(120,\infty)[/tex]arch
Convert the following equation
into slope-intercept form.
-8x + y = -9
0
y = [? ] x + [
Copyright © 200g-2022 International Academy of Science. All Rights Reserved
Enter
0
The slope-intercept form of the given equation is y = 8x - 9
What is slope intercept form?
Using a straight line's slope and the location of its y-axis intersection, the slope-intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope-intercept form.
The slope-intercept form is y=mx+b, where
m is the slope and
b is the y-intercept.
Here, we have
Given equation = -8x + y = -9
Rewrite in slope-intercept form.
Add 8x on both sides of the equation and we get
y = -9 + 8x
y = 8x - 9
Hence, the slope-intercept form of the given equation is y = 8x - 9
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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.
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.
In summery, explain in your own words the steps to SOLVE for x.
To solve for x in any specific equation, we need to isolate x in one side of the equation. we can do that by adding, subtracting, multiplying, or dividing by a specific number on both sides of the equation.
For example:
X + 3 = 7
X + 3 - 3 = 7 - 3
X = 4
We solve for x when we subtract 3 on both sides of the equation.
Simple probabilityYou draw a card at random from a deck that contains 3 black cards and 7 red cards.If necessary, round your answer to 2 decimal places.
The question says you draw a card at random from a deck that contains 3 black cards and 7 red cards.
What is the probability of drawing a black card?
Recall,
Probability = Number of possible outcome
Number of favorable outcome
There are 3 favorable outcomes (the 3 black cards)
There are 10 possible outcomes ( the 3 + 7 = 10 cards)
Therefore,
P(draw a black card) = 3/10
P(draw a black card) = 0.30 (to 2 decimal places)
Jessica was just offered a position as the Head Makeup Consultant. As a manager she will not earncommission or overtime. Her starting salary will be $38,500 per year and is based on a 40 hour workweek paid biweeklyDetermine Jessica's hourly rate. Will Jessica earn more as an hourly paid employee or manager?How much more or less? Show work for credit.
Assuming there are 52 woking weeks in a year (Since it is the standard used by companies). And in week Jessica can have a maximum of 40 hours, we can conclude that;
[tex]\begin{gathered} \text{Hourly rate (H) =}\frac{38,500\text{ per year}}{52\text{ we}eks\text{ per year (40 hours per we}ek\text{)}} \\ \text{Hourly rate (H) = }\frac{38,500}{52(40)} \\ H\text{ = 18.51} \end{gathered}[/tex]Therefore Jessica's hourly rate is $18.51.
And by calculating her salary per year if she is paid hourly, let us again assume that there are 52 working weeks in a year and she works 8 hours per day 5 times a week as the standard working hours. We get;
[tex]\begin{gathered} \text{Yearly Salary (paid by hour) = 18.51/hour x 52 w}eeks\text{ x 8 hours/day x 5 days/w}eek \\ \text{Yearly Salary (paid by hour) = 18.51 x 52 x 8 x 5} \\ \text{Yearly Salar (paid by hour) = 38,500.80} \end{gathered}[/tex]Therefore Jessica's salary per year if she is paid hourly is $38,500.80, so there is a $0.80 difference between her initial salary.
Marks wants to paint a mural. He had 1 1/5 gallons of yellow paint, 1 1/6 gallons of green paint and 7/8 gallon of blue paint. Mark plan to use 3/4 gallons of each paint color. How many gallons of paint will he have left painting the mural?
Yello paint: 1 1/5
Green paint: 1 1/6
Blue paint: 7/8
After using 3/4 of each paint color, we have
- Yellow:
[tex]\begin{gathered} 1+\frac{1}{5}-\frac{3}{4} \\ \frac{5}{5}+\frac{1}{5}-\frac{3}{4} \end{gathered}[/tex]The least common multiple of 5 and 4 is 20, then...
[tex]\begin{gathered} \frac{5\cdot4}{5\cdot4}+\frac{1\cdot4}{5\cdot4}-\frac{3\cdot5}{4\cdot5} \\ \frac{20}{20}+\frac{4}{20}-\frac{15}{20} \\ \frac{20+4-15}{20} \\ \frac{9}{20} \end{gathered}[/tex]So, for yellow paint, we will have 9/20 gallons
- Green:
[tex]\begin{gathered} 1+\frac{1}{6}-\frac{3}{4} \\ \frac{6}{6}+\frac{1}{6}-\frac{3}{4} \end{gathered}[/tex]The LCM of 6 and 4 is 12
[tex]\begin{gathered} \frac{6\cdot2}{6\cdot2}+\frac{1\cdot2}{6\cdot2}-\frac{3\cdot3}{4\cdot3} \\ \frac{12}{12}+\frac{2}{12}-\frac{9}{12} \\ \frac{12+2-9}{12} \\ \frac{5}{12} \end{gathered}[/tex]So, for green paint, we will have 5/12 gallons
- Blue:
[tex]\frac{7}{8}-\frac{3}{4}[/tex]LCM of 4 and 8 is 8
[tex]\begin{gathered} \frac{7}{8}-\frac{3\cdot2}{4\cdot2} \\ \frac{7}{8}-\frac{6}{8} \\ \frac{7-6}{8} \\ \frac{1}{8} \end{gathered}[/tex]So, for blue paint, we will have 1/8 gallons
Now, we add them upp in order to obtain our anwser:
[tex]\frac{9}{20}+\frac{5}{12}+\frac{1}{8}[/tex]The LCM of 8, 12 and 20 is 120
[tex]\begin{gathered} \frac{9\cdot6}{20\cdot6}+\frac{5\cdot10}{12\cdot10}+\frac{1\cdot15}{8\cdot15} \\ \frac{54}{120}+\frac{50}{120}+\frac{15}{120} \\ \frac{54+50+15}{120} \\ \frac{119}{120} \end{gathered}[/tex]In conclusion, he will have left 119/120 gallons of paint
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
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)
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
A 4-pint carton of soy milk costs $0.96. What is the price per cup?
The cost of per cup milk cartons is $ 0.24
Given price of a 4 pint carton = $ 0.96
thus to calculate the price of 1 carton
we would have to use unitary method
in unitary method ,
the cost of multiple or the cost of an item is given and we are supposed to find the cost of a single or multiple items respectively.
Here since the cost of 4 pint cartons are given
we will find the cost of 1 carton by dividing :
the cost of 4 pint cartons / number of cartons
thus we will get 0.96/4 = $ 0.24
Thus the cost of 1 carton is $ 0.24
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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]Question 3 1 pts A pair of designer sneakers was purchased for $120. Since they were purchased their price has increased by 15%. What is the new price, in dollars?
The new price after the increase of 15%
=120(100 + 15)%
=120 * 115%
= 120 * 115/100
= 138
The new price is $138
Identify the factors of the expression x^3 +4x^2-16x-64.
Solution:
Consider the following polynomial:
[tex]x^3+4x^2-16x-64[/tex]By grouping terms, we get that the above polynomial is equivalent to the following expression:
[tex](x^3+4x^2)+(-16x-64)[/tex]Now, we can apply common factor:
[tex]x^2(x^{}+4^{})-16(x+4)[/tex]again, applying a common factor, we get:
[tex](x^2-16)(x+4)[/tex]Note that the left factor is a difference of squares, therefore, the above expression is equivalent to:
[tex](x-4)(x+4)(x+4)[/tex]this is equivalent to:
[tex](x-4)(x+4)^2[/tex]So that, we can conclude that the factors of the given expression are:
[tex](x-4)[/tex]and
[tex](x+4)^{2^{}}[/tex]and we can conclude that:
[tex]x^3+4x^2-16x-64=(x-4)(x+4)^2[/tex]Elisa is driving at a speed of 65 miles per hour. Let h represent the number of hours that Elisa drives at this speed. Write an algebraic expression to represent the number of miles that Elisa travels during this time.(I NEED HELP NOW , I AM IN RISK OF A WHOOPING)
We have
Elisa travels 65 miles per hour
h is the number of hours
the al
13. Michael found that the difference
between two numbers is 259.
What could the two numbers be?
How did you find the numbers?
The numbers whose difference are calculated could be 300 and 41
How to determine the two numbers?From the question, we have the following statement that can be used in our computation:
The difference between two numbers is 259
Represent the two numbers with x and y
So, we have the following representation
x - y = 259
Make x the subject of the formula
This gives
x = 259 + y
Assume y is 41
So, we have
x = 259 + 41
Evaluate the sum
x = 300
Hence, the numbers are 300 and 41
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Using Euler’s formula, how many edges does a polyhedron with 9 faces and 14 vertices have? Thank you
Solve the Euler's formula above to E (Edges)
[tex]\begin{gathered} \text{Substract 2 in both sides of the equation;} \\ \\ F+V-2=E+2-2 \\ F+V-2=E \\ \\ \text{ Rewrite the equation:} \\ \\ E=F+V-2 \end{gathered}[/tex]Use the given data;
Faces; F=9
Vertices: V=14
[tex]\begin{gathered} E=9+14-2 \\ E=21 \end{gathered}[/tex]The polyhedron has 21 edgesSeptima invests $3,000 in an account with an annual interest rate of 5.2% compounded monthly for 3 years.What is the return on investment for Septima's account?16.8%1.3%14.4%5.3%
Given:
Principal, P=$3000
Interest rate, r=0.052
Years, t=3 years
To find the return amount is compounded monthly:
Using the formula,
[tex]\begin{gathered} A=P(1+\frac{r}{12})^{12t}_{} \\ =3000(1+\frac{0.052}{12})^{12\times3} \\ =3000(1+0.00433)^{36} \\ =3505.30 \end{gathered}[/tex]Hence, the return amount on investment is $3505.30.
In percentage,
The return on investment is,
[tex]\begin{gathered} \frac{3505.3}{3000}\times100=16.84 \\ \approx16.8\text{ \%} \end{gathered}[/tex]Hence, the answer is 16.8%.
Please help with this . I am really stuck on it.The graph shows how time required to ring up a customer is related to the number of items being purchased.If it takes 80 seconds to ring up a customer, how many items are purchased?
First, we have to find the slope of the line. Let's use the points (30, 60) and (40, 80). Using the slope formula, we have.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points.
[tex]m=\frac{80-60}{40-30}=\frac{20}{10}=2[/tex]Then, we use one point, the slope, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-60=2(x-30) \\ y-60=2x-60 \\ y=2x-60+60 \\ y=2x \end{gathered}[/tex]Then, we use this equation to find the items purchased for 80 seconds.
[tex]y=2\cdot80=160[/tex]Therefore, if it takes 80 seconds to ring up a customer, the number of items purchased is 160.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.
A pet store has 8 cats, 12 dogs, and 3 rabbits. The ratio 8:23 compares Irby Pets 1 dogs to cats 2 cats to dogs 3 rabbits to cats 4 cats to all animals
The ratio for each animal between the stores is the divition of pet store with Irby Pets so:
For cats is going to be:
[tex]\frac{8}{2}=4[/tex]So the ratio is 4:1
for dogs is going to be:
[tex]\frac{12}{3}=4[/tex]So the ratio is again 4:1
So the total ratio will be 4:1
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
If cos A = 35/37 and sin B = 9/41 and angles A and B are in Quadrant I, find the valueof tan(A - B).
The given expression is tan(A - B)
Since tan (A - B) is equal to
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}\rightarrow(1)[/tex]Since the values of cos A and sin B are
[tex]\begin{gathered} \cos A=\frac{35}{37} \\ \sin B=\frac{9}{41} \end{gathered}[/tex]We will use the rules
[tex]\begin{gathered} \tan ^2A=\sec ^2A-1\rightarrow(2) \\ \cot ^2B=\csc ^2B-1\rightarrow(3) \end{gathered}[/tex]csc B = 1/sin B, cot B = 1/tan B, sec A = 1/cos A
[tex]\begin{gathered} \csc B=\frac{1}{\frac{9}{41}}=\frac{41}{9} \\ \sec A=\frac{1}{\frac{35}{37}}=\frac{37}{35} \end{gathered}[/tex]Substitute the value of csc B in rule (3) to find cot B
[tex]\begin{gathered} \cot ^2B=(\frac{41}{9})^2-1 \\ \cot ^2B=\frac{1600}{81} \\ \sqrt[]{\cot^2B}=\pm\sqrt[]{\frac{1600}{81}} \\ \cot B=\frac{40}{9} \end{gathered}[/tex]Reciprocal it to find tan B
[tex]\tan B=\frac{1}{\cot B}=\frac{9}{40}[/tex]Substitute the value of sec A in rule (2) to find tan A
[tex]\begin{gathered} \tan ^2A=(\frac{37}{35})^2-1 \\ \tan ^2A=\frac{144}{1225} \\ \sqrt[]{\tan^2A}=\pm\sqrt[]{\frac{144}{1225}} \\ \tan A=\frac{12}{35} \end{gathered}[/tex]Substitute the values of tan A and tan B in rule (1) above
[tex]\begin{gathered} \tan (A-B)=\frac{\frac{12}{35}-\frac{9}{40}}{1+(\frac{12}{35})(\frac{9}{40})} \\ \tan (A-B)=\frac{165}{1508} \end{gathered}[/tex]The value of tan(A - B) is 165/1508
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.