Let:
c = total
a = cost of each book
w = flat shipping fee
Therefore, the total is given by:
[tex]c=ab+w[/tex]where:
b = number of books
[tex]c=6x+1.25[/tex]The independent variable is:
"b" books
write a quadratic equation in the form of ax²bx+c=0
The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000
Step 1: Write the equation
y = -400x + 4000
Step 2:
The intercept in the equation represents time in years.
x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.
step 3: Find the x-intercept
To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.
y = $0
[tex]\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }\frac{4000}{400} \\ x\text{ = 10} \end{gathered}[/tex]The x-intercept = 10 years
Step 4:
To find the number of years take for the computer value to depreciate to $2000.
You will substitute the value of y = $2000 and find the value of x.
Therefore
[tex]\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }\frac{2000}{400} \\ \text{x = 5 years} \end{gathered}[/tex]It will take 5 years for the value of the computer to depreciate to $2000.
Solve 2x - 8 < 7...........................................................................
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
2x - 8 < 7
Step 02:
inequality:
2x - 8 < 7
2x - 8 + 8 < 7 + 8
2x / 2 < 15 / 2
x < 15 / 2
The answer is:
x < 15 / 2
(-oo , 15/2)
There is a stack of plates in the backyard. There are 4 plates in the 1st layer, 8 in the second, 16 in the third, 32 in the fourth, and so on. There are total 10 rows/layers. How many total plates are in the stack?
Given that
[tex]\begin{gathered} layer1=4plates \\ layer2=8plates \\ layer3=16plates \\ layer4=32plates \end{gathered}[/tex]Explanation
From the above, it is easy to see that the arrangement of the layers follows a geometric sequence where
[tex]\begin{gathered} first\text{ term = 4} \\ common\text{ ratio = }\frac{second\text{ }term}{first\text{ term}}=\frac{8}{4}=2 \end{gathered}[/tex]Since r>1, therefore the sum of 10 terms, which implies would give the total number of plates that are in the stack can be seen below.
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ therefore; \\ S_{10}=\frac{4(2^{10}-1)}{2-1}=\frac{4(1024-1)}{1}=4(1023)=4092 \end{gathered}[/tex]Answer: 4092
An earthquake in California measured 3.6 on the Richter scale. Use the formula R=log(A/Ao) to determine approximately how many times stronger the wave amplitude of the earthquake was than .
The correct option regarding how many times stronger the wave amplitude of the earthquake was than the standard wave Ao is given by:
A = 3981Ao.
Ratio of A and AoTo find the ratio of A and Ao, measuring how many times a earthquake measuring R in the Richter scale was than Ao, we have to solve the following logarithmic function:
R=log(A/Ao)
The power of 10 in inverse to the logarithm, hence it is applied to both sides of the expression, as follows:
10^R = 10^log(A/Ao).
Since they are inverses, we can remove the power and the logarithm as follows:
A/Ao = 10^R
Hence the formula for how many times stronger and earthquake is than Ao is given as follows:
A = 10^R Ao
In this problem, the Richter measure of the earthquake was of:
R = 3.6.
Hence the ratio is:
A = 10^(3.6)Ao
A = 3981Ao.
Missing informationThe problems asks how many times stronger the earthquake was than Ao.
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The surface area of the solid cone requiring paint rounded to the nearest whole number is how many square centimeters?
In order to calculate the surface area of the cone, first let's calculate its slant height.
If the diameter is 5 cm, the radius is 2.5 cm. Now, using the Pythagorean theorem, we can calculate the slant height s:
[tex]\begin{gathered} s^2=h^2+r^2 \\ s^2=11.4^2+2.5^2 \\ s^2=129.96+6.25 \\ s^2=136.21 \\ s=11.67\text{ cm} \end{gathered}[/tex]Now, we can calculate the surface area using the formula below:
[tex]\begin{gathered} S=\pi rs+\pi r^2^{} \\ S=\pi\cdot2.5\cdot11.67+\pi\cdot2.5^2 \\ S=29.175\pi+6.25\pi \\ S=35.425\pi \\ S=111.29\text{ cm}^2 \end{gathered}[/tex]Rounding to the nearest square centimeter, we have a surface area of 111 cm².
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]Find the equation of the axis of symmetry of the following parabola using graphingtechnology.y = x^2 – 8x + 32
Explanation:
If we graph this parabola we can see the vertex at point (4, 16)
The axis of simmetry is a vertical line that passes through the vertex of the parabola.
Any vertical line's equation is:
[tex]x=a[/tex]'a' is any value of x.
Answer:
The equation of the axis of simmetry is x = 4
The drama club was selling ticketsto the school play. Adult ticketscost $8.00 each, and studenttickets cost $5.00 each. The littletheater holds 142 people and wassold out for both Friday andSaturday. The total sales for thetwo days was $1,948.00.1. How many adult tickets weresold out over the two days?2. How many student tickets weresold out over the two days?
We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:
[tex]A+S=284,(1)[/tex]This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:
[tex]8A+5S=1948,(2)[/tex]To solve this equation we will solve for A in equation (1), by subtracting S to both sides;
[tex]\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}[/tex]Now we will replace this value in equation (2):
[tex]8(284-S)+5S=1948[/tex]Now we will apply the distributive property:
[tex]2272-8S+5S=1948[/tex]Addins like terms:
[tex]2272-3S=1948[/tex]Subtracting 2272 to both sides;
[tex]\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}[/tex]Dividing both sides by -3:
[tex]S=-\frac{324}{-3}=108[/tex]Now we replace this value in equation (1), where we have already solved for A:
[tex]\begin{gathered} A=248-108 \\ A=140 \end{gathered}[/tex]Therefore, there were sold 108 student tickets and 140 adult tickets.
que es el producto para (x+5) (2x-1)?
the given expression is,
(x+ 5) (2x -1)
so the answer is
[tex]\begin{gathered} \mleft(x+5\mright)(2x-1)=2x^2-x+10x-5 \\ \end{gathered}[/tex][tex]=2x^2+9x-5[/tex]so the answer is
2x^2 + 9x - 5
two integers a and b have a product of 36 what is the least possible answer
Answer:
the answer is 12
Step-by-step explanation:
In short, a = 6 and b = 6. We can make a table of various values to help confirm that 12 is the smallest sum.
Answer: 1
Step-by-step explanation: 1 is the least possible answer because an integer is any number and 1x36 would be the least possible answer for the product.
Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) forinifinity and a U for union as needed.-- 5x + 4 >I 19 OR – 22 - 15 – 3-8 -7 -6 -5-4-3-2-] 022345678Clear All Draw:Interval notation for the above inequality and graph is
- 5x + 4 > 19
1st step let us move 4 to the other side by subtracting both sides by 4
- 5x + 4 - 4 > 19 - 4
- 5x > 15
2nd step is move - 5 to the other side by dividing both sides by -5, BUT when we divide the sides of an inequality by a negative number we must reverse the sign of inequality
[tex]\frac{-5x}{-5}<\frac{15}{-5}[/tex]x < -3
The solution is all values smaller than -3
On the number, line draw an empty circle at -3 then draw from it an arrow pointing to the left ( - ve infinity)
The solution is {x : x < -3} or (-00, -3)
Drag the factors to the correct locations on the image. Not all factors will be used.What is the factored form of this expression?27 m 3 + 125n39m + 25n9m2 - 15mn + 25n23m + 5n9m2 + 15mn + 2523m2 – 8mn + 5123m - 5n
Express the sum of the angles of this triangle in two different waysX3/2X1/2X
1) Since the sum of these angles is written in terms of x, we can write it out:
[tex]\begin{gathered} x+\frac{3}{2}x+\frac{1}{2}x\text{ } \\ \frac{2x+3x+x}{2} \\ \frac{6x}{2} \\ 3x \end{gathered}[/tex]Notice that to sum these fractions we had to take the LCM(2, 1) = 2 and rewrite it as a sum.
2) Another way of writing the sum of these angles is writing it as a sum of decimal numbers since we can rewrite fractions as decimal numbers.
3/2 = 3÷2 = 1.5
1/2 = 1÷2 =0.5
1
[tex]\begin{gathered} x+1.5x+0.5x \\ x+2x \\ 3x \end{gathered}[/tex]Can someone help me with 7? I’m desperate
PLS HELP ASAP WILL GIVE BRAINLIST
Answer:
65
Step-by-step explanation:
[tex]-4a + 65 = 2a + 5\\60 = 6a\\a = 10\\[/tex]
KJN = 25 degrees
MJN = 25 degrees
KJM = KJN + MJN = 25 + 25 = 50 degrees
total angles = 360 degrees
JKL = (360 - 50 - 50 )/2 = 130 degrees
LKN is half of JKL = 130/2 = 65
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgets forceditoral and sales combined is12,500,000, what is the total annual budget
Explanation
We are asked to find the total annual budget given that the combined amount for sales and editorial is $12,500,000
To do so, let the total combined amount be x
If we check for the combined percentages for the amount for sales and editorial, we will have
[tex]21\text{ \%}+4\text{ \% = 25\%}[/tex]Thus, we can set up the equation
[tex]25\text{ \% of x = 12,500,00}[/tex]Solving for x
[tex]\begin{gathered} \frac{25}{100}\times x=12500000 \\ \\ \frac{x}{4}=12500000 \\ \\ x=4\times12,500,000 \\ \\ x=50,000,000 \\ \end{gathered}[/tex]Therefore, the total annual budget will be $50,000,000
You have 1/4 of a quiche left over from lunch. If you sent 4/6 of the leftover quiche home with your brother, how much of the quiche do you have left in the dish?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
If the brother took home 4/6, that means that you still have 2/6.
[tex]\frac{1}{4}[/tex] x [tex]\frac{2}{6}[/tex] = [tex]\frac{2}{24}[/tex] which is the same as 1/12
The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.1. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal places.Find the probability that the mean of a sample of 25 people is less than 10.Find the probability that the mean of a sample of 25 people is greater than 10.Find the probability that the mean of a sample of 25 people is between 11 and 12.
The z-score is given by the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where x is the data point, μ is the mean, and σ is the standard deviation.
First
What is the answer for 5p+10 = 8p+1
The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]Which fraction is represented by point A on the numb 0 -1 O- 1 4. 4 1 1
The fraction that represent the point A is -1/4.
Since there are 4 divition in between -1 and 0.
Thus the length of one division is,
[tex]undefined[/tex]0.4(2-) 0.2(9 + 7) A)-3 B - 1 C) 3 D) all real numbers
Let us solve the equation to arrange the steps
[tex]-3(4+3x)+5x=-16[/tex]In the first step, we must multiply the bracket by -3 (distributive property)
[tex](-3)(4)_{}+(-3)(3x)=-12-9x[/tex]Then the equation is
[tex]-12-9x+5x=-16[/tex]Now add the like terms on the left side
[tex]\begin{gathered} -12+(-9x+5x)=-16 \\ -12x+(-4x)=-16 \\ -12-4x=-16 \end{gathered}[/tex]Next step, add 12 to both sides
[tex]undefined[/tex]help meeeeeeeeee pleaseee !!!!!
For the given functions, the two compositions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3*x² + 15
How to find the compositions of the functions?Here we have two functions which are:
f(x) = x² + 5
g(x) = 3x
Now we want to find the compositions:
(f o g)(x) = f( g(x) )
So we just need to evaluate f(x) in g(x), we will get:
f( g(x) ) = g(x)² + 5
f( g(x) ) = (3x)² + 5 = 9x² + 5
The other composition is:
(g o f)(x) = g(f(x))
And we can get this in a similar way:
g(f(x)) = 3*f(x) = 3*(x² + 5) = 3*x² + 15
Learn more about compositions:
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See attached pic for problem. Only need help with #2
SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
[tex]x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }[/tex]Hence
The data plot will be
The linear is given by the form
[tex]\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}[/tex]THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
[tex]\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}[/tex]Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
[tex]\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}[/tex]Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
Which is the equation of the line that passes through the points (-4, 8) and (1, 3)?A. Y=x+4B. Y=-x+12C. Y=-x+4D. Y=x+12
In order to find the equation that passes through both points, we can use the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Using the given points on this equation, we have:
[tex]\begin{gathered} (-4,8)\colon \\ 8=m\cdot(-4)+b \\ b=8+4m \\ \\ (1,3)\colon \\ 3=m+b \\ 3=m+8+4m \\ 5m=3-8 \\ 5m=-5 \\ m=-1 \\ b=8+4\cdot(-1)=8-4=4 \end{gathered}[/tex]Therefore the equation is y = -x + 4 (correct option: C)
A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?
ANSWER
4,410
EXPLANATION
The number of ways we can choose 4 teachers from 7 teachers is,
[tex]_7C_4=\frac{7!}{(7-4)!\times4!}=\frac{7\times6\times5\times4!}{3!\times4!}=\frac{7\times6\times5}{3\times2}=\frac{7\times6\times5}{6}=7\times5=35[/tex]There are 35 ways of choosing 4 teachers out of 7.
And the number of ways we can choose 4 students from 9 students is,
[tex]\begin{gathered} _9C_4=\frac{9!}{(9-4)!\times4!}=\frac{9\times8\times7\times6\times5\times4!}{5!\times4!}=\frac{9\times8\times7\times6\times5}{5\times4\times3\times2} \\ _9C_4=\frac{9\times8\times7}{4}=\frac{9\times(2\times4)\times7}{4}=9\times7\times2=126 \end{gathered}[/tex]There are 126 ways of choosing 4 students out of 9.
The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,
[tex]_7C_4\times_9C_4=35\times126=4,410[/tex]Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.
Compute the square root of 532 to the nearest tenth. Use the "divideand average method.
ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]We calculate by means of the divide and average method.
The first thing is to look for exact roots between those two values
Step 1 estimate
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]Solve for w.4w+6= -22Simplify your answer as much as possible.W8DDХ5?
w= -7
Explanation
[tex]\begin{gathered} 4w+6=-22 \\ \end{gathered}[/tex]
Step 1
The addition property of equality and subtraction property of equality are similar. Adding or subtracting the same number to or from both sides of an equation keeps both sides equal, so we can use this fact to isolate w
a) subtract 6 in both sides of the equation
[tex]\begin{gathered} 4w+6=-22 \\ 4w+6-6=-22-6 \\ 4w=-28 \\ \end{gathered}[/tex]Step 2
The division property of equality states that when we divide both sides of an equation by the same number, the two sides remain equal.so
b) divide both sides by 4
[tex]\begin{gathered} 4w=-28 \\ \frac{4w}{4}=\frac{-28}{4} \\ w=-7 \end{gathered}[/tex]therefore, the answer is
w= -7
I hope this helps you
create a system of equations to represent this situation. be sure to explain the meaning of each variable. graph the system of equations. determine the break even point for Chuck E Cheese and Bright Child, Adventure Plex and Bright Child, Adventure Plex and Chuck E Cheese.
For them, let x = number of children of the party and
A=Adventure Plext cost
B= Bright Child cost
C= Chuck E Cheese cost
So,
[tex]\begin{gathered} A=300+12x \\ B=180+15x \\ C=18x \end{gathered}[/tex]Then, graphing each equation of the system of equations
Now, for determine the break even point for Chuck E Cheese and Bright Child you have
[tex]\begin{gathered} 180+15x=18x \\ 180=18x-15x \\ 180=3x \\ \frac{180}{3}=x \\ 60=x \end{gathered}[/tex]That is, the break even point for Chuck E Cheese and Bright Child occurs when x = 60 children.
For determine the break even point for Adventure Plex and Bright Child you have
[tex]\begin{gathered} 300+12x=180+15x \\ 300+12x-180=180+15x-180 \\ 120+12x=15x \\ 120+12x-12x=15x-12x \\ 120=3x \\ \frac{120}{3}=\frac{3x}{3} \\ 40=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Bright Child occurs when x = 40 children.
Finally, For determine the break even point for Adventure Plex y Chuck E Cheese you have
[tex]\begin{gathered} 300+12x=18x \\ 300+12x-12x=18x-12x \\ 300=6x \\ \frac{300}{6}=\frac{6x}{6} \\ 50=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Chuck E Cheese occurs when x = 50 children.