When you have a function written in explicit form with two variables(let's call them 'x' and 'y'), it is written as a combination of 'x' and 'y' equal to some constant.
[tex]\begin{gathered} F(x,y)=k \\ k\in\mathfrak{\Re } \end{gathered}[/tex]To "solve for x in terms of y", is the same as rewritting this function as an equality in the following form:
[tex]x=f(y)[/tex]Let's try an example to show how this works.
Given the following function:
[tex]y^2+x^{}=2[/tex]Now, solving for x in terms of y, is the same as rewriting x as a function of y.
[tex]x=2-y^2[/tex]The circumference of a circle is 13π in. What is the area, in square inches? Express your answer in terms of pie.
The circumference (C) of a circle with radius r is:
[tex]C=2\pi r[/tex]Given the measure of the circumference (13π in), first, let's substitute it in the equation find r:
[tex]\begin{gathered} 13\pi=2\pi r \\ \text{ Dividing both sides by 2}\pi\text{:} \\ \frac{13\pi}{2\pi}=\frac{2\pi}{2\pi}r \\ \frac{13}{2}=r \\ r=\frac{13}{2}\text{ in} \end{gathered}[/tex]The area (A) of a circumference with radius r is:
[tex]A=\pi r^2[/tex]Knowing r, substitute it to find A:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi *(\frac{13}{2})^2 \\ A=42.25\text{ in}^2 \end{gathered}[/tex]Answer: Area = 42.25 in².
QuestionFind the volume of a rectangular solid with the given dimensions: length 8 feet, width 9 feet, and height 11 feet. Give youranswer without units.
We can use the next formula in order to find the volume
[tex]V=l\times w\times h[/tex]l is the length
w is the width
h is the height
in our case
l=8ft
w=9ft
h=11ft
we substitute the values
[tex]V=8\times9\times11=792ft^3[/tex]7. Georgina balances her budget by using this plan. For every $100 she earns, she budgets $10 for charity, $20 for savings, $20 for books, and $50 for other expenses. What amount does she give to charity each week if her income is $500 per week? A. $500 B. $5 C. $250 D. $50
to solve this question, we can find the percentage she gives to charity o every dollar she earns
if she earns $100, she gives $10 to charity. let's find the percentage on this.
[tex]\frac{10}{100}\times100=0.1\times100=10\text{ \%}[/tex]from the calculation, she gives 10% of are earnings to charity.
now we can find 10% of $500 to solve this question.
[tex]\begin{gathered} 10\text{ \% of \$500} \\ \frac{x}{500}=\frac{10}{100} \\ \frac{x}{500}=0.1 \\ x=0.1\times500 \\ x=50 \end{gathered}[/tex]from the calculations above, she gives out $50 on charity weekly from her $500 income.
The inequality 2c−3<9 represents the amount of money a student can spend on c candy bars. Select the values that best complete the sentence. The solution to the inequality is , and it represents that the student can buy a maximum of whole candy bars.
Answer:
Step-by-step explanation:
1. 2c-3<9
2. 2c<9+3
3. 2c<12
4. c<6
5. c can be: 5,4,3,2,1,0,-1,-2,-3 and so on(infinite solutions)
6. The solution to the inequality is 5, and it represents that the student can buy a maximum of 5 whole candy bars.
Solving a percent mixture problem using a linear equationLaurIn the lab, Chris has two solutions that contain alcohol and is mixing them with each other. He uses 200 milliliters less of Solution A than Solution B. Solution Ais 12% alcohol and Solution B is 18% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 126 milliliters of pure alcohol?
Step 1: Let solution A be A
Let solution B be B
If he uses 200 milliliters less of A than B, then
[tex]undefined[/tex]Which fraction and decimal forms match the long division problem? 9) 7.000 6 37 70 63 TO 63 7 O A. 7 9 and 0.7 B. 9 and 0.777 7 O C. c. and 0.7 D. 9 and 0.7 7.
The given fraction is
[tex]\frac{5}{8}[/tex]So, this means, that five is being divided by eight.
So this is best described by option (a) where, five pounds of oats are being divided equally among 8 horses.
what is the greatest common factors of these numbers? 12 3
Answer:
The GCF of 12 and 3 is 3.
Step-by-step explanation:
The answer is 3 because you have to find the common factors of each and see which one they both have in common, and are the biggest:
The factors of 12 are:
1, 2, 3, 4, 6, and 12.
The factors of 3 are:
1, and 3
Thus, the GCF is 3.
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What is the perimeter of a rectangle with coordinates A (1, 7), B (8, 7), C (8, -3), and D (1, -3)?
A. 35 units
B. 68 units
C. 370 units
D. 34 units
PLEASE HELP ILL GIVE BRANLIEST
The perimeter of the rectangle ABCD will be 34 units. Then the correct option is D.
What is the perimeter of the rectangle?The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The coordinates of the rectangle are A(1, 7), B(8, 7), C(8, -3), and D(1, -3).
The distance between AB will be given as,
AB² = (8 - 1)² + (7 - 7)²
AB² = 49
AB = 7 units
The distance between BC will be given as,
BC² = (8 - 8)² + (-3 - 7)²
BC² = 100
BC = 10 units
Then the perimeter of the rectangle will be given as,
P = 2(AB + BC)
P = 2(7 + 10)
P = 2 x 17
P = 34 units
The perimeter of the rectangle ABCD will be 34 units. Then the correct option is D.
More about the perimeter of the rectangle link is given below.
https://brainly.com/question/15287805
#SPJ1
Find the value of x and y if DEFG is congruent to SPQR
ANSWER
• x = 8
,• y = 10
EXPLANATION
If DEFG is congruent to SPQR, then side QR is congruent to side FG,
[tex]2x-4=12[/tex]Add 4 to both sides of the equation,
[tex]\begin{gathered} 2x-4+4=12+4 \\ 2x=16 \end{gathered}[/tex]And divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]For the same reason, angles F and Q are congruent,
[tex]6y+x=68[/tex]Replace x by the value we found before,
[tex]6y+8=68[/tex]Subtract 8 from both sides of the equation,
[tex]\begin{gathered} 6y+8-8=68-8 \\ 6y=60 \end{gathered}[/tex]And divide both sides by 6,
[tex]\begin{gathered} \frac{6y}{6}=\frac{60}{6} \\ y=10 \end{gathered}[/tex]Hence, the answers are x = 8 and y = 10.
A researcher is studying the relationship between sugar consumption and weight gain. Twelve volunteers were randomly assigned to one of two groups. The first group had five participants which were put on a diet low in sugar and the other group with the remaining seven participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant.Which of the following principles was not used in this study?A.Repeated measures B. Blinding C. Randomization D. Control
Principles in Statitstic Studies
A. Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods.
This is performed in the described study since the same subjects are measured in different periods and in different conditions of weight.
B. Blinding in Statistics. Blinding, or double-blinding, is when a patient does not know what treatment they are receiving so it does not influence the final outcomes. This principle is used here, because none of the participants knew what was given to them.
C. Randomization refers to the practice of using chance methods (random number tables, flipping a coin, etc.) to assign subjects to treatments. We are not sure how the participants were assigned to the specific diet. They were randomly selected. This could refer to randomization.
D. Control refers to directly influency over the conditions of the subject of the study to ensure they all go through the exact same proccesses during the study. We know the groups received different diets in sugar contents, but the rest of their living variables were not controlled, thus this last principle was not used in this study
You pick a card at random. Without putting the first card back, you pick a second card at random. 7 8 9 What is the probability of picking an 8 and then picking a prime number? Simplify your answer and write it as a fraction or whole number.
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]What is the range of the function shown on the graph?уO642-6X-4- 226826-8OA -00
SOLUTION
Looking at the graph, the range is from - 6 on the y-axis and from there going upwards the y-axis. That is y at - 6 to infinity.
So, the range is
[tex]-6So, the correct answer is option B.
Use a table to find (x+3)(x+2).
We would set up the table as shown below
For each cell, we multiply the term for the row by the term for the column. By doing this, the first box is x * x = x^2. The second box is 3 * x = 3x
The third box is x * 2 = 2x
The fourth box is 3 * 2 = 6
By combining them, the equation would be
x^2 + 3x + 2x + 6
= x^2 + 5x + 6
f(x)=x²-12x + 3 find vertex
The function f(x)=x²-12x + 3 is a quadratic function, the vertex is given as x = -b/2a
f(x)=x²-12x + 3
a = 1, b=-12, c=3
x = -(-12)/2(1)
x = 12/2
x = 6
to get the y-coordinate, substitute x = 6 into f(x)
f(6) = 6²-12(6) + 3
= 36-72+3
=-33
the coordinate of the vertex is (6, -33)
a scratching post for a cat is in the shape of a cylinder. if you have had to find the amount of carpeting needed to completely cover the post which formula would you useC=2πRSA=2πRH+2πR^2V= πr^2h
The scratching post is in the shape of a cylinder.
To cover the scratching post with a carpet, the surface of the post has to be covered.
This means that the amount of carpeting to be used will be equal to the total surface area of the pole.
The total surface area of the pole is calculated using the formula:
[tex]SA=2πrh+2πr^2[/tex]where r is the radius of the pole and h is the height of the pole.
The SECOND FORMULA is correct.
To quality for a police academy, applicants are given a lest of physical fitness. The scores are normally distributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected, find the cutoff score.
ANSWER
[tex]71.56[/tex]EXPLANATION
Parameters given:
Mean, μ = 64
Standard deviation, σ = 9
To find the cutoff score, we want to find the score that has a corresponding z-score which represents the top 20% of the data.
To do this, first, we have to subtract 20% from 100%:
[tex]\begin{gathered} 100-20 \\ \Rightarrow80\% \end{gathered}[/tex]Now, we have to use the standard normal table to find the z score that corresponds to the closest value to 80% (0.80) on the standard normal table i.e. P(x > 80).
From the table, we see that the z-score that corresponds to 0.80 (0.79955 from the table) is 0.84.
Now, using the formula for z-score, find the cutoff score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = cutoff score
Solving for x, we have that:
[tex]\begin{gathered} 0.84=\frac{x-64}{9} \\ \Rightarrow0.84\cdot9=x-64 \\ \Rightarrow x-64=7.56 \\ \Rightarrow x=64+7.56 \\ x=71.56 \end{gathered}[/tex]That is the cutoff score.
#7 iDecide whether there is enough information to prove that alb. If so, state the theroem you would usebHNo, there is not enough informationYes. Alternate Interior Angles ConverseYes. Alternate Exterior Angles ConverseYes Consecutive Interior Angles ConverseYes Corresponding Ang
Given:
A figure is given with the corresponding angles.
Required:
Choose the correct statement that proves that the lines a and are parallel.
Explanation:
The given angles in the figure are corresponding angles. They are located within the two parallel lines and the transversal line intersecting them.
The corresponding angles are congruent thus lines a and b will be parallel.
Final Answer:
The last option is the correct answer.
Solve: 2(1 - 5k) = 2k + 38
k=-3
1) Let's solve for k, the following expression:
2(1 - 5k) = 2k + 38 Distribute the factor 2
2 -10k = 2k +38 Subtract 2 from both sides and 2k
-10k -2k = 38 -2
-12k = 36 Divide by -1
12k=-36 Divide both sides by 12
k= -3
2) So k is equal to -3 in this equation.
Got to put this in a equation for each line
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
equation of the line:
we must analyze the lines to find the solution.
line l:
y = 4
line p:
x = - 4
line m:
point 1 (0 , 4)
point 2 (2, 0)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{0-4}{2-0}=\frac{-4}{2}=-2[/tex]Slope-intercept form of the line
y = mx + b
y = -2x + 5
line n:
point 1 (5, 4)
point 2 (0 , -1)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{-1-4}{0-5}=\frac{-5}{-5}=1[/tex]Slope-intercept form of the line
y = mx + b
y = 1x + (-1) = x - 1
The answer is:
line l: y = 4
line m: y = -2x + 5
line n: y = x - 1
line p: x = -4
Find the slope, m of the line that passes through the points 3 83 - .) and (1) 6. -5 16' 6 Enter your answer as a fraction in simplest form in the box.
Given:
The points on the line are,
[tex](\frac{3}{8},-\frac{1}{4})\text{ and (-}\frac{5}{16},\frac{1}{6})[/tex]The slope of the line is calculated as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(\frac{3}{8},-\frac{1}{4}) \\ (x_2,y_2)=\text{(-}\frac{5}{16},\frac{1}{6}) \\ m=\frac{\frac{1}{6}-(-\frac{1}{4})}{-\frac{5}{16}-\frac{3}{8}} \\ m=\frac{\frac{2}{6\times2}+\frac{3}{4\times3}}{-\frac{5}{16}-\frac{3\times2}{8\times2}} \\ m=\frac{\frac{2+3}{12}}{\frac{-5-6}{16}} \\ m=\frac{5}{12}\times\frac{16}{-11} \\ m=-\frac{20}{33} \end{gathered}[/tex]Answer: slope is -20/33
the question is in the picture. Is B one of the right answers? Is B the only right answer?
To answer this question we first need to notice that the sequence of dots increases by a factor of 3 in each drawing. This means that this is a geometric sequence with common ratio 3.
We know that the nth term of a geometric sequence is given by:
[tex]a_n=a_1r^{n-1}[/tex]where a1 is the first term and r is the common ratio. In this case a1=3 and r=3, hence the nth term is:
[tex]a_n=3(3)^{n-1}[/tex]Now, if we add the first 15 stages, this means that we are adding the first 15 terms of the sequence, then our sum will be of the form:
[tex]\begin{gathered} a_1+a_2+a_3+a_4+\cdot\cdot\cdot+a_{15}_{} \\ =3(3)^{1-1}+3(3)^{2-1}+3(3)^{3-1}+3(3)^{4-1}+\cdot\cdot\cdot+3(3)^{15-1} \\ =3(3)^0+3(3)^1+3(3)^2+3(3)^3+\cdot\cdot\cdot+3(3)^{14} \\ =3(3^0+3^1+3^2+3^3+\cdot\cdot\cdot+3^{14}) \\ =3(1^{}+3^1+3^2+3^3+\cdot\cdot\cdot+3^{14}) \end{gathered}[/tex]Then we notice that option a is a correct expression for the sum of the first 15 stages.
We also know that the sum of the first nth terms of a geometric sequence is given by:
[tex]\frac{a_1(1-r^n)}{1-r}[/tex]plugging the values we know, we have that:
[tex]3\frac{(1-3^{15})}{1-3}[/tex]Therefore option d is also a correct expression for the sum of the first 15 stages.
Solve, then identify whether it is an identity or a contradiction. 4(2-3t)+6t= -6t+8
To solve the given equation, we first apply the distributive property of multiplication and reduce like terms:
[tex]\begin{gathered} 4(2-3t)+6t=-6t+8, \\ 8-12t+6t=-6t+8, \\ 8-6t=-6t+8. \end{gathered}[/tex]Now, we notice that the left and the right side of the equation are equal for any choice of t.
Answer: Identity.
21, 16, 11, 6 , ...The next 3. Terms would be ?And is an = an-1 - 5 a recursive or explicit?
Answer:
Step by step solution:
This is an arithmetic sequence a, a+d, a+2d, a+3d, ..., where a is the initial term and d the common difference.
For 21, 16, 11, 6, ....
The initial term a = 21 and the common difference is d = 5, then the next 3 terms are
21, 16, 11, 6, 1, -4, -9. This representation is explicit
can u help me with this question
You have a case in which you have the probability of obtaining six different results: 1, 2, 3, 4, 5 and 6
The probaility of getting a specific number is given by the formula:
p = 1/n = 1/6
where n is tha number of different cases, which is 6.
To calculate the probability of getting two results, you have to multiply the probability of one result with the probaility of the other one.
The probability of getting a 4 is:
1/6
The probability of getting a 3 is:
1/6
Then, the probaility of getting the two previous results is:
P = (1/6)(1/6) = 1/36
the graph of each function is shown. write the function in factored format. do not include complex numbers
Notice that the graph passes through the point (-3,0), this means that the function f(x) has a root on x = -3. Then, we can use sintetic division to find the quotient of x+3 with f(x):
notice that on the last row, the last digit is 0, this means that the remainder is 0 and we can write f(x) in the following factored form:
[tex]\begin{gathered} f(x)=x^3+5x^2+12x+18= \\ (x+3)(x^2+2x+6)_{} \end{gathered}[/tex]Graph the following inequalitys.4x + y ≥ 0
SOLUTION
We want to graph the inequality
[tex]4x+y\ge0[/tex]This becomes
The shaded region is known as the required region and contains the solution set for the inequality
Coordinates we can see from the shaded region are
[tex]\begin{gathered} (2,2) \\ (4,4) \\ (4,6) \\ (6,2) \\ (6,4) \end{gathered}[/tex]To make the line, pick two points at
[tex](-1,4)\text{ and }(1,-4)[/tex]Then join the points with a straight-line and shade the area above the line.
Use the general multiplication rule to solve for the given probability model. For events A and B, calculate P(A∩B) given the following information: P(B)=0.70 and P(A I B)=0.45
Question 3(Multiple Choice Worth 1 points)(02.01 LC)Which of the following tables represents a function?Ox 11 22y 3-34-4Ox2-2-2y 1 2340X 3 -3 2-2y 2 25 5x 4 477y 9876
In a function, every x-value must be associated with only one y-value.
In the first table, we can see that the x-value x = 1 has two different y-values associated, y = 3 and y = -3. Then, this table doesn't represent a function.
Similarly, in the second table, x = 2 and x = -2 each have two y-values associated, and in the fourth table, x = 4 and x = 4 each have two y-values associated. Therefore, they are not functions.
On the other hand, in the third table, there is only one y-value associated with each x-value. In consequence, it is a function.
Simplify. Assume that all variables result in nonzero denominators.
The value of the given expression is (5p+3)/ p
A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is less than the denominator.
Given (6p/p+1) – (p-3/9) + (6/p+1)
We have to simplify the given expression
(6p/p+1) – (p-3/9) + (6/p+1)
(6p2 – (p-3)(p+1) + 6p)/p(p+1)
(6p2 – (p2-3p + p - 3) + 6p)/p(p+1)
(6p2 – p2n + 3p - p + 3 + 6p)/p(p+1)
(5p2 + 8p + 3)/p(p+1)
(5p+3)(p+1)/ p(p+1)
(5p+3)/ p
Therefore the value of the given expression is (5p+3)/ p
To learn more about fractions visit
https://brainly.com/question/10354322
#SPJ1
What is the equation of the lime that is perpendicular to y=1/3x+12 that contains the point (-6,-1)
In order to find the equation of the perpendicular line. Take into account that the realtion between the slopes of two perpendicular lines is given by:
[tex]m_1=-\frac{1}{m_2}[/tex]where m1 and m2 are the slopes of the lines.
The general form of the equation of a line is:
y = mx + b
where m is the slope and b the y-intercept. By comparing the previous equation with the given equation y = 1/3x + 12, you can notice that m=1/3.
If you take this slope as m2, then the slope of the perpendicular line is:
[tex]m_1=-\frac{1}{\frac{1}{3}}=-3[/tex]Next, consider that the equation of a line can be also written as follow:
y - yo = m(x - xo)
where (xo,yo) is a point of the line. In this case the point is (-6,-1).
Replace the values of xo, yo and m=m2, into the previous equation and solve for y:
y - (-1) = (-3)(x - (-6))
y + 1 = -3x - 18
y = -3x -19
Hence, the equation of the perpendicular line is y = -3x - 19