We can determine an expression of y in terms of x by isolating y on one side of the equation, we can do this by means of some algebraic operations to get:
4x + 2y = 8
1. Subtract 4x from both sides of the equation:
4x - 4x + 2y = 8 - 4x
0 + 2y = 8 - 4x
2y = 8 - 4x
2. Divide both sides by 2
2y/2 = (8 - 4x)/2
y = 4 - 2x
y = -2x + 4
Then, the equation of y in terms of x is y=-2x+4
A randomly generated list of numbers from 0 to 4 is being used to simulatean event, with the number 4 representing a success. What is the estimatedprobability of a success?A. 20%B. 75%C. 25%D. 80%
Given:
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing success.
Required:
What is the estimated probability of success.
Explanation:
The probability is
[tex]=\frac{\text{ Number of favorable cases}}{\text{ Total number of cases}}[/tex]0, 1, 2, 3, 4, 5 are choices.
Favorable case is number 4.
So, probability
[tex]\begin{gathered} =\frac{1}{5} \\ =0.2 \\ =20\% \end{gathered}[/tex]Answer:
Option A is correct.
Sally's wallet contains• 5 quarters• 3 dimes• 8 nickels• 4 penniesSally will randomly choose a coin, replace it, and randomly choose another coin. What is teh probability thatshe will choose a dime and then a quater?
Sally's wallet contains the following coins
Quarters = 5
Dimes = 3
Nickels = 8
Pennies = 4
What is the probability that she will choose a dime and then a quarter?
Recall that the probability of an event is given by
[tex]P=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}[/tex]The probability that she will choose a dime is given by
[tex]P(dime)=\frac{3}{5+3+8+4}=\frac{3}{20}[/tex]The probability that she will choose a quarter is given by
(note that replacement is allowed so the total number of coins remains the same)
[tex]P(quarter)=\frac{5}{5+3+8+4}=\frac{5}{20}=\frac{1}{4}[/tex]So, the probability that she will choose a dime and then a quarter is
[tex]\begin{gathered} P(dime\: and\: quarter)=P(dime)\times P(quarter) \\ P(dime\: and\: quarter)=\frac{3}{20}\times\frac{1}{4} \\ P(dime\: and\: quarter)=\frac{3}{80} \end{gathered}[/tex]Therefore, the probability that she will choose a dime and then a quarter is 3/80
By the Remainder Theorem, what can be said about the polynomial function w(x) if w(−5)=3 ?
the remainder must be _________ when w(x) is divided by _________
thanks so much!
well, ding ding ding!! let's recall the remainder's theorem
if some function f(x) has a factor of say x - a, then if we plug the "a" in f(x) what we get is the remainder, that is, the remainder in a division of f(x) by (x-a).
all that mouthful said, well, since we know of w(-5), that means w(x) must have a factor of x - (-5) or namely x + 5.
we also know that w(-5) = 3, well, that means that 3 is the remainder of such division, that is, w(x) ÷ (x + 5), gives us a remainder of 3.
what would be the best first step in solving this system x^2 - 3x + 2y = -4 y = 3x + 2A. isolate x in the first equationB. substitute for y in the first equationc. substitute for x in the second equationD.n isolate x in the second equation
Explanation
we are asked to solve the system of equations:
[tex]\begin{gathered} x^2-3x+2y=-4 \\ y=3x+2 \end{gathered}[/tex]The first step in getting the solution to this will be to substitute for y = 3x +2 in the first equation
Therefore, option B is correct
Can someone explain this to me please thank you !!
The figure can be drawn as,
From the triangle ABC,
[tex]\begin{gathered} \sin 70=\frac{AB}{AC} \\ \sin 70=\frac{h}{400ft} \\ h=400\sin 70ft \\ h=375.87ft \\ \approx376ft \end{gathered}[/tex]Thus, the required value of height is 376 ft.
Question 8 of 10The diagonal of a TV is 30 inches long. Assuming that this diagonal forms apair of 30-60-90 right triangles, what are the exact length and width of the TV?A. 60 inches by 60/3 inchesB. 15 inches by 15/5 inchesC. 60/2 inches by 600/2 inchesO D. 15.2 inches by 15.2 inches
The diagram of the triangle formed is shown below
The length is BC and the width is AB
To find BC, we would apply the cosine trigonometric ratio which is expressed as
Cos# = adjacent side /hypotenuse
hypotenuse = AC = 30
adjacent side = BC
# = 30
Thus, we have
[tex]\begin{gathered} \text{Cos}30\text{ = }\frac{BC}{30} \\ \text{Note, Cos30 = }\frac{\sqrt[]{3}}{2} \\ We\text{ have} \\ \frac{\sqrt[]{3}}{2}=\text{ }\frac{BC}{30} \\ 2BC\text{ = 30}\sqrt[]{3} \\ BC\text{ = }\frac{30\sqrt[]{3}}{2} \\ BC\text{ = 15}\sqrt[]{3} \end{gathered}[/tex]To find AB, we would apply the sine trigonometric ratio which is expressed as
Sin# = opposite side /hypotenuse
hypotenuse = AC = 30
opposite side = AB
# = 30
Thus, we have
Sin30 = AB/30
Recall, sin30 = 0.5
Thus,
0.5 = AB/30
AB = 30 * 0,5
AB = 15
Thus, the correct option is B
In parallelogram DEFG, DE=6 Inches and DF= 6.4 Inches. Diagonals GE and DF Intersect at point H. If GH=4 inches, what is the length of GE?
SOLUTION
Consider the figure below:
It is given that the diagonals DF and GE intersects at H
Recall that the daigonals of parallelogram bisect each other
It follows:
[tex]GH=HE[/tex]Since it is given that GH=4, it follows:
[tex]HE=4[/tex]Using segment addition postulate, it follows:
[tex]\begin{gathered} GE=GH+HE \\ GE=4+4 \\ GE=8 \end{gathered}[/tex]Therefore the required answer is GE=8 inches
On the math test last week,Jacob got 85% of the questions correct. How can this be percent be written as a fraction ?
The number in percent can be expressed as the fraction of 100. So 85% can be expressed as,
[tex]\begin{gathered} \frac{85}{100}=\frac{17\cdot5}{20\cdot5} \\ =\frac{17}{20} \end{gathered}[/tex]85% is expressed as 17/20 in fraction.
Answer: 17/20
Answer:
85/100 = 17/20
Step-by-step explanation: In general, 85% is 85/100, but we can shorten that to an easier answer like 17/20.
find the measure of an angle whose supplement is thirteen times its component. Hint: The supplement and complement of an angle are (180-0)⁰ and (90-0)⁰ respectively.
If the angles are suplemental it means that their sum equals 180º
Let A represent one angle and B represent the other
The first one A measures x and B is 13 times greather then B=13x
A+B=180º
x+13x=180º
14x=180º
x=12.85
A= 12.85º
B= 12.85*13= 167.05º
PLEASE HELP ASAPName all sets to which the number belongs. There may be more thanone answer.Sqaurerootof50
We have to find to which group the square root of 50 belongs.
Not all square roots are irrational, but some are, like the square root of prime numbers.
In this case we have to factorize 50:
[tex]\sqrt{50}=\sqrt{25\cdot2}=\sqrt{25}\cdot\sqrt{2}=5\sqrt{2}[/tex]As we know that the square root of 2 is irrational, a multiple of this has to be irrational.
So the square root of 50 is an irrational number.
Linear function ху 60 10-8 The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x? A) for every change in x by-2, y changes by 4 B) for every change in x by 2, y changes by-4 C) for every change in x by -4, y changes by -2 D) for every change in x by -2, y changes by -4
Here, we want to get how the value of y change relative to a change in value of x
The letters S, E, M, I, T, R, O, P, I, C, A, and L are written on pieces of paper and placed in a hat. Without looking, you draw one letter. Find the probability of drawing a consonant.
Answer:
P = 7/12
Explanation:
There are 12 letters in the hat and 7 of them (S, M, T, R, P, C, L) are consonants. The probability of drawing a consonant is the ratio of the number of consonants to the total number of letters, so the probability is
P = 7/12
Create a box and whisker plot (Label everything!!)
Solution
We have the following data:
11,16,11,15,9,10,11,13,15,17,10,14,17,10,13,15,11,12,12,11,12,14,15,15,13,10,15,12,11
We can calculate the median and the respective quartiles so we need to sort the data and we have:
9 10 10 10 10 11 11 11 11 11 11 12 12 12 12 13 13 13 14 14 15 15 15 15 15 15 16 17 17
Then we have:
Min = 9
Q1 = 11
Median = 12
Q3= 15
Max = 17
And then we can create the boxplot and we got:
Kevin scored at the 60th percentile on a test given to 9840 students. How many students scored lower than Kevin? students
Kevin scored at the 60th percentile on a test given to 9840 students.
Percentile of Kevin = 60th
Number of students = 9840
The objective is to find the number of students, those scored lower than Kevin
Let x be the number of students, those scored lower than Kevin.
The formula for the percentile is as follows;
[tex]\text{ Percentile=}\frac{Number\text{ of students who scored lower than kevin}}{Total\text{ number of students}}\times100[/tex]Substitute the value;
[tex]\begin{gathered} \text{ Percentile=}\frac{Number\text{ of students who scored lower than kevin}}{Total\text{ number of students}}\times100 \\ 60=\frac{x}{9840}\times100 \\ x=\frac{9840\times60}{100} \\ x=5904 \end{gathered}[/tex]Therefore, there are 5904 students who cored lower than Kevin out of 9840
Answer : 5904 students
There are 28 students in a homeroom. How may différent ways can they be chosen tobe elected President, Vice President, Treasurer, and Secretary?
There are 28 students in a homeroom. How many différent ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?
In this problem, we have a permutation
so
Find out 28P4
[tex]28P4=\frac{28!}{(28-4)!}[/tex]28P4=491,400
therefore
the answer is 491,400What is the value of x? ? 21 21 Drawing not to scale 78 156 D787
We can find the value of x, by using the property of issoceles triangle:
A isosceles triangle is a triangle that has two sides of equal length.
In the given figure, triangle have two sides of equal length 21, thus the given triangle is issoceles.
Since, the angle opposite to the equal sides are equal,
so, the third angle of the given triangle is x
The sum of all angles in a triangle is equal to 180 degrees.
In the given figure : x, x & 34
[tex]\begin{gathered} x\text{ + x +34=180} \\ 2x+34=180 \\ 2x=180-34 \\ 2x=146 \\ x=\frac{146}{2} \\ x=73 \end{gathered}[/tex]So, x = 73º
Answer: D) 73º
Find X and y intercepts 7x+10y=40
To find the intercept of the function on the x-axis, replace y = 0 and solve for x:
[tex]\begin{gathered} y=0 \\ 7x+10y=40 \\ 7x+10(0)=40 \\ 7x+0=40 \\ 7x=40 \\ \text{ Divide by 7 from both sides of the equation} \\ \frac{7x}{7}=\frac{40}{7} \\ x=\frac{40}{7} \end{gathered}[/tex]Therefore, the x-intercept of the function is in the ordered pair:
[tex](\frac{40}{7},0)[/tex]To find the intercept of the function on the y-axis, replace x = 0 and solve for y:
[tex]\begin{gathered} x=0 \\ 7(0)+10y=40 \\ 0+10y=40 \\ 10y=40 \\ \text{ Divide by 10 from both sides of the equation} \\ \frac{10y}{10}=\frac{40}{10} \\ y=4 \end{gathered}[/tex]Therefore, the y-intercept of the function is in the ordered pair:
[tex](0,4)[/tex]evaluate the function found in the previous step at x=-2
Given:
[tex]5x^2+2y=-3x-2y[/tex]To evaluate the function at x=-2, we simplify the given relation first:
[tex]\begin{gathered} 5x^2+2y=-3x-2y \\ \text{Simplify and rearrange} \\ 2y+2y=-3x-5x^2 \\ 4y=-3x^{}-5x^2 \\ y=\frac{-3x^{}-5x^2}{4} \end{gathered}[/tex]We let y=f(x):
[tex]f(x)=\frac{-3x^{}-5x^2}{4}[/tex]Next, we plug in x=-2 into the function:
[tex]\begin{gathered} f(x)=\frac{-3x^{}-5x^2}{4} \\ f(-2)=\frac{-3(-2)-5(-2)^2}{4} \\ \text{Simplify} \\ f(-2)=\frac{-14}{4} \\ f(-2)=-\frac{7}{2} \end{gathered}[/tex]Therefore,
[tex]f(-2)=-\frac{7}{2}[/tex]Jenny is selling raffle tickets. For every 3 tickets, she charges $18. Complete the table below showing the number of tickets and the amount Jenny charges. Number of tickets 3 7 10 Х 5 ? Charge ($) 18 30 48
Given that for every 3 tickets, Jenny charges $18.
Let's find the amount charged for 1 ticket:
[tex]\text{Price per ticket = }\frac{18}{3}=\text{ \$6 per ticket}[/tex]Therefore, Jenny charges $6 for each ticket.
For 5 tickets, the charge is:
5 * 6 = $30
For 7 tickets, the charge is:
7 * 6 = $42
For 10 tickets, the charge is:
10 * 6 = $60
For 8 tickets, the charge is:
8 * 6 = $48
During a probability experiment, Jesse draws one marble each from two different jars and records the result. She then places the marbles back in their respective jars and repeats the experiment for a total of 10 trials. On her first trial, Jesse pulls a blue marble from the first far and a green marble from the second jar, and the results are indicated as BG. The results are shown in the table, where B stands for blue, G stands for green, and R stands for red. Trial 1 2 3 4 5 6 7 8 9 10 Result BG RB RR BG RG BB GG BR GB RR Based on the results in the table, what is the experimental probability of pulling a red marble from the first jar and a green marble from the second jar (RG) ? 1 A. 5 B. 1 6 Ос. 1 OD 1 1 10
SOLUTION AND EXPLANATION OF CONCEPT
From the table in the question, the result for Red in the first jar and green in the second trials (RG) occurs in the fifth trials
The formular for probability is give as
[tex]Pr(E)=\frac{required\text{ outcome}}{total\text{ outcome}}[/tex][tex]Pr(RG)=\frac{Number\text{ of trials for RG}}{Total\text{ number ot Trials}}=\frac{1}{10}[/tex]Hence the probability of red in the fir
If the value of tan θ<0 and sin θ>0 , then the angle θ must lie in which quadrant?
Given:
[tex]\tan \theta<0\text{ and }\sin \theta>0[/tex][tex]\text{ we know that }\tan \theta=\frac{\sin \theta}{\cos \theta}\text{.}[/tex][tex]\text{ Replace tan}\theta=\frac{\sin \theta}{\cos \theta}\text{ in tan}\theta<0\text{ as follows.}[/tex][tex]\frac{\sin \theta}{\cos \theta}<0[/tex][tex]\text{Multiply cos}\theta\text{ on both sides.}[/tex][tex]\frac{\sin\theta}{\cos\theta}\times\cos \theta<0\times\cos \theta[/tex][tex]\sin \theta<0[/tex][tex]\text{But given that sin}\theta>0[/tex]hence sine value should be equal to 0.
[tex]\sin \theta=0[/tex][tex]\theta=\sin ^{-1}0[/tex][tex]\theta=\sin ^{-1}\sin (n\pi)[/tex][tex]\theta=n\pi\text{ where n is integer.}[/tex]HELP PLEASE QUICKLYYY
The equivalent expressions are 3a + b + 13a and 16a + b, 20b + 11a - 3b and 11a + 17b and 20b - 5b + 2b and 17b
How to determine the equivalent expressions?From the question, we have the following parameters that can be used in our computation:
3a + b + 13a
Collect the like terms
So, we have
3a + 13a + b
Evaluate
16a + b
Also, we have
20b + 11a - 3b
Collect the like terms
So, we have
11a + 20b - 3b
Evaluate
11a + 17
Lastly, we have
20b - 5b + 2b
Collect the like terms
So, we have
20b - 5b + 2b
Evaluate
17b
Hence, the equivalent expression of 20b - 5b + 2b is 17b
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find any points of discontinuity for each rational functiony= 2x^2 + 3 / x^2 + 2
We have the rational function:
[tex]y=\frac{2x^2+3}{x^2+2}[/tex]and we have to find points of discontinuity.
This points happen when the denominator becomes 0, because the function became undefined in those cases.
In this case it would happen when:
[tex]\begin{gathered} x^2+2=0 \\ x^2=-2 \end{gathered}[/tex]As there is no real value for x that makes the square of x be a negative number, we don't have points of discontinuity for this function.
NOTE: x^2+2 has two complex roots and never intercepts the x-axis.
Answer: this function has no points of discontinuity.
Check for asymptotes.
As there are no discontinuities, we don't have vertical asymptotes.
We will check if there are horizontal asymptotes:
[tex]\lim _{x\to\infty}\frac{2x^2+3}{x^2+2}=\frac{\frac{2x^2}{x^2}+\frac{3}{x^2}}{\frac{x^2}{x^2}+\frac{2}{x^2}}=\frac{2+0}{1+0}=2\longrightarrow y=2\text{ is an horizontal asymptote}[/tex]If we repeat for minus infinity (the left extreme of the x-axis), we also get y=2.
Victor normally sells roadside cashews for $12 per pound and his roadside stands today is discounting the price 25% if Carla buys 2 3/4 pounds of roasted cashews at the Discounted price how much will she pay
Victor sells roadside cashews for $12 per pound.
Today, the price is discounted by 25%. The discount is
25% of $12 = 25/100*$12 = $3
Thus the discounted price is $12 - $3 = $9 per pound
Carla buys 2 3/4 pounds of roasted cashews at that discounted price, thus she will pay:
$9 * 2 3/4
Expressing 2 3/4 as a single fraction:
2 3/4 = 2 + 3/4 = (8+3)/4 = 11/4
Carla will pay:
$9 * 11/4 = $24.75
Carla will pay $24.75
Hi I’m looking to get a step by step solution in solving this problem in the red
Given:
[tex]\begin{gathered} f(x)=13x+2 \\ \\ g(x)=3x^2-13 \\ \\ h(x)=\frac{13}{x+13} \end{gathered}[/tex]Find-:
The inverse of a function.
Explanation-:
(a)
For the inverse of a function, x change as y and y change as x and solve for 'y'
[tex]\begin{gathered} f(x)=13x+2 \\ \\ f(y)=13y+2 \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ \end{gathered}[/tex]Then solve,
[tex]\begin{gathered} y=13x+2 \\ \\ y-2=13x \\ \\ x=\frac{y-2}{13} \end{gathered}[/tex]So, value,
[tex]f^{-1}(y)=\frac{y-2}{13}[/tex](b)
[tex]g(x)=3x^2-13[/tex]So, the value is:
[tex]g(y)=3y^2-13[/tex]The inverse of a function is:
[tex]\begin{gathered} x=3y^2-13 \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ y=3x^2-13 \\ \\ 3x^2=y+13 \\ \\ x^2=\frac{y+13}{3} \\ \\ x=\sqrt{\frac{y+13}{3}} \end{gathered}[/tex]So, the inverse value is:
[tex]g^{-1}(y)=\sqrt{\frac{y+13}{3}}[/tex](c)
[tex]h(x)=\frac{13}{x+13}[/tex]Value of h(y) is:
[tex]h(y)=\frac{13}{y+13}[/tex]Then solve for inverse function,
[tex]\begin{gathered} x=\frac{13}{y+13} \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ y=\frac{13}{x+13} \\ \\ y(x+13)=13 \\ \\ x+13=\frac{13}{y} \\ \\ x=\frac{13}{y}-13 \end{gathered}[/tex]So, inverse value is:
[tex]h^{-1}(y)=\frac{13}{y}-13[/tex]
-5x+2=-9x+38 am crying
The given equation is
[tex]-5x+2=-9x+38[/tex]First, we add 9x on each side.
[tex]\begin{gathered} -5x+9x+2=-9x+9x+38 \\ 4x+2=38 \end{gathered}[/tex]Then, we subtract 2 from each side.
[tex]\begin{gathered} 4x+2-2=38-2 \\ 4x=36 \end{gathered}[/tex]At last, we divide the equation by 4.
[tex]\begin{gathered} \frac{4x}{4}=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Hence, the solution is x = 9.23 The list gives information about the favorite color of each of 22 students.• 6 students chose red.• 2 students chose yellow.• 5 more students chose blue than yellow.• 3 fewer students chose purple than red.• The rest of the students chose green.Which frequency table represents the number of students who chose each color?
ANSWER
Option B
EXPLANATION
We are given the information regarding favorite colors of 22 students.
=> 6 students chose red.
=> 2 students chose yellow.
=> 5 more students chose blue than yellow.
Let the number of students that chose blue be b. This means that:
b = yellow + 5
b = 2 + 5
b = 7 students
7 students chose blue.
=> 3 fewer students chose purple than red.
Let the number of people that chose purple be p. This means that:
p = red - 3
p = 6 - 3
p = 3 students
3 students chose purple.
=> The rest of students chose green.
To find the number of students that chose green, add up the number of students that chose the other colors and subtract from the total number of students.
That is:
22 - (6 + 2 + 7 + 3)
22 - 18
= 4 students
4 students chose green.
Therefore, the correct frequencey table is option B.
How do you write 7 square root x^5 in exponential form
Given:
[tex]7(\sqrt[]{x})^5[/tex]To find the exponential form:
[tex]\begin{gathered} 7(\sqrt[]{x})^5=7(x^{\frac{1}{2}})^5 \\ =7x^{\frac{5}{2}} \end{gathered}[/tex]Hence, exponential form is,
[tex]7x^{\frac{5}{2}}[/tex]S= ut+1/2 at²
U=10 a=-2 t=1/2
The value of the unknown variable, S, is S = 4 3/4
Determining the value of unknown variable in an equationFrom the question, we are to determine the value of the unknown variable in the given equation
From the given information,
The given equation is
S = ut + 1/2at²
Also,
From the given information
u = 10
a = -2
t = 1/2
Substituting the values of u, a, and t into the given equation
S = ut + 1/2at²
S = (10)(1/2) + 1/2(-2)(1/2)²
Simplify
S = 5 + (-1)(1/4)
S = 5 + (-1/4)
S = 5 - 1/4
S = 4 3/4
Hence, the value of S is 4 3/4
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Which number line shows points are to represent the opposite of P
Explanation
The given image marks point p at -3 . Therefore, the opposite of -3 is +3. The corresponding number line that marks R as +3 is given as
Answer: Option 2