Explanation
two lines are parallel when their slopes are equal,
Step 1
convert the equation to the form
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to easily find m
[tex]\begin{gathered} 4x+3y=15 \\ \text{subtract 4x in both sides} \\ 4x+3y-4x=15-4x \\ 3y=15-4x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{15}{3}-4x \\ y=-4x+5 \end{gathered}[/tex]Hence
[tex]\begin{gathered} y=-4x+5\Rightarrow y=mx+b \\ m=\text{slope}=-4 \end{gathered}[/tex]Step 2
Now we have this info to find the equation of the line
[tex]\begin{gathered} P1(3,1) \\ m_1=m_2=-4 \end{gathered}[/tex]apply the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-1=-4(x-3) \\ y-1=-4x+12 \\ \text{add 1 in both sides} \\ y-1+1=-4x+12+1 \\ y=-4x+13 \end{gathered}[/tex]I hope this helps you
find (x) 76° 6x-9 47°
There are two degrees, one variable and one number.
33 over r =11 over 2
Answer:
r=6
Step-by-step explanation:
33/r = 11/2
r/33 = 2/11 multiply both sides of the equation by 33
r = 33 * 2/11 = 6
Find the Midpoint of AB*round to the nearest tenth if necessaryA6,-3), B(2,9)
The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Please put this answer in a easy way (no algebra) use ratios and basic opreations.
The number of students attending the field trip is 304 and the number of adults is 114.
Calculating number of students and adults attending a field tripFrom the question, we are to determine the number of students and adults attending the field trip.
From the given information,
"The ratio of the number of adults to the number of students at a field trip has to be 3:8"
Let the number of students be x and the number of adults be y
Thus,
y/x = 3/8
8y = 3x ------------- (1)
Also,
There are 190 more students on the trip than there are adults
That is,
x - y = 190
Therefore,
x = 190 + y -------------- (2)
Substitute into equation
8y = 3x
8y = 3(190 + y)
8y = 570 + 3y
8y - 3y = 570
5y = 570
y = 570/5
y = 114
Thus, the number of adults is 114
Substitute the value of y into equation (2)
x = 190 + y
x = 190 + 114
x = 304
Hence, the number of students is 304
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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 8z
Answer:
(0, 0)(0.1, 0.005)=====================
Given system2y = x² y = 5x³Substitute the value of y into first equation2*5x³ = x²10x³ - x² = 0x²(10x - 1) = 0x = 0 and 10x - 1 = 0x = 0 and x = 0.1Find the value of yx = 0 ⇒ y = 5*0³ = 0x = 0.1 ⇒ y = 5*(0.1)³ = 0.005Answer:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}2y=x^2\\ \;\;y=5x^3\end{cases}[/tex]
To solve by the method of substitution, substitute the second equation into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=5x^3 \implies 2(5x^3)&=x^2\\10x^3&=x^2\\10x^3-x^2&=0\\\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}10x^3-x^2&=0\\x^2(10x-1)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]x^2=0 \implies x=0[/tex]
[tex]10x-1=0 \implies x=\dfrac{1}{10}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=5(0)^3\\y&=0\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies y&=5\left(\dfrac{1}{10}\right)^3\\y&=5 \cdot \dfrac{1}{1000}\\y&=\dfrac{1}{200}\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
use trigaonamets functions as nessary to find the missing parts the triangle
Given a right angle triangle:
As shown on the acute angles is 21
So,
[tex]\begin{gathered} \cos \text{ 21=}\frac{adjacent}{\text{hypotenuse}}=\frac{6.4}{H} \\ \\ H=\frac{6.4}{\cos 21}=6.855 \end{gathered}[/tex]And:
[tex]\begin{gathered} \tan 21=\frac{opposite}{\text{adjacent}}=\frac{y}{6.4} \\ \\ y=6.4\cdot\tan 21=2.457 \end{gathered}[/tex]the third angle of the triangle =
[tex]90-21=69[/tex]Rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5); 90° counterclockwise rotation about the origin
Given data:
The given coordinates of Rhombus are A(1,0), B(6,-2), C(8,-7), and D(3,-5).
The coordinate of a point after 90 degrees counterclockwise rotation is,
[tex](x,\text{ y)}\rightarrow(-y,x)[/tex]The final coordinate of Rhombus are,
[tex]\begin{gathered} A(1,0)=A^{\prime}(0,\text{ 1)} \\ B(6,\text{ -2)=B'(2, 6)} \\ C(8,\text{ -7)=C'(7},\text{ 8)} \\ D(3,\text{ -5)=D'(5, 3)} \end{gathered}[/tex]Thus, the final coordinate of Rhombus are A'(0,1), B'(2, 6), C'(7, 8) and D'(5, 3).
How much do you owe at the end of five weeks ?
First, find the interest percentage. Divide the amount borrowed by the interest amount.
[tex]\frac{100}{10}=10[/tex]Then, divide the result by 100% to express it as a percentage.
[tex]\frac{10}{100}=0.10[/tex]Once we have the interest percentage as a decimal number, multiply it by the new borrowed amount.
[tex]0.10\times1100=110[/tex]Therefore, you owe $110 at the end of the five weeks.Find the area of the composite figure below. Round your answer to the tenths.
Answer:
54 square units
Explanation:
First, divide the composite figure into common plane shapes as shown below:
Thus, we have two plane shapes:
• A triangle with a base of 10 units and a height of 6 units.
,• A rectangle with a length of 6 units and a height of 4 units.
Therefore:
[tex]\begin{gathered} \text{ Area of the composite figure}=\text{ Area of the triangle+Area of the rectangle} \\ =\frac{1}{2}bh+lh \\ =(\frac{1}{2}\times10\times6)+(6\times4) \\ =30+24 \\ =54\text{ square units} \end{gathered}[/tex]The area of the composite figure is 54 square units.
if (x=5)and y=10 which expression has the greatest value
Let's assume the question was as stated below;
"If x=5 and y=10, which expression has the greatest value?"
a. xy
b. x + y
c. x-y
d. x/y
Answer:
Option A. Expression xy has the greatest value.
Explanation:
To determine which of the given options has the greatest value, let's go ahead and evaluate each of them;
Option A;
[tex]xy=x\ast y=5\ast10=50[/tex]Option B;
[tex]x+y=5+10=15[/tex]Option C;
[tex]x-y=5-10=-5[/tex]Option D;
[tex]\frac{x}{y}=\frac{5}{10}=\frac{1}{2}[/tex]We can see that the expression (xy) gives the greatest value.
Therefore, option A would be our correct answer.
The school budget allows no more than $360 to be spent on balls and bats.The cost of a ball is $6 and the cost of a bat is $24write the inequality to represent this information
Since the school budget allows no more than $360 to be spent on balls and bats, we have:
[tex]\text{total cost of balls and bats, in dollars }\le360[/tex]Now, let's call x the number of balls and y the number of bats that can be bought.
• The cost to buy x balls, in dollars, is 6x.
• The cost to buy y bats, in dollars, is 24y.
So, the total cost of balls and bats, in dollars, is 6x + 24y.
Now, we can use this expression in the above inequality to obtain the inequality:
[tex]\mathbf{6x+24y\le360}[/tex]100 in it takes 10 pounds of potatoes to make 15 pounds of mashed potatoes at this rate how many pounds of mashed potatoes can they make with 15 pounds of potatoes
The box of cereals will weigh
[tex]undefined[/tex]hentIf TR = 11 ft, find the length of PS.IfР P.TentR16d ArcsSnd ArcsRound to 2 decimal places.and Arcs
SOLUTION
This is a length of arc problem.
The formula for finding the length of an arc is:
[tex]\frac{\theta}{360}\times2\pi r[/tex]r=TR=PT=11ft
[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ r=11ft \\ \theta=164^o \end{gathered}[/tex][tex]\begin{gathered} \frac{164}{360}\times2\pi(11) \\ =\frac{164}{360}\times2\times3.14\times11 \\ =31.4698ft \\ =31.47ft(to\text{ 2 decimal places)} \end{gathered}[/tex]The final answer is 31.47ft.
Round 2.8962 to the nearest hundredth. Do not write extra zeros.
To round the number
2.8962 to the nearest hundredth
First check the digit whose place value is hundredth
The digit is 9
You will either round it up or down depending on the next digit immediately after it which is called the decider
If the decider is from 0-4 then we round the number down
If the decider is from 5 -9 then we round the number up
The decider is 6 so we are rounding the number up
2.8962 ≈ 2.90 to the nearest hundredth
When the 9 increases to ten, we can't write 10 down so we write 0 and add 1 to 8 which makes it 9
Answer:
9
Step-by-step explanation:
19. The Millers open a savings account for their newborn son with $430. Find the total amount in the account after 3 years if the simple interest rate is 2.5%.
we get that
[tex]C=430+3\cdot0.025\cdot430=462.25[/tex]On the plans for a treehouse, a beam represented by QR has endpoints Q(-6,2) and R (-1,8). A connecting beam represented by ST has endpoints S(-3,6) and T(-8,5). Are the beams perpendicular? Explain. (Hint:Graph the points if needed).
We have the next graph
QR is the beam in red
ST is the beam in blue
As we can see the beams are not perpendicular because they do not intercept each other and they don't form a 90° angle between each other
The 19% APR is the annual interest rate, but it is compounded monthly. What is the monthly interest rate ?
Answer:
1.583%
Step-by-step explanation:
19% divided by 12% (how many months there are) = 1.583%
4. Solve for y 2x - y = -8
The correct option is y = 2x + 8
what kind of triangle is a triangle with the sides 8, 15, and 16? A. obtuseB. acuteC. right
Lets draw the following picture:
which corresponds to an acute triangle. In acute triangles, all the angles are less than 90°.
Acorn is tossed three times. An outcome is represented by a string of the sort HTT (meaning ahead on the first tos, followed by two tails). The outcomes areIsted in the table below. Note that each outcome has the same probability,Por each of the three events in the table, check the outcomes) that are contained in the event. Then, in the last column, enter the probability of the event.OutcomesmiተብህቡብProbability음THTTTHTTHTHTHITHTEvent At A tail on both the first andthe last tosses$?0Event : Two or more tails0Event Ci Alternating tail and head(with either coming frst)0ContinueSubmit Assignment2022 MID CARDSign out00
The outcome of tossing a coin is either a head or a tail.
Looking at the given table,
Event A = A tail in both the first and last tosses = THT, TTT
Event B = Two or more tails = TTH, TTT, HTT, THT
Event C = Alternating tail and head with either coming first = TTH, THH, HTT, HTH, THT. HHT
Recall,
probability = number of favorable outcome/number of total outcomes
Total number of outcomes = 8
Probability of event A = 2/8 = 1/4
Probability of event B = 4/8 = 1/2
Probability of event C = 6/8 = 3/4
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeAB.CDF3 2Frequency 51015Find the probability that a student earns agrade of A, B, or C.p = [?]Enter a decimal rounded to the nearest hundredth.
The probability of an event is obtained as follows:
[tex]Pr(\text{Event)}=\frac{number\text{ of favourable outcomes}}{number\text{ of sample space}}[/tex][tex]\begin{gathered} Pr(a\text{ student earns a grade of A) = }\frac{number\text{ of students that earn grade A}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of A)=}\frac{5}{35} \\ \\ Pr(a\text{ student earns a grade of B)=}\frac{number\text{ of students that earn grade B}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of B)=}\frac{10}{35} \\ \\ Pr(a\text{ student earns a grade of C)=}\frac{\text{number of students that earn grade C}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of C)=}\frac{15}{35} \end{gathered}[/tex]Therefore, the probability that a student earns a grade of A, B or C=
Pr(a student earns a grade of A) + Pr(a student earns a grade of B) + Pr(a student earns a grade of C).
This becomes;
[tex]\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\text{ }\frac{30}{35}=\frac{6}{7}[/tex]Hence, the probability that a student earns a grade of A, B or C is
[tex]\frac{6}{7}=0.86\text{ (to the nearest hundredth)}[/tex]Find the equation of the line thatis parallel to y = 2x – 7 andcontains the point (-3,6).y = [ ? ]x + []Enter
Answer:
y = 2x +12
Step-by-step explanation:
You want the line through point (-3, 6) that is parallel to y = 2x -7.
Parallel lineThe given line equation is in slope-intercept form ...
y = mx + b . . . . . line with slope m and y-intercept b
This allows us to see that its slope is 2.
The parallel line will have the same slope. All we need to do is find its y-intercept.
InterceptSolving the above equation for 'b', we get ...
b = y - mx
Using (x, y) = (-3, 6) and m = 2, we find 'b' to be ...
b = 6 -(2)(-3) = 12
EquationUsing the values for m and b that we now know, the desired equation is ...
y = 2x +12
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On March 8, 2017, one U.S. dollar was worth 19.61 Mexican pesos.(a) On that date, how many dollars was 149.23 pesos worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many pesos was 63.64 dollars worth?Round your answer to the nearest hundredth of a peso.OPpesosI need help with these two math problems.
ANSWERS
(a) 7.61 USD
(b) 1247.98 MXN
EXPLANATION
We know that on March 8, 2017, 1 USD was worth 19.61 MXN.
(a) To find how many dollars was 149.23 MXN worth on that date, we have to divide this amount by 19.61,
[tex]149.23\text{ }MXN\cdot\frac{1\text{ }USD}{19.61\text{ }MXN}\approx7.61[/tex]Hence, 149.23 Mexican pesos were worth 7.61 US dollars.
(b) Now, to find how many Mexican pesos were 63.64 USD worth on that date, we have to multiply it by 19.61 instead,
[tex]63.64\text{ }USD\cdot\frac{19.61\text{ }MXN}{1\text{ }USD}\approx1247.98\text{ }MXN[/tex]Hence, 63.64 US dollars were worth 1247.98 Mexican pesos.
the factor of 26 are
EXPLANATION
Factors are numbers we can multiply together to get another number.
The factor of 26:
26 divides by 2: 26/2=13
13 divides by 13: 13/13 = 1
2,13 are all prime numbers, therefore no further factorization is possible.
Add the primer factors:
2,13
Add 1 and the number 26 itself:
1,26
The factors of 26 are 1,2,13,26.
if f(x) = 1/x and g(x) = x+1/x find(fog)(x).a) x +1/ x squared b) x / x + 1 c) x squared (x + 1)d) x + 1 / x cubed
We have the following:
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ g(x)=\frac{x+1}{x} \end{gathered}[/tex]now, (f(x) o g(x))
[tex]\mleft(f\: (x)\circ\: g(x)\mright)=\frac{1}{\frac{x+1}{x}}=\frac{x}{x+1}[/tex]The answer is the second option
[tex]\frac{x}{x+1}[/tex]Solve for V5/6= v-5 /4
Okay, here we have this:
Considering the provided equation, we are going to solve it to find the value of y, so we obtain the following:
5/6= v-5 /4
v-5 /4+ 5 /4=5/6 + 5/4
v= 5/6 + 5/4
v=(20+30)/24
v=50/24
v=25/12
Finally we obtain that v is equal to 25/12.
What is the inverse of the statement "If it is winter, then I am cold"?If it is not winter, then I am not coldIf it is winter, then I am coldIf I am cold, then it is winterIf I am not cold, then it is not winter
ANSWER
If it is not winter, then I am not cold.
EXPLANATION
We want to find the inverse of the statement given:
If it is winter, then I am cold
To do this, we have to negate the if statement and the conclusion of the if statement there.
That is we find the negative of the if part and the then part of the statement.
The if part is:
If it is winter
The negative of this is:
If it is not winter
The then part is:
then I am cold
The negative of this is:
then I am not cold
Therefore, the inverse of the statement is If it is not winter, then I am not cold.
ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY DISTRIBUTED WITH A MEAN OF 16 MINUTES AND STANDARD DEVIAITON OF 4 MINUTES.1. IN A RANDOM SAMPLE OF 1000 CUSTOMERS, HOW MANY WAIT 18 MINUTES OR MORE BEFORE BEING SEATED.2. IN A RANDOM SAMPLE OF 500 CUSTOMERS, HOW MANY WAIT LESS THAN 9 MINUTES BEFORE BEING SEATED
Solution.
Calculate the z-score
The formula is shown below
[tex]\begin{gathered} \sigma=4 \\ \mu=16 \\ \end{gathered}[/tex][tex]\begin{gathered} Z_{18}=\frac{18-16}{4}=0.5 \\ P\left(x>0.5\right)=0.30854 \\ n=0.30854\text{ x 1000} \\ n=308.54 \\ n=309(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 309 customers (to nearest whole number) wait 18 minutes or more before being seated
(ii)
[tex]\begin{gathered} Z_9=\frac{9-16}{4} \\ Z_9=-1.75 \\ P\left(x<-1.75\right)=0.040059 \\ n=0.040059\text{ x 500} \\ n=20.03 \\ n=20(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 20 customers (to nearest whole number) wait less than 9 minutes before being seated
Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw $300 automatically every month to pay off his 10-year student loan. Will Rajesh have enough money in the account to cover all of the required loan payments? (Round to the nearest tenth of a year.)
By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.
The Principal Amount(P) = $30,000
Rate of Interest (r) = 2.16 %
Time(t) = 10 years
Number of Times it is Compounded in a year(n) = 12
Now, we have
[tex]A =P(1+\frac{r}{100n}) ^{nt}[/tex]
Putting all the values, we evaluate the amount,
[tex]A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84[/tex]
Hence, the Amount after Compound Interest = $37,225.87
Now, The loan amount that he pays = 300 *12*10 = $ 36,000
Yes, he will have enough money in the account to cover all of the required loan payments.
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encuentra la medida de dos angulos complementarios. A=7×+4 y B=4×+9
Complementary angles mean that they add up to 90.
Thus, we can write:
[tex]\begin{gathered} A+B=90 \\ 7x+4+4x+9=90 \end{gathered}[/tex]We can use algebra to find x:
[tex]\begin{gathered} 7x+4+4x+9=90 \\ 11x+13=90 \\ 11x=90-13 \\ 11x=77 \\ x=\frac{77}{11} \\ x=7 \end{gathered}[/tex]To find measure of the individual angles, A and B, we simple plug in 7 into x of the expressions of A and B.
Angle A:
7(7) + 4 = 53 degrees
Angle B:
4(7) + 9 = 37 degrees