We are given the system of equations -:
[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]
Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.
[tex] \large{2x + 3(6x + 22) = - 14}[/tex]
Expand 3 in the expression so we can combine like terms and isolate x-variable.
[tex] \large{2x + 18x + 66 = - 14}[/tex]
Then combine like terms.
[tex] \large{20x + 66 = - 14}[/tex]
Get rid of 66 from the left side by subtracting both sides by itself.
[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]
To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.
[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]
Simplify to the simplest form.
[tex] \large{x = - 4}[/tex]
Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.
Answer
x = -4I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!
Answer:
A. x = -2
C. x = -4
Step-by-step explanation:
y = 6x + 22
2x + 3•(6x+22) = -14
20x = - 80
x = -4
y = 6x+22
y = 6(-4)+22 = -2
PLEASE HELPPPPpdododp
Answer:
f(x) - g(x) = x^3 - 3x^2 - 4x - 4
Step-by-step explanation:
f(x) - g(x)
x^3 - 2x^2 - 3x - 5 - ( x^2 + x - 1 )
x^3 - 2x^2 - 3x - 5 - x^2 - x + 1
x^3 - 3x^2 - 4x - 4
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
Compare the rules of two games:
Game A: Two six-sided dice are thrown.The numbers on the dice determine which player gets a point.Player 1 gets a point if the product of the numbers on the dice is even.Player 2 gets a point if the product is odd.
Game B: Two six - sided dice are thrown.The numbers on the dice determine which player gets a point.Player 1 gets a point if the sum of the numbers on the dice is even.Player 2 gets a point if the sum is odd.
Which statement accurately describes whether these games are fair?
A: Both Game A and Game B are fair.
B: Game A is not fair,and Game B is fair.
C: Neither Game A nor Game B is fair.
D: Game A is fair,and Game B is not fair.
Answer: Choice B
Game A is not fair, and game B is fair.
==============================================================
We'll start with game A.
The sides of the dice are {1,2,3,4,5,6}
There are 6*6 = 36 ways to roll two dice.
If we roll two odd numbers, say 3 and 5, the product is odd because 3*5 = 15.
If any of the numbers are even, then the product is even. Eg: 4*5 = 20 or 2*6 = 12.
To be an even number, 2 must be a factor.
So you can probably see that it's more likely to get an even number product considering that in order to get an odd product, both values must be odd (which narrows the selection pool). We can say that game A is not fair. It favors player 1 more. If you're sure about this, then I recommend looking at a multiplication table but only focus on the first 6 rows and 6 columns. Ignore the row and column that has 0s in it.
------------------------------
Now onto game B
The rules are nearly the same, except now instead of multiplying the dice values, we add them up.
We still have 6*6 = 36 outcomes.
Here are some handy rules we'll take into account
even+even = eveneven+odd = oddodd+odd = evenIf the first dice rolls to '1', then there are 3 ways to get an even number (rolling either 1,3,or 5 on the second dice) and there are 3 ways to get an odd number (rolling either 2,4,or 6 on the second dice). We can see that there are the same number of ways to get an even sum or an odd sum. Apply this in general to any result that the first dice shows, and this basically leads to the conclusion that half of the 36 sums are even, and the other half are odd. We have a fair game now. Refer to a sum of dice chart if you need more convincing.
Answer:
Game A is not fair, and game B is fair.
Step-by-step explanation:
test on iready
112x/5= 43.60 solve for x
Answer:
x=109/56
dn did djs. hd hd hd hd hd hd
What is the value of x in this number sentence
[tex]\frac{x}{7} - 4 = 6[/tex]
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
[tex] \frac{x}{7} - 4 = 6 \\ \frac{x}{7} = 6 + 4 \\ \frac{x}{7} = 10 \\ x = 10 \times 7 \\ x = 70[/tex]
____________________
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➳ RainbowSalt2²2² ❦
What is the domain of the function y=3 sqrt x?
Answer:
Step-by-step explanation:
y=3√x
domain : all real values≥0
Find r, if 6r7 = 511 8
Answer:
121.857
Step-by-step explanation:
6×7r = 5118
42r = 5118
r = 121.857
Answer:
121.8571428571429
Step-by-step explanation:
r= 5118/42
What is the area of a triangle in square units with the points (-3,-4), (8,-4), (-1,4)
Step-by-step explanation:
base = 11
height = 8
so are is 11 x 8 /2
= 44
ng
Kellen is saving for retirement. He deposits $325 each month at 3.2% annual interest for 20 years. According to his
calculations, at the end of 20 years he should have $109, 061.81 in his account. How much of this did Kellen
contribute and how much of this is interest?
Answer:
PRT%
Step-by-step explanation:
PRT
[tex] = 320 \times 2.3 \times 20 \div 100 = 1472[/tex]
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
If you horizontally stretch the linear parent function, f(x) = x, by a factor of 3,
what is the equation of the new function?
A. g(x) = x - 3
B. g(x) = 3x
O C. g(x) = 3 - x
D. g(x) = 3 *
SUBMIT
Answer:
The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]
Step-by-step explanation:
Horizontally stretching a function:
Horizontally stretching a function f(x), by a factor of a, means that:
[tex]g(x) = f(\frac{x}{a})[/tex]
In this question:
[tex]f(x) = x[/tex], horizontally stretched by a factor of 3, so [tex]a = 3[/tex], and:
[tex]g(x) = f(\frac{x}{3}) = \frac{x}{3}[/tex]
The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]
5 is subtracted from the sum of 8 and 7.
Answer:
10
Step-by-step explanation:
Sum of 8 and 7 = 8 + 7 = 15
5 subtracted from sum of 8 and 7 = 15 - 5 = 10
The answer to this question = 10
What do you mean by a sum?The sum is the result of the addition of two or more numbers.
What do you mean by subtraction?The difference between the two numbers is called subtraction.
How do we evaluate the given question?First, we find the sum of 8 and 7
8 + 7 = 15
Now, we subtract 5 from 15
15 - 5 = 10
∴ The result to the given question = 10
Learn more about the Addition/Subtraction at
https://brainly.com/question/25421984
#SPJ2
A bakers bread calls for 2 1/2 cups of flour he plans to make 2 loaves of bread.
measuring 1/3 cup how many scoops will he need
9514 1404 393
Answer:
15
Step-by-step explanation:
(2 loaves)(5/2 cups/loaf)/(1/3 cup/scoop) = (2)(5/2)(3/1) scoops = 15 scoops
The baker will need 15 scoops of flour.
Benecio skis 748 yd in 3 min. At this rate, how many miles does Benecio ski in an
hour in miles?
Answer:
8.5 miles an hour.
Step-by-step explanation:
There are many ways to do this, but I am going to do it the way I think is the most simple.
First, divide 748 yards by 3 minutes to get the amount of yards per minute. 748 / 3 = 249.33333
Second, divide the previously gotten number (249.33333, [3's go on forever]) by the amount of yards in a mile (which is 1760 yards per mile). This turns into 249.33333 / 1760 = 0.1416666 (6's go on forever). This is miles per minute so you must make it per hour.
You then multiply that infinite number by the amount of minutes in an hour (60 minutes per hour). 0.14166666 * 60 = 8.5 miles per hour.
You are going to Europe for vacation and must exchange your money. The exchange rate of Euros to
Dollars is a proportional relationship. At the Exchange Counter you exchanged 500 dollars and received
375 euros. In the problem above we found that the unit rate described the number of Euros in a Dollar. Now find the exchange rate for Dollars to Euros.
Answer:
The exchange rate for Dollars to Euros is of 1.33.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
Exchange rate for Dollars to Euros.
We want to find the number of dollars in a euro.
In 375 euros, there are 500 dollars, so how many dollars in 1 euro?
375 euros - 500 dollars
1 euro - x dollars
Applying cross multiplication:
[tex]375x = 500[/tex]
[tex]x = \frac{500}{375}[/tex]
[tex]x = 1.33[/tex]
The exchange rate for Dollars to Euros is of 1.33.
Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9. What is the length of Line segment D C? 2 units 3 units 6 units
Answer:
3 units
Step-by-step explanation:
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width.4x+y^2=12, x=yThen find the area S of the region.
Answer:
The Area of the Enclosed Region Is 64/3.
Step-by-step explanation:
As Given in Question
We have, Curve 4x+[tex]Y^{2}[/tex]=12
& X=Y
Solution.
4Y+[tex]Y^{2}[/tex]=12 (X=Y)
[tex]Y^{2}[/tex]+4Y-12=0
[tex]Y^{2}[/tex]+6Y-2Y-12=0
Y(Y+6)-2(Y+6)=0
(Y-2)*(Y+6)=0
Y=2 & -6 (X=Y)
Now at (2,2) & (-6,-6) both curves intersect each other.
The Area Of Enclosed Region is [tex]\int\limits^2_{-6} [(3-Y^{2}/4 )-Y] \, dy[/tex]
by Solving This Equation we get Area of Region = 64/3 .
this equation Solution & Curve Diagram please see In Attachment .
Identify the solutions to the quadratic equation.
Check all that apply.
x2 + 3x-28 = 0
D A. X=4
B. X= 3
O C. x= -5
O D. X = 28
O E. x= -7
Answer:
A and E
Step-by-step explanation:
x²+3x-28=0
x²+7x-4x-28=0
x(x+7)-4(x+7)=0
(x-4)(x+7)=0
x=4, x= -7
Please give brainliest if it helps
Hi pls helppppppppppp
Answer:
it could only accomplish it's goal on Friday
Step-by-step explanation:
all you had to do was multiply 8 with the number of people and 2 with the number of tickets on each day and add them together to see if it was more than 1650. it was only more on Friday
You are working as an office apprentice for the bksb Newcastle Arena. You are helping collect a customer satisfaction survey for the arena. Enter the following replies into the table below.
Answer:
Step-by-step explanation:
If 12 girls can sweep a room in 20hours, how many hours will it take 8 girls to perform the same task, assuming they are sweeping at the same rate?
Answer:
30 hour
Step-by-step explanation:
girls time
12 20 hour
8 x(let)
now,
12/8=x/20
12×20=8×x
240=8x
x=240/8
x=30,,
HELP ME WITH THIS GEOMETRY QUESTION!!! 18 POINTS!
Answer:
72
72
96
120
Step-by-step explanation:
The arcs are in the ratio:
3 : 3 : 4 : 5
Add all numbers in the ratio:
3 + 3 + 4 + 5 = 15
In the ratio, the sum of all numbers is 15.
In the real circle, the sum of the measures of all the arcs is 360.
360/15 = 24
Multiply all numbers in the ratio by 24.
72 : 72 : 96 : 120
Answer:
72
72
96
120
Solve
[tex](6+v)(5v+4)=0[/tex]
Answer:
v = -6 v = -4/5
Step-by-step explanation:
(6+v) ( 5v+4) = 0
Using the zero product property
6+v =0 5v+4 =0
v = -6 5v = -4
v = -6 v = -4/5
Becky's statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times. Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%. Which answer choice shows the correct null and alternative hypotheses for this test?
Answer:
H0 : p = 0.5
H1 : p ≠ 0.5
Two tailed test
Step-by-step explanation:
The test if the true proportion of heads is different from 50%; this means the initial truth, that is the true proportion is 50% ; which is the null ;
H0 : p = 0.5
The researcher intends to test if the true proportion is not 50% ; that is the researcher is n spwcudfic about if the proportion is lower or higher, he just wants to test that the proportion is different, hence the test could go either way ;
Alternative hypothesis ;
H1 : p ≠ 0.5
Since the sign in the alternative hypothesis could be in either direction, then we have a two tailed test
The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle. Enter an exact answer. Do not type your answers as fractions or decimals
Answer:
One leg: 3
So, the hypo: 2*3 = 6
And the third is according to the formula for right angle triangles: a^2 + b^ = c^2
So: √9+36= c
6.7 to get an exact number round it: 7
Answer:
sides are √3 ft,2√3 ft,3 ft
Step-by-step explanation:
let one leg=x
length of hypotenuse=2x
third side=3 ft
(2x)²=x²+3²
4x²-x²=9
3x²=9
x²=9/3=3
x=√3 ft
hypotenuse=2√3 ft
`show that the normal to the parabola y²=8x at (2 4)meets the parabola again in(18, -12)`
Answer:
See Below.
Step-by-step explanation:
We want to show that the normal line to the parabola:
[tex]y^2=8x[/tex]
At the point (2, 4) meets the parabola again at (18, -12).
First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right][/tex]
Implicit differentiation:
[tex]\displaystyle 2y\frac{dy}{dx}=8[/tex]
Therefore:
[tex]\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}[/tex]
Then the slope of the tangent line to the point (2, 4) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1[/tex]
Thus, the slope of the normal line is -1.
And since it passes through the point (2, 4), by the point-slope form:
[tex]y-(4)=-1(x-2)[/tex]
Simplify:
[tex]y=-(x-2)+4[/tex]
By letting x = 18:
[tex]y=-(18-2)+4=-16+4=-12[/tex]
So, the normal line indeed passes through (18, -12).
Answer:
answer is in the picture.
During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 30%, CBS 27%, NBC 26%, and independents 17%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 96 homes, CBS 69 homes, NBC 90 homes, and independents 45 homes.Test with α = 0.05 to determine whether the viewing audience proportions changed.State the null and alternative hypotheses.H0: pABC ≠ 0.30, pCBS ≠ 0.27, pNBC ≠ 0.26, pIND ≠ 0.17Ha: pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17 H0: pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17Ha: pABC ≠ 0.30, pCBS ≠ 0.27, pNBC ≠ 0.26, pIND ≠ 0.17 H0: The proportions are not pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17.Ha: pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17 H0: pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17Ha: The proportions are not pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17.Find the value of the test statistic. (Round your answer to three decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.Reject H0. There has been a significant change in the viewing audience proportions. Reject H0. There has not been a significant
change in the viewing audience proportions. Do not reject H0. There has been a significant change in the viewing audience proportions. Do not reject H0. There has not been a significant change in the viewing audience proportions.
Part 1: Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)
Part 2:
H0:
Ha:
Part 3: The test statistic is given as 3.0081.
Part 4: The p-value is given as 0.39037
Step-by-step explanation:
As per the data
Part 2
H0:
Ha:
Part 3
As per the sample is of 300 homes, the expected values are given as
ABC=p(ABC)*300=0.30*300=90
CBS=p(CBS)*300=0.27*300=81
NBC=p(NBC)*300=0.26*300=78
IND=p(IND)*300=0.17*300=51
Now the values actually are given as
ABC=94
CBS=71
NBC=88
IND=47
So the test static is given as
So the test statistic is given as 3.0081.
Part 4
Now the degree of freedoms are given as 4-1=3
and chi square is given as 3.0081 so for α = 0.05 , the p-value is given as 0.39037
Part 1.
As the value of p in part 4 is greater than the value of α = 0.05, thus Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)
Solve for x in the triangle. Round your answer to the nearest tenth
Step-by-step explanation:
[tex] \tan(67) = \frac{x}{7} \\ 2.355852366 = \frac{x}{7} \\ x = 16.49 = 16.5[/tex]
What is the smallest number you should subtract from 456 to make it divisible by 9?
Help me pleaseeeeeeeee
If you know two corresponding sides of two triangles and you know that the corresponding angles are equal, how can you find out if they are similar triangles? a. the other angles are proportional c. ratios of the sides will be equal b. the vertical angles will be congruent d. ratio of the sides will not be equal Please select the best answer from the choices provided A
Answer:
I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using
-SSS (side-side-side) which would tell you if all three corresponding sides are congruent
-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent
-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent
-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles