All the values of x that solve the given system of equations are as follows:
x = 17/2.
What is a system of equations?A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.
For this problem, we are given two equations, as follows:
x² - 9y² = 72.x + 3y = 9.From the second equation, we have that:
x = 9 - 3y.
Replacing in the first, we have that:
(9 - 3y)² - 9y² = 72.
9y² - 54y + 81 = 72.
54y = 9.
y = 9/54
y = 1/6, as 9/9 = 1, 54/9 = 6.
Hence the solution for x of the system of equations is found by replacement, as follows:
x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.
The solution is x = 17/2.
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Find the measure of KNM
2.5 of what is 3?
Need help ASAP
Katie is buying souvenir gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 50 cents each and the key chains cost $1 each. She must purchase at least 24 gifts and spend no more than $20. Let represent the number of magnets and represent the number of key chains.
Model the scenario with a system of inequalities.
Graph the system of inequalities and choose an appropriate solution for the scenario. Use complete sentences to prove why the solution is appropriate.
The inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40
The magnets are on sale for 60 cents each.
The key chains cost $2 each.
Katie must purchase at least 36 gifts but has to spend less than $40.
Now let x represent the amount of key chains.
Let y represent the amount of magnets.
So, the system of inequalities that form are:
x + y ≥ 36
and
2 x + 0.6 y < 40
Therefore, the inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40
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How do you find the range and domain of this graph?
Answer: Domain {-4,-2,2}
Range{4,6}
Step-by-step explanation:
what is (2x-7)+(5x-15)
Jaspare is planning a road trip. He has found 14 places that he wants to visit, but only has time to stop at 5 places. He is visiting the places in a specific order. How many different ways can he plan his trip?
The number of different ways to plan his trip is 240240
In how many different ways can he plan his trip?The given parameters are
Places, n = 14
Stops, r = 5
From the question, we understand that the places are in specific order
This represents permutation
So, the number of different ways to plan his trip is
Ways = [tex]^nP_r[/tex]
This gives
Ways = [tex]^{14}P_5[/tex]
Apply the permutation formula
Ways = 14!/9!
Evaluate
Ways = 240240
Hence, the number of different ways to plan his trip is 240240
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You are lubricating several motors in the shop. One motor must be lubricated with of 3/16 an ounce of grease, and one larger motor must be lubricated with 3/8 of an ounce of grease. How many ounces of grease will you require? Your answer should be a fraction of an ounce, reduced to its lowest terms.
help me with this precal
Answer: Ok
Step-by-step explanation:
9-0-0
Find the surface area or volume of each rectangular prism. Show your work on a
separate sheet of paper.
Answer:
Formulas for a rectangular prism:
Volume of Rectangular Prism: V = lwh.
Surface Area of Rectangular Prism: S = 2(lw + lh + wh)
Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)
Help please picture attached
Answer:
(a) $878.24
(b) $848.30
(c) Amy would pay less for the golf clubs if she gets them directly from the distributor
Step-by-step explanation:
Part (a)
The wholesale price is $499. When the pro shop gets them from the distributor, it has to pay a mark-up of 10%. 10% expressed as decimal is 10/100 = 0.10
10% of 499 = 0.10 x 499 = 49.90
So total cost including markup for the pro shop is 499 + 49.90 = $548.90
We can compute this directly without computing mark-up cost using the formula
Cost = 499(1+0.10) = 499 x 1.1 = 548.90
The pro shop puts a mark up of 60% which in decimal is 60/100 = 0.6 on the above cost
So the price Amy pays = 548.90(1+0.6) = 548.90 (1.6) = $874.28
Part (b)
Wholesale price = $499
If Amy purchases directly from distributor there is a 70% markup on the wholesale price. 70% = 70/100 = 0.7
So the price Amy would have to pay = 499(1+0.7) = 499 x 1.7 = $848.30
Part (c)
Since the cost of purchasing directly from distributor is less than the cost of purchasing from pro shop the answer is
Amy would pay less for the golf clubs if she gets them directly from the distributor
denny is in the car repair business. Denny recently calculated his total cost conditions. He found that the total cost of repairing s cars is TC(s)=2s^2+10
If the market price is $20, how many cars will Denny be willing to repair?
When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.
How to calculate the value?It should be noted that the total revenue will be:
= price × quantity
= 20 × s
= 20s
where s = number of cars
The marginal revenue will be 20.
The total cost is given as:
= 2s² + 10
The marginal cost will be 4s
We will equate the marginal. This will be:
4s = 20
Divide
s = 20/4
s = 5
Therefore, the number is 5.
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a car rental company charges a daily rate of $26 plus $0.10 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $71. How many miles did you drive?
Answer: 450 miles
Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450
What is the image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin
The image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin is (4,-1)
What is coordinate system?
A coordinate system can be defined as the method used to identifying the location of a point graphically. Most of the coordinate systems use two numbers generally x and y to define a coordinate and to identify location of any point. The center of graph or system is known as origin and generally pointed as zero (0).
what are various point representation in 2d coordinate system?The 2 coordinates is generally written as x and y. There are generally 4 quadrants in 2d coordinate system. These are :
Positive x and Positive y i.e. (x , y)Negative x and Positive y i.e. (-x , y)Positive x and Negative y i.e. (x , -y)Negative x and Negative y i.e. (-x , -y)Now in the given question the point is (-1,-4)
i.e. the point lie in 4th quadrant (-x,-y)
If the point is rotated 90 degree counterclockwise then the point becomes (y , -x)
Thus, point (-1,-4) becomes (4,-1)
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Solve for x.
12x + 7 < -11
OR 5x8 > 40
Answer:
-3/2
Step-by-step explanation:
x < -3/2
PLS CHECK IF THIS ANSWER IS CORRECT
WILL MARK BRAINLIEST
Answer:
I'm pretty sure the answer is 6.
Step-by-step explanation:
Labeling the rooms A, B, and C makes it easier.
Room A - All BUT 4
Room B - All BUT 4
Room C - All BUT 4
Since you can see each room is all but four, you can split the 4 into 2 into 2 OTHER rooms than the one stated. For example, Room A is all but 4, so 2 go to Room B and the other 2 go to Room C because each room is all BUT 4.
Basically, 2+2+2 = 6
Given: p: x is a perfect square. q: x is even
What is a value of x that makes p and q true?
16
30
81
99
Answer:
16
Step-by-step explanation:
16: 16=4^2 and is even. 16/2=8
30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).
81: 81=9^2, but 81 is not even. 81/2=40.5.
99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
Using the normal distribution, it is found that 55.7% of response times are between 4 and 6 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 4.5, \sigma = 1.2[/tex]
The proportion between 4 and 6 minutes is the p-value of Z when X = 6 subtracted by the p-value of Z when X = 4, hence:
X = 6:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 4.5)/1.2
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
X = 4:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4 - 4.5)/1.2
Z = -0.42
Z = -0.42 has a p-value of 0.3372.
0.8944 - 0.3372 = 0.5572 = 55.72%.
Hence:
55.7% of response times are between 4 and 6 minutes.
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Write down two prime numbers that have a sum of 20
3 and 17
7 and 13
Step-by-step explanation:
........
.
A polling organization conducts a study to estimate the percentage of households that have high-speed Internet access. It mails a questionnaire to 1495 randomly
Internet access. Of the 1495 households selected, 22.
a) The best description of the bias in the survey is A. Nonresponse bias.
b) To remedy this bias, B. The polling organization should try contacting households that do not respond by phone or face-to-face.
What is nonresponse bias?Nonresponse bias is the type of bias when survey participants are not interested in the survey or send an empty or unsatisfactory response.
Nonresponse bias means that the sample is filled with those who are not willing or able to respond, making the number of non-respondents surpass the number of respondents.
Thus, a response of 22/1,495 is too significant to be ignored, meaning that the nonresponse bias is much more critical.
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Question Completion:responded.
a) Which of these best describes the bias in the survey?
A. Nonresponse bias
B. Sampling bias
C. Undercoverage bias
D. Response bias
b) How can the bias be remedied?
A. The polling organization should mail the questionnaire to a greater number of households.
B. The polling organization should try contacting households that do not respond by phone or face-to-face.
C. The polling organization should mail the questionnaire to each person in the household.
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]
Ready
Linear Functions: Rate of Change and initial value
-Quiz-Level H
Joaquin's car has a full tank of gas at the start of a trip. The graph shows the amount of gas in the
tank, y, as a function of the distance traveled, x.
What is the initial value of the function?
Answer:
I can answer this is you provide a picture of the graph
Step-by-step explanation
The initial value of the graph is normally the y intercept of the graph. If you provide the graph linked to this question, I could answer it for you.
Answer:
10
Step-by-step explanation:
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
The predicted area of the circle is 49.67 cm²
Function and valuesGiven the expression that represents the least regression line as shown below:
log(Area) = 0.490 + 2.004log(time)
Given that the time after the stone is dropped is 4 seconds, the equivalent area is expressed as:
log(Area) = 0.490 + 2.004log(4)
log(Area) = 0.490 + 8.016
log(Area) = 1.6965cm
Area = 10^1.696
Area= 49.67 cm²
Hence the predicted area of the circle is 49.67 cm²
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A jar contains 360 beans. Of all the beans, 1/4 are white beans and the rest are black beans. What is the ration of white beans to black beans?
Explanation:
1/4 = 0.25
0.25*360 = 90
90 white beans, 360-90 = 270 black beans
The ratio of white to black is 90:270 which fully simplifies to 1:3 after dividing both parts by the GCF 90.
Ximena launches a toy rocket from a platform. The height of the rocket in feet
is given by h(t) = -16t² + 40t +96 where t represents the time in
seconds after launch. What is the appropriate domain for this situation?
The apprοpriate dοmain fοr this situatiοn is t ≥ 0.
What is Functiοn?In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be thοught οf as a rule οr a machine that takes inputs and prοduces οutputs accοrding tο a specific set οf instructiοns οr οperatiοns.
The dοmain οf a functiοn represents the set οf all pοssible input values fοr which the functiοn is defined. In this case, the functiοn h(t) represents the height οf the rοcket as a functiοn οf time t after launch.
Since time cannοt be negative in this cοntext (we can't have negative secοnds), the apprοpriate dοmain fοr this situatiοn is t ≥ 0, which means the functiοn is defined fοr all nοn-negative values οf t after the rοcket is launched.
Therefοre, the apprοpriate dοmain fοr this situatiοn is t ≥ 0.
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There are 1,001 pennies lined up on a table.
Starting at one end of the line, I replace every
third coin with a dime. How much money on
the table?
Answer: 3998 cents, or $39.98
Step-by-step explanation: Hope it helps!
how would you set up the equation: four executive integers whose sum is 30? (Ex: 3n + 3 = 144)
The required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30
In this question, we have been given a statement 'four executive integers whose sum is 30'
we need to write an equation for above statement.
Let n, n + 1, n + 2, n + 3 be four consecutive integers.
The sum of these four consecutive integers is 30.
⇒ n + n + 1 + n + 2 + n + 3 = 30
⇒ (n + n + n + n) + (1 + 2 + 3) = 30
⇒ 4n + 6 = 30
which is a required equation.
Therefore, the required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30
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Use properties of operations to add (−3) and (−17)
14
20
-20
-14
Answer:
Step-by-step explanation:
-20
Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
How much does Mark owe?
ound your answer to the nearest cent.
The amount that he owes will be $6610.54.
How to compute the value?From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
Therefore the amount that will be paid will be:
= ($30.45 × 2) + (15.75 × 415.85 miles)
= $60.90 + $6549.64
= $6610.54
The cost is $6610.54.
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Which matrix represents the system of equations shown below?
4x+2y=4
12x - y = 26
-2
OA. [12326]
12 -1 26
-4
OB. 12 -1 -26
4 2 14
OC. [2²1]
12 -1 26
4x 2y 4
OD. [12x ²Y |26]
-y
So matrix which show equation 4x+2y=4 is [tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .
Given that we have an equation that is 4x+2y=4
So equation is a statement that the values of two mathematical expressions are equal (indicated by the sign =).
So in order to write this equation in matrix form we have to write it into augmented matrix
So augmented matrix is a matrix whose elements are the coefficients of a set of simultaneous linear equations with the constant terms of the equations entered in an added column.
Therefore the matrix will be:
[tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .
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At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.
The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x
The domain is x >= 0 and the range is c(x) >= 9.99
Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.The given parameters are:
One topping = 9.99
Additional topping = 1.25 each
We have x to represent the number of toppings
This means that
C(x) = One topping + Additional topping * x
So, we have
C(x) = 9.99 + 1.25x
How to find the domain and range?We have
C(x) = 9.99 + 1.25x
The smallest number of topping is 0
So, the domain is x >= 0
Substitute 0 for x in C(x) = 9.99 + 1.25x
C(0) = 9.99 + 1.25(0)
This gives
C(0) = 9.99
So, the range is c(x) >= 9.99
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Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Step-by-step explanation:
a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.
We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.
So the equation is C(x) = 9.99 + 1.25x right?
Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!
So the new equation is:
C(x) = 9.99 +1.25(x - 1)
or, C(x) = 9.99 + 1.25x - 1.25
or, C(x) = 1.25x + 8.74
b) We need to find the Domain of C(x).
We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.
So we can choose up to 10 different toppings. And we need at least 1 topping.
∴ Domain is 1 ≤ x ≤ 10.
b) We need to find the Range of C(x).
We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.
Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.
C(10) = 1.25(10) + 8.74
or, C(10) = 12.50 + 8.74
or, C(10) = 21.24
∴ Range of C(x) = [9.99, 21.24]
Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]