Answers
The correct option regarding the solutions of the system of equations for this problem are given as follows:
The solutions are (-1.19, 4.47) and (2.52, 27.92).
How to solve the system of equations?The system of equations for this problem is defined as follows:
4x² + x - y = 0.-x² - 5x + y - 9 = 0.Adding the two equations, we can eliminate the variable y, hence:
3x² - 4x - 9 = 0.
Meaning that this is a quadratic equation with the coefficients given as follows:
a = 3, b = -4, c = -9.
Inserting these parameters into a quadratic equation calculator, the solutions for x of the quadratic equation are given as follows:
x = -1.19 and x = 2.52.
When x = -1.19, the solution for y is calculated as follows:
y = 4x² + x = 4(-1.19)² - 1.19 = 4.47.
When x = 2.52, the solution for y is calculated as follows:
y = 4x² + x = 4(2.52)² + 2.52 = 27.92.
Meaning that the correct option is given by the second option.
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Related Questions
4ft 5 ft 3ft 5ft please help me i dont know
the answer
Answers
83.2 square feet is the area of the figure.
What is Three dimensional shape?A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The given figure is a cone with radius 3 ft and height 5 ft.
We need to find the area of cone=A=πrl+πr²
where l is √r²+h²
A=πr(r+√r²+h²)
=π×3(3+√3²+5²)
=3π(3+√34)
=3×3.14(3+5.83)
=3×3.14(8.83)
=83.2 square feet
Hence, 83.2 square feet is the area of the figure.
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just need help with #7. A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Answers
Surface Area : Volume = 6 : s
What is cube ?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Surface Area of a Cube = 6a² in a square units
Volume of cube = a³ cubic units
where a is the side length of the cube.
Given length of the cube = s
Surface Area of cube A = 6s²
Volume of cube V = s³
Ratio between Surface Area and volume:
Surface Area / Volume = 6s² / s³
Surface Area / Volume = 6 / s
Surface Area : Volume = 6 : s
Hence the ratio between Surface area and volume of cube is 6 : s.
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Of the teacups in Isabella's Tea Shop, 1/3 are indigo and another 1/4 are orange. What fraction of the teacups are either indigo or orange?
Answers
The fraction of the teacups that are either indigo or orange is 7/12.
What is a fraction?A fraction refers to a part of a whole number. It is a proportional value.
A fraction is a quotient that results from a division operation when the numerator is divided by the denominator.
In a proper fraction, the numerator is smaller than the denominator. This is not the case with improper fractions where the numerator is larger than the denominator.
There are complex, proper, and improper fractions.
The fraction of teacups that are indigo = 1/3
The fraction of teacups that are orange = 1/4
The fraction that are either indigo or orange = 7/12 (1/3 + 1/4)
Thus, the fraction or proportion of the Tea Shop's teacups that are either indigo or orange is 7/12.
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Determine if each infinite geometric series is convergent or divergent.
Answers
The solution to the geometric progression are
a) The geometric progression converges , r = 0.1
b) The geometric progression converges , r = 0.2
c) The geometric progression diverges , r = 5
d) The geometric progression converges , r = 0.2
e) The geometric progression diverges , r = 5
f) The geometric progression converges , r = 0.2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A geometric progression is said to converge if the common ratio r lies between -1 < r < 1
So , If -1 < r < 1, the geometric sequence converges
a)
The geometric progression is A = 0.3 + 0.03 + 0.003 + ...
The common ratio r = second term / first term
The common ratio r = 0.03 / 0.3
The common ratio r = 0.1
So , -1 < r < 1 and the GP converges
b)
The geometric progression is A = 0.25 + 0.05 + 0.01 + ...
The common ratio r = second term / first term
The common ratio r = 0.05 / 0.25
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
c)
The geometric progression is A = 0.23 + 1.15 + 5.75 + ...
The common ratio r = second term / first term
The common ratio r = 1.15 / 0.23
The common ratio r = 5
So , r > 1 and the GP diverges
d)
The geometric progression is A = 0.75 + 0.15 + 0.03 + ...
The common ratio r = second term / first term
The common ratio r = 0.15 / 0.75
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
e)
The geometric progression is A = 0.00025 + 0.00125 + 0.00625 + ...
The common ratio r = second term / first term
The common ratio r = 0.00125 / 0.00025
The common ratio r = 5
So , r > 1 and the GP diverges
f)
The geometric progression is A = 128,750 + 25,750 + 5,150 + ...
The common ratio r = second term / first term
The common ratio r = 25,750 / 128,750
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
Hence , the geometric progression is solved
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I never help quick! A kaleidoscope is made of stained glass in the shape of a triangular prism. The bases are equilateral triangles. Find the surface area of the kaleidoscope
Answers
Answer:
46.8 in²Step-by-step explanation:
Total surface area comprises of two bases and 3 faces:
S = 2(1/2*1.5*1.2) + 3(1.5*10) = 46.8 in²Answer:
Solution given:
length=10in
again
base=2√{1.5²-1.3²)=1.49
Total surface area =lateral surface area +2 curved surface area
=perimeter of triangle ×length +2×1/2 base×height
=(1.49+1.5+1.5)×10+1.3×1.49=46.837in²
Which problem solving strategy would be best to solve this problem? Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn? A. write an equation B. make a table, chart or list C. compute or simplify D. guess, check and revise
Answers
The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.
Explanation:The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.
Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.
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In an Arlington, NY school, the heights of the population of girls are normally distributed with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer
Answers
Answer:
Number of girls shorter than [tex]60[/tex] inches are [tex]301[/tex].
Step-by-step explanation:
Given: The heights of the population of girls in an Arlington, NY school follows a normal distribution.
Mean[tex]=63[/tex]
Standard deviation[tex]=2[/tex]
Total number of girls[tex]=450[/tex]
Now using the formula,
Standard normal variant, [tex]z=\frac{x-mean}{standard deviation}[/tex]
Now, substitute the values and replace [tex]x[/tex] by [tex]60[/tex]
So. [tex]z=\frac{60-63}{2}[/tex]
[tex]z=-\frac{3}{2}[/tex] or [tex]-1.5[/tex]
Now, probability of girls shorter than [tex]60[/tex] inches
[tex]p(z>-1.5)=0.668[/tex] look up the value in the normal distribution table
Therefore, number of girls shorter than [tex]60[/tex] inches
[tex]=0.668[/tex]×[tex]450[/tex]
[tex]=301[/tex]
Make a table as y=x^2.
Answers
Answer:
-0
Step-by-step explanation:
Help me
Please help me with both issues
Answers
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is an arithmetic operation in which a number (known as a multiplicand) is multiplied by another number (known as a multiplier) to produce a product.
In this problem, we will need to use of some mathematical operators to solve the problem
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
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Jenson needs to create a graph using the data he collected from the baseball tournament over the weekend. Jenson must create a graph where exact data points are provided.
Which of the following would NOT be a good graph for Jenson to use?
A. Stem-and-Leaf Plot
B. Dot Plot
C. Histogram
Answers
Here's link[tex]^{}[/tex] to the answer:
bit.[tex]^{}[/tex]ly/3gVQKw3
Type the correct answer in the box.
The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year.
Use the data in the table to create the standard form of the function that models this situation, where a, b, and c are constants.
x 0 2 4 6 8 10
f(x) 10 15 18 19 18 15
f(x)=ax^2+bx+c
Answers
Answer:
It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.
To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.
To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.
For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:
f(0) = 10 = a(0)^2 + b(0) + c
f(2) = 15 = a(2)^2 + b(2) + c
f(4) = 18 = a(4)^2 + b(4) + c
Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.
I hope this helps! Let me know if you have any questions or need further assistance.
Step-by-step explanation:
A rock is thrown from the top of a building . The height, h, of the rock t seconds after it thrown is given by h(t) = - 16t ^ 2 - 2t + 240 . How long will it take the rock to reach a height of 180 feet?
Answers
Answer:
1.875 sec
Step-by-step explanation:
Let h(t) = 180
180 = -16t^2 - 2t + 240
16t^2 + 2t - 60 = 0
2(8t^2 + t - 30) = 0
2(t + 2)(8t - 15) = 0
t = -2 or t = 15/8= 1.875 sec
Note: time cannot be negative, so -2 is disregarded
The time is taken by the rock to reach the height of 180 feet is 1.875 sec
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The solution will be:-
Let h(t) = 180
180 = -16t²- 2t + 240
16t² + 2t - 60 = 0
2(8t² + t - 30) = 0
2(t + 2)(8t - 15) = 0
t = -2 or t = 15/8= 1.875 sec
Therefore the time is taken by the rock to reach the height of 180 feet is 1.875 sec
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help i cant solve it
Answers
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
Solve the following system of equations: −2x + 3y = 7 y = 3x + 7 (−5, −1) (−2, 1) (−1, 4) (1, 3)
Answers
Answer:
(-2, 1)
Step-by-step explanation:
−2x + 3y = 7
y = 3x + 7
Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with 3x + 7 and solve for x.
-2x + 3y = 7
-2x + 3(3x + 7) = 7
-2x + 9x + 21 = 7
7x = -14
x = -2
Now substitute x in the second equation with -2 and solve for y.
y = 3x + 7
y = 3(-2) + 7
y = 1
Answer: (-2, 1)
Identify which form is currently written in and then write each equation in standard form.Identify the y-intercept
y=-3x(x+2)
Answers
Answer:
Its in standard form I think. Y intercept is 0,0
Step-by-step explanation:
An angle measures 16° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Answer:
53° and 37°
Step-by-step explanation:
x + (x - 16) = 90
2x - 16 = 90
2x = 106
x = 53
x = 53
x - 53 = ?
90 - 53 = 37
53 - 37 = 16
Help me please please please it’s due tonight!!!!!!!!!!!
Answers
Answer:
A. (4, 18)
Step-by-step explanation:
The "y" coordinate of the midpoint will be equal to the average of the y coordinates of the endpoints, and the x coordinate of the midpoint will be equal to the average of the x coordinates of the endpoints, and so we get that...
The x coordinate of the midpoint = (5 + 3) / 2 = 8 / 2 = 4
The y coordinate of the midpoint = (21 + 15) / 2 = 36 / 2 = 18
So the right answer is A (4, 18)
please help fast
A=___
b=___
c=___
Solve for θ and round your answer to the nearest degree.
θ =___ degrees
Answers
9514 1404 393
Answer:
a = -11b = 13c = 17θ = 93°Step-by-step explanation:
║u║ = √((-2)²+3²) = √13
║w║ = √(4²+(-1)²) = √17
u·v = (-2)(4) +(3)(-1) = -8-3 = -11
Then the formula for cos θ gets filled in as ...
[tex]\cos\theta=\dfrac{-11}{\sqrt{13}\cdot\sqrt{17}}\\\\\theta=\arccos{\left(-\sqrt{\dfrac{121}{221}}\right)}\approx\boxed{93^{\circ}}[/tex]
a = -11b = 13c = 17Consider each of the following word problems.
Write a word sentence to represent what you are going to do with the numerical values.
Include the proper brackets, exponents and operation signs.
Substitute the words with an appropriate variable.
Solve each problem in good form.
1. The school library had a used book sale. Paperbacks were 25 cents each and hardcover books
were $1.25 each. There were 54 paperbacks and 163 hardcover books sold. How much money did
the library raise?
2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $398.60 and her
room costs $115.70 per night. The cab fare from the airport to the hotel is $40.00. If Tamara
stays for two nights, how much does the trip cost, excluding the cost of food?
3. Paula repairs swimming pools and earns $14.50/h for the first 35 h she works in a week. For
hours over 35 h, she earns 1.5 times as much. If she works 48 hours in a week, how much does she
earn?
4. Will and Liam collect baseball cards. Will has 26 cards and Liam has 19. They decided to combine
their cards. Because they shared, their father decided that he would triple the number of cards
that they had. After that, their friend Nestor thought that he would add his cards to their bunch.
Nestor didn’t know how many cards he had but he knew that he could lay them out in rows and that
they would make a square with one side of his square having 8 cards. How many cards did the boys
have altogether?
Answers
The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number
1. Cost of a paperback = 25 cents = $0.25
Cost of a hardcover book = $1.25
There were 54 paperbacks and 163 hardcover books sold.
Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25
2. Cost for round trip airfare = $398.60
Cost of room per night = $115.70
Cost of room for two nights = 2 × $115.70 = $231.40
Cab fare from airport to hotel = $40.00
Total fare from airport to hotel and the return = 2 × $40.00 = $80.00
Total cost = $398.60 + $231.40 + $80.00 = $710
3. Total working hour of Paula = 48 hours
Earning for first 35 hours = $14.50/h × 35
= $507.50
Remaining hours = 48 - 35 = 13 hours
Earning for next 13 hours = ($14.50/h × 1.5) × 13
= $282.75
Total earnings = $507.50 + $282.75 = $790.25
4. Number of cards Will has = 26
Number of cards Liam has = 19
When they combine, total cards = 26 + 19 = 45
When father also shared, total number of cards = 3 × 45 = 135
Number of cards Nestor has = 4 × 8 = 32
Total number of cards = 135 + 32 = 167
Hence all the questions are cleared using multiplication as one of the basic operations.
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50 points plzzzzzzz hurry
Triangles A B C and X Y Z are shown.
Which would prove that ΔABC ~ ΔXYZ? Select two options.
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction = StartFraction A C Over X Z EndFraction
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction , angle C is-congruent-to angle Z
StartFraction A C Over X Z EndFraction = StartFraction B A Over Y X EndFraction , Angle A is-congruent-to Angle X
StartFraction B A Over Y X EndFraction = StartFraction A C Over Y Z EndFraction =
StartFraction B C Over X Z EndFraction
StartFraction B C Over X Y EndFraction = StartFraction B A Over Z X EndFraction , Angle C is-congruent-to angle X.
Answers
Answer:
The answer is 3
Step-by-step explanation:
I hope this help you!! I'm sorry If it wrong..
Have a nice day! <3
Answer:A and C
Step-by-step explanation:
saw the answers
Help!!! Please just answer the question. Thank you!
Let’s compare two different raffles to see which ticket you should buy?
A. Raffle 1: 800 raffle tickets are sold $2.00 each. There is one gran prize for $450 and two consolation prizes of $100 each that will be awarded. What is the expected value of one ticket?
Answers
Answer:
I only see one raffle, but the expected value of one ticket is $2. (I think)
Step-by-step explanation:
Have a nice day!
The expected value E(x) of 1 ticket is $0.40.
How to calculate the total amount?To calculate the total amount by the formula;
Amount = Ticket x Value
Raffle 1
Given;
Tickets = 800
Value = $2 per ticket
Grand ticket = $450 ...for 1
consolation =$100.. for 2
We need to find the expected value of each ticket;
First, we have to calculate the total amount of the 800 tickets
Amount = Ticket x Value
Amount = 800 x 2
Amount = 1600
Next, we have to calculate the total amount of the prizes
Amount = Ticket x Value
Amount = 450 x 200
Amount = 650
The expected value E(x) of 1 ticket is calculated:
E(x) = 650 / 1600
E(x) = $0.40
Thus, the expected value E(x) of 1 ticket is $0.40.
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What is h?
NO LINKS!! I repeat NO LINKS!! Keep them to your self
Answers
Answer:
120°
Step-by-step explanation:
The total sum of the interior angles of a decagon is 1440°
IN THE RECTANGLE BELOW, SOLVE FOR X GIVEN THAT a=51 and ILL BRAINLIEST YOU PLEASE HELP ME
Answers
Answer:
x = 25.5 degrees
Step-by-step explanation:
x is part of an isosceles triangle.
Since a is 51, the supplement (& biggest angle in the x isosceles) is going to be 180 - 51 = 129.
That leaves 51 for the rest of the angles, which we have to divide by 2.
51 / 2 = 25.5 degrees
f ( x ) = 0.1 ( 3 x − 2 ) aWhat is the value of f ( 5 ) ?
Answers
Answer:
3
Step-by-step explanation:
First, plot the graph of the function
and the graph of the line
This line intersects the graph of the function f(x) at 4 different points. So, there are 4 different values for b at which
Only 3 of them have positive values.
At these positive values, f(x)=2 (because the graph of the function and the graph of the line y=2 intersect at these points), then for these three b with positive values,
Write −0.39¯¯¯¯¯ as a fraction in simplest form.
Answers
Answer:
-0.3999... = -⅖
-0.393939... = -13/33
Step-by-step explanation:
Only ones I could think of.
Answer:
-39/100
Step-by-step explanation:
10
y
∝
1
√
x
If
y
=
5
when
x
=
36
find,
y
when
x
=
4
Answers
Answer:
y= 3
Step-by-step explanation:
when y = 5 x= 36
because y = 1[tex]\sqrt{x}[/tex]
so y = 1+ 4
so y= 5
so when x= 4
y = 3
New tablets are on sale for 40% off. They're
normally $149.50. What will I pay for my tablet
when I get 40% off?
Answers
Answer:
$89.7
Step-by-step explanation:
First, find the 40% of 149.5, which is 59.8. Then, subtract the percentage (59.8) from 149.5 which equals 89.7.
So it is $89.7 dollars when it is 40% off.
HOPE THIS HELPS!!!!
BEST OF LUCK!!!
when did u guys start anime? (If you watch it) me I started 2020~(I watched 7 animes by now i know very little but i can't really watch much cause im always busy)
Answers
Answer:
Okay I think you just want to know when I started watching anime. I started watching in 2016/2017.
Step-by-step explanation:
another one 2 more after this
Answers
What is the area of an equilateral triangle with the base of 8 cm? Round your answer to the hundredths place.
Answers
Step-by-step explanation:
[tex] \frac{{x}^{2} \times \sqrt{3}}{4} [/tex]
for x=8, area=16*root(3)
Answer:
Let's find the height:
Half of 8 is 4.
4^2 + 8^2 = 80
80(lets find the square root of 80): 8.944 ^2 = 79.995136 close enough to 80
Your new height is 8.944.
8 x 8.944 = 71.552, 71.552 x 1/2 (basically just dividing by 2) = 35.776 rounded would be = 35.78 cm^2
Formula of area of a triangle:
B(base)H(height) x 1/2(basically just dividing by 2)
In this case 8 is your base and 8.944 is your height.