The point (3, 2) is the solution to given system of equations
Solution:
Given that system of equations are:
[tex]x^2 + y^2 = 13[/tex] ------ eqn 1
[tex]2x - y = 4[/tex] ------- eqn 2
From eqn 2,
y = 2x - 4
Substitute y = 2x - 4 in eqn 1
[tex]x^2 + (2x - 4)^2 = 13\\\\x^2 + 4x^2 + 16 - 16x = 13\\\\5x^2 -16x + 3 = 0[/tex]
Let us solve the above equation by quadratic formula,
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the Quadratic Formula for [tex]5x^2 -16x + 3 = 0[/tex] where a = 5, b = -16, and c = 3
[tex]\begin{aligned}&x=\frac{-(-16) \pm \sqrt{(-16)^{2}-4(5)(3)}}{2 \times 5}\\\\&x=\frac{16 \pm \sqrt{256-60}}{10}\\\\&x=\frac{16 \pm \sqrt{196}}{10}\end{aligned}[/tex]
The discriminant [tex]b^2 - 4ac>0[/tex] so, there are two real roots.
[tex]\begin{aligned}&x=\frac{16 \pm \sqrt{196}}{10}=\frac{16 \pm 14}{10}\\\\&x=\frac{16+14}{10} \text { or } \frac{16-14}{10}\\\\&x=\frac{30}{10} \text { or } x=\frac{2}{10}\\\\&x=3 \text { or } x=0.2\end{aligned}[/tex]
Substitute for x = 0.2 and x = 3 in 2x - y = 4
when x = 3
2(3) - y = 4
6 - y = 4
y = 2
when x = 0.2
2(0.2) - y = 4
0.4 - y = 4
y = 0.4 - 4
y = -3.6
Thus Option D is correct The point is (3, 2)
Drag each expression to show whether it is equivalent to −2.6x−(−5.9x), −2.6x+(−5.9x), or neither. −2.6x−5.9x 5.9x+(−2.6x) 5.9x−(−2.6x) −5.9x+(−2.6x) −2.6x+5.9x −5.9x+2.6x −2.6x−(−5.9x) −2.6x+(−5.9x) Neither
Answer:
The 2 expressions are:
1) −2.6x−(−5.9x) = −2.6x + 5.9x
2) −2.6x+(−5.9x) = −2.6x - 5.9x
Options:
−2.6x−5.9x -> equivalent to 2nd expression
5.9x+(−2.6x) = −2.6x) + 5.9x -> equivalent to 1st expression
5.9x−(−2.6x) = 5.9x + 2.6x = 2.6x + 5.9x -> equivalent to neither expression
−5.9x+(−2.6x) = −5.9x − 2.6x = − 2.6x − 5.9x -> equivalent to 2nd expression
−2.6x+5.9x -> equivalent to 1st expression
−5.9x+2.6x = 2.6x − 5.9x -> equivalent to neither expression
Sierra join a video rental club she paid an inutiatiin fee of 12.75 and it cost 0.75 per video that she rented write and equation show the total amount, t, Sierra pay to rent v videos.
Answer:
12.75 + 0.75v = t
Step-by-step explanation:
12.75 is the fee she has to pay to join so you would add that to the cost of videos she rented. Since 0.75 is the cost of one and you don't know how many she rented you would put a variable which in this case would be "v". So if she payed the fee and rented 2 videos it would be 12.75 + 0.75(2) = 14.25
The correct equation to represent the total amount Sierra pays to rent videos is:
[tex]\[ t = 0.75v + 12.75 \][/tex]
Where [tex]\( t \)[/tex] represents the total cost, [tex]\( v \)[/tex] represents the number of videos Sierra rents, [tex]\( 0.75 \)[/tex] is the cost per video, and [tex]\( 12.75 \)[/tex] is the initial fee Sierra paid to join the video rental club. The term [tex]\( 0.75v \)[/tex] calculates the total cost of renting [tex]\( v \)[/tex] videos, and adding [tex]\( 12.75 \)[/tex] accounts for the initial fee. This equation allows us to determine the total cost [tex]\( t \)[/tex] for any number of videos [tex]\( v \)[/tex] that Sierra rents.
HELP I WILL MARK YOU AS A BRAINLIEST!!
Nick bought raffle tickets to try to win a
prize. He paid $3.00 for 12 tickets.
What is the cost per raffle ticket?
Answer:
$0.25 per ticket
Step-by-step explanation:
$3 for 12 tickets so divided the number of tickets by amount of money spent to find price per ticket.
3/12 = $0.25 per ticket
Answer:
0.25
Step-by-step explanation:
beacuse it is 0.25 because 0.25 times 12 = $3.00
A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?
Answer: 14.9 years, approximately 15years.
Step-by-step explanation:
Formular for finding the amount of a compound interest
A = P ( 1 + r/100 )n
From the question given,
A = $14,000; P = $4,000; n = ? (year)
Rate = 8.75%.
Substitute for these values in the above equation, we therefore have
14,000 = 4,000(1+ 8.75/100)n (is raised to the power of n)
Divide both side by 4,000
14,000/4,000 = 4,000(1+8.75/100)n/4,000.solving the one in bracket fractionally
3.5 = {(100 + 8.75)/100}n
3.5 = (108.75/100)n
3.5 = 1.0875n( raised to the power of n).In order to solve for 'n' to know the number of years, we take the logarithm of both side.
Log.3.5 = Log(1.0875)n
Going by the law of logarithm,
Log 3.5 = nLog1.0875
Checking your log table, log 3.5 =0.5441 and log1.0875 = 0.0364
Equating both and solve for n
0.5441 = 0.0364n
Divide through by the coefficient of n,
n = 0.5541/0.0364
n = 14.9 years
Approximately 15 years
Hence it will take $4,000 at 8.75% rate to amount to $14,000 a period of 14.9 years approximately 15years.
please solve this equation
Evaluate.
12.25 - 7 2/3 = 12 1/4 - 7 2/3 = 12 3/12 - 7 8/12 = 4 7/12
answer: B
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8 degrees when staring at the top of the statue. Then the person looks down at an angle of 14 degrees when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
The height of the statue is 19.5 feet.
Why?
We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.
We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)
Using the trignometric formula, we have:
First triangle:
[tex]tg(\alpha )=\frac{h_{1}}{base} \\\\tg(8\°)=\frac{h_{1}}{50ft}\\\\0.14*50ft=h_1\\\\h_1=7ft[/tex]
Second triangle:
[tex]tg(\alpha )=\frac{h_{2}}{base} \\\\tg(14\°)=\frac{h_{1}}{50ft}\\\\0.25*50ft=h_1\\\\h_1=12.5ft[/tex]
Now, the total height of the statue will be:
[tex]TotalHeight=h_1+h_2=7ft+12.5ft\\\\TotalHeight=19.5ft[/tex]
Have a nice day!
In this question, we utilize trigonometry to calculate the height of the statue. By using the tangent of the given angles and the known distance from the observer to the statue, we can find the lines of sight when looking up and down. Subtracting these two measurements gives us the height of the statue, which we find to be 5.2ft.
Explanation:This question is about applying trigonometry to find the height of an object, in this case, a statue. First, we need to find the height of the line of sight when the person looks up and when they look down. The height for the line of sight when looking up can be found using the formula for the tangent of an angle: tan(θ) = opposite side/adjacent side. Applying this formula, we find that the height of this line of sight is tan(8°) * 50ft = 7.1 ft. Similarly, when looking down, the height is tan(14°) * 50ft = 12.3 ft.
The height of the statue is the difference between these two heights. Therefore, we find: 12.3ft - 7.1ft = 5.2ft
This is a simple application of the concept of the tangent of an angle in a right triangle, a basic part of trigonometry.
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A hotel shuttle service charges $7.50 plus $0.85 per mile . A customer hires a shuttle for a ride to the airport and the total charge is $12.60 . Which equation can be used to determine the number of miles from the hotel to the airport ?
Answer:
6.40=$12.60
Step-by-step explanation:
First, make the equation following the problem.
$7.50 + $0.85 = $12.60
Then, find the number of miles.
$7.50 * $0.85 = $6.40
$6.40=$12.60
Don't need to solve it because it is asking for the equation.
This is a linear equation problem in Mathematics. The equation to find out the number of miles for the given total charge would be 7.50 + 0.85m = 12.60. Through algebraic manipulation, it is found that the shuttle travelled 6 miles.
Explanation:The subject of this question is in the field of Mathematics, specifically under linear equations in algebra. In this problem, the customer is charged a flat fee of $7.50 and then an additional $0.85 per mile. The total charge for this trip was $12.60, and we're tasked with finding the number of miles covered for this charge.
The equation to solve this problem would be 7.50 + 0.85m = 12.60, where 'm' represents the miles. We subtract 7.50 from both sides, then we get: 0.85m = 5.1. To solve for 'm', we divide both sides by 0.85, and we receive m = 6 miles.
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A pet store sold 35 siamese cats. If the ratio of siamese cats to house cats sold was 7:3 what is the combined amount of cats sold
Answer:
50
Step-by-step explanation:
Answer:
50
Explanation:
A rectangle has a heigh if 4x^3 and a width of x^3+3x^2+2x
Answer:
Area = [tex]4x^6+12x^5+8x^4[/tex]
Step-by-step explanation:
The Complete Question:
A rectangle has height [tex]4x^3[/tex] and width [tex]x^3+3x^2+2x[/tex]. What is the area of the rectangle in terms of x?
Solution:
The formula for the area of a rectangle is:
Area = Height * Width
Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:
[tex]A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4[/tex]
This is the area of the rectangle.
Jane is adding 3 1/4 + 2 7/8 using fraction strips.How can she rename the sum of the fraction parts of the problem? Explain your thinking
Answer:
3 1/4 + 2 7/8= 6 1/8
Step-by-step explanation:
1. Cross multiply 1/4 and 7/8 which equals 1 1/8.
2. 3+2+1(from cross multiplying)= 6
Answer: 6 1/8
Using fraction strips, the result of 3 1/4 + 2 7/8 is 6 1/8.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, Jane is adding 3 1/4 + 2 7/8 using fraction strips.
Fraction strips are rectangular pieces (electronic or copied on paper strips) to represent different parts of the same whole. They can be cut apart and manipulated to see how various parts can be added together to make the whole or compare different fractional amounts for equivalency.
First, we will add fraction parts
=> 1/4 + 7 / 8
We can write 1/4 as 2/8 since they have the same values
=> 2/8 + 7/8
Since now the denominators are the same, therefore we can add the numerators directly. Hence, the sum of 2/8 and 7/8
=> 9/8
=> 8/8 +1/8
=> 1 + 1/8
Thus the sum = 3 + 2 + 1 + 1/8
Sum = 6 + 1/8
therefore, the sum of 3 1/4 + 2 7/8 using fraction strips is 6 1/8.
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Can u please help me I dont understand it
Answer:
11.43 kilometers
Step-by-step explanation:
Answer:
11.43 kilometers.
Step-by-step explanation:
All you have to do is add the two distances (AKA numbers, to make it even simpler). It doesn't matter what distance was traveled by train or bus! The point is that the distances traveled were both in kilometers! With that being said, all we have to do is add 7.22 + 4.21, and voila! We get 11.43!
Hope this answer helps! Please rate it and give me Brainliest! :D
Have a great day!
if sin square theta = 0.75, then cos =
Answer:
[tex]\cos\theta=\pm0.5[/tex]
Step-by-step explanation:
Given:
[tex]\sin^2\theta=0.75[/tex]
To find [tex]\cos\theta[/tex]
Using trigonometric relations for sums and differences of squares of the ratios.
We know:
[tex]\sin^2\theta+\cos^2\theta =1[/tex]
Plugging in [tex]\sin^2\theta=0.75[/tex] in the above relation.
[tex]0.75+\cos^2\theta =1[/tex]
Subtracting both sides by 0.75.
[tex]0.75+\cos^2\theta-0.75 =1-0.75[/tex]
[tex]\cos^2\theta =0.25[/tex]
Taking square root both sides.
[tex]\sqrt{\cos^2\theta} =\sqrt{0.25}[/tex]
∴ [tex]\cos\theta=\pm0.5[/tex] (Answer)
Use the graph shown to fill in the blank. When x = 1, then y = a0.
Explanation:
Step 1) Start at 1 on the horizontal x axis number line.Step 2) Draw a vertical line straight down until you reach point P that is marked in the attached image (see below). Point P is on the diagonal line.Step 3) From point P, move horizontally until you reach -2 on the vertical y axis number line.We started with x = 1 and ended up with y = -2. So the point (x,y) = (1,-2) is on the diagonal line. In other words, point P is located at (1,-2).
Which ordered pair belongs to the solution set of the equation y = x2 - 2x + 1?
A. (510)
B. (-1,3)
c. (1,2)
D. (3,4)
The correct ordered pair for the given equation is D. (3,4).
To find the correct ordered pair, we substitute the x-value from each pair into the equation and check if the resulting y-value matches the one in the ordered pair.
Substituting x = 5 into the equation gives us 52 - 2(5) + 1 = 25 - 10 + 1 = 16, which does not match the y-value of 10 in the ordered pair (5,10), so A is not correct.
Substituting x = -1 gives us (-1)2 - 2(-1) + 1 = 1 + 2 + 1 = 4, which does not match the y-value of 3 in (-1,3), so B is not correct.
Substituting x = 1 gives us 12 - 2(1) + 1 = 1 - 2 + 1 = 0, which does not match the y-value of 2 in (1,2), so C is not correct.
Finally, substituting x = 3 into the equation gives us 32 - 2(3) + 1 = 9 - 6 + 1 = 4, which matches the y-value in the ordered pair (3,4), making D the correct answer.
Therefore, the correct ordered pair is D. (3,4).
While in Europe, if you drive 117 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro = 1.26dollars.
You would spend $63.58 on gas per week.
Step-by-step explanation:
Given,
Distance per day = 117 km
Distance in a week = 117*7 = 819 km
1 km = 0.6214 mile
819 km = 819*0.6214 = 508.93 miles
Car's mileage = 42.0 mi/gallons
Let,
x be the gallons for 508.93 miles
x gallons = [tex]\frac{508.93}{42}=12.12[/tex]
Therefore,
12.12 gallons of gas is needed for one week.
1 US gallon = 3.785 liters
12.12 gallons = 12.12*3.785
12.12 gallons = 45.87 liters
Cost of gas per liter = 1.10 euro
Cost of 45.87 liters = 1.10*45.87 = 50.457 euros
1 euro = $1.26
50.457 euros = 1.26*50.457 = $63.58
You would spend $63.58 on gas per week.
Keywords: multiplication, division
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Which scooter uses fewer gallons after 1,350 miles driven?
what is the best approximation of the solution to the equations that these two lines represent
Answer: the answer would be c
Step-by-step explanation:
What is the value of x in the diagram below?
Answer:
were is the diagram
Step-by-step explanation:
A large cheese pizza costs $11.99 a medium cheese pizza costs $8.99 how much do 2 large and 3 medium pizzas cost? (Estimate to)
Answer:
$50.95
Step-by-step explanation:
2(11.99)+3(8.99)=50.95
Gloria bought each of her three younger siblings a movie ticket. Find the total cost of the movie ticket if each cost $9.75. Justify your answer by using the Distributive Property.
Sry if i keep asking questions.
Answer: 29.25
Step-by-step explanation:
3(9.75)
Which of the following systems of linear equations has an infinite number of solutions?
Answer:
Here we do not have the options, but ill try to give an answer.
A system of equations is something of the shape:
A1*x + B1*y = C1
A2*x + B2*y = C2
Where this is a linear relationship, you could have a more complex system, but this will work for the example.
If you want to have a unique solution for a system of equations, you need to have the same number of linearly independent equations (this means that the equations are not repeated, like for example in x + y = 2, and 2x + 2y = 4, where the second equation is equal to two times the first one) than the number of variables, so if we have two variables X and Y, we need to have two linearly independent equations.
If we have less, suppose that you have two variables and only one equation, you will have:
A1*x + B1*y = C1
y = (C1 - A1*x)/B1
Here, for each value of x you have a different value of y, so you have infinite solutions.
So for an answer this you need to find the system where the number of linearly independent equations is smaller than the number of variables.
What is the cube root of 216x18?
Answer:
The correct answer is 15.72 or 6 ∛18
Step-by-step explanation:
Let's calculate the cube root of 216 * 18
∛(216 * 18)
216 = 8 * 27
8 = 2³; 27 = 3³
18 = 9 * 2 or 3² * 2
∛(8 * 27 * 18)
Simplifying:
∛(2³ * 3³ * 3² * 2)
∛(2³ * 3³ * 3² * 2)
2 * 3 ∛(3² * 2
6 * 2.62 = 15.72 or 6 ∛18
PLEASE ITS SUPER SUPER URGENT
3/5 divided by 1/3
Answer: 3/5 * 3/1 is 9/5 I think
Step-by-step explanation: Go to a calculator and type it but I think it’s KCF so yeah
Answer:
9/5 or 1.8
Step-by-step explanation:
3/5 * 3/1 = 9/5 or 9 divided by 5 gets 1.8
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
Answer:
Step-by-step explanation:
slope of line perpendicular to x=4 is 0
reqd. eq. of line is y=-5
Express the shaded Area as both a faction and a decimal
The shaded area's Fraction= 21/100 and Decimal = 0.21.
Step-by-step explanation:
When an area is divided into multiple smaller regions ( smaller squares ) is called parts.
In case of Squares, it can be divided into either rows or columns, sometimes both.
Form the given diagram, the square consists of 10 rows and 10 columns which makes 100 (10×10) parts in it.
One fraction is obtained by dividing it by the total number of parts.
In this square, 21 shaded fractions are given.
∴ The fraction of shaded Area = 21/100.
Decimal of shaded Area=0.21.
Find the value of x and y
Answer:
y = 110°
x = 55°
Step-by-step explanation:
The line is a transversal.
∠Y = 110°, according to the rule of transversals.
Also, 2X = Y, since in a transversal the vertical angles are equal.
Vertical angles are the ones that are at the intersection of the parallel line and the transversal.
So, 2X = Y = 110°
⇒ X = 55°
Hence, X = 55° and Y = 110°.
solve plzz!?!!?!?!?!?
Answer:
[tex]([7]x+[2])^2[/tex]
Step-by-step explanation:
Given:
[tex]49x^2+28x+4[/tex]
We need to factorize the given trinomial.
To solve the above expression we will Split the product of first term and third term to get the second term by either adding or subtracting.
So we get;
[tex]49x^2+14x+14x+4\\\\7x(7x+2)+2(7x+2)\\\\(7x+2)(7x+2)\\\\(7x+2)^2[/tex]
Hence Final Answer is:
[tex]([7]x+[2])^2[/tex]
Mrs. Bollis has 26 yards of fabric to make costumes. Each costume requires 3 yards of fabric. How many costumes can Mrs. Bollis make? How many yards will she have left?
The required number of costume is 8 and remaining fabric is 2 yards.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The total length of fabric is 26 yards.
And, the requirement for each costume is 3 yards.
Now, the number of costumes to be made and the remaining fabric are the quotient and remainder of the following expression,
26 ÷ 3
It gives the quotient and remainder as 8 and 2 respectively.
Hence, the number of costumes and the fabric left are given as 8 and 2 yards respectively.
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y = − 1/3 x + 2
y = x + 2
What is the solution to the system of equations?
A) (0, 2)
B) (2, 0)
C) (-1, 3)
D) (0, -2)
Answer:
I think is d I need help please
Drag each equation to show if it could be a correct first step to solving the equation
4(1 + x) = 20.
Answer:
4+4x=20
4x=20-4
4x=16
x=16/4
x=16
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