System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
What is the discriminant in the quadratic equation?A quadratic equation is the polynomial equation of two degrees in one variable. The general form of a quadratic equation is ax² + bx + c = 0.
The quadratic equation formula for the solution of roots.
[tex]\rm (\alpha ,\beta ) = [ -b[/tex]±[tex]\rm \sqrt{b^{2} - 4ac} /2ac[/tex]]
The discriminant is the [tex]\rm \sqrt{b^{2} - 4ac}[/tex] part of the quadratic equation
If D is greater than zero then the roots are real and distinct.
If D is equal to zero then the roots are real and equal.
If D is less than zero then the roots are imaginary and unequal.
y = x² + 7x + 4
From First option, System of equations
y = x² + x – 4
y = x – 5
So, x - 5 = x² + x – 4
x² + x – 4 - x + 5 = 0
x² + 1 = 0
discriminant = b²- 4×a×c
= 0²- 4×1×1
-4 < 0, therefore the equation has no real roots.
From Second option, System of equations
y = x² + 2x – 1
y = x – 5
So, x - 5 = x² + 2x – 1
x² + 2x - 1 - x + 5 = 0
x² + x + 4 = 0
discriminant = b²- 4×a×c
= 1²-4×1×4
-15 < 0 therefore, the equation has no real roots.
From Third option, System of equations
y = x² + 6x + 9
y = x – 5
So, x - 5 = x² + 6x + 9
x² + 6x + 9 - x + 5 = 0
x² + 5x + 4 = 0
discriminant = b²- 4×a×c
= 5²-4×1×4
9 > 0 therefore, the equation has two different real roots.
From Fourth option, System of equations
y = x² + 7x + 4
y = x – 5
So. x - 5 = x² + 7x + 4
x² + 7x + 4 - x + 5 = 0
x² + 6x + 9 = 0
discriminant = b²- 4×a×c
= 6²-4×1×9 = 0
0 therefore, the equation has one real root.
Since, System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
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Answer:
D on edge
Step-by-step explanation:
Which lines are parallel?
red and green
they go in the same direction, side by side, and will never touch
In what year did the nfl vote to create a $430 million pool of money, funded by the top 15 clubs by revenue to be distributed to the bottom 15 clubs?.
The year in which the NFL voted to create a $430 million fund to help the bottom 15 clubs was 2007.
When did the NFL vote to implement this fund?The NFL voted by a margin of 30-2 in 2007 to create a pool of funds over 3 years that would amount to $430 million.
This money would then be used to help the bottom 15 clubs who might be struggling financially. The hope was that this would make things more competitive in the NFL.
Find out more on the NFL at https://brainly.com/question/7579515.
Will give
BRAINLY AND FIVE STARS and A THANKS
Answer:
k = 12h
Step-by-step explanation:
Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
Hope this helps :)
·[tex]3\sqrt{10}\ times -6\sqrt{30}[/tex]
Due by 12:23
Answer:
-180√3
Step-by-step explanation:
3√10 x - 6√30
= 3x-6 x -√10 x √30
= -18 x√300
= -18 x 10√3
= -180√3
This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show your work.
Answer:
area of the figure: 29.92 m²
formula's:
area of rectangle: length * widtharea of sector: ∅/360 * πr²solving steps:
area of rectangle + area of sector
5.5 * 4 + 30/360 * π(5.5)²
22 + 7.919
29.92 m²
Answer:
Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.
Rectangle
Area of a rectangle = width × length
= 4 × 5.5
= 22 m²
Sector
[tex]\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}[/tex]
[tex]=\dfrac{30 \cdot\pi\cdot5.5^2}{360}[/tex]
[tex]=\dfrac{121}{48}\pi \textsf{ m}^2[/tex]
Total area
total area = area of rectangle + area of sector
[tex]=22 +\dfrac{121}{48}\pi[/tex]
= 29.91943148...
= 29.9 m² (nearest tenth)
what is the value of the expression (-2) to the third power (-2) to the second power
Answer:
-2 to the third power is -8
-2 to the second power is -4
Step-by-step explanation:
-2 to the 3 power = -2× -2×-2
-2 to the second power is -2×-2
Given that lines b and c are parallel, select all that apply.
Which pairs of angles are congruent?
3 and 7
2 and 8
3 and 5
1 and 4
Answer:
3 and 7
1 and 4
Step-by-step explanation:
[3 and 7]
These two angles are prooved congruent by corresponding angles
[1 and 4]
These two angles are prooved congruent by opposite vertical angles.
I need help with this
Answer:
You are correct with B!!
Step-by-step explanation:
(x⁹)²
We have to multiply 9 x 2, regardless of the parenthesis for this one.
9 × 2 is 18.
We cannot simply 18 further.
Carry the x in front of 18.
x¹⁸
**WILL GIVE BRAINLIEST** please help me
Answer:
SORRY
Step-by-step explanation:
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ANSWER
X 12. Find the volume of the composite solid. Use 3.14 for . 5.5 ft Find the volume of the cone using the formula.
Answer: 74.61 ft^3
Step-by-step explanation:
A pair of fair dice is cast. What is the probabiliy that one of the numbers falling uppermost is a 5, given that the two numbers falling uppermost are different?.
Using it's concept, it is found that there is a 0.3333 = 33.33% probability that one of the numbers falling uppermost is a 5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The outcomes are given as follows:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
From the list, we have that:
There are 30 outcomes in which the numbers are different.In those, there are 10 in which one 5 appears.Hence, the probability is given by:
p = 10/30 = 0.3333 = 33.33%.
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X + Y-2 (3X-4Y+3) please simplify this
thanks
Answer:
-5x+9y-6
Step-by-step explanation:
Step 1:
Remove bracket,
x+y-6x+8y-6
collect like terms and simplify,
x-6x+y+8y-6= -5x+9y-6
1. a) Solve the following linear-quadratic system of equations graphically.
y + 2x²– 8x – 1= 0
y+ 2x – 9= 0
b.) GRAPH
c.) Verify your solution (s) algebraically.
Answer:
please see explanation
Step-by-step explanation:
look at the photo
Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
If cat and dog start running away from each other how far away from each other will they be after 30 minutes?
The distance they(Bobby's cat and dog) will be from each other after 30 minutes is 0.5x miles.
Calculation of distanceThe dog runs twice as fast as the cat. Therefore,
Bobby's cat speed = x
Bobby's dog speed = 2x
Therefore,
speed = distance / time
30 minutes = 0.5 hours
Therefore,
distance = speed × time
distance covered by the cat = x × 0.5 = 0.5x
distance covered by the dog = 2x × 0.5 = x
Therefore, the distance they will be from each other after 30 minutes is as follows:
distance = x - 0.5x = 0.5x
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if 2.5kg of potatoes cost £1.40
work out the cost of 4.25kg of potatoes
Answer:2.5 kg of potatoes cost £1.40 Work out the cost of 4.25 kg of potatoes. 1.25kg=70p 2.5 kg=1.40 3.75 kg=2.10 Done.
Step-by-step explanation: hope this helps love!!
A linear function has a y-intercept of 3 and passes through the point (3, 7). Tom compared the slope of the function to the slope of 4x - y = 5. What is the difference in the two slopes?
Answer:
mom mom mom mom mom mom b mom
PLEASE HELP A.S.A.P.!
Solve the equation:
|x-1|+|x-2|=3
Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD
Using the hypergeometic distribution, it is found that there is a 0.0175 = 1.75% probability that all three have a PhD.
The applicants are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, the values of the parameters are as follows: N = 20, k = 6, n = 3.
The probability that all three have a PhD is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,20,3,6) = \frac{C_{6,3}C_{14,0}}{C_{20,3}} = 0.0175[/tex]
0.0175 = 1.75% probability that all three have a PhD.
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pls help!! and thank you
find the area of the circles
Answer:
10) 25π OR 78.5398...yd 11) 1/4π OR 0.785398...ft 12) 100π OR 314.159265....in
Step-by-step explanation:
area of a circle = πr^2 (π x radius squared)
the radius is just half the diameter
so for eg:
number 10)
diameter = 10 yd so radius = 5 yd
5 squared = 25
π x 25 yd = 25π OR 78.5398...yd
i hope this helped :)
Hyperbolas are confusingggg
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 60); y equals one over two hundred forty times x squared minus 60
(0, 60); y equals one over two hundred forty times x squared plus 60
(0, 15); y equals one over sixty times x square minus 15
(0, 15); y equals one over sixty times x squared plus 15
Answer:
I think the answer is A but im not sure
Find the volume of the cone. Round your answer to the nearest tenth.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Radius (r) = 2 cmheight (h) = 8 cmNow, let's apply the formula :
[tex]\qquad \sf \dashrightarrow \:v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]\qquad \sf \dashrightarrow \:v = \frac{1}{3} \times 3.14 \times {(2)}^{2} \times 8[/tex]
[tex]\qquad \sf \dashrightarrow \:v = \frac{100.48}{ 3} [/tex]
[tex]\qquad \sf \dashrightarrow \:v = 33.49333333.....[/tex]
[tex]\qquad \sf \dashrightarrow \:v \approx33.5 \: \: cm {}^{3} [/tex]
The vertices of a quadrilateral drawn in a coordinate plane are (-6,6), (4,6), (2,-5), and (-6,-9). what is the length of the side joining the vertex in quadrant i to the vertex in quadrant 11? a) 2 b) 8 c) 10 d) 12
Using the formula for the distance between two points, it is found that the length of the side joining the vertex in quadrant i to the vertex in quadrant ii is given by:
c) 10
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In quadrant I, both coordinates are positive, hence the vertex is (4,6). In quadrant II, x is negative while y is positive, hence the vertex is (-6,6). Thus, the distance is given by:
[tex]D = \sqrt{(-6 - 4)^2+(6 - 6)^2} = 10[/tex]
Which means that option C is correct.
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Please help! will give brainlest! locks in 30 min!
Answer:
[tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Simplify the expression:
sin [tex]\frac{3pi}{4}[/tex]
Rewrite the angle as a sum or difference with its reference angle:
sin (pi - [tex]\frac{pi}{4}[/tex])
Simplify the expression
(sin [tex]\frac{pi}{4}[/tex])
Evaluate the expression:
[tex]\frac{\sqrt{2} }{2}[/tex]
hope this helps and is right!! p.s. i really need brainliest :)
I went to the store with $20. After buying all my groceries, I spent $15.87. How much money do I have left?
you would have 4.13 left
20-15.87=4.13
Answer:
The answer is $4.13
Step-by-step explanation:
It is easier to do this if we add two zeros at the end of 20 to make it 20.00 so the decimal places line up. Lets take it one place at a time. first is the hundreths, which is 0-7. This is not possible, so we borrow from the tenths, but the tenths is also a zero. The tenths zero has to borrow from the ones zero. Basically, the 2 in 20 becomes 1, and the zeros in the ones and tenths place become nines, and the last zero becomes 10. 10 minus 7 is 3, 9 minus 8 is 1, 9-5 is 4, and 1-1 is 0.
Hope this helps!
X2-7x+6; x2-5x-6 please help
Answer: (x−6)(x−1)(x+1)
How much, in total, did Noel spend to cash her three most recent paychecks?
The total amount of money that was spent by Noel to cash her three (3) most recent paychecks is equal to $10.99.
What is a paycheck?A paycheck can be defined as a financial document that is issued by an employer to an employee as payment for the work done over a period of time.
How to calculate the amount spent.From the table, we can see that the amount of money charged by the bank as check processing fee is equal to $1.99, as well as 1.99% (0.0199) of the amount being cashed by a customer.
Thus, we would compute the amount of money spent by Noel as follows:
Noel = (0.0199 × 100.53) + (0.0199 × 119.38) + (0.0199 × 122.52) + (1.39 × 3)
Noel = 2.00 + 2.38 + 2.44 + 4.17
Noel = $10.99.
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For what value of x does 3^4x=27^x-3?
0 -9
O-3
O 3
O 9
Answer:
the answer to the value of X is 0-3
Use the graphing calculator to graph the quadratic function y = x2 − 5x − 36. Which value is a solution of 0 = x2 − 5x − 36?
−9
−4
4
6
Answer: -4
Step-by-step explanation:
Once you graph it, the solutions are where the graph meets the x axis.
This is at -4 and 9.
PLEASE HELP MEEEEE PLEASE ASAP
Consider the system and find the eigenvalues and the eigenvectors
Eigenvalues are the special set of scalar values which is associated with the set of linear equations in matrix equations.
What are Eigenvalues?
Your information is incomplete. Therefore, an overview will be given. An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in thesame direction or opposite direction to X.
Since the zero vector 0 has no direction, 0 is never allowed to be an eigenvector.
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An eigenvector of a linear transformation and eigenvectors of a system
Ax = Bx can be determined where B is an eigenvalue of A.
What are Eigenvalues?An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in the same direction or opposite direction to X.
The basic equation is
Ax = Bx
here B is an eigenvalue of A.
Since the zero vector has no direction, zero is never allowed to be an eigenvector.
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