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.
Learn more about quadratic equations;
https://brainly.com/question/2263981
Answer:
D on edge
Step-by-step explanation:
Some college friends have decided to go on a road trip over the summer with some friends. Finances are tight and they need to hire a car for the trip. There are two hire companies to choose from: Crazy Curly's charges a base fee of $20 and then 30 cents per mile. Bill's Beauties charges 20 cents per mile and a base fee of $50. - Write a system of equations that can be used to determine at what trip distance Bill's and Curly's rental cost would be the same. - At what trip distance would Bill's and Curly's rentals cost the same amount?
Answer:
300 milesStep-by-step explanation:
Let
y- the amount of charge, x - the number of milesThe equations as per question are below
Crazy Curly's
y = 0.3x + 20Bill's Beauties
y = 0.2x + 50Solve the system by substitution
0.3x + 20 = 0.2x + 500.3x - 0.2x = 50 - 200.1x = 30x = 30/0.1x = 300find the surface area of the triangular prism
Answer:
97.79ft
Step-by-step explanation:
Adding the area of every side together gets the surface area of the whole shape.
Evaluate the expression 10^x-3 for x = 2.
Answer:
1/10 or 0.1
Step-by-step explanation:
10^x-3
10^2-3
10^-1
1/10 or 0.1
Using technology, determine the semi-annual payment on a 3 year loan of $8,561 at 9. 1% compounded semi-annually. Round your answer to the nearest cent. A. $1,662. 47 c. $1,925. 92 b. $1,914. 11 d. $1,991. 12.
The semi-annual payment is $1662.47
What will be the semi annual payment?Given : A 3 year loan of $8,561 at 9.1% compounded semi-annually.
We have to determine the semi annual payment.
We know,
[tex]P=\dfrac{PV.r}{1-(1+r)^{-n}}[/tex]
Where PV is present value of loan.
r is rate of interest
n is time period.
Given loan is calculated semi annually,
So PV = $ 8561
r=9.1 % =9.1/200
and time period is 3 years = 6 number of period as semi annually.
Thus, Substitute,
We get,
[tex]P=\dfrac{8561(\dfrac{9.1}{200})}{1-(1+\dfrac{9.1}{200})^{-6}}[/tex]
[tex]P=1662.47[/tex]
Hence the semi-annual payment is $1662.47
To know more about Amount follow
https://brainly.com/question/25109150
i need help this is really hard i still dont understand plss help
Answer:
(b) 64 sq. in.
Step-by-step explanation:
The shaded area is the difference between the overall area and the areas of the cutout corners.
The overall area is 10 in by 10 in, so is ...
A = s² = (10 in)² = 100 in²
The area of the cutout at each of the four corners is ...
A = s² = (3 in)² = 9 in²
So, the total area of the four cutouts is ...
cutout area = 4 × 9 in² = 36 in²
The remaining area is then ...
100 in² -36 in² = 64 in²
Fine The Gradient of the curve xy=6, at point 1 & 6.
[tex] \\ \\ \\ \\ \\ \\ \\ [/tex]
Thnx ~~
Answer:
[tex]\fbox{Gradient of curve = -6}[/tex]
Step by step explanation:
Given:
Equation of curve ↦ xy = 6
Point ↦(1,6)
To find:
The gradient of curve = ?
Solution:
[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]
Taking log both the side,
[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]
Thanks for joining brainly community!
Multiply. What is the product (3 x 10^9) * (2 * 10^17) in scientific
notation?
?
(3 * 10^9) * (2 x 10^17 = ? * 10^?
DONE
Answer:
[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]
Step-by-step explanation:
[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]
A customer in Maine orders a Dog Treat Bundle for $34.80. The sales tax in Maine is 5.5%. How much sales tax is collected on the order?
Answer/Step-by-step explanation:
GIven;
A customer in Maine orders a Dog Treat Bundle for $34.80.
The sales tax in Maine is 5.5%.
To Find;
How much sales tax is collected on the order?
Solve;
$34.80 * 5.5% = 1.914
Round: 1.914 = 1.91 [Sales tax added]
$34.80 + 1.91 = 32.89 [Total]
Hence, $1.91 sales tax is added and $32.89 is the total (include sales tax)
~Learn with lenvy~
Rewrite 4.86 x 10^12 in decimal notation.
help pleaseee
Answer:
second one down
4 860 000 000 000
Step-by-step explanation:
count out 12 zeros after the 4 and you will find the one in decimal notation
The decimal notation for the given scientific notation is 4860000000000. (option b)
What is decimal notation?The decimal notation is an alternate method to represent the fractional value. It means that it is the fractional representation using base 10. The fractions can be converted into decimals and vice versa.
Given is a scientific notation, 4.86 × 10¹², we need to convert it into a decimal notation,
4.86 × 10¹²
= 4.86 × 10,000,000,000,000
= 4.86 × 100 × 100000000000
= 486 × 100000000000
= 48600000000000
Hence, the decimal notation for the given scientific notation is 4860000000000. (option b)
Learn more about decimal notation, click;
https://brainly.com/question/2273582
#SPJ2
The Bayview community pool has a snack stand where Juan works part time he tracks his total sales during each shift last month this box plot shows the results what fraction of Juan’s shifts had a total sales of $225 or more
first that answers correct gets brainliest and an extra 5 points
25/100
Step-by-step explanation:
if he has a fraction of a bar graph it is 25% if that grah so in other words 25% as a fraction is 25/100
my braincells are disappearing help me
Answer:
Last option
Step-by-step explanation:
In order to manipulate a, you have to divide by 3 on both sides.
ACTIVITY 1: LET'S PRACTICE!
Directions: Write Yes, if the two triangles are congruent and No if not. State the
postulate to justify your answer.
Pa help po please
Answer:
1. YES
1. YES2. YES
1. YES2. YES3.YES
4.NO
Hope it helps
Complete the table below. Show all your work.
NEED ANSWERS QUICKLY! CORRECT ANSWER GETS BRAINLIEST
Write a division problem such that the quotient is the same as 3/7 divided by 5/14
.
Answer:
6 6
---- ÷ ---
16 10
Step-by-step explanation:
equals 5/8
when filing taxes what do you need to know
Answer:
You must know all forms of additional payment and expenses, like medical bills and community expenses that can happen at any given time.
~Hope it helps~
~Be great~
The terminal side of angle λ intersects the unit circle at point (-0.358, 0.934). Based on these coordinates, what is the approximate decimal value of cot(λ)
Answer: -0.383
Step-by-step explanation:
Since this is on the unit circle, the cosine is equal to the x coordinate and the sine is equal to the y coordinate.
Since cot = 1/tan = cos/sin, the approximate value is (-0.358)/(0.934), which is about -0.383.
HELP PLEASE FOR NUMER 3 and 4 PLEAESE ASAP ANI WILL GIVE BRANILESS FOR THE FIRST PERSON
Step-by-step explanation:
what number you need help with
I need help with this
What is the length of the hypotenuse? 5 and 4in
Answer:
1 foot
Step-by-step explanation:
you multiply 5 1/4 inches by two, you would get 10 1/2 inches. if 2 inches equals 1 foot then 5 inches would equal 10 inches and 1/4 would equal 1/2. If you put those numbers together, you get 10 1/2 inches. Therefore the answer is 2 inches = 1 foot.
2. Write a recursive formula for the sequence 5, 18, 31, 44, 57, ... Then find the next term.
Answer: a6=70
Step-by-step explanation:
we know that
In the Arithmetic Sequence the formula is:
an= a1 + d(n−1)
where
a1 is the first term
d is the common difference
n is the number of terms
in this problem
a1=5
a2=18
a3=31
a4=44
a5=57
so
d=a2-a1 or a3-a2 or a4-a3 or a5-a4
d=57-44----> 13
find a6
a6= a1 + d(n−1)
n=6
d=13
a1=5
a6=5+13*(6-1)----> a6=5+13*5----> a6=70
Answer:
A1=5;an=an-1+13. The next term is 70What is 10.66 to the nearest 10th of an inch?
Answer:
10.7
Step-by-step explanation:
the tenth place is the first number that comes after the decimal so, that is the number you are rounding. We take a look following that number and it it is equal to or greater than 5, (which it is), we round up one number.
Answer:
10.7
Step-by-step explanation:
Any number between 1-4 rounds down and 5-9 rounds up, so here you will round up. I've included the decimal places as well below. The number after the decimal point is the tenth's place.
Good luck! Hope this helps
1:30 hours + 40 min + 40 min + 2:05 hours
How many hours will this be?
Answer:
4:55 hrs :)
Step-by-step explanation:
1:30 hours + 40 min + 40 min + 2:05
1:30 hrs + 1:20 hrs + 2:05 hrs
2:50 hrs + 2:05 hrs
4:55 hrs
Have an amazing day!!
Please rate and mark brainliest!!!
you flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble . what is the probability you flip a heads on the coin and draw a purple marble
Answer:
1/3 probability
Step-by-step explanation:
The probability that you flip heads is 1/2, one heads out of two possible (heads and tails).
The probability that you draw a purple marble is 2/3, two purples and three total (2 p +1 w).
To find the probability of both happening, multiply the probabilities together:
(1/2) * (2/3) = (2/6) = (1/3)
PLEASE ANSWER I DONT KNOW THE ANSWER
Answer:
D. 201.1
Step-by-step explanation:
We see that the radius o the given circle is 16, so we do 16^2*pi
then we multiply that be 90/360
which rounds to 201.1
in the expansion of ( x^3 - 2/x^2 ) ^10 , find the coefficient of 1/x^5
Answer:
240
Step-by-step explanation:
We need to find the coeffeicent of the binomial expansion of
[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} [/tex]
Note that
[tex] - 2 {x}^{ - 2} = - \frac{2}{ {x}^{2} } [/tex]
The binomial theorem states that
[tex](x + y) {}^{n} = x {}^{n} y {}^{0} + \binom{n}{1} x {}^{n - 1} y + \binom{n}{2} x {}^{n - 2} y {}^{2} ....... + x {}^{0} y {}^{n} ( \binom{n}{n} )[/tex]
Using this, we let expand our series
[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} = x {}^{30} + \binom{10}{1} ( {x}^{27} 2 {x}^{ - 2} ) + \binom{10}{2} {x}^{24} 2x {}^{ - 4} + \binom{10}{3} {x}^{21} 2x {}^{ - 6} + \binom{10}{4} {x}^{18} 2x { }^{ - 8} + \binom{10}{5} x {}^{15} 2x {}^{ - 10} + \binom{10}{6} x {}^{12}2 x {}^{ - 12} + \binom{10}{7} x {}^{ 9} 2x {}^{ - 14} + \binom{10}{8} x {}^{ 6} 2x {}^{ - 16} + \binom{10}{9} ( {x}^{3} )2x {}^{ - 18} + 2x {}^{ - 20} [/tex]
[tex] \frac{1}{ {x}^{5} } = x {}^{ - 5} [/tex]
So what term in the series eqaul x^-5.
That term is the 10 choose 7 term.
[tex] \binom{10}{7} {x}^{9} 2x {}^{ - 14} [/tex]
Because
[tex] = \binom{10}{7} 2x {}^{ - 14} {x}^{9} = \binom{10}{7} 2 {x}^{ - 5} [/tex]
So we need to compute 10 choose 7.
That equals
10!/3!(7!)= 10×9×8/6= 720/6=120.
So we get
[tex]120(2) {x}^{ - 5} [/tex]
[tex]240 {x}^{ - 5} [/tex]
So the coeffceint u
is 240
Please help with angle addition
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for it.
A sphere has a diameter of 3.8 centimeters.
The volume of the sphere is about
cm3
HELP ME PLSS I WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
Givens
pi = 3.14
d = 3.8
r = d/2
r = 3.8/2 = 1.9
Formula
V = (4/3) * pi * r^3
Solution
V = (4/3) * 3.14 * 1.9^3
V = 4/3 * 3.14 * 6.859
V = 28.7163
Beverly's average mark for nine examination papers was 89.5. How many marks did she score altogether?
Answer:
805.5 out of 900
Step-by-step explanation:
A test is out of 100 and because there are 9 tests: 9 x 100 which equals 900.
To get the average we add up each test mark and divide by the number of tests. The same can be applied here but reversed. So because there were 9 tests we can multiply 89.5 by 9 which gives us 805.5. Beverly scored 805.5 marks out of 900 which makes her average 89.5% for 9 tests.
Brainliest if correct
Determine which of the following is true for expression x^3+x^2-2x
A. The equation is prime
B. x can be factored from each term of the trinomial to obtain x(x^2+x-2),which is completely factored.
C. x can be factored from each term of the trinomial to obtain x(x^2+x-1), and the resulting trinomial can be factored to obtain x(x+2)(x+1), which is completely factored
D. The trinomial is equivalent to (x+2)(x-1)
Answer:
D. The trinomial is equivalent to (x+2)(x-1)
Step-by-step explanation:
1. Factor out the common term x:
= x(x^2+x-2)
2. Factor the equation:
= x(x - 1)(x + 2)
From this, we can see that because the equation was factorable, it is not prime. Option B is not completely factored, so it is incorrect. The final ordered pair shown in Option C is has (x + 1), when it should be (x - 1), so it is also incorrect. Option D is the true statement.