The roots of the Given quadratic equation are x₁ = -2 and x₂ = -12.
What is a Quadratic equation?ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given a quadratic equation, x² + 24 = 14 x
Simplifying the equation using the factorization method,
=> x² + 24 = 14 x
=> x² +14 x +24 = 0
factorize the "x term"
=> x² +12x + 2x +24 = 0
=> x(x +12)+2(x + 12) = 0
=>(x + 2)(x + 12) = 0
x = -2, -12
thus,
the value of x will be either -12 or -2
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how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9
2x+1=3(x+1)-x-2 solve for x
Suppose a shipment of 140 electronic components contains 3 defective components. to determine whether the shipment should be accepted, a quality-control engineer randomly selects 3 of the components and tests them. if 1 or more of the components is defective, the shipment is rejected. what is the probability that the shipment is rejected?
To find the probability that a shipment of 140 electronic components, with 3 defects, is rejected upon testing 3 components, calculate the complement (all non-defective) and subtract from 1.
Explanation:The question involves determining the probability that a shipment containing 140 electronic components, with 3 being defective, is rejected based on a quality-control test of 3 components. To solve, consider the complementary probability - the chance all selected components are non-defective. First, calculate the probability of picking 3 non-defective components: (137/140) * (136/139) * (135/138). Then, subtract this probability from 1 to find the probability of the shipment being rejected.
1 - [(137/140) * (136/139) * (135/138)] equals the probability the shipment is rejected. After performing the calculations, you find that the shipment's rejection probability is determined by the presence of at least one defective component in the tested sample.
PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK
1)Jerome noticed the following house numbers on his street:
305, 318, 331, 344
The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?
A) 292 +13n
B) 292n
C) 292n + 13
D) 13(n + 292)
2) A polynomial expression is shown below.
(mx+8)(2x−4)
The expression is simplified to:
−6x2+28x−32-6x2+28x-32
What is the value of m?
A) 3
B) 4
C) -3
D) -4
3) What is the domain of the function shown below? (PICTURE AT BOTTOM)
A) 2
B) −8 ≤ x <3and 4 ≤ x <8
C) −8 ≤ x < 8
D) −7 ≤ x ≤ 7
Answer:
Jerome noticed the following house numbers on his street:
Answer 292 +13n
A polynomial expression is shown below. What is the value of m?
Answer -3
What is the domain of the function shown below
Answer −8 ≤ x <3and 4 ≤ x <8
Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx
The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
Given an integral expression:
[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
This can be written as:
[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
It is required to find the integral value.
Let u = 5 + (ln (x))²
Differentiate.
[tex]du=2ln(x)*\frac{1}{x} dx[/tex]
Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]
Substitute the values.
[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]
[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]
[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]
Substitute back the value of u.
[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]
Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
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Determing wheter two ratios form a proportion
A basketball player gets 2 free-throw shots when she is fouled by a player on the opposing team. She misses the first shot 40% of the time. When she misses the first shot, she misses the second shot 5% of the time. What is the probability of missing both free-throw shots?
the sum of two numbera is 122. the second number is 18 less than three times the first number. find the numbers. help please!
Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?
The probability that the number selected is the square of a natural number will be 0.20.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Robin randomly selects a number between 1 and 20.
Then the total number of the events will be
Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
The probability that the number selected is the square of a natural number will be
We know that natural numbers 1, 2, 3, 4, 5, and so on.
Then the square of the natural numbers will be
1, 4, 9, 16, 25, ....
Favorable event = 3 {1, 4, 9, 16}
Then the probability will be
P = 4 / 20
P = 1/5
P = 0.20
The probability that the number selected is the square of a natural number will be 0.20.
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what is the answer please
Q.8 What is the tail length?
The tail length of an alligator with a body length of 3.6 feet is approximately 3.2 feet.
The problem states that the alligator's tail length, [tex]\(T\)[/tex], varies directly with its body length, [tex]\(B\)[/tex]. When two quantities vary directly, we can express this relationship using a proportionality constant, often denoted as [tex]\(k\)[/tex]. In this case, we have:
[tex]\(\frac{T_1}{B_1} = \frac{T_2}{B_2}\),[/tex]
where [tex]\(T_1\) and \(B_1\)[/tex] are the initial tail length and body length, and [tex]\(T_2\) and \(B_2\)[/tex] are the final tail length and body length.
Given that an alligator with a body length of 5.4 feet has a tail length of 4.8 feet, we can use this information to find [tex]\(k\):[/tex]
[tex]\(\frac{4.8}{5.4} = \frac{T_2}{3.6}\).[/tex]
Now, solve for [tex]\(T_2\):[/tex]
[tex]\(T_2 = \frac{4.8}{5.4} \times 3.6\).[/tex]
[tex]\(T_2 \approx 3.2\) feet.[/tex]
So, the tail length of an alligator with a body length of 3.6 feet is approximately 3.2 feet.
The tail length is 3.2 feet. This result confirms the direct variation between tail length and body length, where [tex]\(T\)[/tex] is proportional to [tex]\(B\)[/tex] with a proportionality constant of approximately 0.8889 (4.8/5.4).
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PLZZZZZZ HELPPPP
Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5 Enter your answers in the boxes.
The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.
The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.
On solving the equations by substitution method we get x=14 and y=-3
Calculation:Given equations:
[tex]\rm 2x+8y = 4[/tex] (1)
[tex]\rm x=-3y+5[/tex] (2)
On substituting [tex]x=-3y+5[/tex] in equation 1:
[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]
Substituting [tex]\rm y=-3[/tex] in equation 2:
[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]
Therefore the values of x and y for the given equations is 14 and -3 respectively.
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What the complement of 54.6 degree
For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?
Complete the square to form a perfect square trinomial x^2-14x+
Shondra found large candles on sale at her favorite store. She has a large family and many friends, so she bought as many of the candles she could fit in her trunk to give as gifts. Her trunk is 2 feet deep, 4 feet wide, and 3 feet long. If each candle comes in a cube box with 1 foot edges, how many candles will fit in her trunk?
I WILL GIVE U BRAINLY!!!
Which substance has been changed most over time from its original plant material?
A.
peat
B.
anthracite coal
C.
bituminous coal
D.
lignite
A 2 liter drink costs $0.10 per deciliter. How much does the drink cost?
The price of drink is given as 0.10 dollars per deciliter.
It says to find the cost of 2 liters of drink.
We need to convert the units from liters to deciliters.
We know 1 liter = 10 deciliters.
then 2 liters = 20 deciliters.
So we need to find the cost of 20 deciliters of drink at rate of 0.10 dollars per deciliter.
1 deciliter of drink cost = 0.10 dollars.
20 deciliter of drink would cost = 20 x 0.10 dollars = 2.00 dollars.
Hence, 2 liters of drink would cost 2 dollars.
Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x
Shryia read a 480 page long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 pages left to read. Let P(t) denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula.
The correct answer is P(t)=-52t+480. Hope this helped.
The function representing the number of pages Shryia has left to read at a given time is P(t) = 480 - 52t, considering she reads at a constant rate of 52 pages per hour.
Explanation:Shryia read a 480-page book in one session at a constant rate. Since P(t) represents the number of pages she has left to read at time t, after 1.5 hours, she had 402 pages left. To find the rate at which she reads, we can see that in 1.5 hours, she read 480 - 402 = 78 pages. Thus, her reading rate is 78 pages per 1.5 hours, or 52 pages per hour.
At time t=0, the book is completely unread, meaning P(0) = 480 pages. Her reading rate is constant, so the function is linear: for every hour that passes, 52 more pages are read. Therefore, the number of pages left, P(t), decreases by 52 for each hour. The function P(t) can then be defined as:
P(t) = 480 - 52t
whats the distance between (-8,-7) (8,-4)
You were just approved for a $32,000 car loan at an APR of 1.99% for 60 months. As you make payments over time: your payment is , the amount of interest you will pay each month , and the amount of principal you pay each month .
What it Means...
If you borrow $32,000 at 1.99% for 5 years, your monthly payment will be $560.75.
The payments do not change over time. The loan amortizes over the repayment period, meaning the proportion of interest paid vs. principal repaid changes each month. As the loan amortizes, the amount of monthly interest paid decreases while the amount of principal paid increases.
Loan Amount: $32,000Cheryl paid $3 for each pin in her collection. She bought 32 pins in March and 56 pins in April.
How much did Cheryl spend on pins in April?
A.
What is the total amount of money Cheryl spent buying pins?
B.
How many pins did Cheryl add to her collection in March and April?
C.
What is the total cost of the pins that Cheryl bought in April?
D.
What is the difference between the number of pins bought in March and April?
2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8
find the ordered triple
What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?
A. 157.95 cubic units
B. 351.351 cubic units
C. 124.605 cubic units
D. 113.49 cubic units
Final answer:
The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.
Explanation:
To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.
By plugging in the values provided:
a = 3.9 units
b = 5.7 units
c = 3 units
We get:
V = 3.9 units × 5.7 units × 3 units
Doing the multiplication:
V = 66.87 cubic units
Therefore, the volume of the figure is 66.87 cubic units.
Please Help!!
In 1802. Albert Mathieu Favier imagined building a tunnel for horse drawn carriages underneath the English Channel. If the tunnel was 32 miles long and the carriage traveled 12 miles per hour, how long would it take to travel the length of the tunnel?
A. 2 hours and 40 minutes
B. 2 hours and 10 minutes
C. 3 hours and 10 minutes
D. 3 hours and 7 minutes
The hypotenuse of a right triangle is 8 centimeters long. One of the legs of the triangle is 7 centimeters. What is the length of the triangle's other leg?
Answer:
3.87 centimeters
Step-by-step explanation:
sorry its took 3 years lol :)
Answer:
3.87 centimeters
Step-by-step explanation:
Got it right on Imagine math.
5 quarts =how many fluid ounces
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 55 adult smartphone users are randomly selected, find the probability that at least 22 of them use their smartphones in meetings or classes.