Answer:
[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]
Step-by-step explanation:
The quadratic equation is given to be : 8x² - 2x = 1
We need to find the product of its zeros
First finding the number of zeros :
⇒ 8x² - 2x - 1 = 0
⇒ 8x² - 4x + 2x - 1 = 0
⇒ (4x + 1)(2x - 1) = 0
[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]
[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]
Why does a bag of chips puff up in an airplane?
Find the area of a square with apothem 9 in. Round to the nearest whole number.
281 in2
305 in2
458 in2
324 in2
Answer:
The area of the square is 324 square inches.
Step-by-step explanation:
The apothem of the square is 9 inches.
The side of the square is twice the length of the apothem.
Hence, the side of the square is given by
[tex]a=2\times 9=18\text{ in}[/tex]
The area of a square is the given by
[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]
Therefore, the area of the square is 324 square inches.
In how many different ways can a president vice-president and secretary be elected from a class of 15 students
Accuracy is a measure of how close an answer is to the actual or expected value
Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)
From a group of six people, two individuals are to be selected at random. how many possible selections are there
Final answer:
To find the number of possible selections when choosing two individuals from a group of six people at random, use the combinations formula C(6, 2) = 6! / (2!(6-2)!) which equals 15 possible selections.
Explanation:
From a group of six people, selecting two individuals at random involves calculating the number of combinations. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where 'n' represents the total number of items and 'k' represents the number of items to choose.
In this scenario, with n being 6 (the total number of people) and k being 2 (the number of people to select), the calculation would be:
C(6, 2) = 6! / (2!(6-2)!) = (6 * 5) / (2 * 1) = 15
Therefore, there are 15 possible selections when choosing two individuals from a group of six people at random.
what is (13x+9k)+(17x+6k) simplified
The expression (13x+9k)+(17x+6k) simplifies to 30x + 15k. This is done by adding the coefficients of the like terms which in this case are 13x with 17x, and 9k with 6k.
Explanation:The expression (13x+9k)+(17x+6k) is a mathematical expression in algebra with two variables, x and k. The goal here is to simplify the expression by combining like terms. In mathematics, 'like terms' refer to the terms that have the same variables and powers. The coefficients of the like terms can be different.
Now to simplify this expression, we add the coefficients of the like terms. The like terms here are 13x and 17x, and also 9k and 6k.
Add 13x and 17x, you get 30x. And when you add 9k and 6k, you get 15k.
So, the simplified version of the given expression (13x+9k)+(17x+6k) is 30x + 15k.
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The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.
What is the value of x?
What is the value of y?
Answer:
[tex]\text{The value of x and y is } x=5, y=29[/tex]
Step-by-step explanation:
Given the product of two expressions
[tex]4z^2+7z-8\text{ and }-z+3\text{ is }-4z^3+xz^2+yz-24[/tex]
we have to find the value of x and y
First we find the product of
[tex]4z^2+7z-8\text{ and }-z+3[/tex]
[tex](4z^2+7z-8)(-z+3)[/tex]
Opening the brackets
[tex]4z^2(-z+3)+7z(-z+3)-8(-z+3)[/tex]
Using distributive property, a.(b+c)=a.b+a.c
[tex](-4z^3+12z^2)+(-7z^2+21z)+(8z-24)[/tex]
Combining like terms
[tex]-4z^3+(12z^2-7z^2)+(21z+8z)-24[/tex]
[tex]-4z^3+5z^2+29z-24[/tex]
which is required product.
[tex]\text{Now compare above product with given product }-4z^3+xz^2+yz-24[/tex]
[tex]x=5, y=29[/tex]
A liquid substance was left at the scene of the crime. Krisann uses a beaker that measures to the nearest tenth of a liter and finds that it is 4.9 liters. If there are five or more liters of the substance, it needs to be sent to the lab for testing. If it is less than five liters, the test can be done immediately. Does Krisann need to send the substance to the lab? Why or why not?
If the volume of the substance of 4.9 liters is from x rounded to the nearest tenth of a liter, that means 4.85 <= x < 4.95 then this does NOT leads to x > 5. Therefore the substance does not need to be sent to the lab.
A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.
URGENT!!!!!!!!!!11!! Plz HElP
A school typically sells 500 yearbooks each year for $50 each. the economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.the revenue for the yearbook sales is equal to the number of yaerbooks sold times the price of the yearbook. let x represent the number of $5 decreases in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). find the values of a and b.
An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. what is a side length of the original paper if the box has a volume of 675 cubic inches?
a culture started with 5000 bacteria. after 2 hours, it grew to 6500 bacteria. Predict how many bacteria will be present after 18 hrs
If BE−→ B E → bisects ∠ABD and m∠ABE = 62°, find m∠ABD
Based on the definition of an angle bisector, m∠ABD = 124°.
What is Angle Bisector?An angle bisector is a line segment that divides an angle into two smaller angles that are congruent.
BE is an angle bisector, therefore:
m∠ABD = 2(m∠ABE)
m∠ABD = 2(62)
m∠ABD = 124°
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Factoring help. Need step by step guidance ....
35n ^ 2 + 22n + 3
If you guess an answer on two multiple choice questions with the options a, b, or c, what is the probability of you guessing the answer to both questions correctly?
What is the logarithmic function modeled by the following table
x
8
16
32
f(x)
3
4
5
A. F(x)= log_x2
B. F(x)= log_2 x
C. F(x)= 2 log_10 x
D. F(x)= x log_10 2
Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.
What are Logarithms?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.
For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8. In the same way, 2 = log10 100 since 102 = 100. The latter type of logarithms, those with base 10, are known as common or Briggsian logarithms and are denoted by the letter log n.
Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits.
Therefore, Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.
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What are the vertical asymptotes of the function f(x) = the quantity of 2 x plus 8, all over x squared plus 5 x plus 6? x = −3 and x = −2 x = −3 and x = 2 x = 1 and x = −2 x = 1 and x = 2?
One number is 6 less than another. their sum is 12 find the larger number
y=x-6
x+y=12
x+x-6 =12
2x-6=12
2x=18
x=18/2 =9
x=9
y =9-6 =3
9+3 =12
Larger number is 9
Find the exact value of the following limit: the limit as x goes to 0 of the quotient of the quantity e raised to the 3 times x power minus 3 times x minus 1 and x squared.
Type answer as a decimal.
The value of the limit is 4.5 .
What is limit?An output value that a function approaches for the specified input values is referred to as a limit.
Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.
The given limit is,
F(x) = [tex]lim_{x- > 0} (e^{3x}-3x-1)/x^2[/tex]
Differentiate with respect to x,
F'(x) = [tex]lim_{x- > 0} d/{dx}(e^{3x}-3x-1)/x^2[/tex]
= [tex]lim_{x- > 0} d/{dx}(e^{3x}-3x-1)/d/dx(x^2)[/tex]
= [tex]lim_{x- > 0}\ 3e^{3x}-3/2x[/tex]
Differentiate again with respect to x,
F''(x) = [tex]lim_{x- > 0}\ d/dx(3e^{3x}-3/2x)[/tex]
= [tex]lim_{x- > 0} (9e^{3x)}/2}[/tex]
= [tex]9 .e^0/2[/tex]
= [tex]9/2[/tex]
= [tex]4.5[/tex]
The limit of the function is 4.5 .
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Evaluate S5 for 600 + 300 + 150 + … and select the correct answer below
Answer:
Hence,
[tex]S_5=1162.5[/tex]
Step-by-step explanation:
We are asked to evaluate:
[tex]S_5[/tex]
We are given a geometric series.
( since each term of the series are in geometric progression as each term is half of the previous term of the series.
i.e. we have a common ratio of 1/2 )
Also, we know that sum of n terms in geometric progression is given by:
[tex]S_n=a(\dfrac{1-r^n}{1-r})[/tex]
where r is the common ratio.
a is the first term of the series.
Here we have:
[tex]a=600\ ,\ r=\dfrac{1}{2}[/tex]
Hence,
[tex]S_5=600(\dfrac{1-(\dfrac{1}{2})^5}{1-\dfrac{1}{2}})\\\\\\S_5=600(\dfrac{2^5-1}{2^4}})\\\\\\S_5=600(\dfrac{31}{16})\\\\\\S_5=1162.5[/tex]
The sum of the first five terms of the geometric progression 600 + 300 + 150 + … is 1162.5.
What is the ratio of geometric progression?A geometric progression is the series of numbers where the ratio of the two consecutive numbers is always the same.
As it is given to us the sequence 600, 300, 150 is a geometric progression. Therefore, the first term of the progression is 600, while the ratio between the two terms are,
[tex]r = \dfrac{300}{600} = \dfrac{1}{2}[/tex]
Now, we know that the sum of the geometric sequence of the first 5 terms can be written as where the value of the n is 5,
[tex]S=a\dfrac{(1-r^n)}{(1-r)}[/tex]
[tex]S=600\dfrac{(1-(\dfrac{1}{2})^n)}{(1-(\dfrac{1}{2}))}[/tex]
[tex]S = 1162.5[/tex]
Hence, the sum of the first five terms of the geometric progression 600 + 300 + 150 + … is 1162.5.
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house blend coffee is 50% columbian beans and special blend coffee is 80% columbian beans. how much of each should be used to produce 100kg of a blend that is 68% columbian beans
Let us say that,
x = mass of 50% Columbian beans required
y = mass of 80% Columbian beans required
To solve this problem, we set up two mass balance equations:
Overall mass balance: 100 = x + y
x = 100 – y ---> 1
Coffee mass balance: 0.68 (100) = 0.50 x + 0.80 y
68 = 0.50 x + 0.80 y ---> 2
Combining equations 1 and 2:
68 = 0.50 (100 – y) + 0.80 y
68 = 50 – 0.50 y + 0.80 y
18 = 0.30 y
y = 60 kg
Calculating for x using equation 1:
x = 100 – y
x = 100 – 60
x = 40 kg
Answer:
40 kg of 50% Columbian beans required
60 kg of 80% Columbian beans required
Flying against the wind, a jet travels 4400mi in 8 hours. Flying with the wind, the same jet travels 5820mi in 6 hours. What is the rate of the jet in still air and what is the rate of the wind?
How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?
What are the domain, range, and asymptote of h(x) = (1.4)x + 5?
Line LJ is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain.
Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?
5⁄6 · n = 10 (solve for n)
What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?
Answer: [tex]\ a_{n}=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Given: A geometric sequence with its first term [tex]a_1=a=3[/tex]
and second term [tex]a_2=-9[/tex]
We know that the common ratio in of a geometric sequence=[tex]\frac{a_{n}}{a_{n-1}}[/tex]
Thus, common ratio [tex]r=\frac{-9}{3}=-3[/tex]
We know that the explicit rule for geometric sequence is written as
[tex]a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }][/tex]
Thus, the explicit rule for the given geometric sequence is [tex]\ a_{n}=3(-3)^{n-1}[/tex] for every n ,a natural number.
The stack on the left is made up of 15 pennies, and the stack on the right is also made up of 15 pennies. If the volume of the stack of pennies on the left is 360 mm3, what is the volume of the stack of pennies on the right in cubic millimeters? Use 3.14 for pi. (Hint: only enter numerals in the answer blank)
Answer:
360 is the answer. Just type in 360 in the answer blank.
Step-by-step explanation: