Factor 16x 2 + 16x + 4 completely.
a.(16x + 4)(x + 1)
b.(4x + 2)(4x - 2)
c.4(2x + 1)2
A. 15
B. 125
C. 135
D. 45
(25 points) A weather reporter in your area said that the speed of sound in air today is about one thousand one hundred feet per second. What is that speed in scientific notation?
Answer:
1.1 × 103 feet per second
What is the solution to 7(a-1)=7
Which statement is 1?
option 5 btw is none of these
The statement “Angles that measure more than 90 degrees are obtuse angles” has a counterexample
Which is the graph of f(x)=2(3)^x
Answer-
The first graph represents [tex]f(x)=2(3)^x[/tex]
Solution-
The given function is,
[tex]f(x)=2(3)^x[/tex]
Putting x = 1,
[tex]f(x)=2(3)^1=2(3)=6[/tex]
So, the point (x, f(x)) i.e (1, 6) must satisfy or lie on the curve of the function.
Only in case of the first graph, the point (1, 6) lies on the curve.
Therefore, the first graph represents the function [tex]f(x)=2(3)^x[/tex] correctly.
Answer: the first answer is correct
OQ is a diagonal of quadrilateral NOPQ. If NO=PQ, NQO=7y-37, and POQ=2y+93, find POQ such that NOPQ is a parallelogram. A.26° B.63° C.97° D.145°
What are the solutions of 4x4 – 4x2 = 8?
Final answer:
To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation and solve the resulting quadratic equation. The solutions are x = ±√2.
Explanation:
To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation to get 4x^4 - 4x^2 - 8 = 0. This is a quadratic equation in terms of x^2. We can solve this quadratic equation by factoring or by using the quadratic formula.
Factoring the equation, we get (2x^2 - 4)(2x^2 + 2) = 0. Setting each factor equal to zero, we have 2x^2 - 4 = 0 and 2x^2 + 2 = 0.
Solving each equation separately, we get x^2 = 2 and x^2 = -1. Taking the square root of both sides, we get x = ±√2 and x = ±i. Therefore, the solutions of the original equation are x = ±√2.
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
(I know it's 119.954 years, but I have no idea how to get that)
Answer:
It take 119.954 years to earn $ 3000 without depositing any additional funds.
Step-by-step explanation:
Given:
Principal Amount, P = $ 150
Amount, A = $ 3000
Rate of interest, R = 2.5% compounded monthly.
To find: Time, T
We use formula of Compound interest formula,
[tex]A=P(1+\frac{R}{100})^n[/tex]
Where, n is no time interest applied.
Since, It is compounded monthly.
R = 2.5/12 %
n = 12T
[tex]3000=150(1+\frac{\frac{2.5}{12}}{100})^{12T}[/tex]
[tex]\frac{3000}{150}=(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]20=(1+\frac{2.5}{1200})^{12T}[/tex]
Taking log on both sides, we get
[tex]log\,20=log\,(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]1.30103=12T\times\,log\,(1.002083)[/tex]
[tex]T=\frac{1.30103}{12\times\,log\,(1.002083)}[/tex]
[tex]T=119.954[/tex]
Therefore, It take 119.954 years to earn $ 3000 without depositing any additional funds
What is the value of S4 for
A. 5 5/64
B. 5 1/4
C. 5 5/16
D. 5 5/6
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
[tex]S_n=\sum^{\infty}_{n=1}4(\dfrac{1}{4})^{n-1}[/tex]
We need to find the value of S₄.
So, it means sum of 4 terms.
Here it form a geometric series:
a = 4 = first term
r = [tex]\dfrac{1}{4}[/tex] = Common ratio
And sum of n terms whose ratio is less than 1 is given by
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_4=\dfrac{4(1-\dfrac{1}{4}^{4})}{1-\dfrac{1}{4}}\\\\S_4=\dfrac{4(1-0.25^4)}{1-0.25}\\\\S_4=\dfrac{4(1-0.0039)}{0.75}\\\\S_4=5.3125\\\\S_4=5\dfrac{5}{16}[/tex]
Hence, Option 'C' is correct.
Answer: Option 'C' is correct.
Step-by-step explanation:
25. Which is an example of an operation?
A) 12
B) 6ab
C) +
D) y
The range of a relation is
A: the output (y) values of a relation
B: the input (x) values of the relation
C: a set of points that pair input values with output values
D: x and y values written in the form (x,y)
Compare the functions shown below: f(x) = 4 sin (2x − π) − 1 g(x) is points and those points are (−1, 6) (0, 1) (1, −2) (2,−3) (3, −2) (4, 1) (5, 6) h(x) = (x − 2)2 + 4 Which function has the smallest minimum y-value?
Is it possible for a segment to have more than one bisector? Explain your reasoning.
Final answer:
Yes, a segment can have more than one bisector. A bisector divides a segment into two equal parts.
Explanation:
Yes, a segment can have more than one bisector. A bisector of a segment is a line, segment, ray, or plane that divides the segment into two equal parts. Each bisector intersects the segment at its midpoint. Since the definition of a bisector doesn't specify uniqueness, there can be infinitely many bisectors of a given segment, especially in a two-dimensional plane.
For example, if you have a horizontal line segment, you could have one vertical bisector that divides it in the middle, but you could also have an infinite number of bisectors at various angles that also pass through the midpoint. Thus, there are multiple bisectors for any given line segment. Thus, consider two points A and B on a straight line segment AB. According to geometric principles, you can draw a perpendicular bisector that would be unique in the sense that it's the only line that both bisects AB and is perpendicular to it
Which of the following functions illustrates a change in amplitude?
A. y = 3cos4x
B. y = 1+sinx
C. y = -2-cos(x - pi)
D. y = tan2x
Answer:
Correct option is A.
Step-by-step explanation:
Given the following functions we have to choose the option which illustrates a change in amplitude.
Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.
Option A: y = 3cos4x
The parent function is f(x) = cos x.
The amplitude of function changes from 1 to 3.
Option B: y = 1+sinx
The parent function is f(x) = sin x
The amplitude remains same i.e 1
Option C: y = -2-cos(x - pi)
Here also remains same.
Option D: y = tan 2x
The tangent function does not have an amplitude because it has no maximum or minimum value.
Hence, correct option is A.
Answer:
y= 3cos4x
Step-by-step explanation:
use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2=17
The solution of the given quadratic equation is x = 1.37, - 1.37.
What is a quadratic equation?"A quadratic equation is an algebraic equation of the second degree in any variable."
Given quadratic equation:
9x² = 17
⇒ x² = (17 / 9)
⇒ x = ± √(17 / 9)
⇒ x = ± (√17) / 3
⇒ x = 1.37, - 1.37
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The integral represents the volume of a solid. describe the solid. π π 0 sin(x) dx
The sum of two numbers is 49 . the smaller number is 17 less than the larger number. what are the numbers?
Final answer:
To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.
Explanation:
The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.
Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:
x + (x - 17) = 49
Combine like terms: 2x - 17 = 49
Add 17 to both sides: 2x = 66
Divide by 2: x = 33
Since the larger number is 33, the smaller number is 33 - 17, which is 16.
Therefore, the two numbers are 33 and 16.
Helen uses 3/4 cup of oil and 1/3 cup of vinegar to make salad dressing. Which is closest to how many times 3/4 is as great as 1/3?
3
2
3/2
1/2
PLEASE ONLY ANSWER IF YOU KNOW FOR SURE!! :)
A ladder is leaning against a wall. The top of the ladder is 9 feet above the ground. If the bottom of the ladder is moved 3 feet farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?
What is the simplified form of the following expression? 5√8-√18-2√2
A. 2√2
B. 5√2
C. 9√2
D. 15√2
Answer:
Option (B) is correct.
To prove
As given the epression in the question is given by
[tex]= 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex]
Now simplify the above
Terms are written as
[tex]\sqrt{8} = \sqrt{2\times 2\times 2} = 2 \sqrt{2}[/tex]
[tex]\sqrt{18} = \sqrt{3\times 3\times 2} = 3 \sqrt{2}[/tex]
Put in the above expression.
[tex]= 5\times 2 \sqrt{2} -3 \sqrt{2} - 2 \sqrt{2}[/tex]
[tex]= 10 \sqrt{2} -5 \sqrt{2}[/tex]
[tex]=5 \sqrt{2}[/tex]
[tex]Therefore\ the\ expression\ 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\ is\ equivalent\ to\ 5 \sqrt{2} .[/tex]
There are 21 different coffee flavours at the cafe. oddly, each student in my 8 am class has a favourite flavour there. there are just enough students in the class so you can be absolutely sure that 7 students all have the same favourite. how many students are there in the class?
The following table shows the number of hours some students in two universities spend reading each week: School A 7 2 3 10 17 14 10 22 2 School B 9 10 16 18 20 15 17 18 14 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points) Part B: Are the box plots symmetric? Justify your answer. (4 points)
Answer:
that persons work is correct im pretty sure
Step-by-step explanation:
Write the standard form of the line that contains a y-intercept of -3 and passes through the point (3, 0). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
The equation of the line in standard form that has a y-intercept of -3 and passes through the point (3, 0) is y = x - 3.
Explanation:The standard form of a line can be found using the formula y = mx +b, where 'm' is the slope and 'b' is the y-intercept. The y-intercept in this problem is -3, but we need to find the slope to complete the standard form of the line. Since our line passes through the point (3,0) and (0,-3), the slope, m, can be found by using the formula (y2-y1)/(x2-x1), which gives us a slope of 1. So the equation of our line in standard form is y = x - 3.
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How many equations are needed to solve for 1 unknown variable?
what does x equal 3.2x = 64
divide 64 by 3.2 to get x
64/3.2 = 20
x = 20
Amersham station is the highest station in the London Tube at 147 meter above sea level. Waterloo station is the lowest station at 21 meters below sea level. What is the height difference?
Final answer:
The height difference between Amersham station (147 meters above sea level) and Waterloo station (21 meters below sea level) is 168 meters.
Explanation:
To find the height difference between Amersham station, which is the highest station in the London Tube at 147 meters above sea level, and Waterloo station, the lowest at 21 meters below sea level, we simply add the two values together, treating the below sea level as a negative altitude.
147 meters (Amersham altitude above sea level) + (-21 meters) (Waterloo altitude below sea level) = 168 meters.
Therefore, the height difference between Amersham and Waterloo stations is 168 meters.
a scalene triangle has symmetry with respect to a line containing a median of the triangle . true or false
Answer:
False it never will
Step-by-step explanation:
Got it right on my test.
Find the greatest perfect square that is factor of the number. 650
The greatest perfect square that is a factor of 650 is 25
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves,
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
Given the number is 650
To determine the greatest perfect square that is a factor of the number 650.
We need to write 650 as the product of its prime factors, which is 650.
⇒ 650 = 2×5×5×13
So the pair is 5×5 which is 5² or 25
Hence, the greatest perfect square that is a factor of 650 is 25
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