Final answer:
The binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex], as both can be factored into the form (a + b)(a - b).
Explanation:
The question asks which binomials are a difference of squares. A difference of squares is a binomial in the form [tex]a^2 - b^2[/tex], which can be factored into (a + b)(a - b). Analyzing the given options:
[tex]y^4 + 9[/tex]: This is not a difference, it's a sum.
[tex]9x^2 - 16[/tex]: This is a difference of squares because [tex]9x^2 = (3x)^2[/tex] and 16 = [tex]4^2[/tex].
[tex]m^6 - 25[/tex]: This is a difference of squares because [tex]m^6 = (m3)^2[/tex] and [tex]25 = 5^2[/tex].
[tex]p^7 - 1[/tex]: This is not a difference of perfect squares; [tex]p^7[/tex] is not a perfect square.
Therefore, the binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex].
When brad was born ,his grandma put 1,500 in a new account for him . Since then the balance of the account has grown by 6.5% each year with no deposits or withdrawals. Now Brad is 18 and can withdraw the money if he decides to wait until his 21st birthday how much more money will be in the account
Final answer:
Using the compound interest formula, Brad's $1,500 will grow to $1,810.69 by the time he turns 21 due to the 6.5% annual growth rate for three additional years.
Explanation:
Calculating Future Value with Compound Interest
Brad's grandmother initially deposited $1,500 in an account that grows at a rate of 6.5% each year. To calculate the future value of this investment when Brad is 21, we'll use the formula for compound interest:
FV = P(1 + r)^n
Where:
FV is the future value of the money after n years.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of years the money is invested or borrowed for.
In Brad's case:
P = $1,500
r = 0.065 (6.5% converted to a decimal)
n = 21 years old - 18 years old = 3 years
Now, we plug these values into the compound interest formula:
FV = $1,500(1 + 0.065)^3
And calculate the future value.
Therefore, if Brad decides to wait until his 21st birthday to withdraw the money, he would have:
$1,500(1 + 0.065)^3 = $1,500(1.065)^3 = $1,500 * 1.207127 = $1,810.69
Brad will have $1,810.69 in his account by the time he is 21 if he waits, which is more than he would have at 18.
A coordinator will select 4 songs from a list of 11 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
The number of different possible line ups are; 4,233,600
What is permutation and combination?
We are told that;
List of songs = 11 songs
Number of songs to be selected = 4 songs
Thus, the number of different possible line ups is gotten from permutation formula as;
¹¹P₇ = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 = 4,233,600
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Answer:
answer is 7920
somehow you miscalculated
Solve the following inequality: 6x - 9 ≥ 11x - 17.
1. x<=5/8
2.x>=8/5
3.x>=5/8
4.x<=8/5
Answer:
x ≤8/5
Step-by-step explanation:
6x - 9 ≥ 11x - 17
Subtract 6x from each side
6x -6x-9 ≥ 11x - 17-6x
-9 ≥ 5x- 17
Add 17 to each side
-9+17≥ 5x - 17+17
8≥ 5x
Divide each side by 5
8/5≥ 5x /5
8/5≥ x
Which of the following are alternate interior angles? Select all that apply.
A.
∠5 and ∠4
B.
∠6 and ∠5
C.
∠2 and ∠8
D.
∠8 and ∠1
E.
∠3 and ∠5
Answer:
C & E
Step-by-step explanation:
∠3 and ∠5 are alternate interior angles
∠2 and ∠8 are alternate interior angles
The distance between the points (-3,4) and ( 5,4)
Application of the Pythagorean theorem
so the answer is 8 units.
Hope this will help u...
The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus.
How many passengers got on after stop 4?
A:27
B:14
C:22
D:13
Answer gets brainliest
Answer:
b.14
Step-by-step explanation:
xoxoxoxoxoxoxoxoxo you're welcome
whats 4×5/8 please help
Answer:
5/2 = 2 1/2 = 2.5
Step-by-step explanation:
4 * 5/8 = 4/1 * 5/8 = (5 * 4)/(1 * 8) = 20/8 = 5/2 = 2 1/2 = 2.5
Answer is 2.5 because 4 times 5 is 20 and 20 divided by 8 is 2.5
What are these values?
Answer:
what is the values of what?
What is the degree of t-4t^2+2t^3
Answer:
3
Step-by-step explanation:
t-4t^2+2t^3
Rewriting this in order from largest to smallest exponent
2t^3 -4t^2 +t
The highest power is 3
So this is degree 3
What’s the slope of the line that passes through 5,10 and 7,12
Slope of the line passes through (5,10) and (7,12) is 1.
Step-by-step explanation:
Given,
The two points are (5,10) and (7,12).
To find the slope passing through the given points.
Formula
The slope of the line passing through ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Now, putting [tex]x_{1} =5,y_{1}=10, x_{2}=7, y_{2} =12[/tex] we get,
Slope = [tex]\frac{12-10}{7-5}[/tex] = [tex]\frac{2}{2}[/tex] = 1
Hence,
Slope of the line passes through (5,10) and (7,12) is 1.
Answer:
[tex]to \: find \: the \: slope \: of \: the \: line \\ given \: that \: the \: line \: passes \: through \\ (5,
10) \: and \: (7,12) \\
answer \: is \: \: 1
[/tex]
Step-by-step explanation:
[tex]passing \: through \: (5,10) \: and \: (7,12) \\ slope = \frac{y2 - y1}{x2 - x1} \\ here \: y2 = 12 \: \: and \: \: y1 = 10 \\ x2 = 7 \: \: and \: \: x1 = 5 \\ therefore \: \\ slope = \frac{12 - 10}{7 - 5} \\ = \frac{2}{2} \\ = 1[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
In circle N, KL ≅ ML. Circle N is shown. Line segments N J, N M, N L, and N K are radii. Lines are drawn to connect each point on the circle to create secants J M, M L, L K, and K J. M L and K L are congruent. The measure of arc J K is (5 x + 24) degrees, the measure of arc J M is (13 x + 2) degrees, the measure of arc M L is (8 x minus 3) degrees, and the measure of arc K L is (7 x + 7) degrees. What is the measure of Arc J M? 77° 90° 132° 154°
Answer:
[tex]arc\ JM=132^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
we know that
[tex]arc\ JM+arc\ ML+arc\ LK+arc\ KJ=360^o[/tex] ----> by complete circle
substitute the given values
[tex](13x+2)^o+(8x-3)^o+(7x+7)^o+(5x+24)^o=360^o[/tex]
solve for x
[tex](33x+30)^o=360^o\\33x=360-30\\33x=330\\x=10[/tex]
step 2
Find the measure of arc JM
[tex]arc\ JM=(13x+2)^o[/tex]
substitute the value of x
[tex]arc\ JM=(13(10)+2)^o=132^o[/tex]
Answer:
132 maybe
Step-by-step explanation:
A lomy owner has his own fuel supply and needs to refill his storage tank. He has just completely
filled the fuel tank of the lorry with 170 litres from empty. He now has 100 litres of fuel left in his
storage tank. With the price of fuel expected to fall soon he only wants to buy enough for the next
fortnight. Normally his regular short daily trips total 300 km and this leaves just 20 litres in the
lorry's fuel tank. He expects to complete three regular days of 300 km journeys each week, but
this could rise to five. Sometimes the total journeys are longer but his daily trips never total more
than 400 km in a day. He never works more than five days in a week. His storage container holds
4000 litres
How much fuel should he order to be certain that he has enough for the next two weeks?
Answer: He should order for 1046.67 litres fuel to be certain that he has enough for the next two weeks
Step-by-step explanation:
Note that he has just completely
filled the fuel tank of the lorry with 170 litres from empty. He now has 100 litres of fuel left in his storage tank
If his regular short daily trips total 300 km and this leaves just 20 litres in the lorry's fuel tank.
That is 100 litres -20 litres = 80 litres
On 300km, he consumed 80 litres
He plans to complete three regular days of 300 km journeys each week, but this could rise to five. Sometimes the total journeys are longer but his daily trips never total more than 400 km in a day. He never works more than five days in a week. His storage container holds
4000 litres
From all these analysis, we can deduce that the maximum km of journey he should prepare for is
400km × 5 = 2000km for one week
Since he consumed 80 litres of fuel for any 300km
Then,
80/300 = L/2000
L = 1600/3
L = 533.33 litres
The journey for two weeks will be
533.33 × 2 = 1066.67 litres
Recall that he left 20 litres in the tank. Take this away from 1066.67 litres.
1066.67 - 20 = 1046.67 litres
He should therefore order for 1046.67 litres fuel to be certain that he has enough for the next two weeks
1. How are sine functions connected to the unit circle?
2. How are cosine functions connected to the unit circle?
Answer:
1) The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle.
2) The secant function is the reciprocal of the cosine function (secx=1cosx) x = 1 cos .The co-secant function is the reciprocal of the sine function (cscx=1sinx) x = 1 sin . It can be found for an angle t by using the y -coordinate of the associated point on the unit circle: csct=1y t = 1 y .
Step-by-step explanation:
Final answer:
Sine and cosine functions are related to the unit circle with their values representing the y and x coordinates of a point on the circle, respectively. They oscillate between +1 and -1, repeating every 2π radians and are used to model simple harmonic motion, differing by a phase shift of π/2 radians.
Explanation:
The sine and cosine functions are directly related to the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate system. When an angle θ is drawn from the positive x-axis, the coordinates of the point where the terminal side of the angle intersects the unit circle are (cos θ, sin θ).
For the sine function, think of it as projecting the point on the unit circle onto the y-axis. This projection gives the y-coordinate, which is the sine of the angle θ. Therefore, the sine function oscillates between +1 and -1 as the angle θ increases, repeating every 2π radians because this is the circumference of the unit circle.
Similarly, the cosine function is obtained by projecting the point onto the x-axis, providing the x-coordinate or the cosine of the angle θ. It also oscillates between +1 and -1 and repeats every 2π radians. Both sine and cosine functions describe simple harmonic motion when modeling periodic phenomena, and they differ by a phase shift of π/2 radians.
The initial conditions of a sine function with zero phase shift are that the function starts at 0, indicating that, for simple harmonic motion, the initial position is at equilibrium. With a cosine function, the initial value is 1 when the phase shift is zero, indicating that the motion starts at its maximum displacement. This concept can also be used to model wave functions and determine scalar components using triangles.
John saved 65 coins. He saved nickels and dimes only. If he had totally $4.90, how many nickels did he have?
Answer:
Step-by-step explanation:
Let n = nickels and d = dimes
n+d = 65
5n+10d = 490
Solve for n:
n = 65 - d
Substitute the equation:
325 + 5d = 490
5d = 165
d = 33
Can someone pls answer this thanks
Answer:
64 pi
Step-by-step explanation:
divide 50.24 by 3.14 to find diameter
16 = diameter
8 = radius
Area = 8^2 pi = 64 pi
Answer:
A=200.96
Step-by-step explanation:
which binomials below is a factor of this trinomial, x^2 - 6x - 16
I WILL MARK BRAINLIEST
Answer:
(x - 8) and (x + 2) are both factors
Step-by-step explanation:
Given
x² - 6x - 16
Consider the factors of the constant term (- 16) which sum to give the coefficient of the x- term (- 6)
The factors are - 8 and + 2, since
- 8 × 2 = - 16 and - 8 + 2 = - 6, thus
x² - 6x - 16 = (x - 8)(x + 2)
Answer:
x + 2
Step-by-step explanation:
Just took the quiz
Which expression is the same as 2 hundreds, 6 tens, and 804 thousandths?
Choose 1 answer:
©
(2 x 100) + (6 x 10) + (8 x 100) + (4 x
1000)
© (2 x 100) + (6 x 10) + (8 x 7) + (4 x 1000)
© (2 x 100) + (6 x 10) + (8 x HD) + (a < too)
Answer:
(2 x 100) + (6 x 10) + (804 x 10^-3)
Step-by-step explanation:
The figure located at the hundred must be multiplied by 100
The figure located at the tens must be multiplied by 10
The figure located at the ones must be multiplied by 1
The figure located at the tenth must be multiplied by 10^-1
The figure located at the hundredth must be multiplied by 10^-2
The figure located at the thousandths must be multiplied by 10^-3
All the previous expression must be added. Then, 2 hundreds, 6 tens, and 804 thousandths is the same as:
(2 x 100) + (6 x 10) + (804 x 10^-3) = 260.804
Answer:
I think its the 1st one
Q18) Find the percent change from 70 to 56.
Answer:
20%
Step-by-step explanation:
Jus do the math for it and that be your answer right there.
Sadly, my last question was ignored, so I am asking it again... Can someone please help me? If you answer it, go to my profile and answer the old question too, they are the same. You will obtain 18 points if you answer this question and the identical older one.
Answer:
the picture is blocked on my screen just write it out on my answer
Step-by-step explanation:
Answer:
the theoretical probability is 1/5.
the experimental probability is 3/10.
chances are the experimental probobility will approach the theoretical probobility.
Step-by-step explanation:
since blue is one of five equal sizes, the probobility that it will land on blue is 1/5.
the expiromental probobility is the number of times it landed on blue devided by the number of spins. 15/50. this can be simplified by pulling out a 5, leaving us with 3/10.
last it stands to reason that the more times the spinner is spun the closer the experimental probability will model the theoretical probability.
which choices are equivalent to the expression? √(5) x √(20)
Answer:
10 is the answer
Step-by-step explanation:
You have to multiply with whats inside the roots. you would have [tex]\sqrt{5} times \sqrt{20} will give you \sqrt{100} which is 10[/tex]
D(1) =3
D(n) = d(n-1)-14
Answer:
D(1)=3
Step-by-step explanation:
Answer:
The 3rd term is -25
Step-by-step explanation:
This is a recursive formula. It tells us that the first term is 3 and that the common difference is -14.
d(1)=3
d(2) = d(1) -14 = -11
d(3) = d(2) - 14 = -25
The 3rd term is -25
What is the area of the sector that is NOT shaded?
a. 80 pi units2
b. 16 pi units2
c. 20 pi units2
d. 8 pi units2
PLEASE HURRY!! I HAVE LIMITED TIME!! :)
Answer:
area of the shaded sector
= 72°/360°π(10)²
= 0.2×100π. sq. units
=20π sq. units
area of the not shaded region=π(10)²-20π
= (100-20)π = 80π sq. units
A sports franchise would like to increase their Instagram followers by 25%. This means they would need 300,000
more followers. How many followers do they currently have?
a) 75,000
b) 300,000
c) 525,000
d) 1,200,000
Answer:
D. 1,200,000
Step-by-step explanation:
25%=0.25 which if multiplied by 4 = 1 which is the current followers. 300,000 multiplied by 4 = 1,200,000
Using percentages we know that the current followers of the sports franchise are (D) 1,200,000.
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the current followers are:
Let the correct followers be x.Now calculate as follows:
x/100 × 25 = 300,00025x = 30,000,000x = 30,000,000/25x = 1,200,000Therefore, using percentages we know that the current followers of the sports franchise are (D) 1,200,000.
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Solve for x: d 28−x 7+x +8=14
How will the graph of line y = -3x+8 be affected if the 8 is changed to -3?
A. The y-intercept will be moved 3 units downward.
B. The y-intercept will be moved 5 units downward.
C. The y-intercept will be moved 11 units downward.
D. The x-intercept will be moved 3 units to the left.
E. The x-intercept will be moved 11 units to the left.
Answer:
C
Step-by-step explanation:
A y intercept lies on the y axis.
This means that the movement will happen with the y intercept, on the y axis.
8 is the original y intercept.
It is now changed to -3.
-3 is lower than 8 on the y axis so we are moving downward.
Now, to find the number of squares it moves, we can find the difference between 8 and -3.
8-(-3)=11
Therefore, The y-intercept will be moved 11 units downward.
Answer:
C.
Step-by-step explanation:
The -3x tells you the slope (rise/run). In this case, it will go downward because it is negative. It will have a slope of 3/1. The +8 or -3 is the y intercept and tells which direction the original line will go from its' starting point. So you would add those together to know which way the line moves.
Given the sequence.
125, 25, 5, ...
Write the rule an using the geometric sequence formula:
The given sequence follows a geometric pattern, and the common ratio is 0.2. Using the geometric sequence formula, we can find any term in the sequence by substituting the values into the formula.
Explanation:The given sequence 125, 25, 5, ... follows a geometric pattern where each term is obtained by multiplying the previous term by a common ratio. To find the common ratio (r), we divide any term by its previous term. Let's divide 25 by 125 to find the common ratio: r = 25/125 = 1/5 = 0.2.
Now that we have the common ratio, we can use the formula for a geometric sequence:
aₙ = a₁ × r(n-1)
Here, aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the term number. Since the first term (a₁) is 125 and the common ratio (r) is 0.2, we can substitute these values into the formula to find the nth term.
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The rule for the given geometric sequence 125, 25, 5, ... is an = 125 × 5(n-1).
Explanation:The given sequence is 125, 25, 5, ...
To find the rule using the geometric sequence formula, we need to determine the common ratio. The common ratio is found by dividing any term by its previous term. Let's take the first two terms: 125/25 = 5. So, the common ratio is 5.
The formula for a geometric sequence is given by: an = a¹ × r⁽ⁿ⁻¹⁾, where an is the nth term, a¹ is the first term, r is the common ratio, and n is the position of the term.
Using this formula with the first term (a¹ = 125) and the common ratio (r = 5), we can find the rule for the sequence. Let's find the rule for the third term: a³ = 125 × 5⁽³⁻¹⁾ = 125 × 5² = 125 × 25 = 3125.
Therefore, the rule for the sequence is: aⁿ = 125 × 5⁽ⁿ⁻¹⁾.
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What is 4(-1/2) in repeated addition? Help ASAP please!
Answer:
-1/2 + -1/2 + -1/2 + -1/2 = -2
Step-by-step explanation:
You open up the parenthesis to get:
-1/2 + -1/2 + -1/2 + -1/2 =
-2
If x=2 and y=4 what is the answer to 3x + 2y + 4
Answer:
Step-by-step explanation:
x = 2 ; y = 4
3x + 2y + 4 = 3*2 + 2*4 + 4
= 6 + 8 + 4
= 18
Line B is 55 cm long. It is an enlargement of Line A which is 5 cm long. What is the scale factor of the enlargement?
Answer:
11
Step-by-step explanation:
Line B is an enlargement of Line A, which is 5 cm long. Let's say that the scale factor is "k". Then, when we multiply k by the length of Line A, we should get the length of Line B:
(Line A length) * k = (Line B length)
5 * k = 55
k = 55/5 = 11
Thus, the scale factor is 11.
Hope this helps!
Answer:
11
Step-by-step explanation:
Length of enlarged line is: 55 cm
Length of the original line: 5 cm
Let the scale factor be t
Then,
5t = 55
t = 55/5
t = 11
Which number line plots the integers –12, -3, and 7?
Answer:
A
Step-by-step explanation:
It’s just a rough estimate, but using reasoning that -12 is between-10 and -15, -3 is found between 0 and -5, and 7 being between 5 and 10