Answer:
1,296x^4 – 864x^3 + 216x^2 – 24x + 1
Step-by-step explanation:
From binomial theorem we know that:
[tex](a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4[/tex]
[tex]a^4 = 1,296x^4 = (6x)^4[/tex]
a = 6x
[tex]b^4 =1[/tex]
b = -1 or b = 1
We have to satisfy: [tex]4ab^3 = -24x[/tex]. Using b = -1
[tex]4(6x)(-1)^3 = 24x(-1) = -24x[/tex]
We have to satisfy: [tex]4a^3b = -864x^3[/tex]
[tex]4(6x)^3(-1) = (-4)216x^3 = -864x^3[/tex]
We have to satisfy: 6a^2b^2 = 216x^2
[tex]6(6x)^2(-1)^2 = 6(36)x^2 = 216x^2[/tex]
Then, [tex](6x - 1)^4 = 1,296x^4 - 864x^3 + 216x^2 - 24x + 1[/tex]
Complete the equation of the line through (-6,-5) (−4,−4) PLZ HELP !!!
Answer: y=1/2x−2
Step-by-step explanation:
again one question not two
Answer: A) 5m = 50; m = 10
Step-by-step explanation:
The diagram shows 5 "m"s, or 5*m equal to 50. Thus, 5m=50.
Because 5m = 50, divide both sides by 5 to get that m = 10
Hope it helps <3
Answer:
5m=50 and m = 10
Step-by-step explanation:
if 5m = 50, then 50/5=m and 50/5 = 10
Rahim is constructing a proof to show that the opposite angles of a quadrilateral inscribed in a circle are supplementary. Which step would be the third step in his proof, given the following information?
Answer:
B
Step-by-step explanation:
The option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
Rahim is constructing a proof to show that the opposite angles of a quadrilateral inscribed in a circle are supplementary.
From the central angle theorem:
(1/2)mQRS = ∠T because the measure of an inscribed angle is one-half the measure of its intercepted arc.
Thus, the option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.
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Which of the following is a solution of the system
x - 2y < 4 and y > – 2x – 5?
1. (1, - 4)
2. (-8,2)
3. (0,0)
4. (-3,0)
Answer:
Answer B
Step-by-step explanation:
1. (1, -4) is NOT a solution because (1) - 2(-4) < 4 is false.
2. (-8, 2): -8 - 2(2) < 4 is true, and in simplified form is -12 < 4 (true) We must check whether this point (-8, 2) ALSO satisfies y > -2x - 5:
2 > -2(-8) - 5. Yes, this is true, so the given point satisfies both inequalities in Answer B.
help me please(2 + 3 • 2 + 3²) - 4²
Answer:
1solution,
[tex](2 + 3 \times 2 + {3}^{2} ) - {4}^{2} \\ = (2 + 6 + 9) - 16 \\ = 17 - 16 \\ = 1[/tex]
Hope this helps...
Good luck on your assignment...
Answer:
1
Step-by-step explanation:
Multiply
3 by 2 . 2 + 6 + 3 2 − 4 2 Raise 3 to the power of 2 . 2 + 6 + 9 − 4 2 Raise 4 to the power of 2 . 2 + 6 + 9 − 1 ⋅ 16 Multiply − 1 by 16 . 2 + 6 + 9 − 16
Simplify by adding and subtracting.
Add 2 and 6 . 8 + 9 − 16 Add 8 and 9 . 17 − 16 Subtract 16 from 17 .
1
PLZ HELP!! HURRY!!!30POINTS!!
Answer & Step-by-step explanation:
please answer these 2 question correctly and get marked brainliest
Answer:
See below.
Step-by-step explanation:
46.
Theorem:
The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.
The 100-deg angle is an exterior angle whose remote interior angles are angles E and F.
m<E + m<F = 110
5x + 6x = 110
11x = 110
x = 10
m<E = m<FEG = 5x = 5 * 10 deg = 50 deg
Answer: C. 50 deg
47.
A is not true since we know that 5x + 6x must equal 110, not 70.
Answer:
<FEG=50
A. is wrong
Step-by-step explanation:
For the first question, we know <F &<E are remote interior angles which add up to 110 (exterior angle)
so:
[tex]5x+6x+110\\11x=110\\x=10[/tex]
so:
[tex]5x= 5(10)\\FEG=50[/tex]
Now using what we know, we can determine that A. is wrong since 5x+6x is 110° not 70°
Hope this helps!
£80 is divided between Fiona, Pip & Sara so that Fiona gets twice as much as Pip, and Pip gets three times as much as Sara. How much does Fiona get?
Answer:
Fiona got £48
Step-by-step explanation:
let Sara=x
Pip=3x
Fiona=2(3x)
x+3x+2(3x)=£80
4x+6x=£80
10x=£80
10x/10=£80/10
x=£8
therefore Sara(x) got £8
Pip=3x
=3(8)
=£24
Fiona=2(3x)
=2(24)
=£48.
find sin 2a and cot 2a:
Answer:
[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}[/tex]
Step-by-step explanation:
[tex]\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\[/tex]
[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}[/tex]
What are the roots of the equation? x^2 − x − 42 = 0 Enter your answers in the boxes. X= X=
Answer:
x = -6 and x = 7
Step-by-step explanation:
x² - x - 42 = 0
find two number which
a + b = -1
a*b = -42
a = -7
b = 6
x² - x - 42 = 0
(x-7)(x+6) = 0
x-7 = 0
x = 7
x +6 = 0
x = -6
Answer:-6 or 7
Step-by-step explanation:
Which table does not represent a proportional relationship? A 2-column table with 3 rows. Column 1 is labeled x with entries 9, 6, 3. Column 2 is labeled y with entries 3, 2, 1. A 2-column table with 3 rows. Column 1 is labeled x with entries 16, 18, 20. Column 2 is labeled y with entries 4, 4.5, 5. A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 18, 22. Column 2 is labeled y with entries 2, 3, 4. A 2-column table with 3 rows. Column 1 is labeled x with entries 5, 7, 9. Column 2 is labeled y with entries 10, 14, 18.
Answer:
the one with 12, 18, 22
Step-by-step explanation:
in the first one, 9-3=6 and 6-3=3 so -3 is the constant of the proportionality
in the second one 3-1=2, 2-1=1 so here the constant of proprtionality is -1
in the third one 16+2=18, 18+2=20 so the constant of proportionality is 2
fourth one 4 + 0.5= 4.5 and 4.5+0.5= 5, constant of proportionality is 0.5
fifth one 12+6=18, but 18+6=24
and the rest are all proportional
Answer:
12, 18, 22
Step-by-step explanation:
A shoe store marks up the wholesale cost of all shoes they sell by 20%. Calvin wants to buy a pair of shoes that has a price tag of $145. What was the wholesale cost of the shoes?
The sell price is the wholesale price plus 20%
Divide the sell price by 1.2 ( 100% + 20%)
145 / 1.2 = 120.83
The wholesale price is $120.83
Answer:
The wholesale price is $120.83
I need for this problem. Help please!
Answer:
⇒ x = 3.4975
Step-by-step explanation:
Assume cost of each figure = x
Given:
32x + 2.32 = 114.24
Find:
Value of x
Computation:
⇒ 32x + 2.32 = 114.24
⇒ 32x = 114.24 - 2.32
⇒ 32x = 111.92
⇒ x = 111.92 / 32
⇒ x = 3.4975
what is the range of the function?
Answer:
Range { 2,4,9,16}
Step-by-step explanation:
The range of the function is the output of the system
Range { 2,4,9,16}
Answer:
Step-by-step explanation:
Range is ll the y-points the outputs {2,4,9,16}
'15 points in total for brainliest and correct answer, please answer ASAP'
What is the area of the shaded portion if the area of the circle is 56 sq cm?
Answer:
14cm² is the area of the shaded region
Step-by-step explanation:
recognize that those two small triangles plus that arc area is equal to 1/4 of the area of the circle.
56 / 4 = 14cm
)Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week. Finally, she spent $15 on new sunglasses. Which part of the scenario is best represented by a linear increasing interval? Bentley has $40 in her piggy bank. Bentley spent $10 on new flip flops. Bentley got $20 for her allowance. Bentley spent $15 on sunglasses.
Answer:
Bentley got $20 for her allowance.
Step-by-step explanation:
2. Below is a circle with centre C. A, B, D, and E
are points on the circumference. BD is a diameter of
the circle.
Angle CDA is 18° Find the size of angle EDA.
You must show your workings
Answer:
Step-by-step explanation:
45-37
8x17 = 136
The product of the first 50 prime numbers is not divisible by:
A. 26
B. 36
C. 46
D. 86
Answer:
C.46
Step-by-step explanation:
I hope it helps ❤
The product of the first 50 prime numbers is not divisible by 86.
What is meant by prime number?A prime number is a whole number greater than one with only the number one and itself as factors. A factor is a whole number that can be evenly divided by another number. 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are the first few prime numbers. Composite numbers are those that have more than two factors. Only the number 1 and the number itself are divisible by 11. A number must have exactly two factors to be classified as a prime number. 11 is a prime number because it has exactly two factors, namely 1 and 11.The largest known prime number is currently 282,589,933. This prime, as well as the previous seven largest primes discovered, are referred to as Mersenne primes, after the French mathematician Marin Mersenne (1588–1648).Therefore,
First 50 prime numbers are, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
So 86 is not the prime number.
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Jana has £1500 in her bank account.
She has 270 euros of money left from her last holiday and
she wants to put this into her bank account.
The bank will convert the euros into pounds using £1 =
1.1452 euros.
The bank deducts a fee of £0.89 from her savings account
for this conversion.
How much money does Jana now have in her bank
account?
Step-by-step explanation:
She has 234 euros left after the conversion
Total money = 1500 + 234 = 1734
Answer:
£11734.88
Step-by-step explanation:
Jana's 270 Euro converts into pounds as follows:
270 Euro £1
------------------ * ------------------ = £235.77
1 1.1452 Euro
From this we subtact the £0.89 conversion fee, obtaining £234.88 net. We add this amount to the £1500 already in her account, obtaining £11734.88
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Hey there! :)
Answer:
1.
Step-by-step explanation:
If a line has the equation y = x + 6, a parallel line would contain the same slope.
In the equation y = x + 6, there is no coefficient, or slope. This means that the slope, or m = 1.
Thus, a parallel line would contain an equivalent slope, making the slope of the parallel line = 1.
Answer:
1
Step-by-step explanation:
Two lines are parallel if they have the same slope. The slope is the number that comes before x.The slope of the first line is 1, even though it doesn't say 1x, as anything multiplied by 1 is itself, so it is left out.
heleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeep
Answer:
3.625 is ans
Step-by-step explanation:
4.5+0.25_+1.125=3.625
Step-by-step explanation:
this is your answer sis ...
If f(x) = squareroot x + 5 and g(x) = -4x + 4,
which statement is true?
Click on the correct answer.
3 is in the domain of fºg.
3 is not in the domain of fºg.
Answer:
3 is not in the domain of [tex]f\circ g[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=\sqrt{x+5}[/tex]
[tex]g(x)=-4x+4[/tex]
We need to check whether 3 is in the domain of [tex]f\circ g[/tex] or not.
[tex]f\circ g=f(g(x))[/tex]
[tex]f\circ g=f(-4x+4)[/tex] [tex][\because g(x)=-4x+4][/tex]
[tex]f\circ g=\sqrt{(-4x+4)+5}[/tex] [tex][\because f(x)=\sqrt{x+5}][/tex]
[tex]f\circ g=\sqrt{-4x+9}[/tex]
This function is defined if
[tex]-4x+9\geq 0[/tex]
[tex]9\geq 4x[/tex]
[tex]\dfrac{9}{4}\geq x[/tex]
It means domain of the function [tex]f\circ g[/tex] is [tex](-\infty,\dfrac{9}{4}][/tex].
[tex]3\notin (-\infty,\dfrac{9}{4}][/tex]
Therefore, 3 is not in the domain of [tex]f\circ g[/tex].
Which of the following represents the factorization of the trinomial below?
x² - 2x - 48
A. (x-4)(x-12)
B. (x+4)(x-12)
C. (x-6)(x-8)
D. (x+6)(x-8)
Answer: (x-8)(x+6)
Step-by-step explanation: For this equation, you need to figure out what two numbers add up to add -2, and multiply to get -48.
These numbers are +6 and -8. So the factored pair will be (x+6)(x-8)
Hope this helps:)
Answer: d
Step-by-step explanation:
This a trinomial so to find the factorization you need just to solve this equation :
x²-2x-48=0a=1b=-2c=-48Δ=(-2)²-4*1*(-48)=196 so our trinomial has 2 solutions : [tex]\left \{ {{y=\frac{2+\sqrt{196} }{2} } \atop {x=\frac{2-\sqrt{196} }{2} }} \right.[/tex]x=8 and y=-6
the factorisation is f(x)=a* (x-8)(x-(-6))
the answer is : (x+6) (x-8)
What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction?
Negative StartFraction 7 over 8 EndFraction
Negative StartFraction 9 over 14 EndFraction
StartFraction 9 over 14 EndFraction
Answer:
[tex]-\frac{9}{14}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}*-\frac{6}{7}\\\\\frac{3}{2} *\frac{3}{7} \leftarrow \text{Cross Cancel Common Factor}\\\\ -\frac{3*3}{2*7}\\\\-\frac{9}{14}[/tex]
Answer:
negative 9/14
Step-by-step explanation:
What number is represented by point B?
Which point represents the number 2?
Answer:
-1, c
Step-by-step explanation:
Each dot represents 1.
0 - 1 = -1
As labeled, c represents 2.
Triangles D E F and P Q R are shown. Given that StartFraction D F Over P R EndFraction = StartFraction F E Over R Q EndFraction = three-halves, what additional information is needed to prove △DEF ~ △PQR using the SSS similarity theorem? DE ≅ PQ ∠D ≅ ∠P StartFraction D E Over E F EndFraction = three-halves StartFraction D E Over P Q EndFraction = three-halves
Answer:
The correct option is;
DE/PQ = 3/2 which is StartFraction DE Over PQ Endfraction = three-halves
Step-by-step explanation:
The information given bout the triangles are;
DF/PR = FE/RQ = 3/2
Therefore since the given sides of triangle DEF are 3/2 times the sides of triangle PQR, the given sides of triangle DEF have been scaled 3/2 times to get the given sides of triangle PQR
Therefore, to prove that ΔDEF ~ ΔPQR, the ratio of the third side of triangle DEF, that is DE, to the third side of triangle PQR, which is PQ must be three-halves.
Answer:
The answer is DE/PQ = 3/2 or D.
Step-by-step explanation:
Just did it on edge. hope you do good :)
there is two images guys so don get confused PLZ HALP
Answer:
C) 105
Step-by-step explanation:
The box plot suggests that about 50% of hight schools in orange county have more than 105 band members.
This can be inferred from the boxplotvprovided in the attachment. 50% refers to the median of the distribution which is denoted by the vertical line dividing the box into two. Tracing the vertical line to the horizontal label marked from 70 to 150, the vertical line falls on the 105 mark. Hence the value of the median or 50th percentile
What is the range of function in this table?
Answer:
Range{ 2,3,4}
Step-by-step explanation:
The range is the output of the function, in the case the y values
Range{ 2,3,4}
Answer the question now fast
Answer:
second and third choice
Step-by-step explanation:
supplamentary = add up to be 180
What is the distance between the points (-3, 9) and (5, 1)? Round to the
nearest tenth, if necessary.
Answer: 11.3
Step-by-step explanation:
To find the distance, we will need the distance formula.
[tex]D=\sqrt{(x_{2}-x_{1} ) ^2+(y_{2}-y_{1})^2 }[/tex]
Since we know our x and y, we can plug them into this equation.
[tex]D=\sqrt{(5-(-3))^2+(1-9)^2}[/tex]
[tex]D=\sqrt{(8)^2+(-8)^2}[/tex]
[tex]D=\sqrt{64+64}[/tex]
[tex]D=\sqrt{128}[/tex]
[tex]D=11.3[/tex]
The distance between the points is 11.3.