english and maths teacher
Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 ab b2)
Answer:
Step-by-step explanation:
Expanding the right-hand side,
[tex](a-b)(a^{2}+ab+b^{2})=a^{3}+a^{2}b+ab^{2}-a^{2}b-ab^{2}-b^{3}=a^{3}-b^{3}[/tex]
Thus, the identity is true.
20.
(05.07 MC)
A scatter plot is made to model the amount of money left to pay on a mortgage. The data used for the scatter plot are shown in the table:
Number of Months 3 5 1 2 0 4
Money Owed $114,000 $100,000 $118,000 $116,000 $120,000 $112,000
What does the y-intercept of the model represent? (1 point)
The amount of the mortgage that has been paid that month
The monthly payments
The original amount of the mortgage
The number of months it takes to pay off the mortgage
Option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
As we know the line of best is represented by:
y = mx + c
Here m is the slope and c is the y-intercept.
A scatter plot is made to model the amount of money left to pay on a mortgage.
Every month that passes, the amount left to pay decreases.
Plug x = 0 to get the y-intercept
y = c
The y-intercept representing the original amount of the mortgage.
Thus, option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.
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The question is:
Jason has 20 gallons of a 12% alcohol solution. How many gallons, to the nearest tenth, must be replaced by a 36% alcohol solution to give 20% gallons of 15% alcohol solution.
I need and explanation on how to set it up and do it. I have a test today and I don’t understand it.
Answer:
2.5 gallons of the 20% solution must be replaced by the 36% solution.
Step-by-step explanation:
[tex].12(20 - x) + .36x = 20(.15)[/tex]
[tex]2.4 - .12x + .36x = 3[/tex]
[tex]2.4 - .24x = 3[/tex]
[tex] - .24x = - .6[/tex]
[tex].24x = .6[/tex]
[tex]x = 2.5[/tex]
Solve equation by using the quadratic formula. 6x^2 +2x =4?
A) x= 3/2, 1 B) x= 2/3, -1 C) x=3/2, -1 D) x=3/2, 0
Answer:
Answer x=2/3, -1
Option B
Step-by-step explanation:
Answer:
B) x =( 2/3, -1)
Step-by-step explanation:
Equation:
[tex]6x {}^{2} + 2x = 4[/tex]
Solution:
We know that,
[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
According to the problem,
a = 6b = 2c = -4Plugging them on the formulae,we obtain,
[tex]x = \cfrac{ - 2 \pm \sqrt{ 2 {}^{2} - 4 \{6 \times ( - 4) \} } }{2 \times 6} [/tex][tex]x = \cfrac{ - 2 \pm \: \sqrt{4 - 4 \{ - 24 \} } }{12} [/tex][tex]x = \cfrac{ - 2 \pm \: 10 }{12} [/tex][tex]x = \cfrac{ - 1 \pm5}{6} [/tex][tex]\boxed{x = \cfrac{2}{3} \: \rm or - 1}[/tex]Choice B is accurate.
The table represents the function f(x).
A 2-column table with 7 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 66, negative 29, negative 10, negative 3, negative 1, 6.
When f(x) = –3, what is x?
Answer:
-1/2
Step-by-step explanation:
Answer:x is -1
Step-by-step explanation:
adam has 18 counters he gives 10 to lesleay how many of the 18 counters does lesleay get give your answer in simplest form
The fraction of the counters that Lesleay gets is 5/9.
What is the fraction?
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. An example is 1/2.
The fraction of the counters that Lesleay gets = number of counters she gets / total number of counters
10/18 = 5/9
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Solve using substitution method:
X= y/3 +2
7x − 5y = 10
Solve for (x,y)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 5/2 [/tex]
[tex] \qquad \tt \rightarrow \: y = 3/2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)[/tex]
[tex]\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)[/tex]
[tex] \textsf{put value of x in equation 2} [/tex]
[tex]\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 8y = - 4(3)[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2} [/tex]
[tex] \textsf{put value of y in equation 1 } [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{5}{2} [/tex]
Find the sum of the largest and the smallest of the following four numbers:
3.09 3.9 0.39 0.399
PLEASE HELP
Answer:
Using the concepts of Number System, we find that the sum of the largest and the smallest of the given four numbers is 4.29.
Step-by-step explanation:
The given set of numbers is 3.09, 3.9, 0.39 and 0.399.
The given numbers are related to each other as:
3.9 > 3.09 > 0.399 > 0.39
3.9 is greater than 3.09 as
3.9 > 3.09
3 + 0.9 > 3 + 0.09
0.9 > 0.09
90 > 9
0.399 is greater than 0.39 as
0.399 > 0.39
399 > 390
Now, the smallest number in the series is 0.39 and the largest number in the series is 3.9.
The sum of the largest and the smallest of the given four numbers is:
3.9 + 0.39
4.29
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The average of three unique number is 50.if the loweat number is 30 what is the sum of other two numbers
Answer:
The sum of the other two numbers is 120.
Step-by-step explanation:
To find an average, you add all the numbers involved and divide it by the amount of numbers involved. in this case,
(x+y+z) ÷ 3 =50
x=30
Divide both sides by three to remove the denominator.
(30+y+z)÷ 3 (*3) = 50(*3)
(30+y+z)=150
Subtract 30 from both sides.
(30+y+z)-30= 150-30
y+z=120
pleasee help me with this function asap
Answer:
b, c
Step-by-step explanation:
A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.
__
A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.
The value of f(0) is 2, so the y-intercept is 2.
The given function is defined for all values of x, so its domain is all real numbers.
The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.
The function has a stationary point at x=0, so is not decreasing over its entire domain.
_____
Additional comment
The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.
#+3)(2+1) for x = 3.
c+5)(x-5)
Answer:
x=1/3
Step-by-step explanation:
first multiply both bracket to together and then you get, 9x=3
x=1/3, then sub in to other equation and get the rest answer.
hope it helpful
What is m∠C?
Enter your answer in the box.
Answer:
60
Step-by-step explanation:
Total degree of triangle interior angles is 180
So x+2x+3x=180
6x=180
x=30
Measurement of angle C is 2x which is 60 degree
This is confusing please help
Step-by-step explanation:
since we are using Pythagoras
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle),
you want to get the expression
y² = 3² + 3²
so, you pick the ² and put it next to the y left of the "=" sign.
and to the right of the "=" sign you put 3, ², +, 3, ²
Which of the following values can be found by using the formula √1+tan^2 0?
cos and sec can be found
The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.
Let's simplify the given expression and see which of the provided options match:
We are given the expression √(1 + tan²Ø).
Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.
Substitute this identity into the expression:
√(1 + sin²Ø / cos²Ø)
Next, find a common denominator for the fraction inside the square root:
√((cos²Ø + sin²Ø) / cos²Ø)
Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:
√(1 / cos²Ø)
Now, we can take the square root of 1 and cos²Ø separately:
√1 / √cos²Ø
Simplify:
1 / cosØ
The simplified expression is 1 / cosØ, which is equivalent to secØ.
Therefore, the correct option is: secØ.
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Does the chart below represent a proportional relationship? What is the rate of change?
x
y
1
4
2
7
3
10
4
13
Answer:
C will be your answer.
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Find the nth term of the sequence 3, -1, -5, -9.
Answer:
-4n+7
Step-by-step explanation:
because you take away 4 each time and the nber that would come before 3 is 7.
(06.06)
Which of the following demonstrates the Commutative Property of Multiplication?
5(2a − 3) = 10a − 15
10a − 15 = (2a − 3) ⋅ 5
5(2a − 3) = (2a − 3) ⋅ 5
(5 ⋅ 2a) − 3 = 5(2a − 3)
The correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.
What is commutative property?If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
a x b = b x a
So for the expression 5(2a − 3) = (2a − 3) ⋅ 5 suppose 5 is a and ( 2a - 3 ) is b so.
a x b = b x a
5(2a − 3) = (2a − 3) ⋅ 5
Therefore the correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.
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The zeros of a parabola are -4 and 2 and (6,10) is a point on the graph which equation can be solved to determine the value of a in the equation of the parabola
Answer:
Let consider the following linear equation systems by using the known points and second-grade polynomial:
(-1, 7)
a + b + c = 7a+b+c=7
(5, 7)
25\cdot a + 5\cdot b + c = 725⋅a+5⋅b+c=7
(6,10)
36\cdot a + 6 \cdot b + c = 1036⋅a+6⋅b+c=10
After some algebraic manipulation, the values for the polynomial coefficients are found:
a = \frac{3}{5}a= 53 , b = -\frac{18}{5}b=− 518
, c = 10c=10
The polynomial is:
y = \frac{3}{5}\cdot x^{2} - \frac{18}{5}\cdot x+10y= 53
⋅
Step-by-step explanation:
For complete solution see the above attachment!
Fatoumata just accepted a job at a new company where she will make an annual salary of $43000. Fatoumata was told that for each year she stays with the company, she will be given a salary raise of $5000. How much would Fatoumata make as a salary after 3 years working for the company? What would be her salary after tt years?
Fatoumata's salary after 3 years will be $58,000.
Fatoumata's salary after tt years will be $43,000 + (5,000tt).
What is Fatoumata's salary?
The linear equation that can be used to determine Fatoumata's salary after the passage of time is:
Initial salary + (yearly increase x number of years)
$43,000 + 5000t
$43,000 + 5000(3) = $58,000.
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Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 – 24t) – (0.6t2 8 – 18t) what is the additive inverse of the polynomial being subtracted?
The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].
We need to find the additive inverse of the polynomial being subtracted.
What is additive inverse?In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.
Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]
[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]
[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]
The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
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The line ax − by + 3 = 0 is parallel to the line 3x + 2y − 4 = 0 and passes through the point (1, −2). Find a and b.
Answer:
a=9
b=-6
Step-by-step explanation:
How tall is the tree?
5ft
35°
-20ft-
[? ]ft
Answer:
[tex]\boxed{\bf 19ft}[/tex]Step-by-step explanation:
[tex]\bf tan\:\theta =\cfrac{opp}{adj}[/tex]
[tex]\bf tan(35^o)=\cfrac{x}{20}[/tex]
[tex]\bf 20\;tan (35^o)=x[/tex]
[tex]\bf 14ft=x[/tex]
The height of the tree:-
[tex]\bf x+5ft[/tex][tex]\bf 14ft+5ft[/tex][tex]\bf 19ft[/tex]Answer:
19.00 ft to the nearest hundredth.
Step-by-step explanation:
tan 35 = h / 20
h = 20 tan 35
Now we add the man's height
Total height of the tree
= 20 tan 35 + 5
= 19.00 ft to the nearest hundredth.
need help asap! Fill in the blank by entering just a number…
Answer:
x = 6
Step-by-step explanation:
CT is a median, which means it divided AB into two equal parts so we can write the following equation:
7x + 9 = 5x + 21 transfer like terms to the same side of the equation
7x - 5x = 21 - 9 do the extraction
2x = 12 divide both sides by 2
x = 6
Write [tex]\frac{1}{22}[/tex] as a decimal, Also please include the working out plus anyone that includes other examples will be given brainlest!
Thank you!
Do long division (see the attachment).
[tex]\dfrac{1}{22}=0.04545\ldots=0.0\overline{45}[/tex]
The circle above with center O has a circumference of 36. What is the length of minor arc AC? A) 9 B) 12 C) 18 D) 36
Answer:
A) 9
Step-by-step explanation:
⇒ Circumference of a Circle = 2πr
[tex]36=2\pi r[/tex]
[tex]r=\frac{36}{2} \pi[/tex]
[tex]r=\frac{18}{\pi }[/tex]
Length of arc = rθ
θ = angle AC = [tex]90^o[/tex]
Convert [tex]90^o[/tex] to radian
= [tex]\frac{90\pi }{180}[/tex]
= [tex]\frac{\pi }{2}[/tex]
length of arc = 18/π x π/2
= 9
If the nth term of a sequence is 18-8n what is the 8th term
Answer:
[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]
Answer:
-46
Step-by-step explanation:
(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :) )
We know that the nth term of the sequence is 18 - 8n
the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value} )
18 - 8n is sequence
18 - 8(8) is 8th term
18 - 64 is 8th term
-46 is the 8th term
hope this helps!! :)
Given the following formula,A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the desktop computers cost $225 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy n notebooks and dd desktop computers?
Total cost, 18 notebooks and 12 desktop computers:
Total cost, n notebooks and dd desktop computers:
The cost to buy 18 notebooks and 12 desktop computers will be $8100.
The cost to buy n notebooks and d desktop computers will be 300n + 225d
What is the cost of a given material?The cost of a given material is the amount attached and to be paid for getting that material.
From the given information:
The cost of notebook computers = $300The cost of desktop computers is $225 eachThe cost to buy 18 notebooks and 12 desktop computers will be:
= 300(18) + 225(12)
= 5400 + 2700
= $8100
The cost to buy n notebooks and d desktop computers will be:
= 300(n) + 225(d)
= 300n + 225d
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Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1.
A. (3, 0)
B. (6, -4)
C. (0, 1)
D. (3, -1)
Answer: (3,-1)
Step-by-step explanation:
distance between R & S x values: 9
distance between R & S y values: -6
multiply each by 2/3 (the proportion)
9/1 x 2/3 = 6; -6/1 x 2/3= -4
add the answers to R x & y values:
-3 + 6= 3; 3 - 4= -1
Answer:
D
Step-by-step explanation:
using the section formula
(x₁, y₁ ) and (x₂, y₂ ) divided in the ratio m : n , then
point = ([tex]\frac{mx_{2}+nx_{1} }{m+n}[/tex] , [tex]\frac{my_{2}+ny_{1} }{m+n}[/tex] )
thus for R (- 3, 3 ) and S (6, - 3 ) in the ratio 2 : 1
Q = ( [tex]\frac{2(6)+1(-3)}{2+1}[/tex] , [tex]\frac{2(-3)+1(3)}{2+1}[/tex] )
= ( [tex]\frac{12-3}{3}[/tex] , [tex]\frac{-6+3}{3}[/tex] )
= ( [tex]\frac{9}{3}[/tex] , [tex]\frac{-3}{3}[/tex] )
= (3, - 1 )
Kit and Kat are building a kite for the big kite festival. Kit has already
cut his sticks for the diagonals. He wants to position P so that he will
have maximum kite area. He asks Kat for advice. What should Kat
tell him?
Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
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divided it by 7 and added
divided it by 7 and added 25. the result was 34 what was my number?
25. the result was 34 what was my number?
Answer:
your questions is not clear but from my observations
let the number be x
x/7+25=34
x+175/7=34
x+175=238
x=238-175
×=63
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