Answers
Answer:
The answer is 3.
[tex]\longrightarrow{\purple{3}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]
[tex] \\= \frac{(a + b)(6a + b - 7b)}{2( {a}^{2} - {b}^{2}) } [/tex]
[tex] \\= \frac{(a + b)(6a + b - 7b)}{2(a + b)(a - b)} [/tex]
[tex] \\= \frac{6a - 6b}{2(a - b)} [/tex]
[tex] \\= \frac{6(a - b)}{2(a - b)} [/tex]
[tex] \\= 3[/tex]
( OR )
[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]
[tex] \\= \frac{6 {a}^{2} + 6ab + ab + {b}^{2} - 7ab - 7 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} + 7ab - 7ab }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6( {a}^{2} - {b}^{2} )}{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6}{2} [/tex]
[tex] \\= 3[/tex]
Note:[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♬}}}}}[/tex]
Related Questions
Question is in photo.
Thanks
Answers
Answer:
what do you mean for this question. What do you need help on?
A 68-year old retiree has a pension savings of $51,000, a 401k of $58,000, and an IRA account of $68,000. Before 2008, he had 2% more cash in the pension, 12% more in the IRA, and −1% in the 401k. He wants to take out 2% from each account before he turns 72, which will cost him a penalty of an extra 1% from the pension, 2% from the 401k, and 6% from the IRA. What is the relevant information for the amount that the retiree will have in his pension if he doesn't take money out now?
A: The retiree had 2% more cash in the pension in 2008
B: The retiree has a pension savings of $51,000
C: The retiree has a 401k of $58,000
D: The retiree has an IRA account of $68,000
Answers
Answer:
B: The retiree has a pension savings of $51,000
Step-by-step explanation:
Montserrat is training for her first race. In her first training week she runs 3 km, and in the second training week she runs 3.5 km. Every week she runs 0.5 km more than the previous one.
a Find how many kilometres Montserrat runs in her 10th training week.
b Calculate the total number of kilometres that Montserrat will have run by her 15th training week.
Answers
Answer:8
Step-by-step explanation:
0.5*10=5
3+5=8
a. Montserrat runs 7.5 kilometers in her 10th training week.
b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.
To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:
[tex]a_n = a_1 + (n - 1) * d[/tex]
where:
[tex]a_n[/tex] is the nth term (the number of kilometers in the nth week),
[tex]a_1[/tex] is the first term (the number of kilometers in the first week, which is 3 km),
n is the number of weeks (in this case, 10), and
d is the common difference (the amount by which the distance increases each week, which is 0.5 km).
[tex]a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km[/tex]
So, Montserrat runs 7.5 kilometers in her 10th training week.
b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:
[tex]S_n = (n / 2) * (a_1 + a_n)[/tex]
where:
[tex]S_n[/tex] is the sum of the first n terms (the total number of kilometers run by the nth week),
[tex]a_1[/tex] is the first term (3 km),
[tex]a_n[/tex] is the nth term (which we found to be 7.5 km in her 10th week),
n is the number of weeks (15 in this case).
[tex]S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km[/tex]
So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.
To know more about training:
https://brainly.com/question/28942187
#SPJ3
If f(x)=2x2+3x−6, determine the value of f(2)
Answers
Answer: 4
2x2+3(2)−6
lets make sure we do OOO (order of operations correctly)
2x2+3(2)−6
4+3(2)−6
4+6−6
10−6
4
Step-by-step explanation:
The coordinates of point C are . The slope of is . The possible coordinates of point D are and .
Answers
Answer:
The answer is below
Step-by-step explanation:
The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.
The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .
Solution:
Since CD is the perpendicular bisector of AC, hence line CD is perpendicular to AB and divides line AB into two equal parts.
Point C(x, y) is the midpoint of AB.
hence:
x = (2 + 8) / 2 = 5
y = (3 + 1)/2 = 2
The coordinates of point C = (5, 2)
The slope of line AB is:
slope of AB = (1 - 3) / (8 - 2) = -1/3
Since CD is perpendicular to AB, hence the product of the slope of AB and the slope of CD is -1
slope of AB * slope of CD = -1
slope of CD * -1/3 = -1
slope of CD = 3
Line CD has slope of 3 and pass through C(5, 2). The equation of line CD is:
y - 2 = 3(x - 5)
y = 3x - 13
The possible coordinates of point D are (6, 5) and (4, -1), because this point lie on line CD.
Solve for x.
3x + 7
2x + 3)
Answers
Answer: x = 34
Step-by-step explanation:
2x+3+3x+7=180
5x+10=180
5x=170
x = 34
(b) Find the coordinate of the foot of the perpendicular from (4,-2) to line 2x-3y-4=0
Answers
Answer:
{3,-1}Step-by-step explanation:
[tex]carry\: on \: learning[/tex]
i need help asap Please
Answers
Answer: F. is a linear relation.
Step-by-step explanation:
Answer:
G
Step-by-step explanation:
Equation of the eventual line:
(y-4)/(5-4) = x
y-4 = x
y = x + 4
this equation can’t be used to determine the last three values. In fact, for examples:
7 = 2 + 4
7 = 6 (false)
So the relation is non linear
A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?
Answers
Answer:
The rate (or speed) of the wind is 40 meters per minute.
Step-by-step explanation:
Let's define:
S = speed (or rate) of the duck alone
S' = speed (or rate) of the wind.
When the duck travels with the wind, its speed is:
(S + S')
While when the duck travels against the wind, its speed is:
(S - S')
Also, remember the relation:
Distance = Speed*Time
ok, we know that the duck can travel a distance of 2400 m in 10 minutes with the wind, then:
2400m = (S + S')*10 min
And against the wind, it can travel 2/3 of that distance, then we can write:
(2/3)*2400m = (S - S')*10 min
Then we have a system of 2 equations:
2400m = (S + S')*10 min
(2/3)*2400m = (S - S')*10 min
We want to find the speed of the wind, then we want to find the value of S'.
To solve this, we first need to isolate S in one of the equations.
Let's isolate S in the first one:
2400m = (S + S')*10 min
2400m/10min = (S + S')
240 m/min = S + S'
240 m/min - S' = S
Now we can replace this in the other equation:
(2/3)*2400m = (S - S')*10 min
(2/3)*2400m = ( 240 m/min - S' - S')*10 min
Now let's solve this for S'
(2/3)*2400m/10min = 240 m/min - 2*S'
(2/3)*240 m/min = 240 m/min - 2*S'
2*S' = 240 m/min - (2/3)*240 m/min
2*S' = (1/3)*240 m/min
2*S' = 80 m/min
S' = (80 m/min)/2
S' = 40 m/min
The rate (or speed) of the wind is 40 meters per minute.
What are biofertilisiers
Answers
☆ Bio fertilizer :- Biofertilisers are organisms that enrich the nutrient quality of the soil. The main source f biofertilizers are bacteria, fungi and cyanobacteria.
HOPE IT HELPS ❣️The tile along the edge of a triangular community pool needs to be replaced. A right triangles, where the hypotenuse is labeled 8 x squared, the height is labeled 4 x squared + 15, and the base is labeled 8 x + 10. Which expression represents the total perimeter of the pool edge? 12x2 + 15 20x2 + 25 12x2 + 8x + 25 24x2 + 16x + 50
Answers
Answer:
C. 12x² + 8x + 25
Step-by-step explanation:
A. 12x² + 15
B. 20x² + 25
C. 12x² + 8x + 25
D. 24x² + 16x + 50
Hypotenuse = 8x²
Height = 4x² + 15
Base = 8x + 10
Perimeter of the triangle = hypotenuse + height + base
= 8x² + (4x² + 15) + (8x + 10)
= 8x² + 4x² + 15 + 8x + 10
Perimeter of the triangle = 12x² + 8x + 25
C. 12x² + 8x + 25
Answer:The answer is C
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
5
5
A. Infinitely many
B. One
C. Two
D. Zero
Answers
Answer:B
Step-by-step explanation:
simple, there is one point of intersection or where the lines meet
Answer:
B: One solution
Step-by-step explanation:
The graphs show that the two lines intersect at one point. This point represents the ONE solution of this system of equations.
If the lines did not intersect, the system would have no solution.
If the lines coincide, the system would have infinitely many solutions.
The theater sells two types of tickets: adult tickets for $18 and
child tickets for $9.
Last night, the theater sold a total of 221 tickets for a total of
$2466. How many adult tickets did the theater sell last night?
Answers
The answer to your question is 137
A group of people were asked if they had run a red light in the last year where 140 responded "yes," and 208 responded "no." If a person is randomly chosen, find the probability that he/she has run a red light in the last year. Give your answer as a fraction or decimal.
Answers
Answer:
35/87
Step-by-step explanation:
To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.
The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87
Find the length of the missing side
Answers
Answer:
25 in and 9 cm
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the missing side
A
x² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )
x = [tex]\sqrt{625}[/tex] = 25
B
x² + 12² = 15²
x² + 144 = 225 ( subtract 144 from both sides )
x² = 81 ( take square root of both sides )
x = [tex]\sqrt{81}[/tex] = 9
Answer:
A) [tex]\sqrt{7^{2} +24^{2} }[/tex] = 25
B) [tex]15^{2} -12^{2} = B^{2}[/tex]
[tex]B^{2} =81\\[/tex]
B = 9
Step-by-step explanation:
Application: Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?
Answers
Step-by-step explanation:
Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.
A piece of ribbon is x inches long. Find the total length of 7 equal pieces of ribbon. Express the answer in terms of x.
Answers
Answer:
7x
or 7*x
Step-by-step explanation:
How many kilograms equals 984.2 grams?
Answers
how do i solve for x? thank you!
Answers
Answer:
[tex]x = \frac{7}{2}[/tex]
Step-by-step explanation:
[tex]6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }[/tex] [tex][ \ a^x \times a^ y = a^{x+ y} \ ][/tex]
[tex]x - 1 = 2 + \frac{1}{2}[/tex] [tex][ \ b^x = b^y => x = y \ ][/tex]
[tex]x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}[/tex]
Answer:
x = 3.5
Step-by-step explanation
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] and [tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]
Then
36[tex]\sqrt{6}[/tex] = 6² × [tex]6^{\frac{1}{2} }[/tex] = [tex]6^{(2+0.5)}[/tex] = [tex]6^{2.5}[/tex]
Thus
[tex]6^{x-1}[/tex] = [tex]6^{2.5}[/tex]
Since the bases on both sides are equal, both 6, equate the exponents
x - 1 = 2.5 ( add 1 to both sides )
x = 3.5
0lease help I would really appreciate
Answers
Step-by-step explanation:
a)50°
b)75°
c)125°
d)d=40°
Answer:
Step-by-step explanation:
A)180-(60+70)=50
C)180-30=150 150/2=75
B)180-(35+20)=125
D)2d+d+60=180
3d+60=180
3d=120 ; d=40 ; 2d=40×2=80
Consider the graph. Which inequality best represents the graph?
Answers
Answer:
y >= x/2 - 1
Step-by-step explanation:
the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form
y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.
Solve for x. Round to the nearest tenth, if necessary.
K
L
99
х
15°
M
Answers
Answer:
x≈95,6
Step-by-step explanation:
x= cos 15⁰ x 99 ≈95,6
PLS HELP GIVING BRAINLIEST
Answers
Answer:
1. reflection- a figure is flipped over
2. translation- a figure is slide
3. rotation- a figure is turned
2. translation—> a figure is slid
3. Rotation—> a figure is turned
Hope this helps!
translate the sentence into an inequality
the sum of 2 and y is greater than 16
Answers
Answer:
2 + y > 16
Step-by-step explanation:
the sum of 2 and y is greater than 16
2 + y > 16
2 + y > 16
What is the amount of material required to creat a Toblerone box? The triangular base is equilateral.
Answers
Answer:
21 x 3.1 / 2 = 32.55
Step-by-step explanation:
Simplify (4x - 6) - (3x + 6).
Ox- 12
O -X- 12
Ox+ 12
0-x + 12
Answers
Answer:
Ox-12
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
(4x - 6) - (3x + 6) Remove the brackets
4x - 6 - 3x - 6 Collect like terms
4x - 3x - 6 -6
x - 12
The answer is A
help please on all of these
Answers
the answer is on the picture
what should I do if I accidentally break my pet rock that has googly eyes on him? i need to fix Rocky Ronny McRonkster
Answers
Answer:
Try to glue it back together
Step-by-step explanation:
I heard gorilla glue works, but be careful and don't get the glue on your body. If that happens it can cause irritation and call posion control immediately.
What is the relationship between the diameter d and circumference c of a circle
Answers
Answer:
π × d
Step-by-step explanation:
The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option
solve for " x "
[tex]x = 42 - 9[/tex]
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]x = 42 - 9[/tex]
➼[tex]\:x = 33[/tex]
Therefore, the value of [tex]x[/tex] is 33.
[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]
Answer:
x =33
Step-by-step explanation:
x = 42-9
We are solving for x, which is already isolated
42-9 = 33
x = 33
Check 33+9 = 42