(1/2a - 2/3b) ( 3/5a + 2/3b) multiply the following ​

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex](\dfrac{1}{2}a-\dfrac{2}{3}b)(\dfrac{3}{5}a+\dfrac{2}{3}b)=\dfrac{1}{2}a*(\dfrac{3}{5}a+\dfrac{2}{3}b) - \dfrac{2}{3}b*(\dfrac{3}{5}a+\dfrac{2}{3}b) \\\\\\= \dfrac{1}{2}a*\dfrac{3}{5}a + (\dfrac{1}{2}a*\dfrac{2}{3}b) - \dfrac{2}{3}b*\dfrac{3}{5}a- \dfrac{2}{3}b*\dfrac{2}{3}b\\\\\\=\dfrac{3}{10}a^{2} + \dfrac{1}{3}ab - \dfrac{2}{5}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2} +\dfrac{1*5}{3*5}ab-\dfrac{2*3}{5*3}-\dfrac{4}{9}b^{2}\\\\\\[/tex]

[tex]=\dfrac{3}{10}a^{2}+\dfrac{5}{15}ab-\dfrac{6}{15}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2}-\dfrac{1}{15}-\dfrac{4}{9}b^{2}[/tex]


Related Questions

pls help!!! i will give brainliest!!!!! :D

Answers

the answer equals 29.

Answer:

31 cm

Step-by-step explanation:

the scatterplot is rising, so based on an assumption of where a line going through the scatterplot is going to go, you get 41

A contractor bought 12.6 ft? of sheet metal. He has used 2.1 ft? so far and has $210 worth of sheet metal remaining. The equation 12.6x-2.1x = 210 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?​

Answers

Answer:

$20

Step-by-step explanation:

12.6x-2.1x=210

10.5x=210

x=210/10.5

x=20

can someone pls help me

Answers

Answer:10 & 12

Step-by-step explanation:

Answer:

The 5th step will need 32 blocks, and the 6th step will need 64 blocks.

Step-by-step explanation:

Each step requires the blocks to be doubled. The first step has two, 2x2 is 4. There are 4 blocks in the next step. 4x2 is 8. There are 8 blocks in the next step, and so on and so forth. Just multiply by 2. Hope this helped!

I NEED HELP PLEASE!!!!

Answers

Answer:

the answer is x=15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

since angles 84 and 5x + 9 are alternate interior angles they both are equal

i.e

5x +9 = 84

5x = 84 -9

5x = 75

x = 75/5

therefore x = 15

keep smiling

The domine of definition of the function
[tex]f(x) = \frac{1}{ \sqrt{ |\cos(x)| + \cos(x) }} \: is \\ [/tex]

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

Given function is

[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]

Now,

[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]

We know,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]

So, from graph we concluded that cosx > 0 in the following intervals.

[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]

So, if we generalized this we get

[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]

Hence,

Domain of the function is

[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]

[tex]\textsf{More to know :-} \\[/tex]

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]

Find the slope of the line that passes through (1, 2) and (10, 10).

Answers

Slope m = 8 / 9 = 0.88889

Hope it helps!

Please mark Brainliest if you want to :)

neeeeeeed heeeeeelp pleaseeeeeeeee

Answers

Answer:

D

Step-by-step explanation:

Hope this is correct and helps

Answer:

D

Step-by-step explanation:

I'm not completely sure but A is constant cuz it don't move B is increasing C is same as A and D Is decreased

You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles​

Answers

Answer: f(x) = 1.19x, where f(x) is the total cost, and x is the cost per bottle

Cost of 15 bottles: $17.85

Step-by-step explanation:

This question describes a straightforward relation between cost per bottle, and cost for all the bottles.  As such, simply equate one variable to the value of one bottle, and f(x) as the value of every bottle.

Hope it helps :) and let me know if you want me to elaborate.

P.S. f(x) can simply be substituted for "y"

Cost of each bottle=1.19$

Let

no of bottles be x

.The function is given by

[tex]\\ \sf\longmapsto f(x)=1.19x[/tex]

Now

Bottles=15

Cost:-

[tex]\\ \sf\longmapsto f(15)[/tex]

[tex]\\ \sf\longmapsto 1.19(15)[/tex]

[tex]\\ \sf\longmapsto 17.89[/tex]

If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?​

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

Given:

[tex] \rm \longmapsto x = a \sin \alpha \cos \beta [/tex]

[tex] \rm \longmapsto y = b \sin \alpha \sin \beta [/tex]

[tex] \rm \longmapsto z = c\cos \alpha[/tex]

Therefore:

[tex] \rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta [/tex]

[tex] \rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta [/tex]

[tex] \rm \longmapsto \dfrac{z}{c} = \cos \alpha[/tex]

Now:

[tex] \rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } [/tex]

[tex] \rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha [/tex]

[tex] \rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha [/tex]

[tex] \rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha [/tex]

[tex] \rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha [/tex]

[tex] \rm = 1[/tex]

Therefore:

[tex] \rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1[/tex]

Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.​​

Answers

Hello haohaoxNienie!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]

Refer to the attached picture.

Steps :-First find the divisor using the given information (x = - 4).Now, divide x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8 by x + 4.We'll get the remainder as 0.Using the remainder theorem & solving it, we'll get LHS & RHS as 0.Hence proved.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

__________________

Hope it'll help you!

ℓu¢αzz ッ

HELP PLS MARKING BRAINLEIST

Answers

Answer:

1

Step-by-step explanation:

5/5=1

Answer:

4/5

Step-by-step explanation:

You move up four on the y-axis and over 5 on the x-axis and it would meet the next point

Hope this Helps

What is the common difference in the sequence?

Answers

The common difference is the amount between each number in an arithmetic sequence.

For example, the sequence 4,7,10,13,... has a common difference of 3.

01.01 LC)Look at the following numbers: −4, −5, 0, 5 Which pair of numbers has a sum of zero? 5, −5 −5, 0 −4, 5 −4, 0

Answers

Answer:

5, -5

hope this helps

Answer:

Train to BaDussy

Step-by-step explanation:

Freddy bought 3 bags of pebbles to put in his fish tank. Each bag contains 295 pebbles. After he put the right amount of pebbles in his fish tank, he had 104 pebbles left over. How many pebbles did he put in his fish tank?

Answers

295 x 3 = 885

885-104 = 781

781 pebbles

Someone help me and answer these ASAP PLS

1. What are the three major responsibilities of the county commissioners?

2. What are the three major responsibilities of the county sheriff?

3. What is the fundamental purpose for county government?

Answers

Answer:

1. The powers include: budgeting and appropriation of funds for all county activities; building and maintaining county roads; making and enforcing civil and criminal resolutions and ordinances not in conflict with state law, including those for land use and building construction; supporting and implementing.

2. Serves as a licensed peace officer and is responsible for enforcing the criminal laws of the state. Manages and operates the county jail. Provides security for the courts.

3. County governments perform essential administrative functions such as registering voters, supervising elections, keeping records, providing police protection, and administrating health and welfare services.

Step-by-step explanation:

Help pls and show your work!

Answers

1. Turn 1 1/3 into an improper fraction.
2. Now you have 4/3 + 5/6.
3. The LCD of 3 and 6 is 6. Convert 4/3 into 8/6. We multiplied 4/3 by 2 to get the denominator of 6.
4. 8/5 + 5/6 = 13/6

If a line has a slope of 4 and a y-intercept of 3, what is the equation of that line in slope-intercept from???

Answers

Answer:

y=3x-4

Step-by-step explanation:

Please help!!

9.(05.02)
Solve the following system of equations: (5 points)
x - 2y = 5
2x - 4y = 10

Infinitely many solutions

No solutions

(0, 0)

(5, 10)

Answers

Answer:

Infinite solutions

Step-by-step explanation:

If you look at the equation, you will see that if you multiply everything by two (On the 1st equation), you get the 2nd equation. This means that the lines are the same, so infinite solutions.

Step-by-step explanation:

infinitely many solutions :)

Find the area of this triangle.

Answers

Answer:

84 cm²

Step-by-step explanation:

Area triangle = 1/2(b x h)

Area = 1/2(21 x 8)

Area = 1/2(168)

Area = 84

84 cm²

-Chetan K

Questions linked below

Answers

Answer:

The blur of the photo I do not understand sorry

Step-by-step explanation:

ty for the points

Describe the translation of the point to its image. (-2,-3) to (-2,4)

Answers

Up 8 Units, Hope this helps :)

Help me!
A 180
B 115
C 65

Answers

Answer:

ik this

Step-by-step explanation:

i believe its 180

Answer: B) 115

Step-by-step explanation: i hop this help if not sorry :(

Directions: Follow the instructions for the following inequalities. Will give brainlist!


1. 4<7 Multiply both sides by 7, then by 6, then by 3, then by 10

2. 11>-2 Add 5 to both sides, then add 3, then add (-4)

3. -4<-2 Subtract 6 from both sides, then 8, and then 2

4. -8<8 Divide both sides by -4, then by -2

5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

Answers

1) 4<7

×7 ×7

28<49

×6 ×6

168<294

×3 ×3

504<882

×10 ×10

5040<8820

2) 11>-2

+5 +5

16> 3

+3 +3

19>6

+-4 +-4

15>2

3) -4<-2

-6 -6

-10<-8

-8 -8

-18<-16

-2 -2

-20<-18

4) -8<8

÷-4 ÷-4

2<-2

÷-2 ÷-2

-1< 1

5) ~The affect of the inequality sign didn't change. If you add or subtract the same positive or negative number to both sides of an inequality or an equation, the inequality stays the same. If you multiply or divide both sides of an inequality or an equation by the same positive number, the inequality stays the same. This is because when manipulating inequalities there are rules this if a < b then a + c < b + c so we get a new number that replaces a and b yet the inequality symbol stays the same so a still is smaller than b.

Hope this helped you- have a good day bro cya)

helpppppppp plzzzzzzzzzzzzzzzzz (ANSWER ONLY IF YOU KNOW)

Answers

Answer:

1/7 ( a+1 )

Step-by-step explanation:

1/7a + 1/7

1/7 ( a+1 )

find the sum of the first seven terms -3,3,-3,3.
Show your work.

Answers

-3 as there are 3(-3+3) -3 meaning 3(0) -3 so therefore just -3

Two sides of an equilateral triangle are labeled 12 inches and 3x - 6 inches. Find x.

Answers

Answer:

6

Step-by-step explanation:

In equilateral triangle, all the sides are congruent.

3x - 6 = 12

Add 6 to both sides

3x = 12 + 6

3x = 18

Divide both sides by 3

x = 18/3

x = 6

(6d+5)−(2−3d) find the difference

Answers

9d+3 that’s the answer I think though try it

Answer:

10d

Step-by-step explanation:

6d+5 =11d

2-3d = -1d

11d-1d= 10d

Factorize; x cubed - x squared y ?
ASAP, please

Answers

Answer:

x²(x - y)

Step-by-step explanation:

x³ - x²y ( x² is common to both terms so factor it out )

= x²(x - y)

Kent has already saved $150 and he plans to save $20 every week. Proportional or Non-proportional

Answers

Answer:

this problem is  Non-proportional

Step-by-step explanation:

hope this helps

A flock of birds perched on a tree. In the morning, each bird perched 1 tree and 1 bird left. In the afternoon, 2 chicks perched, 1 tree left over. Ask how many birds, how many trees?

Answers

Answer:

2 birds 1 tree

Step-by-step explanation:

I think only not sure

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