[tex](a + b) {}^{2} [/tex]
Expand this expression.​

Answers

Answer 1

Answer:

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

Step-by-step explanation:

[tex](a + b) {}^{2} = (a + b)(a + b) = {a}^{2} + ab + ab + {b}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

Answer 2

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

a^2+2ab+b^2

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

Remember the rule for expanding a binomial squared.

[tex]\twoheadrightarrow\sf (a+b)^2=a^2+2ab+b^2[/tex]

So we square the first term, then multiply the product of the two terms times 2.

[tex]\twoheadrightarrow\sf a^2+2ab+b^2[/tex]

This is our answer.

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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Related Questions

A water ride with heights above and below the starting point can be modeled by the function y = 3 sin ⁡ ( π 2 ( x + 3 ) − 2 ) . Within the interval 0 < x < 5 , when does the ride have a height 1 foot below the starting point?

Answers

The value of x for a height 1 foot below the starting point will be the negative 2.76.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A water ride with heights above and below the starting point can be modeled by the function is given below.

y = 3 sin⁡ (π / 2 (x + 3) − 2), Within the interval 0 < x < 5

We know that π / 2 = 90°

Then the value of x for a height 1 foot below the starting point will be

           1 = 3 sin⁡ (90 (x + 3) − 2)

        1/3 = sin⁡ (90 (x + 3) − 2)

   19.47 = 90 (x + 3) − 2

   21.47 = 90 (x + 3)

0.2385 = x + 3

          x = -2.76

Then the value of x will be the negative 2.76.

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The driving distance from Seattle to Portland is 175 miles. Your car gets 25 miles per gallon. If gasoline is $2.80 per gallon, how much will the round trip from Seattle to Portland and back cost in dollars?

Answers

Answer:

$980

Step-by-step explanation:

Given the cost of gasoline = $2.80/mile

Total Distance = 175miles x 2 (Back and forth)

= 350 miles

Total Cost = Cost of gasoline x Total Distance =

= $2.80 x 350

= $980

The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The driving distance from Seattle to Portland is 175 miles.

Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Now,

Since, The driving distance from Seattle to Portland is 175 miles.

Hence, The total distance from Seattle to Portland and back = 175 + 175

                                                                                            = 350 miles

And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Hence, The cost of gallon = 350/25 x $2.50

                                        = 100 x $2.50

                                        = $250

Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

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Which set of values could be the side lengths of a 30-60-90 triangle?

Answers

Answer is B.

Step-by-step explanation:

Since we know that in 30-60-90 triangle, the side corresponding to angle 90 degrees is two times the length of side corresponding to 30 degree angle. The length of side corresponding to 60 degree angle is  times the length corresponding to 30 degree angle.

We can see from our given choices that the side corresponding to 30 degree angle is 5 units.  

Therefore, the side lengths of a 30-60-90 triangle will be  and option B is the correct choice.  





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if x=-2 solve 4x^3-6x^2+x-1​

Answers

Answer:

-59

Step-by-step explanation:

x = -2

4(-2)³ - 6(-2)² + (-2) - 1

= -32 - 24 - 2 - 1

= - 59

What the person above said is correct

how do you simplify

−(12st3+34s3t+t2−1)

Answers

Answer:

-34s^3t - 12st^3 - t^2 + 1

Step-by-step explanation:

hope this helps

What is the inverse of the function f(x) = 2x + 1?

Answers

Answer:

[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]

Step-by-step explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]

PS. change design according the local requirements.

Answer:

[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]

Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

If m∠1 = 72º, then find the value of m∠2. vertical angles

Answers

If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º

What are vertical angles?

Angles angle are angles that are equal to equal to each other in a line geometry.

Given the following parameters

m∠1 = 72º,

If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º

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Evaluate and simplify the expression when a=4 and b=-1 5 - 2(a + 3b)/2

Answers

Answer:

4

Step-by-step explanation:

We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.

[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]

Find an angle between zero and 360 that is coterminal with 900°

Answers

Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard​

Answers

Answer:

here you go

Step-by-step explanation:

no of times he failed = -3

points he losed = -3 x 4 = -12

no of times he need to hit the target to get 48 points = 6x

equation

-12 + 6x = 48

6x = 60

x = 10

no of points he  will  gain = 10 x 6 = 60

Which of the following probabilities is the greatest for a standard normal distribution? P (negative 1.5 less-than-or-equal-to z less-than-or-equal-to negative 0.5) P (negative 0.5 less-than-or-equal-to z less-than-or-equal-to 0.5) P (0.5 less-than-or-equal-to z less-than-or-equal-to 1.5) P (1.5 less-than-or-equal-to z less-than-or-equal-to 2.5)

Answers

The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

What is a normal distribution?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a statement:

Which of the following probabilities is the greatest for a standard normal distribution:

The options are:

P(-1.5 ≤ z ≤ -0.5)

P(-0.5 ≤ z ≤ 0.5)

P(0.5 ≤ z ≤ 1.5)

P(1.5 ≤ z ≤ 2.5)

As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.

From the Z-curve:

P(-1.5 ≤ z ≤ -0.5)  = 9.2% + 15% = 24.2%

P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%

P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%

P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%

Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

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Answer:

B) P (-0.5 <= z <= 0.5)

Step-by-step explanation:

28.6% of city employees ride the bus to work. Last year, 29.7% of city employees rode the bus to work. What is the relative change from last year to this year?
(Express your answer rounded correctly to the nearest tenth of a percent!)

Answers

A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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3x + 4 divided by 2 = 9.5

Answers

2.5 is your answer because first we divide the numbers then subtract 2 from both sides and simplify

Answer:

2.5

Step-by-step explanation:

First divide 4 by 2

Second, you want x on a side by itself. So you would move 2 over to 9.5. But since 2 is positive, you would subtract 2 from 9.5

Third, you need to get x by itself. So you would divide by 3 on both sides because division cancels out multiplication which is what 3x is. And then you end up with 2.5

3x + 4 / 2 = 9.5

3x + 2 = 9.5

3x = 7.5

3x/3 = 905/3

x = 2.5

And if you want to check it, just substitute 2.5 for x

3(2.5) + 4 / 2 = 9.5

7.5 + 4 / 2 = 9.5

7.5 + 2 = 9.5

9.5 = 9.5

Given 4 c 5 not-equals 0 and c is a real number, what is the multiplicative inverse of 4 c 5 not-equals 0 0 1 startfraction 1 over 4 c 5 end fraction startfraction 1 over 4 c endfraction 5

Answers

The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

Complete question

Given 4c + 5 ≠ 0 and c is a real number, what is the multiplicative inverse of 4c + 5

How to determine the multiplicative inverse?

The expression is given as:

4c + 5

The multiplicative inverse of an expression x is 1/x

This means that:

The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

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Find the domain of the function y = 3 tan(2/3x)

Answers

Answer:

{x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

Step-by-step explanation:

Given the function y=3tan(2/3x)

We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers

Also, the roots of y=3tan(2/3x) is [tex]3\pi n/2[/tex] where n is an integer

Note that the domain of the function cannot be within [tex]3\pi n/2[/tex]

Therefore, {x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

please answer just look at how many points i will give

Answers

Answer:

(6,2)

Step-by-step explanation:

When solving a system of simultaneous equations, we want to see where the graphs intersect.

2x+5y =22 is the red line

x+y = 8 is the green line

They intersect at a point

The point is x=6   y=2

(6,2)

Which equation is made true by the opposite angles theorem? A. 40 − 2x = 85 + y B. x − 8 = 40 − 2x C. x − 8 = 3y − 15 D. 3y − 15 = 85 + y

Answers

Option B. x-8 = 40-2x is the correct equation for the opposite angle theorem.

According to the Opposite angles theorem,

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.


[tex]= > x-8=40-2x[/tex] ( : Because opposite vertex angles are equal)

So option B is correct in the given question

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Answer:

D.) 3y-15 =85+

Step-by-step explanation:

simply put, opposite angles theorem is where the angles are on the opposite side so the parallelogram in the photo shows that 3y-15 is on the opposite angle as 85+y (I also got this one right lol)

graph x=4y , x+y=7.0

Answers

Answer:

First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.

After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.

Side note: Not sure how credentials work on Quora yet. I meant to say I am a student

The equation of the lines can be plotted on the graph after calculating the coordinates on each line.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equation:

x = 4y  

x + y = 7.0

To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.

For the equation of line:

x = 4y

x 0 1 2 3 -1 -2 -3

y 0 4 8 12 -4 -8 -12

For the equation of line:

x + y = 7.0

x 0 1 2 3 -1 -2 -3

y 7 6 5 4 8 9 10

Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.

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The standard deviation for a set of data is 9.5. The mean is 205.

What is the margin of error?

Answers

If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Margin of error

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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Complete the following statement of congruence:
A. TRS
B. RTS
C. STR
D. RST

Answers

Answer:

B. △RTS

Step-by-step explanation:

△MON ≅ △RTS

The system of equations y = one-fourth x minus 1 and y = negative one-half x minus one-fourth is shown on the graph below.


On a coordinate plane, 2 lines intersect at (1, negative three-fourths).

Answers

The solution of the system of equations is (1, -3/4)

How to solve the system of equations?

Here we have the system of equations:

y = (1/4)*x - 1

y = -(1/2)*x - 1/4

To solve it, we use the fact that the variable "y" is the same in both equations, then we can write:

(1/4)*x - 1 = -(1/2)*x - 1/4

Now we can solve that for x:

(1/4)*x - 1 = -(1/2)*x - 1/4

(1/4)*x + (1/2)*x = 1 - 1/4

(1/4)*x + (2/4)*x =  1 - 1/4

(3/4)*x = 3/4

x = 1

To get the y-value of the solution, we just evaluate x = 1 in any of the two given lines, using the first one:

y =  (1/4)*(1) - 1 = -3/4

So the solution is (1, -3/4)

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5 hundreds minus 4 tens?*​

Answers

Answer:

460

Step-by-step explanation:

4 tens is equivalent to 40, so 500-40 is = to 460.

Hope this helps! :D

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

[tex]\large \bold {ANSWER}[/tex]

[tex]\large \boxed { \large \sf \green{460}}[/tex]

[tex]\large \bold {SOLUTION}[/tex]

5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.

500 - 40 = 460

So 5 hundreds minus 4 tens is 460.

Which rational number is equivalent to 5.5?

Answers

Answer:

11/2

Step-by-step explanation:

Multiply by 2/2 to remove the decimal.

5.5 can be written as 5 1/2 or 55/10 or 11/2

If a household is saving 30% of their total bi-weekly gross pay of $2,051.00, determine how many months it will take to save a 20% down payment and 1.5% for closing costs for a property with a purchase price of $281,700.00.
45

46

54

55

(25 POINTS)

Answers

Based on the amount saved per week and the down payment of the property, the number of months it will take to save the amount is 46 months.

How long will it take for the family to save the amount?

First, find out the amount saved per month:

= (30% x 2,051) x 2 payments a month

= $1,230.60

The downpayment is:

= 281,700 x 20%

= $56,340

The closing cost is:

= 1.15 x 56,230

= $843.45

The number of months till the amount is saved is:

= (56,340 + 843.45) / 1,230.60

= 46 months

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Darrel divided 8,675 by 87. His work is shown below
Which answer choice correctly identifies the error Darrel made when dividing?
a b c or d?

Answers

C. He forgot to place a zero in the quotient.

see attachment:

What’s the answer ?

Answers

Answer:

a ) cylinder

b) triangular pyramid

Graph h(x) = 6|x| -4

Answers

Answer:

The graphs below have the same shapes. What is the equation for the red graph?

Answers

The equation for the red graph is f(x)=-x^2.

The question is an incomplete graph of a function is missing

For a complete question refer to the graph attached below

we have [tex]g(x)=4-x^2[/tex]

The vertex of the function g(x) is the point (0,4)

The vertex of the function f(x) is the point (0,0)

What is the vertex?

This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

So, the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

The translation is 4 units down

The equation of the function f(x) is

[tex]f(x)=g(x)-4[/tex]

[tex]f(x)=(4-x^2)-4[/tex]

[tex]f(x)=-x^2[/tex]

Therefore, The answer is f(x)=-x^2

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Given the function f ( x ) = x 2 − 6 x + 10 , what is the average rate of change of the function over the interval [ 4 , 8 ] ?

Answers

The rate of change of the function over the interval [ 4, 8 ] will be 6.

What is the rate of change of the function?

The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.

Given function:-

F(x) = x² - 6x + 10

The formula for calculating the rate of change will be given as:-

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

We have x₁ = 4 and x₂ = 8 given in the question

F(x₂) =  x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =

F(x₂) = 64 - 48 + 10

F(x₂) = 26

F(x₁) =  x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =

F(x₁) = 16 - 24 + 10

F(x₁) = 2

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]

Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.

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Which expression is equivalent to the given expression? 2√/20-4√6
A. 32/30
OB. 16√30
OC. 3/20
D. √120

Answers

Answer:

D.

because 2 times 120 reduced.

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