(a+b)^2-2(a+b)
Factorise (please explain)

Answer:

D) 4 8/12

Step-by-step explanation:

To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12

Step-by-step explanation:

Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)

The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets

so, the answer for the question would be "both the Sets A and B are the empty sets"

The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.

The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.

From the given information:

y = 2x + 4  --- (1)

y = 4x + 1  --- (2)

Using the slope-intercept formula:

y = mx + b

From the first equation, the slope is 2 and in the second equation, the slope is 4.

Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.

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Answer:

See below

Step-by-step explanation:

An area of  2km  x  2km = 4 km^2    

1 km = .62137 miles

2 (.62137)      x      2  (.62137)    =   1.5444 mi^2

Answer: 32 is the answer to the expression you provided.

Step-by-step explanation:

[tex]2^3\times2^2\\2\times2\times2\times2\times2\\4\times4\times2\\16\times2\\\rightarrow32[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{E}\textsf{quation:}[/tex]

[tex]\mathsf{2^3 \times 2^2}[/tex]

[tex]\huge\boxed{S}\textsf{olving:}[/tex]

[tex]\mathsf{2^3 \times 2^2}[/tex]

[tex]\mathsf{= 2\times2\times2 \times2\times2}[/tex]

[tex]\mathsf{= 4\times4\times2}[/tex]

[tex]\mathsf{= 16\times2}[/tex]

[tex]\mathsf{= 32}[/tex]

[tex]\huge\boxed{T}\textsf{herefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{32}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The number of terms in the geometric series is 9

The geometric series given as:

96 - 48 + 24 -....,-3/8 .

Calculate the common ratio (r) as follows

r = T2/T1

Substitute the known values in the above equation

r = -48/96

Evaluate

r = -0.5

The number of terms is then calculated as:

Tn = a * r^n-1

Let n = 9

So, we have:

T9 = a * r^9

Substitute the known values in the above equation

T9 = 96 * (-0.5)^8

Evaluate the product

T9 = -3/8

Hence, the number of terms in the geometric series is 9

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I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.

Hope this helps!

Answer:

Graph B

Step-by-step explanation:

Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = -12

2y = 3x + 12

y = 3/2x + 6

Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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Answer:

4/5 of the students would have protractors.

Step-by-step explanation:

The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.

According to the statement

we have given that the Sumalee sold 6 pecan cheesecakes and 12 apple

cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a

total of $285.

And we have to find that the cost each of one pecan cheesecake and one apple cheesecake.

So, for this purpose,

Let x be the cost of each pecan cheesecake.

and y be the cost of each one apple cheesecake.

Then The equation become

6x + 12y = 270  -(1)

12x + 9y = 285  -(2)

From elimination method

multiply (1) by 12 and (2) by 6 then

72x + 144y = 3240

72x + 54y = 1710

Now eliminate x from them then the equation become

90y = 1530

here y = 17

then the x become

6x + 12y = 270  

6x + 12(17) = 270  

6x = 270-204

6x = 66

and x become 11.

So, The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.

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Answer:

1.09575e+11

Step-by-step explanation:

A trapezoid is a plane figure bounded by four sides. Therefore, the required answers are given below;

a) ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) DE = 5 cm and CF = 5 cm

c) AE = 12 cm

Plane figures are shapes that are formed by straight boundaries referred to as sides. Examples include; square, rectangle, trapezium, etc.

A trapezoid is a family of quadrilaterals., these are figures that have four straight sides.

In the given question, the required answers are:

a) To prove that ΔADE = ΔBCF

Thus,

AE ⊥ DC  (given)

BC ⊥ DC  (given)

<AED = <BFC = [tex]90^{o}[/tex]

AE = BF (height of the trapozoid)

<ADE ≅ <BCF (congruent property of two triangles)

Therefore, it can be concluded that;

ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) Given that AB = 8 cm, and DC = 18 cm.

Then,

CD = DE + EF + FC

18 = DE + 8 + FC   (since EF = AB)

18 - 8 = 2 DE     (since DE = FC)

DE = 5 cm

Thus, DE = 5 cm and CF = 5 cm

c) To determine the value of AE, we have to apply the Pythagoras theorem. So that;

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]13^{2}[/tex] = [tex]AE^{2}[/tex] + [tex]5^{2}[/tex]

169 - 25 =  [tex]AE^{2}[/tex]

[tex]AE^{2}[/tex] = 144

AE = [tex]\sqrt{144}[/tex]

     = 12

AE = 12 cm

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Answer:

y > 3x + 2

Step-by-step explanation:

The slope is 3.       slope = (-7 - 2)/(-3 - 0) = -9/(-3) = 3

The y-intercept is 2.

The equation of the line is y = 3x + 2

The shading is "above" the line.

Answer: y > 3x + 2

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]

▪ [tex] \sf{Area = 72 yd^2}[/tex]

▪ [tex] \sf{BD = 6yd}[/tex]

[tex]\leadsto[/tex] Substitute the values:

[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]

[tex]\leadsto[/tex] Solve for AC:

[tex]\longrightarrow \sf{72=8\times AC}[/tex]

[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]

[tex]\longrightarrow \sf{AC=9}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{AC= \: 9 yd}[/tex]

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

[tex] \frac{1}{2} \times d1 \times d2[/tex]

Therefore:

[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]

Then:

[tex] \frac{16ac}{2} = 72[/tex]

Cross multiply the above into:

[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]

Divide by the coefficient of AC:

[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]

Final answer is 9 yd

The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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Step-by-step explanation:

Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.

Answer:

$64

Step-by-step explanation:

Equation: 50 + 15x = 1010

x = (1010 - 50) ÷ 15 = 64

Since x is the total amount of money deposited in the bank per week, the answer is $64.

Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

The formula exists:

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

The parameters exists:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are: p = 0.5 and n = 13

The probability that at most eleven of the thirteen babies are girls is:

[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then

[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]

By using the binomial distribution formula

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

substitute the values in the above equation, we get

[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]

[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]

So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]

[tex]=0.0016+0.0001=0.0017 \\[/tex]

[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]

[tex]=1-0.0017=0.9983[/tex]

0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

Therefore, the correct answer is option c. 4089/4096

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Answer:

Work(W)=7.5*10⁴J

Step-by-step explanation:

Greetings !

[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]

Option (b) -6 and 7 is the correct option.

The zeroes of the function f and g are x=7 and x=-6 respectively.

The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Put x-7=0

X=7

Now, put x+6=0

So, x=-6

The zeroes of the function f and g are 7 and -6 respectively.

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Answer:

The average price of a ticket is $25.

Step-by-step explanation:

Lets us say 100% = 1

0.75 x 30 + 0.25 x 10 = 25

Answer:

Sean's rocket lands 3 seconds after Kiara's rocket.

Step-by-step explanation:

Kiara:  f(t)= -16t² + 80t

Sean:  h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time.  We need to be suspicious of Sean's rocket launch.  His equation for height has "+64" at the end, whereas Kiara's has no such term.  The +64 is the starting height iof Sean's rocket.  So Kiara has a 64 foot disadvantage from the start.  But if it is a race to the ground, then the 64 feet may be a disadvantage.  [Turn the rocket upside down, in that case.  :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground).  So we can set both equation to 0 and calculate t:

Kiara:  f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring.  I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5.  Kiara's rocket lands in 5 seconds.

Sean:  h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds.  Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.

Answer:

The slope between these two points is m=-4.

Step-by-step explanation:

Greetings !

[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]

Answer:

4/10

Step-by-step explanation:

Let the numerator be 2x and the denominator is 5x. The denominator is 6 more than the numerator so if we add 6 to the numerator both numbers should be equal.

Solve:

2x+6 = 5x

6 = 3x

x = 2

2x = 4

5x = 10

Step-by-step explanation:

Let the numerator be 2x and denominator be 5x,

A.T.Q,

2x+6 = 5x

2x-5x = -6

-3x = -6

3x = 6

x = 2

So, the fraction is 4/10 = 2/5

Answer:

$4.58

Step-by-step explanation:

Lets convert 10 feet to meters.

1 ft = 0.305m

10ft = 0.305 * 10

10ft = 3.05m

Now we will work out the cost of the fabric.

Given 1m = $1.50

3.05m = 3.05 * $1.50 = $4.58 (nearest cent)

The total amount he puts towards emergency savings is $74

The correct option is C.

His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459

Now

that we are aware, his weekly deposits total $459 in total.

His total remuneration is $498 due to an error in his addition of the numbers.

The amount he has each week will be determined by deducting his deposits from his paycheck:

498-459 = 39

He contributes two equal payments of $20 and $15 to his emergency fund.

His entire contribution to emergency savings is = 20 + 15 = 35.

Only need to add the additional $39

To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:

39+35 = 74

the total per week that he can put towards emergency savings = $74

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I understand that the question you are looking for is:

Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?

a. $40

b. $60

c. $74

d. $55

Answer: C. $74

Step-by-step explanation:  C. $74.00

The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

According to the statement

we have to explain all about the APR and tel that why it is important for the consumers.

So, For this purpose,

We know that the

The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.

It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate

APR is the important tool for the consumers because of some reasons which are written below:

APR is important because it can give you a good idea of how much you'll pay to take out a loan.

APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.

So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

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Answer: 177

Step-by-step explanation:

1. 4x4=16

(3-16)^2+8

2. 3-16=-13

(-13)^2+8

3. -13x-13=169

169+8

4.169+8=177

177

Answer:

177

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

[tex](3-4^2)^2+8[/tex]

Parentheses

Begin by calculating the part inside the parentheses.

Following PEMDAS, calculate the exponent first:

[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]

Then carry out the subtraction:

[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]

Exponents

[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]

[tex]\implies (-13)^2+8=169+8[/tex]

Addition

[tex]\implies 169+8=177[/tex]

Therefore:

[tex]\implies (3-4^2)^2+8=177[/tex]