How to complete a square

Answer:

Please check below the step-by-step explanation.

Step-by-step explanation:

Considering the quadratic expression

[tex]ax^2+bx\:+\:c\:=0[/tex]

[tex]a,\:b,\:and\:c\:can\:have\:any\:value,\:except\:that\:a\:can't\:be\:0.[/tex]

[tex]To\:Factorise\:a\:Quadratic\:is\:to:[/tex]

" [tex]find\:what\:to\:multiply\:to\:get\:the\:Quadratic[/tex] "

For example, multiplying [tex](x + 3)[/tex] and [tex](x - 2)[/tex] together will bring [tex]x^2+x-6[/tex]

i.e.

[tex]\left(x+3\right)\left(x-2\right) = xx+x\left(-2\right)+3x+3\left(-2\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]+\left(-a\right)=-a[/tex]

[tex]\left(x+3\right)\left(x-2\right) = xx-2x+3x-3\cdot \:2[/tex]

                       [tex]= x^2+x-6[/tex]

Therefore,  [tex](x + 3)[/tex] and [tex](x - 2)[/tex] are factors of [tex]x^2+x-6[/tex]

Keywords: factorize, quadratic expression

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Answer:

It is irrational

Step-by-step explanation:

if you combine a rational and irrational number it cannot be rational.

Adding a rational and an irrational number always results in an irrational number. The rational number doesn't affect the irrationality of the irrational number.

The result of adding a rational and an irrational number is always an irrational number. For example, if you add the rational number 2 (which can be expressed as a ratio of two integers) and the irrational number sqrt(2) (which cannot be expressed as a ratio of two integers).

The result is 2 + sqrt(2), which is an irrational number.

Because the rational number doesn't affect the irrationality of the irrational number, the sum remains irrational.

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Answer:

see explanation

Step-by-step explanation:

The side of the square = x + 2, thus area is equal to

(x + 2)² ← expand using FOIL

= x² + 4x + 4

Given area = 7 then

x² + 4x + 4 = 7 ( subtract 4 from both sides )

x² + 4x = 3 ← as required

Answer:

the area of the square ABCD = 7

on the other hand, the area of the square ABCD = (2+x)² = x² + 4x + 4

then x² + 4x + 4 = 7

then x² + 4x + 4 = 4 + 3

then x² + 4x = 3

Step-by-step explanation:

Answer:

The slope of given relationship is 7 and it is not - 3  

Step-by-step explanation:

Given as :

The distance cover while walking = d = 21 miles

The speed rate of walking = s = 3 miles per hour

Let The time taken to cover 21 miles = t hours

Now, According to question

∵ Distance = Speed × Time

So, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

Or, t = [tex]\dfrac{d}{s}[/tex]

Or, t = [tex]\dfrac{\textrm 21 miles}{\textrm 3 miles per hour}[/tex]

∴  t = 7 hours

So,  The time taken to cover 21 miles = t = 7 hours

i.e slope of the given relationship = 7

Hence, The slope of given relationship is 7 and it is not - 3  . Answer

Answer:

time = distance / speed

time = 200/10

= 20

Step-by-step explanation:

The time taken to travel a distance of 200 Km will be 5.5 hours.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that the speed is 10 m/s and the distance to be travelled is 200 km.

The time will be calculated as below,

T = Distance / Speed

T = 200000/ 10

T = 200000/10 x 3600

T = 5.5 hours

Therefore, the time taken to travel a distance of 200 Km will be 5.5 hours.

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Answer:

900 × 2 ?

Step-by-step explanation:

900 × 2 ? i dont know but i hope its correct?

Answer:

39 and 19/20

Step-by-step explanation:

Answer

39 19/20  

Step-by-step explanation

39.95/1 x 100/100 = 3995/100

Find the HCF (Highest Common Facror) (if there is)

divide the top and bottom nuber by 5 = 799/20

799/20 simplified = 39 19/20

i hope this helps :)

please give me brainliest i just need 3 more until expert!

Brad spends about the same amount of time doing homework as he does watching videos. The other statements are not true.

The circle graph shows how Brad spends his time outside of school. To determine which statements are true, we need to compare the different activities.

A. To compare working and homework, we can see that Brad spends about ⅔ of his time working and ⅓ of his time on homework. So, A is not true since Brad spends more time on homework than working.

B. To compare watching videos and reading with playing the piano and soccer, we can see that Brad spends about 1/6 of his time on watching videos and reading, and about 3/6 of his time on playing the piano and soccer. So, B is not true since Brad spends more time playing the piano and soccer than watching videos and reading combined.

C. To compare doing homework and watching videos, we can see that Brad spends about ⅓ of his time on both activities. So, C is true since Brad spends about the same amount of time doing homework as he does watching videos.

D. To compare playing piano with playing football and soccer combined, we can see that Brad spends about 1/6 of his time on playing piano, and about 4/6 of his time on playing football and soccer combined. So, D is not true since Brad spends more time playing football and soccer combined than playing piano.

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Answer:

Gery will get 45 £,Eddy will get 135 £ and Bernie will get 270 £ of the total share.

Step-by-step explanation:

Given:

Bernie, Eddy and Gery share £450.

Bernie gets twice as much as Eddy.

Eddy gets three times as much as Gery.

So,

Let Gery gets 'x' share of the amount.

Then,

Eddy's share will be '[tex]3x[/tex]'

and

Bernie's share will be [tex]2\times 3x=6x[/tex]

According to the question.

Total share summation of total share = [tex]450[/tex]

⇒ [tex]x+3x+6x=450[/tex]

⇒ [tex]10x=450[/tex]

⇒ [tex]x=\frac{450}{10}=45[/tex]

So Gery's share = 'x' [tex]= 45[/tex]

Eddy's share = [tex]3x=3\times 45=135[/tex]

Bernie's share = [tex]6x=6\times 45=270[/tex]

Gery will get 45 £,Eddy will get 135 £ and Bernie will get 270 £ of the total share.

The solution is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]

Step-by-step explanation:

The expression is [tex]x^{2} +y^{2} -x+3y-42=0[/tex] and [tex]x+y=4[/tex]

Using substitution method we can solve the expression.

Let us substitute [tex]x=4-y[/tex] in [tex]x^{2} +y^{2} -x+3y-42=0[/tex]

[tex](4-y)^{2} +y^{2} -(4-y)+3y-42=0[/tex]

Expanding and simplifying the expression, we get,

[tex]\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}[/tex]

Let us use the quadratic equation formula to solve this equation,

[tex]\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}[/tex]

Thus, [tex]y=5[/tex] and [tex]y=-3[/tex]

Substituting y-values in the equation [tex]x+y=4[/tex], we get the value of x.

For [tex]y=5[/tex] ⇒ [tex]x=4-5=-1[/tex]

For [tex]y=-3[/tex] ⇒ [tex]x=4+3=7[/tex]

Thus, the solution set is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]

Answer:

m∠A = 90°, m∠B = 60°, m∠C = 30°

Step-by-step explanation:

step 1

see the attached figure to better understand the problem

In this problem we have a right triangle, because the Pythagorean Theorem is satisfied

so

[tex]BC^2=AB^2+AC^2[/tex]

[tex]24^2=12^2+(12\sqrt{3}) ^2\\\\576=576[/tex]

therefore

[tex]m\angle A=90^o[/tex]

step 2

Find the measure of angle B

we know that

In the right triangle ABC

[tex]cos(B)=\frac{AB}{BC}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(B)=\frac{12}{24}[/tex]

[tex]m\angle B=cos^{-1}(\frac{12}{24})=60^o[/tex]

step 3

Find the measure of angle C

we know that

[tex]m\angle B+m\angle C=90^o[/tex] ----> by complementary angles

we have

[tex]m\angle B=60^o[/tex]

substitute

[tex]60^o+m\angle C=90^o\\m\angle C=30^o[/tex]

therefore

m∠A = 90°, m∠B = 60°, m∠C = 30°

Answer:

c

Step-by-step explanation:

m∠A = 90°, m∠B = 60°, m∠C = 30°

ON EDG 20

Answer:

c

Step-by-step explanation:

m∠A = 90°, m∠B = 60°, m∠C = 30°

ON EDG 20

To evaluate the expression 4c - x with c=5 and x=-4, substitute the values to get 4*5 - (-4), which simplifies to 20 + 4, resulting in a value of 24.

To evaluate the expression 4c-x when c=5 and x=-4, substitute the given values for the variables c and x into the expression.

Step 1: Substitute c = 5 into the expression.

4 × 5 - x

Step 2: Substitute x = -4 into the expression.

4 × 5 - (-4)

Step 3: Carry out the multiplications and additions.

20 - (-4) = 20 + 4

Step 4: Add the numbers.

20 + 4 = 24

Therefore, when c = 5 and x = -4, the value of the expression 4c - x is 24.

The value of the expression 4c-x when c=5 and x=-4 is 24.

To evaluate the expression (4c - x) when (c = 5) and (x = -4), follow these steps:

1. Substitute (c = 5) into the expression: [tex]\(4 \times 5 - x\)[/tex]

2. Substitute (x = -4) into the expression: [tex]\(4 \times 5 - (-4)\)[/tex]

3. Simplify the multiplication: (20 - (-4))

4. Simplify further by changing the double negative to addition: (20 + 4).

5. Add the numbers: (20 + 4 = 24).

Therefore, when (c = 5) and (x = -4), the value of the expression (4c - x) is (24). The process involves substituting values, simplifying, and performing addition to obtain the final result.

Answer:

I think the answer is the second choice so B. Also your pretty

Answer:

its d ac/gi=bc/hi

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

N = V16 = 4

P=19

so N + P

Answer:

$768.54 (Approximate)

Step-by-step explanation:

Trey is taking out a loan for $85000. It is a 20-year loan with an APR of 5.85%.

Therefore, if we consider the interest rate is simple interest, then using the simple interest formula, the sum will become after 20 years

[tex]85000(1 + \frac{5.85 \times 20}{100}) = 184450[/tex] dollars.

Therefore, the monthly payment for the loan will be [tex]\frac{184450}{20 \times 12} = 768.54[/tex] dollars. (Answer)

Answer:

what are the numbers you wsnt to find? if you don't know then you've answeref your own question with this, well, question..!

Answer:

12 bottles were sold in the second hour.

Step-by-step explanation:

This problem can be solved by implementing an equation in one variable.

The equation will utilize the given values including total bottles of juice, the amount of juice sold in the first hour and amount of juice remaining at the end.

The equation will also consist of the value to be found out, the amount of juice sold in the second hour.

The value to be found out is substituted by a variable.

The equation is then solved by transfer of values and/or variable on the opposite side of the equal sign.

When a value/ variable is transferred on the opposite side of the equal sign, the sign of the value/ variable becomes the opposite.

The negative sign becomes positive and multiplication becomes division, and vice-versa.

1. In the first hour, \frac{3}{15} of all the juice was sold.

\frac{3}{15} of 30 is calculated as

\frac{3}{15} x 30 = 6

6 bottles are sold in the first hour.

2. At the beginning of the second hour, the amount of juice remaining is assumed to be a.

3. As per the question, at the end of second hour, the remaining juice is \frac{6}{15}.

\frac{6}{15} of 30 is calculated as

\frac{6}{15} x 30 = 12

12 bottles are remaining at the end of the second hour.

4. Alternatively, at the end of second hour, 30 - 6 - a of the juice is remaining.

We get, 24 - a bottles are remaining at the end of the second hour.

We equate the above expression with 12, we get the following equation.

24 - a = 12

Next, we transfer a from left side to the right side of the equation.

24 = 12 + a

Next, we transfer 12 from right side to the left side of the equation.

24 - 12 = a

=> 12 = a

OR

a = 12

Hence, 12 bottles were sold in the second hour.

Mario sold 2/5 of his juice in the second hour after having sold 3/15 in the first hour and ending with 6/15 of the juice left.

Mario started with 30 bottles of juice and sold 3/15 of them in the first hour. To find out how many bottles that is, we multiply the total number of bottles by the fraction sold: 30 bottles x 3/15 = 6 bottles. After the first hour, Mario had 30 bottles - 6 bottles = 24 bottles left.

By the end of his shift, Mario had 6/15 of his original juice left. Again, we multiply the total number of bottles by the fraction left: 30 bottles x 6/15 = 12 bottles. So, at the end of his shift, Mario had 12 bottles unsold.

To find out how many bottles were sold in the second hour, we subtract the number left at the end from the number left after the first hour: 24 bottles - 12 bottles = 12 bottles sold in the second hour. To express this amount as a fraction of the original 30 bottles, we divide 12 by 30 to get 12/30, which simplifies to 2/5. Thus, Mario sold 2/5 of his juice in the second hour.

Answer: x < 30

Step-by-step explanation:

Let the cost of a jean be x

cost of a shirt = $25

cost of 3 jeans = 3x

since he wants to spend less than $115 , this means that

3x + 25 < 115

3x < 115 - 25

3x < 90

x < 30

Answer:25/112

Step-by-step explanation:multiply 5/8 times 5/14.

Answer:

Caroline

Step-by-step explanation:

Anna : 123 words in 3 minutes ....123/3 = 41 words per minute

Caroline : 220 words in 5 minutes...220/5 = 44 words per minute

Caroline is the faster typist <===

Answer:1690

Explanation:

0.11x150=16.50

16.50x31=511.50

0.38x3100=1178.0(this is all we do for the downloads since it says 'downloaded a total of 3100 times')

1178+511.5=1689.5 then u round it up because of the 9 and you get 1690

Im kinda bad at explaining but hope this helps

Answer:

x = 132/2 or x = 67 1/2

Step-by-step explanation:

hjdnnenenenenenehehhehehehebeb

Answer:

2.4 pounds of blueberries for each pie

Step-by-step explanation:

Mary has 12 pounds of blueberries to make 5 pies.

Divide 12 by 5 to see how much pounds of blueberries each pie will have.

There are 2.4 pounds of blueberries for each pie.

The number of pounds of blueberries were in each pie is 2.4

Given that,

Based on the above information, the calculation is as follows:

[tex]= 12 \div 5[/tex]

= 2.4

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Answer:

x-8=18

Step-by-step explanation:

A number is our variable, so we will use X. 8 less than a number would be 8-x and that equals 18 so x-8=18.

Answer:

the right answer is option A. 40°

Step-by-step explanation:

angle BAC= angle BAD - angle CAD

= 120° - 80°

= 40°

Answer:

#2

Step-by-step explanation:

N/A

Bartering was an early way that people exchanged a good or service directly for a good or service. (option 2)

Bartering, the act of exchanging goods or services directly for other goods or services, was an early way that people engaged in trade and commerce.

Before the advent of standardized currency in the form of paper or metal, societies relied on bartering as a means of acquiring what they needed.

In a barter system, individuals would negotiate the exchange of items they possessed, often based on their mutual needs and values.

Hence the correct option is (2).

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Answer:

The answer that gives the best estimate is (1,1)

Step-by-step explanation:

i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y

 intercept or [tex]c_{1}[/tex] = -1. Therefore the equation for this line can be written as

 y = [tex]m_{1}[/tex] x + [tex]c_{1}[/tex]    ⇒    y = [tex]m_{1}[/tex] x - 1 . It can also be seen from this graph that the

 line passes through the point (2 , 2). Substituting these values for x and y  

 respectively we get  2 = 2[tex]m_{1}[/tex] - 1    ∴ [tex]m_{1}[/tex] = [tex]\frac{3}{2}[/tex].  The equation of the first line

 can be written as y = [tex]\frac{3}{2}[/tex] x - 1   ⇒ 2y - 3x = -2

ii) As can be seen on the other line the intercept on the y axis is at (0,2). So

  the y  intercept or [tex]c_{2}[/tex] = 2. Therefore the equation for this line can be  

  written  as  y = [tex]m_{2}[/tex]x + [tex]c_{2}[/tex]    ⇒    y = [tex]m_{2}[/tex] x + 2 . It can also be seen from this  

   graph that  the  line passes through the point (1 , -1). Substituting these

   values for x and  y   respectively we get  1 = 1[tex]m_{2}[/tex] + 2    ∴ [tex]m_{2}[/tex]  = -1 .  The

   equation of the second line  can be written as y = - x + 2   or x + y = 2

iii) Solving the two equations of the two lines respectively as found in i) and

  ii)  we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and  

  when we add this to equation in i) we get 5y = 4 which means that y = 0.8.

  If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.

iv) Therefore we get the solution of the two lines, which is the intersection

    of the two lines as (1.2, 0.8). So the answer that gives the best estimate

    is (1,1)

Answer:

Correct answer is: B: (1/2, 0)

Step-by-step explanation:

Just took the test and that is the correct answer.  Picture w/ correct answer attached.

Answer:

IV/4

Step-by-step explanation:

Go to 15 on the x line and go down 12 and that’s the 4