MATHEMATICS HIGH SCHOOL

What number must be added to the expression below to complete the square? x2+x

Answers

Answer 1
Answer:

Answer:

answer is 1/4

Step-by-step explanation:

proof is (x-1/2)²= x²-2*1/2*x+1/4= x²-x+1/4

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A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?b = –8
b = –4
b = 2
b = 6

Answers

Answer: First option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope of the line and "b" is the y-intercept

We need to write each equation in Slope-Intercept form:

First equation

3y + 12 = 6x\n\n3y=6x-12\n\ny=2x-4

Second equation

2y = 4x + b \n\ny=2x+(b)/(2)

Since, by definition, a system of linear equations has infinitely many solutions when the lines are the same, we can say that:

y=y\n\n2x-4=2x+(b)/(2)

Then, solving for "b", we get:

-4=(b)/(2)\n\n(-4)(2)=b\n\nb=-8

Answer:

-8

Step-by-step explanation:

Just took test lol

Estimate each percent 74% of 238

Answers

It would be 238*74/100 = 176.12
74% of 238 is 176.12

or 238 * .74 = 176.12.

What is the seventh term of (x + 4)8?A. 114,688x2
B. 114,688x3
C. 114,688x4
D. 114,688x5

Answers

The (p+1)-th term of the Newton binomial expansion

(a+b)^(n)

is given by

t_(p+1)=\dbinom{n}{p}\,a^(n-p)\,b^(p)
__________________________

We want the 7th term. Hence, we set p+1 to be 7:

p+1=7~~\Rightarrow~~p=6


Then, the 7th term is

t_(7)=\dbinom{8}{6}\,x^(8-6)\,4^(6)\n\n\n t_(7)=(8!)/(6!\cdot (8-6)!)\cdot x^(8-6)\cdot 4^(6)\n\n\n t_(7)=(8\cdot 7\cdot \diagup\!\!\!\! 6!)/(\diagup\!\!\!\! 6!\cdot 2!)\cdot x^(2)\cdot 4^(6)\n\n\n t_(7)=(8\cdot 7)/(2\cdot 1)\cdot x^(2)\cdot 4^(6)\n\n\n t_(7)=28\cdot x^(2)\cdot 4,096\n\n \boxed{\begin{array}{c} t_(7)=114,688\,x^(2) \end{array}}


Correct answer: \text{A. }114,688\,x^(2).

A rectangular room measures 9 feet by 12 feet. If carpeting costs $20.00 per square yard, what would it cost to carpet the room?

Answers

It would equal $720. 9 times 12 equals 108 ft. Then divide that by 3(3feet in a yard) that equals 36yd, then multiply that by $20 to get $720.

A 65.0 gram sample of some unknown metal at 100.0° C is added to 100.8 grams of water at 22.0° C. The temperature of the water rises to 27.0° C. If the specific heat capacity of liquid water is 4.18 J/ (°C × g), what is the specific heat of the metal?2.25 J/ (°C × g).
1.75 J/ (°C × g).
0.444 J/ (°C × g).
0.324 J/ (°C × g).

Answers

heat gained by the metal = heat lost by the water
65.0* Cs * (100.0°C - 27.0°C) = 100.8 g * 4.18 J/(°Cxg) * (27.0°C - 22.0°C)

Cs = 100.8 * 4.18 * 5.0 / (65.0 * 73) J/(°Cxg) = 0.444J/(°Cxg)

Answer: the fhird option, 0.444 J/(°Cxg)

Which is bigger 20% of 300 or 1/4 of 200

Answers

to find 20% of 300, multiply .2 x 300 = 60
60 is 20% of 300

1/4 = 25%
to find 25% of 200, multiply .25 x 200 = 50
50 is 1/4 of 200

20% of 300 is more than 1/4 of 200
(20/100) *300 = (2/1)*30= 60(1/4) * 200= 200/4 = 50
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