What is the intermediate step in the form (x + a)2 = b as a result of completing the
square for the following equation?
x^2 – 3x = 7x - 30

Answer:

28.57%

Step-by-step explanation:

Find the percent decrease by dividing the change in the number of points by the original number of points, then multiplying it by 100:

((21 - 15) / 21) x 100

(6 / 21) x 100

= 28.57

So, her score decreased by approximately 28.57%

Answer:

198

Step-by-step explanation:

9514 1404 393

Answer:

  k ≈ 0.03719

Step-by-step explanation:

Fill in the given numbers and solve for k.

  750 = 600e^(6k)

  1.25 = e^(6k)

  ln(1.25) = 6k . . . . . take the natural log

  k = ln(1.25)/6 . . . . . divide by 6

  k ≈ 0.03719

Answer:

0.765

Step-by-step explanation:

The dot plot shows the data

x= 20,21,22,23,24,24,25,25,25,26,26,27,28,29,31

The mean x`= ∑x/n =20+21,+22,+23,+24,+24,+25,+25,+25+,26+,26+,27+,28+,29+,31/15= 376/15

=25.067

where n is the sample size= 15

The standard deviation is σ=2.96

( using calculator)

The standard error is calculated as

SE= σ/√n

SE= 2.96/√15

SE= 0.765

147/100

= 1 47/100

100 is the percent out of

and 147 is the percent.

Answer:

147/100

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 147 and 100 is 1

Divide both the numerator and denominator by the GCD

147 ÷ 1

100 ÷ 1

Reduced fraction:  

147/ 100

147/100 simplified to lowest terms is 147/100.

*see attachement for the diagram of the tissue paper

Answer:

Volume of the roll = 3,817.04 cm³

Step-by-step explanation:

The diagram of the roll of the tissue paper given is a model of two cylinders:

✔️Bigger cylinder with diameter (d) of 14 cm and height of 27 cm

✔️ Smaller/inner cylinder with diameter (d) of 4 cm and height of 27 cm

Thus:

The Volume of the roll = volume of bigger cylinder - volume of smaller cylinder

✔️Volume of bigger cylinder = πr²h

r = ½(14) = 7 cm

h = 27 cm

Volume of bigger cylinder = π*7²*27

= 4156.33 cm³

✔️Volume of smaller/inner cylinder = πr²h

r = ½(4) = 2 cm

h = 27 cm

Volume of smaller/inner cylinder = π*2²*27

= 339.29 cm³

✅The Volume of the roll = 4156.33 - 339.29 = 3,817.04 cm³

Answer:

Test = 17.143 ;

Pvalue = 0 ;

Reject the Null ;

(-0.028 ; - 0.022) ;

We conclude that content are different.

Step-by-step explanation:

Given that:

μ1 = μ

n1 = 36 ; n2 = 36

x1 = 0.78616 ; x2 = 0.81111

s1 = 0.04444 ; s2 = 0.00752

Test statistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(0.78616 - 0.81111) / √(0.00444²/36 + 0.00752²/36)

- 0.02495 / 0.0014554

= 17.143

Pvalue :

Z < 17.143

Pvalue = 0

Since Pvalue < α ; Reject the Null

The confidence interval using a confidence interval calculator is (-0.028 ; - 0.022)

Since the interval does not contain Zero ; then we reject the Null and conclude that the content are different.

Answer:

in life problem I solve in my head and not on paper. I enter life's problems calmly and carefully know I can solve them but in math I erase and cry and almost tear my paper apart. someone else can solve your math problem but not your life problem.

Answer:

yes i can but will have to get back to you in about half a hour just doing maths atm with the teacher

Step-by-step explanation:

Answer:

Step-by-step explanation:

I will not give the answer but the rules are:

90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...

180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...

270 Degree Rotation.

Hope at least that helps.

Answer:

x-intercept(s):  

(

−

8

3

,

0

)

y-intercept(s):  

(

0

,

−

4

)

Step-by-step explanation:

The x-intercepts are (83, 0), and the y-intercepts are (0, 4). Matrixes, like numbers, have reciprocals. In the world of matrices, this reciprocal is known as a "inverse matrix."

The concept of a matrix's inverse is a multidimensional generalization of the concept of a number's reciprocal: just as the product of a number and its inverse equals one, the product of an identity matrix and a square matrix equals one.

A A-1 = A-1 A = I because the identity matrix I is the inverse of a matrix. An invertible matrix is one that has a non-zero determinant and can have its inverse determined. Finding the inverse of a 2x3 matrix is impossible because it is not a square matrix.

Response: (8 3, 0) are the x-intercepts.

(0, 4 ) are the y-intercepts.

Therefore,

-3 x-2 y=-8

Add 2 y to both sides

-3 x-2 y+2 y = -8+2 y

Simplify

[tex]$$-3 x=-8+2 y$$[/tex]

Divide both sides by -3

[tex]$$\frac{-3 x}{-3}=-\frac{8}{-3}+\frac{2 y}{-3}$$[/tex]

Simplify

[tex]$$x=-\frac{-8+2 y}{3}$$[/tex]

Response: (8 3, 0) are the x-intercepts.

(0, 4 ) are the y-intercepts.

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Answer:

15.1 yd

Step-by-step explanation:

Since the circumference formula is C = πd, d = C/π

and in this case d = (47.5 yd) / 3.14 = 15.1 yd

The approximate diameter of the pad is 15.1 yd.

The approximate diameter of the helicopter pad is,

⇒ d = 15.12 yards

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A helicopter pad has a circumference of 47.5 yards.

Now,

We know that;

Circumference of circle = 2πr

Hence, We get;

⇒ 47.5 = 2 × 3.14 × r

⇒ 47.5 = 6.28r

⇒ r = 47.5 / 6.28

⇒ r = 7.56

Thus, the approximate diameter of the helicopter pad is,

⇒ d = 2r

⇒ d = 2 × 17.56

⇒ d = 15.12 yards

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Answer:

3/7 is greater than 2/5

Step-by-step explanation:

If you convert the fractions into decimals:

3/7=0.42

2/5=0.4

0.42 is greater than 0.4

Answer:

distance = 11.1666 miles  (round to 11.1667)

11.1667 mi

How I solved it:

Well, I knew that in one hour, she would go 67 miles.

I then divided the hour into 6 sections (10 min, 20 min, 30, 40, 50 and 60)

So, we divide 67/6

and our answer is 11.1666 (round to 11.1667)

Answer:

The given statement is "True".

Step-by-step explanation:

A statistical analytical technique that divides the perceived aggregate unpredictability present throughout an information source even further into 2 components.

If relevant information yet another category independent variable, as well as another quantifiable variable of interest, has been obtained, are using a single-way ANOVA.

Thus the above is the true answer.

Answer:

Step-by-step explanation:

the correct answer is 1 second

The time it will take for the penny to hit the ground is 1 second.

solving this we will get the valve of Y if x is given.

Calculation:-

Given initial feight= 16 feet

h(t)= -16t2 + initial height

for 1 second

⇒ h(1)= -16(1)2 +16

⇒ h = -32 +16

⇒ h = -16 ( 16 feet downward i.e penny will tough the ground)

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Answer:

[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]

Step-by-step explanation:

remember that,

the sum of the interior angles of a triangle is 180°

Thus our equation is

[tex] \displaystyle \angle1 + {72}^{ \circ} + {35}^{ \circ} = {180}^{ \circ} [/tex]

simplify addition:

[tex] \displaystyle \angle1 + {107}^{ \circ} = {180}^{ \circ} [/tex]

cancel 107° from both sides:

[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]

Step-by-step explanation:

Answer:

Solution given:

<1+72+35°=180°[ interior angle of a triangle is 180]

<1=180-107

<1=73 °

Answer:

1

Step-by-step explanation:

We can see that 7 is equal to 6, as opposite angles are the same.

We can also see that 2 is also 6, as corresponding angles are equivalent.

Therefore, 3 is also congruent to 6, as it is equal to 2.

Hope that this helps!

Answer:

y - 6.28 = 3.14( x - 2 )

Step-by-step explanation:

Notice that 6.28 is twice the approximate value of pi:  2(3.14), and that

9.42  is three times pi.  We can deduce immediately that the slope of the line passing through (2, 6.28) and (3, 9.42) is 3.14.

Using the point-slope formula for the equation of a straight line, we get:

y - 6.28 = 3.14( x - 2 )

Answer:

There is no image

Step-by-step explanation:

Try isolating the variable in the equation

Answer:

4

Step-by-step explanation:

First, to get just the multiplication equation, we need to do,

32-12 = 20

20/5 = 4

The number is 4.

Now let's check our work.

4x5+12=32

The answer is 4.

The required number is 4.

Let the number be x.

Given, the product of x and 5 increased by 12 gives 32.

So in equation form,

[tex]5x+12=32\\[/tex]

Subtracting 12 from both the sides,

[tex]5x+12-12=32-12[/tex]

[tex]5x=20\\\\[/tex]

[tex]x=\dfrac{20}{5}[/tex]

Or, [tex]x=4[/tex]

Hence the required number is 4.

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f(x) = x - 5 ln(x)

Get the derivative:

f'(x) = 1 - 5/x

Find the critical points:

• f'(x) = 1 - 5/x = 0   ->   5/x = 1   ->   x = 5

• f'(x) is undefined for x = 0, but that's outside the domain of f(x)

Get the second derivative:

f''(x) = 5/x ^2

Check the sign of the second derivative at the critical point x = 5:

f'' (5) = 5/5^2 = 5/25 = 1/5 > 0

Since the second derivative is positive at this point, this means x = 5 is a local minimum.

Check the value of f(x) at the critical point as well as the endpoints of the given domain:

f (5) = 5 - 5 ln(5) ≈ -3.407

f (1/5) = 1/5 - 5 ln(1/5) ≈ 1.809

f (10) = 10 - 5 ln(10) ≈ -1.513

So we have

• absolute maximum = 1/5 - 5 ln(1/5) at x = 1/5

• absolute minimum = 5 - 5 ln(5) at x = 5

The absolute maximum value is  f(5)=5−5ln(5), and this occurs at x equals 5

The absolute minimum value is  f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5

Given the function f(x)=x−5ln(x),

We are to find the absolute minimum and maximum value of the function

At the turning point f'(x) = x - 5ln(x)

f'(x) = 1 - 5/x

0 = 1 - 5/x

-5/x = -1

-x = -5

x = 5

Find the second derivative of the function;

f''(x) = -5/x²

Substitute the value of x = 5 into the second derivative function to have:

f''(5) = -5/5² = 1/5

Since f''(5) = 1/5 < 0, this is the local maximum and the point x = 5 is the absolute minimum

The absolute maximum value is  f(5)=5−5ln(5), and this occurs at x equals 5

The absolute minimum value is  f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5

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Answer: 664

Step-by-step explanation:

Take the amount of days, and multiply it by the miles per day

so

8 x 83 = 664 miles

Hope this helps!! (^_^)