ten times the reciprocal of a number equals 5 times the reciprocal of 3

Answer:

y = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex]

Step-by-step explanation:

y = 2x² - 2x - 5 ← factor out 2 from the first 2 terms

 = 2(x² - x) - 5

Using the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - x

y = 2(x² + 2(- [tex]\frac{1}{2}[/tex] ) x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² + 2(- [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{1}{2}[/tex] - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex] ← in vertex form

86%

30 students in the class with a mean average of 70% can be expressed as:

total class percent / 30 = 70%

Rearranged, this gives that the class achieved a total of 30x70 or 2100%.

20 boys in the class with a mean average of 62% can be expressed as:

total boys percent / 20 = 62%

Rearranged, this gives that the boys achieved a total of 20x62 or 1240%.

This means that the girls achieved 2100 - 1240 so 860%.

Because there are 30 students and 20 boys, there are 10 girls.

Then work out the mean with a total of 860% and 10 girls.

860/10 = 86%.

Answer:

B STEP 2

Step-by-step explanation:

5/8 is not more than 1

Step-by-step explanation:

I assume the original expression is

2x² + 16x + 11

we need to get this into the form of a(x + b)² + c

let's do the generic multiplication and compare the result to the given expression :

a(x² + 2bx + b²) + c = ax² + 2abx + ab² + c

when we compare this with the original equation, we only need to look at terms with the same variable exponents.

2x² is the only term with "x²".

and ax² is the only term with "x²" in the generic form.

so ?

2x² = ax²

=>

a = 2

16x is the only term with "x" (exponent 1).

2abx is the only term with "x" in the generic form.

16x = 2abx

8x = abx = 2bx

4x = bx

=>

b = 4

11 is the only pure number (constant).

ab² + c is the only constant term in the genetic form.

11 = ab² + c = 2×4² + c = 2×16 + c = 32 + c

-21 = c

so, the solution is

2(x + 4)² - 21

Answer:

X=(-1.5, 7.5)

Step-by-step explanation:

Simplifying

4x2 + -24x + -45 = 0

Reorder the terms:

-45 + -24x + 4x2 = 0

Solving

-45 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-3 + -2x)(15 + -2x) = 0

Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying

-3 + -2x = 0

Solving

-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -2x = 0 + 3

-2x = 0 + 3

Combine like terms: 0 + 3 = 3

-2x = 3

Divide each side by '-2'.

x = -1.5

Simplifying

x = -1.5  

Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying

15 + -2x = 0

Solving

15 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -2x = 0 + -15

-2x = 0 + -15

Combine like terms: 0 + -15 = -15

-2x = -15

Divide each side by '-2'.

x = 7.5

Simplifying

x = 7.5

Solution

x = {-1.5, 7.5}

Answer:

Step-by-step explanation:

Answer:

96 cm or B

Step-by-step explanation:

Base-l*w, 6*6, 36

Side 1-(h*w)1/2, (30)1/2, 15

Side 2-Same as 1

Side 3-Same as 1

Side 4-Same as 1

15+15=30, 15+15=30, 30+30=60, 60+36=96

96 cm

Answer:

Step-by-step explanation:

x-5

=========================================================

Explanation:

The key tells us how to set up the stem and leaf diagram. It says that [tex]24|5[/tex] represents the value 245.

This means that "24" is one of the stems. In fact, it's the smallest stem possible since there's nothing smaller than 240 on this given list of values.

The only leaf associated with this stem is 5. The stem 24 and the leaf 5 combine to form the number 245 as the key indicates.

--------------------------

In the next row is the stem 25. For this stem, we'll have the leaves of: 0, 1, 3, 8. The stem 25 and those leaves mentioned combine to form 250, 251, 253, 258 in that exact order. This time we'll use up four boxes for this row. The last box in this row is blank.

The remaining rows (stems 26 and 27) are handled in pretty much the same fashion. Let me know if you have questions how the boxes are filled in. It helps to start with sorted data from smallest to largest. Luckily, that's already been done for us.

The filled out chart is shown below. I replaced the stems 0,1,2,3 with 24,25,26,27.

Answer: ? What are you talking about?

Step-by-step explanation:

Recall the angle sum identity for cosine,

cos(α + β) = cos(α) cos(β) - sin(α) sin(β)

Then given sin(α) = -1/3, we have

cos(α + β) = cos(α) cos(β) + 1/3 sin(β)

α is in quadrant IV, so 3π/2 < α < 2π, and so sin(α) is negative and cos(α) is positive. Then from the Pythagorean identity, we get

sin²(α) + cos²(α) = 1

⇒   cos(α) = √(1 - sin²(α)) = 2√2/3

β is in quadrant III, so π < β < 3π/2, so both sin(β) and cos(β) are negative. If we multiply both sides of the previous identity by 1/cos²(α) and replace α with β, we get

sin²(β)/cos²(β) + cos²(β)/cos²(β) = 1/cos²(β)

⇒   tan²(β) + 1 = 1/cos²(β)

⇒   1/cos(β) = -√(tan²(β) + 1) = -√58/3

⇒   cos(β) = -3/√58

Also recall that by definition,

tan(β) = sin(β)/cos(β)

⇒   sin(β) = tan(β) cos(β) = 7/3 • (-3/√58) = -7/√58

Putting everything together, we find that

cos(α + β) = 2√2/3 • (-3/√58) + 1/3 • (-7/√58) = -(6√2 + 7)/(3√58)

or more clearly,

[tex]\cos(\alpha + \beta) = -\dfrac{6\sqrt2 + 7}{3\sqrt{58}}[/tex]

Step-by-step explanation:

x = 0,75

y = 0,96

= x - 2y

= 0,75 - 2.0,96

= 0,75 - 1,96

= -1,21

Answer:

42m + 12

Step-by-step explanation:

6 ( 7m + 2 )

= 6 ( 7m ) + 6 ( 2 )

= ( 6 * 7m ) + ( 6 * 2 )

= 42m + 12

Answer:

a

Step-by-step explanation:

do distributive property and u get 42m+12

Answer:  y= (7/4)x

Step-by-step explanation:

Build a table of representative values and then calculate the slope between any 2 of the points.   I'll pick (2,3.5) and  (8,14)    [See attachment. ]

The slope is the Rise/Run:

Rise = (14 - 3.5) = 10.5

Run = (8-2) = 6

Slope = Rise/Run:  (10.5/6) = 1.75

The equation should read y = 1.75x.  

None of the options works, as written, but note that 7/4 looks close to 1.75.  In fact, 7/4 = 1.75.

Use the equation y = 1.75x and enter several values of x (the ounces purchased) and y (the total cost of the purchase).  The attachment summarizes the results (Predicted), along with the actual values (Actual) taken from the graph.  Excellent correlation, considering the difficulty in making precise graph readings.

Therefore y = (7/4)x

Answer:

1

first choice

Step-by-step explanation:

in a function, the x-value never repeats.

(found in brainly)

Answer:

20 por cento de cada um , que colocar

The unemployment rate is approximately 17 per cent. The correct option is A.

To calculate the unemployment rate, we need to consider the number of unemployed individuals (those looking for work) divided by the total labour force (those employed plus those looking for work).

Given:

Total population = 100

Employed individuals = 50

Individuals looking for work (unemployed) = 10

Total labour force = Employed + Unemployed

Total labor force = 50 + 10 = 60

Unemployment rate = (Unemployed / Total labour force) x 100

Unemployment rate = (10 / 60) x 100 ≈ 16.67 percent

Rounding to the nearest whole number, the unemployment rate is approximately 17 per cent.

Therefore, the correct answer is option A.

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Answer:

7+5=12

Step-by-step explanation:

To calculate the mass number of an atom, you have to add the protons and the neutrons. We have 7 neutrons and 5 protons, so your mass number would be 12. Let me know if you have any further questions. :)

Answer:

12x + 3 - 4x - 6 = 5

x=1

5x - 4 + 7 + 6x - 4x = 24

x=3

Answer:

344444444433333338694

Step-by-step explanation:

Answer: y = -3x+5

Step-by-step explanation:

Answer:

The question or equation is not clear.....

The Eubanks Answer:

Step-by-step explanation:hehus

Answer:

7.6

Step-by-step explanation:

Answer:

76/10

Explanation

7 × 10 is 70 + the 6 is 76/10

you can look up fractions on yt

to get a better explication.

Answer:

The answer would be 12

Step-by-step explanation:

15/100 =  X/80

To solve the equation above for X, you first switch the sides to get the X on the left side, then you multiply each side by 80, and then finally divide the numerator by the denominator on the right side to get the answer.

The equation

15/100 = X/80

X/80 = 15/100

X*80/80 = 15*80/100

X = 1200/100

X = 12

Answer:

The area of the shape can be divided into the area of the rectangle, and the area of the semi-circle.

The area of the rectangle can be found by [tex]11*4=44[/tex]

The area of a semi-circle can be found with the formula [tex]\frac{1}{2} \pi r^2[/tex] where r is the radius.

Since we know the diameter of the semi-circle is 4,

the radius will be 4 ÷ 2 = 2.

Therefore, the area of the semi-circle is [tex]\frac{1}{2}\pi 2^2=\frac{1}{2}\pi*4=2\pi[/tex]

Therefore, the area of the shape is [tex]44+2\pi[/tex] or [tex]50.283cm^2[/tex] (3 decimal places)

Answer:

6.6/100 or 3.3/5

Step-by-step explanation:

6.6% or 6 3/5% now since those are all out of 100 (since percentages) you just put #/100 and get your fraction

Answer:

2.8625

This is 916 divided by 320

Answer:

Full Answer - 2.8625

Rounded - About 3

Nearest Tenth - 2.9

Nearest Hundredth - 2.86

Step by Step:

Shown Below  

Hope this Helps

Work Shown:

z = (x - mu)/sigma

z = (72.4 - 69.0)/(2.8)

z = (3.4)/(2.8)

z = 1.2142857 .... which is approximate

z = 1.21

Z-score of a man who is 72.4 inches tall is 0.45.

Understanding the concept of the z-score helps us gauge how far a value is from the mean in terms of standard deviations.

A z-score, denoted as , measures the deviation of a data point from the mean in terms of standard deviations. It's calculated using the formula:

= ( - ) /

Where:

- is the value we want to find the z-score for (72.4 inches in this case).

- is the mean of the dataset (69.0 inches).

- is the standard deviation of the dataset (2.8 inches).

Plugging in the values:

= (72.4 - 69.0) / 2.8 = 1.25 / 2.8 ≈ 0.446

Rounded to two decimal places, the z-score is approximately 0.45.

This means that a man who is 72.4 inches tall is roughly 0.45 standard deviations above the mean height of adult men.

In other words, his height is a bit taller than the average height by about 0.45 times the standard deviation.

This positive value indicates that the man's height is above the mean. If the z-score were negative, it would mean the height is below the mean. By using z-scores, we can compare data points from different distributions and understand how unusual or typical a particular value is within its dataset.

Z-scores help us quantify the relative position of a data point, providing a standardized way to interpret its significance in the context of the dataset's characteristics.

In summary, the z-score of a man who is 72.4 inches tall is approximately 0.45, indicating that his height is slightly above the average height of adult men.

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Answer:

1/4 or .25

Explanation

As for this specific question algebra is something I do in my head and skip many steps for however if you want to proof my answer it would be this.

-0.25-16*.25=-0.25-4

-0.25-4=-0.25-4

-4.25=-4.25

For the function  f(x) = -x-4 the value of f(4) is -8.

The given function is f(x) = -x-4.

We need to find the value of f(4).

To find this we have to replace the x value with 4.

Substitute x=4 in the function:

f(4)=-4-4

f(4)=-8

Hence, the value of f(4) is -8.

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Step-by-step explanation:

7/5 - 2×2/3 × 0.5 = 1.4 - 2×0.5×2/3

= 1.4 - 1 ×2/3

=1/4 × 2/3

=1.5 - 0.6

Answer:

98

Step-by-step explanation:

you at 56 in to 42

Answer:

98

pa brainless

Step-by-step explanation:

please brainless

0.8458 rounded to the nearest tenth is 0.8 given cos is 0.696706709347