Four time the sum of twice a number and six is thirty-two. Find the number

Answer:

ASWKT TAKING X AS ANY NO.

X=1

by substituting we get answer as 2,0

Step-by-step explanation:

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Answer:

Step-by-step explanation:

area of a triangle = 1/2 * base * height

                             = 1/2 * 12 * 17

                             = 102 cm²

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

The polynomial fraction division (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)

A polynomial is a mathematical expression in which the least power of the unknown is 2.

Since we are given the polynomial expression

(1/x + 4) ÷ (x - 3/x² + 7x + 12).

We proceed to divide and simplify as follows.

(1/x + 4) ÷ (x - 3/x² + 7x + 12) = (1/x + 4) × (x² + 7x + 12)/(x - 3)

= (x² + 7x + 12)/(x - 3)(x + 4)

To simplify further, we factorize the numerator. So, we have that

x² + 7x + 12 = x² + 4x + 3x + 12

Factorizing, we have that

x² + 4x + 3x + 12 = x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

So, we have that

x² + 7x + 12 = (x + 3)(x + 4)

So, substituting this into the fraction, we have that

(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)(x + 4)/(x - 3)(x + 4)

Cancelling out (x + 4), we have that

(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)/(x - 3)

So, we have (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)

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The value of c that makes the function, f(x) = x² , x ≠0 and c , x = 0, continuous at x=0 is equals to 3.

The condition for continuity of a function f(x) at x=a : limf(x) = f(a)

x→a

Before convincing the above condition, we have to examine that the limit is exit or not at x=a. To test the condition for existancy of a limit at x=a of a function

f(x), we have to fulfill the following condition: lim f(x) = lim f(x)

x→a⁻ x→a⁺

Sometimes to evaluate a limit, we get indeterminate forms such as 0/0 or ∞/∞. In those cases, we use L'Hospital's Rule.

Now, we have f(x) = x² , x ≠0 and c , x = 0.

limf(x) = lim x² + 3 = (0)² + 3 = 3

x→0 x→0

So, lim f(x) = 3. For f(x) to be continuous

x→0

lim f(x) = f(0) => c = 3. Thus, c will work as

x→0

we have provide function is continuous.

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Complete question:

Find a value of c that makes the following function continuous at x = 0, explain why the value of c works. f(x) = x² , x ≠0 and c , x = 0

Answer:

Yes, (-3,9) makes the equation of y = -3x true

Step-by-step explanation:

y = -3x     (-3,9)

9 = -3(-3)

9 = 9

TRUE

Answer:

Move convo here

Step-by-step explanation:

Answer:

5.42436246 x 10^8

Step-by-step explanation:

- There should only be 1 whole number. => 5

- Other numbers should after the decimal point => .42436246

- Multiply with 10^?

? represents the number of digits is the decimal point moved from the original number. => 8

So, the answer is 5.42436342 x 10^8

The gym option costs less per class for six classes(Option B), and the gym option costs less per class for seven (Option D).

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Here we're specified that:

For high school classes:

For local gym:

For 6 classes:

High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 6 = $(20+60) = $80

(since $20 dollar is one time cost, and $10 was price for each class)

Similarly, joining local gym's $50 cost is one time, and rest of $5 is price for each class.

Local gym : $50 + $(5+5+5+5+5+5) = $20 + $5 × 6 = $(20+30) = $50

For 7 classes:

High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 7 = $(20+70) = $90

Local gym : $50 + $(5+5+5+5+5+5+5) = $20 + $5 × 7 = $(20+35) = $55

Thus, the statements which are true about the average cost for the two options is given by: Option B: The gym option costs less per class for six classes., Option D: The gym option costs less per class for seven classes.

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Answer:

38 feet.

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 35 ft/s

Angle of projection (θ) = 40º

Acceleration due to gravity (g) = 9.8 m/s²

Range (R) =?

Next, we shall convert 9.8 m/s² to ft/s². This can be obtained as follow:

0.3048 m/s² = 1 ft/s²

Therefore,

9.8 m/s² = 9.8 m/s² × 1 ft/s²/ 0.3048 m/s²

9.8 m/s² = 32.15 ft/s²

Thus, 9.8 m/s² is equivalent to 32.15 ft/s².

Finally, we shall determine how far away the soccer ball hit the ground (i.e range) as shown below:

Initial velocity (u) = 35 ft/s

Angle of projection (θ) = 40º

Acceleration due to gravity (g) = 32.15 ft/s²

Range (R) =?

R = u² × Sine 2θ / g

R = 35² × Sine (2×40) / 32.15

R = 1225 × Sine 80/ 32.15

R = 1225 × 0.9848 / 32.15

R = 37.5 ≈ 38 feet.

Thus, the soccer ball hit the ground 38 feet away.

Answer:

The anwser is C.

Step-by-step explanation:

Answer:

$42.00

Step-by-step explanation:

So, something hasn't been subtracted from your bottom line. The bank is saying you only have $26.33. You think you have $68.33.

Let's look for the difference. This is one of those great times when the word in english and the word in math have the same meaning. Difference is telling us to subtract.

68.33 - 26.33

= 42.00

Check:

If you subtract the missing entry, $42.00 from your total,

68.33 - 42.00

you get $26.33, exactly the balance the bank says you have. Now your account is balanced!

Answer:

1.5x + 2

Step-by-step explanation:

(3x + 4)/2 = 1.5x + 2

Answer:

if 1 deposit = $18, she´ll need $52

If she just has $18, she´ll need $232

Answer:

do it your self.

Step-by-step explanation:

Answer:

\(Speed = 219.81\ miles/hour\)

Step-by-step explanation:

Given

\(Speed = 219.809\ miles/hour\)

Solving (a) Approximate to nearest hundredth

\(Speed = 219.809\ miles/hour\)

\(Speed = 219.81\ miles/hour\)  -- Approximated

See (b) for explanation

Solving (b): Steps for (a)

First, we need to note the digit in the thousandth place value

\(Digit = 9\)

Since:

\(9\geq 5\)

We have to increase the digit in the hundredth position by 1

This gives:

\(Speed = 219.81\ miles/hour\)

Hence:

Option B answers the question

Answer:

There are many centeral tendancy like in pie charts, data handling etc. But i think ur asking abt this.. -

- Mean : It is the average ex : 5,5,2 : 5+5+2 /3 = 4

- Median: the middle number (arrange in asc or des order) then find the middle num if there are 2 middle num then find the mean of the 2

ex : 3,4,1,2,5  :  1,2,3,4,5, the middle is 3

-Mode : It is the data that is happening the most frequent

ex: 1,2,2,3,3,3,4,4,5   :    3

Ihope this is usefull !

Answer:

Step-by-step explanation:

they aarre 38 left

Answer:

3√x^5/=15√x

   5√x^2=10√x  

Step-by-step explanation:

multiply 5 by 3.

multiply 2 by 5.

Answer:

$16

Step-by-step explanation:

the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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Answer:

the answer is 14.9

Answer:

1/5(1-x)

Step-by-step explanation:

Distributed

1/5-1/5x

Answer:1/5 (n-1)

Step-by-step explanation: Because say 1/5 and difference means subtract and number means variable and 1 means subtract it with the variable.

The lateral area of the given prism is  450 mm².

The lateral area of any prism is equal to the areas of the sides faces

The base of the prism is triangle

It has 3 side faces

The lengths of the side faces are 5 , 12 , 13 and their height is 15.

The lateral area = (5 × 15) + (12 × 15) + (13 × 15)

The lateral area= 75 + 180 + 195

The lateral area = 450 mm²

Hence, the lateral area of any prism is  450 mm².

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Answer:

37.5

Step-by-step explanation:

1/8 of a circle is 12.5% so times that by 3 and you get 37.5.

Answer:  \(2x^{2}-(3+g)y^{2}-11x\)

Step-by-step explanation:

You add each coeficient with the same type of incognita:

\(x^{2} +x^{2} =2x^{2}\)

\(-3y^{2} -gy^{2} = -(3+g)y^{2}\)

\(-7x-4x=-11x\)

Answer:

48 books

Step-by-step explanation: