If the circumference of a circle is about 15.4 cm, estimate to the nearest whole number the diameter of the circle

Answer:

14.6

Step-by-step explanation:

Hi

\(\sqrt{(x+7)\)   -1 = X

Let's square the whole thing  

so we have :    x+7 +1 = x²

                         x² +x+7 +1 = 0

                         x²+x+8 = 0

no easy way to see a common factor so, let 's resolve by using discriminate.  

Δ = 1-4*1*8

Δ = 1 -32

Δ = -31

as Δ  ≤ 0 , there is no Real answer to your equation  

however , if you need we can find imaginary solutions. Just ask in commentaries

Answer:

its 2

Step-by-step explanation:

the scientific notation is just another mumble jumble way to write the same thing without so many repetitive zeros, so hmmm 780000 has 4 zeros, so what we do is we can say

78 and 4 zeros following it

or we can say

78 * 10⁴, if we get that product, is 780000

in scientific notation, we only leave one digit to the left of the decimal point

so the same thing above can be written as

78 * 10000, can be written as 78.0 * 10000

or as

7.8 * 100000

or as

0.78 * 1000000

check their product

7.8 * 100000, is really just 780000

because we moved the decimal to the left one more slot, it

became 7.8 * 100000

or in

Answer:

780,000 \(=7.8 * 10^5\)

Step-by-step explanation:

Don't worry! I hope you do great on your finals, goodluck<3.

\(a * 10^{b}\)

Variable A represents a number thats absolute value has to be greater than or equal to 1 and less than 10. This is represented below

1 ≤ | a | < 10

Therefore we know that 780,000 will be 7.8, because it is greater than 1 and less than 10 as well can still represent our original number.

\(7.8 * 10^b\)

Assuming you know how powers work, if not I'll go over them very quickly.

For example 8² = 8 * 8, 8³ = 8 * 8 * 8.

what I mean by this is if its in, tenths, hundreths, thousands, 10 thousands..

It's pretty obvious that our number is in the 100 thousands place.

Now if you know you're powers pretty well, this will be easy, although let me try to walk you through it if not.

remember the equation:

\(7.8 * 10^b\)

We are trying to find b.

10 to what power is equal to 100,000

\(10^{1} = 10, 10^{2} = 100, 10^3 = 100, 10^{3} = 1,000, 10^4 = 10,000, 10^5 = 100,000\)

How I like to remember what a power equals is counting the 0's :)

How we know if our answer is correct is plugging it into our equation and solve:

\(7.8 * 10^5\)

We know that 10 to the power of 5 equals 100,000.

\(7.8 * 100,000\)

and using a calculator, or mental math, or doing it the old fashion way, we know that 7.8 * 100,000 is equal to 780,000

2. 8.472 * 10^5 in standard form is

3. The scientific notation of 0.000067 is 6.7 * 10^-5

4. The division gives 4.455 * 10^3

Scientific notation is a way of expressing very large or very small numbers in a compact and convenient way.

In scientific notation, a number is written as a coefficient multiplied by a power of 10.

The coefficient is a number between 1 and 10 (or between -1 and -10 for negative numbers), and the power of 10 indicates the size of the number.

Calculator can be used to get numbers to scientific notation and in standard form

The required division can be performed using calculator to get 4.455 * 10^3

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The specified distance will be 13 cm. Therefore, the distance of 13 cm between points L(5, -8) and M(-7, -3).

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. A number line in mathematics is a horizontal straight line with numbers uniformly spaced apart. A number line can show how all the numbers in a series are represented. Both endpoints of this line continue indefinitely.

The directed line segment from Q to S on a number line has ends at -14 and 2, respectively. A 3:5 division of the directed line segment from Q to S occurs at point R. There will be a 13 cm gap between the two points. Because of this, the separation between points L(5, -8) and M(-7, -3) is 13 cm.

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Step-by-step explanation:

Let the other 4 friends arrange themselves first. There are 4! ways to do so.

Now there are 3 spaces between the 4 friends, and 1 at each end (total 5 spaces)

Example: _F_F_F_F_

Alice can choose to stand in any of the 5 spaces. David can choose to stand in any of the 4 remaining spaces (now Alice and David are not next to each other)

Total number of ways = 4! * 5 * 4 = 480.

Answer: 9000$

Step-by-step explanation:

Let 's use the formula to find the vertex of the parabola:

ax²+bx+c=0

\(\displaystyle x_v=-\frac{b}{2a} \\\\ Where :\\\\ y_v- maximum \ \ income \\\\ y_v=a(x_v)^2+bx_v+c \\\\ Then \ in \ \ our \ \ case : \\\\ -4p^2+1200p =0 \\\\ x_v=-\frac{1200}{-4\cdot 2} =150 \\\\ y_v=-4\cdot (150)^2+150\cdot 1200 \\\\ y_v=150\cdot 1200-150\cdot 600 \\\\ y_v=600\cdot 150=\bf 9000 \\)

Given the expression :

The expression will be equal:

so, the answer is option 4)

Answer:

Step-by-step explanation:

volume of sphere = 4πr³/3

= 4π×512/3

≈ 2143.6 cm³

The shortest possible length of the other side is 15 units, and the longest possible length is 25 units.

Let's denote the shortest possible length of the other side of the triangle as 'x' units. To find the longest possible length, we subtract the lengths of the given side and the shortest side from the perimeter:

Longest possible length = Perimeter - Given side - Shortest side

= 40 - 15 - x

= 25 - x

Since a triangle's perimeter is the sum of its three sides, we can set up an equation:

Given side + Shortest side + Longest side = Perimeter

Substituting the values:

15 + x + (25 - x) = 40

Simplifying:

40 - x + x = 40 - 15

40 = 25 + x

x = 40 - 25

x = 15

Therefore, the shortest possible length of the other side is 15 units, and the longest possible length is 25 units.

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ANSWER:h=10  S=10??    umm i hope i got that right have a nice day btw i responded to your comment

Answer:

\(x = 21 - 2\frac{1}{3}y\)

Step-by-step explanation:

3x + 7y = 63

Minus 7y from both sides, then you get...

3x = 63 - 7y

Now we divide both sides by three to find the value of x:

\(x = 21 - 2\frac{1}{3}y\)

Kieran will have fully cleared the loan after 15 years on charging simple interest at 3% .

While compound interest is computed on the original amount borrowed plus any accrued interest, simple interest just considers the original amount borrowed. For instance, if you borrow $100 for a year at 5% simple interest, your final balance will be $105 instead of $100. Yet if you take out a $100 loan for a year at 5% compound interest, you would end up owing $105.12 since the interest is added to the principal at regular intervals (for example, every month) and the interest for the following period is calculated using the new, higher sum. This indicates that compound interest accumulates more quickly than simple interest and, over time, might result in much higher total interest costs.

Given that, interest rate is 3% of the original amount thus:

r = 0.03P

Also, she pays of $740 thus, after t years the amount is:

P(t) = P - 740t

Now, for t = 1:

P(1) = P - 740 - 0.03P

= 0.97P - 740

For t = 2:

P(2) = 0.97(0.97P - 740) - 740 - 0.03(0.97P - 740)

= 0.94P - 1480.1

Similarly for P(15) = 0.

Hence, Kieran will have fully cleared the loan after 15 years.

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When x = 3, f(x) = 18 + 5√5.

To evaluate the function f(x) = 2(x)² + 5√(x+2), we'll substitute a given value of x into the function and simplify the expression. Let's go through the steps:

Start with the given function: f(x) = 2(x)² + 5√(x+2).

Substitute a specific value for x. Let's say x = 3.

Plug in the value of x into the function: f(3) = 2(3)² + 5√(3+2).

Evaluate the exponent: 3² = 9.

Simplify the square root: √(3+2) = √5.

Multiply the squared term: 2(9) = 18.

Substitute the simplified square root: 18 + 5√5.

Therefore, when x = 3, f(x) = 18 + 5√5.

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Evaluate the function f(x) = 2(x)² + 5√(x+2)

The 6 - digit number when rounded to the nearest thousand and hundred will have a result that is the  556100.

Rounding off makes a  number is made simpler by keeping its value intact but closer to the next number.

Rounding to the nearest thousand:

The original number, 555500, lies between 555000 and 556000.

Since it is equidistant from both, we round it to the nearest even thousand, which is 556000.

Rounding to the nearest hundred:

The rounded number from the previous step, 556000, lies between 555900 and 556100.

Again, it is equidistant from both, but in this case, we round it up to the nearest hundred, which is 556100.

Therefore, when you round the number 555500 to the nearest thousand and hundred, you get the same result, which is 556100.

Thus, the answer is  556100.

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Answer:

139 quarts

Step-by-step explanation:

Answer:

The mechanic would use 139 quarts for the 17 cars.

Answer:

s=24

Step-by-step explanation:

Let individual invest P in account.

The formula for the amount is,

Determine the value of P for A = 10,000, r = 6.4% anf t = 5.

Thus individual invest $7333.2 in account to buy car in five years.

Answer:

5 1/7 pages in one hour. And what does "A.B.C.D." Mean?

Step-by-step explanation:

Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

\(T(t) = T_a + (T_0 - T_a)e^{-kt}\)

Considering the surrounding and initial temperature, we have that the function is given as follows:

\(T(t) = 69 + 135e^{-kt}\)

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

\(185 = 69 + 135e^{-1.5k}\)

\(e^{-1.5k} = \frac{116}{135}\)

\(k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}\)

k = 0.1011.

Hence:

\(T(t) = 69 + 135e^{-0.1011t}\)

Hence the temperature after 4.5 minutes is given as follows:

\(T(4.5) = 69 + 135e^{-0.1011 \times 4.5}\)

T(4.5) = 155ºF.

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The correct general form of Sarah's budget line is 60 > 20BR + 30BC. This equation represents the maximum combination of bus rides and breakfast combos that Sarah can afford within her budget limit of $60.

A budget line represents the different combinations of goods or services that a consumer can afford given their budget constraint. It shows the maximum quantity of one good that can be obtained for a given quantity of another good, given the prices of the goods and the consumer's budget.

In this case, Sarah's budget line is given by the equation 60 > 20BR + 30BC. This equation represents the constraint that Sarah's total expenditure on bus rides (BR) and breakfast combos (BC) should not exceed $60. The coefficients 20 and 30 represent the prices of bus rides and breakfast combos, respectively. The inequality symbol ">" indicates that Sarah's expenditure must be strictly less than $60 to stay within her budget constraint.

Therefore, the correct alternative showing the general form of Sarah's budget line is 60 > 20BR + 30BC. This equation represents the maximum combination of bus rides and breakfast combos that Sarah can afford within her budget limit of $60.

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The ball will take approximately 0.39 seconds to reach maximum height.

In this question we are going to determine the maximum height based on the characteristics inherent to second order polynomials and the quadratic formula.

Mathematically speaking, the function height of the ball represents a parabola, whose vertex represents an absolute maximum. In order to find the time needed for the ball we need to rearrange the given quadratic function:

\(-4.9\cdot t^{2} +3.82\cdot t + (1.7-h) =0\) (1)

The quadratic formula of the equation is:

\(t = \frac{-3.82\pm \sqrt{3.82^{2}-4\cdot (-4.9)\cdot(1.7-h)}}{2\cdot (-4.9)}\)

The discriminant must be zero in order to determine the time needed to reach maximum height:

\(t = -\frac{3.82}{2\cdot (-4.9)} \,s\)

\(t \approx 0,390\,s\)

The ball will take approximately 0.39 seconds to reach maximum height.

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Answer:

The vertex is -5/2 and -9/2

Step-by-step explanation:

I looked it up on math

way

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola y = 2x² + 10x + 8 is (-2.5, -4.5).

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

Then its roots are given as:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in the form (x, y);

a defines how narrower the parabola is, and the "-" or "+" that the parabola will open up or down.

The general form of a parabola is written in the form ax²+bx+c, which is a quadratic equation. While the vertex form of the parabola is written as y=a(x-h)² + k.

Given that the equation of the parabola is y = 2x² + 10x + 8. Now if we compare the general equation of the parabola with ax²+bx+c, the value of a, b, and c will be 2, 10, and 8, respectively.

Further, the vertex of the parabola can be written as,

h =−b/2a

h = -10 / 2(2)

h = -10/4

h = -2.5

k = -(b² - 4ac) / 4a

k = -[10² - 4(2)(8)] / 4(2)

k = (100 - 64) / 8

k = -36/8

k = -4.5

Hence, the vertex of the parabola y = 2x² + 10x + 8 is (-2.5, -4.5).

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The degrees of freedom for a data table can be calculated using the formula:

Degrees of Freedom = (Number of Rows - 1) * (Number of Columns - 1)

In this case, the data table has 10 rows and 11 columns. Plugging these values into the formula:

Degrees of Freedom = (10 - 1) * (11 - 1) = 9 * 10 = 90

Therefore, the degrees of freedom for the given data table is 90.

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Answer:

The first one

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

you are gonna add all the parts together which is seven and because three parts are blue chances are that it might stop at blue three times out of seven

Answer:

y = 40             x = 80

Step-by-step explanation:

520 = 3.25x + 6.5y        x+y=120

x+y=120

x = 120-y

520 = 3.25(120-y)+6.5y

520 = 390-3.25y+6.5y

520 = 390+3.25y

130=3.25y

Divide each side by 3.25

40 = y

x = 120-y

x = 120-(40)

x = 80

The number of tacos sold is 80.

The number of burritos sold is 80.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

Number of Tacos = x

The cost of each taco = $3.25

Number of burritos = y

The cost of each burrito = $6.50

Now,

Total amount after sold = $520

This means,

3.25x + 6.50y = 520 _____(1)

Total number of food sold = 120

x + y = 120 _____(2)

From (1) and (2),

x + y = 120

x = 120 - y _____(3)

Substituting (3) in (2),

3.25 (120 - y) + 6.50y = 520

390 - 3.25y + 6.50y = 520

3.25y = 520 - 390

3.25y = 130

y = 40

Now,

x = 120 - 40

x = 80

Thus,

The number of tacos is 80.

The number of burritos is 80.

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