a number less eleven algebraic

Bob had 50 pencils in the beginning.

A fractional number is expressed in the form -

x/y    {where y ≠ 0)

Given is that Bob gave four - fifths of his pencils to Barbara, then he gave two - thirds of the remaining pencils to bonnie.

Assume that he had {x} pencils in the beginning. We can write -

4x/5 + 2/3(x - 4x/5) = 10

4x/5 + 2x/3 - 8x/15 = 10

x(4/5 + 2/3 - 8/15) = 10

x = 10/0.93

x = 50

Therefore, Bob had 50 pencils in the beginning.

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{QUESTION IN ENGLISH -

Bob gave four fifths of his pencils to Barbara, then he gave two thirds of the remaining pencils to bonnie, if he ended up with 10 pencils for himself... how many pencils did bob have at the beginning?}

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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The equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

here we have given the graph of the

The roots of the given polynomial is

x=-2,x=-1 and x=3

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Therefore the equation of the polynomial is

f(x)=(x+2)(x+1)(x-3)

Therefore the equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

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The equation for this polynomial graphed will be P(x) = a(x + 2)(x + 1)(x – 3)³.

A polynomial expression is an algebraic expression with variables and coefficients.

The graph of the polynomial is given below.

From the graph, the roots of the polynomial will be -2, -1, and 3.

Then the factor of the polynomial will be

(x + 2), (x + 1), and (x – 3)

Then the polynomial will be

P(x) = a(x + 2)(x + 1)(x – 3)³

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Answer:

need a pohot

Step-by-step explanation:

Hope it's help

By applying integration rules and logarithm properties, the indefinite integral of the expression 9/(6 · eˣ + 4) is equal to the logarithmic expression \(\frac{9}{4}\cdot \ln \left|\frac{e^{x}}{6\cdot e^{x}+4} \right|\).

In this question we must apply algebraic substitution and partial fractions to find the indefinite integral:

\(\int {\frac{9}{6\cdot e^{x}+4} } \, dx\)

\(\int {\frac{9\cdot e^{x}}{(6\cdot e^{x}+4)\cdot e^{x}} } \, dx\)

\(9\int {\frac{du}{(6\cdot u + 4)\cdot u} }\)

Partial fraction

\(-\frac{27}{2} \int {\frac{du}{6\cdot u + 4} } +\frac{9}{4} \int {\frac{du}{u} }\)

\(-\frac{9}{4}\cdot \ln (6\cdot u + 4) + \frac{9}{4}\cdot \ln u\)

\(\frac{9}{4}\cdot \ln \left|\frac{u}{6\cdot u + 4} \right|\)

\(\frac{9}{4}\cdot \ln \left|\frac{e^{x}}{6\cdot e^{x}+4} \right|\)

By applying integration rules and logarithm properties, the indefinite integral of the expression 9/(6 · eˣ + 4) is equal to the logarithmic expression \(\frac{9}{4}\cdot \ln \left|\frac{e^{x}}{6\cdot e^{x}+4} \right|\).

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The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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Answer:

The cost of producing 200 units can be calculated by plugging in 200 for q in the equation E = 1.43q + 43,123. This gives us E = 1.43*200 + 43,123 = 286 + 43,123 = $43,409.

Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)

Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).

Step-by-step explanation:

8 ÷ 0.5 = 16

Quotient = 16

Step-by-step explanation:

-coefficent=1

-collect like terms /variables

-add numbbers (1+2)=3p

Answer:

1

Step-by-step explanation:

(p+q)(p-q)/(p+q)(p-q)=1

[It is an identity : a²-b²= (a+b)(a-b)]

Hope this will help:)

Answer: x=6, y=2, z=0

Step-by-step explanation:

We know from the third equation that z=8-4y

and from the first that x=y+4

Substitute into the 2nd equation,

4(y+4)-7(8-4y)=24

4y+16-56+28y=24

32y-40=24

32y=64

y=2

Meaning x=6 and z=0.

Answer:

9-2b

Step-by-step explanation:

Set up equation:

\(9 - 8b + 6b\)

Add like terms

\(9 - 2b\)

The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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Answer:

$22.50

Step-by-step explanation:

So if each topping cost 2.50 then just multiply by 9

Answer: 155

Step-by-step explanation:

Answer:

x = 1 and x = 7

Step-by-step explanation:

The given equation is \(x^2 - 8x + 7 = 0\).

We need to solve the equation.

It is a quadratic equation whose solution is given by :

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

Here, a = 1, b = -8 and c = 7

Put values,

\(x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(1)(7)} }{2(1)}\\\\=\dfrac{8\pm \sqrt{64-28}}{2}\\\\=\dfrac{8\pm 6}{2}\\\\=\dfrac{8+6}{2},\dfrac{8-6}{2}\\\\=7,1\)

So, the values of x are x = 1 and x = 7.

Answer:

1 - 31 + 191 does not represent the distance of the 2 given points.

The distance between the 2 points is 12

Step-by-step explanation:

Remember distance formula: \(d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\)

When we plug in our values into the distance formula into a calc,

d = \(\sqrt{(9-(-3))^2 + (-5-(-5))^2}\)

We get d = 12. This does not equal 1 - 31 + 191 (which equals 161).

Answer:

Sample Response: The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).

Step-by-step explanation:

Answer: 1/40

Step-by-step explanation:

The equivalent value of the fraction is A = 1/40

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p

Let the second fraction be q

Now , A = p/q

when the value of p = 1/8

And , when the value of q = 5

On simplifying the equation , we get

A = ( 1/8 ) / 5

So , the left hand side of the equation is equated to the right hand side by the value of ( 1/8 ) / 5

A = ( 1/8 ) / 5

A = ( 1/8 ) ( 1/5 )

On simplifying , we get

A = 1/40

A = 0.025

Therefore , the value of A = 1/40 = 0.025

Hence , the fraction is A = 1/40

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Answer:

y intercept is -6 put your first point on that y intercept

Step-by-step explanation:

from -6  rise 3 and run 1 (to the right )

whats that point ?  (0,2)

from  that point 2.... run 1 ( to the right and up 3) that will take from x4 to y6

(0,2) (4,6) Two points

y2 -y1 = 6

x2-x1  =2

6/2 simplified is 3/1

Make sense?

Average speed of the car will be the total distance traveled in the total time. Taking distance travelled as 150 in 5 seconds we have average speed as. 30×1=30 m

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

Using the dot plot given, the Percentage of games won is approximately: C. 72%.

In a dot plot, each of the data points of a data distribution is plotted on a dot plot as a dot. The number of dots represents the frequency of each data value in the data distribution.

In the dot plot, there are 18 dots which represents the difference in scores from 18 games between the high school soccer team and its opponent. Therefore, it means that the data points that are above 0, represents the number of games that the soccer team won.

There are 13 out of the 18 games that have a score difference that is positive and greater than 0. This means, the team won 13 games.

Percentage of games won = 13/18 × 100

Percentage of games won ≈ 72%.

Therefore, using the dot plot given, the Percentage of games won is approximately: C. 72%.

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Answer:

h= 9 in

Step-by-step explanation:

A=1/2bh

54=1/2 (12) a

54= (6) a

divide by 6

9= a