How many grams of the isotope remains after 90 days?

The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

8(x² + 2x + 1) = -3 + 8

8(x² + 1) = 5

(x² + 1) = 5/8

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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Answer:

[tex] \frac{27}{8} cm {}^{3} [/tex]

Is the volume of this right rectangular prism.

Step-by-step explanation:

Rectangular prism volume formula is:-

Answer:

[tex]V=\frac{27}{8}\: cm^3[/tex]

Step-by-step explanation:

The formula to find the volume of a rectangular prism is:

V = length × height × width

Let us find now.

[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]

Answer:

= 5.375

Step-by-step explanation:

Use the algorithm method.

7  9 9 10

8 . 0 0 0

- 2 . 6 2 5

5 . 3 7 5

= 5.375

Answer:

5 3/8

Step-by-step explanation:

change it so that every number is a improper fraction and same denominator

64/8 - 21/8 = 43/8 = 5 3/8

The denominator cannot be zero, so

[tex]e^x - 9 = 0 \implies e^x = 9 \implies x = \ln(9)[/tex]

is not in the domain of [tex]f(x)[/tex].

[tex]\ln(x)[/tex] is defined only for [tex]x>0[/tex], and we have

[tex]\ln(x+1) > 0 \implies e^{\ln(x+1)} > e^0 \implies x+1 > 1 \implies x>0[/tex]

so there is no issue here.

By the same token, we need to have

[tex]x+1 > 0 \implies x > -1[/tex]

Taking all the exclusions together, we find the domain of [tex]f(x)[/tex] is the set

[tex]\left\{ x \in \Bbb R \mid x > 0 \text{ and } x \neq \ln(9)\right\}[/tex]

or equivalently, the interval [tex](0,\ln(9))\cup(\ln(9),\infty)[/tex].

Option A. The total share expense that the company would share would be given as 512,000

These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.

The total number of the employees that are knwon to satistfy condition are given as

800 * 0.8

= 640

The options that are estmated that would be exercised

This is given as the employees * share option

= 640×50

=32000.

The total shae for the company would be gotten as

= 32000× $16

This gives us $512,000.

Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.

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The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.

The future values of the savings account are calculated in two installments.

The first installment is for 10 years when the account earns 6% compounded semiannually.

Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.

Future values can be determined using the future value formula or an online finance calculator, as follows:

N (# of periods) = 20 (10 years x 2)

I/Y (Interest per year) = 6%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $3,612.22

Total Interest $1,612.22

N (# of periods) = 32 (8 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)

PMT (Periodic Payment) = $0

Results:

FV = $5,816.85

Total Interest $2,204.63

Thus, the value of the account after 18 years was $5,816.85.

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The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

Given that; 1 - cos(6x) = ?

First, we rewrite using trig identity

1 - cos(2 × 3x)

Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }

1 - ( 1 - 2sin²(x) )

Eliminate the parentheses

1 - 1 + 2sin²(x)

2sin²(x)

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

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Answer: 9x+4

Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.

Answer:

9x + 4

Step-by-step explanation:

9x + 2x - 6 - 2x + 10

Rearranging,

=> 9x + 2x - 2x + 10 - 6

=> 9x + 4

Answer: TRS is congruent to CSE

Step-by-step explanation:

You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.

Angle T has 1 line, so is congruent to C, which also has 1 line.

Angle R has 2 lines, so is congruent to S, which also has 2 lines.

Angle S has 3 lines, so is congruent to E, which also has 3 lines.

You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).

Answer:

12. standard deviation =6.22972...

. variance = 38.80952...

Answer:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=2x^2-x-10[/tex]

The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.

To find these points, factor the quadratic equation, set it to zero, then solve for x.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=2 \cdot -10 = -20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-5)+2(2x-5)[/tex]

Factor out the common term (2x - 5):

[tex]\implies (x+2)(2x-5)[/tex]

Set the factored function to zero:

[tex]\implies (x+2)(2x-5)=0[/tex]

Apply the zero-product property:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts of the graph are:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

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Answer:

Step-by-step explanation:

A new baby grew:

Total inches during two months:

The number paths between c and d of length 2.

Find the number of paths between c and d in the graph of length:

The number of paths between c and d is 0.

There is the number of paths between c and d of length 2.

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Answer:

Distance = 15

Step-by-step explanation:

4 - (-11) = 4 + 11 = 15

Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:

Distance = 1/2 × 36.77

Distance = 36.77/2

Distance = 18.39 ft.

For the height of this triangle, we would apply Pythagorean's theorem:

h² = 25.02² - 18.39²

h² = 626.0004 - 338.1921

h² = 287.8083

h = √287.8083

h = 16.97 ft.

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 36.77 × 16.97

Area of triangle = 311.99 ft².

For area of the rectangle, we have:

Mathematically, the area of a rectangle can be calculated by using this formula;

Area = LW

Area = 36.77 × 31.11

Area = 1143.92 ft².

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The total number of common tangents that can be drawn to the circles is 1

The tangent lines of a circle are the lines drawn, that touch the circle at only one point

The complete question is added as an attachment

From the attached figure, we have the following highlights:

The one point of intersection is the only point where both circles can have common tangents

Since there is only one point of intersection, then the number of common tangents on the circles is 1

Hence, the total number of common tangents that can be drawn to the circles is 1

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The required two-digit number is 75.

In mathematics, it deals with numbers of operations according to the statements.

let the number in tenth place be x.
And has two fewer units than tens.
= x - 2

The two-digit number can be given as
= 10x + (x - 2)

= (11x - 2)

Reversing the digits
= (x - 2)10 + x
= 11x -20

The difference between twice the number and the number reversed is 93.

[tex]2(11x - 2) - (11x - 20) = 93\\22x-4-11x+20 = 93\\11x+16 = 93\\11x = 93-16\\11x = 77\\x = 7[/tex]

Now the required two-digit number is,
=  11x -2
=  11*7 - 2
=  77 -2
= 75

Thus the required two-digit number is 75.

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Given the above information, it is correct to say Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. (Option A)

Recall that the mean (statistically speaking) is a measure of central tendency of a probability distribution along median and mode.

You could also state that it is an expected value. Given that samples of actual value taken from the

Hence, since from 100 samples taken, the number of eggs of 15.1 or less occurred, then the true mean or actual mean is less than 16.

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Answer:

equation 1 has no solution

Step-by-step explanation:

when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1

The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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From the constraint, we have

[tex]x+y+z=9 \implies z = 9-x-y[/tex]

so that [tex]s[/tex] depends only on [tex]x,y[/tex].

[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]

Find the critical points of [tex]g[/tex].

[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]

[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]

Using the given constraint again, we have the condition

[tex]x+y+z = 2x+y \implies x=z[/tex]

so that

[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]

and [tex]s[/tex] depends only on [tex]x[/tex].

[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]

Find the critical points of [tex]h[/tex].

[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]

It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).

Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.

[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]

for all [tex]x[/tex], which indicates a maximum.

We find that

[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]

The second derivative at the critical point exists

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0

[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

[tex]$\frac{d h}{d x}=18-6 x=0[/tex]

⇒ x = 3

It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]

for all x, which suggests a maximum.

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Answer:

10, -7, -35, 5

Step-by-step explanation:

f(9) = -5(-9 + 7) = 10

0 = -5(x + 7)

0 = x + 7

x = -7

f(0) = -5(0 + 7) = -35

-60 = -5(x + 7)

12 = x + 7

x = 5

The limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]

since the degree of the numerator exceeds the degree of the denominator.

Answer:

Step-by-step explanation:

x² + 2x = x(x + 2)

[tex]\sf \dfrac{x +5}{x + 2}-\dfrac{x+1}{x^2+2x}=\dfrac{x + 5}{x +2}-\dfrac{x+1}{x(x+2)}[/tex]

LCM = x(x+2)

                        [tex]\sf =\dfrac{(x+5)*x}{(x+2)*x}-\dfrac{x+1}{x(x+2)}\\\\=\dfrac{x*x + 5*x}{x^2+2x}-\dfrac{x+1}{x^2+2x}\\\\=\dfrac{x^2+5x - (x+1)}{x^2+2}\\\\=\dfrac{x^2+5x -x - 1}{x^2+2x)}\\\\=\dfrac{x^2+4x-1}{x^2+2x}[/tex]

Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. So that the required symbolic language required in the question is: 17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6

Thus the value of x is 90[tex]\frac{2}{3}[/tex].

Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. Some types of fractions are mixed fractions, proper fractions, and improper fractions.

Thus to express the given question in a symbolic language, let the fraction of 17 taken away be represented by x.

So that;

i. a fraction of 17 is taken away from 17 can be expressed as 17 - [tex]\frac{x}{17}[/tex].

ii. remains exceeds one-third of seventeen by six can be expressed as  [tex]\frac{17}{3}[/tex] + 6

Therefore the required symbolic language to the question is:

                  17 - [tex]\frac{x}{17}[/tex]  =  [tex]\frac{17}{3}[/tex] + 6

So that,

[tex]\frac{289 - x}{17}[/tex] = [tex]\frac{17 + 18}{3}[/tex]

cross multiply to have

3(289 - x) = 17(17 + 180)

867 - 3x = 595

3x = 867 - 595

    =272

x = [tex]\frac{272}{3}[/tex]

  = 90[tex]\frac{2}{3}[/tex]

x = 90[tex]\frac{2}{3}[/tex]

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The number of years she had her investment is after 3 years

From the question, the given parameters are:

The number of years (T) is calculated from the following simple interest formula

I = PRT

Substitute the given parameters in the above equation

20.64 = 400 * 1.72% * t

Express 1.72% as decimal without percentage

20.64 = 400 * 0.0172 * t

Evaluate the product

20.64 = 6.88 * t

Divide both sides by 6.88

20.64/6.88 = 6.88/6.88 * t

Evaluate the quotient

3 = t

Rewrite the equation as

t = 3

This means that she had her investment after 3 years

Hence, the number of years she had her investment is after 3 years

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The slopes of the two diagonals of the rhombus are: A. b - f/a - e and -a + e/b - f.

To find the slope, the formula used is: change in y/change in x.

If two lines are perpendicular to each other, their slope values will be negative reciprocals.

In a rhombus, the two diagonals in the rhombus bisects each other at angle 90 degrees. This means that the two diagonals of a rhombus are perpendicular to each other. Therefore, the slope of the diagonals of any rhombus would be negative reciprocals.

The slope of the diagonals of the rhombus given would therefore be negative reciprocals to each other.

Given two endpoints of one of the diagonals as:

(a, b) = (x1, y1)

(e, f) = (x2, y2)

Slope (m) = change in y / change in x = b - f/a - e

The negative reciprocal of b - f/a - e is -a + e/b - f.

Therefore, the slopes of the two diagonals are: A. b - f/a - e and -a + e/b - f.

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Answer:

It's supplementary angle I think

Answer:

one angle is 20° and the other is 70°

Step-by-step explanation:

Complementary angles add up to 90°.

Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].

Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.

As of now, first angle = x and second angle =  3x+10.

Since they are complementary angles, both angles add up to 90°

⇒ 1st angle + 2nd angle = 90°

∴ [tex]x+3x+10 = 90[/tex]  [since 3x and x are like expressions, we should add 3x + x = 4x]

⇒ [tex]4x = 90 - 10[/tex]  [by transposing 10 from LHS to RHS]

⇒ [tex]4x = 80[/tex]

⇒ [tex]x = \frac{80}{4}[/tex]  [by transposing 4 from LHS to RHS]

⇒ [tex]x = 20[/tex]

∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°

Answer:

( 2,-3)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect

The two graphs intersect at x = 2 and y = -3

( 2,-3)