combine like terms to create an equivalent expression

3.26d + 9.75d - 2.65​

a) The area formula for the rectangle is equal to A = r² · sin 2θ.

b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.

c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm

In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:

A = w · h

A = (2 · r · cos θ) · (r · sin θ)

A = 2 · r² · sin θ · cos θ

A = r² · sin 2θ

Where:

Second, perform first derivative test: (r - Constant)

A = 2 · r² · cos 2θ

2 · r² · cos 2θ = 0

cos 2θ = 0

θ = 45°

Third, perform second derivative test: (θ = 45°)

A'' = - 4 · r² · sin 2θ

A'' = - 4 · r² (MAXIMUM)

Fourth, determine the maximum possible area of the rectangle:

A = 4² · sin 90°

A = 16 cm²

Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)

w = 2 · r · cos θ

w = 2 · 4 · cos 45°

w = 8 · √2 / 2

w = 4√2 cm

w = 5.66 cm

h = r · sin θ

h = 4 · sin 45°

h = 4 · √2 / 2

h = 2√2 cm

h = 2.83 cm

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Answer:

20cm

Step-by-step explanation:

The conditional value probability is solved and P ( F | E ) = 6/17

Given data ,

P ( E ) = 0.85

P ( F ) = 0.4

P ( E ∩ F ) = 0.3

Now , the formula for conditional probability to calculate P(F|E):

P(F|E) = P(E ∩ F) / P(E)

We are given that P(E) = 0.85 and P(E ∩ F) = 0.3, so we can substitute those values in:

P(F|E) = 0.3 / 0.85

Simplifying this fraction, we get:

P(F|E) = 6/17

Hence , the probability of F given that E has occurred is 6/17 or approximately 0.35.

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The volume of the stump is 7451.9 cubic inches.

The volume of a cylinder can be calculated using formula below:

V = πr²h

where r is the radius and h is the height of the cylinder

We have circumference (C) = 61 in.

Let's find the radius (r) using the formula:

C = 2πr

61 = 2 * 22/7 * r

r = 9.70 in

h = 2.1 ft  = 2.1 * 12 = 25.2 in

Substituting into V = πr²h:

V = 22/7 * 9.70² * 25.2

V = 7451.9 cubic inches

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Answer:

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Step-by-step explanation:

Answer:24.1104189866

Step-by-step explanation:

the answer to What is 692837 divided by 28736 is 24.1104189866

The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Surface area of a pyramid is expressed as;

area of 4 lateral face + area of base

area of base = 440²

= 193600 units²

area of a lateral = 1/2 bh

= 1/2 × 440 × 356

= 78320

For four surfaces = 4 × 78320 = 313280

Total surface area = 313280+78320

= 391600 units ²

Volume of a pyramid is expressed as;

V = 1/3base area × height

V = 1/3 × 440² × 280

V = 18069333.33 units³

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Answer:

28

Step-by-step explanation:

let's assumed that

x = Jerry's age

y = Carrie's age

if Jerry 4 years older that Carrie

x = y + 4

x + y = 52

(y + 4) + y = 52

2y + 4 = 52

2y = 48

y = 24

x = y + 4

x = 24 + 4

x = 28

(i) The mathematical expression to show Mrs. Chamling's earnings and expenses can be written as:

Weekly earnings = Rs 6,000

Daily food expenses = Rs 250

Daily transportation expenses = Rs 75

Total weekly expenses = (Rs 250 + Rs 75) x 7 = Rs 2,275

Total weekly savings = Weekly earnings - Total weekly expenses

= Rs 6,000 - Rs 2,275

= Rs 3,725

(ii) Mrs. Chamling saves Rs 3,725 in a week.

As for the second part of the question, I am not sure what is being asked. The sentence is incomplete and unclear. Please provide more information or context so I can assist you better.

Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

Answer:

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

Use the compound interest formula:

Where:

Plugging in the values, we get:

Answer: Point P

Step-by-step explanation: over 2 up 1 (2,1)

Answer: M

Step-by-step explanation:

The quantity of milk that should be used for the given amount of flour would be = 11/25

The following steps are being taken to calculate the amount of milk that would be needed for the recipe.

The number of cups of flour for 1⅒ of milk = 5

The quantity of milk needed for 2cups of flour= X

That is;

1⅒milk = 5 flour

X milk = 2 flour

cross multiply;

X milk = 2×1⅒/5

= 11/25

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The expression x = (2 ± √(-12)) / 2 is negative, this quadratic equation does not have real solutions.

The quadratic formula, we need the quadratic equation in the form ax^2 + bx + c = 0. The given equation is x^2 + 1 = 2x - 3. To set it up correctly, we need to move all terms to one side of the equation to have a zero on the other side.

Rearranging the equation, we get x^2 - 2x + 4 = 0. Now we can identify the coefficients a, b, and c.

The correct expression to set up the quadratic formula is:

B) x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 2x + 4 = 0, we have:

a = 1

b = -2

c = 4

Plugging these values into the quadratic formula, we have:

x = (-(-2) ± √((-2)^2 - 4 * 1 * 4)) / (2 * 1)

Simplifying further, we get:

x = (2 ± √(4 - 16)) / 2

x = (2 ± √(-12)) / 2

Since the expression inside the square root is negative, this quadratic equation does not have real solutions.

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Note the full question may be :

Consider the quadratic equation 2x^2 + 5x - 3 = 0. Which expression correctly sets up the quadratic formula?

A) x = (-b ± √(b^2 - 4ac)) / (2a)

B) x = (-b ± √(b^2 + 4ac)) / (2a)

C) x = (-b ± √(4ac - b^2)) / (2a)

D) x = (b ± √(b^2 - 4ac)) / (2a)

The number that is one-third of 343 is 49.

1/3 of 343 can be found by multiplying 343 by 1/3:

1/3 x 343 = (1/3) x (343) = 343/3

To simplify the result, we can divide both the numerator and denominator by the greatest common factor (GCF) of 343 and 3, which is 7:

343/3 = (343 ÷ 7) / (3 ÷ 7) = 49/1

Therefore, 1/3 of 343 is 49.

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Answer: 10/9, 0

Step-by-step explanation:

sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2

Answer:

1)  A = 32.6°, C = 111.4°, b = 12.0

2) A = 53.6°, B = 85.7°, C = 40.7°

Step-by-step explanation:

Given values of triangle ABC:

First, find the measure of side b using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is B, change C for B in the formula and swap b and c:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

Substitute the given values and solve for b:

[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]

[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]

[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]

[tex]\implies b=11.9929519...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]

[tex]\implies \cos(A)=0.842229094...[/tex]

[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]

[tex]\implies A=32.6237394...^{\circ}[/tex]

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]

[tex]\implies \cos(C)=-0.364490987...[/tex]

[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]

[tex]\implies C=111.376260...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

[tex]\hrulefill[/tex]

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]

[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]

[tex]\implies C=40.690560...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]

[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]

[tex]\implies B=85.6625640...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]

[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]

[tex]\implies A=53.6468753...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:

The required constant of proportionality is 5.

A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.

So, the slope is given as,
m = rise/run

From the graph put the value  for any point, we choose (2, 10)

So,
m = 10/2
m = 5

Thus, the required constant of proportionality is 5.

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Answer:

To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.

From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:

Number of stories: 5

Number of cards used: 40

To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).

Ratio = Number of stories / Number of cards used

Ratio = 5 / 40

Now, we can use this ratio to calculate the number of cards needed for 100 stories:

Number of cards for 100 stories = Ratio * Number of stories

Number of cards for 100 stories = (5 / 40) * 100

Calculating the result:

Number of cards for 100 stories = (0.125) * 100

Number of cards for 100 stories = 12.5

Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.

Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.

The highest common factor of 270 and 105 is 15.

finding the prime factorization of 270.

The prime factorization of 270 can be written as:

270 = 2 * 3^3 * 5

From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.

So the values of p, q, and r are:

p = 2

q = 3

r = 5

Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.

The prime factorization of 270 is:

270 = 2 * 3^3 * 5

The prime factorization of 105 is:

105 = 3 * 5 * 7

To find the HCF, we need to find the common factors and choose the highest one.

The common factors of 270 and 105 are 3 and 5.

The highest common factor of 270 and 105 is 3 * 5 = 15.

Therefore, the highest common factor of 270 and 105 is 15.

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The percentage is given by the expression A = ( 7.2 % ) ( 8650.00 ) and the value of A = $ 622.80

Given data ,

Let the initial amount be represented as P

Now , the value of P is

P = $ 8,650.00

On simplifying the equation , we get

Let the percentage value be d = 7.2 %

On simplifying the percentage , we get d = 0.072

So , A = 0.072 ( 8,650.00 )

Multiplying the expression , we get

A = $ 622.80

Therefore , the value of A is A = $ 622.80

Hence , the expression is A = $ 622.80

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You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).

Or as a decimal 0.27.

The missing sides of the triangle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 30º, we have that:

Hence the hypotenuse RS is obtained as follows:

sin(30º) = 6/RS

1/2 = 6/RS

RS = 6 x 2

RS = 12.

Applying the cosine, we have that:

cos(30º) = 6/SX

[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]

[tex]SX = \frac{12}{\sqrt{3}}[/tex]

[tex]SX = 4\sqrt{3}[/tex]

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We can see here that the given side lengths cannot  be used to form a unique triangle because the shorter sides do not add up to the longer side.

The fundamental geometric shape of a triangle has three sides and three angles. It is a triangular polygon with three edges.

We can see here that in order to determine if the given side lengths:

3.4 cm, 3.1 cm, 6.6 cm

can form a unique triangle, many different triangles, or no triangle, we need to check if they satisfy the triangle inequality theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Let's check the conditions:

3.4 cm + 3.1 cm = 6.5 cm

6.5 cm > 6.6 cm (Not satisfied)

3.4 cm + 6.6 cm = 10 cm

10 cm > 3.1 cm (Satisfied)

3.1 cm + 6.6 cm = 9.7 cm

9.7 cm > 3.4 cm (Satisfied)

he specified side lengths cannot be used to create a triangle because the total of the two shorter sides' lengths (3.4 cm and 3.1 cm) is not larger than the length of the longest side (6.6 cm).

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Answer:

The Value of Y is -8

Step-by-step explanation:

I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.

So therefore, the value of y is -8. Hopes this helps :p

The mean height of the plants whose heights are shown by the data set is 16 in.

To find the mean:

Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176

Total number of values = 11 (since there are 11 values in the data set)

Mean = Sum of the values / Total number of values

          = 176 / 11

          = 16

In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.

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The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

To plot the graph of the given function, we simply need to use a graphing calculator.

The given function is;

f(x) = -3log₃(x + 8) - 4

To find the asymptotes of the graph;

x + 8 > 0

x > -8

The vertical asymptotes is at x = -8

The two points with integer coordinates are (2, -7) and (1, -10)

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