Use this function below to help find F(2)?

Answer: Option 'B' is correct.

Step-by-step explanation:

Your anniversary is usually when you are given a job review and possible increase in pay.

As in a job, job review is given at the time of anniversary, then on the basis of their performance there may be increase in pay.

So, Meaning of anniversary in a official way is when work performance of an individual is discussed and if there is good record , there is an increment.

Hence, Option 'B' is correct.

The value of sec 205° is a negative value.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The value of sec 205°.

In the coordinate system, ∠205° lies in the 3rd quadrant.

In third quadrant, only tanθ and cotθ are positive.

So, sec 205° is negative in third quadrant.

Hence we can conclude that the value of sec 205° is negative value.

Learn more about trigonometry here

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Answer with explanation:

The Vertices of quadrilateral A B CD, are A(1, a - 3), B(10, a), C(9, a + 3) and D(0, a).

Mid point of AC= (5,1)

Mid point of B D= (5,1)

Mid point formula of two points having coordinates , (a,b) and (c,d) is , if (x,y), then

    [tex]x=\frac{a+b}{2},y=\frac{c+d}{2}[/tex]

 [tex]So,\rightarrow \frac{a-3+a+3}{2}=1\\\\\rightarrow \frac{2a}{2}=1\\\\\rightarrow a=1[/tex]

So, the coordinates of vertices of quadrilateral A B CD, are A(1, -2), B(10, 1), C(9, 4) and D(0, 1).

Distance formula of two points having coordinates, (a,b) and (c,d) is,

       [tex]=\sqrt{(a-c)^2+(b-d)^2}[/tex]

   [tex]AB=\sqrt{(10-1)^2+(1+2)^2}=\sqrt{81+9}=\sqrt{90}=3\sqrt{10}\\\\BC=\sqrt{(10-9)^2+(1-4)^2}\\\\=\sqrt{1+9}\\\\=\sqrt{10}\\\\CD=\sqrt{(9-0)^2+(3-0)^2}=\sqrt{90}=3\sqrt{10}\\\\DA=\sqrt{(1-0)^2+(1+2)^2}=\sqrt{10}\\\\AC=\sqrt{(9-1)^2+(4+2)^2}=\sqrt{64+36}\\\\AC=\sqrt{100}\\\\AC=10\\\\BD=\sqrt{(10-0)^2+(1-1)^2}\\\\BD=10[/tex]

Opposite sides  AB and CD are equal to 3√10 unit and , BC and AD are equal to √10 unit.

Also,length of Diagonals , AC=B D=10 unit.

∴ The Quadrilateral, AB CD is a Rectangle.

Final answer:

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens, which was determined by solving two linear equations based on the time she spent knitting during two different falls.

Explanation:

Emma likes to knit hats and mittens, and we need to find out how long it takes her to knit a hat and a pair of mittens individually. Given that last fall she knitted 4 hats and 3 pairs of mittens in 46 hours, and this fall she knitted 2 hats and 1 pair of mittens in 18 hours, we can set up two equations to solve for the time it takes to knit each item.

Let's define H as the number of hours it takes to knit one hat and M as the number of hours it takes to knit one pair of mittens. The equations based on the given information are:

4H + 3M = 46 (Last fall's knitting)

2H + 1M = 18 (This fall's knitting)

To solve these equations, multiply the second equation by 2 to align the hats:

2(2H + 1M) = 2(18)

4H + 2M = 36

Now subtract this equation from the first equation to find M:

4H + 3M - (4H + 2M) = 46 - 36

M = 10

Substituting M back into the second original equation:

2H + 1(10) = 18

2H = 8

H = 4

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens.

Final answer:

Angela's total restaurant bill, after adding a 15% tip to her $30.00 original charge, will be $34.50.

Explanation:

To find out how much Angela's total bill will be after leaving a 15% tip at a restaurant, you first need to calculate the tip amount and then add it to the original bill. You calculate the tip by converting the percentage to a decimal and then multiplying by the cost of the meal. In this case, 15% of $30.00 is found by multiplying $30.00 by 0.15 which gives you $4.50. After calculating the tip amount, add it to the original bill to get the total amount Angela will pay.

Tip: $30.00 * 0.15 = $4.50.

Total bill: $30.00 + $4.50 = $34.50.

Therefore, Angela's total bill, including the 15% tip, will be $34.50.

Answer:

The correct option is 1.

Step-by-step explanation:

The vertices of quadrilateral RSTU are R (-3, 1) , S (-2, 3) , T (2, 3) , and U (3, 1).

It is given that quadrilateral RSTU translate four units down to get R'S'T'U'.

The relation between the vertices of RSTU and R'S'T'U' is

[tex](x,y)\rightarrow (x,y-4)[/tex]

The vertices of R'S'T'U' are

[tex]R(-3,1)\rightarrow R'(-3,1-4)=R'(-3,-3)[/tex]

[tex]S(-2,3)\rightarrow S'(-2,3-4)=S'(-2,-1)[/tex]

[tex]T(2,3)\rightarrow T'(2,3-4)=T'(2,-1)[/tex]

[tex]U(3,1)\rightarrow U'(3,1-4)=R'(3,-3)[/tex]

The  vertices of R'S'T'U' are R' (-3, -3) , S' (-2, -1) , T '(2, -1) , and U' (3, -3).

Therefore the correct option is 1.

Using proportions, it is found that the area of a 60º sector of this circle is of [tex]7\pi[/tex] m².

The rule of three is:

360º - [tex]42 \pi[/tex] m²

60º - x m²

Applying cross multiplication:

[tex]360x = 60 \times 42\pi[/tex]

[tex]x = \frac{60 \times 42\pi}{360}[/tex]

[tex]x = 7\pi[/tex]

The area of a 60º sector of this circle is of [tex]7\pi[/tex] m².

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Jacob's estimate of $225 for the basketball team's order is reasonable. Our calculations show a total estimated cost of $223.75, which is close to Jacob's estimate.

To determine if Jacob's estimated total of $225 for the basketball team's order is reasonable, we can perform a quick estimation.

First, let's list the items ordered:

Next, we will estimate the total cost for each category:

Now, summing these estimates: $84.50 + $74.25 + $30 + $35 = $223.75

Thus, Jacob's estimate of about $225 is reasonable, as our estimation shows a total of $223.75, which is close to his figure.

Answer:

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Step-by-step explanation:

An algebraic expression is a mathematical phrase that contains numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide).

We have to form the algebraic expression for the phrase

" The product of 86 and the depth of the river"

Let the depth of the river be 'd'

Therefore, the algebraic expression = Product of '86' and 'd'

= [tex] 86 \times d [/tex]

= 86d.

Therefore, the algebraic expression for the given phrase is "86d".