Find the areas of the sectors formed by angle acb

Answer:

  f(x) = 5^x -2

Step-by-step explanation:

You want the equation for the graph attached.

The graph has a horizontal asymptote for negative values of x, and rises rapidly for positive values of x. This suggests an exponential function.

The graph of the parent exponential function will pass through the point (0, 1), which is 1 unit above the horizontal asymptote. Here, the horizontal asymptote is y = -2, and the graph passes through (0, -1).

This tells us the graph is vertically translated down 2 units and not translated horizontally at all. (Horizontal translation is equivalent to a vertical scale factor. The lack of it tells us the vertical scaling is 1.)

The parent exponential function b^x rises b units above the horizontal asymptote when the value of x is 1. Here, the function rises to +3 from the asymptote of -2 at x=1, so the base of the exponential is 3-(-2) = 5.

The equation for the graph is ...

  f(x) = 5^x -2

Confirmation is shown in the attachment.

#95141404393

1) The difference is 11two

2) The difference is 30 seven

A number base, usually referred to as a numeral system or radix, is a system of digits and rules used to represent numbers. In a positional numeral system, it specifies the number of distinct digits or symbols that can be used to represent values.

Let us first convert to base 10, carry out the operation and then return to the required base.

Hence;

101two = 5 ten

10 two = 2 ten

5 ten - 2 ten = 3 ten or 11two

b) 62seven = 44 ten

23 seven = 17 ten

44 ten - 23 ten = 21 ten or 30 seven

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Answer:

A

Step-by-step explanation:

Negation statements have the word "not" in them or taken out of them.  In this case, not is added to the statement.

Answer:

  y = -4(x +2)² +7

Step-by-step explanation:

You want the equation of the parabola with vertex (-2, 7) that passes through point (-1, 3).

The vertex form of the equation of a parabola is ...

  y = a(x -h)² +k . . . . . . . . vertex (h, k)

We can use (x, y) = (-1, 3) and (h, k) = (-2, 7) to find the value of 'a'.

  3 = a(-1 -(-2))² +7 = a +7

  -4 = a . . . . . . . . subtract 7

Then the vertex form equation for the parabola is ...

  y = -4(x +2)² +7

<95141404393>

If an individual's body fat percentage is 18.8%, this means that 18.8% of their weight is composed of fat. We can use this information to find the weight of the fat in pounds as follows:

Weight of fat = body fat percentage * weight

Weight of fat = 18.8% * 184 pounds

Weight of fat = 0.188 * 184 pounds

Weight of fat = 34.592 pounds

Rounding this to the nearest tenth, we get:

The weight of the fat is about 34.6 pounds.

Answer:

12

Step-by-step explanation:

28 plus 20 equals to 48 and then each divide 4

[tex]y=e . \sqrt{e^x[/tex] is the function in the terms of x.

Assume ln(y) = z, thus the linear equation in terms of x and z,

Since the line is passing through (0, 1) and (-2, 0)

the general linear equation:

z = (0-1)/(-2-0)x + 1

z= 1/2x+1

Substituting the value of z

[tex]ln(y) = 1/2(x)+1\\\\y = e^{(1/2)x+1}\\\\y=e . \sqrt{e^x[/tex]

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The box that depicts the number of dogs at the daycare each day is Box C which shows median of 60. The Option C.

The full data for number of dogs at the daycare each day is:

[tex]47,38,72, 56, 40, 64, 30, 80, 66, 51, 33, 74, 70, 69[/tex]

To get median, we will arrange the numbers in ascending order which is:

[tex]30, 33, 38, 40, 47, 51, 56, 64, 66, 69, 70, 72, 74, 80[/tex]

Since we have an even number of observations (14), the median will be the average of the two middle numbers.

The two middle numbers are 56 and 64. So the median is:

= (56 + 64) / 2

= 120 / 2

= 60.

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7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll

The probability of rolling an even number on the first roll is 3/6 = 1/2, since there are three even numbers (2, 4, 6) out of six possible outcomes.

The probability of rolling a 1 on the second roll is 1/6, since there is only one outcome that will result in a 1.

To find the probability that at least one of these events occurs, we can add their probabilities and subtract the probability that both events occur:

P(even or 1) = P(even) + P(1) - P(even and 1)

Since the events are independent, the probability that both occur is simply the product of their probabilities:

P(even and 1) = P(even) × P(1) = (1/2) × (1/6) = 1/12

Substituting into the formula above, we get:

P(even or 1) = 1/2 + 1/6 - 1/12 = 7/12

Therefore, 7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll

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Answer:

19 $20 bills

Step-by-step explanation:

Let's assume the number of $20 bills in the cash drawer is "x."

The value of the $20 bills can be calculated by multiplying the number of bills by the denomination:

Value of $20 bills = 20 * x

Similarly, the value of the $5 bills can be calculated by multiplying the number of bills by the denomination:

Value of $5 bills = 5 * (50 - x) (since there are a total of 50 bills)

According to the given information, the total value of all the bills is $535:

Value of $20 bills + Value of $5 bills = $535

Substituting the expressions for the values:

20 * x + 5 * (50 - x) = 535

Simplifying the equation:

20x + 250 - 5x = 535

Combining like terms:

15x + 250 = 535

Subtracting 250 from both sides:

15x = 285

Dividing both sides by 15:

x = 19

Therefore, there are 19 $20 bills in the cash drawer.

The formula that of h is h = 9k/16t

Joint variation describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant.

h is inversely proportional to p and directly proportional to t , therefore

h = k t/p

when h = 9 and t = 64 and p is 4

9 = k 64/4

64k = 36

k = 36/64

k = 9/16

h = 9k/16t

therefore the formula of h interns of k and t is

h = 9k/16t

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The transformation that maps the blue triangle into the orange one is a rotation.

First, a translation only moves the figure (it does not change the orientation), and in the image we can see that the orientations are different, then we can discard the translation.

Similarly with the dilation which only changes the size, we can discard that one too.

Finally, if we do a reflection over a given line the orientation can be changed, but there must be a line of symmetry (the line used for the reflection) between the two figures, that we can't see here.

Then the remaining option is the correct one, this is a rotation.

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The length of AB and CB is 7√2.

Using Trigonometry

cos 45 = B/ H

cos 45 = AD / AB

1/√2 = 7 / H

H = 7√2

Then, CB = AB = 7√2

Now, using Pythagoras theorem in ΔABC

AC² = AB² + CB²

14² =  (7√2)² + CB²

CB² = 196 - 98

CB = 7√2

Thus, the length of AB and CB is 7√2.

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The values of sin0 and sin 90 are 0 and 1 respectively

Table and values of a function

Given the following values of theta

Theta = 0 and 90 degrees

If theta = 0 dgrees

Sin (0) = 0

If theta = 90 degrees

Sin(90) = 1

Hence the values of sin0 and sin 90 are 0 and 1 respectively

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You need to match them in straight horizontal lines

Step-by-step explanation:

You need to replace the coordinates in the equations.

For example let's take (-6,-9) first. - 6 is the x coordinate and - 9 is the y coordinate. Let's replace it in the different equations and see which one is accurate.

Y = 2/3 x - 5 = 2/3×(-6) - 5 = - 9

(we were supposed to get y as - 9 and therefore this one is correct)

Our first match —> (-6,-9) & y = 2/3x - 5

Next coordinate, (-9,-11.5)

Replace in second because we found the first one already.

Y = 1/2 x - 7 = 1/2×(-9) - 7 = - 11.5

(y is supposed to be -11.5 so this one is correct too)

(-9,-11.5) & y = 1/2x- 7

Next coord, ( 4,-1)

Y = 6/8×(4) - 4 = - 1

(woah this one is correct too haha, why are they in the exact order-)

(4,-1) & y = 6/8 x - 4

Last ones left are the last two obviously but we can cross check.

Y = 4/8×(-8) + 1 = -3

Correct.

(-8,-3) & y = 4/8 x + 1

The average total cost of producing 5 shirts by the firm is $35.

We can use the following formula to calculate the average total cost (ATC) of producing 5 shirts:

ATC = Total Cost / Quantity

We know that the firm produces 6 shirts at a total cost of $187, so the total cost of producing 5 shirts can be estimated by subtracting the marginal cost of the last shirt from the total cost of producing 6 shirts:

Total Cost of producing 5 shirts = Total Cost of producing 6 shirts - Marginal Cost of the last shirt

                                 = $187 - $12

                                 = $175

Now we can use the formula to find the average total cost of producing 5 shirts:

ATC = Total Cost / Quantity

   = $175 / 5

   = $35

Therefore, the average total cost of producing 5 shirts by the firm is $35.

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Answer:

$6.41 per T-shirt

Step-by-step explanation:

Because we're told the T- shirts have the same price (individually), we can find the price of one T-shirt by dividing the total cost ($44.87) by the total number of T-shirts purchased (7):

Total cost / total number of T-shirts purchased = Cost of one T-shirt

$44.87 / 7 = Cost of one T-shirt

$6.41 = Cost of one T-shirt

The equation of line FG is given as follows:

y = -0.5x - 5.5.

The circle has a center of (1, -1), hence the equation is given as follows:

(x - 1)² + (y + 1)² = r².

Point (-1, -5) is on the circumference of the circle, hence the radius is obtained as follows:

(-1 - 1)² + (-5 + 1)² = r²

r² = 40.

Hence:

(x - 1)² + (y + 1)² = 40.

Applying implicit differentiation, the derivative is given as follows:

2(x - 1) + 2(y + 1)m = 0

2x - 2 +2m(y + 1) = 0

m = (x - 1)/(y + 1)

At x = -1 and y = -5, hence the slope is given as follows:

m = -2/4

m = -0.5.

Hence the equation is given as follows:

y + 5 = -0.5(x + 1).

y = -0.5x - 5.5.

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355.2

i use my notebook and showed my work by doing 3.7x8x12 which is equal to 355.2

If we move 8 units right and end up at the coordinate (5,-3) the starting point is (-3,-3)

In an x-y plane, the x-axis is the axis along the horizontal of the plane. Similarly, the y-axis is the axis along the vertical of the plane.

Thus, the change in the position affects the coordinates of the x and y axis accordingly.

Given:

Change in position: 8 unit rights

Thus, the movement is along the x-axis in the positive direction

Final position: (5,-3)

Starting point can be found by subtracting the movement of the particle from the endpoint.

Thus, Starting position: (5-8,-3) or (-3,-3)

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these are all problems designed to practice the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides, and A, B, C being the corresponding opposite angles.

I

and remember :

sin(90) = 1

a)

4/sin(30) = c/sin(90) = c

4/0.5 = c = 8 cm

b)

17/sin(53) = c/sin(90) = c

c = 21.28630619... cm

c)

6/sin(41) = c/sin(90) = c

c = 9.14551852... cm

The given expression, rewritten by factoring out the greatest common factor is 2y(x³ + 4x - 2x² - 8)

The given expression factored completely is (2xy - 4y)(x² + 4)

From the question, we are to rewrite the given expression by factoring out the greatest common factor and also by factoring completely

The given expression is

2x³y + 8xy - 4x²y - 16y

The greatest common factor is the expression that is common t each of terms in the given expression

The greatest common factor is 2y

Factoring out the greatest common factor

2x³y + 8xy - 4x²y - 16y

2y(x³ + 4x - 2x² - 8)

Factoring the expression completely

2x³y + 8xy - 4x²y - 16y

2xy(x² + 4) - 4y(x² + 4)

(2xy - 4y)(x² + 4)

The complete factoring of the expression is (2xy - 4y)(x² + 4)

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As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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The expressions on the left matched with the simplified form on the right:

-(-9) = 9

|-9| = 9

-|9| = -9

|9| = 9

-|-9| = -9

Mathematical rules to simplify the expressions:

a negative sign multiplied by a negative sign is equal to a positive sign

a positive sign multiplied by a negative sign is equal to a negative sign.

a positive sign multiplied by a positive sign is equal to a positive sign.

Also, this sign | | indicates that the number is positive.

Therefore,

-(-9) = 9

|-9| = 9

-|9| = -9

|9| = 9

-|-9| = -9

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Answer:

This does not make sense

Step-by-step explanation:

f(70) = 6(70) + 2

f(70) = 420 + 2

f(70) = 422

(6x + 2)70

420x + 140

This is not equivalent.

Helping in the name of Jesus.

The rules of the functions are;

(f · g)(x)  = x

(g ·ƒ)(x) = x

Domain of both function = all real numbers

Note that function are defined as laws or rules that are used to show the relationship between two variables.

These variables are the dependent and independent variables.

From the information given, we have that;

f(x)=1+x²,

g(x) = √x - 1

To determine the composite functions, substitute the functions as x

(f · g)(x)  = 1 + (√x - 1)²

expand the bracket

(f · g)(x)  = 1 + x - 1

(f · g)(x)  = x

(g ·ƒ)(x) = √1 + x² - 1

find the values

(g ·ƒ)(x) = 1 + x - 1

(g ·ƒ)(x) = x

the domains of the function are;

(f · g)(x) , all real numbers

(g ·ƒ)(x), x = all real numbers

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Answer:

7.5

Step-by-step

to get this answer you need to multiply 10*75 than divide it by 100

10          0

-----     --------

100        75

The populations that experienced more births than deaths over the five years is the population with a green curve.

When a population experiences more births than death, it leads ot a population explosion and rapid population growth.

As shown in the graph, the population of the in green has higher numbers / year than those in the red.

Thus, it is correct to state that by looking at the graph, the populations that experienced more births than deaths over the five years is the population with a green curve.

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