The area of square abcd is 36 square units and the area of triangle ebf is 20 square units. if line eb is perpindicular to line bf and line ae is equal to 2 find the length of line cf

Answer:

Option a is right.

Step-by-step explanation:

Both standard deviation and range are used as measures of dispersion.  These show the deviations of the data within.

While range is maximum -minimum, the std deviation is the square root of variance and variance is the average of the sum of squares of each entry from the mean.

While range depends only on max and min the std deviation depends on each entry of the sample. Hence std deviation is a better measure.

a. the standard deviation is preferable to the range as a measure of variation because the standard deviation takes into account all of the​ observations, whereas the range considers only the largest and smallest ones.

Answer:

the answer is 14

Step-by-step explanation:

If the value of e is 15 and f is 2. Then the value of the expression [e - (1/2)f] will be 14.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ e - (1/2)f

If the value of e is 15 and f is 2.

Then the value of the expression will be

⇒ e - (1/2)f

⇒ 15 - (1/2) x 2

⇒ 15 - 1

⇒ 14

Thus, the value of the expression will be 14.

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Answer:

Option A - [tex]......,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]                

Step-by-step explanation:

Given : A geometric has [tex]\frac{1}{4}[/tex] as its's fifth term and [tex]\frac{1}{2}[/tex] as common ratio.

To find : Which sequence is geometric ?

Solution :

The geometric sequence is defined as [tex]a,ar,ar^2,ar^3...[/tex]

where, a is the first term and r is the common ratio.

The nth term of the sequence is [tex]a_n=ar^{n-1}[/tex]

We have given, [tex]r=\frac{1}{2}[/tex] and  [tex]a_5=\frac{1}{4}[/tex]

The 5'th term is

[tex]a_5=ar^{5-1}[/tex]

[tex]\frac{1}{4}=a(\frac{1}{2})^{4}[/tex]

[tex]\frac{1}{4}=a(\frac{1}{16})[/tex]

[tex]\frac{16}{4}=a[/tex]

[tex]a=4[/tex]

The sequence form is [tex]4,4(\frac{1}{2}),4(\frac{1}{2})^2,4(\frac{1}{2})^3,4(\frac{1}{2})^4,4(\frac{1}{2})^5...[/tex]

[tex]4,2,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]

From the given sequence Option A matched with result.

Therefore, Option A is correct.

Positive is when the lines are above the X axis

 in this graph it is positive from  [−8, −6) and (−2, 4)

The function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]

A function is positive in intervals where the graph lies above the [tex]\boldsymbol{x-}[/tex]axis.

A function is negative in intervals where the graph lies below the [tex]\boldsymbol{x-}[/tex]axis.

In intervals [tex]\boldsymbol{(-6,-2),(4,8]}[/tex], the graph lies below the [tex]\boldsymbol{x-}[/tex] axis.

In intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex], the graph lies above the [tex]\boldsymbol{x-}[/tex] axis.

So, the function is positive in intervals [tex]\boldsymbol{[-8,-6),(-2,4)}[/tex]

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The cost of one pear and one orange is $0.94.

To find the cost of one pear and one orange, we need to set up an equation. Let's let x be the cost of one pear and y be the cost of one orange. We can set up two equations based on the given information:

We can solve this system of equations by substitution or elimination. Let's use the substitution method. From equation 2, solve for x in terms of y:

x = 0.94 - y

Substitute this expression for x into equation 1:

10(0.94 - y) + 11y = 10.05

Distribute and simplify:

9.4 - 10y + 11y = 10.05

Combine like terms:

9.4 + y = 10.05

Subtract 9.4 from both sides:

y = 10.05 - 9.4

y = 0.65

Now substitute the value of y back into equation 2 to find x:

x + 0.65 = 0.94

Subtract 0.65 from both sides:

x = 0.94 - 0.65

x = 0.29

Therefore, the cost of one pear and one orange is $0.29 + $0.65 = $0.94.

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Answer:

A

Step-by-step explanation:

Answer:

It is D. 98.5

Step-by-step explanation:

Got it right on edge

The smaller of the two possible angles used is;

θ = 15.92°.

We are given;

Range of pass; R = 7.75 m

Speed; u = 12 m/s

Formula for range is;

R = [u²sin (2θ)]/g

Where; θ is the angle at which the ball was thrown.

Thus;

7.75 = 12² × (sin(2θ))/9.8

(sin(2θ)) = (7.75 × 9.8)/12²

(sin(2θ)) = 0.5274

2θ = sin^(0.5274)

2θ = 31.83

θ = 31.83/2

θ = 15.92°

Now, if we assume that this angle is to the vertical, it means the angle to the horizontal is;

90 - 15.92 = 74.08°

In conclusion, the two possible angles are 15.92° and 74.08°.

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The total cost producing 1 camera case is:

                            $ 11

Let the quadratic function be:

[tex]c(x)=ax^2+bx+c[/tex]

Now, c(3)=45

This means:

[tex]9a+3b+c=45------------(1)[/tex]

c(7)=257

This means that:

[tex]49a+7b+c=257----------------(2)[/tex]

and c(12)=792

This imply:

[tex]144a+12b+c=792-------------------(3)[/tex]

On subtracting first equation from second we get:

[tex]40a+4b=212------------(4)[/tex]

and on subtracting second equation from third we get:

[tex]95a+5b=535-----------(5)[/tex]

Now on multiplying equation (4) by 5 and equation (5) by 4 and subtracting both equation we get:

a=6

Putting value of a in equation (4) we get:

b= -7

and putting the value of a and b in equation (1) we get:

c=12

Hence, the cost function is:

[tex]c(x)=6x^2-7x+12[/tex]

Now, the cost of producing 1 camera will be the value of c(x) when x=1

i.e.

[tex]c(1)=6-7+12\\\\\\c(1)=11[/tex]

                 Hence, the answer is:

                        $ 11

To solve the problem we will first name all the points given to us, and then we will find ∠O, and then we will find the value of x.

The value of x is 22°.

Given to us

Looking at the diagram below,

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 56°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(56°) = 180°

∠O = 68°,

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

68° + 90° + ∠OCB = 180°

∠OCB = 180° - 68° - 90°

∠OCB = 22°

Hence, the value of x is 22°.

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Answer:

35

Step-by-step explanation:

(sorry for bad image. I use OperaGX)

The missing value to the nearest hundredth using inverse trigonometric function is 67.11°

Let us say

Cos x = 7/18

x will be the inverse of cosine of (7/18)

The inverse trigonometric functions are the inverse functions of the trigonometric functions and are used to obtain an angle from any of the angle's trigonometric ratios.

x = cos⁻¹ (7/18)

x = 67.11°

Hence, the missing value to the nearest hundredth is 67.11°.

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Area refers to the amount of space inside a shape and is found by counting the inside of the shape. Therefore, the correct answer is option a.

"To count the inside of a shape": This means that when we calculate the area of a shape, we are determining the amount of space or surface area that is enclosed within the boundaries of that shape. In other words, it's the measurement of the total space covered by the shape, and it doesn't include the outer boundary or perimeter.

"To count the outside of a shape" is not an accurate definition for area. The outside of a shape is typically referred to as the perimeter or the circumference, and it represents the measurement of the boundary or the length of the outline of the shape.

"None of the above" is not the correct choice because the area is indeed about measuring the inside of a shape, as explained in the first option.

In summary, when we calculate the area of a shape, we are quantifying the space enclosed within the shape's boundary, not the space on the outside of it.

Therefore, the correct answer is option a.

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Answer:

the answer is B: 128 divided by 8 equals 16

Step-by-step explanation:I know this becasue to check ur answer after doing multiplication you must do division

multiplication-->division

division-->multiplication

subtraction-->addition

addition-->subtraction

Answer:

[tex]a_n = a_{n-1}-13.8[/tex]

Step-by-step explanation:

The recursive rule for the arithmetic sequence is given by:

[tex]a_n = a_{n-1}+d[/tex]          .....[1]

where, d is the common difference of two consecutive terms.

Given the sequence:

−7.4, −21.2, −35, −48.8, −62.6

This is an arithmetic sequence

Here, first term[tex](a_1)[/tex] = -7.4 and d = -13.8

Since,

-21.2+7.4 = -13.8,

-35+21.2 = -13.8 ans so on...

Substitute the given value in [1] we have;

[tex]a_n = a_{n-1}+(-13.8)[/tex]

⇒[tex]a_n = a_{n-1}-13.8[/tex]

Therefore, the recursive rule for the sequence is, [tex]a_n = a_{n-1}-13.8[/tex] and [tex]a_1[/tex]= -7.4

The recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex]  and [tex]\rm a_{1}[/tex] = -7.4.

The recursive rule refers to the first term of the sequence and describe  

the relation to the preceding term with the recursive equation.

The recursive formula for the arithmetic sequence is as follows

[tex]\rm a_{n} = a_{n-1} + d[/tex]

where [tex]\rm a_{n}[/tex] is the nth term and d is a common difference

The arithmetic sequence is given as

−7.4, −21.2, −35, −48.8, −62.6

[tex]\rm a_{1}[/tex] = -7.4 (first term)

d = -21.2+7.4 = -13.8,

d = -35+21.2 = -13.8

Substitute the given value, we get

[tex]\rm a_{n} = a_{n-1} + d[/tex]

[tex]\rm a_{n} = a_{n-1} -13.8[/tex]

Hence, the recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex]  and [tex]\rm a_{1}[/tex] = -7.4.

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Answer:

(x+2) is a factor of P(x)

Step-by-step explanation:

Determine if x + 2 is a factor of p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8

[tex]p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8[/tex]

To determine (x+2) is a factor , we set x+2=0 and solve for x

[tex]x+2=0 , x=-2[/tex]

then we replace x with -2 in p(x)

[tex]p(x) = x^4 + 3x^ 3 + 4x ^2 - 8[/tex]

[tex]p(-2) = (-2)^4 + 3(-2)^ 3 + 4(-2)^2 - 8[/tex]

[tex]p(-2) = 16-24+16- 8=0[/tex]

WE got p(-2)=0 , so (x+2) is a factor of P(x)

Answer:

Step-by-step explanation: