In the given the figure above, m∠BAC = 64° and m∠CBA = 56°. Part I: Find the m∠DEC. Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

Responda:

13 gramas

Explicação passo a passo:

The sides of the regular hexagon ABCDEF can be posed as a. If so, the area of ABCDEF should be 6 times the are of the interior angle in the hexagon, considering there are 6 equilateral triangle that can fit in this regular hexagon,

Area =  6( a * a * sin 60 ) / 2,

Area = ( About ) 2.6 sq units

Now applying cosine for triangle ABC -

AC^2 = AB^2 + BC^2 – ( 2*AB*BC*cos 120 ),

a^2 + a^2 – ( 2a^2 * ( - 0.5 ) ) = a^2 + a^2+a^2 =3a^2,

AC = a√3

The area of ABC should thus be the following -

( a√3 * a√3 * sin 60 )/2 = 1.299038106 sq units

As you can see, the area of ABC is half the area of ABCDEF, thus the ratio of the area of ABC to ABCDEF is 1 : 2

Answer:

3.5 units

Step-by-step explanation:

Answer:

given,

selling price (sp)=rs 5 ×30

=rs 150

now, gain %=20%

cost price (cp)=

[tex] \frac{sp \times 100}{100 + gain\%} [/tex]

[tex] = \frac{150 \times 100}{100 + 20} [/tex]

therefore cp= rs125

now,

again in 2nd case

sp= rs 27×5

therefore sp=rs 135

and cp= rs125

now, sp>cp so,

[tex]gain\% = \frac{sp - cp}{cp} \times 100\%[/tex]

or, gain=

[tex] = \frac{135 - 125}{125} \times 100\%[/tex]

therefore gain %= 8%.... is answer

hope it helps..

Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C = 2A - B

Answer:

22.24° to the positive x-axis.

Given vectors:

A (5, 6)

B (-12, 3)

C = 2A - B             ------------(i)

First let's represent the two vectors in unit notation as follows;

A = 5 i + 6 j

B = -12 i + 3 j

Now substitute these vectors into equation (i) as follows;

C = 2(5 i + 6 j) - (-12 i + 3 j)

C = 2(5 i + 6 j) + (12 i - 3 j)

C = 10 i + 12 j + 12 i - 3 j                   [collect like terms]

C = 10 i + 12 i + 12 j - 3 j

C = 22 i + 9 j                         ----------------(ii)

The direction, θ, of vector C can be calculated as follows;

θ = tan⁻¹([tex]\frac{9}{22}[/tex])

θ = tan⁻¹(0.409)

θ = 22.24°

Since both the x and y components of vector C are positive, the direction of the vector is 22.24° to the positive x-axis.

Answer: B & C

Step-by-step explanation:

Putting the values of x & y in all 4 equations we see that the values satisfy equations B & C only. Hence B & C are correct answers

Answer:

1. Point estimate Md = 2

2. The 90% confidence interval for the difference between means is (1.01, 2.99).

3. The 95% confidence interval for the difference between means is (0.82, 3.18).

Step-by-step explanation:

a) The point estimate of the difference between the two population means is the difference between sample means:  

[tex]M_d=M_1-M_2=13.6-11.6=2[/tex]

2. We have to calculate a 90% confidence interval for the difference between means.

The sample 1, of size n1=50 has a mean of 13.6 and a standard deviation of 2.2.

The sample 2, of size n2=35 has a mean of 11.6 and a standard deviation of 3.

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{50}+\dfrac{3^2}{35}}\\\\\\s_{M_d}=\sqrt{0.097+0.257}=\sqrt{0.354}=0.5949[/tex]

The degrees of freedom for this confidence interval are:

[tex]df=n_1+n_2-2=50+35-2=83[/tex]

The critical t-value for a 90% confidence interval is t=1.663.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.663 \cdot 0.5949=0.99[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 2-0.99=1.01\\\\UL=M_d+t \cdot s_{M_d} = 2+0.99=2.99[/tex]

The 90% confidence interval for the difference between means is (1.01, 2.99).

2. We have to calculate a 95% confidence interval for the difference between means.

The critical t-value for a 95% confidence interval and 83 degrees of freedom is t=1.989.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.989 \cdot 0.5949=1.18[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 2-1.18=0.82\\\\UL=M_d+t \cdot s_{M_d} = 2+1.18=3.18[/tex]

The 95% confidence interval for the difference between means is (0.82, 3.18).

Answer:

Null hypothesis: [tex]\mu_1= \mu_2[/tex]

Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]

And for this case we assume that we have equal variances so that means:

[tex]\sigma =\sigma_1 =\sigma_2[/tex]

For this case the degrees of freedom are given by:

[tex] df= n_1 +n_2 -2[/tex]

And replacing we got:

[tex] df= 20+20 -2= 38[/tex]

And the best answer would be:

a. 38

Step-by-step explanation:

For this problem we want to test the following:

Null hypothesis: [tex]\mu_1= \mu_2[/tex]

Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]

And for this case we assume that we have equal variances so that means:

[tex]\sigma =\sigma_1 =\sigma_2[/tex]

For this case the degrees of freedom are given by:

[tex] df= n_1 +n_2 -2[/tex]

And replacing we got:

[tex] df= 20+20 -2= 38[/tex]

And the best answer would be:

a. 38

Answer:

The above statement is written as

[tex]x + 1 \times \frac{1}{2} of \: x[/tex]

of means multiplication

So the final answer is

[tex]x + \frac{3}{2} x[/tex]

Hope this helps you.

Answer: 25 units

Step-by-step explanation:

Simply do 40(UN)-15(CN) to get 25(UC)

Hope it helps <3

Answer:

Option D is the correct option

Solution,

Here,

UN = 40

CN = 15

Now,

UN = UC + CN

plugging the values,

40 = UC + 15

-UC = 15 - 40

-UC = -25

The difference sign (-) will be cancelled in both sides:

UC = 25

hope this helps...

Good luck on your assignment..

Answer:

T < -25

Step-by-step explanation:

Was correct on TTM

Answer:

  exponential function

Step-by-step explanation:

A geometric sequence is a representation of an exponential function.

__

There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.

Answer:

[tex]d \approx 2.2[/tex]

Step-by-step explanation:

It is the same process as in previous problems.

Once the origin is the point (0, 0):

[tex]d=\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]

[tex]d=\sqrt{(2-0)^2 + (-1-0)^2}[/tex]

[tex]d=\sqrt{2^2 + (-1)^2}[/tex]

[tex]d=\sqrt{5}[/tex]

[tex]d \approx 2.2[/tex]

Answer:

2.2

Step-by-step explanation:

The distance formula

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] with

[tex]x_1=0\\y_1=0\\x_2=2\\y_2=-1[/tex]

[tex]\sqrt{(0-2)^2+(0-(-1))^2}=\sqrt{2^2+1^2}=\sqrt{5}[/tex]

[tex]\sqrt{5} =2.2360...=2.2[/tex]

Answer:

Option A

Step-by-step explanation:

=> 1 ticket = $7

=> 1 bag = $3

Expression # 1:

=> 4($7+$3)

Expression # 2:

=> 4($7)+4($3)

Solving it:

=> $28+$12

=> $40

Answer:

4(7+3)=28+12=40, 4(3)+4(7)

Answer: A and C

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

45, 50, 52, 58, 62, 68, 72, 78, 81, 95

62 + 68 = 130/2 = 65

The median is 65

Answer:

The median of the data is 65

Step-by-step explanation:

I did it on edge and got it right

Answer:

A. Parallel line

Parallel line forms when a plane and a cylinder intersect

hope this helping you..

when a plane and a cylinder intersect it forms into parallel line

A.Parallel line

Answer:

2.4

Step-by-step explanation:

3 3/4 = 3.75

9/3.75 = 2.4

Answer:

14.0008 grams of 27% and 7.9992 grams of 52%

Step-by-step explanation:

We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.

To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.

Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.

Answer:

40x - 16

Step-by-step explanation:

(see attached for reference)

By utilizing the distributive property:

4(10x -4)

= (10x)(4) -4 (4)

= 40x - 16

Answer:

4x10x= 40x           -4x4=-16         40xtimes-4<-----------thats your answer

Step-by-step explanation:

Answer:

Common denominator - 42

Step-by-step explanation:

6 - 6, 12, 18, 24, 30, 36, 42

7 - 7, 14, 21, 28, 35, 42

Hope this helps! :)

Answer:

23.14

Step-by-step explanation:

Solve for the area of the figure by dividing it up into parts.  You can divide into a half-circle and a triangle

Half-Circle

The diameter is 6.  This means that the radius is 3.  Use the formula for area of a circle.  Divide the answer by two since you only have a half-circle.

A = πr²

A = π(3)²

A = 9π

A = 28.274

28.274/2 = 14.137

Triangle

The base is 3 and the height 6.  Use the formula for area of a triangle.

A = 1/2bh

A = 1/2(6)(3)

A = 3(3)

A = 9

Add the two areas together.

14.137 + 9 = 23.137 ≈ 23.14

The area is 23.14.

Answer:

Step-by-step explanation:

The figure consists of a semi circle and a triangle

Area of the figure = Area of semi circle + Area of triangle

Area of semi circle is 1/2πr²

where r is the radius

radius = diameter/2

radius = 6/2 = 3

Area of semi circle is

1/2π(3)²

1/2×9π

14.14 sq. units

Area of a triangle is 1/2×b×h

h is the height

b is the base

h is 6

b is 3

Area of triangle is

1/2×3×6

9 sq. units

Area of figure is

14.14 + 9

= 23.14

Which is 23 sq. units to the nearest hundredth

Hope this helps you.

Answer:

x = 2, -3

Step-by-step explanation:

[tex]x^2 + 2x- 6 = 0\\=>x^2 +3x - 2x- 6 = 0\\=>x(x+3) - 2(x +3) = 0\\=> (x-2)(x+3) = 0\\\\[/tex]

(x-2)  = 0     or (x+3) = 0

x = 2  or x = -3

Thus, two values of x are x = 2, -3

Note: The options given are incorrect.

Answer:

a and b.

Step-by-step explanation:

i’m assuming that the 7 is square root of seven.

ap3x verified

Answer:

Blue Triangle.

Step-by-step explanation:

Using the area formula for a triangle, the pink triangle has an area of 0.5×54×33 in² or 891 in². The blue triangle has an area of 0.5×56×39 in² or 1092 in².

Answer:

Step-by-step explanation:

both shapes are triangles so there area is :

A=( b*h) / 2 where h is the height and b the base

A=  (33*54)/2 = 742.5 in²

A= (56*39)/2=  1092 in²

so the blue triangle has a greather area

Answer:

The original number is 19

Step-by-step explanation:

Let the original number be x

The above expression is written as

3x - 17 = 40

3x = 40 + 17

3x = 57

Divide both sides by 3

3x / 3 = 57/3

x = 19

Hope this helps you.

Answer:

im not sure either the triple is time with three or power of three

if times three:

3x–17=40

19

if power of three:

x³–17=40

x=

[tex] \sqrt[3]{57} [/tex]

Answer:

Step-by-step explanation:

in x²+y²+2gx+2fy+c=0

center=(-g,-f)

radius=√((-g)²+(-f)²-c)

if center is not changed ,then c will change .

Here only coefficients of  E will change.

Answer

The additive inverse is

-x/-y

That is equal to x/y

hope this may help you