What is the transversal ?

Answer:

I) ∠CAB measures 60°.

II) BC measures approximately 15.23 cm.

*Please read notes.

Step-by-step explanation:

We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.

And we want to find I) the measure of ∠CAB and II) the length of BC.

I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.

Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are two side lengths, and C is the angle between the two sides.

Substitute:

[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]

Simplify:

[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]

So:

[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]

Take the inverse sine of both sides. Use a calculator. Thus:

[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]

II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.

The law of cosines is:

[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.

BC is opposite to A. Substitute:

[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]

Simplify:

[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]

Take the square root of both sides:

[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]

BC measures about 15.23 cm.

Notes:

In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.

Answer:

L x W x H

Step-by-step explanation:

if my calculations are correct the length is 2 the width is 3 and the height is 3

Therefore the answer is (2 x 3) = 6 x3

So the answer is 18.

Hope it helps, if it is incorrect than i am extremely sorry, wish you the best of luck and have a great day/midday/evening. BYYEEEEEEE

Answer:

1040 ft./min

Step-by-step explanation:

It's Right :)

Answer: the mean is 11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Add them all together then divide by the nuber of variables

Answer:

20100

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Given equation

y = -1700x + 32000

Where x is the age of car and y is the value of the car.

Then value after 7 years can be calculated as follows,

y = -1700 (7) + 32000

y = -11900 + 32000

y = 20,100

So, the value of car after 7 years will be 20100.

Answer:

write on each line....

equivalent, not equivalent, not equivalent

equivalent, not equivalent, equivalent

not equivalent, not equivalent, equivalent

Shade in each with what ever the fraction says to, for example 2/4 only shade in 2 boxes

Answer: don't know the answer but I hope this helps.

Step-by-step explanation:

Answer:

y = 2x + 6

Step-by-step explanation:

slope-intercept form => y = mx + b

substitute two of the (x, y) into the equations: y = mx + b  to solve for m and b

=> 0 = -3m + b, 6 = 0m + b

6 = 0m + b => b = 6

substitute b = 6 into 0 = -3m + b to solve for m:

=> 0 = -3m + 6 => -3m = -6 => m = 2

plug in b = 6 and m = 2 into the equation y = mx + b:

=> y = 2x + 6

Answer:

x = 4.5

Step-by-step explanation:

Since the perimeters are equal , then the equation relating them is

2x + 3 + 2x - 3 + x = x + 3 + x + 3 + x + 3 , that is

5x = 3x + 9 ( subtract 3x from both sides )

2x = 9 ( divide both sides by 2 )

x = 4.5

Answer:

(98.2884 ; 98.3116)

Step-by-step explanation:

Given :

x = 98.30°F and s = 0.61°F

Sample size. n = 103

Zcritical at 95% = 1.96

Using the confidence interval relation :

x ± margin of error

Margin of Error :

Zcritical * s/√n

1.96 * 0.61/√103 = 0.0116

Lower boundary = (98.30 - 0.0116) = 98.2884

Upper boundary = (98.30 + 0.0116) = 98.3116

(98.2884 ; 98.3116)

Answer:

12mm (triangle)

165mm (whole shape)

Step-by-step explanation:

The triangle is 6 x 4 = 24 ÷ 2= 12

(divide by 2 because its a teiangle)

2nd shape is 10 x 8 = 80

3rd shape is 6 x 12 = 72

72 + 80 + 12 = 165mm

Answer:

y=−x+3

Step-by-step explanation:

The slope-intercept form is y=mx+b, where m is the slope and b

is the y-intercept.

y=mx+b

Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.

Step-by-step explanation:

Answer:

4.17

Step-by-step explanation:

Answer:

14.17

Step-by-step explanation:

0.25 divided by 0.06 =4.166666666667

you take the first 3 numbers 4. 166 round the last number if it is a 5 or higher the number goes up one 4.166 rounds up to 4.17

Answer:

Step-by-step explanation:

Total sum of degrees of a Triangle is 180 deg

Than: 8x-7 + x +7 + 2x + 15 = 180

11x + 15 = 180

x = (180-15) / 11  =15

Answer: 15

c) 2x^2y + 2xy^2

Explanation:

(x^2 y-3y^2+5xy^2)- (-x^2y+3xy^2-3y^2)

(x^2 y+5xy^2 -3y^2)- (-x^2y+3xy^2-3y^2)

x^2 y +5xy^2 -3y^2 + x^2y -3xy^2 + 3y^2

2x^2y + 2xy^2

The option C) 2x²y + 2xy² is equivalent to the given expression (x²y - 3y² + 5xy²) - (-x²y + 3xy² - 3y²).

Mathematically, an expression is an admixture of numbers, variables, operations, and functions that are conjoined according to peculiar rules to depict a mathematical calculation or association. It can be supposed to as a mathematical idiom or formula.

By combining numbers, variables, operators, and functions, mathematical expressions can define a broad lea of calculations and associations.

The given expression is (x²y - 3y² + 5xy²) - (-x²y + 3xy² - 3y²).

(x²y - 3y² + 5xy²) - (-x²y + 3xy² - 3y²)

= x²y - 3y² + 5xy² + x²y - 3xy² + 3y²

= 2x²y + 2xy².

Hence, option C) is correct in that 2x²y + 2xy² is equivalent to the given expression.

Learn more about Expression here:

https://brainly.com/question/34132400

#SPJ6

Answer:

-3=3x+12

Step-by-step explanation:

Answer:

limited resources and facilities for women

lack of scholarships and championships for women

limited opportunities for female athletes

2,4,5

Statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

Title IX is a potent instrument for fighting campus violence because it is a federal (national) legislation. To ensure that all students have equal access to education, the law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

As per the Title IX law:

Thus, statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

Learn more about the Titel IX law here:

https://brainly.com/question/13838817

#SPJ2

Answer:

354294

Step-by-step explanation:

Use the formula

[tex]a_{n} = a_{1} r^{n - 1}[/tex]

In your problem [tex]a_{1}[/tex] = 6   r = -3    n = 11

11th term = [tex]a_{11}[/tex] = [tex]6(-3)^{11 - 1} = 6(-3)^{10}[/tex] = 6(59049)

                       = 354294

Answer:

Step-by-step explanation:

10 games, 8 rides

Answer:

isosceles triangle

Step-by-step explanation:

the first one is isosceles triangle

Answer:

slope=-12

Step-by-step explanation:

slope =y2-y1/x2-x1

5-17/-1-(-2)

-12/-1+2

-12/1

-12

Answer: No you can not make any triangles with 2 inches, 2 inches and 4 inches. hoped this helped!

Step-by-step explanation:

Answer:

$1.50

Step-by-step explanation:

The computation is shown below:

Given that

The cost of each cupcakes be 0.50 cents

And, the cost of doughnuts be $25

So for two doughnuts the cost would be 2.50

And, for two cupcakes, the cost would be 0.50 × 2 = 1

So, the more amount would be

= 2.50 - 1

= $1.50

Hence, the same would be considered and relevant too

Answer:

lol xdxdxd how you not know fraction? this is basic math this is why you failed lolol

Step-by-step explanation:

Answer:  $ 126.65

Step-by-step explanation:

149/100)*15 =

(149*15)/100 =

2235/100 = 22.35

15% of $149 is 22.35

so ,

   real price-15% of real price= sale preice

  $149-$22.35=$126.65

Answer:

$ 126.65

Step-by-step explanation:

$ 149 multiply 15 % which is 0.15

Which is $ 22.35

Take $ 149 - $22.35 = $126.65