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Answer:

Given: A = 72°, a = 34, b = 21

Calculated: B = 35.97°, C = 72.03°, c = 34.00

Step-by-step explanation:

[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]

[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin B}{21} [/tex]

[tex] \sin B = \dfrac{21\sin 72^\circ}{34} [/tex]

[tex] \sin B = 0.5874 [/tex]

[tex] B = \sin^{-1} 0.5874 [/tex]

[tex] B = 35.97^\circ [/tex]

C = 180° - 72° - 35.97°

C = 72.03°

[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]

[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin 72.03^\circ}{c} [/tex]

[tex]c = \dfrac{\sin 72.03^\circ \times 34}{\sin 72^\circ}[/tex]

[tex] c = 34.00 [/tex]

Given: A = 72°, a = 34, b = 21

Calculated: B = 35.97°, C = 72.03°, c = 34.00

Answer:

[tex]B\approx35.97^\circ\\C\approx72.03^\circ\\c\approx34[/tex]

Step-by-step explanation:

Law of Sines

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

Given information

[tex]A=72^\circ\\a=34\\b=21[/tex]

Check if solutions exist

As [tex]A=72^\circ < 90^\circ[/tex] and that [tex]a > b\rightarrow 34 > 21[/tex], then there exists only one possible triangle by the Ambiguous Case

Solve the triangle

[tex]\frac{sin(72^\circ)}{34}=\frac{sin(B)}{21}\\ \\ 21sin(72^\circ)=34sin(B)\\\\\frac{21sin(72^\circ)}{34}=sin(B)\\ \\B=sin^{-1}(\frac{21sin(72^\circ)}{34})\\ \\B=35.97394255^\circ\approx35.97^\circ[/tex]

[tex]A+B+C=180^\circ\\\\72^\circ+35.97394255^\circ+C=180^\circ\\\\107.97394255^\circ+C=180^\circ\\\\C=72.02605745^\circ\approx72.03^\circ[/tex]

[tex]\frac{sin(72^\circ)}{34}=\frac{sin(72.02605745^\circ)}{c}\\\\c*sin(72^\circ)=34sin(72.02605745^\circ)\\\\c=\frac{34sin(72.02605745^\circ)}{sin(72^\circ)}\\ \\c=34.00502065\approx34[/tex]

Answer:

1, 4, 5, 6, & 9 are the only digits that can be the last digit of the square of a natural number.

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

Subtracting x from both sides, we get 5=45, which is false.

Answer:

2

Step-by-step explanation:

Answer:

the correct answer is 2

Step-by-step explanation:

hope you have a great day -TJ

may i pls have brainliest thank you

Depth is 3.81

Step-by-step explanation:

V = l x w x d

11.43 = 2.5 x 1.2 x d

11.43 = 3 x d

÷3

3.81 = d

Hope this helps!

Answer:

Solution

20%× X= 5%×680

or, X=170.

The required number is 170.

Slope = change in Y / change in x

slope = (1-5) /(3-2)

Slope = -4/1

Slope = -4

Answer:

slope = -4

Step-by-step explanation:

The formula for finding slope is (y2 - y1)/(x2 - x1)

x1 = 2

y1 = 5

x2 = 3

y2 = 1

Plugging in our numbers,

(1 - 5)/(3 - 2) = -4/1

= -4

Answer:

$28.26

Step-by-step explanation:

In order to find out how much each gallon of gas cost, you need to divide the $48.67 by the 15.5 gallons. This would equal 3.14 So the cost for one gallon is $3.14

Then you would need to multiply this number by the 9 gallons to get the price. Which would equal $28.26

The area of triangle ACD and ABC are 17 and 46.75 square units respectively

The formula for finding the area of a triangle is expressed as:

A = 0.5bh

where:

b is the base

h is the height

Area of the triangle ACD = 0.5DE * AC

Area of the triangle ACD = 0.5(2)(17)

Area of the triangle ACD = 17 square units

For the triangle ABC

Area =  0.5(BE)(AC)

Area= 0.5(5.5)(17)

Area = 46.75square units

Hence the area of triangle ACD and ABC are 17 and 46.75 square units respeectively

Learn more on area of triangle here:  https://brainly.com/question/17335144

There are three section here

First section is the event of only E, the second is the event of only F, and the third is the event of the overlap of E and F

E or F means the total unit of events. Which is (only E)+(only F)-(E and F)

Using substitution we get 45=20+45-(E and F)

solving the equation

E and F=65-45

E and F=20

Therefore, P(E and F) is 20

I hope this helps, if you have any questions please ask!

Answer: x=-3

Step-by-step explanation:

In this question, they simply want you to find a pair of x and y-coordinates that would be valid in this equation.

We can take a random number for x, like, say, 3.

y = 2x + 6

y = 2(3) + 6

y = 6 + 6

y = 12

Since giving the value of 3 to x results in y being 12, we can safely say that the coordinates (3, 12) would be valid in this equation. Therefore:

(12) = 2(3) + 6

Let me know if you need me to explain anything.

- Breezyツ

Answer:

Multiplication.

Parentheses comes first, regardless of PEMDAS. When you see parentheses, only the P for parentheses in PEMDAS should be your main concern.

Answer:

Option E

Step by step explanation:

We know that angle J is a right angle meaning it's an angle 90 degrees. So to find angle L;

90+40+L=180

130+L=180

L=180-130

So therefore angle L =50 degrees

Now to find side J which is the opposite in the triangle,we use tan because it has adjacent and opposite which is what we're looking for;

Tan 40 degrees =opposite/26

We cross multiply

Opposite =Tan 40 degrees×26

Opposite =21.8

Side J=21.8

With side J found we can find side L using Pythagoras theorem

L^2=21.8^2 +26^2

L^2=475.24+676

L^2=1,151.24

L=Square root of 1,151.24

L=33.9

Answer:

  A) Angle L= 50 degrees, side L= 31.0, side J= 40.4

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. The given side of k is opposite the given angle K, so the sine or tangent functions can be used to find missing sides. If we want to start with the hypotenuse, we can use the relation ...

  Sin = Opposite/Hypotenuse

  sin(40°) = 26/j

  j = 26/sin(40°) ≈ 40.4 . . . units (matches choice A)

Similarly, we can use the tangent relation to find side ℓ:

  Tan = Opposite/Adjacent

  tan(40°) = 26/ℓ

  ℓ = 26/tan(40°) ≈ 31.0 . . . units (matches choice A)

Of course, angle L is the complement of 40°:

  L = 90° -40° = 50°

The solution to the triangle is L = 50°, ℓ = 31.0, j = 40.4.

Answer:

(1+1)+1=3 therefore 3×10¹

Answer: 3 times 10 to the power of just 0

Step-by-step explanation:

(1+1) + 1 is 3

So now we must put the number 3 in standard form...

The answer for this would be 3 times 10 to the power of 0

Answer:

Area of a triangle = l*b

                              = 183/5*50/3

                              = 36.6*16.66

                              = 609.756 m

Answer:

6 cupcakes for £5

Step-by-step explanation:

Given :-

Two options

To Find :-

Which is better value for money

Solving :-

Find the cost of one cupcake of the two options

1. 6 cupcakes = £5

=> 1 cupcake = £0.83

2. 4 cupcakes = £3.50

=> 1 cupcake = £0.875

Solution :-

It would be wiser to purchase 6 cupcakes for £5

Answer:

3x-9

Step-by-step explanation:

Answer:

does this help?........

Answer:

  7 cubic units

Step-by-step explanation:

There are 6 unit cubes on the bottom layer, and one on the top layer. The total volume is ...

  6 +1 = 7 . . . . cubic units

Answer:

1. A: 1

2. B 2[tex]\pi[/tex]

Step-by-step explanation:

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day! :)

Answer:

perimeter =22units

Step-by-step explanation:

30units is supposed to be the are and its supposed to be 30 units squared

Answer: 1.2y+5

If 1+4 =5 and 2.1y-0.9y=1.2y then 1+2.1y-0.9y+4 = 1.2y+5

#A

3 has two images 2,7 hence not a function

#B

Every domain has unique range hence function

#C

3 has two images hence not a function

#4

-1 has two images hence not a function

Answer:

y = 4 1/3x+ 6  

Step-by-step explanation:

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept. The y-intercept occurs at x=0 or point (0,b).

-18 -8 / -2 - 4 =  -26 / -6  = 4 1/3  perp = - 4 1/3  =  y=4 1/3 x+b

Step 2. -18 -8 / -2 - 4 =  -26 / -6  = 4 1/3  perp = - 4 1/3  is a vertical line or parallel to the y-axis. So a line perpendicular to x= 4 1/3  is a horizontal line parallel to the x-axis.

Step 3. Therefore y= 4 1/3  is a horizontal line parallel to the x-axis. Now, the line needs to pass through point (5,6) or x=5 and y=6. Then, y=b=6 or y=6 is the equation of the line. but then  x = 4 1/3   so y = 4 1/3x + 6  

Step 4. ANSWER: The equation is  y = 4 1/3x+ 6  where slope m=4 1/3 and y intercept b=6.  

Answer:

5

Step-by-step explanation:

-20 / -4 = 5

A negative divided by a negative is positive!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

[tex]\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }[/tex]

Step-by-step explanation:

We would like to solve the given quadratic equation by completing the square method .The given equation is ;

[tex]\longrightarrow x^2=12x +17[/tex]

Subtract 12x to both sides ,

[tex]\longrightarrow x^2-12x = 17 [/tex]

Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,

[tex]\longrightarrow x^2-2(6)(x) = 17 [/tex]

Add 6² on both sides ,

[tex]\longrightarrow x^2-2(6)(x) + 6^2=17+6^2 [/tex]

Now LHS is in the form of (a-b)² = a²-2ab+b² ; so that ;

[tex]\longrightarrow (x -6)^2 = 17+36 [/tex]

Simplify RHS ,

[tex]\longrightarrow (x-6)^2=53 [/tex]

Put square root on both sides,

[tex]\longrightarrow (x-6) = \pm\sqrt{53}[/tex]

Add 6 on both sides,

[tex]\longrightarrow x = 6\pm\sqrt{53} [/tex]

Separate the two solutions ,

[tex]\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}} [/tex]

And we are done!

The perpendicular bisector of the diameter divides the diameter into two equal parts i.e. the radius

From the diagram of the circle, we have two diameters, each of which have two endpoints.

This means that there are four endpoints in the figure.

Next, we connect adjacent endpoints on the diagram

When the endpoints are connected, the shape formed is a square

See attachment for the sketch

Read more about constructions at:

https://brainly.com/question/1686819

Using proportions, it is found that they pay the bank $2332.72 each month.

A proportion is a fraction of a total amount.

Their payments are given by:

Then, the total amount is:

1,711.22 + 539.83 + 81.67 = $2332.72.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

Equivelant fractions.

Step-by-step explanation:

Ask your self..

How did the 1/3 become 7/21?

Its very simple multiply 1/3's numerator and denominator by 7

So its going to be.. 1 x 7 = 7

3 x 7 = 21

Therefore, we have 7/21