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Answer:

Step-by-step explanation:

The basic 30-60-90 triangle ratio is:

Side opposite to 30° angle is : x

Side opposite to 60° angle is : x √3

Side opposite to 90° angle is : 2x

From the diagram we learn that

x√3 = 10

[tex]x = \frac{10}{\sqrt{3}}=\frac{10*\sqrt{3} }{\sqrt{3}*\sqrt{3}}\\\\x=\frac{10\sqrt{3}}{3}= 5.77\\[/tex]

∠T = 30°, Side opposite to ∠T is AC = 5.77

∠A = 90°, side opposite to ∠A is TC = 2x = 2*5.77 = 11.54

Answer:

Step-by-step explanation:

SecA - TanA

= 1/CosA - SinA/CosA

= 1 - SinA/CosA

We know that Sin2A = 2SinACosA  and Cos2A = Cos²A - Sin²A

Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2

       CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2

Now substituting the values back,

=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

// we know that Sin²θ + Cos²θ = 1

=> Sin²(A/2) + Cos²A/2 -  2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

//We know that numerator is of form a² + b² - 2ab which is (a - b)².

//Similarly denominator is of form a² - b² which is (a - b)(a + b)

=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)]² /  [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]

= R.H.S

Hence proved.

Answer:

37.5%

Step-by-step explanation:

Calculation to determine the theoretical probability that the tree is not within the acres of apple trees

Using this formula

P=(Number of all orchard acres - Apple acres)/(Total orchard acres)*100

Where,

P represent Probability

Let plug in the formula

P=(40 acres- 25 acres)/40 acres

P=15 acres/40 acres *100

P=3/8*100

P=.375*100

P=37.5%

Therefore the THEORETICAL PROBABILITY that the tree is not within the acres of apple trees is 37.5%

Answer:

the answer is 37.5

Step-by-step explanation:

it is

Answer:

B

Step-by-step explanation:

-10 + 3x - x - 7x + 5x + 7 + 2x

combine like terms

-10 + 3x - x - 7x + 5x + 7 + 2x

-3 + 3x - x - 7x + 5x + 2x

the -7x and the 5x + 2x cancel out to 0, so for the x terms we are left with 3x -x to get 2x

= 2x - 3

it's 1 beacuse the exponent has no power so its 1

The correct answer from the given matrix shows that the value of a12 is 1

This refers to a rectangular array of numbers that is arranged in rows and columns to indicate a mathematical property.

Hence, we can see that from the matrix given, we can see that there are different values for each one and to find a12, we can see that because there is no power in the exponent, the answer is 1.

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9514 1404 393

Answer:

  can't be done. x = 6, not 36

Step-by-step explanation:

Without the diagram we must speculate that the 150 cm length is the hypotenuse. Then we have ...

  150² = (7x)² +(24x)² = (49 +576)x² = 625x² . . . . Pythagorean relation

  150²/625 = x² = 36 . . . . . divide by 625

  x = √36 . . . . . . . . . . . take the square root

  x = 6

Answer:

138

Step-by-step explanation:

x is an exterior angle of a triangle.

If you didn't know, an exterior angle of a triangle is equal to the sum of its opposite interior angles.

The opposite interior angles of x have measures of 80 degrees and 58 degrees.

Hence, x = 80 + 58 = 138

Answer:

138

80+58 = 138

180 - 138 = 42

42+x = 180

x = 180-42 = 138

Step-by-step explanation:

Answer:

7 sqrt(2) = c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

7^2 + 7^2 = x^2

49+49 = c^2

98 = c^2

Taking the square root of each side

sqrt(98) = sqrt(c^2)

sqrt(49*2) = c

7 sqrt(2) = c

Step-by-step explanation:

gradient(m)=change in y/change in x

=5-1/-9-(-4)

=4/-9+4

=4/-5

equation now

y-y1=m(x-x1)

y-1=4/-5[x-(-4)]

y=4/-5(x+4)+1

y=-4/5x-16/5+1

y=-4/5x-21/5

Answer:

y = -4/5x - 11/5

Step-by-step explanation:

First, find the slope using the slope formula.

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{1-5}{-4-(-9)}\\\\m=-\frac{4}{5}[/tex]

Then, use the point-slope formula and substitute the values for the variables. I'll use (-4, 1) in this instance.

[tex]y-y_1=m(x-x_1)\\\\y-1=-\frac{4}{5}(x+4)\\\\y-1=-\frac{4}{5}x-\frac{16}{5}\\\\y=-\frac{4}{5}x-\frac{11}{5}[/tex]

Answer:

15:4

Step-by-step explanation:

Multiply the fractions to get a common denominator. Multiply 3/4 by 5 and your get 15/20 and multiply 1/5 by 4 and you get 4/20. The numerators represent the ratio.

Answer:

A

Giải thích:

f(1)=f(x)

f(-1) và f(-2)= f(-x)

=> f(1)=f(-1) =A. f(x)=f(-x)

Answer:

32

Step-by-step explanation:

The sum of the angles of a triangle is 180

58+90+x = 180

148+x = 180

x = 180-148

x=32

The angle sum property of a triangle:

The total measure of the three angles of a triangle is 180°

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 58 \degree \: + \: 90 \degree \: = \: 180 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 148 \: = \: 180 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 180 \degree \: - \: 148 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 32 \degree}}}[/tex]

Answer:

The property showed in the number 21 is the distributive property

Answer:

Angle BCD=35°

HOPE IT HELPS

Answer

25mm of rain fell each second

Step-by-step explanation:

we know that 500 mm fell in 20 minutes

so, we have to divide 500 by 20 giving us the amount of rain that fell each minute:

500/20 = 25

therefore, 25mm of rain fell each minute

hope this helped:)

Answer:

25 mm per minute

Step-by-step explanation:

Take the amount of rain and divide by the number of minutes

500/20

25 mm per minute

Answer: y=80/5x+80

Step-by-step explanation:

At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.

Answer:

x = (cy+b)/a

Step-by-step explanation:

ax-b=cy

Add b to each side

ax-b+b=cy+b

ax = cy +b

Divide each side by a

ax/a = (cy+b)/a

x = (cy+b)/a

Answer:

Its c

Step-by-step explanation:

Answer:

3x+ 7 =49

Step-by-step explanation:

49-7= 42

42 divided by 3 = 14

her daughter is 14 years old

I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.

have a great day!

Answer:

y = -x+3

Step-by-step explanation:

Slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -1x +b

Using the point for x and y we can calculate b

-2 = -1(5)+b

-2 = -5+b

Add 5 to each side

-2+5 = b

3 = b

y = -x+3

Answer:

1-10, -3, 2, 7

im sorry if i give a wrong answer

The answers are summarized below.

The equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-a)²+(y-b)² = r²

Where (a, b) is the centre and 'r' is the radius

We have a circle with centre (0, 0) and radius of 5.

Now, Substituting these value into the equation form, we have

(x-0)²+(y-0)² = 5²

x² + y² = 25

Hence, the equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

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Answer:

.38

Step-by-step explanation:

Given that they have green eyes, we only look at the green row

Total is 3+5+5 = 13

Red hair is 5

P( red hair ) red / total = 5/13 =.384615385

Answer:

Condition relative frequency is 0.38

Step-by-step explanation:

P( red hair given that has green hair ):

[tex]{ \boxed{ \bf{P( \frac{red}{green}) }}}[/tex]

From baye's theorem:

[tex]P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)} [/tex]

[tex]{ \sf{ = \frac{5}{(3 + 5 + 5)} }} \\ \\ = { \sf{ \frac{5}{13} }} \\ \\ = { \sf{0.384615…}}[/tex]

Answer:

Step-by-step explanation:

[tex]\displaystyle \ \Large \boldsymbol{} \frac{a-\sqrt{a} }{\sqrt{a}-1 } -\frac{\sqrt{a}+1 }{a+\sqrt{a} } :\frac{\sqrt{a}+1 }{a} = \\\\\\\frac{\sqrt{a}(\sqrt{a} -1 ) }{(\sqrt{a}-1) } -\frac{\sqrt{a}+1 }{\sqrt{a}(\sqrt{a}+1 )}\cdot \frac{\sqrt{a}\cdot \sqrt{a} }{\sqrt{a}+1 } = \\\\\\\sqrt{a} -\frac{\sqrt{a} }{1+\sqrt{a} } =\frac{a+\sqrt{a}-\sqrt{a} }{1+\sqrt{a} } = \\\\\\\frac{a}{\sqrt{a}+1 } \cdot \frac{\sqrt{a}-1 }{\sqrt{a}-1} } =\boxed{\frac{a\sqrt{a} -a}{a-1} }[/tex]

Answer:

70

Step-by-step explanation:

we have the angle of vertex in the isosceles triangle = 180-2*bottom coner= 180-65/2=50

3 angles in the equilateral triangle are equal to 60

we have 50 + 60 +h =the angle of PQR =180

h=70

Answer: h = 70°

In the triangle with Angle R = 65

It is a isoceles triangle as two sides are equal

So base angles will be equall too

Then the third angle will which is the q one will be

65+65+q = 180

q = 180 - 130

q = 50

In the other triangle with all sides equal will be equilateral triangle which means all angles equal = 60

So

Now ATQ

60 + 50 + h = 180

h = 180 - 110 (Angles on a straight line adds upto 180)

h = 70

Must click thanks and mark brainliest

Answer:

6 - 3x = 4 - X-3 - 2x

-3x+x+2x=4-6-3

0x=-5

No solutions

Answer:

6.52 x 10^3 is just basically 6.52 × 1000, which is 6520. But 652,000 ÷ 10^2 is just 652000 ÷ 100, which is 6520. That's why they have the same answer.