find the value of the trigonometric ratio.​

x + ( x + 1 ) + ( x + 2 ) = -42

Opening the brackets and simplifying :

x + x + 1 + x + 2 = -42

3x + 3 = -42

Now , solving equation :

[tex]\bf \rightarrow \: \:3x \: + \: 3 \: = \: -42[/tex]

[tex]\bf \rightarrow \: \: 3x \: = \: -42 \: - 3[/tex]

[tex]\bf \rightarrow \:3x \: = \: -45 \: [/tex]

[tex]\bf \rightarrow \:x \: = \: \frac{ - 45}{ \: 3} \\ [/tex]

[tex]\bf \rightarrow \:x \: = \: \cancel\frac{ - 45}{ \: 3} \: \: ^{ - 15} \\ [/tex]

[tex]\bf \rightarrow \:x \: = \: - 15[/tex]

[tex]{\boxed{ \Large{ \red{ \rm{ \underline{ Now \: \: substitute}}}}}}[/tex]

[tex]\bf \implies \: \:x \: = \: - 15[/tex]

[tex]\bf \implies \: \:x \: + \: 1 \: = \: - 15 \: + \: 1 \: = \: - 14[/tex]

[tex]\bf \implies \: \:x \: + \:2 \: = \: - 15 \: + \: 2 \: = \: - 13[/tex]

-15 , -14 and -13 are the three consecutive integers.

Step-by-step explanation:

Area=b×h

= (x+5)×(x+6)

=x^2+6x+5x+30

=x^2+11x+30

If u simplify u will get (x+5)(x+6) as answer.

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Answer:

y=x+15

Friend swims 40 minutes

Step-by-step explanation:

We  re told that you want to swim 15 minutes longer than your friend. In word problems, longer or more always means addition. This means we will add 15 minutes to your friend's swim time (x) so we can figure out how long you swam (y).

This gives us the equation: y=x+15

Part two:

We know that you swam 55 minutes. This means y=55.

55=y=x+15

55=x+15

Now we want to get x alone, or isolate it. We can do this by subtracting 15 from both sides.

55-15=x+15-15

15-15= 0 and 55-15= 40

40=x

Thus your friend swam 40 minutes

(Remember that whatever you do to one side of the equation, you have to do to the other. If you add 2 to the left hand side, you have to add 2 to the right hand side. If you, like we did above, subtract 15 from the right, you have to subtract 15 from the left too)

Answer:

m∠BCA = 43°

Step-by-step explanation:

ABCD is a kite having m∠BAD = 46° and m∠ABC = 114°

∠BAD and ∠BCA are the vertex angles of the kite.

Since, diagonal of kite bisect the vertex angles

m∠BAC = m∠DAC = [tex]\frac{1}{2}(46^{\circ})[/tex]

m∠BAC = 23°

By applying triangle sum theorem in ΔABC,

m∠ABC + m∠BCA + m∠BAC = 180°

114° + m∠BCA + 23° = 180°

m∠BCA = 180° - (114° + 23°)

             = 43°

Using Pythagoras theorem

[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=17^2-8^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=289-64[/tex]

[tex]\\ \Large\sf\longmapsto P^2=225[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{225}[/tex]

[tex]\\ \Large\sf\longmapsto P=15ft[/tex]

Answer:

Step-by-step explanation:

we have : the length of the ladder is the hypotenuse of the triangle ; the length of the ladder, which is far from the wall, is the right angle side of the triangle (draw your own illustration)

Answer:

[tex]14 \frac{5}{1000} [/tex]

Step-by-step explanation:

[tex]14.005 = 14 \frac{5}{1000} [/tex]

proper frac 14 1/200

improper frac 2801/200

Answer:

A=2(wl+hl+hw)

A=2(6ft×7ft+6ft×7ft+6ft×6ft)

A=2(42ft²+42ft²+36ft²)

A=2(120ft²)

A=240ft²

Step-by-step explanation:

Answer:

it took 7 boys 21 days to clear a piece of land.

Answer:

14cm + 3cm =17cm

Step-by-step explanation:

now find the area

A 45-45-90 triangle follows a unique pattern. It has two congruent sides and one side that = x * sqrt(2).

If AC = 9sqrt(2), then AB is also 9sqrt(2).

To find CB, we need to multiply 9sqrt(2) by sqrt(2).

9sqrt(2) * sqrt(2) = 9 * 2 = 18

CB = 18

Hope this helps!

Answer:

Step-by-step explanation:

(b)

(i)

(ii)

(a) Cumulative frequency is 500, median is at 249, 250, the horizontal line from point 250 on y-axis intersecting the graph at approximately 52%, this is the median

(b)  Vertical line from the 45% mark intersects the graph at approximately 177th point. The number of candidates passed the test:

(iii) P(pass) = 323/500 = 0.626 or 62.6%

Answer:

-1,2 can be plotted together with these four points ...

Answer:

ratio of Sophia's sweets to Isabel's sweets is

13:8

Answer:

you first have to find the number of sweets that sophia got.by subtracting the total number of sweets minus the number of sweets that isabel got which will be

42-16=26

therefore the ratio will be

16:26

8:13

I hope this helps

Answer:

152

Step-by-step explanation:

Substitute the given value for x.

[tex]8(3(6)+1)\\8(18+1)\\8(19)\\152[/tex]

Answer:

152

Step-by-step explanation:

8(3x+1)

Let x = 6

8(3*6+1)

Multiply inside the parentheses

8(18+1)

Add inside the parentheses

8(19)

Multiply

152

Answer:

Step-by-step explanation:

x+65 = 180                            Consecutive angles in llgm are supplementary

x = 180-65                             Subtract equal amounts from both sides.

x = 115

y + 65 = 90                           This hard to explain without letters. The lines are parallel. The right angle is an extension of the right vertical parallel line. So the left two angles are 90 degrees because of the perpendicular angles.

y = 90 - 65

y = 25

Answer:

Use pythagoras theorem

Answer:

= -8x^5 y^4

Step-by-step explanation:

Multiply the numbers: -2 . 4 = -8

-2x^3 yx^2 y^3

Simplify x^3 x^2 : x^5

= -8x^5yy^3

Simplify yy^3 : y^4

= -8x^5 y^4

Answer:

The first line:

y₁ = (2/3)*x + 6

Has the larger y-intercept, by 5 units.

Step-by-step explanation:

Here we need to find the equation for each line.

First, some theory.

A linear relationship can be written as:

y = a*x + b

where a is the slope and y is the y-intercept.

We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ -x₁)

And, if a line is:

y = a*x + b

a perpendicular line to that one must have a slope equal to:

-(1/a).

Now we can answer this question.

We know that the first line, let's call it y₁, passes through the points (3, 8) and (-3, 4), then its slope will be:

a = (8 - 4)/(3 - (-3)) = 4/6 = 2/3

then the line is something like:

y₁ = (2/3)*x + b

to find the value of b, we can use the fact that we know that the line passes through the point (3, 8)

this means that when x = 3, we must have y₁ = 8

replacing these in the above equation, we get:

8 = (2/3)*3 + b

8 = 2 + b

8 - 2 = b = 6

then the equation for this line is:

y₁ = (2/3)*x + 6

Now let's find the equation for the other line, that we will call y₂.

We know that this line is perpendicular to:

y = (1/3)*x - 2

The slope of that line is:

a = (1/3)

then the slope of a line perpendicular to that one will be:

slope = -(1/a) = -(1/1/3) = -3

slope = -3

then we have:

y₂ = -3*x + b

to find the value of b, we can use the fact that our line passes through the point (2, -5)

This means that when  x = 2, we must have y₂ = -5

then:

-5 = -3*2 + b

-5 = -6 + b

-5 + 6 = b = 1

b = 1

then this equation is:

y₂ = -3*x + 1

Now we know both equations:

y₁ = (2/3)*x + 6

y₂ = -3*x + 1

Which equation does have the larger y-intercept?

We can see that the first line has an y-intercept of 6, and the second line has an y-intercept of 1, then the first line has the larger y-intercept, and is larger by 5 units.

Answer:

m/_6=60

Step-by-step explanation:

angles 3 and 6 are same side interior angles makeing them suplimentary.

180-/_3=/_6

180-120=60

it works both ways as well!

Answer:

Find the mean:

Find the variance:

Find the range:

Find the mean:

Find the variance:

The difference:

The mean:

Find the value of x and the data points:

The points are:

The mean deviation:

Note. Mean absolute deviation is different, this is the average of absolute values of mean deviations:

Answer:

 R=.2,P=.25, G=.55

Step-by-step explanation:

Answer:

1,041,958.5, or 104,195 1/2

Step-by-step explanation:

All you have to do is 15787.25 times 66, because 15787.25 is the price for on acre, so 66 acres will be 15787.25 times 66. If you want to put it in fraction form, you can do 15787 1/4 times 66. I hoped you liked this answer!

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Answer:

x = - 1, x = - 0.5

Step-by-step explanation:

Given

2x(x + 1.5) = - 1 ← distribute parenthesis on left side

2x² + 3x = - 1 ( add 1 to both sides )

2x² + 3x + 1 = 0 ← in standard form

(2x + 1)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - 0.5

Answer:

C

Step-by-step explanation:

Given

10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides

30x + 20 > 14x - 28 ( subtract 14x from both sides )

16x + 20 > - 28 ( subtract 20 from both sides )

16x > - 48 ( divide both sides by 16 )

x > - 3 → C

Answer:

The value of 3^-2 is 1/9

Step-by-step explanation:

This is because negative exponent such as [tex]2^{-1}[/tex] transfer to 1/2. Therefore, you might notice a pattern of negative exponent -> fraction. 3^-2 -> 1/(3^2)-> 1/9

PLEASE MARK BRAINIEST IF THIS HELPED!!!

Answer:

Step-by-step explanation:

Concept:

Here, we need to know the idea of exponents.

The exponent of a number says how many times to use the number in a multiplication.

Any number to the 0th power, it is equal to 1.

Solve:

Question 1. What is the value of 3⁻²?

Question 2. What is the value of 3⁰?

Question 3. What is the value of 3¹?

Question 4. What is the value of 3³?

Hope this helps!! :)

Please let me know if you have any questions

Answer:

-44, -42, -40, -38, -36

Step-by-step explanation:

"preceding" requires an indication of the direction.

but I assume the usual left to right direction. in that sense the provided 5 even numbers are directly preceding -35

Answer:

Step-by-step explanation:

a) 9.5 feet above the ground

b)  max height at  of 34.5 feet  5 feet horizontal distance

c) 10.87 feet away