cos40°+sin40°/cos40°-sin40°​

0.001, 0.014, 0.1, 9.41

Answer: 2(10y+3x)(10y-3x)

Step-by-step explanation:

2(100y²- 9x²)

2[ (10y+3x)(10y-3x) ]

Answer:

20

Step-by-step explanation:

If the three numbers are x, x+1, and x+2, then:

x (x+1) (x+2) = 990

x (x² + 3x + 2) = 990

x³ + 3x² + 2x - 990 = 0

(x - 9) (x² + 12x + 110) = 0

Since x must be a whole number, x = 9.  You can also use simple trial and error to find that the three numbers are 9, 10, 11.

The sum is:

9 + 10 + 11 = 20

The value of  [tex]f(g(x))=-6x-5[/tex]

Given functions are, [tex]f(x)=-2x-3,g(x)=3x+1[/tex]

We have to find composite function [tex]f(g(x))[/tex].

         [tex]f(g(x))=f(3x+1)\\\\f(g(x))=-2(3x+1)-3\\\\f(g(x))=-6x-2-3\\\\f(g(x))=-6x-5[/tex]

Learn more about the composite function here:

https://brainly.com/question/10687170

To find (fxg)(X), you need to multiply the two given functions, apply the distributive property, and then combine like terms. The result for (fxg)(X) is -6x² - 11x - 3.

Step-by-step Explanation:

Therefore, (fxg)(X) = -6x² - 11x - 3.

Answer:

Pythagorean Theorem

hypotenuse^2 = side^2 + side^2

16^2 = 7^2 + side ^ 2

256 - 49 = side^2

side x = sq root (207)

207 = 9 * 23 Therefore,

side x = 3 * sq root (23)

answer is A

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Given the 2 equations

2x - y = 11 → (1)

3x - 2y = 6 → (2)

Multiply (1) by - 2 and adding will eliminate y

- 4x + 2y = - 22 → (3)

Add (2) and (3) term by term

(3x - 4x) + (- 2y + 2y) = (6 - 22)

- x = - 16 ( multiply both sides by - 1 )

x = 16

Substitute x = 16 into (1) or (2) for corresponding value of y

(1) : 32 - y = 11 ( subtract 32 from both sides )

- y = - 21 ( multiply both sides by - 1 )

y = 21

Solution is (16, 21 ) → d

Answer:

It's d. (16,21).

Step-by-step explanation:

2x -  y =  11 .............(1)

3x – 2y = 6...........(2)

Multiply the first equation by -2:

-4x + 2y = -22.......(3)

Adding (2) + (3):

-x = -16

x = 16.

Substitute for x in equation (1):

2(16)  - y = 11

-y = 11-32 = -21

y = 21.

Answer: The general equation for the lateral area of a pyramid is LSA=(1/2)pl

P is the perimeter

L is the slant

Answer:

4.50

Step-by-step explanation:

3 divided by 2 is 1.5, which is equivalent to $1.50. So each drink cost 1.50. 1.50 x 3 = 4.50.

Answer is:

37 nickels

Answer:

it takes 97 nickels

Step-by-step explanation:

4.85÷0.05=97

Answer:

the y-intercept is -6

Step-by-step explanation:

3x+5y=30

    -5y -5y

(30-)3x=30-5y(-30)

3x-30=5y/y

3/5x-6=y

Hello There!

To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.

Let's Test It!

"9+12=21" 21 is greater than 15

"9+15=24" 24 is greater than 12

Yes This Does Form A Triangle!

Answer:

Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.

Step-by-step explanation:

There are multiple different ways to prove that this answer is correct.

To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.

3x3=9

4x3=12

5x3=15

Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.

If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.

In this case, we get

9^2 + 12*2 = 15^2

If we simplify, we get:

81+144 = 225

And if simplified further, we get:

225=225,

Which is a true statement, proving that these side lengths do make up a right triangle.

Hope this helps!

Answer:

Step-by-step explanation:

Look at the picture.

If polygons ABCD and EFGH are similar, then corresponding sides are in proportion.

[tex]\dfrac{GH}{CD}=\dfrac{FG}{BC}[/tex]

We have

[tex]GH=z,\ CD=10,\ FG=6,\ BC=8[/tex]

Substitute:

[tex]\dfrac{z}{10}=\dfrac{6}{8}[/tex]          croaa multiply

[tex]8z=(10)(6)[/tex]

[tex]8z=60[/tex]           divide both sides by 8

[tex]z=\dfrac{60}{8}\\\\z=7.5[/tex]

Hello There!

X=2

To solve this, we first need to understand that when we see an X in parentheses, we multiply the number before it in this case 4 by X.

The answer is 2 because we multiply 4 by 2 which is the x value so 4*2 is equal to 8 and they we add 9 to it because the sum of 6 and 3 is 9.

Finally, our answer we get is 17 so our X value is 2.

Have A Great Day!

Answer:

I believe it's 22/15

Step-by-step explanation:

17x -6 + 3x - 5 = 1x + 11 + 4x first you add the 17x and 3x and 1x and the 4x

which it would be: 20x - 6 -5 = 5x + 11;

20x - 11 = 5x + 11,

 -5            -5

15x - 11 = 11

      +11   +11

15x = 22

15       15     Divide

x = 22/15

Hope my answer has helped you if not i'm sorry.

Answer:

They are equivalent

Step-by-step explanation:

x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent

Answer:

Δ = 60

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the discriminant

Δ = b² - 4ac

Given

3x² + 6x = 2 ( subtract 2 from both sides )

3x² + 6x - 2 = 0 ← in standard form

with a = 3, b = 6 and c = - 2

b² - 4ac = 6² - (4 × 3 × - 2) = 36 - (- 24) = 36 + 24 = 60

Answer:

The coordinates of vertex A" is (3 , 1)

Step-by-step explanation:

* Lets revise The translation of a point

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

∵ Δ ABC has a vertex A = (-4 , 2)

∵ The Δ ABC is translated 2 units right and 5 units down to form

   triangle A′B′C′

- From the rule above the x coordinate id added by 2 and the

 y-coordinate is subtracted by 5

∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)

∴ The image of vertex A is A' = (-2 , -3)

∵ Δ A'B'C' is then translated 5 units right and 4 units up to form

   triangle A″B″C″

- From the rule above the x coordinate is added by 5 and the

 y-coordinate is add by 4

∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)

* The coordinates of vertex A" is (3 , 1)

Answer:

it is a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since the triangle is right with hypotenuse QR

Use Pythagoras' identity to solve for QR

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

QR² = 8² + (8[tex]\sqrt{3}[/tex] )²

       = 64 + 192

       = 256 ( take the square root of both sides )

QR = [tex]\sqrt{256}[/tex] = 16

Final answer:

The length of QR is approximately 2.25 units. Since qr and qs are similar, the length of QR is also approximately 2.25 units.

Explanation:

The length of QR can be determined based on the given information about the vectors near S, R, and T. The vectors near S start at about 6 units away, while vectors near R and T start at about 4 units. Using the equation qr|d² = qs|D², we can find that as|¶R = D² / d² = 36 / 16 = 2.25. Since qr and qs are similar, the length of QR is also approximately 2.25 units.

Answer:

86

Step-by-step explanation:

Since something minus a negative is just adding, we get 37-(-8)=37+8 or 45. We can do the same with 11-(-30) which is 11+30 or 41. So 45+41=86

Answer:

86.

Step-by-step explanation:

Work out the 'inner' parentheses first:

(37 - (-8)] + [11 - (-30)]

= (37 + 8) + (11 + 30)

Now the outer parentheses:

= 45 + 41

= 86.

Answer:

The smallest number that is in the domain of fog is 3

Step-by-step explanation:

f(x) = [tex]\sqrt{8x}[/tex] (as corrected in comments)

g(x) = x-3

we need to find fog = f(g(x))

For finding f(g(x)) we put the value of g(x) inside the f(x)

f(g(x))=[tex]\sqrt{8(x-3)}[/tex]

The domain of this function is x ≥ 3

because if value of x is less than 3 than the result would be negative and we know √f(x) ≥ 0

So, the smallest number that is in the domain of fog is 3

Answer:

"It is translated 1 unit left and stretched vertically by a factor of 3"

Step-by-step explanation:

The parent function here is y = x^2

Let's give out some general rules of transformation:

If y = f(x) is a parent function, then

1. If we have y = a * f(x)

| a | > 1 is a stretch;  

0 < | a | <1 is a compression, vertically for both

and

2. If we have y = f(x-c), this means horizontal translation to right c units and y = f(x+c) means horizontal translation c units left

Looking at y = 3(x+1)^2, we can say that "it is vertical stretch by a factor 3 and horizontal translation 1 units left"

Answer:

Girls: 9; Boys: 11

Step-by-step explanation:

16-7=9

14-3=11

Answer:

Option c. 30,000

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

y ----> safe load in pounds

x ----> length in feet of a horizontal beam

we have

For [tex]x=15\ feet, y=2,000\ pounds[/tex]

Remember that

[tex]k=y*x[/tex]

substitute

[tex]k=2,000*15=30,000[/tex]

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

Area of a triangle is 1/2 x base x height.

The base is 6 units long and the height is 4 units.

Area = 1/2 x 6 x 4 = 12 square units.

Answer:

199

Step-by-step explanation:

For this problem, you have to write an formula.

a(n)=a(1)+(n-1)d

n is the term you are trying to find (in this case it's 50).

a(1) is the first term in the sequence (in this case it's 3).

d is the common difference (in this case it's 4).

Plug those in, and you get:

a(50)=3+(50-1)4

And you can easily solve that and get a(50)=199.

Answer:

199

Step-by-step explanation:

Step-by-step explanation:

We know any line that is parallel to other line has same slope.

Here, m1=m2

So, slope will be -1/2.

For this case we have by definition, that if two lines are parallel then their slopes are equal. That is to say:

[tex]m_ {1} = m_ {2}[/tex]

If we have a line of the form:

[tex]y_ {1} = - \frac {1} {2} x_ {1} + b_ {1}[/tex]

Then a parallel line will be given by:

[tex]y_ {2} = - \frac {1} {2} x_ {2} + b_ {2}[/tex]

That is, the slopes are the same!

Answer:

Option C

Answer:

-1

Step-by-step explanation:

Given equation of line is:

x - y = 8

In order to find the slope of other line we have to convert the given equation in standard form

So,

-y = -x + 8

Multiplying the equation with -1

y = x - 8

The co-efficient of x is the slope of the line.

Here the co-efficient is 1 so the slop of line is 1.

We know that the producct of slopes of perpendicular lines is -1.

Let m2 be the slope of the other line then

1 * m2 = -1

m2 = -1

So the slope of line perpendicular to line x-y = 8 will be: -1 ..

92 boxes

1379/15=91.93 but u need a full box so 92

Answer:

92

Step-by-step explanation:

Given:

Number of Paperweights = 1,379

Number of Paperweights that each box can hold = 15

Number of boxes needed = 1379 ÷ 15 = 91.933 boxes

Because 0.933 of a box is of no use to anyone, we simply round this number up to the next whole box and just have the last box partially full.

This gives us 92 boxes.

Answer:

(-2,0.2)

Step-by-step explanation:  

we have

[tex]f(x)=2(3)^{x}[/tex]

[tex]g(x)=10log(x+3)[/tex]  

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The intersection points are (-1.9,0.2) and (1,6)

see the attached figure

therefore

The solution of the system of equations are the points (-1.9,0.2) and (1,6)