Directions: Solve for x. Round to the nearest tenth.
3.
2
.
48°
17
29
x
х
х
67°
4.
5.
29°
16°
12
X
Х
37
6.
7.
15
х
589
51°
х
22

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Answer:

y=3/5x-14

Step-by-step explanation:

parallel lines have the same slope, so m=3/5

y=mx+b

-23=3/5(-15)+b

-23=-9+b

-14=b

y=mx+b

y=3/5x-14

Answer:

b and d I think!!

Step-by-step explanation:

The details of the relationship between the numbers is a word problem that can be used to find the values in the other missing values as presented in the attached drawing .

A word problem is a presentation of a mathematical question using verbal statements.

Please find attached the possible diagram in the question obtained from a similar question posted online

The value in the square is -6

The value in the circle to the top right of the square = -3

Therefore;

The value in the circle to the right of the square with 12 is therefore found by dividing 12 by the value of the circle to the left of 12 as follows;

12 ÷ 2 = 6

The value in the blank square is the product of the values in the two circles (The circle at the top (-3) and the circle at the bottom right (6) of the triangle) as follows;

The figure completed with the missing values in the circles and squares  are presented in the attached drawing created with MS Word

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The two equations are:

y(x) = x + 2

r(x) = 2x

And the graph can be seen below, the solution is (2, 4)

We know that the yellow flower is 2 centimeters tall and grows at a rate of 1cm per day, then after x days the height is:

y(x) = x + 2

And the red one starts at 0 centimeters, and then grows at a rate of 2cm per day, so the height equation is:

r(x) = 2x

The graph of the two linear equations can be seen on the image below:

The solution is the point where the lines intersect, in this case is the point (2, 4).

Which means that after 2 days both plants will have a height of 4 cm.

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The axis of symmetry for the function f(x) is x = 8 , and h(x) is x = 3

The axis of symmetry is a hypothetical straight line that splits a form into two identical halves, making one half the mirror image of the other. Both pieces are overlaid when folded along the axis of symmetry.

A straight line called the axis of symmetry is what gives an object its symmetrical form and exactly the same reflections are produced on each side of the axis of symmetry on the graph.

From the given information:

f(x) = -4(x - 8)² + 3

Use the vertex form, y = a ( x − h )² + k, to determine the values of a, h, and k.

Since the value of a is negative, the parabola opens down, and the vertex (h, k) is (8, 3).

The distance (p) from the vertex and the focus of the quadratic equation can be calculated by using the formula:

P = 1/4a

Replacing the value of a from above:
P = 1/4(-4)

P = -1/16

The focus of a parabola can be determined by adding the p to the y-coordinate k if the parabola opens up or down. Thus, (h, k + p) = (8, 47/16).

Thus, the axis of symmetry is finally estimated by finding the line that passes through the vertex and the focus;

Axis of symmetry x = 8

For the graphical function of h(x); we use the following points on the graph to determine the equation of the parabola: (1,-2), (3,2), (5,-2)

Thus, h(x) = -x² + 6x - 7

Rewriting the function in its vertex form, we have:

y = - (x - 3)² + 2

Using the vertex form;

The vertex (h,k) = (3,2). The axis of symmetry (x) is the line that passes through the vertex and the focus, x = 3.

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Answer:

36 yards x 144 yards

Step-by-step explanation:

Let the width of the rectangle field be x and the length be 4x.

The perimeter is 2(4x + x). So:

2(4x + x) = 360

10x = 360

x = 36

Then the width is 36 yards and the length is 144 yards.

Answer:

\(y=\frac{9}{2}x+5\)

Step-by-step explanation:

To find the equation of the a line that passes through the two given points, we must first find the slope between the two points. We can do this by using the slope formula. The slope formula is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.

By plugging in (-2, -4) and (0, 5) for (x₁, y₁) and (x₂, y₂) respectively, we get:

\(y=\frac{5-(-4)}{0-(-2)}=\frac{9}{2}\)

So the slope is 9/2. Now we that we have found the slope, we can write an equation. Normally, when we are given two points, we would pick one of the points and plug it into the point-slope form and then solve for slope-intercept form. Here, notice that one of the points give, (0, 5), is the y-intercept. Knowing this, we can plug in 5 for the y-intercept into the slope-intercept form to get our equation. Remember, slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Pugging in 9/2 for m and 5 for b we get:

\(y=\frac{9}{2}x+5\)

which would be our equation.

I hope this helps. Happy studying.

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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Answerc

Step-by-step explanation:

simple

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:

good luck passing

Step-by-step explanation: -3 -2 1 x 1 2

Answer: slope equals 2/3

Step-by-step explanation:

The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

Here,

The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:

V = h/3 * (A + √(A*B) + B)

where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.

In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:

A + B = 40 + 12 = 52 m²

√(AB) = √(4012) = √(480) = 4*√(30)

Substituting these values into the formula, we get:

V = 3/3 * (52 + 4√(30) + 12)

V = 68 + 4√(30)

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Answer:

Step-by-step explanation:

Find the length of AB:

Now as we know:

sine = opposite / hypotenuse

cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Correct choice is A

1/3 of a gallon divided by 3 gallons = 1/9

Answer:

1/3 is for 3 gallons is 1/9

Answer:

Step-by-step explanation:

1200(1+.08*2)= 1392

Answer:

112cm³

Step-by-step explanation:

Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top

from the figure we know that

length of the cuboid is 10 cm

Width is 2 cm

height is 5 cm

now the formula for Volume of cuboid is Length×Width×Height

so,

Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)

Now we will ignore the cuboid on top and find the volume of the one at the bottom

From the figure, we know that its dimensions are

length = 2cm

height = 3cm

width = 2cm

Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)

Adding (1) and (2)

100cm³ + 12 cm³ = 112cm³

Therefore the volume of the given figure is 112cm³

The volume of the box is 112 cm³.

We have,

The figure can be considered as two boxes.

Now,

One box:

Volume.

= Length x Width x height
= 10 x 2 x 5

= 100 cm³

Another box:

Volume.

= Length x Width x height
= 2 x 2 x 3

= 12 cm³

Now,

The volume of the box.

= 100 + 12

= 112 cm³

Thus,

The volume of the box is 112 cm³.

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Answer:

They are equivalent

Step-by-step explanation:

\(3(3a+4) = 3(3a)+(3)(4) = 9a+12\)

Explanation: if you distribute the 3 to the formula within the parenteses, you will get the same equation as 9a+12

Answer:

Six less than five times a number is less than fourteen

Step-by-step explanation:

I had the same question on my homework haha

Answer:

She can make 2 bouquets

Step-by-step explanation:

Divide 8 and 6 by two.

8/2= 4

6/2= 3

she can only make two identical bouquets without any flowers left over

Answer:B

Step-by-step explanation:

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

-6

Step-by-step explanation:

6x-9x=21-3

-3x=18

x=-6

Answer:

14 ft - 8 ft = 6 ft

Step-by-step explanation:

You basically just need to subtract it! :)