Write as an equation and solve: Eight less than the number is 31.

The question is an illustration of right-angled triangles

The approximated value of x is 33.5 degrees

The given parameters are:

[tex]\theta = x[/tex]

[tex]Hypotenuse = 58[/tex]

[tex]Opposite = 32[/tex]

To determine the measure of angle x, we simply make use of the following sine ratio.

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

So, we have:

[tex]\sin(x) = \frac{32}{58}[/tex]

[tex]\sin(x) = 0.5517[/tex]

Take arc sine of both sides

[tex]x = \sin^{-1}(0.5517)[/tex]

This gives

[tex]x = 33.5[/tex]

Hence, the approximated value of x is 33.5 degrees

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Answer:

Not a parallelogram.

Step-by-step explanation:

By the midpoint formula, the midpoint of a segment between [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] is:

[tex]\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}[/tex].

A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.

The two diagonals of quadrilateral [tex]{\sf ABCD}[/tex] are segment [tex]\sf{AC}[/tex] and segment [tex]{\sf BD}[/tex], respectively.

Using the midpoint formula, the midpoint of segment [tex]{\sf AC}[/tex] (between [tex]{\sf A}\; (3,\, 3)[/tex] and [tex]{\sf C}\; (-3,\, 1)[/tex]) would be:

[tex]\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}[/tex].

Likewise, the midpoint of segment [tex]{\sf BD}[/tex] (between [tex]{\sf B}\; (1,\, 2)[/tex] and [tex]{\sf D}\; (-1,\, 4)[/tex] would be [tex](0,\, 3)[/tex].

Thus, quadrilateral [tex]{\sf ABCD}[/tex] would not be a parallelogram since the midpoints of its two diagonals are not the same.

Answer:

:/

Step-by-step explanation:

Answer:

Sure

Step-by-step explanation:

Answer:

They would need 24 pints of chocolate to make 6 boxes of candy

Answer:

y= -4x+8

Step-by-step explanation:

y-y1= m(x-x1)

y-4 = (-4)(x-1)

y-4 = -4x+4

y = -4x+4+4

y = -4x+8

Answer:

The length of RS is 22

The length of UV is 22

Step-by-step explanation:

6x-8. ---------- equation (i)

4x+2 ------------ equation (ii)

Now,

equating equation i and ii, we get

6x-8 = 4x+2

or, 6x-4x = 2+8

or, 2x = 10

or, x = 10/2

.°. x = 5

Then,

length of RS = 6x-8

= 6×5-8

= 30-8

= 22

Again

length of UV = 4x+2

= 4×5+2

= 20+2

= 22

618 hope this helps you have an amazing week

Answer:

24mph

Step-by-step explanation:

convert 20 mins and 30 mins to hrs by dividing by 60

4/(20/60)=12

6/(30/60)=12

12+12=24

Cyclist's average speed is 12 mph.

Speed is calculated as the ratio of the distance travelled by an object to the time taken to cover the distance.

It can also be defined as the rate of change of position of anything in any direction.

Speed is a scalar quantity as it does not have direction.

Total distance travelled by the cyclist = 4 miles + 6 miles

                                        = 10 miles

Total time taken by the cyclist = 20 minutes + 30 minutes

                                                  = 50 minutes

We need the average speed in mph or miles per hour.

We know that,

60 minutes = 1 hour

1 minute = 1/60 hour

50 minutes = [tex]\frac{1}{60}[/tex] × 50 hour

                   = [tex]\frac{5}{6}[/tex] hour

Average Speed = Total distance travelled / Total time taken

                          = 10 miles / (5/6) hour

                          = 10 × [tex]\frac{6}{5}[/tex]

                          = 12 miles per hour

Hence the average speed of the cyclist is 12 miles per hour.

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Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03

The first step is to find the cost per ounce of each bottle.

For the 16 ounce bottle:

= 2.10 / 16

= $0.13 per ounce

For the 20 ounce bottle:

= 3.15 / 20

= $0.16

The 16 ounce size is therefore better and the amount saved per ounce is:

= 0.16 - 0.13

= $0.03

In conclusion, the 16 ounce is better as it saves $0.03 per ounce.

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X is the input.

Three times the input would be 3x

Increased by two would be adding two at the end.

Answer: B. y = 3x + 2

Answer:

m is -3/2

c is -5/2

Step-by-step explanation:

The standard linear equation is given by;

[tex]{ \tt{y = mx + c}}[/tex]

» m is the slope and c is the y-intercept

Then, our slope is;

[tex] { \tt{2y + 3x = - 5 }} \\ \\ { \tt{2y = - 3x- 5}} \\ \\ { \tt{y = - \frac{3}{2}x - \frac{5}{2} }}[/tex]

Answer:

i think students attend Coast middle School 80 students

Step-by-step explanation:

students attend Coast middle School x students

75%x = 60

x = 60×100/75

x = 80

Answer:

80 students attend

Step-by-step explanation:

75% is the same as 3/4 so you divide 60 by 3 to get 20 then you can multiply that by 4 to get 80

Answer:

base = 6.8 in

Step-by-step explanation:

area of triangle = 1/2 base height

where height = 4.4 in

              area = 14.96 in²

plugin values into the formula

14.96 = 1/2 base (4.4)

base = 14.96 (2)

               4.4

base = 6.8 in

Answer : Susan is correct

Susan is correct because if you get that chart and turn all the numbers to decimals and divide the chart in half you will get the answer to 1.4/0.2 because the chart has 14 slots and if you divide that by 2 you will get 7 just think of 1.4/0.2 as 14/2.

Answer:

A. No, it does not represent a proportional relationship.

B. Yes, it represents a proportional relationship.

C. No, it does not represent a proportional relationship.

Step-by-step explanation:

think of the increase for X and Y, if they increase at the same rate for both and and for X to Y, they have a proportional relationship.

The original number of spoons is 958

Let the total number of spoon be x.

The first day, 25 spoons were removed.

So, the remaining spoon (r) is:

[tex]r =x -25[/tex]

15% of the remaining spoon were used.

So, we have:

[tex]15\% \times r =15\% \times (x -25)[/tex]

This 15% represents 140 spoons.

So, the equation becomes

[tex]15\% \times (x -25) = 140[/tex]

Express 15% as decimal

[tex]0.15 \times (x -25) = 140[/tex]

Divide both sides by 0.15

[tex](x -25) = 933[/tex]

Remove brackets

[tex]x -25 = 933[/tex]

Add 25 to both sides

[tex]x= 958[/tex]

Hence, the original number of spoons is 958

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Answer:

True

Step-by-step explanation:

If corresponding angles are congruent, the lines are parallel

Answer:

502.655

Step-by-step explanation:

The actual answer was 502.655

Answer:

Step-by-step explanation:

Wind, friction and terrain (flat versus hilly) all oppose motion of the bike.  Air resistance increases as the bicyclist goes faster (there's none at 0 mph, a significant amount at 30 mph, a greater amount at 40 mph, and so on).

Answer: For the first 5 months she pays a monthly$15 membership fee. Use the explicit rule f(n) = 15n + 10

Step-by-step explanation:

The table of the ordered pairs and the graph is plotted.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Emma who pays $10 to join a gym. For the first 5 months she pays a monthly $15 membership fee. The explicit rule that represents the situation above is f(n) = 15n+10.

We have the function as -

f(n) = 15n+10.

We can create a table as follows -

[n]         f[n]

1            25

2           40

3           55

4           70

5           85

Refer to the graph of the function f(n) = 15n+10 attached.

Therefore, the table of the ordered pairs and the graph is plotted.

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Answer:

Step-by-step explanation:

Another way to do it is to multiply by 100 and divide by 2. That's probably the simplest way to do it.

Aslan of course would get the right answer. It's direct and it does give the right answer.

Lucy also did it correctly.

Jack is the only one who will not get it right.

Answer:

.44 or 11/25

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

2/9 divided by 1/2 can be changed to multiplication by using the inverse of the fraction you are divining by, which makes 2/9 times 2/1, or 2/9 times 2, which is 4/9

Step-by-step explanation:

that is very simple. you do understand the word "perimeter" ? it just means the distance when walking around the whole shape once.

and that clearly means to just add all side lengths.

that's it.

so, 25 + 18 + 18 + 20 + 17 = 98 ft

was there any other problem with this you did not understand ?

Answer:

Step-by-step explanation:

Sam's car is 1 ft in front of the start line and its speed is 13.5 ft/s.

The distance after x seconds is:

Alice's car the speed 12 ft/s and after 3 seconds is 40 ft in front of the start line.

The distance after x seconds is:

After 15 seconds the distance from the start line is:

As we see Sam is further from the start line than Alice