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3 years ago

Two lines and a ray intersect to form five angles. The angles are numbered in the diagram 1 through 5.

Mathematics

1 answer:

Anton [14]3 years ago

7 0

Answer:

$\angle 2 =145^\circ$

Step-by-step explanation:

Given

$\angle 4 = 55^\circ$

Required

Find $\angle 2$

From the attached image, we have:

$\angle 5 = 90$ --- right angle

So, we have:

$\angle 5 +\angle 4 = 90 + \angle 4$

Substitute: $\angle 4 = 55^\circ$

$\angle 5 +\angle 4 = 90 + 55$

$\angle 5 +\angle 4 = 145$

To solve for $\angle 2$ , we have:

$\angle 2 =\angle 5 +\angle 4$ --- Vertically opposite angles

So:

$\angle 2 =145^\circ$

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WARRIOR [948]

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3 years ago

Write an equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number

NeTakaya

Answer:

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Step-by-step explanation:

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3 years ago

The table shows linear relashonsips between x and y write an equation in slope intercept form for this relashonsip!!!!!!!!!!!!!!

Alchen [17]

Answer:

$y=-2x+6$

Step-by-step explanation:

Slope-intercept form is given as $y=mx+b$ , where $m$ is slope and $b$ is the y-intercept.

To find the slope of a line that passes through two points $(x_1, x_2)$ and $(y_1, y_2)$ , use the slope formula:

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1, y_1)\implies (1, 4)\\(x_2, y_2)\implies (0, 6)$

The slope of the line that passes through these two points is:

$m=\frac{6-4}{0-1}=\frac{2}{-1}=-2$

Now substitute $m=-2$ and any point to solve for $b$ :

$y=mx+b,\\6=-2(0)+b,\\6=0+b,\\b=6$

Therefore, the slope-intercept form of a line that is represented by the table is $\boxed{y=-2x+6}$

8 0

3 years ago

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in sec

vlada-n [284]

Answer:

A)0 sec to 2 sec

B) 2 sec - 3 sec.

C)During 3 to 4 secs water balloon's height decreasing the fastest

D)The height of the water balloon at 16 seconds is 0

Step-by-step explanation:

Given : A linear model with ordered pairs at 0, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

x y

0 60

2 80

3 80

4 20

6 0

7 0

8 0

A) During what interval(s) of the domain is the water balloon's height increasing

We can refer the table balloon height increasing from 60 to 80 and then starts decreasing

So, interval = 0 sec to 2 seconds

So, interval(s) of the domain is the water balloon's height increasing is 0 sec to 2 sec

B) During what interval(s) of the domain is the water balloon's height staying the same

We can see that for 2 to 3 secs the height of the balloon is remaining same 80

So, interval(s) of the domain is the water balloon's height staying the same is 2 sec - 3 sec.

C)During what interval(s) of the domain is the water balloon's height decreasing the fastest

During 3 to 4 - Decrease = $\frac{60}{1}=$ 60 ft/s

During 4 to 6 - Decrease = $\frac{20}{2}$ = 10 ft/sec

During 3 to 4 secs water balloon's height decreasing the fastest

D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds

After 6 secs balloon has reached ground so it will remain on ground

Hence the height of the water balloon at 16 seconds is 0

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3 years ago

Sam is rolling a number cube with the numbers 1, 1, 2, 2, 3, and 3 printed on it.

avanturin [10]

Answer:

0.3333

Step-by-step explanation:

You first need to see how many ways he can roll a sum of 4. There are 12 ways. Treat each face as it's own value. There are 2 of each number on the die, so each face of the die is it's own event.

The 12 ways..

1-2. Rolls a 1 with the one of the 1-faces, then rolls a 3 with either of the 3-faces on the second roll. This counts for 2 different sums of 4.

1 (first 1 face) - 3 (first 3 face)

1 (first 1 face) - 3 (second 3 face)

3-4. He rolls a 1 but it's a different face than the other one than the one he rolled above. This gives us 2 more sums of 4

1 (other 1 face) - 3 (first 3 face)

1 (other 1 face) - 3 (second 3 face)

That's 4 total ways, the same logic will apply for the two 2 faces, and the two 3 faces. Each will have 4 more outcomes, giving us 8 more

There are 36 total outcomes (6*6 = 36), so

P(sum of 4) = 12/36 = 0.3333

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4 years ago