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3 years ago

Consider the scatter plot.

Mathematics

1 answer:

Leno4ka [110]3 years ago

4 0

Answer:

The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Step-by-step explanation:

We are given a scatter plot with a best fit line as shown on the given graph.

The equation of the best fit line is given by:

y = 0.75x + 5

So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Since the distance shown on the y axis is already 5 when the time started at 0 minutes.

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O is the centre of the circle. AB is a diameter.

viktelen [127]

Answer:

The value of a is 63° and the value of b is 27°

Step-by-step explanation:

In the given figure

∵ OA, OB, and OC are radii of the circle O

→ The radii of a circle are equal

∴ OA = OB = OC

In Δ AOC

∵ OA = OC

∴ Δ AOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OAC and ∠OCA are the base angles of the triangle

∴ m∠OAC = m∠OCA

∵ m∠OAC = a°

∴ m∠OCA = a°

→ The sum of angles in any triangle is 180°

∵ a° + a° + m∠AOC = 180°

∵ m∠AOC = 54°

∴ a° + a° + 54 = 180°

→ Add the like terms

∴ 2a° + 54 = 180°

→ Subtract 54 from both sides

∴ 2a° = 126°

→ Divide both sides by 2

∵ m∠OAC = m∠OCA = 126 ÷ 2

∴ a° = 63

∴ The value of a is 63°

In ΔBOC

∵ OB = OC

∴ Δ BOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OBC and ∠OCB are the base angles of the triangle

∴ m∠OBC = m∠OCB

∵ m∠OBC = b°

∴ m∠OCB = b°

∵ ∠AOC is an exterior angle of ΔBOC at the vertex O

→ The measure of the exterior angle equals the sum of the measure

of the opposite interior angles to this vertex

∵ ∠OBC and ∠OCB are the opposite interior angle of ∠AOC

∴ m∠OBC + m∠OCB = m∠AOC

→ Substitute their measures

∵ b° + b° = 54°

→ Add the like terms

∴ 2b° = 54

→ Divide both sides by 2

∴ b° = 27

∴ The value of b is 27°

3 0

2 years ago

A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take

Allisa [31]

Answer:

1/30 of a ton

Step-by-step explanation:

Write this as an expression:

1/3 of a ton and 1/2 of a ton were taken to the site.

4/5 of a ton were remove from the site.

Amount of a ton at the site = $\frac{1}{3}+ \frac{1}{2}- \frac{4}{5}$

Solve the equation by finding common denominators (when the bottom numbers are the same).

$(\frac{1}{3}+ \frac{1}{2})- \frac{4}{5}$ Focus on the first part. The least common multiple (LCM) of 3 and 2 is "6", which will become the denominator.

For 1/3 to become ?/6, multiply top and bottom by 2.

For 1/2 to become ?/6, multiply top and bottom by 3.

$(\frac{2}{6}+ \frac{3}{6})- \frac{4}{5}$

Now we can add the numerators together over the same denominator.

$\frac{5}{6}- \frac{4}{5}$

Do the same thing as before and change the denominators. The LCM of 6 and 5 is "30".

For 5/6 to become ?/30, multiply top and bottom by 5.

For 4/5 to become ?/30, multiply top and bottom by 6.

$\frac{25}{30}- \frac{24}{30}$

Subtract the numerators:

$\frac{1}{30}$ Answer in tons

Therefore there was 1/30 of a ton of rock left at the construction site.

7 0

3 years ago

Read 2 more answers

the radius of a gold atom is 1.35 angstroms. how many gold atoms would it take to line up a span of 8.5 mm?

serg [7]

The angstrom, also known as the angstrom unit, is a measure of displacement equal to 0.0000000001 meter (10 -10 m). It would be helpful to convert the units of angstrom to mm. We do as follows:

diameter = 2 x 1.35 x10^ -10 m ( 1000 mm / 1 m ) = 2.7 x 10^-10 mm / atom

Number of gold atoms = 8.5 mm / 2.7 x 10^-10 mm / atom = 31481481481.481 atoms

6 0

3 years ago

Read 2 more answers

Can someone please help me on solving: x+y=-4

timama [110]

Answer: x=-1 and y= -3

Step-by-step explanation:

Solve for x, x+y=-4

Minus y from both sides so it'll be X=-y-4

Now substitute -y-4 in x-y=2 and solve for y

-y - 4 -y=2

Add like terms, -2y - 4=2

Add 4 to both sides -2y=6

Divide both sides by -2 $\frac{-2y}{-2} = \frac{6}{-2}$

y= -3

Substitute -3 in x=-y - 4

x=-(-3) - 4

- × (-3)= 3

3 - 4= -1

x= -1

5 0

2 years ago

A triangle has side lengths of 5a +3 inches and 2a +3 inches. If the perimeter of the triangle is 3a + 12 inches, which expressi

JulsSmile [24]

Answer:

A. 2a+6

Step-by-step explanation:

I did the test and this is what I got.

7 0

3 years ago