Lukas plotted these points on the number line.

Point A: −12
3

Point B: −2
3

Point C: −11
3

Point D: −22
3

Which point did he plot incorrectly?

Point
Please mark BRAINLIEST

rate of change:

[tex]\sf \bold{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

coordinates taken: (0, 0), (2, 1)

[tex]\rightarrow \dfrac{1-0}{2-0}[/tex]

[tex]\rightarrow \dfrac{1}{2}[/tex]

Take 2 points

[tex]\\ \rm\rightarrowtail m=\dfrac{1+1}{2+2}[/tex]

[tex]\\ \rm\rightarrowtail m=\dfrac{2}{4}[/tex]

[tex]\\ \rm\rightarrowtail m=\dfrac{1}{2}[/tex]

Answer:

I think the answer is A but im not sure

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now, from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

The statements that are true for the considered equilateral triangle are:

For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.

For this case, referring to the figure attached below, we have:

Since the triangle is equilateral, there can be 6 congruent triangles like BOD.

Thus, Area of triangle ABC = 6 × Area of triangle BOD

Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]

Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]

The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.

We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).

[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]

Using Pythagoras theorem too, we can get the value of x as:

[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]

Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]

This isn't 65 sq. cm.

Thus, the statements that are true for the considered equilateral triangle are:

Learn more about tangent ratio here:

https://brainly.com/question/14169279

Answer:

Heres the answer Hope this helps!:)

y = mx + p

p = - 7 since the line cuts the y-axis in -7

and m the slope ?

we choose 2 points (-2 ; 0) and (0 ; - 7)

we move of 2 units towards the left to go down of 7 units

=> m = - 7/2

y =  - 7/2x - 7

or

y = -3,5x - 7

Answer:x = 154°

Step-by-step explanation:

The central angle and the angle between the tangents are supplementary, so

x + 26° = 180° ( subtract 26° from both sides )

x = 154°

Answer: 154 degrees

Step-by-step explanation: subtract 180 from 26 To get it .

Answer:

38.69

Step-by-step explanation:

=$38.69411765

=$38.69 (to the nearest cent)

(100/85) \$32.

Answer:

Step-by-step explanation:

Givens

V = 75716

pi = 3.14

r = ?

Formula

V =  (4/3) pi * r^3

Solution

75716 =  (4/3) * 3.14 * r^3              Multiply both sides by 3/4

75716 * 3/4 = 3.14 * r^3

56787 = 3.14 r^3                           Divide by 3.14

56787 / 3.14 = 3.14 * r^3/3.14

18085 = r^3

∛18985 = ∛ r^3

r = 26.25

Answer:

c. 141 eighth-grade band students

Part B:

y = 3x

1/3y = x

Answer:

76

Step-by-step explanation:

We know the rule when finding the derivative :

Deriving

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{d}{dx}(76x + 1) [/tex]

[tex]\qquad \sf  \dashrightarrow \:76 {x}^{1 - 1} + 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:76 {x}^{0} + 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:76[/tex]

Here, we have got a constant number, therefore for any value of x it will be 76

Therefore, derivative of 76x + 1 at x = 1 is 76

Answer:

100in^3

Step-by-step explanation:

1. Split the shape into 2 separate rectangles.

2. Use the volume of a rectangle formula for each and add together (look at picture above).

I hop this helps! Have a blessed rest of the night!

Answer:

please mark me as brainlest

Step-by-step explanation:

b is the answers for the question

Answer:

300 text messages sent or received

Step-by-step explanation:

.16 x 300 = 48 which is the same amount as the unlimited texting

Answer:

300

Step-by-step explanation:

this is the answer to this question

Answer:

Step-by-step explanation:

if the measure of <A is 110°

Then the measure of <B is also 110°

Answer:

The answer is C. A triangle is made up of a total angle of 180°, therefore C. is more than 180°

Answer:

  B) 125x^21 -64y^3

Step-by-step explanation:

You want to identify the difference of cubes among the expressions given.

The coefficient 3 is not a cube.

125x^21 -64y^3 = (5x^7)^3 -(4y)^3 . . . . . a difference of cubes

The coefficient 9 is not a cube.

The expression is not a difference.

<95141404393>

Step-by-step explanation:

1.7

1.8

2.2

2.4

The other person got no 1 wrong take note

Answer:

[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]

Step-by-step explanation:

To complete the steps:

[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]

I think the question you are answering a question that does not require simplification so ignore the last bit (= 1/3)

Answer:

False

Explanation:

sin t can never be greater than 1 or less than -1

Answer:

egg: 4 eggs per dollar

peanuts: 0.4 pounds per dollar

t p: 2 rolls for a dollar

apples: 3 apples per dollar

Answer:

$104

Step-by-step explanation:

$260 - 60% = $104

Answer:

B, 20

Step-by-step explanation:

The Pythagorean Theorem states that the two shortest lengths in a right triangle (in our case, 12 and 16), is equal to the longest length in a right triangle (c). So,

a²+b²=c²

Substitute 12 and 16 for a and b, our side lengths

12²+16²=c²

144+256=400

400=c²

Square root both c and 400, which gives us...

20=c

So, the value of x is 20.

Answer:

1. Z-24 < 12

2. A-12.65 ≤ 26,000

3. Z-999 < 500

4. -10x ≥ 25

5. f - -1 < 0 or f+1 < 0

6. y/14 ≥ 0.5

Answer:

18.75

Step-by-step explanation:

Answer:

6x² + 4x + 10

Step-by-step explanation:

(2x - 2)(3x + 5)

2x(3x + 5) - 2(3x + 5)

6x² + 10x - 6x + 10

6x² + 4x + 10 ans.

hope this helps you !

Answer:

Put 4.96 in the second box then solve which the answer is 6.76

Step-by-step explanation: