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3 years ago

Make a line plot of the measurements

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

7 0

Um, well start from 0 on the number line. End with 1 on the number line. After 0 try to estimate 1/4 on the line. Draw 1/3 next, then 1/2. Start plotting the 'x's on the fractions. there are 2'1/4', 3'1/2' and 3'1/3'. There :3

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If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

kondaur [170]

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here, $x_1=-8, y_1=-6, x_2=-4, y_2=-14$

$$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)$

$$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)$

$$P(x, y) =(-6, -10)$

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here, $x_1=-6, y_1=-10, x_2=-8, y_2=-6$

$r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}$

$r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}$

$r=\sqrt{(-2)^{2}+(4)^{2}}$

$r=\sqrt{20}$ units

The standard form of the equation of a circle is

$(x-a)^{2}+(y-b)^{2}=r^{2}$ , where (a, b) are center and r is the radius.

Here, center = (–6, –10) and $r=\sqrt{20}$

$(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}$

$(x+6)^{2}+(y+10)^{2}=20$

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

4 0

2 years ago

Please help me thank you

fgiga [73]

I hated probability in middle school. I'm not 100% sure but I would go with the 3rd answer choice, 3/100.

3 0

3 years ago

Total surface area of a cube is 1014cm^2. It's volume will be :

Karolina [17]

Answer:

Option A (2197 cm³)

Step-by-step explanation:

For a cube with length of each side "a" , it's

Total Surface Area = 6a²
Volume = a³

_____________________________________________

According to the question ,

Total Surface Area = 1014 cm²

Let the length of each side of cube be 'a'.

Using the formula ,

$6a^{2} =1014$

$=> a^{2} =\frac{1014}{6} = 169$

$=> a = \sqrt{169} = +13 \: or -13$

But length can't be negative . So , length of each side = 13 cm

∴ Volume of cube = 13³ = 2197 cm³

8 0

3 years ago

Mr. Larson is debating between investing $10,000 into an account that pays 4% interest compounded daily or 4.9% compounded weekl

AVprozaik [17]

9514 1404 393

Answer:

4.9% weekly

Step-by-step explanation:

The compound interest formula is ...

A = P(1 +r/n)^(nt)

where A is the account balance that results from investing P at rate r compounded n times per year for t years.

Filling in the values for the two scenarios, we find ...

A = 10,000(1 +0.04/365)^(365·3) ≈ 11,274.89

A = 10,000(1 +0.049/52)^(52·3) = 11,582.74

The higher interest rate will earn Mr. Larson the most money in three years. (4.9% weekly)

5 0

2 years ago

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.

Murljashka [212]

Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (−5/8,−41/16)
Focus: (−5/8,−5/2)
Axis of Symmetry: x=−5/8
Directrix: y=−21/8 x. y
−3. 20
−2. 5
−5/8. −41/16
 0. −1
1. 8

3 0

2 years ago