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3 years ago

8

Mr. Christensen is arranging his students into groups for the next school debate. When he puts them in groups of 5, two students

are left out. When he puts them in groups of 4, one student is left out. When he puts them in groups of 7, four students are left out. What is the least number of students Mr. Christensen has?

1 answer:

Alenkinab [10]3 years ago

7 0

The least amount of students mr Christensen has would be 5 because if he puts them in a group of 4 and one is left out that would equal to 5.

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Q3: Identify the graph of the equation and write and equation of the translated or rotated graph in general form. (Picture Provi

natta225 [31]

Answer:

b. circle; $2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0$

Step-by-step explanation:

The given conic has equation;

$x^2-5x+y^2=3$

We complete the square to obtain;

$(x-\frac{5}{2})^2+(y-0)^2=\frac{37}{4}$

This is a circle with center;

$(\frac{5}{2},0)$

This implies that;

$x=\frac{5}{2},y=0$

When the circle is rotated through an angle of $\theta=\frac{\pi}{3}$ ,

The new center is obtained using;

$x'=x\cos(\theta)+y\sin(\theta)$ and $y'=-x\sin(\theta)+y\cos(\theta)$

We plug in the given angle with x and y values to get;

$x'=(\frac{5}{2})\cos(\frac{\pi}{3})+(0)\sin(\frac{\pi}{3})$ and $y'=--(\frac{5}{2})\sin(\frac{\pi}{3})+(0)\cos(\frac{\pi}{3})$

This gives us;

$x'=\frac{5}{4} ,y'=\frac{5\sqrt{3} }{4}$

The equation of the rotated circle is;

$(x'-\frac{5}{4})^2+(y'-\frac{5\sqrt{3} }{4})^2=\frac{37}{4}$

Expand;

$(x')^2+(y')^2-\frac{5\sqrt{3} }{2}y'-\frac{5}{2}x'+\frac{25}{4} =\frac{37}{4}$

Multiply through by 4; to get

$4(x')^2+4(y')^2-10\sqrt{3}y'-10x'+25 =37$

Write in general form;

$4(x')^2+4(y')^2-10x'-10\sqrt{3}y'-12 =0$

Divide through by 2.

$2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0$

8 0

4 years ago

PLEASE HELP and explain! ill give brainliest if you do

EastWind [94]

Area of the rectangle

$= l \times b$

$= 8 \times 6$

$= 48 {in}^{2}$

Area of the semicircles

$= 2 \times ( \frac{1}{2} \pi {r}^{2} )$

$= \pi {r}^{2}$

$= \pi {3}^{2}$

$= 9\pi$

$= 9 \times 3.14$

$= 28.26 {in}^{2}$

Area of the figure

$= 48 + 28.26$

$= 76.26 {in}^{2}$

= 76.3in²

(rounded)

6 0

3 years ago

Read 2 more answers

Which number is greater: 87 or 13.688?how do you know?

just olya [345]

When comparing two numbers, you usually start by comparing the numbers on the left of the decimal point, if you find one of them greater than the other, then you've got your answer ready. If the numbers on the left of the point are equal, then you start comparing the decimal part.

In the two numbers given, we have 87 and 13.688. We start by comparing the numbers before the point, we will find that these numbers are 87 and 13.
Comparing these two, we can see that 87 is greater than 13.

Therefore: 87 is greater than 13.688

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3 years ago

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Give 10 rational numbers between 2/3 and 4/5

hram777 [196]

Step-by-step explanation:

2/3=0.66666666666

4/5=0.80000000000

10 rational numbers between them

0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79

3 0

3 years ago

Read 2 more answers

This is my last assignment, pls help

Oduvanchick [21]

15 bushes I think because if u divide them both by two u get the answers check it urself

4 0

3 years ago