3/5 of the students in a class were boys. The teacher divided the boys equally into groups so that each group of boys had 1/10 of the number of students in the class. The teacher then divided the girls equally into groups such that each group of girls had 1/5 of the number of students in class.
a) Find the number of groups of boys and the number of groups of girls.
b) If there were 16 girls in the class, how many boys were there in each group?

9514 1404 393

Answer:

Step-by-step explanation:

The partial products are apparently derived by multiplying parts of each value on either side of the decimal point:

  1.5 × 3.50 = (1 + 0.5)(3 + 0.50) = 1×3 + 0.5×3 +1×0.50 +0.5×0.50

  = 3 + 1.5 + 0.50 + 0.25 . . . . . partial products

Their sum is ...

  3 + 1.5 + 0.50 + 0.25 = 5.25

Zoe spent $5.25 on apples.

Answer:

5i[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

i² = - 1 ⇒ i = [tex]\sqrt{-1}[/tex]

Given

[tex]\sqrt{-175}[/tex]

= [tex]\sqrt{25(7)(-1)}[/tex]

= [tex]\sqrt{25}[/tex] × [tex]\sqrt{7}[/tex] × [tex]\sqrt{-1}[/tex]

= 5i[tex]\sqrt{7}[/tex]

Answer:

[tex]5i\sqrt{7}[/tex]

Step-by-step explanation:

In order to solve this question we need to know how to multiply roots. You will need to understand that when we multiply [tex]\sqrt{a}[/tex] by [tex]\sqrt{b}[/tex], the following is true.

[tex](\sqrt{a})(\sqrt{b}) = \sqrt{ab}[/tex]                       (1)

From the question it self we know that [tex]\sqrt{ab}[/tex] is equal to [tex]\sqrt{-175}[/tex]. We also know that [tex]i^{2} = -1[/tex] or in other words [tex]i = \sqrt{-1}[/tex].

Now we will need to factors [tex]\sqrt{-175}[/tex] so that at the end we will end up representing [tex]\sqrt{-175}[/tex] as a product of [tex]\sqrt{-1}[/tex] and some other number. In order to determine the unknown number we will just have to divide [tex]\sqrt{-175}[/tex] by [tex]\sqrt{-1}[/tex]. From the equation (1) that I mention at the start we can figure out that......

[tex]\sqrt{a} = \frac{\sqrt{-175} }{\sqrt{-1} } = \sqrt{175}[/tex]   (in our case [tex]\sqrt{a}[/tex] is the unknown number we are trying to find)

Now we can rewrite [tex]\sqrt{-175}[/tex] as the following.....

[tex]\sqrt{-175} = (\sqrt{175})(\sqrt{-1})[/tex]

From here we substitute [tex]\sqrt{-1}[/tex] with [tex]i[/tex] and simplify [tex]\sqrt{175}[/tex]. In order to simplify [tex]\sqrt{175}[/tex] we will have to factor [tex]\sqrt{175}[/tex] in a way that we will see [tex]\sqrt{175}[/tex] as a multiple of a perfect square root. An so we get the following

[tex]\sqrt{-175} = (\sqrt{175})(i) = (\sqrt{7})(\sqrt{25} )(i) = (\sqrt{7})(5)(i) = 5i\sqrt{7}[/tex]

Step-by-step explanation:

We know ,

Area=pi *r^2

=3.14*49=153.86Meter sq

Answer:

No Soultion

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

distribute

3y + 6 = 5 + 3y

subtract 3y from both sides

6 = 5

no solution since 6 can never equal 5

Answer: He is 28 years old

Step-by-step explanation:

:0

:)

Answer:

0.619

Step-by-step explanation:

Answer:

0.619

Step-by-step explanation:

Fist divide 13/21. I used a claulator since thats allows in my class. When you do that you get 0.619047619. to round we look at the thrid and fourth decimal places, which are 9 and 0. Since zero is less than nine we round down to get the answer.

7: Answer: [tex](x,y)=(\frac{5}{4},\frac{3}{2} )[/tex]

Substitute the value of Y:

[tex]-2x-3(10x-11)=-7[/tex]

Solve for X:

[tex]-2x-3(10x-11)=-7[/tex]

[tex]x=\frac{5}{4}[/tex]

Substitute the value of X:

[tex]x=\frac{5}{4}[/tex]

[tex]y=10*\frac{5}{4}-11[/tex]

Solve for Y:

[tex]y=10*\frac{5}{4}-11[/tex]

[tex]y=\frac{3}{2}[/tex]

Solution:

[tex](x,y)=(\frac{5}{4},\frac{3}{2} )[/tex]

8: Answer: [tex](x,y)=(3,-2)[/tex]

Substitute the value of Y:

[tex]4x-3*(-2)=18[/tex]

Solve for X:

[tex]4x-3*(-2)=18[/tex]

[tex]x=3[/tex]

Solution:

[tex](x,y)=(3,-2)[/tex]

9: Answer [tex](x,y)=(0,-2)[/tex]

Substitute the value of Y:

[tex]-3x+6(-2+5x)=-12[/tex]

Solve for X:

[tex]-3x+6(-2+5x)=-12[/tex]

[tex]x=0[/tex]

Substitute the value of X:

[tex]x=0[/tex]

[tex]y=-2+5*0[/tex]

Solve for Y:

[tex]y=-2+5*0[/tex]

[tex]y=-2[/tex]

Solution:

[tex](x,y)=(0,-2)[/tex]

10: Answer [tex](x,y)=(-3,-6)[/tex]

Substitute the value of Y:

[tex]-5x-(6+4x)=21[/tex]

Solve for X:

[tex]-5x-(6+4x)=21[/tex]

[tex]x=-3[/tex]

Substitute the value of X:

[tex]x=-3[/tex]

[tex]y=6+4x(-3)[/tex]

Solve for Y:

[tex]y=6+4x(-3)[/tex]

[tex]y=-6[/tex]

Solution:

[tex](x,y)=(-3,-6)[/tex]

Please mark me brainliest if this helped you :)

Answer: the correct answer is to teacha don’t like you assigning this bullish!+ when will you ever in your life use this feel bad for y’all I dropped out

Step-by-step explanation:

Answer:

x ≈ 11.5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify Variables

Angle = 35°

Opposite Leg = x

Hypotenuse = 20

Step 2: Solve for x

Answer:

40B +30M ≤ 300

200B +80M ≤ 1200

Step-by-step explanation:

The inequality functions are as follows:

For 40 cartridges per book and 30 cartridges per magazine and at most 300 cartridges are used

So the function would be

40B +30M ≤ 300

Now the another would be

There are 200 pages for printing a book and 80 pages are required for printing a magazine also she used at most 1,200 pages

So, the function would be

200B +80M ≤ 1200

Answer:

multiply all of it

Step-by-step explanation:

11.3 x 6 x 8 x 8

10.3 x 13 x 9 x 5

=

26145849.6

Reduce

Answer:

1/3

Step-by-step explanation:

Answer:

3,1are right answer. but I ju

St thinking

Answer:

what are the answers?

Step-by-step explanation:

Answer:

$1.56 d per pound

Step-by-step explanation:

18.72/12= 1.56

Answer:

x ≥ -4 or x ≥ [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

9 ≤ | 4x + 7 |

4x + 7 ≥ 9

4x ≥ 2

x ≥ [tex]\frac{1}{2}[/tex]

4x + 7 ≥ -9

4x ≥ -16

x ≥ -4

Answer:

[tex]x=1+\sqrt{5} , x=1-\sqrt{5}[/tex]

Step-by-step explanation:

exchange y for 1:

[tex]1=x^2-2x-3[/tex]

and solve (I used an online calculator - symbolab and mathaway are my favorites).

Answer:

what are you talking about???

Step-by-step explanation:

brainliest and chill bro

Answer:

AE = 30

GD = 5

GF = 10

Step-by-step explanation:

Centroid of medians divide median in the ratio 2 : 1

Therefore,

AG : GE : 2 : 1

Let AG = 2x & GE = x

Since, AG = 20....(given)

Therefore, 2x = 20

x = 20/2

x = 10

GE = x = 10

AE = AG + GE = 20 + 10 = 30

CG : GD : 2 : 1

Let CG = 2x & GD = x

Since, CG = 10....(given)

Therefore, 2x = 10

x = 10/2

x = 5

Since, GD = x

Therefore, GD = 5

BF = 30

2x + x = 30

3x = 30

x = 30/3

x = 10

GF = 10

Answer:

Step-by-step explanation:

h(f(g(2)))=

h(f(3*2-11))) = h(f( -5))=

h((2*(-5)^2) +4*(-5) +10) = h (50 -20 +10) = h(40)

now calculate h(40) but check if you wrote corectly the equation

Answer:

— What is (g × h)(x)?

The answer is 3x²+x-2

— What is g(k(x))?

The answer is 12x - 2 or 2(6x-1)

— What is k(g(0))

The answer is -8

Explanation:

Given these functions —

[tex]f(x) = 5 {x}^{2} - 4x + 1 \\ g(x) = 3x - 2 \\ h(x) = x + 1 \\ k(x) = 4x[/tex]

Find (g × h)(x)

[tex](g \times h)(x) = g(x) \times h(x)[/tex]

Substitute g(x) = 3x - 2 and h(x) = x + 1

[tex](3x - 2) \times (x + 1) \\ (3x - 2)(x + 1)[/tex]

Multiply the polynomial.

[tex]3 {x}^{2} + 3x - 2x - 2[/tex]

Subtract - 2x out of 3x —

[tex]3 {x}^{2} + x - 2[/tex]

Thus, the answer is —

[tex](g \times h)(x) = 3 {x}^{2} + x - 2[/tex]

Find (g(k(x))

Substitute k(x) = 4x in g(x).

[tex]g(x) = 3x - 2 \\ k(x) = 4x[/tex]

[tex]g(k(x)) = g(4x)[/tex]

[tex]g(4x) = 3(4x) - 2[/tex]

Distribute 3 in 4x —

[tex]g(4x) = 12x - 2[/tex]

Thus the answer is —

[tex]g(k(x)) = 12x - 2[/tex]

Alternative Solution

[tex]g(k(x)) = 2(6x - 1)[/tex]

Find k(g(0))

Given two functions — k(x) and g(x)

[tex]k(x) = 4x \\ g(x) = 3x - 2[/tex]

Evaluate the value of g(0) as we substitute x = 0 in g(x)

[tex]g(0 ) = 3(0) - 2 \\ g(0) = 0 - 2 \\ g(0) = - 2[/tex]

Since we need to find k(g(0)), our currently input is g(0).

From k(x) and g(0) —

[tex]k(x) = 4x \\ g(0) = - 2[/tex]

Substitute g(0) = -2 in k(x)

[tex]k(g(0)) = 4(g(0)) \\ k( - 2) = 4( - 2) \\ k( - 2) = - 8[/tex]

Thus, the answer is —

[tex]k(g(0)) = - 8[/tex]

Answer:

D 1/6

Step-by-step explanation:

There are 6 total marbles and only one of them is red so

1=red

6=total

1/6

PLZ MARK ME BRAINLIEST

Answer: 5/8 of the project is done

Answer:

0.315 per lb

Step-by-step explanation:

Answer:

y=-1/4x+1

Step-by-step explanation:

The perpendicular equations slope is the negative reciprocal of the other lines, so if I had 2 as a slope, the perpendicular line's slope would be -1/2, I think. Then you just use the found slope and the given point to solve for b, then use the b value you get for the final equation.

Answer:

c is the answer

2 1/2 X 2 1/3 ( 1/2 and 1/3 is in power)

2 1/2+1/3

2 5/6

Answer:

Your slope would be -5/3

Step-by-step explanation:

To find the slope from two points, you would use the formula y2-y1/x2-x1

In this case, the equation would look like -12-8/3-(-9)

-12 - 8 = -20

3 - (-9) = 12

-20/12 = -5/3

Answer:

39.44

Step-by-step explanation:

Answer:

39.4418605

Step-by-step explanation:

Answer:

x = 1 and y = 6

Step-by-step explanation:

Add these equations

-2x+y=4

2x+y=8

2y=12

    2

y = 6

Plug in 12 for y.

-2x+(6) = 4

     -6    -6

-2x = -2

     -2

x = 1