The ratio of boys to girls is 5 to 7 there are 45 boys in the school play how many girls are in the play

Answer:

E and F

Step-by-step explanation:

✔️To eliminate the variable y, we can multiply the first equation, -x + 4y = 1 by 7 and the second equation, 8x - 7y = 42 by 4. This will leave us with the variable x alone to solve for.

✔️Alternatively, we may decide to eliminate the variable x first by multiplying the first equation, -x + 4y = 1 by 8. Both equations would be equivalent, thus when we can easily eliminate the variable x leaving us with variable y to solve for.

Answer:

you need three pencil cases to hold all of your pencil

Answer:

3

Step-by-step explanation:

18 = 7 +7 + 4

Since each box can carry 7 pencils, we need three to hold all of them.

Hope this helps!!

Answer:

log(4) +3 log(x) +7 log(y)

Step-by-step explanation:

Hope it helps!

Answer:

4×6_7482&÷&&÷,geggeve

Answer:

[tex]35degrees[/tex]

......the answer is 2a + 2b

Answer:

Circumference = 37.68

Area = 113.04

Step-by-step explanation:

Circumference = π × d

Circumference = 3,14 × 12 feet

Circumference = 37.68

Area = π × r²

Area = 3,14 × 6 × 6

Area = 113.04

Answer:

B. 8 + 5

Step-by-step explanation:

5 - (-8)

= 5 + 8

= 8 + 5

Figure #1

use the smaller part of the figure with the dimensions of 1x2x3 and find the volume of that 1x2x3= 6m

find the area of the bigger part 3x6x3= 54m

54+6= 60m³

Figure #2

smaller part 2x2x7= 28m

bigger part 7x5x3= 105m

105+28= 133ft³

Answer:

v= LxWxH

3x5x2x7x5x7=7350

1x2x4x3x6x3=432

36/6 = 6

20/10 = 2

15/8 = 1 7/8

13/6 = 2 1/6

Hope this helped!

Answer:

6, 2, 8 7/8, 2 1/3

Step-by-step explanation:

36/6 represents a division: 36 divided by 6

answer: 6

20/10 also division: 20 divided by 10

answer: 2

15/8 also division (long division...) 15 divided by 8

you will have a remainder (that will become your numerator)

the decimal of that division is 1.875 as a fraction that is a mixed number:

8 AND 875/1000  but!! you are not done yet (that fraction has to be simplified)

If you divide the fractional portion by the greatest common factor (125) you can simplify your fraction to 8 7/8

13/6 is 13 divided by 6 = 2 with a remainder of 2 = 2 2/6 simplified = 2 1/3

Answer:

292.5 square cm

Step-by-step explanation:

13 x 9 / 2 = 58.5 x 5 = 292.5 square cm

Hope that helps!

Answer:

first is 4+4=8.........second is 22×2=11 ..........third is 8÷11=0.7272727273 u can do it 0.72

Step-by-step explanation:

hope this help

Answer:

0.72

Step-by-step explanation:

Answer:

Step-by-step explanation:

equal

Answer:

the answer is D. 30

Step-by-step explanation:

I got it wright

Answer:

$90 profit

Step-by-step explanation:

Answer:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]

Required

Evaluate

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]

Rewrite as:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {cos(x)\ sin(x)\ sin(2x)} \, dx[/tex]

In trigonometry:

[tex]sin(2x) = 2\ sin(x)\ cos(x)[/tex]

Divide both sides by 2

[tex]\frac{1}{2}sin(2x) = \frac{2\ sin(x)\ cos(x) }{2}[/tex]

[tex]\frac{1}{2}sin(2x) = sin(x)\ cos(x)[/tex]

[tex]\frac{1}{2}sin(2x) = cos(x)\ sin(x)[/tex]

Substitute [tex]\frac{1}{2}sin(2x)[/tex] for [tex]cos(x)\ sin(x)[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin(2x)\ sin(2x)} \, dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin^2(2x)} \, dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, dx[/tex]

Let [tex]u = 2x[/tex]

Differentiate:

[tex]du = 2 \ dx[/tex]

Make [tex]dx[/tex] the subject

[tex]dx = \frac{1}{2}du[/tex]

Substitute [tex]\frac{1}{2}du[/tex] for [tex]dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, \frac{1}{2}du[/tex]

Substitute 2x for u

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(u)} \, \frac{1}{2}du[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}*\frac{1}{2}\int\limits {sin^2(u)} \, du[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]

At this point, we apply the reduction formula:

Which is:

[tex]\int\limits {sin^n(u)} \, du = \frac{n-1}{2}\int\limits sin^{n-2}(u)\ du\ - \frac{cos(u)sin^{n-1}(u)}{n}\du[/tex]

Let n = 2; So, we have:

[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{2-2}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]sin^0(u) = 1[/tex]

So, we have:

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits 1\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

Integrate 1 with respect to u

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du[/tex]

Recall that:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]

So, we have:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}[ \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du][/tex]

Open bracket

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}u - \frac{cos(u)sin(u)}{8}[/tex]

Recall that:  [tex]u = 2x[/tex] and  [tex]du = 2 \ dx[/tex]      [tex]dx = \frac{1}{2}du[/tex]

So, the expression becomes:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}2x - \frac{cos(2x)sin(2x)}{8}[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8}[/tex]

Add constant c

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex]

----------------------------------------------------------------------------------------

In trigonometry:

[tex]sin(2\theta) = 2sin(\theta)cos(\theta)[/tex]

Divide both sides by 2

[tex]\frac{1}{2}sin(2\theta) = \frac{2sin(\theta)cos(\theta)}{2}[/tex]

[tex]\frac{1}{2}sin(2\theta) = sin(\theta)cos(\theta)[/tex]

Replace 2x with [tex]\theta[/tex]

[tex]\frac{1}{2}sin(2*2x) = sin(2x)cos(2x)[/tex]

[tex]\frac{1}{2}sin(4x) = sin(2x)cos(2x)[/tex]

----------------------------------------------------------------------------------------

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex] becomes

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{2*8} +c[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{16} +c[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{x}{4} - \frac{sin(4x)}{16} +c[/tex]

The solution can be further simplified as:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]

Step-by-step explanation:

this is geometric sequence

G1=Go(1+r)^n

G1=1700(1+11%)^1

G1=1700(1+0.1)

G1=1700*0.1

G1=170 per year

G1=170*12 per month

G1=2040

Answer:

a toxin or other foreign substance which induces an immune response in the body, especially the production of antibodies.

Answer:

Step-by-step explanation:

A(10,6), M(5, -4), B(x,y)

5 = (10+x)/2

x = 0

-4 = (6+y)/2

-8 = 6+y

y = -14

B(0, -14)

The required coordinate of B is given as (0, -2 ).

Given that,

To determine the coordinates of B, If the midpoint of AB Is (5,-4) and the coordinates of A are (10,-6).

The midpoint is that point the line whose length from both the ends of the line is equal.

Here,

We have given two coordinates one of the endpoints A of AB and the other is midpoint M i.e. A(10, -6) and M(5, -4).

Definition of midpoint says,

x = [x₁ +  x₂] / 2 ; y = [y₁ + y₂] / 2

x₁ = 10, x = 5 , y₁ = -6 , y = -4

now,
5 = [10 + x₂] / 2 ; -4 = [-6 + y₂] / 2

x₂ = 10 - 10 ; y₂ = -8 + 6

x₂ = 0 : y₂ = -2

Thus, the required coordinate of B is given as (0, -2 ).

Learn more about midpoints here:
brainly.com/question/28224145

#SPJ2

Answer:

2x-1 greater than or equal to 5

Answer:

125[tex]cm^{3}[/tex]

Step-by-step explanation:

5x5x5= 125

[tex]\huge{\mathfrak{\purple{Answer}}}[/tex]

Equation: x² - 15x = 16

Factors: x = -16 and x = 1

[tex]\huge{\mathfrak{\purple{Explanation}}}[/tex]

Given

A number squared minus fifteen times the number is equal to 16.

Equation: x² - 15x = 16

Factors:

x² - 15x - 16 = 0

So,

(x - 16) (x + 1)

=> x - 16 = 0, x + 1 = 0

= x = -16 and x = 1

#HopeItHelps

Answer:

5x³-13x²+24x+12

Step-by-step explanation:

Start by distributing (5x+2) into (x²-3x+6)

It is easiest to start with 5x.

When distributing 5x, your answer should be: 5x³-15x²+30x.

Then, distribute the 2 just as you did for 5x.

Your answer for that should be: 2x²-6x+12

After that, add the like- terms from both answers together.

5x³-15x²+30x+2x²-6x+12

The final answer is then: 5x³-13x²+24x+12

Answer:

Parallel: y = -7x+33

Perpendicular: y = (⅐)x + 31/7

Step-by-step explanation:

y+7x = 5

Slope of the line is -7.

Slope of any parallel to the line is also -7.

Slope of any perpendicular to the line is ⅐.

Answer:

m = 9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.