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Answer:

$90 profit

Step-by-step explanation:

[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

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Answer:

[tex]35degrees[/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:

B. 8 + 5

Step-by-step explanation:

5 - (-8)

= 5 + 8

= 8 + 5

Answer:

Step-by-step explanation:

equal

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:

292.5 square cm

Step-by-step explanation:

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

Hope that helps!

Answer:

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

Step-by-step explanation:

Hope it helps!

Answer:

4×6_7482&÷&&÷,geggeve

Answer:

the answer is D. 30

Step-by-step explanation:

I got it wright

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:

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

Step-by-step explanation:

5x5x5= 125

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

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:

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

Answer:

m = 9

Step-by-step explanation:

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

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:

[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]

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

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Answer:

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

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:

2x-1 greater than or equal to 5

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:

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.