6x³ + 3x
how do you factor out the GCF in this question??

The half life of the substance is 6.92 days.

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

[tex]\rm N = N_o e^{-kt}[/tex]

The concentration will reduce to half therefore

[tex]\rm N= \dfrac{N_o}{2}[/tex]

so,

[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]

ln 0.5 = - 0.1001 * t(1/2)

-0.693 = -.1001 * t(1/2)

t(1/2) = 6.92 days.

Therefore the half life of the substance is 6.92 days.

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Answer:

21. x = 18.1

22. x =28.7

Step-by-step explanation:

SOH = sin(theta) = opp/hyp

CAH = cos(theta) = adj/hyp

TOA = sin(theta) = opp/adj

21. You would be using tangent.

tan(theta) = Opp/Adj

tan(32°) = x/29

x = 29 * tan(32°)

x = 18.1

22. You would be using cosine

cos(theta) = Adj/Hyp

cos(43°) = 21/x

x * cos(43°) = 21

x = 21 / cos(43°)

x = 28.7

Use a Calculator to help you solve for those side lengths or degrees.

If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using

I am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.

The area of the prism is 12x² inches². Thus, the correct option is B.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

For a prism, the lateral sides of a prism are made up of rectangles which consist of the height and the length of the base. Therefore, a triangular prism has an equilateral base with a side length x inches. The height of the prism is four times as long as the side length. The lateral area will be,

Lateral Area = 3(x×4x) = 12x² inches²

Hence, the area of the prism is 12x² inches². Thus, the correct option is B.

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The income tax that will be paid for the year will be RS 4199.

The total income that the ma gets will be:

= 39990 + 2000

= 41990

The tax rate is given as 10%. Therefore, the income tax that will be paid this year will be:

= 10% × 41990

= 4199

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The slant height can be found using Pythagoras theorem, the slant height is the hypotenuse side of the pyramid. Therefore, slant height = √34 meters

The base of the pyramid is a square.

Therefore,

area of a square = l²

where

hence,

area of the base  = l

36 = l²

l = √36

l = 6 meters

Therefore, using Pythagoras theorem,

l² = 5² + 3²

l² = 25 + 9

l² = 34

l = √34 meters

slant height =  √34 meters

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Answer:

none

Step-by-step explanation:

4x - 6 = 2(2x + 3)

4x - 6 = 4x + 6

Everything cancels out meaning there are no real solutions

The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.

Rational function are functions that are written as a ratio. For instance a/b can be expressed as rational function.

According to the question, we are to plot the graph of the function 10/x

The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.

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Two supplementary angles when addd together equal 180.

let one angle = x

The second angle is 5 times that so would be 5x

x + 5x = 180

Simplify:

6x = 180

Divide both sides by 6:

X = 30

One angle is 30, the second angle would be 150

The answer is 150

Answer:

  6√3 ±3 ≈ {7.392, 13.392}

Step-by-step explanation:

The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.

__

Radii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.

A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...

  AB = √(21² -3²) = √432 = 12√3

This is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...

  6√3 ±3 ≈ {7.392, 13.392}

Answer:

6√3 ± 3

Step-by-step explanation:

AC is the radius of Circle C ⇒ radius = 12

DB is the radius of Circle D ⇒ radius = 9

Therefore, CD = AC + DB = 12 + 9 = 21

AE is the radius of Circle E ⇒ radius = 3

BF is the radius of Circle F ⇒ radius = 3

If AB is the common tangent of Circles C, D, E and F, then:

∠CAB =∠AEF = ∠DBA = ∠BFE = 90°

(as the tangent to a circle is always perpendicular its the radius).

Also AB = EF

To find the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F, we first need to find the length of EF (marked by x on the attached diagram).

CD is the hypotenuse of a right triangle with base equal to EF and a smaller leg of the difference between the radii of Circles C and D.

(Refer to the green shaded triangle on attachment 1)

Therefore, to find EF (x), use Pythagoras' Theorem a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ a² + b² = c²

⇒ 3² + x² = CD²

⇒ 3² + x² = (12 + 9)²

⇒ 9 + x² = 441

⇒ x² = 432

⇒ x = √432

⇒ x = 12√3

⇒ EF = 12√3

As the radius of Circles E and F is 3, the possible diameter of the circle with its center as the midpoint of EF is 6 less or 6 more than the length of EF.

⇒ diameter = EF ± 6

                   = 12√3 ± 6

As the radius is half of the diameter, the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F is:

⇒ radius = diameter ÷ 2

               = (12√3 ± 6) ÷ 2

               = 6√3 ± 3

(see attachments 2 and 3 → the possible circles are shown in orange)

Answer:

In order for each child to receive a book, first distribute one book to each.

This can be done in [math] 5\times 4\times 3 = 60 [/math] ways.

The remaining two books can be distributed in [math] 3^2 [/math] ways.

Total number of ways[math] = 60 \ times 9 = 540 [/ math]

if it's diameter is 19, then its radius must be half that, or 9.5.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=9.5\\ h=4.5 \end{cases}\implies V=\pi (9.5)^2(4.5)\implies V\approx 1275.9~ft^3[/tex]

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[tex]\textsc{heya!}[/tex]

[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:

[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:

[tex]\textsc{solution:}[/tex]

[tex]\textsc{explanation:}[/tex]

divide both sides by 9; after performing this operation, we obtain:

[tex]\bold{x=\frac{6}{9}}[/tex]

divide top & bottom by 3; we obtain the solution

[tex]\bold{x=\frac{2}{3}}[/tex]

[tex]\textsc{hopefully\;helpful!}[/tex]

by: [tex]^da_n^cIn_g}[/tex]

have a great rest of your day ahead ~ = )

~

Answer:

x=6, y=4

Step-by-step explanation:

x - y = 2

2x = 3y => 2x - 3y = 0

x - y = 2 | ×(-2) => -2x + 2y = -4

2x - 3y = 0

-2x + 2y = -4

2x - 3y = 0

___________

0 - y = - 4 | ×(-1)

y = 4

Substitution in x - y = 2:

x - 4 = 2 | +4

x = 2+4 = 6

Answer:

D. 60

Step-by-step explanation:

60 is the only number that 3 and 4 and 5 all go into.



4 does not go into 15, so not answer A.



5 does not go into 12, so not answer B

3 does not go into 20, so not answer C

D is correct. 4 and 5 and 3 all go into 60.

Explanation:

Draw out a 10 squares.

Shade in 4 of them to represent 4/10 = 0.40 = 0.4

Then use another color to shade another 4 squares. You should have 4+4 = 8 squares shaded, out of 10 total, giving 8/10 = 0.80 = 0.8

This is one visual way to see how 0.4 x 2 = 0.8

In other words, 0.4 x 2 means we have two copies of 0.4 added together. You could write it as 0.4 x 2 = 0.4 + 0.4 = 0.8 if you wanted.

See the diagram below.

Answer:

-10,-13,-16 and importance of being in a good night friends ni pta nhi hai to you

Factorize the numerator and denominator, then simplify:

10/45 = (2×5)/(9×5) = 2/9

Now,

1/9 = 1/10 + 1/90

1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900

1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000

and so on, which is to say

1/9 = 1/10 + 1/100 + 1/1000 + …

or

1/9 = 0.111…

so that multiplying both sides by 2 gives

2/9 = 0.222…

Answer:

The measure of a minor arc is less than 180° , and equal to the measure of the arc's central angle . A major arc is the longer arc connecting two endpoints on a circle. The measure of a major arc is greater than 180° , and equal to 360° minus the measure of the minor arc with the same endpoints.

The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The values of the angels will be calculated by using the trigonometry property.

Sin A = Perpendicular / Hypotenuse

Sin A = 9 /41

Cos A = Base / Hypotenuse

Cos A =  40 / 41

Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

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Answer:

it is b

Step-by-step explanation:

The solution is Option A.

The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point A be A ( x , y )

Now , the vertex A is reflected over the line y = x

When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )

So , the coordinates of the point A' ( -2 , 10 )

Now , the coordinates of the point A will be

A ( x , y ) = A ( 10 , -2 )

Therefore , the value of A is A ( 10 , -2 )

Hence , the coordinates of the point before reflection is A ( 10 , -2 )

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Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

The explicit formula for the amount of money in his account at the beginning of month n is  a(n) = 2300 + (n − 1)200.

The explicit formula would be a linear function. A linear function is a function that has a single variable raised to the power of 1.The rate of increase in the account is a constant amount : $200

Amount of money at the beginning of the  month = beginning balance + (number of months - 1) x rate of increase

a(n) = 2300 + (n − 1)200

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Answer:

X= -3

Step-by-step explanation:

(4+5)-1/3(40-4)=X

X=9- 1/3(36)

X=9-12

Answer:

Mr. Garcia had 5 kilograms of blueberries at first

Step-by-step explanation:

to make this easiest, we can imagine that we're undoing mr. garcia's actions.

So, we can start by 'unpacking' mr garcia's bags

we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags

(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)

so,

1/4  x 9 = 9/4

(9 = 9/1 [if that is how you're used to multiplying a fraction])

Then, he also sold 2 3/4 kilograms

so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first

2 3/4 + 9/4 =  2 + 12/4

(12/4 = 3)

2 + 3 = 5

So, Mr. Garcia had 5 kilograms of blueberries at first

Using proportions, it is found that the homeowner would have to pay $2,750 in property tax each year.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax at a rate of 25 mills means that for each $1,000 in value of the home, he pays $25 in taxes. Hence, for a home of value of $110,000, the amount he pays in taxes is given by:

A = 110 x 25 = $2,750.

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Answer:

[tex]\mathsf {SA = 112 in.^{2} }[/tex]

Step-by-step explanation:

[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]

[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]

[tex]\textsf {Solving :}[/tex]

[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]

[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]

[tex]\implies \mathsf {SA = 2 (56)}[/tex]

[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]

Answer:

Train A = 466

Train B = 60

Step-by-step explanation:

La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%[/tex].

The question gives:

Then, you will have:

[tex]6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500[/tex]

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