reduce 12/16 to simplest terms

Given polynomial with descending degrees of x would be,

x^4z^4 + x^3 - x^2z + z^3

In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4

We need to write given polynomial by descending degrees of x.

The highest degree of x in above polynomial is 4

x^3 + z^3 - x^2z + x^4z^4

then the second term would be x with degree 3.

x^3 + z^3 - x^2z + x^4z^4

the third term would be x with degree 2

x^3 + z^3 - x^2z + x^4z^4

and the last term is the term x with degree 0:

x^3 + z^3 - x^2z + x^4z^4

Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^3

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y = -18(x-7)² + 1 is the vertex form of the given equation.

y = a (x − h) 2 + k, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (-a).

Given that y = -18x² + 252x - 881, where a = -18, b = 252 and c = -881

h = -b/2a

h = -252/2*(-18) = 7

k = ah² + bh + c = -18*49 + 252*7 - 881 = 1

Therefore, putting the values in y = a (x − h) 2 we get,

y = -18(x-7)² + 1

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Answer:

g(x)=−x−5, find g(1)g(1)

Step-by-step explanation:

g(x)=−x−5, find g(1)g(1)

Answer: 2012

Step-by-step explanation: biggest shift in pop

Answer: Read explanation

Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.

Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.  

Make any corrections if you want! Make it more comfortable to your style!

The exponential function giving the concentration after t hours is given as follows:

[tex]C(t) = 0.00372(0.9359)^t[/tex]

The standard modelling of an exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

The meaning of the variables of the equation are given as follows:

The initial value of the exponential function is given as follows:

a = 0.00372.

After eight hours, the concentration is given as follows:

C(8) = 0.00219.

Hence the rate of change is obtained as follows:

[tex]C(t) = 0.00372b^t[/tex]

[tex]0.00219 = 0.00372b^8[/tex]

[tex]b^8 = \frac{0.00219}{0.00372}[/tex]

[tex]b = \sqrt[8]{\frac{0.00219}{0.00372}}[/tex]

[tex]b = \left(\frac{0.00219}{0.00372}\right)^{\frac{1}{8}}[/tex]

b = 0.9359.

Hence the equation is:

[tex]C(t) = 0.00372(0.9359)^t[/tex]

The problem is given by the image at the end of the answer, and it asks for the exponential function modelling the situation.

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Answer:

1.3000

Step-by-step explanation:

To Round Numbers...

1 ) Decide which is the last digit to keep ( In this case it would be the hundredths )

2 ) Leave it the same if the next digit is less than 5 (this is called rounding down)

3 ) But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Hope this helps! :)

A)  the domain is:

D: [0, 6]

The range is:

B)  

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

And the graph can be seen at the end.

Here we have the linear equation:

d(t) = (1/2)*t + 2

This refers to the amount of water in a barrel for six rainy days, where t is the number of days.

So the domain goes between t = 0 and t = 6.

The range will go between:

d(0) = (1/2)*0 + 2 = 2

d(6) = (1/2)*6 + 2 = 3 + 2 = 5

So the domain is:

D: [0, 6]

The range is:

T: [2, 5]

b) The complete sentences are:

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                             2013           2012           2011           2010

Sales            $ 620,000   $ 580,000   $ 450,000   $ 600,000

Trend Analysis      103%             97%              75%             100%

Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.

To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.

The other years' results are compared to the base year's by dividing each year's result by the base year's.

Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.

2013 (D) = 103% ($620,000/$600,000 x 100)

2012 (C) 97% ($580,000/$600,000 x 100)

2011 (B) 75% ($450,000/$600,000 x 100)

2010 (A) = 100% ($600,000/$600,000 x 100)

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Expression which placed on the right side of equal sign is,

[tex]2+3^3 =2 +3\times 3\times 3[/tex]

[tex]2+3^3= 2+27[/tex]

[tex]2+3^3= 29[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

What do you mean by equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given, a expression 2 + [tex]3^3[/tex] = ?  

what can  be placed right side of the expression?

so, first we calculate the [tex]3^3[/tex] which means 3 x 3 x 3 = 27.

then , add 2 and 27 and the answer is 29.

but the answer is not present into the option.

Final answer will be 29 which placed right side of the equation 2 + [tex]3^3[/tex] = 29.

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The proof to the above diagram is ∠1 + ∠3 = 180

Supplementary angles are angles whose sum equals 180°

If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.

∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3

Also ∠1 + ∠2 = 180°( sum of angles on a straight line)

making ∠2 the subject of the equation

∠2 = 180 - ∠1

But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3

substituting ∠2 for ∠3 in the equation, we have

∠3 = 180 - ∠1

which is further simplified as,

∠1 + ∠3 = 180°

Which  means both angles are also supplementary.

In conclusion,  both angles are supplementary as ∠1 + ∠3 = 180

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Step-by-step explanation:

f(x) = 2x - 3

f(m) = 5

that means

5 = 2m - 3

8 = 2m

m = 4

f(-2) = n

that means

n = 2×-2 - 3 = -4 - 3 = -7

so,

m + n = 4 + -7 = -3

Here is what i did

I used a graphing calculator

DT is congruent to TD.

A line segment is always equal to itself.

Given,

The figure;

We have to find the segments which are congruent because of the reflexive property of congruence.

Reflexive property of congruence;-

An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry. If angle A is an angle, then angle A is a congruent angle of angle A

Here,

DT = TD,

A line segment is always equal to itself.

So, DT is congruent to TD.

Congruence;-

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

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Answer:  x = 8   y = 21

Step-by-step explanation:

7x + 12 = 12x - 28

40 = 5x

x = 8

180 = 12(8-28) + 9y - 77

180 = 96 - 28 - 77 + 9y

180 = -9 + 9y

189 = 9y

y = 21

Answer:

x=8

y=21

Step-by-step explanation:

9y-77+12x-28=180

9y+12x=285

7x+12=12x-28

5x=40

x=8

9y+96=285

9y=189

y=21

Check the picture below.

[tex]~~~~~~\textit{initial velocity in meters} \\\\ S = -5t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&16\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ 0=-5t^2+16t+16\implies 5t^2-16t-16=0 \\\\\\ (5t+4)(t-4)=0\implies t= \begin{cases} -\frac{4}{5}\\\\ 4 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

the equation for meters is usually as you see in the picture but for this exercise it got rounded from -4.9 to -5, which is fine.

let's notice that "t"  has two values, however the seconds cannot be a negative value, so we dismiss that one.

The ball will strike the ground 4 seconds after it is thrown When an object is thrown upward, its height , in meters, is given by the quadratic equation S = -5t² + vt + h

To find the time at which the ball will hit the ground, we need to determine when the height (S) of the ball becomes zero. At that moment, the ball will be at ground level.

The height (S) of the ball is given by the quadratic equation:

S = -5t² + vt + h

where:

S = height of the ball in meters

t = time of flight in seconds

v = initial velocity in meters/second (upward velocity, so it's positive)

h = height above level ground from which the object is thrown

Given that the initial velocity (v) is 16 meters/second, and the height above the ground (h) is 16 meters, we can substitute these values into the equation:

S = -5t² + 16t + 16

Now, to find the time (t) at which the ball hits the ground, we need to solve for t when S = 0:

0 = -5t² + 16t + 16

This is a quadratic equation in standard form (ax² + bx + c = 0), and we can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula is given by:

t = (-b ± √(b² - 4ac)) / 2a

In our case, a = -5, b = 16, and c = 16. Plugging these values into the quadratic formula:

t = (-(16) ± √(16² - 4*(-5)16)) / 2(-5)

t = (-16 ± √(256 + 320)) / -10

t = (-16 ± √576) / -10

Now, find the two possible solutions for t:

t₁ = (-16 + √576) / -10

t₁ = (-16 + 24) / -10

t₁ = 8 / -10

t₁ = -0.8 seconds

t₂ = (-16 - √576) / -10

t₂ = (-16 - 24) / -10

t₂ = -40 / -10

t₂ = 4 seconds

We have two solutions for t: t = -0.8 seconds and t = 4 seconds. However, we can disregard the negative value for time, as time cannot be negative in this context.

So, the ball will strike the ground 4 seconds after it is thrown.

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If each day a player of climbing shoes cost 84 it cost 169 to buy six days of climbing one pair of climbing shoes and one harness. The amount that the harness cost is $25.

Cost of climbing = ( $10×6)

Cost of climbing = $60

Harness cost = Total cost  - (Cost of climbing  + Cost of shoes)

Harness cost =$169 - ($60 + $84)

Harness cost =$169 - $144

Harness cost =$25

Therefore $25 is the harness cost.

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The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.

G = C×(w×h²/l)

Where,

C = constant

C = G×l/(w²h²)

Weight (w) = 6 in

Height (h) = 2 in

Length (l)= 10 ft

Maximum ton (G) = 8 t

C = 8×10/(6×2²)

C = 80/24

C = 10/3

G = (10/3)×(w×h²/l)

So, Maximum weight

G = (10/3)×(6×2²/24)

G = 10/3 t

G = 3.33 tones

The maximum weight is 3.33 tones.

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Answer:

99

Step-by-step explanation: 99

Answer: 13

Step-by-step explanation:

Answer: 9.57

Step-by-step explanation:

do 9 - -0.87 first.

that will give you 9.87

then you subtract 0.3

final answer: 9.57

Answer:

92

Step-by-step explanation:

3+3=6

The division that can match the model is that 6 ÷ 1/5 = 30.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. It is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

It is a process of repeated subtraction. It is the inverse operation of multiplication. It is defined as the formation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of those smaller numbers equals the larger number taken.

In this case, the division will be:

= 6 ÷ 1/5

= 6 × 5

= 30

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The width of a rectangle is (7x+y) meters.

What is the area of a rectangle?

A flat surface of a specific shape can be thought of as the area it occupies in space. In terms of the "number of" square units, it is measured (square centimeters, square inches, square feet, etc.) The number of unit squares that can fit inside a rectangle is the area of that shape. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes.

Area of the rectangle is = (7[tex]x^{2}[/tex]+8xy+[tex]y^{2}[/tex]) square meter

length of the rectangle is = (x+y) meters

we know, the area of the rectangle= length×width

So, the width of the rectangle = (7[tex]x^{2}[/tex]+8xy+[tex]y^{2}[/tex])/(x+y) meters

=(7x+y)(x+y)/(x+y) meters

=(7x+y) meters

Hence, The width of a rectangle is (7x+y) meters.

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The surface area of the cylinder in term of π is 6764πmm^2

A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.

The total surface area of a cylinder is 2πr(r+h)

Where r is the radius and h is the height of the cylinder

therefore T.S.A= 2×38π(38+51)

T.S.A=76π×89

The total surface area(T.S.A) of the cylinder =6764πmm^2

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x = [tex]x^{2}[/tex] - 20  is equivalent to  [tex]x^{2}[/tex] - x - 20 = 0 .

What do you mean by algebraic expression?

Algebraic expressions are mathematical expressions that result when you perform operations such as addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions have different components. Variables, constants, terms, and coefficients in algebraic expressions. A symbol that does not have a fixed value is called a variable.

Given equation:

x = [tex]x^{2}[/tex] - 20

⇒ [tex]x^{2}[/tex] - 20 - x = 0

⇒ [tex]x^{2}[/tex] - x - 20 = 0

Therefore, x = [tex]x^{2}[/tex] - 20  is equivalent to  [tex]x^{2}[/tex] - x - 20 = 0 .

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Answer:

y = 8 [tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

an exponential function can be expressed in the form

y = a [tex]b^{x}[/tex]

to find a and b use points that lie on the graph

using (0, 8 ) , then

8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8

y = 8[tex]b^{x}[/tex]

using (1, 4 ) , then

4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )

[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]

y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function

The Required Factors   (x + 1) (x - 3 ) (x + 2) (x - 2).

Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0

Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable

Now, factorize the polynomial of degree 4 as follows.

= (x + 1) (x - 3) (x^2 - 4)

Then, again factorize polynomial of degree 2.

Therefore  (x + 1) (x - 3 ) (x + 2) (x - 2)

This is the required factors.

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The dimensions of the cup that minimize the construction cost are 2 x 2 x 5 in

Given:  Capacity = 20 in³, cost of material for the side = 12¢/in² and cost of material for the base = 60¢/in²

In order to calculate the dimension of the cup

Let h and x represent the height and square base respectively

Thus, the capacity (volume) of the pencil cup is can be represented as:

V = x²h     (where V = 20)

20 = x²h

h = 20/x²

At minimum cost, we have:

C(x) = 60x² +  12(4xh)

C(x) = 60x² +  48xh         (put h = 20/x²)

C(x) = 60x² +  48x(20/x²)

C(x) = 60x² +  960/x

Differentiating with respect to x, we have:

C(x) = 120x - 960/x²      (multiply through by x²)

120x³-960 = 0

120x³ = 960

x³ = 960/120

x³ = 8

x = ∛8 = 2 in

For the height:

h = 20/x²

h = 20/2²

h = 20/4 = 5 in

dimensions = 2 x 2 x 5 in

Therefore, the dimensions of the cup that minimize the construction cost are a 2 x 2  square base and  height of 5 in

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The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

Given,

The points which the line passes through = (6, 4)

Slope = 2/3

We have to find the equation of line;

Linear equation;

Y = mx + b is one way to represent a linear equation.

Here,

x is 6 and y is 4

Slope, m is 2/3

Then,

Substitute the values in y = mx + b

Here,

y = mx + b

4 = 2/3 (6) + b

4 = 12/3 + b

4 = 4 + b

b = 4 -4

b = 0

Then,

The equation of line is, y = 2/3x + 0

That is,

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

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