Help with Pre Calculus

The function which is used to represent the graphed geometric sequence is

[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is of the form a,ar,ar^2, ...

The common ratio will be ar/a.

From the graph, we can find out the sequence as 80,20,5, ...

Here we can see that the sequence is in Geometric Progression.

First term a=80

Common ratio r= ar/a

= 20/80

=1/4

General term of Geometric sequence is

[tex]f(x) = a {r}^{x - 1} [/tex]

Substituting the value a = 80 and r = 1/4,

we get,

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

Hence, the correct answer is

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

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Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

The polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved. Example, x² + 3x + 5.

As per the given informations, the first polynomial is 2x² + 2x + 1.

The second polynomial equal is 5x² + 4x + 6.

Now, the sum of the two polynomial can be written as,

Sum = 5x² + 4x + 6 + 2x² + 2x + 1 = 7x² + 6x + 7

Therefore, the polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: length = 11 \: \: in[/tex]

[tex]\qquad \tt \rightarrow \: width = 4 \: \: in[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let the measures be :

[tex] \textsf{\large Area of rectangle :} [/tex]

[tex]\qquad \tt \rightarrow \: Area = length \sdot width [/tex]

[tex]\qquad \tt \rightarrow \: 44 = x \sdot(x + 7)[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x = 44[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 44 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 11x - 4x - 44 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x(x + 11) - 4(x + 11) = 0[/tex]

[tex]\qquad \tt \rightarrow \: (x + 11)(x - 4) = 0[/tex]

possible values of x = -11 and 4

[tex] \textsf{But the acceptable value of x = 4} [/tex]

[ length or width of rectangle can't be negative ]

[tex]\qquad \tt \rightarrow \: length = x + 7 = 4 + 7 = 11 \: \: in[/tex]

[tex]\qquad \tt \rightarrow \: width = x = 4 \: \: in[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.

We need to find the volume of the copper wire.

The formula to find the volume of a cylinder is πr²h.

Now, the volume of the copper wire=πr²h=[tex]\frac{22}{7} \times (0.6)^{2} \times 200000=2,26,080[/tex] mm³=226.080 cm³

If the density of copper is 8.9 g/cm³, find the mass of the wire.

We know that [tex]Density=\frac{Mass}{Volume} }[/tex].

⇒8.9 g/cm³=[tex]\frac{Mass}{226.080}[/tex]

⇒Mass=2,012.112 g/cm³

Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

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Answer:

2.4 × 10⁶

Step-by-step explanation:

Given:

To calculate the value of R, substitute the given values into the given formula:

[tex]\begin{aligned}\sf R & = \sf \dfrac{x^2}{y}\\\\ \implies \sf R& = \sf \dfrac{(3.8 \times 10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{3.8^2 \times (10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44 \times 10^{10}}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44}{5.9} \times \dfrac{10^{10}}{10^4}\\\\& = \sf 2.4474... \times 10^{(10-4)}\\\\& = \sf 2.4474... \times 10^6\\\\\end{aligned}[/tex]

Therefore, the value of R to 1 decimal place is 2.4 × 10⁶

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

Exponent Rules used

[tex](a^b)^c=a^{bc}[/tex]

[tex]{a^b}{a^c}=a^{b-c}[/tex]

[tex]R = \frac{ {x}^{2} }{ y} \\ \\ R = \frac{ {(3.8 \times {10}^{5})}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{ ({3.8})^{2} \times ( { {10}^{5} )}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10 - 4} }{5.9} \\ \\ R = 2.45 \times {10}^{6} [/tex]

The trigonometric relation is solved and the length of side DE is given by the relation DE = 3.8 ( tan 40° )

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔEFD

Now , the measure of side EF = 5 units

The measure of side DF = 3.8 units

And , from the trigonometric relations , we get

tan θ = opposite / adjacent

On simplifying , we get

tan 40° = DE / DF

Multiply by DF on both sides , we get

DE = 3.8 ( tan 40° )

Hence , the trigonometric relation is solved

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The attached graph represents the solution set of [tex]3e^x > \frac 12^x[/tex]

The complete options are not given.

So, I would plot the graph that represents the solution set

The inequality is given as:

[tex]3e^x > \frac 12^x[/tex]

Start by splitting the inequalities as follows:

[tex]f(x) > 3e^x[/tex]

[tex]g(x) > \frac 12^x[/tex]

The above means that we plot the graphs of f(x) and g(x) to represent the solution set

See attachment

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The remainder represented by synthetic division is -5.

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.

Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

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Answer:

v ≥ 5

Step-by-step explanation:

v ≥ 5

Answer:

80 m is distance traveled

Step-by-step explanation:

if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled

The loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

The cash flow statement is a financial statement that gives aggregate data regarding the cash inflows that a company receives.

The loss on sales of equipment will be:

Cost of equipment = $500

Less accumulated depreciation = $375

Less sale of equipment = $25

Here, the loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

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Answer:

x° = 75

(x + 30)° = 105°

Step-by-step explanation:

supplementary angle is two angles that sum is 180°

x° + (x + 30)° = 180°

2x + 30 = 180°

2x + 30 - 30 = 180 - 30

2x = 150

2x / 2 = 150 / 2

x° = 75

plug in 75,

75 + 30 = 105

check: 75 + 105 = 180

Answer: 75 degrees

Step-by-step explanation:

Do you see how both sides of the angle come together to form the straight line seen at the bottom? This means that these are supplementary angles.

Supplementary Angles: Both sides have to add up to a total of 180 degrees.

With this, form an equation: x+(x+30)= 180

Get rid of the parenthesis:

x+x+30= 180

Combine like terms.

2x+30= 180

2x= 180-30

2x= 150

x= 150÷2

x= 75

Checks:

x+x+30= 180

75+75+30= 180

You can also check using the equation in its simplified form: 2x+30= 180.

2x+30=180

2(75)+30=180

150+30=180

Hence x=75

I assume you meant to type f(x)=2^x.

Step-by-step explanation:

z = 4√3

y = ?

Z° = 90° - 30° = 60°

Y° = 30°

• Find y.

y/sin(Y) = z/sin(Z)

y/sin(30°) = 4√3/sin(60°)

y/(1/2) = 4√3/(1/2 √3)

y . 1/2 √3 = 4√3 . 1/2

y . 1/2 √3 = 2√3

y = 2√3 . 2/√3

y = 4√3/√3

y = 4

The answer is A.

Reason:

I'm assuming that the swimmer travels along the 50 meter side

Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.

The profits at x = $185 is 0 and the graph is attached below:

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Function is to model the profits of a new pet-monitoring system, so, if the profits are y and x then y = f(x)

The curve shows that y is negative at values of x< $95, then the profits increase when x varies between $95 and $140.

The profits reach a maximum at $140 and then the profits start to reduce as x increases again.

So, the profits at x = $185 is 0.

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Answer:

a on edge

Step-by-step explanation:

I js did it

The equation will be given as y = 6x for the given information in the question.

The complete question is as below:-

Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.

And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be

y = 6x

Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.

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Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

We need to pay attention to what symbols to use.

Solid circle

Empty circle

Arrow

Square brackets: [ and ]

Curved brackets: ( and )

Union of sets: ∪

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     [tex]-4[/tex]

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     [tex]0[/tex]

So, the first part of our range is:

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    [tex]2[/tex]

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    [tex]\infty[/tex]

So, the second part of our range is:

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

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Answer:

x = -2, y = 3

Step-by-step explanation:

2x + 3y = 5

5x - 2y = -16

In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.

We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:

10x + 15y = 25

10x - 4y = -32

Now we can subtract:

19y = 57

y = 3

Since we know the value of y, we can substitute it into one of the original equations:

2x + 3(3) = 5

2x + 9 = 5

2x = -4

x = -2

All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

          x³ + 8x² + 100x = -800

x³ + 8x² + 100x + 800 = 0

Then the factor of the equation will be

x³ + 8x² + 100x + 800 = 0

x² (x + 8) + 100(x + 8) = 0

        (x² + 100)(x + 8) = 0

Then all the solution of the equation will be

x = 10i, -10i, and -8.

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

2 bases 3 rectangles, folds properly.

Answer:

52=x-15(being vertically opposite angle)

52+15=x

x=67

Answer:

y+3=10

solution,

y+3=10

y+3-3=10-3

y=7

thus,

y=7ans

Answer:

5

Step-by-step explanation:

As seen in the figure, we know that because ΔABC is isosceles, ∠B = ∠C, so we know that 75 = 3x, x = 15. Next, following the rule that all angles in a triangle sum to 180°, we can set up this equation and solve it:

  4y + 10 + 75 + 75 = 180

                          4y = 180 - 160

                            y = 20

                         ∴ y = 5

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24[/tex]

Item a:

The probability is one subtracted by the p-value of Z when X = 984, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{984 - 959}{263}[/tex]

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{984 - 959}{43.24}[/tex]

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

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The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

For the given figures we need to find the unknown angles.

In the first figure to find angle p first apply the angle sum property to the triangle.

That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)

⇒p=67°.

p=67° is a vertically opposite angle to the other triangle.

To find q:

67°+98°+q=180°

⇒q=15°.

In the second figure to find angles x and y apply the angle sum property to the triangle.

That is, 28°+(53°+x)+17°=180°

⇒98°+x=180°

⇒x=82°.

To find y:

x+y+17°=180°

⇒82°+y+17°=180°

⇒y=81°

In the third figure to find angles x and y apply the angle sum property to the triangle.

That is, 100-x+30+4x+7x=180°

⇒10x=80°⇒x=10°.

Now the angles of the triangle are 100-10=90°, 30+4x=70°

y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).

In the 4th figure, to find angle 's' use the isosceles triangle concept.

That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)

⇒s=28°

In the 5th figure, to find angle 'm' use the isosceles triangle concept.

That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)

⇒2m=145°

⇒m=72.5°

Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

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