Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form.
36, 12, 4, ...

Answer:

All students have to take at least one math class and one language class. Twenty students take calculus, and thirty students take statistics.

For the functions f(x) = 3x - 4 and g(x) = x - 41,

Information given in the question

functions f(x) = 3x - 4

functions g(x) = x - 41

ƒ(4) - 2g(3) = ?

the expression ƒ(4) - 2g(3) is solved by substituting x = 4 in f(x)

f(4) = 3 * 4 - 4

f(4) = 12 - 4

f(4) = 8

and x = 3 in g(x)

2g(3) = 2(3 - 4)

2g(3) = 2 *-1

2g(3) = -2

substituting ƒ(4) - 2g(3)

= 8 - 2

= 6

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Answer:

Step-by-step explanation:

Let the missing part be x.

According to triangle proportionality theorem we have:

Answer:

Step-by-step explanation:

7 and 8

In both Cases Value of Z is 1. as per given details in the question.

A Z-score is a numeric measure of the relationship of a value to the mean of a group of values. Z-scores are measured in  standard deviations from the mean. A z-score of 0 indicates that the data point's value is equal to the mean.

Z Value is calculated by formula:

Expected salary = Average salary ± (Z × Standard deviation)

a.  Z value is calculated below:

Expected salary = Average salary ± (Z × Standard deviation)

$1,100 = $1,000 + (Z × $100)

Z = $100 / $100

Z = 1

Again

Expected salary = Average salary ± (Z × Standard deviation)

$900 = $1,000 - (Z × $100)

Z = $100 / $100

Z = 1

In both Cases Value of Z is 1.

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⇒ To find f(4) it means that in the place of x in the function f plug in 4 and simplify to find f(4)

[tex]f(4)=3(4)-4\\f(4)=12-4\\f(4)=8[/tex]

⇒Now let us find 2g(3),meaning in the place of x in the function g plug in 3 and simplify to find g(3) after that then multiply the results by 2 as indicated.

[tex]g(3)=(3)-41\\g(3)=-38[/tex]

Meaning 2(g(3))= 2(-38)

⇒2(g(3))=-76

⇒N0ow let us find the value of  f(4) - 2g(3)

⇒[tex]f(4) - 2g(3)=8-(-76)\\ f(4) - 2g(3)=8+76\\ f(4) - 2g(3)=84[/tex]

⇒The answer is 84

Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion.

(a)

[tex]\frac{PQ}{AB}[/tex] = [tex]\frac{RS}{CD}[/tex] ( substitute values )

[tex]\frac{PQ}{6}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )

8 × PQ = 72 ( divide both sides by 8 )

PQ = 9 cm

(b)

[tex]\frac{AD}{PS}[/tex] = [tex]\frac{CD}{RS}[/tex] ( substitute values )

[tex]\frac{AD}{10.5}[/tex] = [tex]\frac{8}{12}[/tex] ( cross- multiply )

12 × AD = 84 ( divide both sides by 12 )

AD = 7 cm

(c)

given 2 similar figures with ratio of sides = a : b , then

ratio of areas = a² : b²

here ratio of sides CD : RS = 8 : 12 = 2 : 3

then ratio of areas = 2² : 3² = 4 : 9

let the area of PQRS be x , then using proportion

[tex]\frac{4}{48}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )

4x = 432 ( divide both sides by 4 )

x = 108

then area of PQRS = 108 cm²

The three  numbers are -5, -15, and -10 .

Equations of straight lines and equations of degree less than 1 are called "linear equations". The linear equation formula can be written as Y = mx + b. where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slope indicates the direction and slope of the line. This is because (0,y) is the point where the line intersects the y-axis.

b=3a

c=b+5

b-2c=5

b-2(b+5)=5

b-2b-10=5

-b=15

b=-15

c=-15+5

c=-10

-15=3a

a=-5

The numbers are -5, -15, and -10

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1. M represents slope.

2. (-1-1)/(-2+4) = -2/2 = -1  

3. Take any of the two given y's and their corresponding x's.

I'll take (3,12) and (4,13)

Plug into y2-y1/x2-x1

13-12/4-3 = 1/1 or 1 over 1

4. 4-0/1-0 = 4/1

Don't worry about the points; keep growing and learning!

Lines x + 5 = 0 and y = 4x + 4 intersect on a standard (x, y) coordinate plane.

To find the y-coordinate of the point where the two lines intersect.

given lines  are x +5 =0 and y=4x+4

we need to find point of intersection at point of intersection both line will have same point

Let point of intersection be (a,b)

then

a+5 = 0 and b = 4a+4

from 1st equation we have

a = -5

from the 2nd

b = 4a+4

b = 4(-5)+4

b = -20+4

b = -16

Hence y coordinate of point of intersection is -16

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The simplified expression for the given functions f and g is 11-x

What is the value of the function?

The value of the function at a point can be found by substituting the point in the function. This value also depend on the nature of the Function.

We are given a function

f(x) =6-x

Now when we say f(2x) it means the x in the function should be replaced with 2x

Hence the function becomes

f(2x) =6-2x

Similarly

g(x) = (x/3)+8

g(3x-9)= (3x-9/3)+8

g(3x-9)= x-3+8

g(3x-9) = x+5

Now we are asked to add the functions, we simply add the new functions and simplify them

f(2x) + g(3x-9)

=6-2x+x+5

=11-x

Which is the required value

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Answer:

=========================

Simplify f(2x) + g(3x - 9):

Firstly find the inverse of g(x):

Now solve the equation:

Answer:

The lim for f(1-x^2) is 1

Step-by-step explanation:

Lim f(1 - x^2) as x -> 0

break them apart

Lim (1) - lim (x)^2

where the lim of 1 = 1

for the lim of x^2, sub the value of x = 0, so now:

Lim (1-0) = 1

The graph of the function f is shown in the figure above. The value of lim ƒ(1-x²) is 1. Therefore, the correct option is option A.

In mathematics, a function is a phrase, regulation, or statute that establishes the connection between an independent variable and a dependent variable.

In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.

Lim f(1 - x²) as x -> 0

Lim (1) - lim (x)²

where the lim of 1 = 1

for the lim of x², substituting the value of x = 0, so now:

Lim (1-0) = 1

Therefore, the correct option is option A.

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When we want to estimate a population parameter then we use hypothesis test.

What is hypothesis test?

In hypothesis testing, an analyst examines a statistical sample with the aim of demonstrating the plausibility of the null hypothesis.

By measuring and reviewing a representative sample of the population under study, statistical analysts test a hypothesis. All analysts use a random population sample to test the null hypothesis and the alternative hypothesis.

Main body:

As the researchers want to understand the difference between to states they need to do a hypothesis test.

Hence a hypothesis test is done.

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The maximum height reached by the rocket is 122.5 m.

In this question, given parameters:

time (t) = 5.0 seconds

By applying second equation of motion the maximum height of the model rocket would be,

h = v₀t + 1/2 (gt²)

where, v₀ is the initial velocity

g is acceleration due to gravity

(9 = 9.8 m/s²)

Since initial velocity v₀ = 0 we get an equation,

h = 0 + 1/2 (gt²)

h = 1/2 (9.8 x 5²)

h = 122.5 m

Therefore, the maximum height is 122.5 m.

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Answer:B

Step-by-step explanation:

The unit rate of the fraction 2/3 will be 0.67 (approx.).

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following fraction -

2/3

Assume the fraction to be m = 2/3. So, we can write -

2 = 3m

We can write it as -

y = mx      ....Eq[1]

for [y] = 2

[x] = 3

We have to find the slope of the straight line represented by equation [1] for x = 3 and y = 2. We can proceed -

2 = 3m

m = 2/3

m = 0.67 (approx.)

Therefore, the unit rate of the fraction 2/3 will be 0.67 (approx.).

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The Equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

Number of soda produced in 8 hours = 12000

We know

The number of soda produced varies directly with the hours works

Consider the number of bottle produced = b

Number of hours = h

Then the relationship will be b directly proportional to h

b ∝ h

b = k × h

Where k is the constant

Then substitute the values in the equation and find the value of k

12000 = k × 8

k = 12000/8

k = 1500

The equation will be

b = 1500h

Hence, equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

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The unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.

What is the unit rate?

A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.

For 1/8,

Divide the numerator and denominator by '8', to make the denominator 1.

                        [tex]=\frac{\frac{1}{8}}{\frac{8}{8}} \\\\\=\frac{0.125}{1} \\=0.125[/tex]

for 1/4,

Divide the numerator and denominator by '4', to make the denominator 1.

                            [tex]=\frac{\frac{1}{4}}{\frac{4}{4}} \\\\\\\=\frac{0.25}{1} \\\\=0.25[/tex]

Hence, the unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.

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Answer:

5q + 9

Step-by-step explanation:

The Concept in that Question is adding Like-Terms

6q + 4 - q + 5 = ( 6q - q ) + ( 4 + 5 ) = 5q + 9

A polynomial is described as a mathematical expression that contains one or more algebraic in which a constant is multiplied by one or more variables that give rise to a non-negative integral power such as ax² + bx + c.

By considering a polynomial with two terms. Methods and polynomials can be used with these methods.

        2x³ - 5x² = x²(2x - 5)

         x³ - 27  then this be factored as

         x³ - 27 = (x - 3)(x² + 3x + 3²).

         x³ + 27 = (x + 3)(x² - 3x + 3²).

           x² - 16  =  (x + 4)(x - 4)

where perfect-square trinomial and factoring by grouping require more than two terms.

Therefore, the polynomial that has two terms in the factoring methods the Common Factor, the Difference of cubes, the sum of cubes, and the difference of squares can only be considered.

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Answer:

one solution

Step-by-step explanation:

5 + ×/3/3+6×/9 multiple each term by 9

45 + 3x=3×+54+×

x=.9

The equation of g(x) after the translation up is g(x) = 4x² - 10

The given parameter represents the function f(x) in the question.

This function is given as

f(x) = 4x² - 13

The translation is given as

3 units up.

i.e. a translation up by 3 units

Mathematically, this can be represented as

(x, y) = (x, y + 3)

So, we have

g(x) = f(x) + 3

Substitute the known values in the above equation, so, we have the following representation

g(x) = 4x² - 13 + 3

Evaluate the like terms

g(x) = 4x² - 10

Hence, the equation of g(x) is g(x) = 4x² - 10

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Answer:

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

According to the diagram, angle BCD is exterior angle and angles BAC & ABC are remote interior angles of the triangle ABC.

As we know, the exterior angle is the sum of remote interior angles.

Answer:

x = 12

Step-by-step explanation:

Exterior Angle Theorem

The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Given angles:

Apply the exterior angle theorem and solve for x:

[tex]\implies m \angle BCD=m \angle BAC+m \angle ABC[/tex]

[tex]\implies 6x+2=3x+15+2x-1[/tex]

[tex]\implies 6x+2=3x+2x+15-1[/tex]

[tex]\implies 6x+2=5x+14[/tex]

[tex]\implies 6x+2-5x=5x+14-5x[/tex]

[tex]\implies x+2=14[/tex]

[tex]\implies x+2-2=14-2[/tex]

[tex]\implies x=12[/tex]

Answer:

n = 4/21

Step-by-step explanation:

[tex]\frac{7}{3} =\frac{4}{9n}[/tex]

==> cross multiply (multiply top of first fraction by bottom of second fraction and top of second fraction by bottom of first fraction)

7 x 9n = 4 x 3

==> simplify

63n = 12

==> divide both sides by 63

n = 12/63

==> simplify fraction

n = 4/21

The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.

Given that

The function f(x)=5000(0. 98)0. 3x represents the number of white blood cells.

We need to evaluate this, for this

f ( x ) = 5000 * ( 0.98 ) ^(0.3 x)

f ( 1 ) = 5000 * 0.98^(0.3) = 5000 * 0.99396 = 4,969.788

f ( 5 ) = 5000 * 0.98 ^(5*0.3) = 5000 * 0.98^(1.5) = 5000 * 0.97 = 4,850.753

Average rate of change:

( 4,850.753 - 4,969.788 ) / ( 5 - 1 ) = - 29.75

Hence the answer is The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.

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Answer:

3x² + 2x

Step-by-step explanation:

x(3x + 2) ← multiply each term in the parenthesis by x

= 3x² + 2x

Answer: 3x^3 + 2x

Step-by-step explanation:

when multiplying 3x and another x, it combines and adds up to making 3x^2. You add coefficients. Thus 2 being the coefficient. And same matter for x times 2, they go together as 2x.

3x + x = 3x^2

x + 2 = 2x

Answer:

If RU = 16, UT = 20, and SR = 16, what is the perimeter of △SUT?    S    U

If SV = 38, SU = 26, and the perimeter of △SUV is 102, what is the value of RU?

If S‾V ≅ U‾V , SR = 4x − 1 and RU = x + 8, what is the value of SU?     V

Answer: SAS Similarity Theorem.

Step-by-step explanation:

Due to the fact the triangles contain a singular angle per each one, whilst using the process of elimination - we are able to configure that the answer is not the AA postulate. This prevalent factor also formulates a conclusion that the answer is unable to be SSS either.

The 28 and 11.2 (Hypotenuse) sides contrive the answer SAS.

SSA is NOT adequate.

By using the SAS congruence rule, we can prove that AC = BD

What is SAS congruence Rule?

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

What is CPCT?

When we study the congruent triangle, we come across the term CPCT. Corresponding Parts of Congruent Triangles are abbreviated as CPCT. Congruent triangles have equal corresponding parts, as is well known. We frequently use the abbreviation cpct in short terms rather than the complete form while discussing triangle topics and answering inquiries.

In the given figure, we have:

ABCD is a quadrilateral, where AB=DC and ∠DAB=∠CDA

Construction: Joining the two diagonal AC and BD;

Now,

In △ABD and △BAC;

⇒AB=DC                       [ Given ]

⇒  ∠DAB=∠CDA          [ Given ]

⇒  AB=BA            [ Common side ]

∴  △ABD≅△BAC         [ SAS Congruence rule ]

So,

AC = BD, by CPCT;

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