Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:

A)

ƒ(n) = 9 + 2(n – 1)

B)

ƒ(n) = 5 + 3(n – 1)

C)

ƒ(n) = –3 + 2(n – 1)

D)

ƒ(n) = 3 + 2(n – 1)

Answer:

[tex]\frac{-1}{4}[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.

If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]

Answer:

3/4

Step-by-step explanation:

Fraction of total area of the circle each color occupies in the spinner.

purple = 1/8

red = 1/4

orange = 1/8

yellow = 1/8

green = 1/4

blue = 1/8

Landing on yellow or purple: 1/8 + 1/8 = 1/4

Not landing on yellow or purple = 1 - 1/4 = 3/4

Answer:

F

Step-by-step explanation:

There are 6 digits in the repeating pattern.

279 / 6 = 46.5 remainder 3.

we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.

The height of the pyramid is [tex]16ft.[/tex]

The centroid of the base sits just above the right pyramid. Oblique pyramids are non-right pyramids. A right pyramid is typically assumed to be a regular pyramid because it has a regular polygon base.

To find the height of the pyramid:

l=the slant height of the right pyramid.

b=the length side of the square base of the right pyramid.

h=the height of the right pyramid.

Pythagorean Theorem: [tex]l^{2} =h^{2} +(\frac{b}{2} )^{2}[/tex]

Solve:h

[tex]h^{2} =l^{2} +(\frac{b}{2} )^{2}[/tex]

[tex]h^{2} =20^{2} -12^{2}[/tex]

[tex]h^{2} =256[/tex]

[tex]h=16ft[/tex]

Therefore, The height of the pyramid is [tex]16ft.[/tex]

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Answer:

The height of the pyramid is 16ft

Step-by-step explanation:

Amount of money earned per number of hours of work =  [tex]f(g(x)) = 6x^{3} + 4[/tex]

To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.

Required calculation -

Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]

Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]

we are to find the composite function [tex]f(g(x))[/tex]

Substituting g(x) into the x of f(x), we find:

[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]

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Answer:

f(g(x)) = 6x3 + 4 dollars over hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

13

GH 13000 is the amount of his sales for that month.

how to find sales of the month?

total income = salary + commission

total income = GH530 (given)

salary = GH200 (given)

Commission is 3% on the sales above Gh2000 (given)

Let sales be x

total income = salary + commission

530 = 200+3%(x-2000)

530-200=0.03(x-2000)

330/.03=x-2000

11000=x-2000

x= 13000

total sales = GH13000

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]

[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

There is two of them each getting $16.32

So take the $16.32 × 2=$32.64

Answer:

Step-by-step explanation:

First, you have to multiply. 15x4=60. All you need to do is add a zero to that product. You will get 600. Product means the answer to a multiplication problem. That is why you would have to multiply to get your answer. Your answer to that part is 600. 15*40= 600. Then, you would do 45+15= 60. 600/60= 10. Your answer is 10.

Answer: (2;3).

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{4x=-3y+17} \atop {3x-4y=-6}} \right. \ \ \ \ \left \{ {{4x+3y=17\ |*4} \atop {3x-4y=-6\ |*3}} \right. \ \ \ \ \left \{ {{16x+12y=68} \atop {9x-12y=-18}} \right. \\Let's\ sum \ up\ these\ equations:\\25x=50\ |:25\\x=2.\\4*2=-3y+17\\8+3y=17\\3y=9\ |:3\\y=3.[/tex]

if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.

Figuratively, we have:

If we have the following, two events A and B are said to be independent.

                            [tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]

Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.

The likelihood of the event B will then be.

                            [tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]

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I understand that the question you are looking for is:

Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.

Considering the definition of a right triangle and its properties, the value of the third angle of a triangle with two angles measuring 79 degrees and 23 degrees is 78 degrees.

A triangle is a polygon that is determined by three line segments called sides, or by three non-aligned points called vertices.

In other words, a triangle is a polygon made up of three sides, as well as three vertices and three interior angles.

One of the properties of any triangle is that the sum of the interior angles is equal to 180°.

In this case, you know that:

So the value of the missing angle can be calculated by:

79° + 23° + missing angle = 180°

Solving:

102° + missing angle = 180°

missing angle= 180° - 102°

missing angle= 78°

Finally, the value of the third angle of a triangle with two angles measuring 79 degrees and 23 degrees is 78 degrees.

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Answer:

The answer is 78.

Step-by-step explanation:

Person above is right and I'm also taking the test!!

Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.

A linear function is modeled by:

y = mx + b

In which:

Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:

C(g) = 4g + 69.

She wants to keep her bill at $83.80 per month, hence:

C(g) = 83.80

4g + 69 = 83.80

4g = 14.80

g = 14.80/4

g = 3.7.

Sarah can use 3.7 gigabytes while staying within her budget.

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Answer:

The other person is correct!

Step-by-step explanation:

Yes

Answer:

D.

Step-by-step explanation:

Yes, because it passes the vertical line test.

Answer:

[tex]20a^2-70a[/tex]

Step-by-step explanation:

1) Expand by distributing terms.

[tex]10\times2a+10a\times-7[/tex]

2) Take out the constants.

[tex](10\times2)aa+10a\times-7[/tex]

3) Simplify [tex]10\times2[/tex] to [tex]20.[/tex]

[tex]20aa+10a\times7[/tex]

4) Use Product Rule:[tex]x^ax^b=x^{a+b}[/tex].

[tex]20a^2+10a\times-7[/tex]

5) Simplify [tex]10a\times-7[/tex] to [tex]-70a.[/tex]

[tex]20a^2-70a[/tex]

Thank you,

Eddie

Answer:

20a² - 70a

Step-by-step explanation:

(10a)(2a-7)

= 10a*2a + 10a*-7

= 20a² - 70a

Answer:

x>4

Step-by-step explanation:

3x - 2 >10  add 2 to both sides

3x > 12  Divide both sides by 3

x >4

Answer:

[tex]x > \bf 4[/tex]

Step-by-step explanation:

To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:

[tex]3x - 2 > 10[/tex]

⇒ [tex]3x - 2 + 2 > 10 + 2[/tex]      [Add 2 to both sides]

⇒ [tex]3x > 12[/tex]

⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex]                         [Divide both sides by 3]

⇒ [tex]x > \bf 4[/tex]

Step-by-step explanation:

-3p+6p is 3p

-3 + 6 = 3

So when you simplify the equation you get 3p

Answer:

[tex]\frac{15x^{4}y^{3}}{5x^{3}} \ \ \text{and }\ -10x^{5}\div 2x^{3}y[/tex]

Step-by-step explanation:

the Quotient of Powers Property :

let a be a number where  a ≠ 0

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

……………………

[tex]\frac{15x^{4}y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times 5x^{3}\times x \times y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times x \times y^{3}}{1}[/tex]

[tex]= 3 x y^{3}[/tex]

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

[tex]-10x^{5}\div 2x^{3}y[/tex]

[tex]= [-5 \times (2x^{3}) \times x^2] \div [(2x^{3}) \times y][/tex]

[tex]= -5 \times x^2 \div y[/tex]

[tex]= -5 x^2 \div y[/tex]

Answer:

  9

Step-by-step explanation:

The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.

The expanded form of the number can be written as ...

  a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...

  +10×10^68 +11×10^66 +... +43×10^2 +44×10^0

Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...

  10 mod 45 = 10

  100 mod 45 = 10

This lets us conclude that any positive power of 10 mod 45 is 10.

In short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...

  a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45

  = (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45

  = (((225 mod 45) +(901 mod 45))×10 +44) mod 45

  = ((0 +1)×10 +44) mod 45

  a_44 mod 45 = 54 mod 45 = 9

__

Additional comment

The result can be confirmed by a suitable calculator.

__

The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.

Answer: 9

Step-by-step explanation:

we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344

on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.

Answer:8 feet

Step-by-step explanation:

Explanation:

The area of the circle with radius 10 is...

A = pi*r^2

A = pi*10^2

A = 100pi

The surface area of the sphere with radius 5 is...

SA = 4pi*r^2

SA = 4pi*5^2

SA = 100pi

Both results are the same, so the claim is true. We can think of surface area as the amount of wrapping paper needed to cover the sphere.

Answer: A) 23,00

Step-by-step explanation:

A=23,00

B=8,600

C=12,00

D=3,600

Answer:

20

Step-by-step explanation:

x^2+18x-160

If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.

To check you can plug 20 in for x. When you do that, y = 600.

Answer:

7.52 m^3

Step-by-step explanation:

This is like compound interest in a banking calculation

Future volume = 5 (1 + .06)^7 = 7.52 m^3

Given the percentage taken off and the reduced price, the original price of the item is $142.

Given the data in the question;

The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.

Hence 80% of the original price will give the reduced price.

Let the original price be represented by x

80% × x = $113.60

We solve for x

80/100 × x = $113.60

80x/100 = $113.60

Cross multiply

80x = $11360

x = $11360/80

x = $142

Given the percentage taken off and the reduced price, the original price of the item is $142.

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The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.

According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.

By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.

We can consequently evaluate the determinant of the quadratic equation in discuss as follows;

Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12

Hence, the determinant in this case is; 13.

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The perpendicular bisector of a chord passes through the center of a circle.

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.

The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.

Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.

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