The number 144 can be represented by 12x12 square grid which of the following can be also represented on a square grid??
A. 39 b.50 c.70 d.81

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

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Answer: 358

Explanation:  370 - 12 = 358

Step-by-step explanation:

Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

Asked: Find the value of x = ?

Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

⇛√{1 + (2/3)} = (0.6)²⁻³ˣ

⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ

⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ

⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ

⇛√(5/3) = (0.6)²⁻³ˣ

Squaring on both sides then

⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²

⇛√(5²/3²) = {0.6}(²⁻³ˣ)²

⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²

⇛5/3 = {0.6}(²⁻³ˣ)²

[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]

⇛5/3 = (0.6)²*²⁻³ˣ*²

⇛5/3 = (0.6)⁴⁻⁶ˣ

⇛5/3 = (6/10)⁴⁻⁶ˣ

⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ

⇛5/3 = (3/5)⁴⁻⁶ˣ

⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ

[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]

Base are the same, so the exponents must be equal.

[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x

Shift the number 4 from RHS to LHS, changing it's sign.

⇛-1 - 4 = -6x

⇛-5 = -6x

⇛x = {(-5)/(-6)}

[tex]\mathsf{\therefore}[/tex] x = 5/6

Answer: Hence, the value of x for the given problem is 5/6.

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(3^-2 × 4^-2)^-3 = 12^x In the given expression find the value of x. https://brainly.com/question/25746273?referrer

Find theFind tha amount of profit per bag by subtracting:

2.99 - 1.90 = 1.09

He made $1.09 profit per bag.

Now multiply the profit per bag by the number of bags:

1.09 x 12 = 13.08

Total profit = $13.08 amount of profit per bag by subtracting:

2.99 - 1.90 = 1.09

He made $1.09 profit per bag.

Now multiply the profit per bag by the number of bags:

1.09 x 12 = 13.08

Total profit = $13.08

To form the vector notation for the translation:

   --> must find how much the new graph moved horizontally from the old

        graph

            --> the graph moved 8 units horizontally

   --> must find how much the new graph moved vertically from the old

        graph

           --> the graph moved 4 units vertically

In vector notation, that would be (8,4)

Hope that helps!

Answer:

distance in 3 hours = 150 miles

distance in 1 hour = 150/3 = 50 miles

distance in 9 hours = 50 × 9 = 450 miles

Answer:

Sammy's dad traveled 450 miles in 9 hours.

Step-by-step explanation:

mph = [tex]\frac{Miles}{Hours}[/tex]

Miles = 150

Hours = 3

Plug into the formula of distance/time

[tex]\frac{150}{3} = 50mph[/tex]

Sammy's dad is driving at 50mph

In three hours you can use this formula:  [tex]50mph=\frac{miles}{9}[/tex]

Multiply both sides by 9:  [tex]50mph * 9 =\frac{miles}{9} *9[/tex]

Solve:

[tex]50mph * 9 =miles[/tex]

[tex]450 =miles[/tex]

Sammy's dad traveled 450 miles in 9 hours.

Hope this helped! :)

Answer:

AB ≈ 6.53

Step-by-step explanation:

using the cosine ratio in the right triangle

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{5}{AB}[/tex] ( multiply both sides by AB )

AB × cos40° = 5 ( divide both sides by cos40° )

AB = [tex]\frac{5}{cos40}[/tex] ≈ 6.53 ( to the nearest hundredth )

Function:

[tex]\sf 2\left(3\right)^{x}+2[/tex]

Find y-intercept:

[tex]y=2\left(3\right)^{0}+2[/tex]

[tex]y=\sf 4[/tex]

option B is correct as it cuts y-intercept at 4

Answer:

This is a positive exponential graph with a y-intercept of 4 (when x is 0, y is 4)

Hope this helps!

Answer:

-58/7

Step-by-step explanation:

Alright so this is a system of equations. First we'll solve the system, and then find the ratio afterwards.

[tex]3x-5y = 11\\2x+3y =5\\[/tex]

Isolate for y on both.

[tex]2x + 3y = 5\\3y = 5-2x\\y = \frac{5-2x}{3}[/tex]

and

[tex]3x - 5y = 11\\-5y = 11-3x\\y = \frac{11-3x}{-5}[/tex]

Set both equations equal to each other:

[tex]\frac{11-3x}{-5} = \frac{5-2x}{3}\\ \\\frac{3(11-3x)}{-5} = 5-2x\\ \\3(11-3x) = -5(5-2x)\\\\33 - 9x = -25 + 10x\\33 = -25 + 19x\\58 = 19x\\\frac{58}{19} = x[/tex]

We've got x, now let's solve for y:

[tex]y = \frac{11-3x}{-5} = \frac{11-3(\frac{58}{19}) }{-5}[/tex]

Now we got both x and y, and what they equal.

[tex]y = \frac{-7}{19}\\[/tex]

[tex]x = \frac{58}{19}[/tex]

The ratio of x to y, is essentially [tex]\frac{x}{y}[/tex]. So we will calculate that.

[tex]\frac{\frac{58}{19} }{\frac{-7}{19} } = \frac{58}{19} * \frac{19}{-7} = \frac{-58}{7}[/tex]

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

Explanation:

The point (-7,-3) means x = -7 and x = -3

Right off the bat, the first equation x = -7 is proven true based on the first coordinate.

Let's now plug the coordinates into the second equation.

y = -x-10

-3 = -(-7)-10

-3 = 7-10

-3 = -3

Which is a true statement.

Both equations are true when (x,y) = (-7,-3)

This is why it is a solution to the system. It turns out it's the only solution to this system. This system is consistent and independent.

You can use a graphing tool like Desmos to plot the two equations, and you should see them crossing at the point (-7,-3)

Answer:

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

x = -7

y = -x - 10

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the first equation, for x, into the first equation:

x = -7

y = -x - 10

y = -(-7) - 10 <== multiplying two negatives, makes a positive

y = 7 - 10

y = - 3 <== the value of y

Now, we find the value of x by substituting - 3 for y:

y = -x - 10

- 3 = -x - 10

+10     +10

7 = -x <== you can't have a negative variable

/-1    /-1

-7 = x <== the value of x

(x, y) ==> (-7, -3)

Therefore, yes (-7,-3) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

The possible outcomes of an event is the sample space

The product of the sample spaces of the single events determines the total number of possible outcomes of a compound event

Assume that the number of outcomes of n single events are:

[tex]n_1[/tex], [tex]n_2[/tex], [tex]n_3[/tex],........ [tex]n_n[/tex]

When these single events are combined, they form a compound event.

The number of outcomes of the compound event is the product of the number of outcomes of the single events.

i.e.

[tex]Outcomes = n_1 * n_2 * ......... n_n[/tex]

Hence, the product of the sample spaces of the single events determines the total number of possible outcomes of a compound event

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First, let's solve this equation by subtract 38 from both sides:-

[tex]\bigstar[/tex] 47-38=n

hence, the answer is:-

9=n

or

[tex]\bigstar{\underline{\boxed{\pmb{n=9}}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

Step-by-step explanation:

Given is the quadratic function

In order to have two real roots the discriminant should be posivive

We need D > 0

There is no solution as b² is never negative

Answer: 0.0139358  

Step-by-step explanation: 999,999,999,999,999,999,999,999,999,999,999% sure!

Answer:

93

Step-by-step explanation:

19x-2 =  18x+3

x=5

15(5) -2=93

18(5)+3=93

Answer:

550.5323531336038

Step-by-step explanation:

I have a hint: if you ever need help with triangle trigonometry questions go to carbside depot trigonometry calculator it is a literal life savor

The possible value of ∠Y to the nearest tenth of a degrees in triangle WXY is 85.1 degrees.

Let's find angle Y using sine rule,

Hence,

x / sin X = y / sin Y

where

8.5 / sin 100° = 8.6 / sin Y

cross multiply

8.5 sin Y = 8.6 sin 100°

sin Y = 8.6 sin 100° / 8.5

sin Y = 8.4693466759 / 8.5

Y = sin ⁻¹ 0.99639372657

Y = 85.1325941735

∠Y = 85.1°

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To find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).

Area of sector = ∅/360 × πr², where ∅ = central angle, and r = radius of the circle.

Given the following:

The area of the circle she wants to find is: 74°/360°.

Since the area of the whole circle is, πr², therefore, to find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).

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Answer:

[tex]\sqrt[4]{e};\frac1{4e}[/tex]

Step-by-step explanation:

The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.

[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]

Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.

[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]

At this point we Replace the value we found in the equation to find it's y coordinate

[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]

6.965 + 3.25 + 1.79 = 12.005, now, let's apply a 7% taxation on that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 12.005}}{\left( \cfrac{7}{100} \right)12.005}\implies 0.84035~\hfill \underset{total~bill}{\stackrel{12.005~~ + ~~0.8435}{12.84535}} \\\\\\ 20~~ - ~~12.84535\implies 7.15465~~\approx ~~ \$7.15[/tex]

[tex]\huge\mathsf\blue{♧ANSWER♧}[/tex]

[tex]\huge \mathfrak \blue{\frac{ - 7}{8} }[/tex]

Answer:

78°F

Step-by-step explanation:

75.5°F on Saturday...

75.5 + 6 = 81.5 on Sunday

81.5 - 3.5 = 78°F on Monday

The expression that represents the temperature change is

N = L + 6°F + 3.5°F

The temperature on Monday is 85°F.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Temperature:

Saturday = L= 75.5°F ______(1)

Sunday = M = Rose by 6°F

M = L + 6 _____(2)

Monday = N = Dropped by 3.5°F

N = L + 6 - 3.5 _____(3)

The expression that represents the temperature change:

From (1), (2), and (3) we get

N = L + 6°F + 3.5°F

The temperature on Monday:

N = 75.5 + 6 + 3.5

N = 85°F

Thus,

The expression that represents the temperature change is

N = L + 6°F + 3.5°F

The temperature on Monday is 85°F.

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Each ticket could have cost up to $31.

What is the discount?

A discount is a reduction in the price of an item or service. It is often offered as an incentive to encourage customers to purchase or use a particular product or service. The discount amount may be a percentage of the total price, a fixed dollar amount, or a combination of both.

Let the cost of each ticket be $x. Then the total cost for 5 tickets would be 5x. After applying the $30 group discount, the total cost would be 5x - $30.

We know that the total cost was under $125, so we can set up the inequality:

5x - $30 < $125

Simplifying this inequality, we get:

5x < $155

Dividing both sides by 5, we get:

x < $31

Hence, each ticket could have cost up to $31.

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The volume of the fountain cup in gallons is 4775.2 gallons

Since the fountain cup is in the shape of a frustum, its volume is given by

V = πh/3(r² + rr' + r'²) where

So, substituting the values of the variables into th equation, we have

V = πh/3(r² + rr' + r'²)

V = π × 8 ft/3[(4 ft)² + 4 ft × 6 ft + (6 ft)²]

V = π × 8 ft/3[16 ft² + 24 ft² + 36 ft²]

V = π × 8 ft/3 × (76 ft²)

V = 608π ft³/3

V = 1910.088 ft³/3

V = 636.69 ft³

V ≅ 636.7 ft³

Since there are 7.5 gallons per cubic foot,

The volume of the fountain cup in gallons is V = 636.7 ft³ × 7.5 gallons/ft³ = 4775.2 gallons

So, the volume of the fountain cup in gallons is 4775.2 gallons

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[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

Let's use distance formula ~

[tex]\qquad \sf  \dashrightarrow \: d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = \sqrt{(2 - ( - 4)) {}^{2} + (0 - 1) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = \sqrt{(2 + 4) {}^{2} + ( - 1) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = \sqrt{ {}^{} 36+ 1{}^{} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = \sqrt{ {}^{} 37{}^{} } [/tex]

Therefore, the required distance is [tex]\sf \sqrt{37}[/tex] units

Answer:

60 days.

Step-by-step explanation:

Let the actual time be x, then:

x - 0.25x = 45

0.75x = 45

x = 45/0.75

= 60 days.