What is the value of x in 2x+8+3x+5=123

Answer:

[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]

Step-by-step explanation:

Given the geometric sequence

[tex]a_1=\dfrac{2}{3}\\ \\a_n=3a_{n-1},[/tex]

then

[tex]a_1=\dfrac{2}{3}\\ \\a_2=3a_1=3\cdot \dfrac{2}{3}=2\\ \\a_3=3a_2=3\cdot 2=6\\ \\a_4=3a_3=3\cdot 6=18\\ \\a_5=3a_4=3\cdot 18=54\\ \\...[/tex]

Hence,

[tex]b_1=a_1=\dfrac{2}{3}\\ \\b_2=a_3=6=\dfrac{2}{3}\cdot 9\\ \\b_3=a_5=54=\dfrac{2}{3}\cdot 9^2\\ \\...[/tex]

Thus, the explicit formula is

[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]

The sale price of the top after the 50% off discount is $8.44.

To calculate the sale price of the top with a 50% discount, follow these steps:

Step 1: Find the discount amount. The discount amount is 50% of the original price. To calculate this, multiply the original price by 0.50 (50% as a decimal):

Discount amount = 16.88 * 0.50 = 8.44

Step 2: Subtract the discount amount from the original price to find the sale price:

Sale price = Original price - Discount amount

Sale price = 16.88 - 8.44 = 8.44

When the customer applies the 50% off discount, they will pay $8.44 for the top, which is half of the original price of $16.88. This means they are getting a 50% discount on the original price.

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Step-by-step explanation:

To complete the square, take half of the second coefficient, square it, then add the result to both sides.

(-8/2)² = (-4)² = 16

x² − 8x + 16 = 9 + 16

Solving:

(x − 4)² = 25

x − 4 = ±5

x = 4 ± 5

x = -1 or 9

Answer:

part 1: x^2 + -8 x=9

part 2: Add 16 to each side

part 3: (x-4)^2 =25

part 4: -1 and 9

Answer: 8

Step-by-step explanation:

32/2 (50%)  = 16

32/4 (25%)  = 8

Add these together and you'll get 24. Subtract that from the initial amount and you'll have 8.

Answer: you can get 8 gum balls

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

For the first circle 2 x 2in = 4 to find diameter

4 x 3.14 = 12.56

6in x 2 = 12

12 x 3.14 = 37.68

simplify

12.56/37.68

6.28/18.84

3.14/9.42

So the answer is 1/3 since 3.14 x 3 = 9.42

Also since the radius is 3 times longer

Answer:

1/3

Step-by-step explanation:

It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.

Step-by-step explanation:

Given,

Distance covered = [tex]30\frac{1}{3}[/tex] = [tex]\frac{91}{3}[/tex] miles

Time taken =[tex]\frac{1}{3}[/tex] hour

We know that;

Distance = Speed * Time

[tex]\frac{91}{3} = Speed*\frac{1}{3}[/tex]

Multiplying both sides by 3

[tex]3*\frac{91}{3} = Speed*\frac{1}{3}*3[/tex]

91 = Speed

Bob was driving at 91 miles per hour.

Now,

Distance to cover = 100 miles

Time required = x

Distance = Speed * Time

[tex]100=91x\\91x=100[/tex]

Dividing both sides by 91

[tex]\frac{91x}{91}=\frac{100}{91}\\x=1\frac{9}{91}[/tex]

It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.

Keywords: fraction, distance

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Answer:

Answer is B. (4,0)

Step-by-step explanation:

2x - y = 8

x + y = 4

solve the equation

2x - y = 8

y = 4 - x

substitute the value of y into the equation

2x - (4 - x) = 8

solve the equation

x = 4

substitute the value of x into an equation

y = 4 - 4

solve the equation

y = 0

answer is (4,0)

Difference in elevation is 6 meters.

Answer: -4

Step-by-step explanation: -5 + 1= -4

Answer:b/9

Step-by-step explanation: the expression b divided by 9 is b/9

Answer: b ÷ 9

Step-by-step explanation:

Well, since the question is to write an expression for b divided by 9, you just write b divided into 9 parts.

NOTE: Remeber, an expression is an equation but WITHOUT an answer.

Hope this helps! Please feel free to correct me if I'm wrong!

Yo sup??

To solve the 31st one just imagine and add all the cubes.

Start from the left side and keep on counting in your mind.

You will end with 25 cubes

For the 32nd one you can just draw a chart to know it.

Since this man has no bro or sis he is a single child.

The man in the picture is himself.

He is pointing to his picture and saying that 'that guys dad is my dad' and since he's a single child therefore its him itself.

So the answer is that man itself.

For the last one again try to draw a chart and connect the dots with the information.

So Lakisha had a bull dog. Since she has a bull dog she can't have Paul as her brother because paul is the brother of that girl who has her pet as horse.

This means paul is the brother of either Angela or Jessica. But its given that the brother of Angela is Ken therefore Paul is the brother of Jessica.

So the relations are

Lakisha-Bull dog, Stephen

Angela-Ken,XXXXX

Jessica-horse,Paul

Hope this helps.

Answer:12.2%

Step-by-step explanation:

Her total paycheck minus her salary = the commission amount

So

6500 - 1000 = 5500

So....her commission as a percentage of sales  = 5500/ 45000 = about 12.2%

A/b= h

h=12 ft

Step-by-step explanation:

The formula for area is given as ;

A=b*h

A/b= h .................equation for h

If Area=96 ft²  and b =8 then h=96/8 =12 ft

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Answer:

She makes $60 per hour

Step-by-step explanation:

There are 5 days in a week and 40 divided by 5 is 8 and 8x10=80 and 80 subtracted by 20 gives you 60.

Final answer:

After deducting childcare expenses, Sally's actual hourly wage is $7.50 per hour.

Explanation:

The original question is about calculating Sally's actual hourly wage after accounting for childcare expenses. Sally works 40 hours a week and earns $10 per hour. However, she incurs a cost of $20 per day for childcare. Assuming she works 5 days a week, her weekly childcare expenses are $20 x 5 = $100. Therefore, her weekly take-home pay after childcare is (40 hours x $10/hour) - $100 = $400 - $100 = $300. Now, to find Sally's actual hourly wage after childcare expenses, divide her take-home pay by the number of hours worked: $300 / 40 hours = $7.50 per hour.

Step-by-step explanation:

Equation of given line is:

[tex]y = \frac{2}{5} x + 1 \\ equating\: it \: with \: y = m_1x + c, \:we\:find \\ slope \: of \: given \: line \: (m_1 )= \frac{2}{5} \\ y - intercept \: (c) = 1 \\ let \: the \: slope \: of \: required \: line \: be \: m_2. \\ \therefore \: m_1 \times m_2 = - 1..( \because \: lines \: are \: \perp) \\ \therefore \: \frac{2}{5} \times m_2 = - 1 \\ \therefore \:m_2 = - \frac{5}{2} \\ \\ equation \: of \: required \: line \: in \: slope \: \\intercept \: form \: is \: given \: as: \\ y = m_2x + c \\ \huge \orange{ \boxed{\therefore \: y =- \frac{5}{2}x + 1}} \\ [/tex]

Answer:

There are 38 vocab. words in both weeks

Step-by-step explanation:

There are a few steps to this problem:

First, we know that there are 15 vocab. words in week 1.

Then, in week 2 there are 8 more words than in week 1. So that means 15+8 which equals 23.

Finally, we know that there were 15 words in the first week, and 23 in the second week. So now how many words were there in both weeks? To answer that, you add the number of words in the first week, to the number of words to the second week.

23 + 15 = 38 words total in both weeks

Answer:

no answer

Step-by-step explanation:

x^2+4x+5=0

(x+2)^2+1=0

(x+2)^2=-1

this is impossible,

so this equation has no answer

Answer:

Step-by-step explanation:

Final answer:

To find the radius of the volleyball given its surface area, use the formula for the surface area of a sphere (4πr²) and solve for r. The approximate radius of the volleyball would be 4.25 inches based on a surface area of 227 square inches.

Explanation:

The surface area of a sphere formula is 4πr², where r is the radius. Given that the volleyball's surface area is about 227 square inches, we can find the radius by rearranging the formula as follows:

Answer:

4 + 9i

Step-by-step explanation:

a complex number by definition must have a real and imaginary components

imaginary components are denoted by the letter i, where i = √(-1)

the only choice with a real and imaginary components is 4 + 9i

Answer:

4 +9i

Step-by-step explanation:

trust me bro

Answer:

106

Step-by-step explanation:

Given:

Thirteen fewer than three times his thinking number is 305.

Question asked:

What number is Tomás thinking ?

Solution:

Let Toma's thinking number be [tex]x[/tex]

As 13 fewer than 3 times his thinking number is 305.

The equation will be:

[tex](3 times of x) - 13 = 305[/tex]

[tex]3x - 13 = 305[/tex]

Adding both side by 13

[tex]3x = 318\\[/tex]

Dividing both side by 3

[tex]x = 106[/tex]

Thus,  Tomàs was thinking of a number is 106

[tex]\bf \cfrac{cot(A)}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{\frac{tan(A)}{1}}\implies \cfrac{1}{tan(A)}\cdot \cfrac{1}{tan(A)} \\\\\\ \cfrac{1}{[tan(A)]^2}\implies \cfrac{1}{tan^2(A)}\implies \cfrac{1^2}{tan^2(A)}\implies \left( \cfrac{1}{tan(A)} \right)^2\implies cot^2(A)[/tex]

Final answer:

To simplify cotA/tanA, we recognize that cotA is the reciprocal of tanA. The expression simplifies to cosA^2/sinA^2, which can also be written as cotA^2.

Explanation:

To simplify the expression cotA/tanA, we can use the fundamental trigonometric identities that relate the cotangent and tangent functions. The cotangent function, cotA, is the reciprocal of the tangent function, tanA, which means cotA = 1/tanA. Therefore, when we simplify cotA/tanA, we are effectively dividing the reciprocal of the tangent function by the tangent function itself.

The simplification would thus be:

Answer:

0.7 km

Step-by-step explanation:

Actual distance in cm = 7(10000)

= 70 000 cm

Actual distance in km = 0.7 km

Answer:

0.7

Step-by-step explanation:

Answer:

She can buy 62 smoothies

Step-by-step explanation:

The salesman's commission for selling a car at Sal's car shop is $901.50.

To calculate the salesman's commission for selling a car at Sal's car shop, we must first determine the sale price's profit margin over the dealership's purchase price. The profit is found by subtracting the purchase price ($16,235) from the selling price ($22,245).

Profit = Selling Price - Purchase Price
Profit = $22,245 - $16,235
Profit = $6,010

Next, we calculate the commission by taking 15% of the profit:

Commission = Profit * Commission Rate
Commission = $6,010 * 0.15
Commission = $901.50

Therefore, the salesman's commission for selling the car is $901.50.

Answer:

Volume of box = 12x³ + 10x² - 14x - 8

Step-by-step explanation:

Volume of box = Length × Width × Height

Volume of box = (x + 1) (4x - 2) (3x + 4)

Volume of box = (4x² - 2x + 4x - 2) (3x + 4)

Volume of box = (4x² - 2x - 2) (3x + 4)

Volume of box = 12x³ + 10x² - 14x - 8

Answer:

12x^3+22x^2-2x-8

Step-by-step explanation:

i took the test ^^

Answer:

C:x=30:both angles measure 114 degrees

Step-by-step explanation:

in 2 parallel lines with a transversal, the marked angles are alternate exterior angles, which means that both angles are congruent(equal)

ur equation is: 2x+54=4x-6

60=2x

x=30

we have now eliminated options a and b

CHECK:

2*30+54=60+54=114

4*30-6=120-6=114

114=114

Answer:

- 3a + 6

Step-by-step explanation:

subtract and add like items together like

- 4a + a = -3a

b-b= 0

and

9-3 = 6

so the answer is

-3a +6