Which two operations are needed to write the expression that represents "eight more than the product of a number and twa
multiplication and subtraction
division and subtraction
multiplication and addition
division and addition

The explicit function is f(n) = 3f(n - 1)

Given, sequence is 16, 48, 144, 432 ….

We have to find the explicit function.

Now, if we observe the given sequence, every term is three times its previous term.

That is, the next term in sequence is obtained by multiplying the previous term by 3

48 = 16 x 3

144 = 48 x 3

432 = 144 x 3

So, explicit function f(n) will be  

nth term = 3 x (n – 1)th term

F(n) = 3 x f(n – 1) [ since nth term is f(n)  ]

We derived the above function just by generalizing the sequence and making it into the function.

The nth term is obtained by multiplying the n - 1 term with 3

Hence explicit function is f(n) = 3f(n - 1)

Part A: The number sentence is -3 + 12 - 2. Part B: The addition equation is 9 = -3 + 12 - 2.

Part A: To find the total yardage gained or lost by the running back, we need to add together each of the individual yardage changes. The running back first lost 3 yards, then gained 12 yards, and finally was pushed back 2 yards. The number sentence that represents this sequence of events is:

-3 (loss of 3 yards) + 12 (gain of 12 yards) - 2 (loss of 2 yards).

Part B: To rewrite this as an addition equation, we need to make sure that the total change in yardage is on one side of the equation, and the individual changes are on the other side, all connected by addition. We can do this by adding the losses as negative numbers to the gains. The total yardage gained or lost is the sum of these individual changes:

-3 + 12 + (-2).

Now, we calculate the sum:

-3 + 12 = 9,

9 + (-2) = 7.

So, the addition equation that represents the total yardage is:

7 = -3 + 12 - 2.

Answer:

no solution

Step-by-step explanation:

5d - 8 = 1 + 5d

Add 9 to both sides

5d = 9 + 5d

Subtract 5d

0 does not equal 9

No solutions

The given equation has no solution.

The given equation is 5d-8=1+5d.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here,

5d - 8 = 1 + 5d

⇒ 5d-5d=1+9

⇒ 0≠9

Therefore, the given equation has no solution.

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Answer:

x=3, y=1. (3, 1).

Step-by-step explanation:

x+3y=6

4x-6y=6

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

simplify 4x-6y=6 into 2x-3y=3

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

x+3y=6

2x-3y=3

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

3x=9

x=9/3

x=3

3+3y=6

3y=6-3

3y=3

y=3/3

y=1

Answer:

Step-by-step explanation:

[tex]1010-n=101\qquad\text{subtract 1010 from both sides}\\\\1010-1010-n=101-1010\\\\-n=-909\qquad\text{change the signs}\\\\n=909[/tex]

Steps to solve:

1010 - n = 101

1010 + (-n) - 1010 = 101 - 1010

-n = -909

-n/-1 = -909/-1

n = 909

_______

Best Regards,

Wolfyy :)

Answer:

X=1 and -4

hope this helps you!

(p.s please mark me as brainlyest)

Step-by-step explanation:

tell me if you want/need the explanation why and I'll gladly give it to you.

Answer:

5 units

Step-by-step explanation:

The radius is the distance from the centre of the circle to a point on the circumference.

Use the distance formula to calculate the radius r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

r = [tex]\sqrt{(1+3)^2+(5-2)^2}[/tex]

  = [tex]\sqrt{4^2+3^2}[/tex]

  = [tex]\sqrt{16+9}[/tex]

  = [tex]\sqrt{25}[/tex] = 5

Answer:

commutative property is C+2+0=C+2

(As a+b=b+a is the law of commutative property of addition )

Answer:

Each class donated $300

Step-by-step explanation:

1,792 has to be rounded to 1,800, because the answer is estimated, so 1,800 divided by 6 is 300

This might be wrong, but if not yw lol

Answer:

1 page per 14/27 minute

Step-by-step explanation:

9/7 page / 2/3 min =

1 page / 2/3 * 7/9 min =

1 page / 14/27 min

Answer:

Explanation:

The expression that you want to simplify is:

This is the simplification step-by-step:

1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:

[tex]5x\times \frac{1}{x^{-7}}\times x^{-2}=\frac{5x\cdot x^{-2}}{x^{-7}}[/tex]

2. For equal bases that are multiplying, add the exponents:

[tex]\frac{5x\cdot x^{-2}}{x^{-7}}=\frac{5x^{1-2}}{x^{-7}}=\frac{5x^{-1}}{x^{-7}}[/tex]

3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)

[tex]\frac{5x^{-1}}{x^{-7}}=5x^{-1}x^{7}[/tex]

4. Simplify adding the exponents with the same base:

[tex]5x^{-1}x^{7}=5x^{-1+7}=5x^6[/tex]

And that is the final expression in its most simple form.

Answer:

Solve the inequality for u.

-18>-38-5u

Simplify your answer as much as possible.

Step-by-step explanation:

Answer:

Law of cosines

Step-by-step explanation:

In this problem i need to use the law of cosines, because the angles are unknown.

we know that

The formula of the law of cosines is equal to

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

[tex]a=7\ units\\b=8\ units\\c=10\ units\\C=\theta[/tex]

substitute in the formula

[tex]10^2=7^2+8^2-2(7)(8)cos(\theta)[/tex]

[tex]100=49+64-112cos(\theta)[/tex]

[tex]100=113-112cos(\theta)[/tex]

[tex]112cos(\theta)=113-100[/tex]

[tex]112cos(\theta)=13[/tex]

[tex]cos(\theta)=\frac{13}{112}[/tex]

using a calculator

[tex]\theta=cos^-1(\frac{13}{112})[/tex]

[tex]\theta=83.33\°[/tex]

Answer:

∠P = 85°

Step-by-step explanation:

The sum of the interior angles of a kite = 360°, thus

∠P + ∠D + 119 + 71 = 360, that is

∠P + ∠D  + 190 = 360 ( subtract 190 from both sides )

∠P + ∠D = 170°

The opposite angles  P and D are congruent, thus

∠P = [tex]\frac{170}{2}[/tex] = 85°

Gain percentage made by Mr William by selling the table at Rs. 1050 is 12.30%.

Given that  

Mr. William bought an old table for RS 850

Mr. William spent 1/10 of the cost price on its repairs.

Mr. William sold the table for Rs 1050.

Need to determine gain or loss percent.

Let’s first calculate total money spent by Mr William on Table

Total money spent by Mr William on Table = Amount at which Mr. William bought an old table + amount spent on repairs

[tex]=\text { Cost price }+\frac{1}{10} \text { of the cost price }=850+\frac{1}{10} \text { of } 850=850+85=935[/tex]

So Total money spent by Mr William on Table = 935

Money generated by selling the table = Rs 1050

As Money generated by selling the table is more that Total money spent by on Table so there is a gain.

Gain by selling the table = Money generated by selling the table - Total money spent by Mr William on Table

= 1050 – 935 = 115

[tex]\text { Gain percentage }=\frac{\text { gain amount }}{\text { Money spent on table }} \times 100[/tex]

[tex]=\frac{115}{935} \times 100=12.299 \approx 12.30 \%[/tex]

Hence gain percentage made by Mr William by selling the table at 1050 is 12.30%.

Answer: 77

Step-by-step explanation: Based on the order of operations or PEMDAS, parentheses are always done first.

So our first step in this problem is to simplify (9 + 2) to get 11.

So we now have (7) (11) which is 77.

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

12x - 4y = - 8 ( subtract 12x from both sides )

- 4y = - 12x - 8 ( divide all terms by - 4 )

y = 3x + 2 ← in slope- intercept form

Answer:

Ci = x

Cs = 5 + 0.5x

Step-by-step explanation:

The site itoons costs $1 per song with no montly fee, so the cost can be expressed as

Ci = 1.x = x

Where x is the number of songs Wendell will download

The site song-R-Us.com charges $5 a month and $0.5 per song. The equation of the cost is

Cs = 5 + 0.5x

Answer:

460

Step-by-step explanation:

919 ÷2 = 459.5 so you have to round to the nearest hole so when its 5 or more you round up to the nearest whole and when its 4 or less you round down so your answer is 460

Answer:

equation is:

5x + 10 = 3x + 16

To find when the total will be same, solve the equation

2x = 6

x = 3

Answer:

Derrick's (10+5x)

Darlene's (16+3x)

for part two:

Derrick worked 6 hours

and darlene worked 8 hours

i think

Step-by-step explanation:

Answer:

0.75°C

Step-by-step explanation:

Person A     Person B          Person C

-3                   4                      8

-1                   -4                     -2

0                    2                      5

2                     -3                   1

To get Fatima mean value, we have to add all the given values together  

= - 3 + 4 + 8 - 1 - 4 - 2 + 0 + 2 + 5  +  2  - 3  + 1

= 9  

Estimate is 9 deg above Actual Temperature in 12 readings

The formula for our Mean Value will be, the added values divided by actual temperatures  

Added values = 9  

Actual temperature = 12  

Mean value = 9 ÷ 12 = 0.75°C above actual Temperature

Answer:

The answer would be 22.

Step-by-step explanation:

Since we have 2 bases one being 5 and the other 10, if you multiply the base of the smaller triangle by 2 you get 10. Whatever the sides are for the smaller triangle multiply those by 2. ONce you get all the numbers for the large triangle add them all to get the perimeter.

[tex]\bf \stackrel{\textit{\Large Similar Triangles}}{\cfrac{\stackrel{base}{5}}{\underset{perimeter}{11}}=\cfrac{\stackrel{base}{10}}{\underset{perimeter}{x}}}\implies 5x=110\implies x=\cfrac{110}{5}\implies x=22[/tex]

Answer: 345

Step-by-step explanation:

15% + 100% = 115%

100%.......300£

115%..........x£

x = 115*300/100

x= 345

Final answer:

To find the new price of the laptop after a 15% increase, add the 15% increase to the old price of £300 to get £345.

Explanation:

The new price of the laptop is £345.

Answer:

[tex]\sin A = \frac{a}{b}[/tex]

Step-by-step explanation:

Given:

We took here a Right Angle Triangle,Δ ABC at angle B as 90°

Side opposite to angle A = a

Side opposite to angle B = b = Hypotenuse

Side opposite to angle C = c

To Find:

Sin A = ?

Solution:

Property of a Sine rule for a Right Angle Triangle.

[tex]\sin A =\frac{\textrm{side opposite to angle A}}{Hypotenuse}\\\sin A =\frac{a}{b}[/tex]

∴ [tex]\sin A = \frac{a}{b}[/tex]

When dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.

When dividing 117 into equal groups of 3, we are essentially finding how many groups of 3 can be formed with a total of 117 items. This can be visualized as distributing 117 items equally into 3 groups.

Step 1: Perform the division:

117 ÷ 3 = 39

Step 2: Interpret the result:

The quotient 39 represents the number of equal groups of 3 that can be formed using 117 items. Each group will have 3 items.

Step 3: Final answer:

117 can be divided into 3 equal groups, and each group will have 39 items.

In summary, when dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.

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Answer:

3.75 miles per hour

Step-by-step explanation:

speed = distance/time

=412/110

=3.75 miles per hour

Answer:

642

Step-by-step explanation:

639 -127 = x -130

x = 639 -127 +130 = 639 +3 = 642

Answer:

642

Step-by-step explanation:

use inverse operations

first find the difference of 639 and 127 to get 512

then using inverse operations add 512 to 130 to get 642

check by subtracting 642 by 130 to get 512

Answer:

234 ÷ g

Step-by-step explanation:

Convert "234 divided by g" into algebraic form, which is:

234 ÷ g

It can also be written as 234/g.

An expression is has no equal sign, as opposed to an equation, which has an answer.

Answer:

Josie bought 40 adult tickets and 32 children tickets.

Step-by-step explanation:

x+y=72

22x+10y=1200

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

x=72-y

22(72-y)+10y=1200

1584-22y+10y=1200

1584-12y=1200

12y=1584-1200

12y=384

y=384/12=32

x+32=72

x=72-32=40

x=40, y=32. (40, 32)