Last month Bill spent $6,000. How much did bill spend on taxes last month? (1) The total amount Bill spent on taxes was 70% of the amount he spent on groceries. (2) 40% of the total amount Bill spent last month was spent on taxes and groceries.

Answer:

Step-by-step explanation:

(a - b)(a + b) = a² - b²

(8 - n⁷)(8 + n⁷) = 8² - (n⁷)² = 64 - n¹⁴      {(aˣ)ⁿ = aˣ*ⁿ }

Or

Use FOIL method

(8 - n⁷)(8 + n⁷) = 8*8 + 8*n⁷ + (-n⁷)*8 + (-n⁷)*n⁷

                       = 64 + 8n⁷ - 8n⁷ - n⁷⁺⁷

                       = 64 - n¹⁴

Answer:

(- 1, 8 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(8, - 1 ) → (- 1, 8 )

The image of (8, -1) after a reflection over the line y = x is, (- 1, 8).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

A point (8, - 1) is reflected over the line y = x.

Now, We know that;

The image of point (x, y) after reflection over the line y = x is,

⇒ (x, y) → (y, x)

Thus, The image of (8, -1) after a reflection over the line y = x is,

⇒ (8, - 1) → (- 1, 8)

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Answer:

Step-by-step explanation:

((b+2)(b+12)/(b+2)(b+3))*(b+3)

= (b+12)

Answer:

n=-1.5

Step-by-step explanation:

6-4n=12

Subtract 6 from 12

-4n=12-6

Simplify

-4n=6

Divide each side by -4

-4n/-4=6/-4

Simplify

n=-1.5

Answer: 40%

Step-by-step explanation:

Answer: 2/5 or 40%

Step-by-step explanation: 15 + 10 = 25 and 10/25 simplifies to 2/5.

Answer:

a number squared plus twice a number minus one equals zero

Step-by-step explanation:

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

Answer:

It will take him 15 hours, Good luck!!

Step-by-step explanation:

Answer:-8, -6,-3, 4 is the correct answer

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

Answer:

there was no data available for those numbers

Step-by-step explanation:

if you want to graph at intervals of (for example) 15, but your numbers are ranging from 115 - 200, you don't want to a huge blank space from 0 - 115 on the y-axis.

if you create a break at the bottom (and only the bottom) you can start at 100 and have intervals of 15 from there. this eliminates dead space on a graph.

Answer:

-16% change

Step-by-step explanation:

The formula for a percent decrease is [tex]\frac{original-new}{original}\cdot100[/tex]. The original value was 986, and the new value is 828.24, so we can substitute inside the equation.

[tex]\frac{986-828.24}{986} \cdot100\\\\\frac{157.76}{986} \cdot100\\\\0.16\cdot100\\\\16[/tex]

So the percent change is -16%.

Hope this helped!

The 2 unknown numbers are 4 and 5 .

Let the numbers be x and x + 1.

From the given information,

[tex]\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ [/tex]

But, as we know -5 is not a natural number,

Hence, x = 4 .

So the 2 unknown numbers are :

★ Solution :

Let the number be x and x + 1.

[tex]\rule{130}1[/tex]

[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]

[tex]:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}[/tex]

⠀

We know that -5 is not a natural number. Hence, x = 4.

[tex]\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.[/tex]

Answer:

(x-10)(5x+2)

Step-by-step explanation:

this is the answer of the question.you can clearly see in the pic of the solution

Answer:

C.

Step-by-step explanation:

The relationship is proportion if y/x is constant.

So it is C because 12/4 = 15/5 = 18/6 = 3.

Answer:

x=6

Step-by-step explanation:

127-83=9x-10

44=9x-10

+10.0 +10.0

54=9x

divide by 9 on both sides

x = 6

Answer:

[tex]3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay[/tex]

Answer:

8,3

Step-by-step explanation:

This question is not correctly written

Complete Question

A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for cost of the number of games Mr. Yao bought

Answer:

Variable expression for the cost of the number of games that Mr Yao bought =

$20x

Where x = number of games that he bought.

Step-by-step explanation:

A variable expression can be defined as a mathematical expression where there is at least one (or more) unknown variable(s)that we have to look or solve for.

The unknown variable is always represented by letters of the alphabet, a, b, x, y e.t.c.

A variable expression can also be called an algebraic expression.

From the above question, we are told that:

Cost of a gaming console = $299.99

If you buy a game with the console = Additional $20.00

My Yao bought = x number of games

Variable expression for the cost of the x number of games that Mr Yao bought

$20 × x

= $20x

Where x = number of games that Mr Yao bought.

Step-by-step explanation:

1 / (sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the first fraction by ½ cos 10°.

½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the second fraction by ½ sin 10°.

½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)

Combine fractions.

(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)

Change ½ to sin 30°, and change ½√3 to cos 30°.

(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)

Use angle sum formula.

sin(30° − 10°) / (½ sin 10° cos 10°)

sin 20° / (½ sin 10° cos 10°)

Multiply top and bottom by 4.

4 sin 20° / (2 sin 10° cos 10°)

Use double angle formula.

4 sin 20° / sin 20°

4

We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.

Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'

1 / sin(10°) - √3 / cos(10°)

= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)

Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).

2(cos(10°) - √3sin(10°)) / 2sin(20°)

We can now bring the two on the bottom to the numerator, becoming 1 / 2.  Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) /  2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).

4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))

= 4((sin(30 - 10°)) / sin(20°) = 4

Answer:

3n + 2

Step-by-step explanation:

[tex]−n+(−4)−(−4n)+6[/tex]

Open the parentheses

[tex] - n - 4 + 4n + 6 \\ [/tex]

Add similar elements

[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]

Answer:

[tex] - n + 6[/tex]

Step-by-step explanation:

[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]

Answer:

                x = 1388.89

Step-by-step explanation:

x    - the sale price of new refrigerator

18%x = 0.18x   - the discount

0.18x = 250

x = 250÷0.18 = 1388.8888...

x = 1388.89

Answer:

the total she earns with "d" hours of dog walking and "b" hours of babysitting is given by:  8 d + 12 b

Step-by-step explanation:

If we use "d" to represent the number of hours that Susan walks the dog, and we define "b" as the number of hours she babysits, then the expression that represents the amount she earns by walking the dog is: $8 times d = 8 d

Similarly, the amount she earns by babysitting is $12 times b = 12 b

Then the total she earns with "d" hours of dog walking and "b" hours of babysitting is:  8 d + 12 b

Answer:

Line PQ. Not enough Info for the Plano tho.

Step-by-step explanation:

Look at the 2 points, and thats the name of the line.

Answer:

g(x) = -3|x|.

Step-by-step explanation:

Multiplying by 3 stretches the graph vertically by a factor 3 and the negative reflects in the x-axis.

The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by

f ( x ) = -3 | x |

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs),

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be g ( x ) = | x |

Now , let the transformed function be f ( x )

The value of the function f ( x ) is calculated by

Step 1 :

Vertical stretch by a factor of 3

The Vertical stretch by a factor is done by

k: y = k × f(x)

So , multiplying the parent function by 3 , we get

f ( x ) = 3 | x |

Step 2 :

Reflection in the x-axis ,

The value of f ( x ) is multiplied by -1

So ,

f ( x ) = -3 | x |

Therefore , the transformed function f ( x ) = -3 | x |

Hence , The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by

f ( x ) = -3 | x |

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Answer:

Step-by-step explanation:

taking A(3, 3), B(6, 6), C(9,3) and D(6,0)

we have:  [tex]y_A=y_C\quad and\quad x_B=x_D[/tex] so the AC and BD are diagonals, that means:

AB = BC = CD = DA = s

[tex]s=\sqrt{(6-3)^2+(6-3)^2}=\sqrt{3^2+3^2}=\sqrt{18}\\\\\\A=s^2=(\sqrt{18})^2=18[/tex]

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

Answer:A)Gives hints to reader about a future event.

Step-by-step explanation:

Answer:

A) Gives hints to reader about a future event.

Step-by-step explanation:

Foreshadowing is one of the storytelling device that gives hints to readers about the future events.

Hope this helps ;) ❤❤❤

Answer:

$605

Step-by-step explanation:

The correct question is

Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?

a. $550

b. $605

c. $625

d. $750

e. $825

For the first $40 that Taho works, he earns $11 x 40 = $440

For the extra $10 (since he worked 50 hrs that week)

1½ of $11 per hr = 1.5 x $11 = $16.5

for the 10 days extra = $16.5 x 10 = $165

total pay = $440 + $165 = $605

Answer:

Step-by-step explanation:

Given the expressions :

The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.

Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.

Let the original price = x

Expression 1 : The list price of the item is 80 percent of the original price

List price = 80% of x

List price = 0.8x

Expression 2: The price of the item has been reduced by 80 percent

Price = x - 80% of x

Price = x - 0.8x

Price = 0.2x

Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.

Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.

Answer:

[tex]\boxed{12}[/tex]

Step-by-step explanation:

[tex]6/\frac{1}{2} =6*2=12[/tex]

Answer:

B. $200,000

Step-by-step explanation:

Let x be the amount placed at 5.5%

3x is the amount placed at 5%

This leaves the rest for the 4.5 %   500000- x - 3x = 500000-4x

Assuming simple interest

I = PRT where I is interest, P is principle, rate is rate and t  is time

Interest for the 5.5% for 1 year is

I = x * .055 * 1 = .055x

Interest for the 5.% for 1 year is

I = 3x * .05 * 1 = .15x

Interest for the 4.5% for 1 year is

I = 500000-4x * .045 * 1 = 22500 - 0.18 x

Add the interest together to get the income for 1 year

.055x+  .15x+22500 - 0.18 x=25,000

Combine like terms

0.025x+22500=25000

Subtract 22500

.025x =2500

Divide by .025

x =100000  

short term notes is 100000

3*x = 300000 = government bonds

The rest is utility bonds 500000- 100000-300000 = 100000

We want how much more in government bond than utility bond

300000 -100000 = 200000

Answer:

200000

Step-by-step explanation:

the short term =x

government bonds =3x

utility bonds: 500000-4x

0.055x+3(0.05(x)+0.045(500000-4x)=25000

0.055x+0.15x+22500-0.18x=25000-22500

0.055x+0.15x+22500-0.18x-22500=2500

0.025x=2500

x=2500/0.25

x=100000

government bonds=3x=3(100000)=300000

utility bond=(500000-400000)=100000

government bonds than in utility bonds:

300000-100000=200000