If p=7 and q=1, what is 4pq squared + (-7)pq squared +5p?

For the exponents, I don’t know how to distribute the squared/power of two within each term.

Answer:

If just combining like terms: 3x^2 + 12

If solving for x: 2i, -2i

Step-by-step explanation: Combine like terms, so 3x^2 + 12 = 0; move the 12 to the other side by subtracting (3x^2 = -12), then divide both sides by 3, which gives x^2 = -4. Then get the square root of both sides to cancel out the power on the x. Since -4 is negative, use imaginary numbers, which makes x = 2i and x = -2i

Step-by-step explanation:

(-4,0)

(0, -4)

(1, -5)

(6, 0)

The answer to this given simplification (3x^-4)6/9x^-12 is 2 x^8.

What are exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. In this essay, let's study more about exponents.

given:

(3x^-4)6/9x^-12

=x^-4 . 3 . 6 / 9 . x^-12

= 2. x^-4 /  x^-12

=2 x^8

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Answer:

5 square mile

Step-by-step explanation:

1 square km = 0.3 square mile

13 square km = 5.01 square mile

5.01 rounded equals 5

hope that helps <3

The linear inequality represented by the given graph in the attached image is y > -3x + 6.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The graph of the linear inequality. Let's pick two points from the graph to frame the linear equation

The slope-intercept form of the equation is Where m is the slope and b is the y-intercept is (0,6) from the graph so b=6.

Find out slope m by using the general formula. Pick two points (0,6) and (2,0).

Slope = ( y₂ - y₁)  / ( x₂ - x₁ )

Slope = ( 0 - 6 ) / ( 2 - 6 )

Slope = -3

m = -3

So the equation is y = -3x + 6

Now we check the inequality sign by testing any point on the shaded area let's pick (4,0). let's plug in 4 for x  and 0 for y

y= -3x + 6

0 = -3(4) + 6

0 > -6

Inequality:  y > -3x + 6.

Therefore, the inequality represented by the given graph is y > -3x + 6.

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Answer: y≥4x−6

Step-by-step explanation: I took the test and this was the right answer for me.

An equivalent expression for 4d⁻³/22d⁹ is: B. 2d⁻³/11d⁻⁹

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁹

Expression = 2d⁻³/11d⁹

By applying the law of indices, we have:

Expression = 2 × 1/11d(⁹ ⁻ ⁽⁻³⁾)

Expression = 2/11d¹²

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Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Question 2

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

Applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.

sin X/x = sin W/w = sin Z/z [according to the law of sines].

Given:

Measure of angle X = 60°

Measure of angle Z (∠XZW) = 180 - 60 - (180 - 83) = 23°

x = WZ = ?

z = XW = 1.5

Plug in the values into sin X/x = sin Z/z

sin 60/WZ = sin 23/1.5

WZ = (sin 60 × 1.5)/sin 23

WZ = 3.32

Find ZY using the sine ratio;

sin ∅ = opp/hyp = ZY/WZ

sin 83 = ZY/3.32

ZY = (sin 83)(3.32)

ZY = 3.30

Therefore, applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.

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Scientific e Notation: 2.2222222e+57

Scientific Notation: 2.2222222 x 10^57

Answer:

I am pretty sure the answer is 2.2222222e+57.

Answer:

-22 I arrived as fast as I could

Answer:

25 quarters and 4 dimes. Louisa used 21 more quarters than she did dimes.

Step-by-step explanation:

q=number of quarters

d=number of dimes

6.65=.25q+.10d   6.65 (the total) is equivalent to the amount of quarters times .25 (the value of a quarter) plus the amount of dimes times .10 (the value of a dime)

Now divide 6.65 by .25.

26 quarters can be used.

26 times .25 = 6.50

26 quarters is $6.50

29-26=3

3 times .10 = .30

.30+6.50=6.80

This is too much. Let's try taking off one quarter.

Now we have 25 quarters. .25 times 25 = 6.25

29-25=4 (This means there will be 4 dimes if she used 25 quarters, but let's see)

4 times .10 = .40

.40 + 6.25=6.65

6.65 is the total amount she had to pay, so we did it. Solving this showed us that she used 25 quarters and 4 dimes. This equals $6.65, the amount she paid, uses only quarters and dimes, and uses a total of 29 coins.

I hope this helps you! Please mark as Brainliest answer! I worked really hard to type all of this out for you.

Answer:

89.14%

Step-by-step explanation:

279 Out of 313 is 89.14%. Follow the below steps to calculate what percent is 279 out of 313 or how to write 279/313 as a percentage.

Step 1: Percentage Formula = Number 1/Number 2 x 100

Step 2: plugin the 279 and 313 to the percentage formula and we get 279/313 x 100 = 89.14%

[tex]\stackrel{\textit{\LARGE sides}}{\cfrac{x}{2}+(x-5)+(x-2)~}~ = ~~13\implies \cfrac{x}{2}+2x-7=13 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{x}{2}+2x-7 \right)=2(13)}\implies x+4x-14=26\implies 5x-14=26 \\\\\\ 5x=40\implies x=\cfrac{40}{5}\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(8)}{2}\implies 4\hspace{5em}(8)-5\implies 3\hspace{5em}\underset{Longest}{(8)-2\implies 6}[/tex]

The number of terms in the sequence with d=5 , a₁ = -9 and aₙ=141 is 31 terms.

Arithmetic Sequence

The nth term of the sequence { a , a+d , a+2d , ... , a+(n-1)d } is given by

aₙ=a+(n-1)d       ...(i)

where , a = first term ,

d = common difference ,

n = number of terms ,

aₙ = nth term of the sequence .

It is given in the question that

first term (a) = -9

common difference (d) = 5

and nth term (aₙ) = 141

Substituting the values in equation (i) we get ,

141 = -9 + (n-1)5

simplifying further we get

141+9=(n-1)5

150 = 5n - 5

150+5 = 5n

155 = 5n

n=155/5

n=31.

Therefore , There are 31 terms in the sequence with d=5 , a1 = -9 and aₙ=141 .

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Answer:

There were 132 children admitted.

There were 165 adults admitted.

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information and defined variables:

[tex]\textsf{Equation 1}: \quad x+y=297[/tex]

[tex]\textsf{Equation 2}: \quad 3x+7y=1551[/tex]

Solve the first equation for y:

[tex]\implies x+y=297[/tex]

[tex]\implies x+y-x=297-x[/tex]

[tex]\implies y=297-x[/tex]

Substitute the found expression for x into the second equation and solve for y:

[tex]\implies 3x+7y=1551[/tex]

[tex]\implies 3x+7(297-x)=1551[/tex]

[tex]\implies 3x+2079-7x=1551[/tex]

[tex]\implies 2079-4x=1551[/tex]

[tex]\implies 2079-1551-4x=1551-1551[/tex]

[tex]\implies 528-4x=0[/tex]

[tex]\implies 528-4x+4x=0 + 4x[/tex]

[tex]\implies 528= 4x[/tex]

[tex]\implies \dfrac{528}{4}= \dfrac{4x}{4}[/tex]

[tex]\implies x=132[/tex]

Substitute the found value of x into the expression for y and solve for y:

[tex]\implies y=297-x[/tex]

[tex]\implies y=297-132[/tex]

[tex]\implies y=165[/tex]

Therefore:

The nth terms of the arithmetic sequences;

I. Tn = 3 + √2 + ( n - 1) √2

ii. Tn = 2/ √3 + ( n - 1) 1/ √3

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + ( n - 1)d

Where;

i. a = 3 + √2

d = √2

Substitute the values, we have;

Tn = 3 + √2 + ( n - 1) √2

ii. a = 2/ √3

d = 1/ √3

Substitute the value, we have;

Tn = 2/ √3 + ( n - 1) 1/ √3

Thus, the nth terms of the arithmetic sequences are Tn = 3 + √2 + ( n - 1) √2 and Tn = 2/ √3 + ( n - 1) 1/ √3 respectively

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Answer:

i would choose investment A

Step-by-step explanation:

A is simply the best anwser choice

Answer:

If I were Sam, I would buy the bond with a 3% interest rate since selling at any time is not a priority. The bond would provide a steady income from the investment, which is what he his needing.If I were Julia, I would invest in the stock, which has long-term growth potential. This would allow her to sell the investment at any time in the future.

Step-by-step explanation:

SAMPLE ANSWER!!!

Based on the balances in Reese Corp's trial balance, the current assets total can be found to be B. $5,555,000

The total of the current assets can be found by the formula:

= Inventory + Accounts Receivable + Cash

Solving then gives:

= 775,000 + 2,695,000 + 2,085,000

= $5,555,000

In conclusion, the current assets for Reese Corp is $5,555,000 .

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We are given a table for input and output values and the relation between them.

Consider the table,

Input           Output = Input × itself + (-5)           Output

0                                        

1

6    

                                                                              95

                                                                              59

                                                                              76

For Input = 0 :

Output = Input × itself + (-5)

Output = 0 × 0 - 5

Output = -5

Now, for Input = 1,

Output = Input x Itself + (-5)

Output = (1) × 1 + (-5)

Output = 1 - 5

Output = - 4

For Input = 6,

Output = Input x Itself + (-5)

Output = (6) × 6 + (-5)

Output = 36 - 5

Output = 31

For Output = 95,

Output = Input x Itself + (-5)

95 = (Input)²+ (-5)

95 + 5 = (Input)²

(Input)² = 100

Input = √100

Input = 10

For Output = 59,

Output = Input x Itself + (-5)

59 = (Input)²+ (-5)

59 + 5 = (Input)²

(Input)² = 64

Input = √64

Input = 8

For Output = 76,

Output = Input x Itself + (-5)

76 = (Input)²+ (-5)

76 + 5 = (Input)²

(Input)² = 81

Input = √81

Input = 9

Therefore the complete table will be:

Input           Output = Input × itself + (-5)              Output

0                     Output = 0 × 0 + (-5)                          -5

1                      Output = 1 × 1 + (-5)                             -4

6                     Output = 6 × 6 + (-5)                          31

10                  95 = Input × itself + (-5)                      95

8                    59 = Input x Itself + (-5)                      59

9                    76 = Input x Itself + (-5)                      76

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By using  Matrix method it denotes that the equations are consistent and have a single solution.

Matrix method, we will use the formula, [tex]X=A^{-1} B[/tex] where,

[tex]\[{\rm{X}} = \left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\][/tex]

[tex]\[{A^{ - 1}} = \frac{{adjA}}{{|A|}}\][/tex]

[tex]\[{\rm{B}} = \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\][/tex]

So, we will have to find [tex]A^{-1}[/tex], for that, we will first find the determinant of matrix A, that is |A|, then we will find the cofactors of matrix A, take its transpose, and that will be Adj A.

Therefore, we will be able to get the inverse of matrix A using

[tex]A^{-1}[/tex] =Adj A|A|

and hence We then substitute all the obtained values of [tex]A^{-1}[/tex] and B in the main formula and do necessary calculations to get the value of x, y and z accordingly.

Complete step-by-step answer:

It is given in the question that, we have to solve the system of equations,

2x-y+4z=33

X+2y-3z=−26

-5x−3y+5z=23

Applying the matrix approach.

Therefore, the first step is to convert the supplied equations into matrix form. Thus, it can be expressed as follows.

[tex]\[\left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\[[/tex][tex]= \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right][/tex]

[tex]\[|{\rm{A}}| = \left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\][/tex]

= 2(10+9) + 1(5-15) + 4(-3+10)

= 38-10+28

=56

Since we have |A|≠0.

Hence, it denotes that the equations are consistent and have a single solution.

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The length of EC will be 154 units.

We have the data that:

BD is the bisector of AC at point E.

This means that AE = EC

Also, AE + EC = AC

AE + AE = AC

2 AE = AC

Now,

AE = 2x² - 8 and AC is 5x² - 25

Substituting the values, we get that:

2 (2x² - 8) = 5x² - 25

4x² - 16 = 5x² - 25

5 x² - 4 x² = 25 - 16

x² = 9

x = 3 ( as length cannot be negative)

AE = EC = 2x² - 8

EC = 2 (9)² - 8

EC = 162 - 8

EC = 154 units.

Therefore, we get that, the length of EC will be 154 units.

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a. Straight-line method: $36,000 $36,000

b. Sum-of-the-years'-digits method: $60,000 $48,000

c. Double-declining-balance method: $79,200, $47,520

d. Activity method based on hours worked: $30,600, $21,600

e. Activity method based on units of output $40,000 $34,000

b. Straight line method

Depreciation expense = (Cost of asset - Salvage value) / Useful life

Depreciation expense=( $198,000 -  $18,000 ) / 5

Depreciation expense = $36,000

b.  Sum-of-the-years'-digits method

Sum-of-the-year digits = (Remaining useful life / Sum of the years ) x  (Cost of asset - Salvage value)

Sum of the years = (1 +2 +3 +4 + 5 )

Sum of the years = 15

Year 1 Depreciation expense = (5/15) × ( $198,000 -  $18,000 )

Year 1 Depreciation expense = $60,000

Year 2 Depreciation expense = (4/15) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $48,000

c.  Double-declining-balance method

Depreciation factor = 2 x (1/Useful life)  

Depreciation factor =2 x(1/5)

Depreciation factor = 0.4

Year 1 Depreciation expense = 0.4 x  $198,000

Year 1 Depreciation expense= $79,200

Year 1 Book value =  $198,000 - $79,200

Year 1 Book value= $118,800

Year 2 Depreciation expense= 0.4 x $118,800

Year 2 Depreciation expense= $47,520

d.  Activity method based on hours worked

Activity method = (Hours worked  / Total machine hours) x  (Cost of asset - Salvage value)

Year 1 Depreciation expense = (1,700 / 10,000) x ( $198,000 -  $18,000 )

Year 1 Depreciation expense  = $30,600

Year 2 Depreciation expense = (1,200 / 10,000) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $21,600

e. Activity method based on units of output

Activity method  = (Output produced / Total machine output capacity) x  (Cost of asset - Salvage value)

Year 1 Depreciation expense =  ( 40,000 / 180,000) x ( $198,000 -  $18,000 )

Year 1 Depreciation expense = $40,000

Year 2 Depreciation expense=  ( 34,000 / 180,000) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $34,000

Therefore the Straight-line method is $36,000 $36,000.

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Answer:

[tex] \: \: \: \: \: { \rm{2 \: \: \: 3 \: \: \: 4}} \\ { \underline{ \times \: \: 0. \: \: 3 \: \: 5}} \\ { \rm{ 1 \: \: 1 \: \: 7\: \: 0}} \\ { \underline{ + 7\: \: 0\: \: 2 \: \: 0 }} \\ { \underline{ \: \boxed{ 8\: \: 1 \: .\: \: 9 \: \: 0}}}[/tex]

Answer: 81.9

Answer:

40 yellow marbles

Step-by-step explanation:

1. Divide 64 by 8 (Determine how many sets there are)

64/8 = 8

2. Multiply 8 by 5 (Because for every 8 purple marbles there are 5 yellow ones)

8*5 = 40

Answer:

$611.17 per acre

Step-by-step explanation:

11001 ÷ 18 = 611.16666...

So, the answer is an infinite decimal, so we round it to the nearest hundredth.

The number is 5.67

Let the number be 'x'

The difference of four times a number and seven = 4x - 7

Ten more than the number = 10 + x

According to the condition given in the question,

The difference between four times a number and seven is equal to ten more than the number.

4x - 7 = 10 + x

4x - x = 10 + 7

3x = 17

x = 17/3 = 5.67

We can verify the answer,

Consider the LHS,

=> 4x - 7 = 4(5.67) - 7 = 22.68 - 7 = 15.68

Consider the RHS,

=> 10 + x = 5.67 + 10 = 15.67

Both LHS and RHS are equal.

Therefore the number that satisfies the given condition is 5.67

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Answer:1/1850

Step-by-step explanation: Davide 10% from 18500

The dimensions of the rectangular field with area 120 square meters is 10 meters by 12 meters.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given perimeter of the rectangular plot is 44 meters.

let the length is x , and width = y

Therefore perimeter = 2 (x + y)

or, 2 (x + y) = 44

or, x + y = 22

or, y = 22 - x

Now the area of the field is given as 120 square meters.

Area of the fields in terms of x is given by:

x ( 22 - x ) = 22 x - x²

Therefore  22 x - x² = 120

or,   x² -22x +120 = 0

or,  x² - 10x - 12x + 120 = 0

or, x (x -10) -12(x-10)=0

or, (x-10)(x-12) = 0

Now either the value of x is 10m or the value of x is 12m

Therefore the dimensions of the rectangular field is 10 meters by 12 meters.

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Answer: 54

Step-by-step explanation:

3x=72-x       ==> 3x and 72-x are both congruent angles, so they're equal

3x+x=72-x+x

4x=72

x=18

3x=

3(18)=54 degrees