Use the situation and diagram below to answer the following. The figure shown to the right is made up of a rectangle and a triangle. 10. Write a formula for the perimeter P in terms of x.​

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

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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Answer:

72

Step-by-step explanation:

$48 + $20 = $68

$68 - $32 = $36

$36 × 2 = $72

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%

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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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.

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!!!

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

Answer:

f(1) = 9

Step-by-step explanation:

where x is 1, y is 9

The number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A piece of wood was 12 feet long. Kendra cut the wood into pieces __

2/3 foot.

Let x be the number of pieces:

12/x = 2/3

x = 36/2

x = 18

Thus, the number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

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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

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]

here u go I hope this is the answer ur looking for!

Answer:1/1850

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

Step-by-step explanation:

(-4,0)

(0, -4)

(1, -5)

(6, 0)

After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.:

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

What is coordinates of the vertices?

The triangle's vertices' coordinates are [tex](x_{1} ,y_{1} )[/tex], [tex](x_{2},y_{2})[/tex], and [tex](x_{3},y_{3} )[/tex]. The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

Given:

Triangle PQR and vertices of triangle are

[tex]P=(3,8)\\Q=(-5,7)\\R=(0,2)[/tex]

The following rule results in a reflection about the y-axis:

                      [tex](x, y) ---- > (-x, y)[/tex]

Using the rule on each of our vertices, we have:

[tex](3, 8) ---- > (-3, 8)\\(-5, 7) ---- > (5, 7)\\(0, 2) ---- > (0, 2)[/tex]

Therefore,

After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

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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:

  x = 155°

Step-by-step explanation:

Given hexagon ABCDEF, you want to find the measure of interior angle E. Angles at vertices A, B, C, D, and F are specified.

The sum of the interior angles of an n-sided polygon is ...

  angle sum = (n -2)180°

For the 6-sided polygon given, the sum of interior angles is ...

  (6-2)180° = 720°

The interior angle at vertex B is 360° -80° = 280°.

The interior angle at vertex D is 180° -115° = 65°.

Then the sum of interior angles is ...

  A +B +C +D +E +F = 720°

  85° +280° +30° +65° +x +105° = 720° . . . . . substitute known values

  565° +x = 720° . . . . . . . collect terms

  x = 155° . . . . . . . . . . subtract 565°

__

Additional comment

The angles in the attached figure are drawn to scale.

An alternate solution might draw segment CX through vertex B so that the figure containing angle x has no reflex interior angles. Then the interior angles of pentagon ABXEF will total 540°. Known angles in that figure are A=85°, B=100°, X=95°, F=105°. Then E=x=540° -385° = 155°.

We took this approach initially, to verify that the angle sum of the given hexagon remained 720° even with the reflex interior angle at B.

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.

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:

$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.

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 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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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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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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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:

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