-2x + 14y = -29
x-7y=19
elimination process

A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).

As given in the question,

Area of the square field = 22,500square feet

Let 'a' be the side and 'd' be the diagonal length of the square

a² =22,500

⇒a =150 foot

Using Pythagoras theorem

d² =a² +a²

⇒d² = 2(150)²

⇒d² =45000

⇒d =212.13

    ≈ 212 nearest foot (approximately)

Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with  area of 22,500 square feet as given.

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Answer:

Step-by-step explanation:

31320=x+0.08x

31320=1.08x

swap the sides

1.08x=31320

Divide by 1.08

x=29000

Answer: x - 6 = -12

Step-by-step explanation: first, we'll solve for x in 6 - x = 12. We'll isolate the variable by subtracting 6 from both sides, which gives us -x = 6. Now we'll divide both sides by -1 to get x and we will get -6 = x. So for the expression, we'll sub in the value we got for x from the equation, -6. -6 - 6 = -12.

Answer:

-12

Step-by-step explanation:

Answer:

Steve: $138.00

Jenna: $72.00

Step-by-step explanation:

Steve:

[tex]\frac{23}{35}[/tex] x 210 = 138

Jenna:

[tex]\frac{12}{35}[/tex] x 210 = 72

I'm not really sure what this means, but i'll do what i think is right!

Answer:

Steve: $138

Jenna: $72

Step-by-step explanation:

If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.

To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.

hope this helps!

Answer:

x = 5j-k

Step-by-step explanation:

(x-j) (5x+k) = 0

(x-j) * (5x+k) = 0

x - 5j + k = 0

x + k = 5j

x = 5j - k

mous this mobail phonffyuuyy

Answer: m<ABC = 45 degrees, m<DBC = 36 degrees

Step-by-step explanation:

set both equations equal to 81 because they add up to form one angle:

5x + 6 + 9x - 9 = 81

Combine like terms

14x - 3 = 81

Add three to both sides

14x = 84

Divide by 14 to find x

x = 6

To find the angles:

Measurement of angle ABC:

9(6) - 9 = 45 degrees

Take the original angle of 81 and subtract the angle you just found to find the remaining angle:

81 - 45 = 36

Therefore, the angle of DBC is 36 degrees

Triangle ABC is an isosceles right triangle.

Because of A(-8,7) B(-4,2) C(1,6)

So AB=√[-8-(-4)]²+(7-2)²

=√41

BC=√(-4-1)²+(2-6)²

=√42

AC=√(-8-1)²+(7-6)²

=√82

AB=BC

AB²+BC²=AC²

So triangle ABC is an isosceles right triangle.

What is isosceles right triangle?

An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

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Answer:

E

Step-by-step explanation:

Say the distance is 'd'

time for going  =  d/15

time for returning  = d/30

average speed =  total distance / ( total time)

                           =  2d / ( d/15 + d/30 )  

                                 solve for average speed  = 20 mi/hr

Answer:

$13

Step-by-step explanation:

For 50 people it will cost you 150 + 50(10) or 500

150 +500 = 650  Divide that among 50 people and you get a cost of $13 a person.

The inequality graph of the system of inequalities is graph (a)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The system of inequalities is given as

-2x + 3y < 9

x^2 - y <= 10

4x + y > 3

In the above system of inequalities, there are two linear inequalities and a parabola inequality

The inequality symbols in the linear inequalities are opposite

This means that the region between both lines would be shaded

Also, for the parabola; the upper part would be shaded.

This is so because when y is made the subject of the formula, the symbol  becomes >=

Using the above as a guide, the inequality graph of the system of inequalities is graph (a)

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Answer:

x>3

Step-by-step explanation:

2x+6-6 > 12-6    ditch the 6

2x/2 > 6/2          divide by 2

x>3

The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

In the given question

The price of 1 pound apple = $0.99

The price of 1 pound Peaches = $1.09

The price of 1 pound Pears = $1.19

Total pounds of apples bought = 3.18 pounds

price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)

=3.18*0.99

=$3.15    ...(i)

Total pounds of Peaches bought = 1.45 pounds

price of 1.45 pounds of peaches = 1.45*1.09

                                                 = $1.59    ...(ii)

Total pounds of Pears bought = 1.71 pounds

price of 1.71 pounds of pears = 1.71*1.19

                                                = $2.04     ...(iii)

Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.

Substituting the values from equation (i),(ii)and (iii) we get ,

Total bill = $3.15 + $1.59 + $2.04  

= $6.78

Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

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Answer: 3√6

Step-by-step explanation:

√54​=

√(9*6)=3√6

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.

Given the data in the question;

To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.

Sine of angle n = Opposite of angle n / Hypotenuse

sin(n) = Opposite / Hypotenuse

Plug in the given values and simplify

sin(n) = Opposite / Hypotenuse

sin (n) = 2 / 2√5

Next, rationalize the denominator.

Cancel out the common factor 2.

sin (n) = 2 / 2√5

sin (n) = 1 /√5

Multiply both the numerator and the denominator by √5.

sin (n)  = (1×√5) / (√5 × √5)

sin (n)  = √5/5

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

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Answer:

900,000 mph

Step-by-step explanation:

I am assuming the m in he problems is standing for miles.

250m/sec x 60 sec/min x 60min/hour  The sec cross out and the minutes cross out and you are left with miles be hour.

Answer:

3/4 of 5. It equals 3 3/4.

Step-by-step explanation:

The question asks for 3/4 of 5 cups of milk.

Answer:

.033

Step-by-step explanation:

When there is a proportional relationship the constant of proportionality is y/x and in this case that would be  10/300 and that would be .033 rounded to three decimal places.

The value of x will be 2. So, Option B is correct for the equation [tex]3^{2x} = 9^{3x - 4}[/tex]

In the given question, the equation is [tex]3^{2x} = 9^{3x + 4}[/tex], we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,

           => [tex]3^{2x} = 9^{3x -4}[/tex]  => [tex]3^{2x} = 3^{2(3x - 4)}[/tex]

We know according to the property of exponents if [tex]x^{m} = x^{n}[/tex], then m = n.

Similarly, in this equation the base of both RHS and LHS are the same, We get

           => 2x = 2(3x - 4)

           => 2x = 6x - 8   =>  4x = 8

           =>  x = 2

We get value of x = 2.

Hence the value of x for this equation will be 2 and option B is correct.

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Answer: 10

Step-by-step explanation:

First you can re-order = 36/9 + 6

36/9=4

Then add 4+6

It equals 10

Answer:

its 1

Step-by-step explanation:

i just know

2,290,000 in scientific notation is 2.29 x 10⁶.

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.

Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.

Now the given number is,

2,290,000

To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.

So, factorizing 2,290,000 we get,

2,290,000 = 229 x 10,000

Now converting 10,000 into multiples of 10

Since, 10,000 = 10 x 10 x 10 x 10

So, 2,290,000 can be written as,

2,290,000 = 229 x 10 x 10 x 10 x 10

Multiplying and divide 229 by 100 we get,

2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100

Rearranging we get,

2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)

Since, (229 x 100) / 100 = 2.29 x 100

2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)

And 100 = 10 x 10

Therefore we get,

2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10

Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶

Therefore we get,

⇒ 2,290,000 = 2.29 x 10⁶

this is the required scientific notation of 2,290,000 .

Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.

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Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

A bisector divides an angle or segment into two equal halves.

Given the data in the question;

Since XZ is a  perpendicular bisector of segment WY,

Segment WX is equal to Segment XY

Segment WX = Segment XY

Plug in the given values and solve for k.

6k + 8 = 11k - 12

Collect like terms

6k - 11k = -12 - 8

-5k = -20

Divide both sides by the coefficient of k

-5k/-5 = -20/-5

k = 4

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

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The solution of the given expression  [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex] which is a negative integer in decimal form.

The numbers of the number line are called integers. They include positive numbers, zero, and negative numbers.

Zero is neither considered a negative nor a positive number.

[tex]5.5\\[/tex] is a positive number and a smaller number when compared from [tex]8.1[/tex].

When a smaller number is subtracted from a larger number it results in subtraction with a negative sign.

[tex]5.5 - 8.1 \\= -2.6[/tex]

The subtraction of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex].

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Answers:  

2.857142 mph

4.190476 ft per second

Both values are approximate

=======================================================

Work Shown:

21 min = 21/60 = 0.35 hrs which is exact

distance = rate*time

rate = distance/time

rate = (1 mile)/(0.35 hrs)

rate = (1/0.35) mph

rate = 2.857142 mph which is approximate

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

21 min = 21*60 = 1260 seconds

1 mile = 5280 ft

rate = distance/time

rate = (5280 ft)/(1260 seconds)

rate = (5280/1260) ft per second

rate = 4.190476 ft per second approximately

Answer: 2.857 miles/hr

4.19 ft/sec

Step-by-step explanation:

60 min=1 hr.

1 mi/21 min*60 min=

60 min*1 mi/21 min=2.857 miles/hr

60 sec=1 min

60*60 sec=1 hr

1 hr=3600 sec

2.857 miles/hr=

2.857/3600 miles/sec=0.00079 miles/sec

1 mile=5280 ft

0.00079 miles/sec=

0.00079*5280 ft/sec=4.19 ft/sec

If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

So, to find the probability:

Apply values in the formula:

Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

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