I need the linear Equation !

Answer:

ubtract

36

from both sides of the equation.

x

2

+

14

x

=

−

36

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of

b

.

(

b

2

)

2

=

(

7

)

2

Add the term to each side of the equation.

x

2

+

14

x

+

(

7

)

2

=

−

36

+

(

7

)

2

Simplify the equation.

Tap for more steps...

x

2

+

14

x

+

49

=

13

Factor the perfect trinomial square into

(

x

+

7

)

2

.

(

x

+

7

)

2

=

13

Solve the equation for

x

.

Tap for more steps...

x

=

±

√

13

−

7

The result can be shown in multiple forms.

Exact Form:

x

=

±

√

13

−

7

Decimal Form:

x

=

−

3.39444872

…

,

−

10.60555127

…

Step-by-step explanation:

Answer: 250000

Step-by-step explanation:

multiple 10 4 times then multiply 25 at the end

[tex] \bold{1: 3a + 2a \: = 5a}[/tex]

[tex]\bold{2: - 5b - 7b = - 12b}[/tex]

[tex]\bold{3: - a {}^{2} - 9 a{}^{2} = - 10a {}^{2}}[/tex]

[tex]\bold{4: 3a {}^{x - 2} + 5a {}^{x - 2} = 8a {}^{x - 2}}[/tex]

[tex] \bold{5: 18x - 11x = 7x}[/tex]

[tex]\bold{6: 5a - 8a + a - 6a + 21a = 13}[/tex]

The reduction of similar terms is an operation that aims to convert two or more similar terms into a single term.

In these cases you must add or subtract either addition, subtraction or subtraction and addition, using the law of signs.

[tex]\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\bold{Law \: of \: signs: }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \end{gathered} [/tex]

The number of groups, using the combination formula, for each case, is given as follows:

a) Same number of students from each grade: 1,245,816,000

b) At least two grade nine students: 31,650,886,995.

c) James and Lucy are in it: 2,481,256,778.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For item a, the groups are taken as follows:

Hence the number of groups is:

[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]

For item b, the total number of groups, without considering the restriction, is:

[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]

The number of groups with none students from grade 9 is:

[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]

The number of groups with one student from grade 9 is:

[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]

Using complementary events, the number of groups with at least two grade 9 students is:

38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.

For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:

[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]

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Answer:

12 inches

Step-by-step explanation:

Let be "x" the top inches (in the model) of a eighty four foot building.

According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.

Knowing this, we can set up the following proportion: 3/21=x/84

The final step is to get to the bottom of for "x" in order to calculate its value.

Answer:

Generally, more selective schools may require or recommend a writing score, while less selective ones may not (though there certainly are exceptions). It's worth noting that most schools no longer require the ACT with Writing, though many schools recommend it.

Step-by-step explanation:

The equation (in slope-intercept form) of the line passing through the points with the given coordinates (−2,3) , (−3,2) is y = x + 5

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Hence, let's find the slope of the line using the coordinates (-2, 3) and (-3, 2).

Therefore,

m = 2 - 3 / -3 + 2

m = - 1 / -1

m = 1

Therefore, lets find the y-intercept using (-2, 3)

y = x + b

3 = -2 + b

b = 3 + 2

b = 5

Hence, the equation of the line in slope intercept form is y = x + 5

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The amounts drained by each pipe, considering a system of equations, are given as follows:

The variables to the system of equations are presented as follows:

A water tank holds a total of 5,600 gallons, hence:

x + y + z = 5600.

Pipe B drains twice as much as pipe A, hence:

y = 2x.

Pipe C drains 65 gallons more than pipe B, hence:

z = 65 + y = 65 + 2x.

Replacing the last two equations into the first, the amount drained by Pipe A is obtained as follows:

x + y + z = 5600.

x + 2x + 65 + 2x = 5600

5x = 5535

x = 5535/5

x = 1107 gallons.

Hence the remaining amounts are given as follows:

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Answer: c. 1

Step-by-step explanation:

[tex]\displaystyle\\(cot\theta)(sin\theta)(sec\theta)=\\\\\frac{cos\theta}{sin\theta}(sin\theta)\frac{1}{cos\theta} =\\\\\frac{cos\theta (sin\theta)(1)}{sin\theta(cos\theta)}=\\\\1[/tex]

Answer:

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

Answer:

$1580.69

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]

where:

Given:

Substitute the values into the formula to calculate the monthly payment:

[tex]\implies \sf PMT=\dfrac{12000(0.00415)\left(1+0.00415\right)^{60}}{\left(1+0.00415\right)^{60}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{49.8\left(1.00415\right)^{60}}{\left(1.00415\right)^{60}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{63.84764727}{0.2820812705}[/tex]

[tex]\implies \sf PMT=226.3448656[/tex]

Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:

[tex]\implies \sf 226.3448656 \times 60=\$13580.69[/tex]

To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:

[tex]\implies 13580.69-12000=\$1580.69[/tex]

Therefore, the interest Jessie will pay over the life of the loan is $1580.69.

Answer: 25 1/3

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

2000/4=500

500/20=25

Answer: 125

Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.

If a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

The initial population was 5000

The population in 2015 is 6000

let the rate of growth be r

aₙ = arⁿ-¹

6000 = 5000 r⁵⁻¹

6000/5000 = r⁴

6/5 = r⁴

r = 1.2⁻⁴

r = 0.48

r = 48%

the annual percentage rate of growth 48/5 = 9.6

Therefore, if a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

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To find the distance between the points shown we subtract each point and the x-axis

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2– x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Since the two points are on the same coordinate on the x -axis

To find the distance between the two points we subtract the y coordinates of the two points and the x axis.

In conclusion the distance between the two points is found by subtracting the two points and the x -axis

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According to the given depression angle, ship is 4.4 miles apart from ship B.

Depression angle:

Depression angle refer an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.

Given,

A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles from the ship located at point A.

Here we need to find the distance between the two ships.

Here we know the following,

Distance between plane and Ship A = 5 miles.

And the depression angle = 74°, 48°

Let us consider the following, that they sit on a line,

So under this situations,

=> 80 - 48 - 74 = 58 degrees.

The next thing we have to do is bring this 74 degree angle inside the diagram. Because it is congruent to this interior angle because they are alternate.

Then it can be written as,

=> x = sin 74°/5

=> x = 4.4

Therefore, the two ships are 4.4 miles apart from each other.

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Each individual paid the sum of $23.4 including state tax at the restaurant

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".

In the problem, their total bill is $50.88 and they gave a 30% tip

We should fid 30% of 50.88

0.3 * 50.88 = $15.264

30% of $50.88 is $15.264

If we add this up and then find the state tax to it.

15.264 + 50.88 = 66.144.

Find 6% of 66.144 to determine the state tax.

0.06 * 66.144 = 3.96864

The total amount spent is 66.144 + 3.96864 = 70.11264

We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088

Rounding this to the nearest cent, we have 23.4.

We can say each person paid $23.4 at the end of the day

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The kite's elevation relative to the ground is 6.45 feet.

Elevation simply means the height above sea level.

In this case, Jose flies a kite 17 1/2 ft above the ground and he increases its elevation by 4 3/4 ft by letting out some strung. and then changes its elevation by - 15.8 ft.

This will be illustrated as:

= 17.5 + 4.75 - 15.8

= 6.45 ft

The elevation is 6.45 feet.

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Answer:

0.000348 (rounded)

Step-by-step explanation:

Please tell me if this is wrong.

The shape of the sampling distribution of the daily proportions of overripe oranges is approximately normal.

The correct answer option is option C

Sampling distribution refers to a probability distribution in which samples are drawn from a population which is taken from a larger population.

Types of sampling

Shapes of sampling distribution:

Number of oranges Toni's restaurant receives everyday = 200

Population of overripe oranges = approximately 11%

Therefore, it the supplier's claim is true of overripe oranges is true, shape of the sampling distribution is approximately normal.

Complete question:

Toni runs a restaurant that receives a shipment of 200 oranges every day. According to the supplier, approximately 11% of the population of these oranges is overripe. Suppose that Toni calculates the daily proportion of overripe oranges in her sample of 200. We can assume the supplier's claim is true, and that the oranges each day represent a random sample. What will be the shape of the sampling distribution of the daily proportions of overripe oranges?

Choose 1 answer:

Skewed to the left

Skewed to the right

Approximately normal

Uniform

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This question requires you to find simple interest. Total money in the account after 10 years is $189,000

The total money can be calculated as follows:

Given,

=Deposit×Interest×Year

=18,000×8.5%×10

=18,000×[tex]85/100[/tex]×10

=$171,000

=$171.000+$18.000

=$189,000

Hence, the simple interest or total money in the account after 10 years without any withdrawals of additional deposits is $189,000.

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The amount of money in the account after 10 years will be $42113.64.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

As per the given,

Principle amount P = $18000

Rate of interest r = 8.5% = 0.085

Time t = 10

By continuous compounding interest formula,

P = (18000)[tex]e^{0.085\times10}[/tex]

P = $42113.64

Hence "The amount of money in the account after 10 years will be $42113.64".

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Deondra read at rate 40 pages per hour.

What is the meaning of the rate?

The rate at which something occurs or changes, as well as the quantity or frequency with which it does so over a period of time.

What is the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that, Deondra read 18 pages in 2/5 of an hour.

Use unitary method to calculate the required value:

In 2/5 hour, she read 18 pages.

In 1 hour, she read 18/(2/5) pages.

In 1 hour, she read 18 × (5/2) pages = 40 pages.

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Step-by-step explanation:

if p(A)=0.17, p(B)=0.42 and p(AorB)=0.59, are A and B mutually exclusive

Answer:

The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]

Step-by-step explanation:

The slope of a line can be found with the following formula

[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where [tex]x_2 > x_1[/tex]

Then substituting the values ​​with the given ones we have

[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]

So the slope of the line passing through the given points is [tex]-1[/tex]

Answer:

22.3 gm

Step-by-step explanation:

720 is this many half lives :   720 / 1690

   so there will be this much left   30 gm ( 1/2)^(720/1690) = 22.3 gm

The car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.

According to the question,

We have the following information:

Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells. And the original price of the model car was $40.

The first day:

40*5/100

200/100

2

The price on the first day = $38

The second day:

38*5/100

190/100

1.9

The price on the second day = 38-1.9

The price on second day = 36.1

The third day:

36.1*5/100

180.5/100

1.805

The price on third day = $34.295 (36.1-1.805)

1 dollar = 100 cents

Price of car in cents = 3429.5 cents

B) Percent discount from the original price:

Let's take it to be x.

40 - (40x/100) = 34.295

-40x/100 = 34.295-40

-40x/100 = -5.705

40x = 570.5

x = 570.5/40

x = 14.265%

Hence, the car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.

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Answer:

1. Given.

2. Definition of congruent segments.

3. Segment Addition Postulate.

4. Substitution Property of Equality.

5. Transitive Property of Equality.

6. Subtraction Property of Equality.

7. Definition of congruent segments.

Step-by-step explanation:

Statement 1

[tex]\overline{AB} \cong \overline{CD}; \; \overline{CE} \cong \overline{AE}[/tex]

Reason:  Given.

Statement 2

[tex]AB=CD; \;CE=AE[/tex]

Reason:  Definition of congruent segments.

Congruent segments are segments that have the same length.

Statement 3

[tex]AE+EB=AB; \; CE+ED=CD[/tex]

Reason:  Segment Addition Postulate.

A line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.

Statement 4

[tex]CE+EB=CD[/tex]

Reason:  Substitution Property of Equality.

For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.

Statement 5

[tex]CE+ED=CE+EB[/tex]

Reason:  Transitive Property of Equality.

For all numbers a, b and c, if a=b and b=c, then a=c.

Statement 6

[tex]ED=EB[/tex]

Reason:  Subtraction Property of Equality.

For all numbers a, b and c, if a=b, then a-c=b-c.

Statement 7

[tex]\overline{ED} \cong \overline{EB}[/tex]

Reason:  Definition of congruent segments.

Congruent segments are segments that have the same length.

Answer:

x = 4 ; y = -1

Step-by-step explanation:

y = -2x + 7

x + 2(-2x+7) = 2

x -4x + 14 = 2

-3x = 2 -14

-3x = -12

-3/-3 x = -12/-3

x = 4

y = -2* 4 + 7

y = -8 + 7

y = -1

Answer:$583.93 is the original price

Answer:

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

The given function is the combination of three lines:

The values of the function at the given points are: