2) 2x-3y=-1
y = x - 1

Answer:

SAS Congruence Postulate Theorem (Side-Angle-Side Postulate Theorem)

Step-by-step explanation:

The following pictures shows that 2 pairs of sides are equal between the 2 triangles and a single pair of angles are equal. Thus we know that SAS Congruence Postulate Theorem proves that these triangles are congruent.

Answer:

x = -1

Step-by-step explanation:

Rewrite the equation as 6x + 8 = 2

Subtract  8 from both sides of the equation.
6x = 2 − 8

Subtract 8 from 2.

6x = −6

Divide each term in 6x = −6 by 6 and simplify.

Divide each term in 6x = −6 by 6.
[tex]\frac{6x}{6} = \frac{-6}{6}[/tex]

Simplify the left side.
[tex]x=\frac{-6}{6}[/tex]
Simplify the right side.

Divide -6 by 6

x = -1

After two years, compound interest increases your wealth. By the end of two years, compound interest has generated more money than simple interest.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money. Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the given information provided in the question,

[tex]M = s(1+\frac{i}{c_p} )c_p*y[/tex]

Where,

M represents the amount of money,

s represents the initial amount that is $300,

cp represents the compounding period.

Number of years, y = 2

M = 318,479 for Patrick's investment.

M = 331,482 for Brooklyn

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Answer:

x=11

Step-by-step explanation:

we know these 2 angles added together is equal to 180 so we can make these 2 equations equal to 180

(6x+12)+(10x-8)=180

16x+4=180

16x=176

x=11

Hopes this helps please mark brainliest

The slope of the line will be;

⇒ m = - 11/8

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

11x + 8y = 176

Now,

We know that;

The standard form of equation of line with slope m and y - intercept at b is,

⇒ y = mx + b

First way;

The  equation of line is,

⇒ 11x + 8y = 176

We can change it into standard form of equation of line as;

⇒ 11x + 8y = 176

⇒ 8y = - 11x + 176

⇒ y = - 11/8x + 22

By compare, We get;

Slope (m) = - 11/8

Second way;

The  equation of line is,

⇒ 11x + 8y = 176

⇒ y = - 11/8x + 22

Differentiate with respect to x,

⇒ dy/dx = - 11/8

⇒ m = - 11/8

Thus, The slope of the line will be;

⇒ m = - 11/8

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The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 100 inches will be 4.55.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.

Distance traveled in one rotation = Perimeter of the wheel.

⇒ 2π(3.5) = 21.99

The number of rotations = 100/21.99 = 4.55

Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 100 inches will be 4.55".

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Answer:

$3.96

Step-by-step explanation:

Use the formula:
[tex]p(1+\frac{r}{n} )^{nt}[/tex]

p is our initial investment

r is the interest rate

n is the term

t is time

doing this we get

[tex]200(1+\frac{.04}{1})^{0.5}[/tex]

where t = 0.5 because the term is 6 months or half a year

We get a value of 203.96 which is the amount of money being paid after 6 months.

The interest is then our initial value of $200 subtracted from our final value.

[tex]203.96-200= 3.96[/tex]

Answer:

see explanation

Step-by-step explanation:

80 and 11x + 1 are a linear pair and sum to 180° , that is

80 + 11x + 1 = 180

81 + 11x = 180 ( subtract 81 from both sides )

11x = 99 ( divide both sides by 11 )

x = 9

The value of C be sinC = - 371.932.

Given, the side of the triangle be c = 300

and the angles of the triangle be A = 1200 and B = 1350

Now, using the law of sines, we get

a/sinA = b/sinB = c/sinC = k

sinA/sinB = c/sinC

sin(1200)/sin(1350) = 300/sinC

0.8066/-1 = 300/sinC

sinC = - 371.932

Hence, the value of C be sinC = - 371.932.

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Answer:

- 371.932.

Step-by-step explanation:

The probability for the given case is 1/3.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The probability of an event cannot be negative.

A spinner has numbers indicated on it from one to six.

Suppose A be the event spinner lannds on 1.

And, B be the event the spinner land on 4.

Now, the probability of any event is the ratio of number of favorable outcome to the total number of outcomes which is given as,

P(A) = 1/6

And, P(B) = 1/6

Thus, the probability of event A or B is given as,

P(A or B) = P(A) + P(B)

              = 1/6 + 1/6

              = 1/3

Hence, the probability that the spinner lands on 1 or 4 is 1/3.

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Answer: its 2/5 + 1/10

Step-by-step explanation: iready got it right

Investment in the share of stock in xyzzy corporation is not a good investment.

In order to determine if the investment is a good investment, the present value of the cash flows from the investment has to be determined. The investment is a good investment if the present value of the cash flows is equal or greater than the cost of the stock.

Present value is the sum of the discounted cash flows from a project.

Present value = 5 / 1.08 + 5 / 1.08² + 5 / 1.08³ + 120 / 1.08³ = 108.15

The present value of the cash flows is less than the cost of the stock today. This means that the stock is not a good investment.

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30% of the area under the normal curve lies to the left of -0.52 z - score.

What is z - score?

The relationship between a value and the mean of a group of values is quantified by a Z-score. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean.

To find the z - score, divide your data point by your standard deviation after taking your data point and subtracting the mean from it.

Here, 30% = 0.30

So,

P(Z < z) = 0.30

From z - table, z - score for the probability 0.30 is -0.5244

-0.5244 ≈ -0.52

Hence, 30% of the area under the normal curve lies to the left of -0.52

z - score.

The option (c) is the correct answer.

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Answer:

A = {1,2,3,4,5}

B = {5,6,7,8,9}

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

Explanation:

Consider the set

A = {1,2,3,4,5}

The mean is found by adding up all the values to get 15, then divide by the number of values (5) to get 15/5 = 3

The standard deviation is a bit more complicated, and it depends which version you select (sample vs population). Let's say we go for the population standard deviation. Using a calculator gets us a population standard deviation of roughly 1.414; this value tells us how spread out the data set is. The higher the value, the more spread out the data set will be.

Now consider adding some fixed value to each item in set A. Let's add 4 to each value

We go from A = {1,2,3,4,5} to B = {5,6,7,8,9}

If you were to use a calculator, then the population standard deviation is still roughly 1.414 but the mean is now 7. The standard deviation hasn't changed because the values are still spread out the same way.

Note: infinitely many answers are possible for sets A and B.

The distance in kilometers from Sanjay's house to Carl's house is 4.55 kilometers.

According to the question,

We have the following information:

Dyna's house is 6.85 kilometers from Carl's house. Sanjay's house is 2 3/10 kilometers closer to Carl's house than Dyna's house is.

(Closer means that the distance will be [tex]2\frac{3}{10}[/tex] kilometers less than 6.85 kilometers.)

Now, converting the mixed fraction into decimal point:

23/10 = 2.3 kilometers

Now, let's take the distance from Sanjay's house to Carl's house to be x kilometers.

x = 6.85 - 2.3

x = 4.55 kilometers

Hence, the distance in kilometers from Sanjay's house to Carl's house is 4.55 kilometers.

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The rate of change at which the value of the auto is -950/year.

What is the Rate of Change?

It is said that the rate at which one quantity changes in relation to another is known as the rate of change function.

In simple terms, when calculating the rate of change in one item, the amount of change in another is divided by the comparable amount of change in another.

From the given data of question,

[tex]V(t) = 24000*0.95^{t}[/tex]

Then, by definition, the rate of change =[tex]\frac{d(v(t))}{dt} = \frac{d(24000*0.95^{t} )}{dt}[/tex]

                                                                 =  [tex]24000*0.95^{t}*ln(0.95)[/tex]

For time (t) = 5 years

[tex]\frac{d(v(t))}{dt} = 24000*0.95^{5}*ln(0.95)[/tex]

         = 24000*0.7737*(-0.0512)

         = -950

Hence, the rate of change of the value of the auto is -950/year.

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Answer:

aprox 57 days

Step-by-step explanation:

2560-1934=626

626/14=44.7142857143

2560/44.7142857143=57.25 days

Answer:

I notice the x intercepts affects the slope of the equation

Step-by-step explanation:

Answer:

Given: The equation of the rainbow has a shape of a parabola:

In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points

We will draw a line that will be intersected with the parabole at two points and one of them has x = 4

See the following picture:

As shown in the figure, the plane takes off from the point (-18, 0)

And it makes a slanted line that cuts through the rainbow at two points.

The equation of the linear function will be: y = 0.5x + 9

The table of the linear function will be as follows:

2. What is the domain and range of the rainbow?

Domain = all the possible value of x = ( -∞, ∞ )

Range = all the possible value of y = ( -∞ , 27 )

3. Explain what the domain and range represent in context.

The domain is all the possible values of x that can be substituted into the function

So, as we have a polynomial function, the domain will be all real numbers

The range is all the possible values of y that will be results when we have substituted with the x-values

As we have a parabola, the range will be ( -∞ , 27 )

What are the X- and y-intercepts of the rainbow?

As shown in the figure:

There are two points:

Step-by-step explanation:

The system of equation to represent Zendaya blueberries and grapes sells is as follow:

x + y = 33

2.50x + 1.25y = 55

Zendaya runs a farm stand that sells blueberries and grapes.  Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes.

The system of equation that can be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold can be represented as follows:

Therefore,

let

x = number of pounds of blueberries

y = number of pounds of grapes

Hence,

x + y = 33

2.50x + 1.25y = 55

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The area of the circle is  [tex]225\pi \ in.[/tex]

Hence, Option A is the correct answer.

A circle is a round-shaped figure that has no corners or edges. The Diameter is the longest chord of the circle. It divides the circle into two equal halves.

Diameter of the circle (d)= 30 in.

The radius of a circle is the distance from the center of the circle to any point on its circumference. The diameter is twice the radius of the circle.

The radius of the circle will be =d/2

                                             = [tex]\frac{30}{2}[/tex]

                                             = 15 in.

So, the radius of the circle is 15 in.

The area of the circle is given by [tex]A = \pi r^2[/tex]

So we have,

[tex]A = \pi r^2[/tex]

[tex]A = \pi 15^2[/tex]

[tex]A =225\pi \ in.[/tex]

Hence, the area of the circle is [tex]225\pi \ in.[/tex]

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Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                   Depreciation        B.O.Y         Expense      Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $26,000          $0           $26,000         $5,200            $5,200  $20,800

2   $26,000    $5,200          $20,800          $4,160           $9,360  $16,640

3   $26,000   $9,360          $16,640           $3,328           $12,688   $13,312

What is the double-declining-balance method?

One of the depreciation methods in use is the double-declining-balance method, however it places more expense in the initial years of an asset's life.

The straight-line rate, which is calculated as the product of 100/estimated useful life multiplied by 2, is doubled in this depreciation technique.

The double rate is applied to the remaining balance at the end of each year for the depreciation expense.

The depreciation expense for the most recent year is calculated as the difference between the ending balance from the prior year and the residual value.

Auto  = $26,000

Estimated useful life = 10 years

Residual = $600

Depreciable amount = $26,000 - $600 = 25,400

Straight-line depreciation rate = 100/10 = 10%

Double-declining depreciation rate =10% x 2 = 20%

Depreciation Expense:

1st year = 26000 x 20/100 = 5200

2nd year = 20800 x 20/100 = 4160

3rd year = 16640 x 20/100 = 3328

4th year = 13312 x 20/100 = 2662.40 = 2662

5th year = 10650 x 20/100 = 2130

6th year = 8520 x 20/100 = 1704

7th year = 6808 x 20/100 = 1361.6 = 1361

8th year = 5446 x 20/100 = 1089.2 = 1089

9th year = 4357 x 20/100 = 871.4 = 871

10th year = 3486 x 20/100 = 697.2 = 697

Year Cost   Accumulated  Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y         Expense      Depreciation   Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $26,000          $0           $26,000         $5,200            $5,200  $20,800

2   $26,000    $5,200          $20,800         $4,160           $9,360  $16,640

3   $26,000   $9,360          $16,640           $3,328           $12,688   $13,312

4   $26,000  $12,688           $13,312           $2,662           $15,350   $10,650

5  $26,000  $15,350            $10,650          $2,130           $17,488     $8,520

6   $26,000   $17,488           $8,520           $1,704           $19,192    $6,808

7   $26,000    $19,192          $6,808            $1,362           $20,554  $5,446

8   $26,000   $20,554          $5,446           $1089           $21,643   $4,357

9   $26,000  $21,643           $4,357           $871              $22,514   $3,486

10  $26,000  $22,514           $3,486         $697          $23,211     $2,789

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The constant percent rate of change of the function is option (d) 55% decay

The equation of the function is given as

f(x) = 32(0.45)^x

The above function is an exponential function

An exponential function is represented as

y = ab^x

Where b represents the growth or decay factor

So, we have

b = 0.45

We can see that the value of b is less than 1

This means that the graph would represent a decay

The percent rate of change is then calculated as

Rate = 1 - b

This gives

Rate = 1 - 0.45

Evaluate

Rate = 0.55

Rewrite as

Rate = 55%

Hence, the rate of change is 55% decay

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The school dance committee can be chosen in 1,86,70,176 ways.

Given, that  7 freshmen, 8 sophomores, 9 juniors, and 9 seniors are eligible to be on the committee.

Also, the school dance committee consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors

So, the number of ways in which the committee can be chosen are

C(7 , 2)×C(8 , 3)×C(9 , 4)×C(9 , 5)

On solving C(7 , 2), we get

C(7 , 2) = (7×6)/2 = 21

On solving C(8 , 3), we get

C(8 , 3) = (8×7×6)/(3×2) = 56

On solving C(9 , 4), we get

C(8 , 3) = (9×8×7×6)/(4×3×2) = 126

On solving C(9 , 5), we get

C(9 , 5) = (9×8×7×6×5)/(5×4×3×2) = 126

So, C(7 , 2)×C(8 , 3)×C(9 , 4)×C(9 , 5) = 21×56×126×126

= 1,86,70,176

The committee can be chosen in 1,86,70,176 ways.

Hence, the school dance committee can be chosen in 1,86,70,176 ways.

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Answer:

2x^3+x^2-23x-4

Step-by-step explanation:

x^2(2x+1)-5x(2x+1)-4(2x+1)

2x^3+x^2-10x-5x-8x-4

=2x^3+x^2-23x-4

The depreciation expenses foe each year is 4375.

Given,

In the question;

The cost of the truck is $20,000 with an estimated life of four years.

The residual value of the truck is $2,500.

To find the depreciation expenses for each year.

Now, According to the question:

Based on the given condition:

Formulate:

(20,000-2,500) ÷ 4

= 17500/4

Cross out the common factor:

= 4375

Hence, The depreciation expenses foe each year is 4375.

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Answer:

15 is the answer

The correct option is A . 12(3+2+4) shows the greatest common factor of these three values using the distributive property

A factor is an integer in mathematics that, when multiplied by other integers, produces the desired results. The resultant total is also known as the factors. The numbers can often be combined in a broad variety of ways. If you are familiar with the multiplication tables, it will be simple for you to determine the factors.

When two or more numbers are combined, the largest number is the greatest common factor (GCF). They are divided by the biggest number, which yields a natural number (factor). There are a few things that both share once all the variables that effect the number have been identified. The term "largest common factor" refers to the common factor among the others having the highest number.

The product of the common prime factors of 2 or more numbers is the greatest common factor(GCF) of the numbers.

Using the distributive property, it can be written that  .a(b+c) = ab + ac

Step 2

Write each number as the product of its prime factors. The product of the common factors is the greatest common factor(GCF) of the numbers.

The numbers,36 , 24 , 48  can be factored as follows.

36 = 2 * 2 * 3 * 3

24 = 2 * 2 * 3 * 2

48 = 2 * 2 * 3 * 2 * 2

Hence, the greatest common factor(GCF) of these numbers is equal to  

2 * 2 * 3  or 12 .

Take out the greatest common factor(GCF), 12 from the expression,  36+24+48 using the distributive property to obtain the result.

36+24+48 = 12 * 3 + 12 * 2 + 12 * 4

                 = 12 ( 3 + 2 + 4 )

Hence, the correct option is A .

Option B is incorrect as the factored out term is 6, which is not the greatest common factor(GCF) .

Option C is incorrect as the factored out term is 4, which is not the greatest common factor(GCF) .

Option D is incorrect as the factored out term is 3, which is not the greatest common factor(GCF) .

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Answer:

x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°

Step-by-step explanation:

Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15

So m∠c=45 degrees and ∠CBA is 75 degrees.

180-(45+75)=60 degrees.

So ∠DBC is 105 degrees.