3x-5y=15
x-4y=12
solve with substitution
system of equations

the Area will be 280 inch².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The base of triangle = 20inch

The height of triangle  = 14inch

Area is = (base * height) =  (20*14)

Area = 280 inch²

Hence the Area will be 280inch²

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Answer:

-626.8

Step-by-step explanation:

78 -716 + (0.8)(14)

78 - 716 + 11.2

(78 -716) + 11.2

-638 + 11.2

-626.8

Answer:

About 2.1 pounds a month.

Step-by-step explanation:

In this question, we know the amount of weight gained and the time it took, 20 pounds and 9.5 months.

to find the rate, we can do:

20/9.5

about 2.1

So, the answer will be:

about 2.1 pounds / month

The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28

A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.

Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).

Divide the divisor by the outcome you just got (the first term of the eventual quotient).

By following the above rules where

2x3-4x2+3x+2 is divided by the x-3, We get the following equation

where

quotient is 2x2+2x+10

and the remainder is 28

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The value of the digit 4 in the number 3.04 is 0.04.

What is the Place Value of a digit ?

Place value is the value a digit in a number represents based on the number's place within the whole.

Here, The place value of the digit 4 is hundredths.

So, Value of digit 4 =  4/100 = 0.04.

Hence, Value of digit 4 in 3.04 is 0.04.

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Ordered triplet (-2, -6, 3) is the solution of the system of equations

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

How to determine if an ordered triplet is solution to system of equations?

To determine if an ordered triplet is a solution to a system of three equations, we substitute the values of the variables into each equation. If the ordered triple makes all three equations true, it is a solution to the system.

According to the given question:

System of equations are

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

Now, substituting (-1, 2, 0) in every equation to check if LHS = RHS for each.

1. 3x + 4y - z = 5

    LHS = 3(-1) + 4(2) - 0 = -3 + 8 = 5 = RHS

2. 5x-y + 3z = -7

   LHS = 5(-1) - 2 + 0 = - 5 -2 = -7 = RHS

3. 9x + 5y + 7z = -21

   LHS = 9(-1) + 5(2) + 0 = -9 + 10 = 1 ≠ RHS

Therefore (-1, 2, 0) is not the solution for the system of equations.

Similarly substituting (-2, -6, 3) in every equation.

Clearly (-2, -6, 3) satisfies the system of equations.

Hence (-2, -6, 3) is the solution to the system of equations.

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Answer:

y = 10/17x - 7

Step-by-step explanation:

→ Write in standard form

y = 10/17x + c

→ Substitute in (17, 3)

3 = 10 + c

→ Solve for c

c = -7

→ Rewrite

y = 10/17x - 7

Subtracting the polynomials, 3x + 7 is subtracted from -x + 2, the result is: -4x - 5.

To find the difference of two polynomials, like terms should be combined and simplified together.

Subtracting 3x + 7 from -x + 2, we have the following:

(-x + 2) - (3x + 7)

Open the parentheses:

-x + 2 - 3x - 7

Combine like terms

-x - 3x + 2 - 7

= -4x - 5

Therefore, the result is -4x - 5.

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System A: (1, -1)

System B: No solution

Answer:

System A

The system has a unique solution: x=1, y=-1

System B

The system has no solution

Step-by-step explanation:

System A

Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:

5x + 3y = 2

-4x - 3y = -1

We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1

If x=1:

5+3y=2

3y=-3

y=-1

Since we have specific answers for x and y, we can say the system has a unique solution.

System B

If y is equal to both 5x+8 and 5x+5, that means

5x+8=5x+5

Subtracting 5x from both sides we get 8=5, which is illogical.

Therefore the system has no solution

Answer:

Step-by-step explanation:

The domain and the range of the transformed graph are given as follows:

The definitions of the domain and of the range of a function are given as follows:

After the reflection over the y-axis, the domain of the function is of:

[-2,5].

(as the reflection over the y-axis changes the signal of the x-values of the function).

After the translation of 3 units right, the domain of the function is of:

[1,8].

As the translation adds 3 to each value of x of the function.

After the vertical stretch by a factor of 2, the range of the function is of:

[-6,12].

As the stretch means that all the output values of the function are multiplied by 2.

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Answer: the answer is A,B,E

Step-by-step explanation:

Answer: The answer is (four/seven)

Yes, because it forms a straight line.

Arithmetic; it's a linear function.

Step-by-step explanation:

2023 Edgen

If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30

Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.

How to solve?

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

p = (0.27 + 0.33)/2 = 0.30

then the sample proportion would be 0.30

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The total change in the stock market from the beginning of the day to the end of the day is 89.75

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

At the beginning of the day, the stock market goes up 30 1/2 points.

At the end of the day, the stock market goes down 120 1/4 points.

The total change in the stock market from the beginning of the day to the end of the day.

= 120(1/4) - 30(1/2)

= 481/4 - 61/2

= 120.25 - 30.5

= 89.75

Thus,

The total change in the stock market from the beginning of the day to the end of the day is 89.75

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A student can take one of each subject in 40 different ways as calculated using the properties of permutation and combination..

So there are four separate math classes, five different science courses, and two different history courses.

There are now 4 ways to complete a math course.

There are 5 different ways to take science courses.

There are two ways to take a history course.

Total ways are now calculated as the product of the potential ways for each course, which equals 4 × 5 x 2 or 40 ways.

As a result, there are 40 possible combinations for three subjects.

In mathematics, a permutation of a set is, if the set also has an ordered structure, the rearranging of its members into a sequence or linear order. The technique of altering an ordered set's linear order is known as permutation.

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The distance between N and PS is 3.2.

What is the midpoint of the segment?

Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.

From the below figure,

N is the intersection of the red and blue circles.

I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).

Then the formula for the red circle is:

             (x-2)² + (y-4)² = 4.

The formula for the blue circle is

                  x² + y²- 16 = 0.

Solving for x and y yields intersections

               (0, 4) and (3.2, 2.4),

the first being S and the latter being N.

Hence, the distance between N and PS is 3.2.

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Answer:

  (2n -5)(3n -2)

Step-by-step explanation:

You want to factor 6n² -18n +10.

You want to start by finding factors of the product (6)(10), the first and last coefficients, that have a sum equal to -18, the linear term coefficient.

This sum is negative, but the product is positive, so both factors will be negative. Listing the smallest magnitude first, we have ...

  60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)

The sums of these pairs are -61, -32, -23, -19, -17, -16. This identifies the pair of interest as (-4)(-15).

From here, there are a couple of ways you can proceed. One is to write the linear term as a sum using these values:

  6n² -4n -15n +10

Now, you can factor by grouping:

  = (6n² -4n) -(15n -10)

  = 2n(3n -2) -5(3n -2)

  = (2n -5)(3n -2) . . . . . . . . the factorization you want

Another way you can do this is to write binomial factors using the leading coefficient for each one. The product of these must be divided by the leading coefficient for it to remain equal to the original trinomial.

  = (6n -4)(6n -15)/6

The denominator of 6 is used to reduce each of the binomial factors.

  [tex]=\dfrac{(6n-4)(6n-15)}{2\cdot3}=\dfrac{6n-4}{2}\cdot\dfrac{6n-15}{3}[/tex]

  = (3n -2)(2n -5) . . . . . . . the factorization you want

The area of the triangle in the image is 1/20 square centimeters.

This is a rather trivial problem.

On the image, we can see a triangle where the height and the base are known quantities.

Remember that for a triangle of height H and base B, the area is given by the formula:

A = B*H/2

Here we can see that:

H = (1/6) cm

B = (3/5) cm

Then we can replace these two fractions on the area formula, we will get:

A = (1/6 cm)*(3/5 cm)/2

A = (3/5*6 cm²)/2

A = (3/30*2 cm²)

A = (3/60 cm²) = (1/20 cm²)

That is the area of the triangle in the image.

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Answer:

6115

Explanation:

[tex]70000(1-0.15)^{15} \approx 6115[/tex]

No cup of ketchup remains.

Brown Sugar =1/4 C

Cider Vinegar = 1/2 C

Ground Cumin = 1tsp

Ketchup           = 2/3 C

Pepper             = 1tsp

Total Quantity of Ketchup =9 cups

1 batch of barbecue sauce =2/3 Cup

x batch of barbecue sauce =9 Cups

x batch of barbecue sauce = 9 Cups *1 batch of barbecue sauce

                                                               2/3 Cup

x batch of barbecue sauce =13[tex]\frac{1}2}[/tex] batches

we know that;

1 batch of barbecue sauce =2/3 Cup

Therefore,

The total number of ketchup Cups used = Total  batch of barbecue sauce *quantity for1 batch of barbecue sauce

               =       13[tex]\frac{1}2}[/tex] batches * 2/3 Cup

The total number of ketchup Cups used =  9 Cups  

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In the discrete distribution the probability that x equals 5 is 0.51

A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum

The summation of the discrete probabilities must be always equal 1,

The probaility of 2 is 0.16

The probaility of 6 is 0.30

The probaility of 8 is 0.21

We need to find The probaility of 5

To find the probaility of 5, we can subtract the probaility of all other numbers from 5.

Probability (X = 5) = 1 - (0.25+0.16+0.08) = 0.51

Therefore, in the discrete probability distribution the probability that x equals 5 is 0.51

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Given two calculations are different.

What is a square of a number?

The square of any number can be calculated by multiplying the number by itself twice.

Let 'a' be any number then the square of this number 'a' will be

                        a² = a × a

Now  - 3² = - (3) × (3)

               = -9  ----------(I)

and (-3)² = (-3) × (-3)

              = 9 ----------(II)

By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.

But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.

Hence, These two calculations are different.

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Answer:

I didn't know kindergardeners had Brainly.

Answer:f(4)=−2f(3)=(−2)∗(+640)=−1280

The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Vocabulary Use the terms divisor, dividend, quotient, and remainder.

Now,

If we have to find the divisor , then we can use the divide rule as;

⇒ Divisor = (Dividend - Remainder) / Quotient

Thus, The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

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The graph of the line that represents the given equation, 3x - 4y = 8, is shown below

From the question, we are to graph the line that represents the given equation.

The given equation is

3x - 4y = 8

To graph the line, we will determine x-intercept and y intercept of the line.

The x-intercept in the point where y equals zero on the line

and

The y-intercept in the point where x equals zero on the line

Determining the x-intercept

3x - 4y = 8

Set y = 0

3x - 4(0) = 8

3x = 8

x = 8/3

The x-intercept is (8/3, 0)

Determining the y-intercept

3x - 4y = 8

Set x = 0

3(0) - 4y = 8

-4y = 8

y = 8/-4

y = -2

The y-intercept is (0, -2)

Using the x-intercept and y-intercept, the graph of the line is shown below

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The statement that is used to prove the congruence of angles PTR and STQ is given by:

Lines PQ and RS intersect at an angle less than a right angle.

Congruent angles are angles that have the same measure.

One example of congruent angles is for vertical angles, as these angles are opposite by the same vertex in crossing segments, with an angle less than a right angle of 90º, and then these two angles will be congruent.

The common vertex in the segment given at the end of the answer is of:

T.

The vertical angles are both acute angles, that is, angle measures that are less than 90º, which is the reason for the correct statement.

The diagram is given by the image presented at the end of the answer.

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The proportionality constant from the original figure to the scaled copy is 2/9.

The constant of proportionality is the ratio between two given integers in what is known as a proportional relationship. The proportionality constant is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

We have here

To make a scaled duplicate, a four-sided figure is resized.

The proportionality constant from the original figure to the scaled copy is: 8/36 = 10/45 = 12/54 = 2/9.

As a result, the proportionality constant from the original figure to the scaled copy is 2/9.

Hence, the proportionality constant from the original figure to the scaled copy is 2/9.

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The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean

T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.

The z-core formula is:

Z₁=[tex]\frac{x-m}{s}[/tex]

Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.

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Complete question:

Which of the following is a fundamental difference between the t statistic and a z-score?

A) The t statistic uses the sample mean in place of the population mean

B) All of the choices are differences between t and z.

C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.

D) The t statistic uses the sample variance in place of the population variance.