Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.

x – y = 7

3x – 2y = 8

Step 1: x = y + 7
Step 2: 3(y + 7) – 2y = 8
Step 3: 3y + 7 – 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1
In which step did Ernesto make the first error?

Answer:

WATER IS not wet

Step-by-step explanation:

Water is NOT wet by itself, however it makes other materials wet when it sticks to the surface of them.

Answer:

Water isn't wet by itself, but it makes other materials wet when it sticks to the surface of them. Wetness is the ability of a liquid to adhere to the surface of a solid, so when we say that something is wet, we mean that the liquid is sticking to the surface of a material.

Number of ways to choose the 5 pints of ice-cream from the given 8-varieties of ice-cream is equal to 56.

As given in the question,

Total varieties of ice-cream available in the ice-cream shop is equal to 8

Number of pints of ice-cream to choose =  5 pints

Number of ways to choose the 5 pints of ice-cream out of 8 varieties is given by :

= ⁸C₅

= ( 8! ) / ( 5! ) ( 8 - 5 )!

= ( 8 × 7 × 6 × 5! ) / ( 5! × 3! )

= ( 8 × 7 × 6 ) / ( 3 × 2 × 1)

= 56 ways

Therefore, number of ways to choose the 5 pints of ice-cream from the given 8-varieties of ice-cream is equal to 56.

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Answer:

A

Step-by-step explanation:

( 2, -5 )

( -2, -5)

Hope this helps dude

Answer:

A is your answer :)

Step-by-step explanation:

The solution to the system of equations is (1, 8).

From the question, we have the following parameters that can be used in our computation:

y-x=7 y=3x+5

To find the solution to the system of equations y - x = 7 and y = 3x + 5, we can substitute the second equation into the first equation to eliminate y:

y - x = 7

y = 3x + 5

Substituting y = 3x + 5 into the first equation:

3x + 5 - x = 7

2x = 2

x = 1

Now that we have found x = 1, we can substitute it back into either equation to find y:

y = 3x + 5

y = 3 * 1 + 5

y = 8

So the solution to the system is (x, y) = (1, 8).

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Evaluating the line integral integrate C 2xds gives 16/3

We can break the given curve into two parts as mentioned in the question: the parabola and the horizontal line segment. Let's integrate over each part separately.

For the parabola, we can parameterize the curve as x = t and y = t^2 where t goes from 0 to 2. Using the formula for line integrals, we get:

integrate (2t)(sqrt(1 + 4t^2)) dt from 0 to 2

This can be solved using u-substitution (u = 1 + 4t^2) and simplifying the resulting integral to get:

(4sqrt(17) + 2sqrt(5))/3

For the horizontal line segment, we can parameterize the curve as x = t and y = 4 where t goes from 2 to 4. Using the formula for line integrals, we get:

integrate 2 dt from 2 to 4

This simplifies to 4.

Adding the results of the two integrals, we get the final answer:

16/3

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Answer:

B, C, D

Step-by-step explanation:

edge 2023

The equation which is equivalent to 60% of 25 is x = 0.6 * 25

An equation is used to show the relationship between variables, numbers.

Let x represent the value of 60% of 25. Hence:

x = 60% of 25

x = 0.6 * 25

Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25

x/25 = 60/100

6/10 = x/25

Answer:

The answer is 8.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

distance over time equals speed

.

Answer:

  (b)  x = 5

Step-by-step explanation:

You want to know the value of x if the acute and obtuse angles of an isosceles trapezoid are marked 51° and (28x-11)°.

The acute and obtuse angles in an isosceles trapezoid are supplementary, so ...

  51° +(28x -11)° = 180°

  28x = 140 . . . . . . . . . divide by °, subtract 40

  x = 5 . . . . . . . . . . . divide by 28

The value of x is 5.

__

Additional comment

None of the other answer choices makes any sense, as the angle cannot be greater than 180°. 28x less than 180° means x < 6.4, so there is only one viable answer choice.

None of the answers with decimal values can work, since multiplying by 28 will result in a number with a decimal fraction. The sum of that and other integers cannot be 180°.

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The sales tax on this printer is $20.94

A sales tax is a consumption tax imposed by the government on the sale of goods and services.

Given that, the price of a printer is $349.00 having a 6% sales tax.

Sales tax = 6% of $349.00

$349.00 x 0.06 = $20.94

Hence, the sales tax on this printer is $20.94

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Answer:

x= -2

Step-by-step explanation:

since we know what y equals we fill it into the second equation

3(x+4)= -2x+2

3x+12=-2x+2

   -12.      -12

3x=-2x-10

+2x +2x

5x=-10

/5. /5

x= -2

hopes this helps please mark brainliest

The sale price of the shirt after a 20% discount is $13.60.

To find the sale price of the shirt, we need to multiply the original price by the percentage discount and then subtract the result from the original price.

The percentage discount is 20%, or 0.2 as a decimal.

So, the discount amount is:

0.2 x $17 = $3.40

Therefore, the sale price of the shirt is:

$17 - $3.40 = $13.60

Thus, the sale price of the shirt after a 20% discount is $13.60.

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The point estimate for the proportion is 0.049

From the question, we have the following parameters that can be used in our computation:

(0.022, 0.076)

The midpoint of the confidence interval is a good estimate for the population proportion.

The midpoint can be calculated as:

midpoint = (upper limit + lower limit) / 2

Substituting the given values, we get:

midpoint = (0.076 + 0.022) / 2

midpoint = 0.049

Hence, the point estimate for the proportion of people who don't show up for their flights is 0.049, which is option (b).

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it could most likely be 40%? im not sure tho hope this helps

Answer:

The image is inserted below.

Step-by-step explanation:

The blue line is the line that passes through the point (1,-1) which is marked as A on the graph.

The green line is the new line you need to graph that is parallel to the original line and has a slope of 1.

Answer:

30.00

Step-by-step explanation:

Answer:

1

9

3 red

2 blue

5 green

Total

3

+

2

+

5

=

10

Probability of blue is

2

10

~~~~~~~~~~~~~~~~~~~~~~~

Second condition:

3 red

1 blue

5 green

New total

3

+

1

+

5

=

9

Probability of green is

5

9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Total probability of selecting this path is:

2

10

×

5

9

=

2

9

×

5

10

=

2

9

×

1

2

=

1

9

Answer: The area of a triangle is 1036.8 square units.

To find the area of a triangle, we can use the formula

Area = (1/2) * base * height

In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:

Area = (1/2) * (32 + 64) * 21.6

Area = (1/2) * 96 * 21.6

Area = 1036.8

Therefore, the area of the triangle is 1036.8 square units.

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Answer:

number 1 is 74

Step-by-step explanation:

number 4 is 100

number 2 is I think either 160 or 32

an I'm sorry I don't know what number 3 is but I hoped I helped

Answer:

36 miles.......................

Answer:

7

Step-by-step explanation:

Answer:

A. 136 sq. cm.

Step-by-step explanation:

First find the area of the rectangle:

16 times 7 is 112

13-7 is 6

16-8 is 8

The formula for the area of a triangle is ab/2

thus:

6 times 8 is 48/2

Which is 24

Add 112 with 24

Which is 136

Thus the answer is A. 136 sq. cm.

Hope this helps!

The probability that the insurance representative will sell a policy to three out of four prospective clients is 0.0256.

The probability that the insurance representative sells to more than two prospective clients is 0.0272.

To calculate the probability that the insurance representative will sell a policy to a specific number of prospective clients out of four, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = \((n C k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of exactly k successes (selling a policy) out of n trials (appointments).

(n C k) represents the combination or "n choose k" which calculates the number of ways to choose k successes out of n trials.

p is the probability of success on a single trial (probability of making a sale).

(1 - p) is the probability of failure on a single trial (probability of not making a sale).

Using this formula, we can calculate the probability of selling a policy to three out of four prospective clients.

Probability of selling a policy to three clients:

P(X = 3) = (4 C 3) * (0.20)^3 * (1 - 0.20)^(4 - 3)

Calculating:

P(X = 3) = 4 * 0.008 * 0.80

P(X = 3) = 0.0256

To calculate the probability that she sells to more than two clients, we need to sum the probabilities of selling to three clients and selling to all four clients.

Probability of selling to more than two clients:

P(X > 2) = P(X = 3) + P(X = 4)

Substituting the values:

P(X > 2) = \(0.0256 + (4 C 4) * (0.20)^4 * (1 - 0.20)^(4 - 4)\)

Calculating:

P(X > 2) = 0.0256 + 1 × 0.0016 × 1

P(X > 2) = 0.0272

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The rate of $18 an hour will be approximately  $157248  for a year .

In order to find how much $18 an hour is in a year,

We need to know how many hours are present in a year.

The number of weeks in 1 year is = 52 weeks ;

and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .

So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .

We get that 1 year consists of 8736 hours ,

Now , multiplying the number of hours by $18 ,

We get ,

⇒ 8736 × 18 = $157248 .

Therefore , $18 an hour will be $157248 for a year .

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The biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

A biconditional statement is defined as a statement that combines both an converse and conditional statement.

It is written in the "if and only if" from.

It is a statement that states a condition depends on another being and vice versa.

From the statement given;

"if a polygon has four sides, then it is a quadrilateral

The biconditional statement is ;

Polygon has four sides if and only if it is a quadrilateral.

Thus, the biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

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The equation to represent the number of pages Jesse has read y =30x, where x represent the number of days and y represents the number of pages.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The steepness of straight line is known as slope. The equation of a straight line that passes through the origin is y = mx.

Given that Jesse can read 30 pages in a day.

In x days, he can read (30 × x) = 30x pages.

The equation of line that represents the number of pages Jesse has read is

y = 30x.

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Answer:

20 ,70

Step-by-step explanation:

Complementary angles sum up to 90

2x + 4x + 30 = 90

     6x  + 30 = 90

Subtract 30 from both sides

6x = 90 - 30

6x = 60

x = 60/6

x = 10

2x = 2*10 = 20

4x +30 = 4*10 +30 = 40 +30 = 70

Answer:

20 and 70

Step-by-step explanation:

2x + 4x + 30 =90

6x=90-30

6x=60

x=60/6x

x=10

so, 2x= 20 and 4x=40

20,70