What are the x coordinates of the solutions to the system of equations . - x + y = 2 y = x^2 - 4

Answer: 6.5 hours on Friday

Step-by-step explanation:

Friday = x hours

Saturday = x-3 hours

Total hours in 2 days = 10 hours

x+x-3=10

2x-3=10

2x=10+3=13

x=13/2=6.5 hours

x-3=6.5-3=3.5 hours

So, Friday is 6.5 hours and Saturday is 3.5 hours

Answer:

P(both students passed the exam) = 0.61948

Step-by-step explanation:

From the given information:

P(both students passed the exam) = P(both are science students or both are art major students or one is from each group)

= P (both are science students) + P(both are art students) + P(one from each group)

where;

P (both are science students) = (50/100) (0.9) × (44/99) × (0.9) = 0.18

P(both students are art) = (50/100) (0.7) × (49/99) 0.7 = 0.1213

P(one of the student are from each group) = (50/100) (0.9) ×(50/99) (0.7) + (50/100) (0.7)× (50/99)(0.9) =0.3182

P(both students passed the exam) = 0.18 + 0.1213 + 0.3182

P(both students passed the exam) = 0.61948

Answer:

2

Step-by-step explanation:

Velocity/Time, or 8/4 equals 2.

Hope this helps!

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.

To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.

If 2 hours of studying = 44 marks

If 3 hours of studying = 66 marks

If 4 hours of studying = 88 marks

Then total sum of hours of studying = 9 hours

9 hours of studying = Sum of all marks

                                 = 44 + 66 + 88

                                 = 198

1 hour of studying = 198/9

                              = 22 marks

So, the test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

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Answer:

6q or 6 * q

Step-by-step explanation:

As you do not know what the value of the variable q is, you are essentially changing it from word form to expression form.

"product" in math means multiply, so you are multiplying 6 with q.

6q is your answer.

~

Answer:

6+9=15

6×9=54

Step-by-step explanation:

didnt know which one you wanted but hope this helps

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

The amount of total dinner bill, including tip is found to be $92.40.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole.

When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. To indicate that a number is a percentage, use the sign %.

So,

Amount of tip:

15 % of 82.95 = 15*82.95 / 100

15 % of 82.95 = 12.4425

Total cost =  82.95 + 12.4425

Total cost =  95.3925

Total cost =  $92.40

Thus, the amount of total dinner bill, including tip is found to be $92.40.

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Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

Step-by-step explanation:

If you want to find out how many times larger something is than something else, you have to divide. We will set up a problem that looks like this:

\(\frac{2.1*10^8}{4.2*10^2}\)

Diving 2.1 by 4.2 gives us .5; to divide the exponents, we remember that if we divide like bases we have to subtract the exponents. 10 is our base in both cases, so 8 - 2 gives us 6, resulting in:

\(.5*10^6\)

However, this isn't in scientific notation. We need to move the decimal one more place to the right, which in trn reduces the exponent by 1:

\(5*10^5\)

Answer:

so where are the 3 consecutive numbers?

Answer:g(x) = f(x) + 1.5

Step-by-step explanation:g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

After using the deductive reasoning the procedure always produces the number 8.

Procedure:

Let the number be x.

We have to add 5 to the number x.

So the expression is x + 5.

We have to multiply the sum by 3.

Now the expression is 3(x + 5).

Now we have to subtract 7.

Now the expression is 3(x + 5) - 7.

Then we have to decrease this difference by the triple of the original number.

The triple of original number is 3x.

Now the expression is {3(x + 5) - 7} - 3x.

Now solving this expression

= {3(x + 5) - 7} - 3x.

First simplify the bracket

= 3x + 15 - 7 - 3x.

= 8

Now we can se that the after following the whole procedure the answer is 8.

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Answer:

50

Step-by-step explanation:

35/n x 100 = 70%

÷100 both sides

35/n = 0.70

x n both sides

35 = 0.70n

÷0.70 both sides

50 = n

Thus, the number you're after is 50

(n is a variable - representing an unknown number or value)

Check:

35/50 x 100 = 70%

Hope this helps!

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.

Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.

It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.

The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.

Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.

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Answer:

The airplane is approximately 159.892 miles away from the airport.

Step-by-step explanation:

Let consider the following convention, north is represented by +y axis and east is represented in +x axis. Then, we represented each displacement by vectors:

i) An airplane flies 225 miles south

\(\vec r_{A} = - 225\,\hat{j}\,\,\,[mi]\) (Eq. 1)

ii) Then 175 miles northwest

\(\vec r_{B} = 175\cdot \cos 135^{\circ}\,\hat{i} + 175\cdot \sin 135^{\circ}\,\hat{j}\,\,\,[mi]\) (Eq. 2)

The resulting vector position is the sum of the two vectors above:

\(\vec r = \vec r_{A}+\vec r_{B}\) (Eq. 3)

\(\vec r = -225\,\hat{j}+(175\cdot \cos 135^{\circ}\,\hat{i}+175\cdot \sin 135^{\circ}\,\hat{j})\)  \([mi]\)

\(\vec r = 175\cdot \cos 135^{\circ}\,\hat{i}+(-225+175\cdot \sin 135^{\circ})\,\hat{j}\)  \([mi]\)

\(\vec r = -123.744\,\hat{i} -101.256\,\hat{j}\)

Lastly, we find the distance of the airplane from the airport by Pythagorean Theorem:

\(\|\vec r\| = \sqrt{(-123.744\,mi)^{2}+(-101.256\,mi)^{2}}\) (Eq. 4)

\(\|\vec r\| \approx 159.892\,mi\)

The airplane is approximately 159.892 miles away from the airport.

Answer:

A

Step-by-step explanation:

G is a similar angle to L. Tell me if it helps.

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

a) The initial deposit in the account is given as follows: 1,287.39 euros.

b) The interest rate of the account is given as follows: 3%.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

Considering the balances after 5 and 6 years, the interest rate is obtained as follows:

r = 1524.60/1480.50 - 1

r = 0.03.

Considering the balance after 5 years, the initial deposit is obtained as follows:

P(1 + 0.03 x 5) = 1480.5

P = 1480.5/1.15

P = 1,287.39 euros.

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Answer:

a₂ = -3

a₃  = -1

Step-by-step explanation:

We have to  insert two arithmetic means between -5 and 1

Let a₁ and b₂ be the two arithmetic means between -5 and 1

-5, a₂, a₃, 1

Here,

We know that the nth term of an Arithmetic sequence

aₙ = a₁ + (n-1)d

a₄ = -5 + (4-1)d

1 = -5 + 3d    

1  + 5 = 3d

3d = 6

Dividing both sides by 2

d = 2

Also

a₂ = a₁ + (2-1)d

a₂ = -5 + d

a₂ = -5 + 2          ∵ d = 2

a₂  = -3

a₃ = a₁ + (3-1)d

a₃  = -5 + 2d

a₃  = -5 + 2(2)   ∵ d = 2

a₃  = -5 + 4

a₃  = -1

Thus,

a₂ = -3

a₃  = -1

Thus, the sequence becomes:

-5, -3, -3, 1

Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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-3/8 ÷ -1/4 = -3/8 *-4/1= 12/8 = 1 4/8, 1 1/2

Using a system of equations, the amount of solution a and b required to make the required gallons of the solution are 29.41 and 20.59 respectively.

Let :

a + b = 50 - - - - (1)

0.24a + 0.41b = 50 × 0.31

0.24a + 0.41b = 15.5 - - - - (2)

From (1) :

a = 50 - b - - - - (3)

Substituting (3) into (2)

0.24(50 - b) + 0.41b = 15.5

12 - 0.24b + 0.41b = 15.5

0.17b = 15.5 - 12

0.17b = 3.5

b = 20.588

From (3) :

a = 50 - 20.588

a = 29.412

Therefore, about 29.41 gallons of solution a and 20.59 gallons of solution b is required.

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