How many solutions does each system of equations have? Part A: {3x−y=13y+3=9x

Answer:

24

Step-by-step explanation:

If 4/6 of the items are jackets and the rest are gloves, this means 1 - 4/6 = 2/6 = 1/3 of the items are gloves in Saginaw Elementary School's lost and found.

We do 72 total items × 1/3 items are gloves = 24 items in the lost and found are gloves

Answer:

y= -5x

Step-by-step explanation:

The formula for direct variation is y=kx

Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.

Let the numbers be x and y where x is larger value and y is smaller number.

According to ques,

x - y =88

and we need to make product of numbers i.e 'xy' minimum.

So we can take x = 88 + y ------(2)

substituting value of x in xy, we get

(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.

derivative of  (1) is 2y + 88

Equating it to zero, we get

2y + 88 = 0

subtracting 88 from both sides, we get

2y = -88

Dividing 2 from both sides, we get

y = -44 ------(3)

Substituting value of y from (3) in (2), we get

x = 88 - 44

x = 44

So, we get value of x as 44 and y as -44 to get their product as minimum.

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Answer:

3

Step-by-step explanation:

The factorial of a number n is the product of all the positive integers from 1 to n. In other words, n! = 1 * 2 * 3 * ... * n. For example, the factorial of 5 is 5! = 1 * 2 * 3 * 4 * 5 = 120.

In this case, we are asked to find the value of the expression 10!/(4!7!). To do this, we first need to evaluate the factorials in the numerator and denominator of the expression. Since 10! = 1 * 2 * 3 * ... * 10, we have:

10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 3628800

Similarly, since 4! = 1 * 2 * 3 * 4 and 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7, we have:

4! = 1 * 2 * 3 * 4 = 24

7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040

Now that we have evaluated the factorials in the expression, we can plug these values into the expression and evaluate it:

10!/(4!7!) = 3628800 / (24 * 5040) = 3628800 / 120960 = 3

Therefore, the value of the expression 10!/(4!7!) is 3.

Note: It is important to remember that the factorial of 0 is defined to be 1, so 0! = 1. This means that any expression involving 0! can be simplified by replacing 0! with 1. For example, the expression 10!/(4!7!0!) can be simplified as follows:

10!/(4!7!0!) = 10!/(4!7!1) = 10!/(4!7) = 10!/(24 * 7) = 10!/168 = 3628800/168 = 3

This is the same result we obtained above using the factorials of 10, 4, and 7.

The value of the given expression is 30.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 10!/(4!7!).

Now, (10×9×8×7!)/(4!7!)

= (10×9×8)/(4×3×2×1)

= 5×3×2

= 30

Therefore, the value of the given expression is 30.

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The following, find 2 solutions and 2 non solutions is [tex]x=\frac{30-5 y}{2}[/tex]

What is non solutions?

Ideal solutions are those that follow Raoult's law throughout the whole concentration range. A solution is said to as a non-ideal solution if it violates Raoult's law.

[tex]$$2 x+5 y=30$$[/tex]

[tex]Move $5 y$ to the right side[/tex]

[tex]$$2 x=30-5 y$$[/tex]

[tex]Divide both sides by 2[/tex]

[tex]$$\frac{2 x}{2}=\frac{30}{2}-\frac{5 y}{2}$$Simplify$$x=\frac{30-5 y}{2}$$[/tex]

Non solutions, in the plural, refer to anything that falls short of offering a fix for a problem. These batteries also lose their charge, rendering them useless for solving the more significant issue of storing and utilizing renewable energy.

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The value of x is 27 in the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

We need to find the value of x.

The given two angles are (4x+7) and 5(x-4).

The two angles are opposite angles so the two angles are equal.

Let us equate 4(x+7) and 5(x-4).

4x+7=5(x-4).

Apply distributive property on RHS

4x+7=5x-20

4x-5x=-20-7

-x=-27

Multiply both sides by minus

x=27.

Hence, the value of x is 27.

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The example of rational function is option(1) which is f(x)=3x²+1 over x-1

What is Rational Function ?

Hence, the example of rational function is option(1) which is f(x)=3x²+1 over x-1.

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Answer: Exact Form: s = 5/4

Decimal Form: s = 1.25

Mixed Number Form: s = 1 1/4

Answer:

-1 /3

Step-by-step explanation:

To get from one point to the next, go DOWN1 and OVER3.

DOWN1 and OVER3 is the slope -1/3

From B to C it looks like DOWN2 and OVER6. That is -2/6. But that can be reduced to -1/3. So its the same.



The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.

The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).

The slope of the graph gives the unit rate, which is calculated as m = y/x.

Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.

Therefore:

Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.

Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.

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The resistance of wire to the nearest hundredth of one mile of the wire with mentioned details is 2.59 ohm.

Firstly we will convert length of wire to feet. As per the known information, 1 mile is 5280 feet. Moreover, as known resistance and length are directly proportional to each other.

Resistance 1/Resistance 2 = length 1/length 2

0.65/Resistance 2 = 1325/5280

Rewriting the equation according to length 2

Resistance 2 = (0.65×5280)/1325

Performing multiplication on Right Hand Side of the equation

Resistance 2 = 3432/1325

Performing division on Right Hand Side of the equation

Resistance 2 = 2.59 ohm

The resistance of wire is 2.59 ohm.

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Answer: $892.44

Step-by-step explanation:

Take 27 times 18.66 = $503.82

Then take 34 times 11.43 = $388.62

Then add them to find total

503.82 + 388.62 = $892.44

The owner only owe $892.44

A triangle has three angles that measure 16˚, 38˚ and 126˚ will lead to

There are an infinite number of triangles produced when no side is specified.

The three angles produce an unlimited number of distinct triangles if side lengths are not provided.

The option that offered just angles—namely, angles of 16˚, 38˚ and 126˚—and no sides—meets the requirement for the production of an infinite number of triangle sides.

When there are options have sides or a side is provided, but not in accordance with that, to form an infinite number of triangles.

This condition forms infinite number of triangles

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Answer:

C) Infinite (More than one)

Step-by-step explanation:

The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

Given that,

A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.

We have to calculate the anticipated total number of heads produced by this method.

We know that,

Either head or tail will appear when a coin is tossed.

The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."

So,

1/2n=N

Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

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The equation used to represent the situation:

Cost per pound = Total Cost of Turkey / Number of Pounds

A formula known as an equation uses the equals sign to express how two expressions are equal. The meanings of the word equation and its translations into other languages might vary slightly; Finding the values of the variables that cause the equality to be true is the first step in solving an equation with variables.

Quantity = 19 pounds

Total Cost = $25.65

Now to calculate the cost of Turkey per pound, we can use the following equation:

Cost of Turkey per pound = Total Cost / Quantity of Pounds

Cost per pound = 25.65 / 19

Therefore, the cost of turkey per pound = $1.35

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Answer:

Step-by-step explanation:

The given sequence is an arithmetic sequence with a common difference of 4. The 77th term of the sequence is the 77th term of the arithmetic sequence, which is given by the formula:

a_n = a_1 + (n - 1) * d

where a_n is the nth term of the sequence, a_1 is the first term of the sequence, and d is the common difference. Substituting the values for a_1, n, and d into this formula, we get:

a_77 = -8 + (77 - 1) * 4

= -8 + 76 * 4

= -8 + 304

= 296

Therefore, the 77th term of the sequence is 296.

∇f(x, y) of the function  f(x, y) = 1 / squareroot (x^2 + y^2) is

Given function is f (x, y) = 1 / squareroot (x ^ 2 + y ^ 2)

∇f(x, y) that is the gradient of the function is ([tex]f_{x}[/tex], [tex]f_{y}[/tex])

[tex]f_{x}[/tex] = partial differentiation of the given function with respect to x

= - x / ( (x ^ 2 + y ^ 2) ^ 3/2)

[tex]f_{y}[/tex] = partial differentiation of the given function with respect to y

= - y / ( (x ^ 2 + y ^ 2) ^ 3/2)

Hence, the ∇f(x, y), the gradient of the function is:

(- x / ( (x ^ 2 + y ^ 2) ^ 3/2) , - y / ( (x ^ 2 + y ^ 2) ^ 3/2))

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Answer:

t = 39

Step-by-step explanation:

t - 52 = - 13 ( isolate t by adding 52 to both sides )

t = - 13 + 52 = 39

the integer from the solution set S that makes the equation true is 39

Answer:

[tex] \sf \: t = 39[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The equation is,

→ t - 52 = -13

Then the value of t will be,

→ t - 52 = -13

→ t = -13 + 52

→ [ t = 39 ]

Hence, the value of t is 39.

The orientation factor in a chemical reaction relates the frequency factor to the collision factor and depends on the extent of complexity of the reactants in a reaction.

Does the orientation factor depend on temperature?

The direction of the collision between the chlorine atoms and the ozone determines the pace of reaction; if the direction is incorrect, no reaction takes place. The right orientation will allow for response. The direction of collisions is independent of temperature.

According to the Collision Theory, molecules must collide with sufficient activation energy to break and re-form existing bonds, as well as with favorable spatial orientation, in order for a chemical reaction to occur.

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The equation of the line n parallel to line m will be y = 3/2x - 9. The correct option is A.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lime m perpendicular to the line y = -2/3x + 6 will be,

y = 3/2x + c

The line n is parallel to n and passes through the point (4,-3),

y = 3/2x + c

-3 = (3/2 x 4)  + c

-3 = 6 + c

c = -9

The equation of line n will be written as,

y = 3/2x - 9

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-480 ÷ 8 = -60

2x = -120

-20 × 3 = -60

(2 × 3) × (-5 × 2) = -60

The statement which is true for the inequality will be equal to 9 > -5, so 9 is located to the right of -5 on a horizontal number line.

A straight line of numbers is shown visually as a number line. This line is employed to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

As per the given inequalities given in the question,

1.

-10 > -15, so -10 is located to the left of -15 on a horizontal number line.

The statement is wrong because -10 is located on the right side of -15

2.

8 > -13, so 8 is located to the left of -13 on a horizontal number line.

The statement is wrong because 8 is located on the right side of -13.

3.

9 > -5, so 9 is located to the right of -5 on a horizontal number line.

This statement is true, that 9 is located to the right of -5.

4.

-6 < 1, so -6 is located below 1 on a vertical number line.

This statement is true, that -6 is located to the below of -5.

5.

-14 > 7, so -14 is located below 7 on a vertical number line.

This statement is false.

6.

11 < -13, so 11 is located to the right of -13 on a horizontal number line.

This statement is also false.

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Answer:

Step-by-step explanation:

The best bank depends on the amount that Gerard will deposit. He can open an account with My bank and receive $100, or he can open with New bank and deposit lets say $5000 and he would receive an additional $250 because of the 5% bonus. It depends on the amount that Gerard is putting into the bank account when he opens it.

We can conclude that it is more likely that a child has side effects compared to an adult

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The given information is expressed as

Side effect no side effect total

Adult 7 43 50

Children 22 28 50

Total 29 71 100

Probability is expressed as

Number of favorable outcomes/number of total outcomes

For the probability that an adult has side effects,

Total number of outcomes = 50

Number of favorable outcomes = 7

Probability that an adult has side effects = 7/50 = 0.14

For the probability that a child has side effects,

Total number of outcomes = 50

Number of favorable outcomes = 22

Probability that an adult has side effects = 22/50 = 0.44

Therefore, it is more likely that a child has side effects compared to an adult

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a^45d^9

To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:

(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n

Answer: 1,961,256a³⁰d¹⁴

Step-by-step explanation:

[tex]\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^{k-1}x^{n-k+1}y^{k-1}\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial[/tex]

                                        [tex](a^3+d)^{24}[/tex]

[tex]The \ fifteenth\ term=C^{15-1}_ {24}(a^3)^{24-15+1}d^{15-1}\\\\The \ fifteenth\ term=C^{14}_{24}(a^3)^{10}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{(24-14)!14!} a^{30}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{10!14!}a^{30}d^{14} \\\\The \ fifteenth\ term=1,961,256 a^{30}d^{14}[/tex]

189.55

...

.............

...

The right-angled triangle have angle B = 40°, side c = 20.9 and b = 13.4 approximately to the nearest tenth.

We shall use the trigonometric ratios of sine and cosine of the angle 50° to get the length of the sides and apply the rule of the sum of interior angles of a triangle to get the angle B.

sin50° = opposite/hypotenuse

sin50° = 16/c

c = 16/(sin50°) {by cross multiplication}

c = 20.9

cos50° = adjacent/hypotenuse

cos50° = b/20.9 {by cross multiplication}

b = 20.9 × cos50°

b = 13.4

The sum of interior angles of a triangle is equal to 180° so;

angle B = 180° - (90° + 50°)

angle B = 180° - 140°

angle B = 40°

Therefore, by application of trigonometric ratios sine and cosine, we have the sides of the right-angled triangle b = 13.4, c = 20.9, and the angle B = 40°.

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Let x is average for rest of seven test. Then average for remaining test is x= 2.27

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The middle point of the set of values is the mean. It represents the mean of the data set's values. In statistics, the centre number, also known as the mean, is referred to as the average.

We want the TOTAL average to equal 94

4/9 of the 5 scores have an average of 178

Let x = average of the 5 remaining test, which is worth 5/9 of the total average.

We get: 94 = (4/9)(178) + (5/59)(x)

94=712/9+59x/9

846=712+59x

846-712=59x

134=59x

134/59=x

Solve: x = 2.27

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