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The number of real solutions of the system are 2 if y=x²-3, y = -2x +4

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4). There is often only one solution to a system of linear equations, however it is possible for there to be infinite or no solutions (parallel lines) on occasion (same line).

Given,

y=x²-3 -----(1)

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

Solving equations 1 and 2, we get

x²-3=-2x +4

x²+2x-3-4=0

x²+2x-7=0

We have to solve by using quadratic formula,

x= (-b±√b²-4ac)/2a

x= (-2±√2²-4(1)(-7))/2(1)

x= (-2±√4+28)/2

x= (-2±√32)/2

x= (-2±4√2)/2

x= -1±2√2

x= -1-2√2, -1+2√2

Thus, the system has two solutions.

Therefore, the number of real solutions of the system are 2.

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Answer:

the approximate sample proportion is 87%, which means that 13% of the people surveyed do not participate in the city’s recycling program.

Divide the base for that period by the appropriate commission rate to determine your commission for that period. Mark earns more money.Since $1680 > $1080, Mark earns more.

This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.

Mark: $24/h; 150% OT

Calculate Mark's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.5

Mark's OT wage is 1.5*$24 = $36

Mark worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Joe: 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Mark earns more.

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Answer:

Step-by-step explanation:

[tex]x^{2} -6x[/tex]

Mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is 4.

As per the question the data given is 3, 5, 7, 4, 2, 1, 4, 3, 4.

Now we have to determine the mode of the given distribution.

Mode: A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

The simple way to determine the mode is the most repeated data.

The number or the value which is "repeated more number of times compared to the other values".

From the data given:

3 repeated two times.

5 repeated one time.

7 repeated one time.

4 repeated three times.

2 repeated one time.

1 repeated one time.

Therefore the value of mode is 4.

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All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Congruent Figures :

Those figures which covers each other/one another exactly then they are congruent Figures.

There are 4 ways by which we can prove any 2 triangles as congruent :

If they are having -

Three pairs of side are equal then the triangles are congruent.

If any 2 pairs of angles and 1 side are equal then the triangles are congruent.

If any two pairs of sides and the included angle are equal then the triangles are congruent.

If any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.

So, all three pairs of corresponding sides are equal then are congruent to each other.

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The given equation A) 5x -2 + x = x - 4 and B) 5x + x = x - 4 are not equivalent.

The term equation in math refers the mathematical statement that is made up of two expressions connected by an equal sign.

Here we have given that the tow equations are

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

And we need to find if they are equivalent or not.

While we looking into the given question, we have given the following equations,

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

In order to find if they are equivalent or not, we have to simplify each of then then we get,

=> A) 6x - 2 = x - 4

=> A) 6x - 2 - x + 4

=> A = 5x + 2

Now, we have to do the same to simplify the equation (B), then we get

=> B) 6x = x - 4

=>  B = 6x - x + 4

=> B = 5x + 4

Now, we compare the two solved equation,

=> A = B

=> 5x + 2 = 5x + 4

Here the variable part is equal but the constant value is not same.

Therefore, we have identified the the two equation are not equivalent.

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199 feet in meters

1 foot = 0.3048 meters

[tex]0.3048(meters)\times199(feet)[/tex]

[tex]=\fbox{60.66}[/tex]

The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.

The Multiplicative Inverse of the number 6 is "1/6" .

The Inverse (Multiplicative) of the number is the number that when multiplied by the original number gives the product as 1 .

which means the product of the number and its multiplicative inverse is 1 .

the number is given to be 6 .

So , let the multiplicative inverse of 6 be = x .

So , According to Definition of Multiplicative Inverse ,

we can write : x * 6 = 1

dividing both side by "6" .

we get ;

x = 1/6 .

Therefore , the multiplicative inverse is 6 .

The given question is incomplete , the complete question is

What is the Multiplicative Inverse of 6 ?

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The polynomial function p(x) = 5x³ - 5x² - 10x have zeros of 0, -1 and 2

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial.

The polynomial function given is

p(x) = 5x³ - 5x² - 10x

The zeros of the function are 0, 2, -1

To test the zeros if they are the roots of the polynomial

p(0) = 5(0)³ - 5(0)² - 10(0)

p(0) = 0

p(2) = 5(2)³ - 5(2)² - 10(2)

p(2) = 0

p(-1) = 5(-1)³ - 5(-1)² - 10(-1)

p(-1) = 0

The zeros are 0, -1, and 2 to the polynomial

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On a frictionless horizontal table, the rocket-powered hockey puck moves at an angle of 61.9° above the horizontal in 3 seconds.

The significance of non-zero digits is constant. Between any two significant digits, there can be no zeros. Only the final or trailing zeros in the decimal section are important. Between any two non-zero digits, all zeros are important. Seven significant digits are seen in, for instance, 108.0097. There is never any significance for any zeros that are both to the right and left of the decimal point and a digit that is not zero.

given

Then, using the formula that relates the tangent of angle, vertical component of velocity, and horizontal component of velocity to find the direction in which the puck is moving.

Displacement is the smallest distance between the two points.

The vector representation of velocity is,

s = 1/2at2

= 1 .80 m

The puck moves at an angle 61.9° above the horizontal.

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The variance of 2, 4, 6, 8, 10 is 8.

To calculate the variance of a set of numbers, you first need to calculate the mean of the set. The mean of 2, 4, 6, 8, 10 is 6. Then, for each number in the set, you need to calculate the difference between that number and the mean, and square the result. Finally, you need to sum those squared differences and divide by the number of items in the set.

Here's the calculation:

(2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2 = (-4)^2 + (-2)^2 + 0^2 + (2)^2 + (4)^2 = 16 + 4 + 0 + 4 + 16 = 40

40 / 5 = 8

So, the variance of 2, 4, 6, 8, 10 is 8.

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

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Answer:

98 laps

Step-by-step explanation:

(5x 14) + (2 x 14)

70+ 28 =98

The value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation 3x²+2kx+27=0

Here, a=3,b=2k,c=27

It is given that roots are real and equal.

b²-4ac=0

(2k)²-4(3)(27)=0

4k²-324=0

4k²=324

Divide both sides by 4

k²=81

Take square root on both sides

k=±9

Hence, the value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

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The formula of commutative property of addition is a + b = b + a and the formula of commutative property of multiplication is a × b = b ×  a.

The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The commutative property of addition states that a + b = b + a

The commutative property of multiplication states that a × b = b ×  a.

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The required length of licorice for $1.80 is given as 18 in.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
The price of licorice is proportional to its length. It costs $0.50 to buy 5 in; it is uncertain how much licorice you can get for $1.80.
Let the price be y and the length be x,
according to the quesiton,
y = kx,
put y = 0.50 and x = 5
0.50 = 5k
k = 0.1

Now

y = 0.1 x
for
y = 1.8
1.8 = 0.1x
x = 18

Thus, the length of licorice necessary for $1.80 is specified as 18 in.

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The measure of the angle m∠COD is 20 degrees

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

The measures of the angles:

m∠BOD = 46 and m∠BOC = 26.

The measure of the angle m∠COD is the difference between of the above angles

Using the above as a guide, we have the following:

Measure of the angle m∠COD = Difference of angles m∠BOD and m∠BOC

Mathematically, this is represented as

Measure of the angle m∠COD =  m∠BOD - m∠BOC

Substitute the known values in the above equation, so, we have the following representation

Measure of the angle m∠COD =  46 - 26

Evaluate the difference

Measure of the angle m∠COD =  20

Hence, the angle is 20 degrees

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Answer:

40 minutes

Step-by-step explanation:

rate = distance/time = miles/hr

rate = 240 mi/2 hr = 120 mi/hr

time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes

(0.67 hr)(60 min/hr) = 40 minutes

Answer:

approximately 1.732

Step-by-step explanation:

To solve this expression, we need to start by performing the operations inside the parentheses first. The square root of 8 is equal to 2, so 3 minus 2 is equal to 1. Then, we can divide 1 by the square root of 3, which is equal to approximately 1.732. Therefore, the expression 3 minus square root of eight divided by square root of 3 is equal to approximately 1.732.

Always begin by separating the variable y from the inequality's left side is the first step to graph an inequality.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

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The measure of the angle ∠GKJ, m∠GKJ, at the circumference of the circle H, which is subtends the same arc GJ as the angle ∠GHJ at the center of the circle is 27°

An arc of a circle is a part of the circle's circumference.

The measure of angle ∠GHJ, m∠GHJ = 54°

The measure of angle ∠GKJ, m∠GKJ = Required

Please find attached a possible drawing of the circle H created with MS Word and based on a similar question posted online

The circle, Angle at the Center Theorem states that the angle subtended at the center by arc is twice the angle subtended by the arc at the circumference of the circle.

The question indicates that the angle subtended by the arc GJ at the center of the circle, ∠GHJ = 2 × The angle subtended by the arc GJ at the circumference, ∠GJK

Therefore;

m∠GHJ = 2 × m∠GKJ

54° = 2 × m∠GKJ

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Answer: see below

Step-by-step explanation:

The domain of a graph consists of all the input values shown on the x-axis

We want to find the left-most x value and the right-most x value.

-8, 3

since there is a hole at the point where x=3 we will use a paratensesis

D:xE[-8,3)

Therefore, the Z set represents the all integers numbers .

Describe integer.

An integer is a whole number, not a fraction, that can be negative, positive, or zero. The numerals  set of 5, 1, 5, 8, 97, and 3, 043 are a few examples. Non-integer numbers include 1.43, 1 3/4, 3.14, and other numbers.

According to the given question:

The set of integers represented here by Z is..., 2,..., 1, 0, 1, 2,... Q stands for the collection of rational numbers (the set of all possible fractions, including the integers).

The set of real numbers is designated as R. The group of complex numbers is designated as C.

Therefore, the Z set represents the all integers numbers .

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Yes,  All equilateral triangles are similar to each other.

No,  All equilateral triangles are not congruent to each other.

The fact that every angle in an equilateral triangle is equal to 60 degrees is one of its characteristics.

According to the AAA Triangle Similarity Postulate, two triangles are similar  if all of their angles are identical to their corresponding angles in another triangle.

According to the AAA Postulate, all equilateral triangles are similar because their angles are all 60 degrees.

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

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We calculated standard deviation 4 for the given set of numbers.

In the statistics, standard deviation is an estimation that implies how far each data value apart from the mean value. A high standard deviation indicates that all data are dispersed around the mean. And a low score of standard deviation implies data values are close enough in relation to the mean.

Let, X be the list of data value, X² be the square of the data value.

    X          X²

   2           4

   4           16

  6            36

  8            64

  10         100

  12         144

  14        196

we add all the data value and get ∑X = 56

We add all the squared value and get ∑X² = 560

Standard deviation is calculated by using the formula

SD =

√ [∑X²/N - (∑X/N) ²]

where N is the number of data present N= 7

SD = √[560/7 - (56/7)²]

     = 4

Hence, calculated standard deviation is 4

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62,800,000 is the product of (6.28 x 10^3) x 10,000.

It refers to the result of one or more multiplications.

Given number is (6.28 x 10^3) x 10,000.

6.28 x 10^3 =  6280

Therefore, 6280 x 10,000 = 628,000,00

Hence, the product of (6.28 x 10^3) x 10,000 is  628,000,00.

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The value of a,b,c,d, and e is 45, 60, 58, 77, and 135 respectively, required to complete the two-way table.

A two-way table shows the connections between two sets of category data visually. Labels are positioned at the top and left sides of the table, which has rows and columns.

The sums for each row are displayed to the right, while the sums for each column are displayed at the bottom. 

We must create a two-way table based on the issue to ascertain the worth of each letter.

| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

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| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

Given that:  

Angle CBD=6x-40

Angle BFH=4x

From the given diagram, angle CBD=angle BFH ("corresponding angles")

Therefore 6x-40=4x,

                  6x-4x=40,

                   2x=40,

                    x=20

now Angle CBD= 6(20)-40

                          = 80