How many solutions does the system of linear equations have?
y = 4x - 7
y = x – 3
Choose 1 answer:
Exactly one solution
No solutions
Infinitely many solutions

Answer:

I think A is the answer.

U're welcome amigo.

The difference between points C and D is √289 units.

What is Distance formula?

The distance formula is a mathematical formula used to determine the distance between two points in a plane. The formula is:

d = √((x2 - x1)² + (y2 - y1)²)

"C" and "D" are points in a two-dimensional coordinate system. C is represented by the coordinates (-1, 11) and D is represented by the coordinates (7, -4).

The difference between these two points is the distance between them, which can be calculated using the distance formula:

√((x2 - x1)² + (y2 - y1)²)

Where x1, y1 are the coordinates of point C and x2, y2 are the coordinates of point D.

Substituting the values, we get:

√((7 - (-1))² + (-4 - 11)²) = √((8)² + (-15)²) = √(64 + 225) = √289

Hence, the difference between point C and D is √289 units.

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Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.

A mathematical equation is a formula that connects two statements using the equal sign (=) to signify equivalence. A mathematical statement demonstrating the equality of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two phrases on either side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.

given

per mile the cost is $0.85

Base fee is 14.95

0.85x+14.95= 125.15

0.85x=125.15 - 14.95

0.85x = 110 . 92

x= 110 . 92 / 0.85

x= 130. 49

Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.

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The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

a line equation that is perpendicular to the line 2xy=5 and passes through the point (6, 4)

The slope of the given equation 2x-y=5 is first determined.

The line's equation is y=mx+b. where'm' represents the slope

Hence, The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

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If Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour,  the standard deviation is 2.191.

Using this formula to find the Standard deviation

Standard deviation = √ Sample size  × Estimated drivers × (1 - Estimated drivers)

Let plug in the formula

Standard deviation = √ 30 × 0.20 × (1- 0.20)

Standard deviation = √ 30 × 0.20 × 0.80

Standard deviation = √ 4.8

Standard deviation = 2.191

Therefore we can conclude that the standard deviation is 2.191.

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Answer:

The total cost of their stay at the StarWatch camping site will be £108. This includes the special offer of 5 nights for the price of 4.

Lila and Wassim have saved £130 by the time of their holiday. This means they have saved £22 extra.

a)  Her down payment algebraically  is 0.15y (b). number of monthly payments must Linda make12 months (c) The total amount of the monthly payments algebraically is  12x (d) The  first term a

and the common ratio d  a1 = 0.15y, d = x  (e)  The total amount Linda pays for the washer and dryer on the installment plan algebraically is 12x + 0.15y (e) the finance charge algebraically (12x + 0.15y) - y = 12x - 0.85y

The given parameters that will help us get the solutions are

If y = cost of washer and dryer

x = cost for one month.

Down payment = 0.15y

Numbers of months = 12months

Amount of monthly payment = 12x

First term and common ratio = a1 = 0.15y and d = x

Total amount for washer and dryer 12x + 0.15y

Finance charge

(12x + 0.15y) - y

12x - 0.85y

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Complete question:

2. Linda bought a washer and dryer from Millpage Laundry Supplies for y dollars. She signed an

installment agreement requiring a 15% down payment and monthly payments of x dollars for one

year.

a. Express her down payment algebraically.

b. How many monthly payments must Linda make?

c. Express the total amount of the monthly payments algebraically.

d. If Linda models her payment plan as an arithmetic sequence, give the first term a

and the common ratio d

e. Express the total amount Linda pays for the washer and dryer on the installment plan

algebraically.

f. Express the finance charge algebraically.

Answer:

(x+2)(4x-1)

For this problem, use the FOIL (first, outside, inside, last) method

You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.

(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)

Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.

4x^2+7x-2

The statement (c) describes that the graph of f is shifted 5 units down to create the graph of g. The solution has been obtained using the concept of vertical translation.

What is translation?

Translation is the act of moving a shape or a figure from one position to another. It is classified into two types:

Now, for a function f(x) we define a vertical translation of N units as:

g(x) = f(x) + N

If N is positive, the translation is upwards.

if N is negative, the translation is downwards.

We are given g(x) = f(x) - 5

This shows that N is negative and therefore, there is translation of 5 units downwards.

Hence, the graph of f is shifted 5 units down to create

the graph of g.

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     (x-2)² + ( y + 1)² = 34 is the equation of the circle in standard form.

What is the short definition of a circle?

To put it simply, a circle is a spherical shape without any edges or line segments. In terms of geometry, it has the shape of a closed curve.

                                             The circle's points are set apart from the center by a predetermined amount.

The endpoints of the diameter (7,−4) and (−3,2)

the center of the circle is the midpoint of the diameter.

So, the coordinates of the center  

                      (h,k) = ( 7 + (-3)/2  , -4 +2/2)

                                = ( 4/2 , -1 )

                                 = ( 2 , -1 )

the radius of the circle is just half of the length of the diameter.

So,                 r = 1/2√(-3 -7 )² + ( 2 - (-4))²

                        = 1/2√(10)²  + ( 2 +4 )²

                        = 1/2√100 + 36

                        = 1/2√136

                         = √136/2

                        = 2√34/2

                         = √34

substitute the values of h, k, and r into the standard equation of the circle

                       ( x-h)² + ( y-k)² = r²

                      ( x - 2)² + ( y -(-1))² = (√34)²

                       (x-2)² + ( y + 1)² = 34

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Step-by-step explanation:

x = my number

3(x + 21)

multiply sum of 21 and my number by 3

=

(2/3)x + 84

84 more than 2/3 of my number

3(x + 21) = (2/3)x + 84

9(x + 21) = 2x + 3×84 = 2x + 252

9x + 189 = 2x + 252

7x + 189 = 252

7x = 63

x = 9

my number is 9.

Answer:

≈[tex]4.4117647059\times10^{10}[/tex] computations in five minutes.

Step-by-step explanation:

[tex]\frac{5*60}{6.8\cdot10^{-9}}[/tex] = [tex]4.4117647059\times10^{10}[/tex].

Proof in the image.

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In  linear equation, Length of each piece of fabric is 3/2  yards.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Number of pieces of fabric = 3

Total length of a fabric  = 2 1/4 yards

                                     = 9/4 yards

Therefore,

Length of each piece of fabric = 9/4 ÷ 3

                                             = 3/4 yards

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The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is, [tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

[tex]\int\limits^a_b f({x} )\, dx[/tex] = f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]\int\limits^_[/tex] ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Integrate the given iterated integral.

We get:

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) ([tex]\int\limits^5_0dt[/tex] ) ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [t][tex]0 to s^{5}[/tex] ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [tex](s^{5} -0)[/tex] ds

= [tex]\int\limits^1_0[/tex] [tex]s^{5}[/tex]cos ([tex]s^{6}[/tex] )ds

Then,

[tex]s^{6}[/tex] = t       when s = 0

[tex]\frac{dt}{ds}[/tex] = 6[tex]s^{5}[/tex]         t = 0  

[tex]\frac{dt}{6}[/tex] = [tex]s^{5}[/tex]  ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] cos(t) [tex]\frac{dt}{6}[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [tex]\int\limits^1_0[/tex] cos(t) dt

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [sin(t)][tex]0to1[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [ sin(1) - sin(0) ]

[tex]I[/tex] = [tex]\frac{sin(1)}{6}[/tex]

[tex]I[/tex] = 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

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Part 1: Where x is: time in hours. Where y is: distance in miles.

Part 2: The table is filled for the values of time and distance.

Part 3: y/x is fixed equation is proportional.

Total distance refers to the actual travel distance between the origin and destination locations of the material.

The formula for the distance is:

Distance = speed * time

Part 1:

The equation formed for the stated condition is:

y = 3x.

Where x is: time in hours.

Where y is: distance in miles.

Part 2: The table is filled for the values of time and distance.

Part 3:

For the equation.

y = 3x.

x = 1, y = 3 : y/x = 3

x = 2, y = 6 ; y/x = 3

As, y/x is fixed equation is proportional.

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The complete question with table is attached.

Answer:

A) 1 to 2

Step-by-step explanation:

Total number of people: 623

Successes: 216

Failures: 623 - 216 = 407

Ratio of successes to failure = 216/407

Since 216 is approximately half of 407, the ratio is approximately 1/2.

Answer: A) 1 to 2

The value of GL is 161.We can find by using supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees. For example angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.There are a total of two supplementary quantities and their units.

The sum of two angles is equal to 180° then they are supplementary angles. Each of the angles is said to be a supplement of another angle. Hence we can determine the supplement of an angle by subtracting it from 180°.

Now

According to supplementary angles

GL + LK =180

GL         =180- LK

GL         = 180 -19

GL      = 161

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The code is 4321.

A = 4

B = 3

C = 2

D = 1

14) Probability that exactly 5 of the students will graduate is 0.1636.

15) Probability that atleast 8 of the students will graduate is 0.2405.

We have , In a college,

The freshmen graduate enters = 64%

Probability of sucess , p = 64% = 0.64

Probability of failure , q = 1 - 0.64 = 0.36

Randomly selected entering = 10 , i.e, n = 10.

This follows a Binomial probability distribution with the parameters, n = 10 and p = 0.64.

Using Binomial probability formula,

P(X = x) = ⁿCₖ pᵏ (1 - p)ⁿ⁻ᵏ

(14) Probability that exactly 5 of the students will graduate = P(x = 5),

P( x = 5) = ¹⁰C ₅ (0.64⁵) (0.36⁵)

= 0.1636

15) Probability that at least 8 of the students will graduate, P(x ≥8) = P(X= 8) + P(X= 9) + P(X= 10)

= ¹⁰C₈ 0.64⁸ 0.36² + ¹⁰C₉ 0.64⁹ 0.36¹ + ¹⁰C₁₀ 0.64¹⁰ 0.36⁰ = 0.2405

Hence, the required probabilities are 0.1636 and 0.2405.

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Answer:

30%

Step-by-step explanation:

3 pizzas = 30 slices.  count yellow 1+6+2 = 9

9/30 = 30%

Answer:

d

Step-by-step explanation:

According to the information, the sets of ingredients that have a proportional relationship with the original recipe are: option A, C and D.

To check the proportional relationship of the ingredients with the recipe we must carry out the following procedure.

Option A.

First, we need to establish how many times 6 is in 12 because this recipe includes 6 parts oil and the original recipe includes 12 parts oil.

Once we identify this number, we must divide the amounts of the original recipe by 2 to identify if the other values are correct.

In accordance with the above, option 1 would be proportional to the main recipe. For the other options we must perform the same procedure:

In the case of case C. we identify that 24 is twice 12, so we would have to multiply each ingredient by 2 to check the proportional relationship

In the last case (option D), we identify that the proportion is 3/4 with respect to the original recipe, so we must carry out the same procedure keeping this proportion in mind.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Attached image

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Answer:

Step-by-step explanation:

9 7/12 - 5 4/12 = 4 3/12

Answer:

The answer is 20

Answer: 254 in^2

Step-by-step explanation:

The total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination is given by (n^3 + 3n^2)/3.

The LU decomposition version of Gauss elimination involves 3 phases which are :

The flops in decomposition phase is (n^3)/3, forward-substitution phase is n^2 and back-substitution phase is 2n^2. By adding all the flops for these 3 disinct phases we get (n^3 + 3n^2)/3 as total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination.

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Answer:

m∠1 = 64

m∠2 = 117

m∠3 = 117

Step-by-step explanation:

m∠1 = 64

m∠2 = x+64 = 180

        = x = 117

m∠2 = 117

m∠3 = 117

The vertices of the image after transformation is K(5,-2), L(-1,3) and M(4,-5)

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

According to the given question,

with respect to the mirror

the vertices of the image of the triangle is

J (2,-5) ---------->! (5,2)

K (-1, -3) --------> K'(-1,3 )

L (-4, 5) --------->"(4,-5 )

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