which classification describes the following system of equations x=5 y=6 -x-y+z=0
?
A. inconsistent and dependent
B. consistent and dependent
C. consistent and independent
D. inconsistent and independent

ANSWER

25

EXPLANATION

We are given that p and q intersect to form <1 and <2 that are adjacent.

Let us represent that with a diagram:

We have that <1 and <2 are supplementary.

This means that they add up to 180 degrees.

So:

<1 + <2 = 180

4x - 3 + 3x + 8 = 180

Collect like terms:

4x + 3x + 5 = 180

7x = 180 - 5

7x = 175

x = 175 / 7

x = 25

That s the value of x for which <1 and <2 are supplementary.

The value of the unknown angle in the triangle is as follows;

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The external angle is ∠JRS.

Therefore, m∠S can be found as follows:

∠JRS = m∠S + m∠T

Hence,

m∠S  = 3x + 4

m∠T = 8x + 4

∠JRS = 140°

Hence,

140 = 3x + 4 + 8x + 4

140 = 3x + 8x + 4 + 4

140 = 11x + 8

140 - 8 = 11x

132 = 11x

x = 132 / 11

x = 12

Therefore,

m∠S  = 3(12) + 4 = 40 degrees.

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Answer: You have to use a calculator

Step-by-step explanation:

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Law of Cosines

Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:

We have a = 14, b = 9, θ = 71°. Substituting:

The length of CD is 13.96

Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.

To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.

The change in temperature is therefore:

= | temperature at 6 am - temperature at 6pm |

= | -5 - 7 |

= | - 12 °F|

The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.

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Step-by-step explanation:

12/4 = x/8

1st: cross multiply

96 = 4x

2nd: divide both sides by 4

96/4 = 4x/4

therefore x = 24

Answer:

A

Step-by-step explanation:

The range is the y values.  The y value is as low as -10 and as high as 8.

Answer:

11200

Step-by-step explanation:

If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

Consider the first odd integer as x

Then the next consecutive odd integer = x+2

The 6 times the second integer=  6(x+2)

= 6x+12

Sum of an integer and 6 times the next consecutive odd integer is 61

Then the equation will be

x + 6x+12 = 61

Add the like terms in the equation

(1+6)x + 12 = 61

7x +12 = 61

Move 12 to the right hand side of the equation

7x = 61-12

7x = 49

x = 49/7

x = 7

The second number is

x+2 = 7+2

= 9

Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

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Answer:

y = 2x

Step-by-step explanation:

The slope is 2.  Find a point on the line, to go back to the line, go up two and one to the right.  You will be back on the line.  This pattern repeats over and over and again.

The values of the vectors obtained from the vector diagram are;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

K = 2.5

A vector can be expressed as a line segment that has a direction.

The given parameters are;

The straight lines are; OAN, OMB, APB, and MPN

AN = 3•OA

The midpoint of OB = M

The vectors

[tex] \overrightarrow{OA} = a[/tex]

[tex] \overrightarrow{OB} = b[/tex]

[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]

From the question diagram, we have;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{AN} [/tex] = 2•a

[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]

[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]

[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]

[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

Given that we can write;

[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]

x × (-2•a + k•(-a + b)) = -3•a + 0.5•b

-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b

Which gives;

-2•x - k•x = -3...(1), and x•k = 0.5...(2)

From (2), x = 0.5÷k

From (1), -2×(0.5÷k) - k×(0.5÷k) = 3

-k - 0.5 = -3

-k = -3 + 0.5 = -2.5

k = 2.5

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The measure of the angles are 56.25° and 33.75°.

The value in a complementary angle is equal to 90°.

Let the first angle = x

The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x

Therefore, they'll be added together as follows:

x + 0.6x = 90°

1.6x = 90°

Divide

x = 90/1.6

x = 56.25

The second angle will be:

= 0.6x

Since x = 56.25, this will be used in the illustration below.

= 0.6x

= 0.6 × 56.25

x = 33.75

Therefore, the second angle is 33.75.

This illustrates the concept of complimentary angles.

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A

1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle

2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.

We can finally write

x+88 +50 +50 = 180

x +188 =180 subtract 188 from both sides

x= 180-188

x= -8

3) So x=-8 is the answer.

We will break apart the figure into triangles, rectangles, squares etc. We will then find area of each individual figure and sum it.

We can break apart the figure as shown below:

We will solve as follows:

The statement p is: Saturn is a planet.

The statement q is: Hong Kong is a city.

Now the first part of our composite proposition is:

This means that we have to negate the statement q, this would be: Hong Kong is not a city.

Now we make the disjunction between the statement p and the negation of q, then we have:

The second part of our composite porposition is:

This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:

Finally we make the disjunction between the statements discussed so far, hence the statament

means:

Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.

Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.

The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.

The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.

Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.

The length will then be L = 18(41/19) = 738/19 cm.

As a check, the area should be A = LW = (738/19)(41/19) = 30258 cm2

sorry if this isn't much help but i had a similar problem once and i used the same steps for your question

Answer:

12 m

Step-by-step explanation:

area = (side)²

(side)² = area

√(side)² = √(area)

side = √(area)

side = √(144 m²)

side = 12 m

Answer:

x = 10

Step-by-step explanation:

(5x + 3) and 53 are corresponding angles and are congruent , then

5x + 3 = 53 ( subtract 3 from both sides )

5x = 50 ( divide both sides by 5 )

x = 10

The value of 'x' is highlighted in the box

The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.

Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.

The sum of all the three sides of a triangle is equal to the perimeter of the triangle.

Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.

Therefore:

Side AB = side XY = 12 cm [corresponding congruent sides]

Side AC = side XZ = 14 cm [corresponding congruent sides]

Side BC = side YZ = 10 cm [corresponding congruent sides]

Find the perimeter of triangle ABC by adding all three triangles together.

Perimeter of triangle ABC = side AB + side AC + side BC

Perimeter of triangle ABC = 12 + 14 + 10

Perimeter of triangle ABC = 36 cm

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Answer:

I don't know men iam grade 7 student

The probability that a student walks to school is 7/15

The tree diagram represents the given parameter

From the tree diagram, we have the following parameters

P(Rain) = 2/5

P(Rain and walk) = 1/6

P(No rain) = 3/5

P(No rain and walk) = 2/3

The probability of walking to school is then calculated as

P = P(Rain) x P(Rain and walk) + P(No rain) x P(No rain and walk)

Substitute the known values in the above equation

So, we have

P = 2/5 x1/6 + 3/5 x 2/3

Evaluate the products

P = 1/15 + 6/15

Evaluate the sum

P = 7/15

Hence, the probability is 7/15

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Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in  6.34 days.

The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:

2 x 4 days = 8 days.

In general, we can use the growth formula:

P(t) = Po . 2^(t/Td)

Where:

P(t) = population at time t

Po = initial population

Td = doubling time

Parameters given:

Td = 4 days

P(t) = 3Po

Plug those parameters into the formula:

3 Po = Po . 2^(t/4)

3 = 2^(t/4)

log 3 = (t/4) log 2

t = 4 . log 3 / log 2 = 6.34 days.

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Answer:

You would each pay $6.42

Have a good one!

Answer:

Step-by-step explanation: it is true because when the numerator and denominator both are positive integers both are negative integers it is a positive rational number.

The location on the number line to plot the sum of the given number is shown in the image attached below.

In Mathematics, a number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Note: Each interval on this number line represents 1/10.

Next, we would add the given numbers together as follows:

Number = −1 3/10 + 2/5

Number = −13/10 + 2/5

Number = (-13 + 4)/10

Number = -9/10 or -0.9.

Therefore, the sum would be located between -4/5 and -1.

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Answer: [tex]-10 < x < 0, x > 12[/tex]

Step-by-step explanation:

[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].

Multiply by the decimal form of the percentage,

60 * 0.18 = 1.08

So the discount is for $1.08 off,

60 - 1.08 = 58.92

Giving a total of $58.92 after the discount is applied

Solution

- The question would like us to solve the following

- The solution is outlined below:

Final Answer

The answer is x < 33