how many solutions does y = 3x - 5 and 6x - 2y = 10 has?
A. 1 solution
B. 2 solutions
C. No solutions
D. Infinitely many solutions

ANSWER:

x-intercept = 5

y-intercept = 2

On substituting x = 0, we'll get y intercept

2(0) + 5y = 10

5y = 10

y= 10/5

y = 2

Similarly, on substituting y= 0 ,we'll get x-intercept

2x+5(0) = 10

2x= 10

x=10/2

x=5

I hope this helps you...

Answer:

Step-by-step explanation:

Y-intercept is on the Y-axis . So, value of x = 0

2*0 + 5y = 10

         5y = 10

           y = 10/5

y = 2

y-intercept = 2

X-intercept is on the X-axis. Value of y= 0

2x + 0 = 10

2x = 10

x =10/2

x = 5

x-intercept = 5

5.25 + 13

= 18.25

Xavier rode his bicycle for a total of 18.25mi in one week.

9514 1404 393

Answer:

  c.  x = 7-t; y = -1/(t -7)

Step-by-step explanation:

To find the parametric equation for x, use the equation for t and solve for x.

  t = 7-x

  x = 7 -t . . . . . . add x-t to both sides

__

To find the parametric equation for y, substitute the equation for x.

  y = 1/x

  y = 1/(7-t)

To make this match the available choices, we need to multiply numerator and denominator by -1.

  y = -1/(t -7)

The parametric equations are ...

  x = 7 -t; y = -1/(t -7) . . . . . . matches choice C

Answer: it is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

m² +2d + 8 +d = 5² + 2*4 + 8 + 4

                       = 25 + 8 + 8 + 4

                       = 45

Answer:

150 miles

Step-by-step explanation:

60*2.5=150

To show that a tree has at most   \(n/2\)many vertices that have degree 3 or higher, we will use proof by contradiction.

Assume that there exists a tree with more than \(n/2\) vertices that have a degree of 3 or higher. Let V be the set of vertices in the tree, and let \(V_3\) be the set of vertices in V that have a degree 3 or higher. Let k be the number of vertices in\(V_3.\)

Since the tree has n vertices, there are n-k vertices in V that have degree 1 or 2. Since each vertex in the tree has degree at least 1, we have \(n-k ≤ n\), which implies that k ≥ 0.

Now, consider the sum of degrees of all vertices in the tree. By definition of a tree, this sum is twice the number of edges in the tree, which is n-1. Therefore, we have:

\(2(n-1) = Σ_degrees\)

where \(Σ_degrees\) is the sum of degrees of all vertices in the tree.

Let d_i be the degree of the i-th vertex in V_3. Since each vertex in V_3 has degree 3 or higher, we have d_i ≥ 3 for all i. Therefore, the sum of degrees of vertices in V_3 is at least 3k.

Let m be the number of vertices in V that have degree 1 or 2. Let d_j be the degree of the j-th vertex in V that has degree 1 or 2. Since each vertex in V that has degree 1 or 2 has degree at most 2, we have d_j ≤ 2 for all j. Therefore, the sum of degrees of vertices in V that have degree 1 or 2 is at most 2m.

Since V is the disjoint union of \(V_3\) and the set of vertices in V that have degree 1 or 2, we have:

\(Σ_degrees = Σ_{i=1}^k d_i + Σ_{j=1}^m d_j\)

Combining the inequalities \(3k ≤ Σ_{i=1}^k d_i and Σ_{j=1}^m d_j ≤ 2m, we get:\\Σ_degrees ≥ 3k + Σ_{j=1}^m d_j ≥ 3k\)

where the last inequality follows from for all j.

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Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

Given data :

60 mph for 3 hours = 180 miles

55 mph for 4 hours = 220 miles

Total distance covered = 220 + 180

Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

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The volume of this figure is equal to 1,099 m³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have the following:

Volume, V = 3.14 × 5² × 12

Volume, V = 942 m³.

Volume of a hemisphere = 2/3 × πr³

Volume of a hemisphere = 2/3 × 3.14 × 5³

Volume of a hemisphere = 157 m³.

Volume of figure = Volume of cylinder + Volume of hemisphere

Volume of figure = 942 + 157

Volume of figure = 1,099 m³.

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Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These sources help gather accurate information about TV viewership

Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These devices track viewership and other data for TV programming and provide valuable insights for advertisers and media companies. Additionally, Nielsen also collects data through diaries, where households manually record their TV viewing habits. All of this data helps to inform important decisions in the media industry.

Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These sources help gather accurate information about TV viewership, allowing for the analysis of audience data in terms of demographics and other relevant factors.

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Answer:

Option: A is the correct answer A.

Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other.

Step-by-step explanation:

We know that a perpendicular line segment is formed with the help of paper folding in following steps: Draw a line segment on a paper. Fold the paper so that the endpoints of the line segment are on each other. The crease that is formed on the paper and pass through the line segment is the perpendicular line to the given line segment. The point on the line segment is the mid point of the line segment. Hence, option: A is the correct answer.

Option: B is the correct answer i.e. "Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other."

Thus, Option: B is the correct answer i.e. "Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other."

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The length of the string is 12.35 cm if the 126 g ball is tied to a string. It is pulled to an angle of 8.00 ∘ and released to swing as a pendulum.

Simple Harmonic Motion is described as a motion in which the restoring force is proportionate to the body's displacement from its mean position.

As we know, the period T of a simple pendulum of length L is:

\(\rm T = 2\pi \sqrt {\dfrac{L}{g}}\)

T = 12/17 = 0.705 sec

\(\rm 0.705 = 2\pi \sqrt {\dfrac{L}{9.81}}\)

Squaring both sides and solving:

We get:

L = 0.123 m  or

L = 12.35 cm

Thus, the length of the string is 12.35 cm if the 126 g ball is tied to a string. It is pulled to an angle of 8.00 ∘ and released to swing as a pendulum.

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Answer:

350,391 is the answer

Answer:

C).

Step-by-step explanation:

One of the points on the graph that the path of bike b crosses is (6,60).

When you divide this to find the unit rate you get 10/1 therefore the equation of bike b= y+10X

Answer:

A

Step-by-step explanation:

use both points to find the slope using the equation

y2-y1/x2-x1, so , -2-4/2-0 = -6/2 = -3. slope or m = -3

then the y int can be any y point, so either -2 or 4. in this case they used 4.

Answer:

Step-by-step explanation:

-4x + 5y = 7

 8x - 10y = -15

-8x + 10y = 14

 8x - 10y = -15

0 ≠ -1

no solution

a) \(m=\frac{-12-4}{5-(-7)}=\frac{-16}{12}=\boxed{-\frac{4}{3}}\)

b) We know the equation is \(y=-\frac{4}{3}x+b\), where b is a constant. If we substitute in the coordinates of point a, we get that:

\(4=-\frac{4}{3}(-7)+b\\4=\frac{28}{3}+b\\b=-\frac{16}{3}\)

This means the y-intercept is \(\boxed{\left(0, -\frac{16}{3} \right)}\)

To find the x-intercept, we can set the equation equal to 0 and solve for x.

\(0=-\frac{4}{3}x-\frac{16}{3}\\\frac{16}{3}=-\frac{4}{3}x\\x=-4\)

So, the x-intercept is \(\boxed{(-4, 0)}\)

c) \(\left(\frac{-7+5}{2}, \frac{4-12}{2} \right)=\boxed{(-1, -4)}\)

d) \(ab=\sqrt{(-7-5)^{2}+(-12-4)^{2}}=\boxed{20}\)

e) The perpendicular bisector must pass through the midpoint, (-1, 4), and have a slope that is the negative reciprocal (so in this case, 3/4). Substituting into point-slope form,

\(y-4=\frac{3}{4}(x+1)\\y-4=\frac{3}{4}x+\frac{3}{4}\\\boxed{y=\frac{3}{4}x+\frac{19}{4}}\)

f) If ab is a diameter of said circle, this means it is centered at the midpoint, (-1, 4), and has a radius of 20/2=10. This means the equation is

\(\boxed{(x+1)^{2}+(y-4)^{2}=100}\)

Answer:

To get the answer of this, we need to multiply 2/3 by 90 centimeters to get 2/3s of the total length. Sometimes it is easier to just think, "what is a third of 90?" and then double it, but the foolproof way to get the answer is to multiply the fraction by 90/1.

2/3 * 90/1 = 180/3. Divide out and the answer is:

60 centimeters

Step-by-step explanation:

22! / 20! × 2!

\(21 \times 11 = 231 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

The elements of Z3[x]/(x^2 - x) are of the form ax + b that is multiplication table, where a and b are elements of Z3.

The multiplication table is:

  | 0   1   x   1+x   2   2+x

-------------------------------

0 | 0   0   0    0   0   0

1 | 0   1   x   1+x  2  2+x

x | 0   x  2x  2+x   x  1+2x

1+x| 0  1+x 2+x   2  2+x  x

2 | 0   2   x   2+x  1  1+x

2+x| 0  2+x 1+2x  x  1+x 2

Note that in this table, we use the fact that x^2 - x = 0, which implies that x^2 = x.

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The interconversion of states of matter involves processes such as melting, vaporization, sublimation, condensation, freezing, and solidification.

The three states of matter are solid, liquid, and gas. These states can be interchanged through physical processes such as heating, cooling, and changes in pressure.

Solid to Liquid: This process is called melting or fusion. When a solid is heated, it gains energy, and the intermolecular forces holding the particles together weaken. As a result, the solid particles start to move more freely, and the substance transitions into the liquid state.

Liquid to Gas: This process is called vaporization or evaporation. When a liquid is heated, its particles gain energy, and their kinetic energy increases. Eventually, some particles gain enough energy to overcome the intermolecular forces holding them together and escape into the surrounding space as gas particles.

Solid to Gas: This process is called sublimation. Some substances have a direct transition from the solid state to the gas state without passing through the liquid state. When heated, the solid particles gain enough energy to break free from the solid structure and directly form a gas.

Gas to Liquid: This process is called condensation. When a gas is cooled, its particles lose energy, and their kinetic energy decreases. As a result, the gas particles slow down, come closer together, and form a liquid. This can be observed, for example, when water vapor in the air condenses into liquid water droplets on a cold surface.

Liquid to Solid: This process is called freezing or solidification. When a liquid is cooled, its particles lose energy, and their kinetic energy decreases. The particles slow down and come closer together, forming a regular arrangement, which results in the formation of a solid.

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

It takes 14 pints of blueberries to make 4 jars of blueberry jam, hence the number of pins for one jar is:

14/4 = 3.5.

It takes 3.5 pins to make 1 jar of blueberry jam.

For 10 jars:

10 x 3.5 = 35 pins.

It takes 35 pins to make 10 jars of blueberry jam.

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Answer:

0.21ft/min

Step-by-step explanation:

   \(\sf Volume \ at \ given \ time = \dfrac{dV}{dt}= 20 \ cubic \ feet /min\)

             h = d

             h = 2r

             \(\sf r = \dfrac{h}{2}\)

            Volume of heap = (1/3) πr²h

                     \(\sf V =\dfrac{1}{3}\pi r^2h\\\\V =\dfrac{1}{3}\pi (\frac{h}{2})^2h\\\\V =\dfrac{1}{3}\pi \dfrac{h^2}{4}*h\\\\V=\dfrac{1}{12}\pi h^3\)

Take derivative w.r.t time,

                     \(\sf \dfrac{dV}{dt}=\dfrac{1}{12}\pi * 3h^2 \dfrac{dh}{dt}\)

                     h = 11 ft

                     \(\sf 20 = \dfrac{1}{12}\pi *3*11*11*\dfrac{dh}{dt}\\\\20=\dfrac{121}{4}\pi \dfrac{dh}{dt}\\\\\)

               \(\sf \dfrac{20*4}{121*\pi }=\dfrac{dh}{dt}\\\\ \dfrac{80}{120*3.14}=\dfrac{dh}{dt}\)

                        \(\sf \dfrac{dh}{dt}=0.21\)

             The height is increasing at the rate of 0.21 ft/min

For #8, two lines in the same plan that never intersect and are equidistant at all points are parallel lines.

The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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The constant of proportionality is the cost per pound of oranges, and it is 3.47 dollars per pound.

A general proportional relationship can be written as:

y = k*x

Where k is the constant of proportionality.

In this case, we can define the variables:

x = number of pounds oranges.

y = cost of these oranges.

Here we know that the cost of 6 pounds of oranges is $20.82, replacing these values we will get:

$20.82 = k*6 lb

$20.82/6lb = k

$3.47 per lb = k

The constant of proportionality is 3.47 dollars per pound.

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Answer:

74 and 740

Step-by-step explanation:

1. 74

2. 740

7.4×10=74.0

7.4×100=740.0

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Answer:

Step-by-step explanation:

Line 1

Line 2

The system is inconsistent if slopes are same, so we should have:

answer p=15

step by step explanation