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3 years ago

Which system of inequalities has a lot of solution?

Mathematics

2 answers:

Naddik [55]3 years ago

7 0

Answer:

(a) 2x + 4y ≥ 3 ; 2x + 4y ≤ 3

Step-by-step explanation:

When inequalities are involved, the resulting solution is generally a region since for a value of x, we have y greater than or less than a particular value and vice versa.

When a system of equations with inequalities are solved, the intersection of all the equations in the system is the solution.

In the first option, we see that the both equations have 2x+4y=3 as common. So, it is the solution of the first system of inequalities.

Similarly, the solution of second system of inequalities is 2x+4y>3 and the third system is none since they don't intersect at all.

Here, 2x+4y > 3 denotes a region and 2x+4y=3 is the equation of a straight line.

Hence the first system has a solution that is a line.

nydimaria [60]3 years ago

4 0

Answer:

(for question 7: Its the last one)

(for question 8: its the first one)

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At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed st

EastWind [94]

Answer:

C. Left-handed: 48, Right-handed: 504

D. Left-handed: 30, Right-handed: 315

Step-by-step explanation:

We are given that there are 58 left-handed students and 609 right-handed students at East Middle School and these numbers of students are proportional to the number of left and right handed students at East Middle School.

Given the above information, we are are to determine which two options could be the the numbers of left-handed and right-handed students at West Junior High.

Ratio of right handed to left handed students at East Middle School = $\frac{609}{58} = 10.5$

Checking for ratios of the given options:

A. $\frac{483}{42} =11.5$

B. $\frac{378}{28} =13.5$

C. $\frac{504}{48} =10.5$

D. $\frac{560}{56} =10$

E. $\frac{315}{30} =10.5$

Therefore, the possible numbers of left-handed and right-handed students at West Junior High could be C. Left-handed: 48, Right-handed: 504 and D. Left-handed: 30, Right-handed: 315.

7 0

2 years ago

Read 2 more answers

Help asap pleeeas!

olga_2 [115]

The answer to this question is C.2 I think

6 0

2 years ago

Read 2 more answers

The polygons below are similar. Find the value of y. 4.5 12 16 Guess: 16

elena55 [62]

I believe its 4.5
I could be wrong though

8 0

2 years ago

Whats the surface area of the prism below,and please explain how you got the answer :)

nevsk [136]

Answer: 480 units^2

IN DEPTH EXPLANATION TO HELP YOU FOR FUTURE PROBLEMS:

Front:
b*h/2 = sa
12*5/2 = 30
Front = 30 units^2

Back:
b*h/2 = sa
12*5/2 = 30
Back = 30 units^2

Right:
w*l = sa
14*13 = 182 units^2
Right: 182 units*2
(figures out the length by using
pythagorean theorem)

Left:
w*l = sa
5*14 = 70 units^2
Left: 70 units^2

Bottom:
w*l = sa
12*14 = 168 units^2

ADD ALL THE UNITS:
168 + 70 + 182 + 30 + 30 = 480

4 0

3 years ago

Given: Tangents LA and LB, m∠AOB=110°. Find: m∠ALO.

Yuri [45]

Answer:

The measure of angle ALO = 35°

Step-by-step explanation:

* Lets talk about the tangents to a circle drawn from a point

outside the circle:

- They are equal in length

- They are perpendicular to the radii at the point of tang-ency

- If we join the points of tang-ency withe the center of the circle

and join the outside point with center of the circle, we

formed two congruent triangles

* Now lets check our problem

- AL and LB are two tangents to the circle O ant points A and B

∴ LA = LB ⇒ (1)

- OA and OB are radii in circle O

∴ OA = OB ⇒ (2)

∴ OA ⊥ AL and OB ⊥ BL ⇒ radius and tangent

∴ m∠OAL = 90° , m∠OBL = 90

∴ m∠OAL = m∠OBL ⇒ (3)

* From (1) , (2) , (3)

- The two triangles LAO and LBO are congruent ⇒ SAS

- SAS is one case of congruence

∵ The lengths of two sides and the measure of the including

angle between them in one triangle equal to the

corresponding sides and angles in the second triangle,

then the two triangles are congruent

∴ m∠LOA = m∠LOB

∵ m∠AOB = 110°

∴ m∠LOA = m∠LOB = 110/2 = 55°

* In ΔLAO

∵ m∠ LAO = 90° , m∠LOA = 55°

∴ m∠ALO = 180 - (90 + 55) = 180 - 145 = 35°

* The measure of angle ALO = 35°

8 0

3 years ago