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2 years ago

For which values of a the system has no solution: x≤5, x≥a

Mathematics

1 answer:

soldi70 [24.7K]2 years ago

7 0

Given:

The system of inequalities is

$x\leq 5$

$x\geq a$

To find:

The values of a for which the system has no solution.

Solution:

We have,

$x\leq 5$ ...(1)

It means the value of x is less than or equal to 5.

$x\geq a$ ...(2)

It means the value of x is greater than or equal to a

Using (1) and (2), we get

$a\leq x\leq 5$

But if a is great than 5, then there is no value of which satisfies this inequality.

Therefore, the system has no solution for a>5.

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A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units.

Mekhanik [1.2K]

Answer:

Volume of shaded portion = (600 - 36π) units³

Step-by-step explanation:

Volume of the shaded portion = Volume of pyramid - Volume of cone

Volume of pyramid = ⅓*l*w*h

Where,

l = length of base of pyramid = 15 units

w = width of base of pyramid = 10 units

h = height of pyramid = 12 units

Plug in the values to find the volume of the pyramid

Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³

Volume of Cone = ⅓πr²h,

Where,

r = radius = ½ of diameter = ½ of 9 = 3 units

h = height = 12 units

Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12

= π*3*12 = 36π units³

Volume of shaded portion = (600 - 36π) units³

3 0

2 years ago

The equation t = x 2 - 1936 represents jake's profit at his cell phone store, t represents the total amount of money and x is th

ankoles [38]

Set t=0 so
x²-1936=0
(x-44)²=0
x=44 phones he must cell to break even

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2 years ago

The amount of water that the girls on the basketball and soccer teams drink during one practice session is recorded in the dot p

Radda [10]

Answer:

Step-by-step explanation:

We have two dot plots, one for the Basketball Team and one for the Soccer Team.

Notice that there are 16 girls in the Basketball Team and 16 girls in the Soccer Team.

Basically, the median is between the 8th and 9th term in each data set. Specifically, is the mean between them.

<h3>For Basketball Team</h3>

$m_{basketball} =\frac{32+32}{2}=32$

Because the 8th and 9th term are both equal to 32.

<h3>For Soccer Team</h3>

$m_{soccer}=\frac{64+64}{2}=64$

Because the 8th and 9th term are both equal to 64.

If we subtract them to find the difference, it would be

$\Delta m=64-32=32$

Basically, the Soccer Team drank 32 more ounces of water than the Basketball Team.

Therefore, the right answer is B, that's the closest one.

4 0

2 years ago

Read 2 more answers

The Venn diagram shows the number of patients seen at a pediatrician’s office in one week for colds, C, ear infections, E, and a

MArishka [77]

Answer:

Correct answers: 1 question: How many p both? The Venn diagram shows the number of patients seen at a infections pediatrician's office in ... pediatrician's office in one week for colds, C, ear infections, E, and allergies, A.

1 answer

Step-by-step explanation:

4 0

2 years ago

estimate the total weight of two boxes that weigh 9.4 lb and 62.6 lb using rounding and compatible numbers. which estimate is cl

Scorpion4ik [409]

<span><span>1. </span>We have 2 boxes weighs:
=> 9.4 lb and 62.6 lbs.
Now, let’s estimate the total weight of this 2 boxes using rounding and compatible numbers.
For 9.4 lbs , the rounded and compatible number is 9 lbs
And for 62.6 lbs, the rounded and compatible number is 63 lbs
=> now, let’s try adding both numbers if we get a close answer
=> 9 +63
=> 72 = the estimated and rounded answer is 72.
Let’s check if we have close answer
=> 9.4 + 62.6
=> 72</span>

5 0

2 years ago