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mrs_skeptik [129]
3 years ago
13

Ten less than 5 times the value of a number is equal to 10 times the quantity of

Mathematics
1 answer:
grandymaker [24]3 years ago
5 0

Answer:

52

Step-by-step explanation:

given that the number is a

The expression for Ten less than 5 times the value of a number is given by

5a - 10

10 times the quantity of  12 more than one-fourth of the number.

a/4 is one-fourth  of number

12 more than one-fourth of the number

a/4 + 12

expression for  10 times the quantity of  12 more than one-fourth of the number. is given by

10(a/4 + 12) = 10a/4 + 12*10 = 2.5a + 120

Given that the above two expression are equal

equating them we have

5a - 10 = 2.5a + 120

adding 10 both sides

=>5a - 10+ 10  = 2.5a + 120 + 10

=> 5a = 2.5a + 130

subtracting 2.5a from both sides

=> 5a - 2.5a = 2.5a + 130 - 2.5a

=> 2.5a = 130

dividing both side by 2.5

=> a = 130/2.5 = 52

Thus, value of a is 52

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A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola y equals = 100 100 minus −x squa
masha68 [24]

Answer:

Step-by-step explanation:

Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola

y=100-x^2

This parabola has vertex at (0,100) and symmetrical about y axis.

Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.  

Hence coordinates of any rectangle are

(a,0) (-a,0), (a, 100-a^2), (-a, 100-a^2)

Length of rectangle = 2a and width = 100-a^2

Area of rectangle = lw = 2a(100-a^2)=200a-400a^3

To find max area, use derivative test.

A' = 200-800a^2\\A"=-1600a

Hence maxima when first derivative =0

i.e. when a =2

Thus we find dimensions of the rectangle are l =4 and w = 96

Maximum area = 4(96) = 384

5 0
3 years ago
Solve for x<br> 4x – 4&lt;8<br> AND<br> 9x +5 &gt; 23
Leno4ka [110]

Answer:

x<3 AND x>2

Step-by-step explanation:

First, 4x-4<8. Adding 4 to both sides, 4x<12, and dividing by 4, x<3.

Next, 9x+5>23. Subtracting 5 from both sides, 9x>18, and dividing by 9, x>2.

Therefore, x<3 AND x>2.

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What is 417 in expanded from ?
myrzilka [38]

Answer:

400 + 10 + 7

Step-by-step explanation:

it could be 4 times 100 plus 10 times 1 plus 1 times 7

4 0
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A 7-pound box of raspberries costs $26.88. What is the price per ounce?
pishuonlain [190]

Answer:

26.88/7 = $3.84 per ounce

Step-by-step explanation:

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3 years ago
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