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2 years ago

14. A sum of $2700 is to be given in the form of 63 prizes. If the prize is of

Mathematics

2 answers:

bezimeni [28]2 years ago

8 0

Answer:

15 at $100
48 at $25

Step-by-step explanation:

Let x represent the number of higher-value ($100) prizes. Then (63-x) is the number of $25 prizes. The total value of the prizes is ...

100x +25(63 -x) = 2700

75x = 1125 . . . . . . . . . subtract 1575 and simplify

x = 15 . . . . . . . . . divide by 75; number of $100 prizes

63-x = 63 -15 = 48 . . . . number of $25 prizes

There are 15 $100 prizes and 48 $25 prizes.

aliina [53]2 years ago

7 0

Answer:

$100 prize = 15, $25 prize = 48

Step-by-step explanation:

Let,

$100 prize = x

$25 prize = y

=> x + y = 63 (1)

=> 100x + 25y = 2700 (2)

=> 100x/25 + 25y/25 = 2700/25

=> 4x + y = 108 (3)

On subtracting 2 and 3

=> 4x + y - (x + y) = 108 - 63

=> 4x + y - x - y = 45

=> 3x = 45

=> x = 15

=> 15 + y = 63

=> y = 63 - 15

=> y = 48

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Does anyone know how to do this ?

goldenfox [79]

Answer: D) 32

Step-by-step explanation:

The area of a parallelogram equals its base times its height. Substitute the base and area into this formula to solve for the height:

A=bh

40=(5)(h)

h=8

If ABCD is a parallelogram, opposite sides are parallel, so AB is parallel to DC. If AB is parallel to DC, EB is parallel to DC. Since EB is parallel to DC, quadrilateral EBCD has at least one pair of parallel sides, making it a trapezoid. The area of a trapezoid is equal to $\frac{h(b_{1}+b_{2}) }{2}$ where h is the height, $b_{1}$ is one base, and $b_{2}$ is the other base. Plug the necessary values into the formula:

A= $\frac{h(b_{1}+b_{2}) }{2}$

$b_{1} =AB-AE\\DC=AB\\b_{1} =DC-AE\\b_{1} =5-2\\b_{1} =3$

$b_{2} =5$

h=8

A= $\frac{8(3+5)}{2}$

A=32

The answer is D) 32.

6 0

2 years ago

19.5+24+7.5 =<br> 19.5+__+24 =<br> ___+24+___=

krek1111 [17]

See attached photo for solution

please give a thanks or brainliest if you found my answer helpful :)

8 0

3 years ago

Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84

guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

10/20 is simplified to 1/2

k = 1/2

5 0

2 years ago

To take an Uber, it costs $4.00 plus an additional $1.50 per mile traveled.

slava [35]

You traveled 11 miles because if you did use 28.00 and $1.50 then you take that answer and then add the $4.00 and $3.00 you will get $7 so you just subtract that for the other number and you get 11 miles because it is $1.50 per mile

7 0

3 years ago

Juan scored 15 points more on this test than

maw [93]

Juan's least integer scores in both tests will be 85 and 100 respectively.

Test average of his two scores is atleast 92

Let :

Score on test 1 = b
Score on test 2 = b + 15

Average score can be related thus:

(Sum of score ÷ number of test) ≥ 92
(b + b + 15) ÷ 2 ≥ 92
(2b + 15) ÷ 2 = 92
2b + 15 = 184
2b = 184 - 15
2b = 169
b = 169 ÷ 2
b = 84.5

Therefore, since both scores are integers, his least scores on both tests will be ::

85 and (85 + 15) = 100

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8 0

2 years ago