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3 years ago

Share £56 in the ratio 3:4

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

8 0

Answer:

£24 : £32

Step-by-step explanation:

Add the parts of the ratio 3 + 4 = 7

Divide the amount by 7 to find the value of one part

£56 ÷ 7 = £8 ← one part of the ratio

3 parts = 3 × £8 = £24

4 parts = 4 × £8 = £32

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Find the missing number: 2016 · 199 = 2016·? +2016 · 98 Pls tell how you did it as well

Alex Ar [27]

Answer:

101

Step-by-step explanation:

Given the expression:

2016 · 199 = 2016·? +2016 · 98

We could rewrite the expression such that the missing value equals x

2016 * 199 = 2016 * x + 2016 * 98

Using BODMAS:

401184 = 2016x + 197568

401184 - 197568 = 2016x

203616 = 2016x

Divide both sides by 2016

203616 / 2016 = 2016x / 2016

101 = x

Hence, missing value is 101

4 0

3 years ago

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Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

mel-nik [20]

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

$(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2$

$\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y$

$\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y$

$\implies 4x +8x-10y+2y = 16 + 1 -25-4$

$\implies 12x - 8y = 17 - 29$

$\implies 12 x - 8 y = - 12$ ---------(1)

Similarly, QO = RO

$\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2$

$\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y$

$\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y$

$\implies - 8x -4x-2y-6y=4+9-16-1$

$\implies -12 x - 8 y = 13 - 17$

$\implies 12 x + 8 y = 4$ ------------(2)

By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

y = 2

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3 years ago

Which pair of angles must be supplementary?

Alex_Xolod [135]

∠3 and ∠4 are angles that must be supplementary.

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3 years ago

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The seating capacity of a theater is 250. Tickets are $3 for children and $5 for adults. The theater must take in at least $1100

maksim [4K]

Answer:

x + y ≤

3x + 5y ≥ 1100

Step-by-step explanation:

Given:

Seating capacity of theater = 250

Cost of each child ticket = $3

Cost of each adult ticket = $5

Cost per performance = $1100 at least

Find:

System of inequalities

Computation:

Let;

x = Number of children's tickets

y = Number of adult tickets

x + y ≤

3x + 5y ≥ 1100

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3 years ago

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Lady_Fox [76]

Answer:

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