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rosijanka [135]
3 years ago
14

ABCD is a parallelogram. What is the measure of ∠ACD?

Mathematics
1 answer:
Igoryamba3 years ago
8 0

Step-by-step explanation:

Here

5x+16+7x-3+6x+5 = 180(being sum of triangle)

or, 18x=180-18

or, x= 162/18

so, x = 9

now,

here,

<ACD = <ACB(diagonals of parallelogram bisect eachother)

or, <ACD = 7x-3

or, <ACD = 7×9-3

or, <ACD = 63-3

So, <ACD = 60°

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Suppose that the functions q and r are defined as follows.
satela [25.4K]

Answer:

(r o g)(2) = 4

(q o r)(2) = 14

Step-by-step explanation:

Given

g(x) = x^2 + 5

r(x) = \sqrt{x + 7}

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

g(x) = x^2 + 5

g(2) = 2^2 + 5

g(2) = 4 + 5

g(2) = 9

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

r(x) = \sqrt{x + 7}

r(9) = \sqrt{9 +7{

r(9) = \sqrt{16}{

r(9) = 4

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

So, first we calculate r(2)

r(x) = \sqrt{x + 7}

r(2) = \sqrt{2 + 7}

r(2) = \sqrt{9}

r(2) = 3

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

g(x) = x^2 + 5

g(3) = 3^2 + 5

g(3) = 9 + 5

g(3) = 14

Hence:

(q o r)(2) = 14

8 0
3 years ago
How to factorise the difference of perfect squares. for the g on the top and j on the top
Fed [463]

Answer:

see explanation

Step-by-step explanation:

A difference of two squares is factored as

a² - b² = (a - b)(a + b)

(g)

1 - 81y²

= 1² - (9y)²

= (1 - 9y)(1 + 9y)

(j)

64x² - 25y²

= (8x)² - (5y)²

= (8x - 5y)(8x + 5y)

7 0
3 years ago
If M is the midpoint of PQ and X is the midpoint of PM then PX = a PQ
tino4ka555 [31]

Answer:

found this i think this should help with your question

Step-by-step explanation:

Download pdf
3 0
3 years ago
Who is first president of Czech republic?
Mariana [72]
The first President of the Czech Republic was Václav Havel
6 0
3 years ago
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Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be
kvv77 [185]
Answer:

Angle A must be acute.

Explanation:

Both angle A and C must be acute. The sum of the angles in a triangle is 180°.

An obtuse angle is more than 90°, so the sum of the remaining 2 angles has to be less than 90°.

Note that it is impossible to have:

<span>2 right angles in a triangle, because <span>90°+90°=180</span>° and the third angle still needs to be added.1 obtuse and 1 right angle in a triangle, their sum is more than 180°2 obtuse angles in a triangle, their sum is more than 180°</span>

It is possible to have an obtuse-angled isosceles triangle, but the vertex angle must be obtuse and the equal base angles will be acute.

8 0
3 years ago
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