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3 years ago

Someone help me with this question plzzz

Mathematics

1 answer:

asambeis [7]3 years ago

7 0

Answer:

Step-by-step explanation:

As per Janayda,

From the figure attached,

In ΔTRQ,

m∠TRQ + m∠RQT + m∠QTR = 180°

25° + m∠RQT + 35° = 180°

m∠RQT = 180° - 60°

m∠RQT = 120°

Since, m∠RQT + m∠PQT = 180° [Linear pair of angles]

m∠PQT = 180° - m∠RQT

= 180° - 120°

= 60°

In right angled triangle TPQ,

m∠TPQ + m∠PQT + m∠PTQ = 180°

90° + 60° + m∠PTQ = 180°

m∠PTQ = 180° - 150°

= 30°

Similarly, other angles can also be evaluated from the given information.

In ΔQTP and ΔNTP,

TP ≅ TP [Reflexive property]

NP ≅ PQ [Given]

ΔQTP ≅ ΔNTP [By LL postulate for congruence]

Therefore, Janayda is correct.

While Sirr is incorrect.

Since, there is not the enough information to prove ΔRTQ and ΔMTN equal, Isabelle is incorrect.

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At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while

aliya0001 [1]

Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

Let the height of the pole is x cm,

Also, let the angle of elevation of the sun to the pole at 3 pm is $\theta$

Thus, by the question,

$tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}$

$\implies tan\theta = \frac{x}{x}$ ( at 3pm the height of shadow = height of the pole)

$\implies tan\theta = 1$

$\implies \theta = 45^{\circ}$

Again, according to the question,

When the angle of elevation is $(\theta - 12^{\circ})$ ,

The height of shadow = x + 95,

$\implies tan(45-12)^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x$

$\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}$

$\implies -0.3505924068 x = - 61.6937213538$

$x=175.969930202\approx 175.97\text{ cm}$

4 0

3 years ago

In the figure, line segment VR is parallel to line segment US and m<1 = 45 degrees what is m<4?

Jobisdone [24]

The measure of ∠4 is 45°.

Solution:

Line segment VR is parallel to the line segment US.

m∠1 = 45°

∠1 and ∠4 are corresponding angles.

<em>If two lines are parallel, then the corresponding angles are congruent.</em>

m∠1 = m∠4

45° = m∠4

m∠4 = 45°

The measure of ∠4 is 45°.

3 0

3 years ago

Of 560 marbles in a bag, 65% are red and the rest are blue. After 28 red marbles are replaced with blue ones, how many blue marb

jonny [76]

Answer: The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

$n_b=560-364=196.$

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

5 0

3 years ago

Read 2 more answers

Arithmetic and Geometric Sequences (Context)

V125BC [204]

The formula for compound interest

A = P( 1 + r/n) ^ (nt)

A is the amount in the account at the end

P is the principal balance or the amount initially invested

r is the annual interest rate in decimal form

n is the number of times it is coupounded per year

t is the number of years

A = 1800 ( 1+ .0375/1) ^ (1*6)

A = 1800 ( 1.0375)^6

A = 2244.92138

Rounding to the nearest cent

A = 2244.92

7 0

1 year ago

(4 - 10) - ( 8 ÷ ( -2))

NeTakaya

The answer would be -2

(4-10)-(8 ÷(-2))

(-6)-(-4)

-6+4

-2

5 0

3 years ago

Read 2 more answers