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3 years ago

What is the value of x?

Mathematics

2 answers:

sdas [7]3 years ago

6 0

Answer:

x = 3

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠TRQ is an external angle and ∠RTS, ∠RST are interior angles, hence

45x = 25x + 57 + x

45x = 26x + 57 ( subtract 26x from both sides )

19x = 57 ( divide both sides by 19 )

x = 3

morpeh [17]3 years ago

5 0

<u>Answer:</u>

x = 3

<u>Step-by-step explanation:</u>

We are given expression for measure of angles of two corners of a triangle, while for the third corner, we know the exterior angle.

We know that the sum of all three angles of a triangle is 180°.

So we can write it as:

$2 5 x + ( 5 7 + x ) + ( 1 8 0 - 4 5 x ) = 180$

$25x+x-45x=180-180-57$

$-19x=-57$

$x=\frac{-57}{-19}$

x = 3

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You have two circles, one with radius r and the other with radius R. You wish for the difference in the areas of these two circl

gtnhenbr [62]

Answer:

maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

Step-by-step explanation:

We know that area of circle is given by

$A=\pi \times (radius)^{2}$

For circle with radius 'r' we have

$A_{1}=\pi \times (r)^{2}$

For circle with radius 'R' we have

$A_{2}=\pi \times (R)^{2}$

Now according to given condition we have

$A_{1}-A_{2}\leq \frac{5}{\pi }$

$\Rightarrow \pi r^{2}-\pi R^{2}\leq \frac{5}{\pi }\\\\\Rightarrow (r^{2}-R^{2})\leq \frac{5}{\pi ^{2}}\\\\(r+R)(r-R)\leq \frac{5}{\pi ^{2}}\\\\\because (a^{2}-b^{2})=(a+b)(a-b)\\\\(r+R)=10(Given)\\\\\Rightarrow(r-R)\leq \frac{5}{10\pi ^{2}}\\\\\therefore (r-R)\leq\frac{1}{2\pi ^{2}}$

Thus maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

6 0

3 years ago

Find the volume of a regular cube if the length of a side is 10 cm. (Hint: V = I³.)

ivanzaharov [21]

Answer:

1000 cm

Step-by-step explanation: I can't explain it sorry.

3 0

3 years ago

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-3,6,-9,12,-15 which of the following represents the general term for the sequence give?

Mademuasel [1]

The general term for the sequence $a_{n}=(-1)^{n} 3 n$

<h3><u>Solution:</u></h3>

Given sequence is -3, 6, -9, 12, -15

We have to find the general term of sequence

The terms in the sequence are found out by using the recursive definition:

$a_{n}=(-1)^{n} 3 n$

Let us use this definition to find out the terms and check if it matches our given sequence

$\begin{array}{l}{\text { For } n=1:-(-1)^{n} 3 n=(-1)^{1} \times 3 \times 1=-3} \\\\ {\text { For } n=2:-(-1)^{n} 3 n=(-1)^{2} \times 3 \times 2=1 \times 6=6} \\\\ {\text { For } n=3:-(-1)^{n} 3 n=(-1)^{3} \times 3 \times 3=-1 \times 9=-9} \\\\ {\text { For } n=4:-(-1)^{n} 3 n=(-1)^{4} \times 3 \times 4=1 \times 12=12} \\\\ {\text { For } n=5:-(-1)^{n} 3 n=(-1)^{5} \times 3 \times 5=-1 \times 15=-15}\end{array}$

Thus the general term is given by $a_{n}=(-1)^{n} 3 n$

7 0

3 years ago

The probability that an event will occur is 25/25 . Which of these best describes the likelihood of the event occurring? (5 poin

lianna [129]

Certain just makes the most

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3 years ago

Which of the following describes the transformation of g (x) = 3 (2) Superscript negative x Baseline + 2 from the parent functio

Tanzania [10]

Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

Step-by-step explanation:

The parent function is $f(x)=2^{x}$

The transformation function is $g(x)=3(2)^{-x} +2$

In the transformed function, the function is added +2, which shifts the graph by 2 units up.

Also, the function is multiplied by 3, which stretches the function $f(x)=2^{x}$ vertically by a factor of 3 units.

The variable x is multiplied by -1, such that the function reflects across y-axis.

Thus, the correct answer is option d.

The graph is attached below which shows the parent function and the transformed function.

The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

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3 years ago

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