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2 years ago

Find the value of x in the figure.

Mathematics

2 answers:

VARVARA [1.3K]2 years ago

6 0

Answer:

x=28

Step-by-step explanation:

maksim [4K]2 years ago

4 0

$\huge\bold{To\:find:}$

✎ The value of $x$ .

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

$\sf\purple{The\:value\:of\:x\:is\:28°. }$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

Since it is right-angle,

$Sum \: of \: angles \: = 90° \\ ⇢ (2x + 1) + 33 ° = 90° \\ ⇢2x + 34° = 90° \\ ⇢2x = 90° - 34° \\⇢ 2x = 56° \\⇢ x = \frac{56° }{2} \\ ⇢x = 28°$

$\sf\blue{Therefore,\:the\:value\:of\:x\:is\:28°.}$

$\huge\bold{To\:verify :}$

$(2x + 1) + 33° = 90° \\ ➡ \: 2 \times 28° + 1 + 33° = 90° \\ ➡ \: 56° + 34° = 90° \\ ➡ \: 90° = 90° \\ ➡ \: L.H.S.=R. H. S$

Hence verified.

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘$

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The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.

<h3>What is a circle?</h3>

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle in which the shaded region is shown.

The radius of the small circle r = 3 cm

The radius of the large circle R = 3+4 = 7 cm

The area of the shaded region:

= area of the large circle sector - an area of the small circle sector

= (120/360)[π7²] - (120/360)[π3²]

= 49π/3 - 3π

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= 13.34π square cm

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3 years ago

Solve the equation 2^(2x+1)+8=17×2^x.

myrzilka [38]

Oooh, looks fun

ok
erm
we might want to know some properties
$(x^m)(x^n)=x^{m+n}$
$(a^b)^c=a^{bc}$
if $a^m=a^n$ where a=a, then assume m=n

$2^{2x+1}=(2^{2x})(2^1)$
so
$(2^{2x})(2)+8=17(2^x)$
$(2^{2x})(2)+2^3=17(2^x)$
$(2^x)^2(2)+2^3=17(2^x)$
minus 17*2^x both sides
$(2^x)^2(2)+2^3-17(2^x)=0$
use u subsitution, u=2ˣ
$(u)^2(2)+2^3-17(u)=0$
solve $2u^2+8-17u=0$
or
$2u^2-17u+8=0$
ac method
2 times 8=16
what 2 number multiply to get -17 and add to get 16
-16 and -1
2u²-1u-16u+8=0
(2u²-1u)+(-16u+8)=0
u(2u-1)+(-8)(2u-1)=0
(u-8)(2u-1)+0
u-8=0
u=8

2u-1=0
2u=1
u=1/2

now
u=2ˣ

8=2ˣ
$2^3=2^x$
3=x

and
$\frac{1}{2}=2^x$
$2^{-1}=2^x$
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2 years ago

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Step-by-step explanation:

nth term = 1 - 5n

6th term = 1 - 5(6)

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2 years ago