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3 years ago

Please please help!! and explain!

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

4 0

angles in a triangle add up to 180

so x = 180 - ( 70 + 90 ) = 20

this is because the two other angles in the both of the identical triangles are 70 and 90

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Kristen filled his 52 ounce mug full of his favorite soda at the gas station it cost a total of $1.07 how much money is it for e

NikAS [45]

Answer:

$0.02

Step-by-step explanation:

$1.07 / 52 = $0.0205769230769

Simplified is $0.02

4 0

3 years ago

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In a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?

Leokris [45]

Answer:

Step-by-step explanation:

94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers

7 0

3 years ago

Solve the following equation:

Rama09 [41]

Complete the square.

$z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0$

$\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4$

Use de Moivre's theorem to compute the square roots of the right side.

$w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)$

$\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2$

Now, taking square roots on both sides, we have

$z^2 + \dfrac12 = \pm w^{1/2}$

$z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2$

Use de Moivre's theorem again to take square roots on both sides.

$w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)$

$\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}$

$w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)$

$\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}$

3 0

1 year ago

PLEASE HELP!!! THX

PSYCHO15rus [73]

Answer: 1) Product property of logarithm,

2) Subtraction property of logarithm

3) Equality property of logarithm

Step-by-step explanation:

By the Product property of logarithm,

log a + log b = log(a.b)

And, By the Subtraction property of logarithm

log a - log b = log(a/b)

Also, by the equality property of logarithm,

log(a) = log(b) ⇒ a = b

Given expression,

$log_2(5)+log_2(x+2)-log_2(x+1)=log_2(7)$

$\implies log_2(5(x+2))-log_2(x+1))=log_2(7)$ (Product property of logarithm)

$\implies log_2(\frac{5(x+2)}{2(x+1)})=log_2(7)$ (Subtraction property of logarithm)

$\implies \frac{5(x+2)}{2(x+1)}=7$ ( Equality property of logarithm )

$\implies 5(x+2)=7(x+1)$ ( Multiplicative property of equality )

$\implies 5x+10=7x+7$ ( Distributive property of equality )

$\implies 3=2x$ (subtraction property of equality )

$x=\frac{3}{2}$ (division property of equality )

3 0

3 years ago

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Which expressions are equivalent to –

olga_2 [115]

Answer:

The answer to your question is 10¹/⁴

Step-by-step explanation:

Expression

$\frac{10}{10^{3/4}}$

To solve this problem use the law of exponents.

-Use the division rule of exponents.

If the base if the same in the numerator and denominator, it stays the same and the exponents are subtracted.

10¹ ⁻ ³/⁴ = 10¹/⁴ This is the result

7 0

3 years ago