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3 years ago

P- (9-(m + q)); use m=4, p=5, and q=3

Mathematics

1 answer:

Tcecarenko [31]3 years ago

6 0

Answer:

Step-by-step explanation:

p-(9-(m+q))

5-(9-(4+3))

=5-(9-7)

=5-2

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Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$

Blizzard [7]

$\begin{cases}a\equiv1\pmod7\\b\equiv2\pmod7\\c\equiv6\pmod7\end{cases}$

$a^{81}\equiv1^{81}\equiv1\pmod7$

$b^{91}\equiv2^{91}\pmod7$

$2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7$
$8\equiv1\pmod7$
$2\equiv2\pmod7$
$\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7$

$c^{27}\equiv6^{27}\pmod7$

$6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7$

$\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7$

6 0

3 years ago

Find the area of the trapezoid below to the nearest tenth.

kondor19780726 [428]

Answer:

Area of trapezoid = 67.6 square units

Step-by-step explanation:

Area of a trapezoid is given by the expression,

Area of the trapezoid = $\frac{1}{2}(b_1+b_2)h$

Here, $b_1$ and $b_2$ are the parallel sides of the given trapezoid.

And ' $h$ ' = Height between the parallel sides

From the given triangle ABE,

m(∠ABE) = m(∠ABC) - m(∠EBC)

m(∠ABE) = 120° - 90°

= 30°

By applying cosine rule in the given triangle,

cos(30°) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{\sqrt{3} }{2}=\frac{BE}{AB}$

$\frac{\sqrt{3} }{2}=\frac{BE}{6}$

BE = $3\sqrt{3}$ units

By applying sine rule in ΔABE,

sin(30°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{2}=\frac{AE}{AB}$

$\frac{1}{2}=\frac{AE}{6}$

AE = 3 units

Length of $b_1=BC=10$

Length of $b_2=AD=(AE+EF+FD)$ [AE = FD, since given trapezoid ABCD is an isosceles trapezoid]

$b_2=3+10+3$

$b_2=16$

Height between the parallel sides $h=3\sqrt{3}$

Area of the trapezoid = $\frac{1}{2}(BC+AD)BE$

= $\frac{1}{2}(10+16)(3\sqrt{3})$

= $39\sqrt{3}$

= 67.6 square units

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3 years ago

Below are two different functions, f(x) and g(x). What can be determined about their slopes? F(x)= 3x ? 3 The function g of x go

julsineya [31]

The slope of g(x) would be 5-2/1-0=3
they have the same slope

3 0

4 years ago

at noon aretha can watch a football game basketball game or a documentary about horses on tv.at 3:00,she can watch different foo

kap26 [50]

Hello, well because she has three options at noon and three options at 3:00, you multiply 3*3 which is 9. So there are 9 possible outcomes. You can also create a chart to show this;

Football
-football
-movie
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Basketball
-football
-movie
-concert

Documentary
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Hope this helps :)

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3 years ago

Jenny read 150 pages of a book in 5 hours. Which rate is proportional to the rate at which Jenny read?

erik [133]

Answer:

she would have read 30 pages per hour

Step-by-step explanation:

hope this helps

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3 years ago