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2 years ago

On the map below, all numbered streets run parallel to each other. Both 3rd and 4th streets are intersected by King Avenue.

Mathematics

1 answer:

frosja888 [35]2 years ago

4 0

X=105°

Y=105°

Z=105°

let the angle below 75° which is the 4th Street be A

75°+A=180°[being adjacent angle]

A=105°

X=A[Verticall opposite angle]

Z=A[Corresponding angle]

Y=X[alternate angle]

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What is the value of the 12th term in the sequence 4, 12, 36, 108, ...?

mafiozo [28]

C. 236,196 is your answer

5 0

3 years ago

Can u help me ASAP. i need to know how to do it step by step

12345 [234]

Answer:

Step-by-step explanation:

$f(x) =4x^3-8x^2+ax+b$ has a factor $2x-1$ and

when divided by $x+2$ , remainder is 20.

To find:Remainder when divided by (x-1) ?

Solution:

$2x-1$ is a factor

$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$ when we put this value of x to the function, it will become 0.

i.e.

$\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)$

Remainder is 20 when f(x) is divided by $x+2$

i.e.

$f(-2) =20$

$\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)$

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

$5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}$

By equation (1):

$a+2(18) = 3\\\Rightarrow a = -33$

So, the equation becomes:

$f(x) =4x^3-8x^2-33x+18$

$\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}$

So, when divided by (x-1), remainder will be <em>19</em>.

4 0

3 years ago

2.Solve the system using substitution.

Lena [83]

2x+2y=38
y=x+3

First you would substitute the y for x+3
2x+2(x+3)=38

You would multiply the 2 by the x+3
2x+2x+6=38

Add the 2x and the 2x
4x+6=38

Subtract the 6 on both sides
4x=32

Divide the 4 on both sides
x=8

Now substitute the x in the second problum for 8
y=8+3

Add the 8 and the 3 to solve for y
y=11

Your answers
x=8
y=11
the correct answer would be A:(8,11)

3 0

3 years ago

Least common multiple of 6 and 8

miskamm [114]

Answer:

8={8,16,24,32,40}

6={6,12,18,24,33}

so the least common multiple is 24

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2 years ago

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