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VLD [36.1K]
2 years ago
11

Given A is between Y and Z YA = 5.5, AZ = 2x, and YZ = 41.5 =, find AZ

Mathematics
2 answers:
STatiana [176]2 years ago
8 0

Answer:

AZ=36

Step-by-step explanation:

We have been given that point A is between point Y and Z such that YA=5.5, AZ=2x and YZ=41.5.

Using our given information, we can set an equation as:

YZ=YA+AZ

Substitute given values:

41.5=5.5+2x

Switch sides:

5.5+2x=41.5

5.5-5.5+2x=41.5-5.5

2x=36

Since AZ=2x, so the length of segment AZ is 36 units.

morpeh [17]2 years ago
4 0
YZ = YA + AZ
41.5 = 5.5 + AZ
AZ = 41.5 - 5.5
AZ = 36

So, your final answer is AZ = 36

Hope this helps!
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B)the LCM of three numbers is 24 and their G.C.D is 4. If two<br>find the other number​
kicyunya [14]

6

Step-by-step explanation:

because 6*4=24, so the G.C.D is 4 and the other number is 6

4 0
3 years ago
For which pair of functions is the vertex of k(x)7 units below the vertex of f(x)?
kvv77 [185]

Answer: Option C

f(x) = x^2;\ k (x) = x ^ 2 -7

Step-by-step explanation:

Whenever we have a main function f(x) and we want to transform the graph of f(x) by moving it vertically then we apply the transformation:

k (x) = f (x) + b

If b> 0 then the graph of k(x) will be the graph of f(x) displaced vertically b units down.

If b> 0 then the graph of k(x) will be the graph of f(x) displaced vertically b units upwards.

In this case we have

f (x) = x ^ 2

We know that this function has its vertex in point (0,0).

Then, to move its vertex 7 units down we apply the transformation:

k (x) = f (x) - 7\\\\k (x) = x ^ 2 -7.

Then the function k(x) that will have its vertex 7 units below f(x) is

k (x) = x ^ 2 -7

3 0
3 years ago
What is 32/48 in SIMPLEST form? PLEASE EXPLAIN THOROUGLY!
kari74 [83]
Hi There!

<span>What is 32/48 in SIMPLEST form?

</span>32÷16=2
48÷16=3

<span>So the answer is </span><span>2/3</span>
7 0
3 years ago
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Given the points J(4,-7) and L(-2,13), find the coordinates of point k on JL such that the ratio of jk is 1:4
Irina-Kira [14]

Answer:

The coordinates of point k are (-2.8,-3)

Step-by-step explanation:

we shall use the internal division formula to find the coordinates of point k

Mathematically, the formula is as follows;

Let’s call the coordinates of point k (x,y)

(x , y) = mx2 + nx1/(m + n) , my2 + ny1/(m + n)

From the question;

m = 1 , n = 4

x1 = 4, x2= -2

y1 = -7 , y2 = 13

Substituting these values in the equation, we have the following;

1(-2) + 4(4)/(1 + 4) , 1(13) + 4(-7)/(1+4)

(-2+16)/5, (13 -28)/5

= -14/5, -15/5

= (-2.8, -3)

3 0
3 years ago
Simplify the number into simplest radical form. Use the factor tree to help determine the factors. StartRoot 96 Endroot StartRoo
NikAS [45]

Answer:

[tex]4608\sqrt{3}[/tex]

Step-by-step explanation:

1. \sqrt{96} *\sqrt{6}* 2*\sqrt{6}*4 *\sqrt{6} *4*\sqrt{3}

2. \sqrt{2^{5} *3} \sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}   <em>factoring 96</em>

<em>since \sqrt{2^{5}*3 } = \sqrt{2^{5} } \sqrt{3}</em>

3. \sqrt{2^{5} } \sqrt{3}\sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}

<em>using exponent rule - (a^{b}) ^{c} = a^{bc}</em>

<em> \sqrt{2^{5} } = 2^{5/2}</em>

4. 2^{5/2}\sqrt{3}\sqrt{2*3} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}

<em>doing some simple simplification and 4=2^{2}  and 6=2*3</em>

5. 2^{5/2} \sqrt{3} \sqrt{2} \sqrt{3} *2\sqrt{2} \sqrt{3} *2^{2}\sqrt{2} \sqrt{3}*4\sqrt{3}

<em>collecting the roots on one side and applying exponent rule</em>

6. \sqrt{3} \sqrt{3}\sqrt{3} \sqrt{3}\sqrt{2} \sqrt{2}\sqrt{2} *2^{5/2+1+2+2} \sqrt{3}

<em>Applying exponents rule on all \sqrt{3} and \sqrt{2}</em>

<em>7. 2^{1/2+1/2+1/2} *2^{5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}</em>

<em>combining all powers of 2</em>

8. 2^{1/2+1/2+1/2+5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}

<em>Simplifying</em>

9. 2^{9} *3^{2}\sqrt{3}

10. 512*9\sqrt{3}

11. 4608\sqrt{3}

3 0
3 years ago
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