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Tema [17]
3 years ago
11

Given that

2 \sqrt{32} = {2}^{x} " alt="32 \sqrt{32} = {2}^{x} " align="absmiddle" class="latex-formula">
, find the value of x
​
Mathematics
1 answer:
Gelneren [198K]3 years ago
5 0

Answer:

x = 7.5 or 15/2

Step-by-step explanation:

2^{5} \cdot2^{5/2} = 2^{15/2}

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A line that passes through the point (–1, 3) has a slope of 2. Find another point on the line
bezimeni [28]
Y-y1=m(x-x1)
for slope=m
a point =(x1,y1)

slope=2
point= (-1,3)
y-3=2(x+1)
y-3=2x+2
y=2x+5
test given points

A.
(1,5)
5=2(1)+5
5=7
false

B.
(1,4)
4=2(1)+5
4=7
false

C.
(-3,2)
2=2(-3)+5
2=-6+5
2=-1
false

D.
(0,5)
5=2(0)+5
5=0+5
5=5
true

answer is D
6 0
3 years ago
Read 2 more answers
State the restrictions on the range for y=x^4+8x^3+k
sveticcg [70]
Answer: The range is y \ge k-432

The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.

Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
4x^2(x + 6) = 0
4x^2 = 0 or x+6 = 0
x = 0 or x = -6

It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function

y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
y = k - 432

So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value

So that's why the range is y \ge k - 432

Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction. 
3 0
3 years ago
F = (4x-3)au carre - (x+3)(3-9x)
Vinvika [58]

Answer:

<em>Translater</em>

Step-by-step explanation:

<em>F = (4x-3) squared - (x + 3) (3-9x)</em>

<em>- develop and reduce (4x-3) to the edge</em>

<em>- show that F = (5x) squared</em>

<em />

  • <em>(NOT AN ANSWER ITS TO HELP OTHERS WHO DOESN"T KNOW FRENCH)</em>
7 0
3 years ago
The figure are similar find x
Misha Larkins [42]
Is there a picture that suppose to come with this
4 0
3 years ago
What is the slope of the line on the graph?
Bogdan [553]

Answer:

m=-2

Step-by-step explanation:

Take 2 points (0,0) and (-3,6)

m(slope)= m = rise/run = y2 - y1/ x2 - x1

y2-y1= 6-0=6

x2-x1 = -3-0 = -3

m=6/-3 = -2

y=-2x

4 0
3 years ago
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