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KATRIN_1 [288]
3 years ago
10

Ln(x-5)-ln(x-4)=-2 Please help solve

Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0
X-5/ X-4=. e^-2
-4+5e^2 / e^2-1

Or ≈ 5.15652
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In triangle abc, ac=10, bc=8, angle b =90 degrees and angle bda = 90. how long is line bd
WITCHER [35]
The complete question in the attached figure

we know that
<span>applying the Pythagorean theorem in triangle ABC
</span>AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6

in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4

in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1

in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2

equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)---------->  BD=4.8 units

the answer is BD=4.8 units


4 0
3 years ago
Samuel spent $16 for 4 erasers and 2 pencils. Alva spent $10.50 for 3 erasers and 1 pencil. How much does 5 erasers and 3 pencil
9966 [12]

Answer:

Step-by-step explanation:

Let E = Erasers and P = Pencils

4E + 2 P = $16…(1)

3E + 1P = $10.50…(2)

Multiply (2) by 2 to make Pencils in (1) and (2) equal.

6E + 2P = $21…(3)

Subtract (3) from (1) to eliminate P

2E = $5 => Erasers = $2.50 each

Substitute this value for Erasers into (3)

6 * $2.50 + 2P = $21

2P = $21 - $15 = $6 => Pencils = $3

Therefore 5 Erasers + 3 Pencils cost

5 * $2.50 + 3 * $3 = $12.50 + $9 = $21.50

3 0
3 years ago
Read 2 more answers
What is the measure of the smallest angle in the triangle whose vertices are D(4,1), E(4, -2), and F(-2, -2)? Round to the neare
Diano4ka-milaya [45]
27 
I hope this is right
8 0
3 years ago
Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three
RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

f(x)=x^{2}

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

g(x)=-5x^{2}+100x-450

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

g(x)=-5x^{2}+100x-450

Complete the square

g(x)=-5(x^{2}-20x)-450

g(x)=-5(x^{2}-20x+100)-450+500

g(x)=-5(x^{2}-20x+100)+50

g(x)=-5(x-10)^{2}+50

The vertex is the point (10,50)

so

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

5 0
3 years ago
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Sixteen is the same as one and two-tenths times a number added to negative 8
Archy [21]

Answer:

20

Step-by-step explanation:

16=1 2/10R + -8

16+8= 12/10R

24=12/10R

R=20

3 0
3 years ago
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