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3 years ago

If AD=6 and AB=24, find AC

Mathematics

1 answer:

ruslelena [56]3 years ago

6 0

When a perpendicular is dropped from the right-angle (C) to the opposite side AB, the metric relations apply:
BD*BA=a^2 ..........................(1)
AD*AB=b^2...........................(2)
BD*DA=DC^2........................(3)

Given AD=6, AB=24, using metric relation (2) above, we have
b^2=6*24=144
=>
b=sqrt(144)=12

By the way, we conclude that this is a 30-60-90 triangle because b/AB=(1/2)=sin(B) => B=30 degrees.

Answer: b=12

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Two banks are running promotions on savings accounts in anticipation of higher interest rates in the future.

chubhunter [2.5K]

Answer:

<h2>First Federal Bank is best</h2>

Step-by-step explanation:

First national bank gives:

$5,449.03 after 4 years being compounded annually at a rate of 2.15%

First federal bank gives:

$5,468.12 after 4 years at a rate of 2.25%

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3 years ago

Seventeen is three times the difference between four times a number and five

expeople1 [14]

17 = 3(4x - 5)

<em><u>Distributive property.</u></em>

17 = 12x - 15

<em><u>Add 15 to both sides.</u></em>

32 = 12x

<em><u>Divide both sides by 12.</u></em>

x = 2.67. (This is your answer.)

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2 years ago

Can someone help me on this question?

notsponge [240]

Answer:

x = 19.6

Step-by-step explanation:

By applying cosine rule in ΔBCD,

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

= $\frac{BC}{BD}$

$\frac{\sqrt{3}}{2}=\frac{BC}{16}$

BC = $8\sqrt{3}$

Now, by applying sine rule in ΔBAC,

sin(45)° = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{\sqrt{2}}=\frac{AB}{BC}$

$\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}$

x = $8\sqrt{6}$

x = 19.59

x ≈ 19.6

3 0

2 years ago

Urgent help!!! <br><br> Write equation in slope intercept form.<br><br> 1.25 (25) = 31.25

Fantom [35]

The equation in slope intercept form is, $31.25 = 1.25 \times 25 +0$ . The given equation is obtained by comparing the standard equation of the straight line.

<h3>What is a slope of a straight line?</h3>

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

$\rm m =\dfrac{y_2-y_1}{x_2-x_1}$

The given equation is;

1.25 (25) = 31.25

31.25=1.25 (25)

The standard equation of the slope intercept form. is;

$\rm y = mx +x$

On comparing the given equation with the above equation, we get;

y=31.25

m=1.25

x=25

c=0

The equation in slope intercept form is;

$31.25 = 1.25 \times 25 +0$

Hence, the above equation is the slope intercept form.

Learn more about the slope of the straight line;

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2 years ago

a polygon has an area of 225 square meters. A similar polygon is created with an area that is triple the first. By what factor i

GuDViN [60]

The area of the original polygon is:
A = 225 m ^ 2
The similar polygon area is:
A '= (k ^ 2) * (A)
Substituting values:
3 * 225 = (k ^ 2) * (225)
Clearing k we have:
k ^ 2 = 3
k = (3) ^ (1/3)
Answer:
The length of each side increased by:
k = (3) ^ (1/3)

6 0

3 years ago