What is the coordinate of the focus

Determine whether each expression can be used to find the length of side AB. Match Yes or No for each

tankabanditka [31]

Answer:

$(a)\ AB = \frac{7}{\sin (B)}$ $\to Yes$

$(b)\ AB = \frac{24}{\cos (B)}$ $\to Yes$

$(c)\ AB = \frac{24}{\cos (A)}$ $\to No$

$(d)\ AB = \frac{7}{\cos (A)}$ $\to Yes$

Step-by-step explanation:

Given

$BC =24$

$AC = 7$

Required

Select Yes or No for the given options

$(a)\ AB = \frac{7}{\sin (B)}$ $\to Yes$

Considering the sine of angle B, we have:

$\sin(B) = \frac{Opposite}{Hypotenuse}$

$\sin(B) = \frac{7}{AB}$

Make AB, the subject

$AB = \frac{7}{\sin(B)}$

$(b)\ AB = \frac{24}{\cos (B)}$ $\to Yes$

Considering the cosine of angle B, we have:

$\cos(B) = \frac{Adjacent}{Hypotenuse}$

$\cos(B) = \frac{24}{AB}$

Make AB the subject

$AB = \frac{24}{\cos(B)}$

$(c)\ AB = \frac{24}{\cos (A)}$ $\to No$

Considering the cosine of angle B, we have:

$\cos(A) = \frac{Adjacent}{Hypotenuse}$

$\cos(A) = \frac{7}{AB}$

Make AB the subject

$AB = \frac{7}{\cos(A)}$

$(d)\ AB = \frac{7}{\cos (A)}$ $\to Yes$

<em>This has been shown in (c) above</em>

3 0

3 years ago

Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)

Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

$d=\sqrt{(3)^{2}+(9)^{2}}$

$d_D_E=\sqrt{90}\ units$

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

$d=\sqrt{(11)^{2}+(-10)^{2}}$

$d_D_F=\sqrt{221}\ units$

step 4

Classify the triangle by the measure of its sides

we have

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

6 0

3 years ago

What do you need to know?

cupoosta [38]

Answer:

incorrect

Step-by-step explanation:

the volume of a cube = s³ ( where s is the length of the side )

to find s take the cube root

s = $\sqrt[3]{27}$ = 3

since 3 × 3 × 3 = 27

4 0

3 years ago

The initial number of views for a certain website was 15. The number of views is growing exponentially at a rate of 22% per week

Oksi-84 [34.3K]

t he number of views expected to be four weeks from now can be calculated using the equation:

F = P ( 1+i)^n

Where F is the future views

P is the present views

i is the percent increase in views

n is the number of weeks

F = 15 ( 1+ 0.22)^4

F = 33 views

8 0

3 years ago

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What is the solution of this system of linear equations? 3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.X + 6 y – S

Scrat [10]

Answer:

(0,6)

Step-by-step explanation:

The given system of equations is

$y = \frac{3}{2}x + 6$

and

$\frac{1}{2}y - \frac{1}{4}x = 3$

We substitute the first equation into the second equation to get:

$\frac{1}{2} ( \frac{3}{2}x + 6) - \frac{1}{4}x = 3$

We expand to get:

$\frac{3}{4} x + 3 - \frac{1}{4}x = 3$

We group similar terms to get:

$\frac{3}{4}x - \frac{1}{4}x = 3 - 3$

$\frac{1}{2}x = 0$

$x = 0$

Put x=0 in to the first equation to get:

$y = 6$

Therefore the solution is (0,6)

3 0

3 years ago

Read 2 more answers