All categories

3 years ago

Let the function f be defined by f(x)=12-5x b)evaluate f(-1)

Mathematics

2 answers:

Alexxx [7]3 years ago

6 0

F(-1) = 12 - 5(-1)
f(-1) = 12 + 5
Solution: f(-1) = 17

OverLord2011 [107]3 years ago

5 0

F(x) = 12-5(-1)
= 12-(-5)
= 17

You might be interested in

Which real-world scenario can be described using the algebraic expression c/4?

Romashka [77]

Answer:

Baking c cookies and dividing them evenly among 4 friends.

Step-by-step explanation:

7 0

2 years ago

Using the following image, if you EG = 59, what are x, EF, and FG.

Harman [31]

Answer:

$x=6\,\,units\,,\,EF=34 \,\,units\,,\,FG=25\,\,units$

Step-by-step explanation:

Given: $EG =59 \,\,units$

To find: $x,EF,FG$

Solution:

From the image, $EG=EF+FG$

Put $EF=8x-14\,,\,FG=4x+1\,,\,EG=59$

$8x-14+4x+1=59\\12x-13=59\\12x=59+13\\\\12x=72\\x=\frac{72}{12}=6$

$EF=8x-14=8(6)-14=48-14=34\\FG=4x+1=4(6)+1=24+1=25$

Therefore,

$x=6\,\,units\,,\,EF=34 \,\,units\,,\,FG=25\,\,units$

8 0

3 years ago

What is the unit rate of 8 miles and 92 minutes?

Alinara [238K]

11.5 minutes per mile

5 0

3 years ago

Prove :

Sauron [17]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{1}{\sec\alpha+1}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

We can convert sec(α) to 1 / cos(α):

$\displaystyle \frac{1}{1/\cos\alpha+1}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

Multiply both layers of the first fraction by cos(α):

$\displaystyle \frac{\cos\alpha}{1+\cos\alpha}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

Create a common denominator. We can multiply the first fraction by (1 - cos(α)):

$\displaystyle \frac{\cos\alpha(1-\cos\alpha)}{(1+\cos\alpha)(1-\cos\alpha)}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

Simplify:

$\displaystyle \frac{\cos\alpha(1-\cos\alpha)}{1-\cos^2\alpha}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

From the Pythagorean Identity, we know that cos²(α) + sin²(α) = 1 or equivalently, 1 - cos²(α) = sin²(α). Substitute:

$\displaystyle \frac{\cos\alpha(1-\cos\alpha)}{\sin^2\alpha}-\frac{\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha }{\sin^2\alpha }-\frac{1}{\sec\alpha -1}$

Subtract:

$\displaystyle \frac{\cos\alpha(1-\cos\alpha)-\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Distribute:

$\displaystyle \frac{\cos\alpha-\cos^2\alpha-\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Rewrite:

$\displaystyle \frac{(\cos\alpha)-(\cos^2\alpha+\cos\alpha)}{\sin^2\alpha}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Split:

$\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{\cos^2\alpha+\cos\alpha}{\sin^2\alpha}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Factor the second fraction, and substitute sin²(α) for 1 - cos²(α):

$\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{\cos\alpha(\cos\alpha+1)}{1-\cos^2\alpha}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Factor:

$\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{\cos\alpha(\cos\alpha+1)}{(1-\cos\alpha)(1+\cos\alpha)}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Cancel:

$\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{\cos\alpha}{(1-\cos\alpha)}=\frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Divide the second fraction by cos(α):

$\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}=\displaystyle \frac{\cos\alpha}{\sin^2\alpha}-\frac{1}{\sec\alpha-1}$

Hence proven.

7 0

2 years ago

5. Palmer goes to L.A. one weekend. He has a bank account with a balance

dsp73

Answer:

$50

Step-by-step explanation:

To find the total amount that Palmer spent, you would first add up all his purchases. This can be represented by adding $90 + $110 + $100, which adds up to $300.

To find out how much Palmer has left, just subtract $300 from his initial $350 ($350 - $300 = $50.) This gives you a final answer of Palmer having $50 in his bank account.

3 0

3 years ago