All categories

2 years ago

Evaluate function at the given value using the remainder theorem.

Mathematics

1 answer:

garik1379 [7]2 years ago

5 0

Answer:

Step-by-step explanation:

$f(a)=a^4-2a^3 -10a^2 -7a \\\\f(-2) = (-2)^4-2(-2)^3 -10(-2)^2 -7(-2)\\\\~~~~~~~~~=16-2(-8)-10(4)+14\\\\~~~~~~~~~=30+16-40\\\\~~~~~~~~~=46-40\\\\~~~~~~~~~=6$

You might be interested in

Vita saved $72 last December. This amount represents 2/9 of the total amount she saved last year. What is the total amount Vita

GrogVix [38]

$\dfrac{2}{9} \text { of the saving} = \$72$

-----------------------------------------------
Find 1/9 :
-----------------------------------------------
$\dfrac{1}{9} \text { of the saving} = \$72 \div 2$

$\dfrac{1}{9} \text { of the saving} = \$36$

-----------------------------------------------
Find 9/9 :
-----------------------------------------------
$\dfrac{9}{9} \text { of the saving} = \$36 \times 9$

$\dfrac{9}{9} \text { of the saving} = \$324$

-----------------------------------------------
Answer: The total amount is $324.
-----------------------------------------------

7 0

3 years ago

Tripp and Rico are two dogs. Tripp weighs exactly 35 pounds more than Rico. Together, they weigh exactly 49 pounds. How much doe

babymother [125]

Call the weights of the two dogs $t$ and $r$ .

We know that Tripp weights 35lbs more than Rico, or:
$t=r+35$

We also know that the total weight of both dogs is 49lbs.:
$t+r=49$

Now, by substitution:
$(r+35)+r=49$
$2r+35=49$
$2r+35-35=49-35$
$2r=14$
$r=\frac{14}{2}$
$r=7$
Rico weighs 7lbs.

Then:
$t=r+35$
$t=7+35$
$t=42$
Tripp weighs 42lbs.

To check our work:
$t+r=49$
$42+7=49$
$49=49$ CHECK!

5 0

3 years ago

Solve this system of equations by using the elimination method -2x-2y=-6, 3x+4y=8

adoni [48]

Step-by-step explanation:

- 2x-2y=-6

3x+4y=8

multiply equation (1) by 3 and equation (2) by 2

- 6x-6y=18

6x+8y=16

Add

2y=34

y= 34÷2

y=17

substitute 17 for y in equation (2)

3x+4y=8

3x+4(17)=8

3x+68=8

3x=8-68

3x=-60

x=-60÷3

x=-20

x=-20,y=17

8 0

3 years ago

The feet of the average adult woman are 24.6 cm long, and foot lengths are normally distributed. If 16% of adult women have feet

nevsk [136]

Answer:

Approximately 16% of adult women have feet longer than 27.2 cm.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The feet of the average adult woman are 24.6 cm long

This means that $\mu = 24.6$