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2 years ago

-3(k-8)-(k+5)=23 please explain how to do this

Mathematics

2 answers:

VMariaS [17]2 years ago

6 0

Answer:

k = -1

Step-by-step explanation:

Use the distributive property to eliminate parentheses. That property tells you that the outside factor multiplies each term inside parentheses:

-3(k -8) -(k +5) = 23

-3k -3(-8) -k -(+5) = 23

-3k +24 -k -5 = 23 . . . . simplify

-4k +19 = 23 . . . . . . . . . collect terms

-4k = 4 . . . . . . . . . . . . . subtract 19 from both sides

k = -1 . . . . . . . . . . . . . . . divide both sides by -4

_____

The rule for manipulating equations is, "any operation performed on one side of the equation must also be performed on the other side." Operations include addition, subtraction, multiplication, division, application of a function. Using the distributive property and collecting terms are ways to simplify equations that don't affect the truth of the equal sign (if those are done correctly).

In general, you make use of inverse operations to undo the operations you don't want. The goal is to get the variable by itself on one side of the equal sign.

lora16 [44]2 years ago

3 0

Answer:

k = -1

Step-by-step explanation:

-3(k-8)-(k+5)=23

Distribute

-3k +24 -k-5 = 23

Combine like terms

-4k +19 = 23

Subtract 19 from each side

-4k +19-19 = 23-19

-4k = 4

Divide by -4

-4k/-4 = 4/-4

k = -1

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1 year ago

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2 years ago

Consider two vectors A and B A=14i and B= -4i+8j

DaniilM [7]

Assuming $\mathbf a,\mathbf b\in\mathbb R^3$ , you have

$\mathbf a\cdot\mathbf b=(14)(-4)+(0)(8)=-56$

so

$((\mathbf a\cdot\mathbf b)\,\mathbf i)\cdot\mathbf a=(-56\,\mathbf i)\cdot(14\,\mathbf i)=(-56)(14)=-784$

Next,

$\mathbf a+\mathbf b=(14\,\mathbf i)+(-4\,\mathbf i+8\,\mathbf j)=10\,\mathbf i+8\,\mathbf j$

Then

$(\mathbf a+\mathbf b)\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\10&8&0\\-4&8&0\end{vmatrix}=112\,\mathbf k$

$((\mathbf a+\mathbf b)\times\mathbf b)\times\mathbf k=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&112\\0&0&1\end{vmatrix}=\mathbf 0$

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2 years ago

Suppose that the weights of passengers on a flight to Greenland on Frigid Aire Lines are normal with mean 175 pounds and standar

Natali5045456 [20]

Answer:

The minimum weight for a passenger who outweighs at least 90% of the other passengers is 203.16 pounds

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 175, \sigma = 22$