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2 years ago

Evaluate the following expression: -1(5,-1) + 2(1,1). A. (5,-2) B. (-3,3) C. (7,1) D. (-5,2)

Mathematics

2 answers:

Gre4nikov [31]2 years ago

8 0

I believe that the answer should be B

myrzilka [38]2 years ago

6 0

$-1[5;\ -1]+2[1,\ 1]=[(-1)(5);\ (-1)(-1)]+[(2)(1);\ (2)(1)]=[-5;\ 1]+[2;\ 2]\\\\=[-5+2;\ 1+2]=[-3;\ 3]$
Answer: B

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2 years ago

Please Hurryyy

Helga [31]

The measure of angle J is 19.8°, and the correct option is D.

<h3>What is the formula of cosine?</h3>

The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles cosC.

The following formula is used to find the angle j is;

$\rm j^2 = h^2 + i^2 -2hicosC$

Triangle HIJ has side lengths h=12, i = 17, j = 7.

Substitute all the values in the formula;

$\rm j^2 = h^2 + i^2 -2hicosJ\\\\(7)^2=(12)^2+(17)^2-2 \times 12 \times 17 cosJ\\\\49=144+289-408cosJ\\\\144+289 -49 =408cosJ\\\\384 =408cosJ\\\\cosJ=\dfrac{384}{408}\\\\cosj = 0.94\\\\J =cos^{-1}(0.94)\\\\J=19.8$

Hence, the measure of angle J is 19.8°, and the correct option is D.

Learn more about law cosine here;

brainly.com/question/17289163

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3 0

1 year ago

PLEASE HELP QUICKLY I NEED HELP LESS THEN 5 MINUTES ILL GIVE BRAINLIEST I ONLY HAVE 5 MINUTES LEFT HELP IM FREAKING DESPERATE

yKpoI14uk [10]

Answer:

it would be C.) no distance was covered

Step-by-step explanation:

because the graph did not move on the y-axis

hope this helps

3 0

3 years ago

Can you factor -2x + 6 to get -2(x - 3)

QveST [7]

Answer:

Yes

Step-by-step explanation:

Divide -2x + 6 by -2, then bring the -2 outside the bracket

6 0

2 years ago

I will give lots of points please help

aalyn [17]

Answer:

a) 81π in³

b) 27 in³

c) divide the volume of the slice of cake by the volume of the whole cake

d) 10.6%

e) see explanation

Step-by-step explanation:

The cake can be modeled as a <u>cylinder </u>with:

diameter = 9 in
height = 4 in

$\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in$

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

$\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}$

$\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}$

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

$\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}$

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

$\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}$

Probability is approximately 10.6% (see above for calculation)

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

3 0

1 year ago