MATHEMATICS HIGH SCHOOL

Find the slope of the ordered pair. M(3,8) N(5,14)

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Slope formula, change if y over change of x

14 - 8 = 6

5 - 3 = 2

6/2 = 3

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Determine which ordered pair is a solution of y = –5x + 10. a. (–15, 5)b. (2, 0) c. (–1, –5) d. (3, 25)

Answers

y = - 5 x + 10
A ) x = - 15, y = 5
5 = 75 + 10
5 ≠ 85
B ) x = 2, y = 0
0 = - 5 · 2 + 10
0 = 0 ( correct )
C ) x = - 1, y = - 5,
- 5 = 5 + 10
- 5 ≠ 15
D ) x = 3, y = 25
25 = - 15 + 10
25 ≠ - 5
Answer:
B ) ( 2, 0 )

Answer:

B. (2,0)

Step-by-step explanation:

The given equation is;

$y=-5x=10$

If an ordered pair is a solution, then the ordered pair must satisfy the given equation.

For (-15,5),we have

$5=-5(-15)+10$

$5=75+10$ ,this is FALSE.

For (2,0), we have

$0=-5(2)+10$

$0=-10+10$ , this is TRUE

For (-1,-5), we have;

$-5=-5(-1)+10$

$-5=5+10$ , this is FALSE.

For (3,25), we have;

$25=-5(3)+10$

$25=-15+10$ , this is FALSE

A catering service offers 12 appetizers, 9 main courses, and 7 desserts. A banquet chairperson is to select 8 appetizers, 8 main courses, and 6 desserts for a banquet. In how many ways can this be done?

Answers

$12-appetizers, \ 9- main\ courses, \ 7\ desserts\n \n selection:\ 8\ appetizers,\ 8\ main\ courses, 6\ desserts\n\na=the\ number\ of\ selection\ of\ appetizers:\n \n{12 \choose 8}= (12!)/(8!\cdot (12-8)!) = (12\cdot11\cdot10\cdot9\cdot8!)/(8!\cdot4\cdot3\cdot2) =11\cdot5\cdot9=495\n \nc=the\ number\ of\ selection\ of\ main\ courses:\n \n{9 \choose 8}= (9!)/(8!\cdot (9-8)!) = (9\cdot8!)/(8!\cdot 1) =9$

$d=the\ number\ of\ selection\ of\ desserts:\n \n{7 \choose 6}= (7!)/(6!\cdot (7-6)!) = (7\cdot6!)/(6!\cdot 1) =7\n \nthe\ number\ of\ selection\ sets\ the\ banquet:\n \na\cdot c\cdot d=495\cdot9\cdot7=31185$

[(12! / (8!*4!) ]* [9! / (8!*1!) ] * [ 7!/ (6!*1!)] = ( 12 * 11 * 10 * 9 / 4 * 3 * 2 * 1) * 9 * 7 = 45 * 11 * 9 * 7 = 31185 ways

What is reference angle for 150 degrees

Answers

30 degrees because you want to find the angle between the 150 degrees and it's supplement- if it was 340 then it would be 20 degrees

10 times as many as hundreds is 60 hundreds or thousands

Answers

60 hundreds if it says hundreds then it would still be that

What is the measure of the missing angle?

Triangle with two angles labeled

Answers

Ive already solved this =/ the answer is 40 becuase the grand total sum of all the angles on a triangle is always 180 and because we already have 140 of that taken care of (70+70=140) we know that 180-140=40 therefore 40 is are missing angle.

F(x) = 4x^2 - 3x + 2kx + 1 What's the value of k for which the function has two zeros??
Can someone show me step by step?

Answers

$f(x)=4x^2-3x+2kx+1=4x^2+(2k-3)x+1\n\na=4;\ b=2k-3;\ c=1\n\nfunction\ has\ two\ zeros\ when\ \Delta=b^2-4ac > 0\n\n\Delta=(2k-3)^2-4\cdot4\cdot1=4k^2-12k+9-16=4k^2-12k-7 > 0\n\na_k=4;\ b_k=-12;\ c_k=-7\n\n\Delta_k=(-12)^2-4\cdot4\cdot(-7)=144+112=256\n\nk_1=(-b_k-√(\Delta_k))/(2a_k);\ k_2=(-b_k+√(\Delta_k))/(2a_k)$

$√(\Delta_k)=√(256)=16\n\nk_1=(12-16)/(2\cdot4)=(-4)/(8)=-(1)/(2);\ k_2=(12+16)/(2\cdot4)=(28)/(8)=(7)/(2)\n\na_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\n\nAnswer:k\in(-\infty;-(1)/(2))\ \cup\ ((7)/(2);\ \infty)$

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