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3 years ago

Find the slope of the line through the points (-9, 19) and (-13, 11).

Mathematics

1 answer:

Sidana [21]3 years ago

8 0

Answer:

slope is 2

Step-by-step explanation:

slope is m= y2-y1/x2-x1= 19-11/-9+13= 8/4=2

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Find the equation of the parabola that passes through

valentinak56 [21]

so we have the points of (0,-7),(7,-14),(-3,-19), let's plug those in the y = ax² + bx + c form, since we have three points, we'll plug each one once, thus a system of three variables, and then we'll solve it by substitution.

$\bf \begin{array}{cccllll} \stackrel{\textit{point (0,-7)}}{-7=a(0)^2+b(0)+c}& \stackrel{point (7,-14)}{-14=a(7)^2+b(7)+c}& \stackrel{point (-3,-19)}{-19=a(-3)^2+b(-3)+c}\\\\ -7=c&-14=49a+7b+c&-19=9a-3b+c \end{array}$

well, from the 1st equation, we know what "c" is already, so let's just plug that in the 2nd equation and solve for "b".

$\bf -14=49a+7b-7\implies -7=49a+7b\implies -7-49a=7b \\\\\\ \cfrac{-7-49a}{7}=b\implies \cfrac{-7}{7}-\cfrac{49a}{7}=b\implies -1-7a=b$

well, now let's plug that "b" into our 3rd equation and solve for "a".

$\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill$

3 0

3 years ago

Suppose for a cookout you need to make 100 hamburgers. YOu know that 2 pounds will make 9 hamburgers. HOw many pounds will you n

Citrus2011 [14]

$\bf \begin{array}{ccll}
lbs&burgers\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&9\\
x&100
\end{array}\implies \cfrac{2}{x}=\cfrac{9}{100}\implies \cfrac{2\cdot 100}{9}=x$

8 0

3 years ago

Two particles, A and B, are initially 37.5 m apart. A is projected in a straight line directly towards B with initial speed 2 ms

Arisa [49]

Answer: 6.66 metres

Step-by-step explanation:

Given that the two particles, A and B, are initially 37.5 m apart.

Acceleration a = velocity/time

Make time t the subject of the formula.

Time t = velocity/acceleration

Time taken by particle A will be

Time t = 2/0.6 = 3.33 seconds

Let's use 2nd equation of motion

S = Ut + 1/2at^2

Distance covered by particle A will be achieved By substitute the values for speed and acceleration into the formula

S = 2 × 3.33 + 1/2 × 0.6 × 3.33^2

S = 6.66 + 0.3 × 11.1

S = 9.99 m

Time taken by particle B will be

Time t = 3/0.4 = 7.5 seconds

Distance covered by particle B will be by using the same formula

S = 3 × 7.5 + 1/2 × 0.4 × 7.5^2

S = 22.5 + 0.2 × 56.25

S = 33.75 metres

Adding the distance covered by particle A

Distance = speed × time

Distance = 2 × 3.33 = 6.66

the distance from A's starting point to C. Is 6.66 metres

6 0

3 years ago

PLEASE HELP 10 POINTS

Whitepunk [10]

Complementary means sum = 90, so 90-57 to get the other angle at 23 degrees

Supplementary means sum = 180, so 180-52 to get the other angle at 128 degrees

8 0

3 years ago

How do you write this out please help

Galina-37 [17]

X is less than or equal to 3

6 0

3 years ago