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Anastaziya [24]
2 years ago
5

Please help!! asap!!!

Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
6 0

Solution:

Rewrite 3 ≥ y - 2 for easier calculation:

y - 2 ≤ 3

Move the term:

y ≤ 3 + 2

y ≤ 5

When graphing the solution, filled dot (black arrow) is used for ≤ and ≥ while empty dot (white arrow) is used for < >

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Step-by-step explanation:

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Answer: A 100

I did the text the other day

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Determine the most specific name for quadrilateral JKLM if the coordinates of the vertices are:J(-4,6), K(-1,2), L(1,6), M(4,2)J
Arturiano [62]

To finish the demonstration that the quadrilateral JKLM is a rhombus we need to prove that side JK is congruent with side LM.

The length of a segment with endpoints (x1, y1) and (x2, y2) is calculated as follows:

\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}

Substituting with points L(1,6) and M(4,2) we get:

\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{3^2+(-4)^2} \\ LM=\sqrt[]{9+16^{}} \\ LM=5 \end{gathered}

Given that opposite sides are parallel, all sides have the same length, and, from the diagram, the quadrilateral is not a square, we conclude that it is a rhombus.

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Step-by-step explanation:

I would say 5.6 but that's my opinion

8 0
2 years ago
Two princesses, Nat and Kat, are gifted with a savings account from their royal parents, Matt and Pat, when they turn 5 years ol
Arte-miy333 [17]

Answers and Step-by-step explanations:

(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:

m = (21200 - 6200) / (7 - 2) = 3000

Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:

y = 3000x + b

6200 = 3000 * 2 + b

b = 200

Nat's equation is y = 3000t + 200.

(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:

y = a(x - h)² + k, where (h, k) is the vertex

Plug in our vertex:

y = a(x - 20)² + 44100

We also have the point (9, 32000), so put that in to find a:

32000 = a(9 - 20)² + 44100

-12100 = a * 121

a = -100

So Kat's equation is y = -100(t - 20)² + 44100.

(c) In order to find the age when they have the same amount, we set the two equations equal:

3000t + 200 = -100(t - 20)² + 44100

-100(t² - 40t + 400) + 44100 = 3000t + 200

-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0

-100t² + 1000t + 3900 = 0

t² - 10t - 39 = 0

(t - 13)(t + 3) = 0

t = 13 or t = -3   --   obviously, years can't be negative, so t = 13.

Note, however, that t is the number of years <em>after</em> Kat and Nat are 5, so we need to add 13 to 5:

13 + 5 = 18

The age is 18.

4 0
3 years ago
Read 2 more answers
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