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Firlakuza [10]
2 years ago
14

Help me please.

Mathematics
1 answer:
mart [117]2 years ago
5 0

Answer:

∧ABC ≈ ∧PQR  Angle-Angle Similarity Postulate

∧  ABC ≈ ∧  DEF   Side-Side-Side Similarity Postulate

Step-by-step explanation:

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Graph the line and the parabola and find the points of intersection: y= 3-x ; y=x(squared)+x-12
melomori [17]

Answer:

Step-by-step explanation:

We have to graph a line y = 3 - x which has the slope = -1 and y intercept 3.

We will select two points where line intersects at x = 0 and y = 0

The given line will intersect x-axis at (3, 0) and at y- axis (0, 3).

Joining these two points we can draw a straight line showing y = -x + 3

Now we will draw the parabola given by equation y = x² + x - 12

We will convert this equation in vertex form first to get the vertex and line of symmetry.

Standard equation of a parabola in vertex form is

y = (x - h)² + k

Where (h, k) is the vertex and x = h is the line of symmetry.

y = x² + x - 12

y = x² + 2(0.5)x + (0.5)²- (0.5)²-12

y = (x + 0.5)² - 12.25

Therefore, vertex will be (-0.5, -12.25) and line of symmetry will be x = 0.5

For x intercept,

0 = (x + 0.5)² - 12.25

x + 0.5 = ±√12.25

x = -0.5 ± 3.5

x = -4, 3

For y- intercept,

y = (0+0.5)² - 12.25

 = 0.25 - 12.25

y = -12

So the parabola has vertex (-0.5, - 12.25), line of symmetry x = 0.5, x intercept (4, 0), (and y-intercept (0, -12).

Now we have to find the points of intersection of the given line and parabola.

For this we will replace the values of y

3 - x = x² + x - 12

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

x = 3, -5

For x = 3

y = 3- 3 = 0

For x = -5

y = 3 + 5 = 8

Therefore, points of intersection will be (3, 0) and (-5, 8)

 

4 0
2 years ago
Given: ABCD is a trapezoid, AB = CD, BK ⊥ AD, AK = 10, KD = 20 Find: BC AD
alexdok [17]

Answer:

<u> BC = 10 and AD = 30</u>

Step-by-step explanation:

In figure-1 , AB = CD ,BK ⊥ AD,  AK = 10,  KD = 20.

Since, line AD is sum of AK and  KD, then

AD = AK + KD

AD = 10 + 20

AD = 30

Since, BC ║AD and BK ⊥ AD then similarly we construct CL ⊥ AD

so, BC = KL and AK = LD

KL = AD - LD

KL = 20 - 10

KL = 10

Since, BC = KL then BC = 10

Hence, <u> BC = 10 and AD = 30</u>

4 0
3 years ago
Can someone please help me and explain to me how to do this geometry problem please? thank you!! ❤
Dennis_Churaev [7]
Measures of angles 2, 3, 4, added equal 180

3 0
3 years ago
How do you write 2/9 as a %
Dmitriy789 [7]
The answer is 22.222222%.
5 0
3 years ago
Read 2 more answers
Name the pair of opposite rays with endpoint N.
Elza [17]

Answer:

<h2>Possible Answers: NA and NX or NM and NC.</h2>

Step-by-step explanation:

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3 0
3 years ago
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