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Svetach [21]
3 years ago
5

Allison claims that the (triangle)ABQ is similar to (triangle)RPQ, given that AB and PR are parallel. Which of Allison's claims

supporting her argument are correct? Select all that apply. <1 = <2 because they are vertically opposite angles.<ABQ = <QPR because they are corresponding angles.<1 = <2 because they are alternate interior angles.<BAQ = <QRP because they are alternate interior angles.(triangle)ABQ and (triangle)RPQ are not similar by AA similarity.

Mathematics
1 answer:
S_A_V [24]3 years ago
3 0
I draw the two triangles, see the picture attached.

As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.

Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>

Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles. 
BAQ = QRP because they are alternate interior angles. 

Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar. 

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Answer:

8 hours

Step-by-step explanation:

We have that;

B = number of bacterial cells, B, in a container after t hours

t = time taken in hours

The function is;

B=25x2t

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400 = 25x2t

t = 400/25x2

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3 years ago
David is a professional ice skater who has skated in 10 competitions. ​His scores in the competitions are as follows: 204, 310,
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3 years ago
The graph of y = x^2 -3 is translated in 4 units to the left of the graph to give the graph A
Vedmedyk [2.9K]

Answer:

a) b = 8, c = 13

b) The equation of graph B is y = -x² + 3

Step-by-step explanation:

* Let us talk about the transformation

  • If the function f(x) reflected across the x-axis, then the new  function g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then the new  function g(x) = f(-x)
  • If the function f(x) translated horizontally to the right  by h units, then the new function g(x) = f(x - h)
  • If the function f(x) translated horizontally to the left  by h units, then the new function g(x) = f(x + h)

In the given question

∵ y = x² - 3

∵ The graph is translated 4 units to the left

→ That means substitute x by x + 4 as 4th rule above

∴ y = (x + 4)² - 3

→ Solve the bracket to put it in the form of y = ax² + bx + c

∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)

∴ (x + 4)² = x² + 4x + 4x + 16

→ Add the like terms

∴ (x + 4)² = x² + 8x + 16

→ Substitute it in the y above

∴ y = x² + 8x + 16 - 3

→ Add the like terms

∴ y = x² + 8x + 13

∴ b = 8 and c = 13

a) b = 8, c = 13

∵ The graph A is reflected in the x-axis

→ That means y will change to -y as 1st rule above

∴ -y = (x² - 3)

→ Multiply both sides by -1 to make y positive

∴ y = -(x² - 3)

→ Multiply the bracket by the negative sign

∴ y = -x² + 3

b) The equation of graph B is y = -x² + 3

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3 years ago
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Answer:

Step-by-step explanation:

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I = PRT/100

Where

I = interest

P = principal(amount borrowed from the bank)

R = 9% ( rate at which the interest is charged

T = number of years

At the end of the loan,she had paid a total of 24215. This means that the interest + the principal = 24215

Therefore,

The interest = 24215 - 16700 = 7515

Therefore

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Which of the following shows the length of the third side, in inches, of the triangle below? (1 point)
GrogVix [38]

Answer:

2, sqrt of 7633

Step-by-step explanation:

for now, we'll leave the 3rd side as x

y using the Pythagorean theorem, we can conclude that (1) 48^2+x^2=73^2 or (2) 48^2+73^2=x^2.

1. If we conclude the x isn't the longest, the x would be 3025 which is the sqrt of 55, now is invalid because the 2 smallest sides can't be more than the longest side when they add up 55+48>73 so that is invalid

2. Then, it leaves us with only 1 choice left! concluding that the 3rd side is the longest. Which the answer is sqrt of 7633

6 0
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