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3 years ago

Select ALL choices where 3 is the GCF of the pair of n umbers,

Mathematics

1 answer:

padilas [110]3 years ago

3 0

Answer:

A, B, D

Step-by-step explanation:

A: factors of 9= 1, 3, 9/factors of 15= 1, 3, 5, 15. Their largest common one is 3

B: factors of 9= 1, 3, 9/factors of 21= 1, 3, 7, 21. Their largest common factor is 3

C: factors of 12= 1, 2, 3, 4, 6, 12/ factors of 18= 1, 2, 3, 6, 9, 18. Their largest common factor is 6, not 3

D: factors of 15= 1, 3, 5, 15/ factors of 27= 1, 3, 9, 27. Their biggest common factor is 3.

E: factors of 30= 1, 2, 3, 5, 10, 15, 30/ factors of 45= 1, 3, 5, 9, 15, 45. Their largest common factor is 15, not 3.

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The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion

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Answer:

The pair of triangles that are congruent by the ASA criterion isΔ ABC and Δ XYZ.

The pair of triangles that are congruent by the SAS criterion is Δ BAC and ΔRQP.

Step-by-step explanation:

Two triangles are congruent by ASA property if any two angles and their included side are equal in both triangles .In triangles Δ ABC and Δ XYZ the equal side 5 is between the two equal angles. So these triangles are congruent by ASA criterion.

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3 years ago

Item cash car (paid off) credit card debt motorcycle debt savings

MrMuchimi

Answer:

Step-by-step explanation:

add his cash,car that's paid off,and his savings.

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3 years ago

Which inequality is represented by the graph? y≥35x−1.5 y≤35x−1.5 y<35x−1.5 y>35x−1.5

Setler79 [48]

Answer:

y > 0.6x - 1.5

Step-by-step Explanation:

We need two points, to get to the equation of the graph.

Since we've got the following equation for two points (x1, y1), (x2, y2):-

$\boxed{ \mathsf{ \red{y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1}) }}}$

okay soo

I found two points that lie on this graph, not on the shaded region but yeah the dotted line which defines the graph.

one point is <u>(0, -1.5)</u> which lies on the y axis(the point where the dotted line touches the y axis)

other point is <u>(2.5, 0)</u> and this lies on the x axis

placing these points in the place of (x1, y1) and (x2, y2) in the above mentioned equation

$\mathsf{\implies y - ( - 1.5) = \frac{0 -( - 1.5)}{2.5 -0 } (x -0 )}$

you can take any one as (x1, y1) or (x2, y2).

so upon solving the above equation we get

$\mathsf{\implies (y + 1.5) = \frac{0 + 1.5}{2.5 } (x )}$

$\mathsf{\implies y + 1.5 = \frac{ 1.5}{2.5 } x }$

$\mathsf{\implies y + 1.5 = \frac{ \cancel{1.5}\:\:{}^3}{\cancel{2.5}\:\:{}^5 } x }$

$\mathsf{\implies y + 1.5 = \frac{ 3}{5 } x }$

multiplying both sides by 5

$\mathsf{5y + 7.5 = 3x}$

okay so this is the required equation of the dotted line

now we'll find the inequality

for this check whether the origin (0,0) lies under the shaded region or not

in this case it does

replacing x and y with 0

$\mathsf{\implies5(0) + 7.5 = 3(0)}$

$\mathsf{\implies0 + 7.5 = 0}$

this is absurd, 7.5 is not equal to 0 so we're gonna replace that equals sign with that of inequality

7.5 is greater than 0! so,

$\mathsf{\implies7.5 > 0}$

this goes for the whole equation, since we didnt swap any thing from left to right side of the equation or vice versa we can use this sign, to obtain the required inequality

$\mathsf{5y + 7.5 > 3x}$

dividing this inequality by 5, since there's no co-efficient in front of y in the given answers

we get

y + 1.5 > 0.6x

taking 1.5 to the RHS

that is the last option

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