The mean of a set of data is 45 years. Find the missing numbers in the data set {40, 45, 48, ?, 54, ?, 45}. Explain the method or strategy you used.
Answers
315-232=83.
The 2 numbers can each have different values, such as 41 and 42, or 40 and 43. The numbers must add up to 83, though.
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5 times the sum of 12 and a number is 80What is the value of the unknown number
Answers
Answer:
see below
Step-by-step explanation:
1) Slope from P to Q is F/E
2) Definition of slope
3) F'/E' = F/E
Answers
Answer is step 2, 8x - 8= 12 + 4x
The student did not distribute the 2 into the parentheses properly which ruined their entire problem. With 2(4x-4) , you must multiply everything in parentheses by 2.
so 2 x 4x = 8x
2 x -4 = -8
making it 8x- 8 = 12 + 4x ( on the right side all you did was combine like terms)
Answers
2x+4y=0
substitute y with 0
2x+4(0)=0
solve the equation
2x+0=0
2x=0
divide by 2 on both sides
x=0
4x+8y=7
substitute y with 0
4x+8(0)=7
solve the equation
4x+0=7
4x=7
divide by 4 on both sides
x=7/4 or x=1 3/4 or x=1.75
3x-7y=-29
2x+2y=6
solve the bottom equation
3x-7y=-29
x=3-y
substitute for x
3(3-y)-7y=-29
solve the equation
y=19/5
now substitute for y
x=3-
solve for x
x=-4/5
the possible solution of the system is the ordered pair
(x,y)=()
how do this?
y= x+2
y= -4x+7
Answers
y= x+2
y= -4x+7
As you can see both the expressions, x+2 and -4x+7 are equal to "y". That means they are equal to each other too.
So let's equal them and solve it.
Now we have x's value we will plug it in the first equation to find "y".
(1,3)
Answers
Final answer:
The triangles ΔLMN and ΔPQR are similar as per the AA similarity postulate. This is because ΔLMN and ΔPQR have two pairs of congruent corresponding angles: ∠LMN and ∠PQR, and ∠LM and ∠PQ, contemporaneously proving the AA (Angle-Angle) similarity postulate.
Explanation:
The given problem involves two triangles ΔLMN and ΔPQR. Here, ΔLMN is the original triangle, and ΔPQR is a dilated version of ΔLMN by a scale factor of one-half centered at point M.
For the AA (Angle-Angle) similarity postulate, we need to confirm that two angles of one triangle are congruent to two angles of another triangle. If we can establish this, we can deduce that the two triangles are similar.
Firstly, it is given that m∠LMN is 90°. As a property of dilation, it preserves the measures of angles. This means that m∠PQR will also be 90°. Secondly, since the dilation happens at point M, ∠M of ΔLMN will be the same as ∠P of ΔPQR. Thus, we have two sets of corresponding angles (LMN and PQR, and LM and PQ) that are congruent, satisfying the AA similarity postulate. Therefore, we can conclude that ΔLMN is similar to ΔPQR by the AA similarity postulate.
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Final answer:
The triangles ΔLMN and ΔPQR can be proven similar by the AA similarity postulate.
Explanation:
The triangles ΔLMN and ΔPQR are similar to each other by the AA (Angle-Angle) similarity postulate.
AA similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In this case, since ΔPQR is a dilation of ΔLMN with a scale factor of one half, the angles of ΔPQR are congruent to the corresponding angles of ΔLMN.
Therefore, we can conclude that ΔLMN ~ ΔPQR by the AA similarity postulate.
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