Answers:
Expression for the total number of quarters is 40*1.20
Amount of money you have left is 6 dollars
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Explanation:
You start with 40 quarters. 20% of this is 0.20*40 = 8 which means you found 8 more quarters. The total goes from 40 to 40+8 = 48.
A slight shortcut is to write 40*1.20 = 48
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48 quarters = 48*0.25 = 12 dollars
Or you can divide by 4 to determine the total value of the quarters in dollars.
If you spent half (50%) of that money, then you'll be left with 6 dollars.
Answer:
60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides in a right triangle. Here, we're given the side Adjacent and the side Opposite the angle of interest. This makes it appropriate to choose the relation ...
Tan = Opposite/Adjacent
For our angle of elevation α, this means ...
tan(α) = 125/72
α = arctan(125/72) = 60.058°
α ≈ 60°
The angle of elevation is about 60°.
1) Expression 1: 16x^3 y
2) Expression 2: 24 xy^5
Procedure:
1) find the greatest common factor of the coefficients, 16 and 24:
16 = 2^4
24 = (2^3)*3
=> greatest common factor = 2^3 = 8
2) find the greatest common factor of x^3 y and xy^5
That is the common letters each raised to the lowest power:
=> xy
3) Then, the result is 8xy
Answer: |81-x|<5
Step-by-step explanation:
Given: Temperature of an enclosure for a pet corn snake should be an average of 81° F.
Temperature in the enclosure should not vary by more than 5° F.
Let x= Temperature in the enclosure
Then, difference between average and current temperature should less the 5.
i.e. |81-x|<5 (required absolute value equation )
hence, the absolute value equation could be used to determine the minimum and maximum temperatures recommended for the corn snake enclosure:
|81-x|<5
Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
