Answer:
77
Step-by-step explanation:
b is present in both ratios, find first the LCM of 8 and 6, which is 24.
Multiply a:b=3:8 by 3 to get a:b=9:24
Similarly, multiply b:c=6:11 by 4 to get b:c=24:44
Then we conclude
a:b:c=9:24:44
Since there is no common factor among the three numbers, this is the simplest ratio possible.
If a,b and c are integers, the smallest values for a,b and c are 9,24,44.
Add up the three numbers to get the least value of a+b+c=77.
1. Add 6x to both sides
-10 > 14 + 2x + 6x
2. Simplify 14 + 2x + 6x to 14 + 8x
-10 > 14 + 8x
3. Subtract 14 from both sides
-10 - 14 > 8x
4. Simplify -10 - 14 to -24
-24 > 8x
5. Divide both sides by 8
- 24/8 > x
6. Simplify 24/8 to 3
-3 > x
7. Switch sides
x < -3
Answer: 24) C. SSS only
26) D. DH = HF
<u>Step-by-step explanation:</u>
24.
<u>Statement</u> <u>Reason</u>
1. BD = CA 1. Given
2. AB = CD 2. Given
3. AD = AD 3. Reflexive Property
4. ΔABD = ΔDCA 4. SSS Congruency Theorem
<em>We have no information about the angles so cannot use SAS Theorem.</em>
26. G H F
E H D
Line up the letters to find the congruent sides:
⇒ GH = EH
HF = HD
GF = ED
<h3>
Answer: C) 3</h3>
The rule we'll use is a^b*a^c = a^(b+c). So we add the exponents.
That means 5^n*5^3 = 5^(n+3)
So 5^n*5^3 = 5^6 turns into 5^(n+3) = 5^6
The bases are equal to 5, so the exponents be equal to one another.
n+3 = 6
n+3-3 = 6-3
n = 3
So 5^3*5^3 = 5^(3+3) = 5^6.
In
order to solve for a nth term in an arithmetic sequence, we use the formula
written as:<span>
an = a1 + (n-1)d
where an is the nth term, a1 is the first value
in the sequence, n is the term position and d is the common difference.
First, we need to calculate for d from the given
values above.
<span>a3 = 20.5 and a8 = 13
</span>
an = a1 + (n-1)d
20.5 = a1 + (3-1)d
</span>an = a1 + (n-1)d
13 = a1 + (8-1)d
<span>
a1 = 23.5
d = -1.5
The 11th term is calculated as follows:
a11 = a1 + (n-1)d
a11= 23.5 + (11-1)(-1.5)
a11 =
8.5</span>
