The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is _____.

Answers

Answer 1

Answer: Term for an AP = a + (n-1)d.

The third term = a + (3 -1)d = a + 2d = 21

The eight term = a + (8 - 1)d = a + 7d = 56

a + 2d = 21
-
a + 7d = 56
__________
0 -5d = -35

-5d = -35

d = -35/-5

d = 7

Substitute d = 7 in a + 2d = 21

a + 2d = 21
a + 2*7 = 21
a + 14 = 21
a = 21 - 14
a = 7

The first term, a = 7.

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If abx - 5 = 0, what is x in terms of a and b?

Answers

Here we want to have x on one side of equation so,
we put number 5 on right side of equation:
abx=5
then we divide both sides by ab to obtain x on left side:
Result:
x= $(5)/(ab)$

$abx - 5 = 0$

$abx - 5 +5= 0+5$

$abx=5$

$(abx)/(ab) = (5)/(ab)$

$x= (5)/(ab)$

The perimeter of a square garden is to be at least 22 feet but not more than 36 feet. Find all possible values for the length of its sides.

Answers

5.5
5.75
6
6.25
6.5
6.75
7
7.25
7.50
7.75
8
8.25
8.50
8.75

Copy and complete:
__:11= 1/3 :6

Answers

Answer:

11/18:11=1/3:6

Step-by-step explanation:

x:11=x/11 so

x/11=1/3/6

x /11=1/3*6

x=11/18

If ΔABC is similar to ΔDEF, the m∠A = 50°, and m∠E = 70°, what is m∠C?A) 60°
B) 70°
C) 90°
D) 120°

Answers

Answer: A) $60^(\circ)$

Step-by-step explanation:

Given: ΔABC is similar to ΔDEF

Therefore,

∠A=∠D=50°

∠B=∠E=70°

∠C=∠F

Using Angle sum property, in triangle ABC, we get

$\angle{A}+\angle{B}+\angle{C}=180^(\circ)\n\n\Rightarrow\ 50^(\circ)+70^(\circ)+\angle{C}=180^(\circ)\n\n\Rightarrow\ 120^(\circ)\angle{C}+=180^(\circ)\n\n\Rightarrow\ \angle{C}=180^(\circ)-120^(\circ)\n\n\Rightarrow\ \angle{C}=60^(\circ)$

The angle sum property of a triangle says that, the sum of all the angles in a triangle is $180^(\circ)$ .

Ok so if they are similar that means equal angles so 50+70=120 then 180-120=60 so the answer is A. #TeamAlvaxic

Use the equation below and choose the correct answers for c, the total of the payments, and the monthly payment. Carl Carpenter buys a drill press. The price, including tax, is $725.00. He finances the drill press over 24 months after making a $50 down payment. The true annual interest rate is 14%. What are Carl's monthly payments (principal plus interest)? Amount of Interest to the nearest penny, c = $ . Total of payments = amount financed + c = $ . Total of payments ÷ number of payments = monthly payment = $

Answers

(0.14×675×52)÷(2×12)=204.75
675+204.75==879.75
879.75/24==36.65

Make a formula to find the of the diameter 'a' if the area is 'A'.

Answers

Answer:

$2\sqrt{(A)/(\pi)} = a$

Step-by-step explanation:

I am assuming that you are referring to the diameter and area of a circle. If this is false, then please note that my answer is wrong.

Ok, we know that the area formula for a circle is A = $\pi r^(2)$ , where r is the radius.

We also know that the diameter, a, is two times the radius. Thus, $a = 2r$ , which also means that $(1)/(2) a = r$ . This means that we can substitute the radius (r) with half the diameter ( $(1)/(2)a$ ) in the area formula equation:

$A = \pi *((1)/(2) a)^(2)$

Your question asks us to find the diameter, which means we must solve for, or isolate, the diameter (a):

$A = \pi *((1)/(2) a)^(2)\n(A)/(\pi) =((1)/(2) a)^(2)\n(A)/(\pi) =(1)/(4) a^(2)\n(4A)/(\pi) = a^(2)\n\sqrt{(4A)/(\pi)} = a\n2\sqrt{(A)/(\pi)} = a$

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