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emmasim [6.3K]
2 years ago
10

What is a secant of a circle

Mathematics
1 answer:
Rasek [7]2 years ago
5 0

In geometry, a secant of a curve is a line that intersects the curve at a minimum of two distinct points. In the case of a circle, a secant will intersect the circle at exactly two points.

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What numbers multiply to 0.32 and also add to 1.2
mylen [45]
.08 x .04 is the right answer

6 0
3 years ago
Solve the proportion
mario62 [17]

Answer:

\boxed{\sf x = 5}

Step-by-step explanation:

\sf Solve  \: for  \: x  \: over  \: the  \: real \:  numbers:  \\ \sf \implies  \frac{2}{x - 3}   =  \frac{5}{x}  \\  \\  \sf Take  \: the \:  reciprocal  \: of  \: both \:  sides:  \\ \sf \implies  \frac{x - 3}{2}  =  \frac{x}{5}  \\  \\  \sf Expand  \: out \:  terms \:  of \:  the \:  left  \: hand \:  side:  \\  \\ \sf \implies \frac{x}{2}  -  \frac{3}{2}  =  \frac{x}{5}  \\  \\  \sf Subtract \:  \frac{x}{5}   -  \frac{3}{2}  \: from  \: both  \: sides: \\  \sf \implies \frac{x}{2}  -  \frac{3}{2} - ( \frac{x}{5}   -  \frac{3}{2} ) =  \frac{x}{5} - ( \frac{x}{5}  -  \frac{3}{2} ) \\  \\  \sf \implies \frac{x}{2}  -  \frac{3}{2} -  \frac{x}{5}    +   \frac{3}{2} =  \frac{x}{5} -  \frac{x}{5}  +  \frac{3}{2}  \\  \\  \sf \frac{x}{5}  -  \frac{x}{5}  = 0 :  \\  \sf \implies \frac{x}{2}  -  \frac{x}{5}  -  \frac{3}{2}  +  \frac{3}{2}  =  \frac{3}{2}  \\  \\  \sf  \frac{3}{2}   -   \frac{3}{2}   = 0:  \\  \sf \implies \frac{x}{2}  -  \frac{x}{5}  =  \frac{3}{2}   \\  \\ \sf \frac{x}{2}  -  \frac{x}{5} =  \frac{5x - 2x}{10}  =  \frac{3x}{10} :  \\   \sf \implies \frac{3x}{10}  =  \frac{3}{2}   \\  \\ \sf Multiply \:  both  \: sides \:  by \:  \frac{10}{3}  : \\   \sf \implies \frac{3x}{10}  \times  \frac{10}{3}  =  \frac{3}{2 }  \times  \frac{10}{3}   \\  \\ \sf \frac{3x}{10}  \times  \frac{10}{3}  =   \cancel{\frac{3}{10} } \times( x) \times  \cancel{ \frac{10}{3} } = x :  \\  \sf \implies x =  \frac{3}{2}  \times  \frac{10}{3} \\  \\   \sf  \frac{3}{2}  \times  \frac{10}{3}  = \cancel{ \frac{3}{2} }  \times \cancel{ \frac{3}{2} }  \times 5 :   \\ \sf \implies x = 5

8 0
3 years ago
Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription see cells if Erica man $42.80 on Monday
Kay [80]
Erica would have sold 121 subscriptions in 3 days.
4 0
3 years ago
Read 2 more answers
Delaware was the first state to enter the Union and Hawaii was the 50th. If we order the positions of entry for the rest of the
Anna71 [15]

Answer:

State A was the <u>12th</u> state to enter the Union. State B was the <u>11th</u> state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}

x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}

x = \frac{-1 \pm 23}{2}

x_1 = \frac{-1 + 23}{2}

x_1 = 11

x_2 = \frac{-1 - 23}{2}

x_2 = -12

The negative solution has no sense in the context of our problem, then the solution is x = 11.

5 0
3 years ago
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