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Sveta_85 [38]
3 years ago
11

1000^m/100^n=10^zexpress z in terms of m and n

Mathematics
1 answer:
Hitman42 [59]3 years ago
3 0

\dfrac{1000^m}{100^n}=10^z\\\\\dfrac{10^{3m}}{10^{2n}}=10^z\\\\10^{3m-2n}=10^z\\\\\boxed{z=3m-2n}

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The perimeter of a rectangle must be less than 156 feet. If the length is known to be 66 feet, find the range of possible widths
balu736 [363]

x = perimeter

x<156

length = 66

so, in order to calculate perimeter you need to add two lengths and two widths

so

156 (perimeter) - 2 (66) = two widths

156 - 132 = 24 (remember this number is two widths added together)

so 24 twice the width SO 12 would be the number that the width can't be larger than

the width has to be less than 12

w < 12

5 0
3 years ago
O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
andriy [413]

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28°  ∠ACD=31°  &  line AB=AC .

According To the Question,

  • a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

  • b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

        thus , ∠ABC=76° .

  • c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°)  ⇔  104˚

   

  • d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre  

For Diagram, Please Find in Attachment  

4 0
3 years ago
PLEASE BE QUICKKK!!
elena-s [515]

Answer:

The Answer would be C, i think

Step-by-step explanation:

5 0
3 years ago
The average of 10 numbers is -5. A new number is added to the list making the average -6. What is the new number?
Shtirlitz [24]

Answer:

- 16

Step-by-step explanation:

Average is calculated as

average = \frac{total}{count}

Thus for the given 10 numbers we have

\frac{total}{10} = - 5 ( multiply both sides by 10 )

total = - 50

let the number added be x, then

\frac{total+x}{11} = - 6 ( multiply both sides by 11 )

total + x = - 66, that is

- 50 + x = - 66 ( add 50 to both sides )

x = - 16

The new number is - 16

4 0
3 years ago
$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earne
worty [1.4K]
I'm assuming this is a yearly interest.

2500*.04=100
7500*.05=375

so that would be $475 earned from interest
3 0
3 years ago
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