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Pie
3 years ago
10

The smiths spent 2,000 on clothes in a particular year if they increase the amount they spend on clothes by 10% each year the sm

iths will spend a total
Mathematics
1 answer:
Finger [1]3 years ago
6 0

They always increase their spending by 10%, so we can always take the previous year's spending and find 110% of it by multiplying by 1.10.

They start at 2,000

In 1 year, they spend 2000×1.1

In 2 years, they spend 2000×1.1×1.1

In 3 years, they spend 2000×1.1×1.1×1.1

In 4 years, they spend 2000×1.1×1.1×1.1×1.1

Because they only ask for four years, you could probably just multiply that out. But what if they asked for the 20th year? or the fiftieth? You wouldn't want to calculate that, you would want to find a pattern.

Well really, we want to keep track of repeated multiplication, which we can do by using exponents. Look carefully at the pattern:

year 1 = 2000×1.11

year 2 = 2000×1.12

year 3 = 2000×1.13

year 4 = 2000×1.14

Do you see it?

year n = 2000×1.1n

Finding patterns like this are going to be critical for geometric series
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Using identity evaluate: (104)²​
SOVA2 [1]

Answer:

104×104=10816

Step-by-step explanation:

104²=104×104

=10816

8 0
2 years ago
A pair of parallel lines are cut by a transversal. Which of the following statements about the new angle pairs are now always tr
Hoochie [10]

Answer:

The true statements are:

* The Corresponding Angles Congruent ⇒ B

* Same Side Interior Angles are supplementary ⇒ C

* Alternate Interior Angles are congruent ⇒ F

Step-by-step explanation:

∵ Lines m and l are parallel

∵ Line t intersects them

∵ Corresponding angles are equal in measures

∴ ∠1 = ∠5 ⇒ corresponding angles

∴ ∠3 = ∠7 ⇒ corresponding angles

∴ ∠2 = ∠6 ⇒ corresponding angles

∴ ∠4 = ∠8 ⇒ corresponding angles

∵ The alternate interior angles are equal in measures

∴ ∠3 = ∠6 ⇒ alternate interior angles

∴ ∠4 = ∠5 ⇒ alternate interior angles

∵ The same side interior angles are supplementary

∴ m∠3 + m∠ 5 = 180° ⇒ same side interior angles

∴ ∠3 and ∠5 are interior supplementary angles

∴ m∠4 + m∠ 6 = 180° ⇒ same side interior angles

∴ ∠4 and ∠6 are interior supplementary angles

The true statements are:

* The Corresponding Angles Congruent ⇒ B

* Same Side Interior Angles are supplementary ⇒ C

* Alternate Interior Angles are congruent ⇒ F

6 0
2 years ago
Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real
garik1379 [7]

The complete question is

"Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

0 = 2x^2 – 7x – 9

0 = 4x^ 2 – 3x – 1

The quadratic equations that have real number solutions are; 4x^2 – 3x – 1, and 2x^2 – 7x – 9.

<h3>What is the formula for Discriminant?</h3>

The formula for finding the discriminant is

b^2 - 4ac

The solution contains the term \sqrt{b^2 - 4ac} which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

For the quadratic equation 2x^2 - 7x - 9

b^2 - 4ac

= (-7) ^2 - 4( 2) ( -9)\\\\= 49 + 72 = 121

This equation has two real number solutions.

For the quadratic equation 4x^ 2 - 3x- 1

b^2 - 4ac

= (-3) ^2 - 4( 4) ( -1)\\\\= 9 + 16 = 25

This equation will have two real number solutions.

Learn more on discriminant here:

brainly.com/question/1537997

#SPJ1

5 0
2 years ago
Find the area of the regular 18-gon with radius 10 mm
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Answer:

Step-by-step explanation:

Find the area of the regular 18-gon with radius 10 mm

3 0
3 years ago
If AB = CA and m1 = 45°, what is m3?
navik [9.2K]

Answer:

B 45 degrees

Step-by-step explanation:

if AB and CA are = the M2 = 90 degrees

in an right triangle ware one angle is 90 degrees and one is 45 degrees the outer one will be 45 degrees  

the total of the angles in a triangle is 180 degrees so 180 - 90 = 90

90 - 45 = 45

so the remaining angle is 45.

4 0
2 years ago
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