How to answer equations with rational numbers?

How much will $600 amount to be if it is invested at 10% interest compounded semiannually (two times a year) for 4 years?

Orlov [11]

=600(1+0.1/2)^8 Use the calculator to get the answer :-)

7 0

3 years ago

Joe had $2. He found a quarter but he lost a dollar in the vending machine. How much money does he have now

luda_lava [24]

1.25$ ( 1 dollar and 25 cents )

6 0

2 years ago

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Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

3 0

3 years ago

what types of problems can be solved using the greatest common factors? What types of problems can be solved using the least com

gayaneshka [121]

What types of problems can be solved using the greatest common factor? What types of problems can be solved using the least common multiple? Complete the explanation.
<span>*** Use the words 'same' and 'different' to complete the following sentences.*** </span>

<span>Problems in which two different amounts must be split into (the same) number of groups can be solved using the GCF. Problems with events that occur on (different) schedules can be solved using the LCM.</span>

7 0

3 years ago

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A tree struck by lightning in a storm breaks and falls over to form a triangle with the ground. The tip of the tree makes a 36°

liraira [26]

Answer: approximately 49 feets

Step-by-step explanation:

The diagram of the tree is shown in the attached photo. The tree fell with its tip forming an angle of 36 degrees with the ground. It forms a right angle triangle,ABC. Angle C is gotten by subtracting the sum of angle A and angle B from 180(sum of angles in a triangle is 180 degrees).

To determine the height of the tree, we will apply trigonometric ratio

Tan # = opposite/ adjacent

Where # = 36 degrees

Opposite = x feets

Adjacent = 25 feets

Tan 36 = x/25

x = 25tan36

x = 25 × 0.7265

x = 18.1625

Height of the tree from the ground to the point where it broke = x = 18.1625 meters.

The entire height of the tree would be the the length of the fallen side of the tree, y + 18.1625m

To get y, we will use Pythagoras theorem

y^2 = 25^2 + 18.1625^2

y^2 = 625 + 329.88

y^2 = 954.88

y = √954.88 = 30.9 meters

Height of the tree before falling was

18.1625+30.9 = 49.0625

The height of the tree was approximately 49 feets

5 0

3 years ago