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3 years ago

1.Which characteristics will prove that ΔDEF is a right, isosceles triangle?

Mathematics

1 answer:

nika2105 [10]3 years ago

3 0

Answer: The lengths of DE and EF are congruent, and their slopes are opposite reciprocals.

Step-by-step explanation: A right isosceles triangle doesn’t need to have the same slope.

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(a) A photography student borrows RM2 500 to buy a camera. The bank loans this money at a rate of 9 % capitalized monthly. What

Monica [59]

Answer:

The student will have to reimburse 2,991.03 two years later.

Step-by-step explanation:

This is a compound interest problem:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

A is the amount the student will have to reimburse two years later.

P is his loan. so $P = 2,500$

The bank loans this money at a rate of 9 % capitalized monthly. This means that $r = 0.09$ and $n = 12$ , since the money is compounded monthly, this means, 12 times in a year.

He will have to reimburse two years later, so $t = 2$

$A = P(1 + \frac{r}{n})^{nt}$

$A = 2,500(1 + \frac{0.09}{12})^{24}$

$A = 2,991.03$

The student will have to reimburse 2,991.03 two years later.

6 0

3 years ago

Use the pythagorean theorem to find the distance between the points (4,3) and (-4,-3)

maxonik [38]

Draw a right triangle (attachment below):

Length of the vertical line = 6 units

Length of horizontal line = 8 units

a^2 + b^2 = c^2

6^2 + 8^2 = 100

Square root of 100 = 10

The distance between the two points is 10 units.

7 0

3 years ago

Read 2 more answers

Twice the difference of a number and 5 is 7

zysi [14]

The difference of a number and 5 = n - 5

Twice that = 2(n - 5)

‘is’ is the equal sign, so the expression before is equal to 7.

Equation: 2(n - 5) = 7

3 0

3 years ago

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Stephanie has an aquarium that is in the shape of a right rectangular prism, 50 centimetres long, 25 centimetres wide and 30 cen

Bess [88]

To solve this, we are going to use the volume formula for a rectangular prism: $V=lwh$
where
$V$ is the volume of the prism
$l$ is the length of the prism
$w$ is the width of the prism
$h$ is the height of the prism

We are also using the volume of a sphere formula: $V= \frac{4}{3} \pi r^{3}$
where
$V$ is the volume of the sphere
$r$ is the radius of the sphere

Part A: Since she <span>wants a layer of marbles in the bottom of the tank about 5 centimeters deep, the height of this little rectangular prism will be 5 centimeters, so </span> $h=5$ . Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(5)$
$V=6250 cm^{3}$
Now that we know that she wants to cover a volume of 6250 $cm^{3}$ with marbles, lets find the volume of each marble.
We know that the diameter of each marble is 1 cm. Since the radius is of a sphere is half its diameter, $r= \frac{1}{2} =0.5$ . Lets replace that value in our volume formula:
$V= \frac{4}{3} \pi r^{3}$
$V= \frac{4}{3} \pi (0.5)^{3}$
$V=0.52 cm^{3}$
Now, let $x$ the number of marbles she will need to cover a volume of 6250 $cm^{3}$ :
$0.52x=6250$
$x= \frac{6250}{0.52}$
$x=12019.23$
Since we know that each bag of marbles has 500 marbles, we are going to divide the number of marbles she will need by the number of marbles in each bag:
$\frac{12019.23}{500} =24.03$

We can conclude that to fill a layer of 5 cm with marbles, she will need 24 bags of marbles.

Part B: We know that she already have 5 cm of her aquarium filled with marbles, and that she also added water <span>until it’s level is 3 centimeters below the top of the tank, so to find the height of this new rectangular prism, we are going to subtract 5 cm plus 3 cm from the original height of her aquarium:
</span> $h=30-(5+8)$
$h=30-13$
$h=17cm$
Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(17)$
$V=21250cm^{3}$
Remember that $1litre=1000cm^{3}$ . So:
$(21250cm^3)( \frac{1litre}{1000cm^{3})} =21.25liters$

We can conclude that there are 21.25 liters of water in the tank.

6 0

3 years ago

Jon has painted 4/5 of his house the next day he painted 2/3 of what he had left. What fraction of the House is left to paint

lukranit [14]

After Jon’s painted 4/5 of the house, he has 1/5 left. 1/3 of 1/5 is 1/15, so 2/3 of 1/5 is 2/15. He has 1/5 = 3/15 left to paint, and he paints another 2/15, so the leaves him with 3/15 - 2/15 = 1/15 of the house left to paint.

5 0

3 years ago

Read 2 more answers