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3 years ago

15

Recognizing Right Triangle Scenarios

1 answer:

Alex Ar [27]3 years ago

6 0

Answer:

Wendy leaves school to go home. She walks 60 yards north and then 80 yards west. She is 10 yards from the school.

Step-by-step explanation:

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4 Abi is going to buy ingredients to make 65 hot chocolate drinks.

Semenov [28]

Answer:

To make 65 chocolate drinks, she needs:

12 g of chocolate powder and 5 marshmallows per drink.

Then she needs:

12g*65 = 780 grams of chocolate powder.

We know that the chocolate powder comes in jars of 250g, such that each one costs £2.99

If she buys 3 jars, she will have: 3*250g = 750g

So she will not have enough, then she needs to buy 4 jars.

Then in chocolate powder, she will pay 4 times £2.99 = £11.96

And for marshmallows, she needs:

65*5 = 325 in total.

Marshmallows come in bags of 120, then the number of packs that Abi needs to buy is:

325/120 = 2.7

That should be rounded up (because she can not buy a 0.7 of a bag)

Then she needs 3 bags, and each bag costs £1.45

Then the total cost in marshmallows is 3*£1.45 = £4.35

8 0

3 years ago

A number divided by three, then increased by four is nine.<br> (As an equation)

Mama L [17]

Answer:

x = 15

Equation = x

__. +4=9

3

Step-by-step explanation:

x = number

x

__. + 4 =9

3

First, you subtract 4 on both sides of the equation to get x by itself.

x

__. = 5

3

Then, you multiply the denominator (3) on both sides to get x by itself

x = 15

7 0

3 years ago

The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. I

Elanso [62]

Answer:

$NK \approx 7.001$ , $MK = 2$ , $MF \approx 7.001$ , $A_{AMNFD} = 49.007$

Step-by-step explanation:

According to the statement, we find the following inputs:

$\angle MDK = \angle DMF = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$MD = 9$

$NF = 5$

Given than longer base and shorter base are parallel to each other, we conclude that:

$\angle KND = 180^{\circ} -\angle NKD - \angle KDN$

$\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}$

$\angle KND = 45^{\circ}$

$\angle FND = 90^{\circ}-\angle KND$

$\angle FND = 45^{\circ}$ (By definition of complementary angles)

$\angle FND = \angle NFM = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}$

$\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}$ (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

$MO = DO = \frac{\sqrt{2}}{2}\cdot MD$ (By theorem for 45-45-90 Right Triangle)

$NO = OF = \frac{\sqrt{2}}{2}\cdot NF$ (By theorem for 45-45-90 Right Triangle)

If we know that $MD = 9$ and $NF = 5$ , then we find that:

$DO = MO \approx 6.364$

$NO = OF \approx 3.536$

The value of MK is obtained from the following relationship:

$MK = \frac{MD-NF}{2}$

$MK = \frac{9-5}{2}$

$MK = 2$

And the value of KD is calculated from this expression:

$KD = MD-MK$

$KD = 9-2$

$KD = 7$

Now by the Pythagorean Theorem we find that:

$NK = \sqrt{(NO+DO)^{2}-KD^{2}}$

$NK = \sqrt{9.9^{2}-7^{2}}$

$NK \approx 7.001$

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

$MF = NO + DO \approx 7.001$

Lastly, the area of the isosceles trapezoid is determined by the following formula:

$A_{AMNFD} = NF\cdot NK + MK\cdot NK$

$A_{AMNFD} = NK\cdot (NF+MK)$

If we know that $NK \approx 7.001$ , $NF = 5$ and $MK = 2$ , then the area of the figure is:

$A_{AMNFD} = (7.001)\cdot (5+2)$

$A_{AMNFD} = 49.007$

8 0

3 years ago

The opposite value of -51

dolphi86 [110]

+51 or positive 51 or 51

7 0

3 years ago

Read 2 more answers

The distribution of employee incomes for a company is skewed. Which statement is true in that case?

Yakvenalex [24]

I want to say D or B but not sure

8 0

3 years ago

Read 2 more answers