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3 years ago

Comparing Methods to solving systems.

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

3 0

Answer:

$x = - 1 \\ y = 1$

Step-by-step explanation:

$x - y = - 2$

$x = y - 2$

$7x + 2y = - 5$

$7(y - 2) + 2y = - 5 \\$

$7y - 14 + 2y = - 5$

$9y = 14 - 5$

$9y = 9$

$y = \frac{9}{9} = 1$

$x = y - 2 = 1 - 2 = - 1$

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3 years ago

A certain recipe requires 415 cups of flour and 237 cups of sugar. a) If 49 of the recipe is to be made, how much sugar is neede

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3 years ago

A scale model of a ramp is a right triangular prism as given in this figure. in the actual ramp, the triangular base has a heigh

kakasveta [241]

The surface area of the actual ramp including the underside is 16.8 ft²

The height of the actual ramp = 1.2 feet

The height of the model = 6 cm

<h3>What is the surface area of a right triangular prism?</h3>

A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.

The surface area of a right triangular prism

= (Perimeter of the base × Length of the prism) + (2 × Base Area)

Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm

Actual base = 16 cm × 0.2 ft/cm = 3.2 ft

convert the units

9 cm = 9 cm × 0.2 ft/cm = 1.8 ft

10 cm = 10 cm × 0.2 ft/cm = 2 ft

The surface area of a right triangular prism

= (Perimeter of the base × Length of the prism) + (2 × Base Area)

Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)

= 16.8 ft²

Hence, the surface area of the actual ramp including the underside is 16.8 ft²

Learn more about the area here:

brainly.com/question/25292087

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3 years ago

Hey everyone !

zhuklara [117]

Answer:

The measure of the largest angle is 120°

Step-by-step explanation:

Lets explain how to find the measure of an angle from the length of the

sides of the triangle

- We can do that by using the cosine rule

- If the three angles of the triangle are A , B , C, then the side opposite

to angle A is BC , the side opposite to angle B is AC and the side

opposite to angle C is AB, So to find measure of angle A use the rule

$cos(A)=\frac{(AB)^{2}+(AC)^{2}-(BC)^{2}}{2(AB)(AC)}$

Lets solve the problem

- Assume that the triangle is ABC where AB = 14 cm , BC = 10 cm and

AC = 6 cm

- We need to find the measure of the largest angle

- The largest angle is opposite to the longest side

∵ The longest side is AB

∴ The largest angle is C

By using the rule above

∴ $cos(C)=\frac{(AC)^{2}+(BC)^{2}-(AB)^{2}}{2(AC)(BC)}$

∵ AB = 14 cm , BC = 10 cm , AC = 6 cm

∴ $cos(C)=\frac{(6)^{2}+(10)^{2}-(14)^{2}}{2(6)(10)}$

∴ $cos(C)=\frac{36+100-196}{120}$

∴ $cos(C)=\frac{-60}{120}=-0.5$

∴ cos(C) = -0.5 ⇒ that means angle C is obtuse angle

∴ m∠C = $cos^{-1}(-0.5)=120$

* The measure of the largest angle is 120°

8 0

3 years ago

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