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2 years ago

ABC congruent DEF find the measure of the given angles or the lengths of the given sides

Mathematics

1 answer:

Mrac [35]2 years ago

7 0

Answer:

m∠A = 20° and m∠D = 20°

Step-by-step explanation:

Congruent triangles have equal angles, equal sides, equal perimeters, and equal areas

Let us solve the question

∵ The two triangles ABC and DEF are congruent

∴ m∠A = m∠D

∵ m∠A = x + 10

∵ m∠D = 2x

→ Equate their measures

∴ 2x = x + 10

→ Subtract x from both sides

∵ 2x - x = x - x + 10

∴ x = 10

→ Substitute x by 10 in the measures of angles A and D to find them

∵ m∠A = 10 + 10

∴ m∠A = 20°

∵ m∠D = 2(10)

∴ m∠D = 20°

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Rewrite the radical expression as an expression with rational exponents.

nadya68 [22]

Answer: $(\sqrt[3]{x} )^8$

Step-by-step explanation:

Radical expression :

Cube root of any expression 'a' = $\sqrt[3]{a}$

Radical exponent:

'a' to the power n = $a^n$

Similarly cube root of x = $\sqrt[3]{x}$

cube root of x to the power of 8 = $(\sqrt[3]{x} )^8$

Now , the required radical expression with rational exponents for "cube root of x to the power of 8" = $(\sqrt[3]{x} )^8$

Hence, the required expression = $(\sqrt[3]{x} )^8$

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3 years ago

The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its

Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

Shape: Triangle

Represent the height with h and the base with b

$b = 3 + 2h$

$Area = 22$

Required

Find the length of the base

The area of a triangle is calculated as thus;

$Area = \frac{1}{2} * b * h$

Substitute 22 for Area and 3 + 2h for b

The formula becomes

$22 = \frac{1}{2} * (3 + 2h) * h$

Multiply both sides by 2

$2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h$

$44 = (3 + 2h) * h$

Open the bracket

$44 = 3 * h + 2h * h$

$44 = 3h + 2h^2$

Subtract 44 from both sides

$44 - 44 = 3h + 2h^2 - 44$

$0 = 3h + 2h^2 - 44$

Rearrange

$0 = 2h^2 +3h - 44$

$2h^2 +3h - 44 = 0$

At this point, we have a quadratic equation; which is solved as follows:

$2h^2 +3h - 44 = 0$

$2h^2 + 11h - 8h - 44 = 0$

$h(2h + 11) - 4(2h + 11) = 0$

$(h - 4)(2h + 11) = 0$

Split the above

$(h - 4) = 0\ or\ (2h + 11) = 0$

$h - 4 = 0\ or\ 2h + 11 = 0$

Solve the above linear equations separately

$h - 4 = 0$

Add 4 to both sides

$h - 4 + 4 = 0 + 4$

$h = 0 + 4$

$h = 4$ ---- First value of h

$2h + 11 = 0$

Subtract 11 from both sides

$2h + 11 - 11 = 0 - 11$

$2h = 0 - 11$

$2h = -11$

Divide both sides by 2

$\frac{2h}{2} = -\frac{11}{2}$

$h = -\frac{11}{2}$ ------ Second value of h

Since height can be negative, we'll discard $h = -\frac{11}{2}$

Hence, the usable value of height is $h = 4$

Recall that $b = 3 + 2h$

Substitute 4 for h

$b = 3 + 2(4)$

$b = 3 + 8$

$b = 11$

Hence, the length of the base is 11 meters

3 0

3 years ago

What is the formula for the volume of a hemisphere?

saw5 [17]

Answer:

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Step-by-step explanation:

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3 years ago

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ElenaW [278]

Answer:

B. 91 degrees

Step-by-step explanation:

supplementary angles = 180 degrees, so 180-89 = 91

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3 years ago

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1 year ago

ABC congruent DEF find the measure of the given angles or the lengths of the given sides ​

ABC congruent DEF find the measure of the given angles or the lengths of the given sides