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3 years ago

Find the measure x of an angle that is complementary to a 67° angle.

Mathematics

1 answer:

Masteriza [31]3 years ago

7 0

Answer:

23°

Step-by-step explanation:

A complementary angle is 90°, so you can do 90°-67° =23°

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The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the

Tresset [83]

Original:
The width and length of a rectangle are consecutive odd integers
so W = x and L = x + 2

If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7

A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
(x - 5)(x + 12) = 0
x = 5 and x = -12

From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet

Area of original = 5 x 7 = 35

answer
the area of the original rectangle: 35 ft^2

4 0

3 years ago

Determine whether this situation represents independent or dependent events. "Three green jelly bean, five red jelly beans and t

igor_vitrenko [27]

Answer:

Independent Events

Step-by-step explanation:

Given

$Green = 3\\ Orange = 2\\ Red = 5$

Required

Dependent or independent event

The probability of selecting a green jelly remains unchanged before and after selecting the first orange jelly.

Before selecting the orange jelly:

$P(Green) = \frac{Green}{Total}$

$P(Green) = \frac{3}{10}$

After selecting the orange jelly:

$P(Green) = \frac{Green}{Total}$

$P(Green) = \frac{3}{10}$

Because the probabilities remain unchanged, the selection of a green jelly is independent of the selection of the first orange jelly.

5 0

2 years ago

Which additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply.

Ad libitum [116K]

Consider the given triangles.

Given: $\angle C \cong \angle Q$

ASA congruence criterion states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

AAS congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Consider the first part:

1. In triangles ABC and QPT

If we take $\angle B \cong \angle P , BC \cong PQ$ along with the given condition.

Then the triangles are congruent by ASA congruence criterion.

2. If we take $\angle A \cong \angle T$ and $AC= TQ=3.2$ along with the given condition.

Then the triangles are congruent by ASA congruence criterion.

3. As, $\angle C \cong \angle Q$ , $\angle A \cong \angle T$ and $\angle B \cong \angle P$ , so the triangles can not be congruent.

4. If we take $\angle A \cong \angle T$ and $BC \cong PQ$ along with the given condition.

Then the triangles are congruent by AAS congruence criterion.

5. If we take AC=TQ=3.2 and CB=QP=3.2 along with the given condition, then the triangles are congruent but by SAS congruence criteria neither by ASA nor AAS congruence criterion.

7 0

3 years ago

Read 2 more answers

There are 12 boys and 13 girls in a class. If the teacher randomly chooses a student's name out of a hat, what is the probabilit

balu736 [363]

If there are 12 boys and 13 girls, there are 25 kids in the class total. This means that 13/25 are girls. In order to know the probability, you must divide 13 by 25, which gets an answer of 0.52, which is equal to 52%.

52%

7 0

3 years ago

Read 2 more answers

What is the answer to this question 2x + x + x + 2y x 3y x y

nikklg [1K]

Answer:

2 x (3 y^3 + 2)

Step-by-step explanation:

Simplify the following:

2 x + x + x + 2×3 y y x y

2 y×3 y = 2 y^2×3:

2 x + x + x + 2×3 y^2 x y

2×3 = 6:

2 x + x + x + 6 y^2 x y

6 y^2 x y = 6 y^(2 + 1) x:

2 x + x + x + 6 y^(2 + 1) x

2 + 1 = 3:

2 x + x + x + 6 y^3 x

Grouping like terms, 2 x + x + x + 6 y^3 x = 6 x y^3 + (2 x + x + x):

6 x y^3 + (2 x + x + x)

2 x + x + x = 4 x:

6 x y^3 + 4 x

Factor 2 x out of 6 x y^3 + 4 x:

Answer: 2 x (3 y^3 + 2)

3 0

3 years ago