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3 years ago

Use the relationships between the angles to find the value of x (please answer)

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

4 0

Step-by-step explanation:

$x + 15 \degree = 102 \degree \: \\ (corresponding \: \angle s) \\ \therefore \: x = 102 \degree - 15 \degree \\ \huge \red { \boxed{\therefore \: x = 87 \degree}}$

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If the coordinates (-2, 1), (1, 1), and (1, 4) are translated 5 units right, the new coordinates would be ______? *If the coordi

Natali5045456 [20]

I would say B . From the 5 Units

4 0

3 years ago

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F(x) = x^2. What is g(x)

Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)

If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

4 0

3 years ago

Suppose a cylinder has a diameter of 18 feet and a height of h feet. Which equation can be used to find V, the volume of the cyl

IrinaVladis [17]

Answer: option A

Step-by-step explanation:

The volume of a cylinder can be calculated with the formula:

$V=\pi r^2h$

Where r is the radius and h is the height of the cylinder.

The radius is diameter divided by 2, then:

$r=\frac{18ft}{2}\\\\r=9ft$

Substitute the radius into the formula. Then you get the following equation that can be used to find V, the volume of the cylinder:

$V=\pi (9)^2h$

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3 years ago

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Myles said that 5 x 0.13 is 6.5. Do you agree? Explain.<br><br> Brainliest if correct!

77julia77 [94]

No he is not, 10*0.13=1.3, so 5*0.13=0.65

6 0

3 years ago

Read 2 more answers

Can someone help me with this please

Bingel [31]

Answer:

A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

A.3: ∠2 ≅ ∠3

B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

opposite angles of a parallelogram are congruent
corresponding angles where a transversal crosses parallel lines are congruent
alternate interior angles where a transversal crosses parallel lines are congruent
vertical angles are congruent
any two angles with the same measure are congruent

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

<u>Center</u>

∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

<u>Right</u>

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

∠2 ≅ ∠3

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

∠ACD ≅ ∠CAB (30°)

∠CDA ≅ ∠ABC (90°)

∠DAC ≅ ∠BCA (60°)

<u>Right</u>

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

<em>Additional comment</em>

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

a ≅ b ≅ c ⇒ (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

a ≅ b ≅ c ≅ d ⇒ (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

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2 years ago