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3 years ago

65.874 to one decimal place

Mathematics

1 answer:

Makovka662 [10]3 years ago

8 0

65.9 because the hundreds placr rounds up since it is above 5

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A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is e

mojhsa [17]

Answer:

V = 4/3 x pi x r^3

972 x pi= 4/3 x pi x r^3

729 = r^3

The cubic root of 729 is 9 because 9 x 9 x 9 = 729.

The radius is 9 inches, and the diameter is 18 inches.

The volume of the box is 18 in x 18 in x 18 in or 5832 in.³.

Step-by-step explanation:

7 0

2 years ago

Please help with 3. 4. 5.

Eddi Din [679]

3.
$\text{The Triangle Sum Theorem:}\\m\angle A+m\angle B+m\angle C=180^o$
$x+2x-1+3x+1=180\\6x=180\ \ \ |:6\\x=30$
$x^o=30^o\\(3x+1)^o=(3\cdot30+1)^o=91^o\\(2x-1)^o=(2\cdot30-1)^o=59^o$
4.
$r-6+3r-3+5r=180\\9r-9=180\ \ \ |+9\\9r=189\ \ \ |:9\\r=21$
$(r-6)^o=(21-6)^o=15^o\\(3r-3)^o=(3\cdot21-3)^o=60^o\\(5r)^o=(5\cdot21)^o=105^o$
5.
$\text{The Exterior Angle Theorem:}\\m\angle CAB+m\angle ABC=m\angle DCB$
$2g+9g=110\\11g=110\ \ \ |:11\\g=10$
$m\angle A=2\cdot10^o=20^o\\m\angle ACB=180^o-110^o=70^o\\m\angle B=9\cdot10^o=90^o$

4 0

3 years ago

Unit 8 right triangles and trigonometry homework 3 similar right triangles and geometric mean

Ugo [173]

The right triangles that have an altitude which forms two right triangles

are similar to the two right triangles formed.

Responses:

1. ΔLJK ~ ΔKJM

ΔLJK ~ ΔLKM

ΔKJM ~ ΔLKM

2. ΔYWZ ~ ΔZWX

ΔYWZ ~ ΔYZW

ΔZWX ~ ΔYZW

3. x = 4.8

4. x ≈ 14.48

5. x ≈ 11.37

6. G.M. = 12·√3

7. G.M. = 6·√5

<h3>What condition guarantees the similarity of the right triangles?</h3>

1. ∠LMK = 90° given

∠JMK + ∠LMK = 180° linear pair angles

∠JMK = 180° - 90° = 90°

∠JKL ≅ ∠JMK All 90° angles are congruent

∠LJK ≅ ∠LJK reflexive property

ΔLJK is similar to ΔKJM by Angle–Angle, AA, similarity postulate

∠JLK ≅ ∠JLK by reflexive property

ΔLJK is similar to ΔLKM by AA similarity

By the property of equality for triangles that have equal interior angles, we have;

ΔKJM ~ ΔLKM

2. ∠YWZ ≅ ∠YWZ by reflexive property

∠WXZ ≅ ∠YZW all 90° angle are congruent

ΔYWZ is similar to ΔZWX, by AA similarity postulate

∠XYZ ≅ ∠WYZ by reflexive property

∠YXZ ≅ ∠YZW all 90° are congruent

ΔYWZ is similar to ΔYZW by AA similarity postulate

Therefore;

ΔZWX ~ ΔYZW

3. The ratio of corresponding sides in similar triangles are equal

From the similar triangles, we have;

$\dfrac{8}{10} = \mathbf{ \dfrac{x}{6}}$

8 × 6 = 10 × x

48 = 10·x

$x = \dfrac{48}{10} = \underline{4.8}$

3. From the similar triangles, we have;

$\mathbf{\dfrac{20}{29}} = \dfrac{x}{21}$

20 × 21 = x × 29

420 = 29·x

$x = \dfrac{420}{29 } \approx \underline{14.48}$

4. From the similar triangles, we have;

$\mathbf{\dfrac{20}{52}} = \dfrac{x}{48}$

20 × 48 = 52 × x

$x = \dfrac{20 \times 48}{52} = \dfrac{240}{13} \approx \underline{18.46}$

5. From the similar triangles, we have;

$\mathbf{\dfrac{13.2}{26}} = \dfrac{x}{22.4}$

13.2 × 22.4 = 26 × x

$x = \dfrac{13.2 \times 22.4}{26} \approx \underline{ 11.37}$

6. The geometric mean, G.M. is given by the formula;

$G.M. = \mathbf{\sqrt[n]{x_1 \times x_2 \times x_3 ... x_n}}$

The geometric mean of 16 and 27 is therefore;

$G.M. = \sqrt[2]{16 \times 27} = \sqrt[2]{432} = \sqrt[2]{144 \times 3} = \mathbf{12 \cdot \sqrt{3}}$

The geometric mean of 16 and 27 is 12·√3

7. The geometric mean of 5 and 36 is found as follows;

$G.M. = \sqrt[2]{5 \times 36} = \sqrt[2]{180} = \sqrt[2]{36 \times 5} = \mathbf{ 6 \cdot \sqrt{5}}$

The geometric mean of 5 and 36 is 6·√5

Learn more about the AA similarity postulate and geometric mean here:

brainly.com/question/12002948

brainly.com/question/12457640

7 0

2 years ago

If the car wheel rotates 5 times per second about how many miles does the car travel in one hour??

iVinArrow [24]

Answer:

18000

Step-by-step explanation:

If we want to find how many miles it travels in one hour, we need to find jow many seconds are in one hour because as the problem said, it's wheel rotates 5 times per second.

there are 3600 seconds in an hour, so we multiply 3600 by 5, and we get 18000.

The car travels 18000 miles in one hour.

8 0

3 years ago

A principal gathered data about the distance, in miles, that his teachers and bus drivers live from school. The box plots below

Gekata [30.6K]

Answer:

We choose C

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo

Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.

From the picture, we can find that:

The interquartile range of the bus drivers is: 20 -10 = 10
The interquartile range of the teachers is: 30 -15 = 15

So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

We choose C

4 0

3 years ago