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1 year ago

A triangle has a base length of 3.1 cm and corresponding height of 4.2 cm, correct to

Mathematics

1 answer:

Svetradugi [14.3K]1 year ago

4 0

Answer:

The upper bound of the area is 6.69375 cm²

The lower bound of the area is 6.32875 cm²

Step-by-step explanation:

The question relates to measurements and accuracy

The given information are;

The base length of the triangle = 3.1 cm

The height of the triangle = 4.2 cm correct to one decimal place

The lower bound for the base length of the triangle = 3.05 cm

The upper bound for the base length of the triangle = 3.15 cm

Similarly, the lower bound for the height of the triangle = 4.15 cm

The upper bound for the height of the triangle = 4.25 cm

The formula for calculating the area of a triangle is given by the following formula;

Area of a triangle = 1/2 × Base × Height

The upper bound of the area = 1/2 × The upper bound of the base × The upper bound of the height

The upper bound of the area = 1/2 × 3.15 × 4.25 = 6.69375 cm²

The upper bound of the area = 6.69375 cm²

The lower bound of the area = 1/2 × The lower bound of the base × The lower bound of the height

∴ The lower bound of the area = 1/2 × 3.05 × 4.15 = 6.32875 cm²

The lower bound of the area = 6.32875 cm²

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Jenna mixed two shades of purple paint. For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint.

emmasim [6.3K]

Answer:

$\frac{12}{35}$

Step-by-step explanation:

Given :

→ For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint.

i.e, The ratio of red paint to blue paint is 3:5

→ For Purple Majesty, she used a blue to red paint ratio of 7 to 4.

i.e, The ratio of red paint to blue paint is 4:7

To find :

1) Compare the ratios of red paint to blue paint.

$\frac{3}{5}\times \frac{4}{7}=\frac{12}{35}$

2) The ratio for Purple People Eater can be expressed in fraction form as :

$=\frac{3}{5}$

3) The ratio for Purple Majesty can be expressed in fraction form as :

$=\frac{7}{4}$

4) To compare these fractions, rewrite them with a common denominator

For common denominator

Multiply numerator and denominator by 4 in $\frac{3}{5}$

$\Rightarrow\frac{3\times 4}{5\times4}=\frac{12}{20}$

Multiply numerator and denominator by 5 in $\frac{7}{4}$

$\Rightarrow\frac{7\times 5}{5\times4}=\frac{35}{20}$

Common denominator is 20

6 0

1 year ago

Read 2 more answers

1. Find three rational numbers between 7/12 and 7/11

Sonbull [250]

Step-by-step explanation:

In this problem, we need to find three rational numbers between 7/12 and 7/11.

First rational no :

$c=\dfrac{\dfrac{7}{12}+\dfrac{7}{11}}{2}\\\\c=\dfrac{161}{264}$

Second rational no :

$d=\dfrac{\dfrac{7}{12}+\dfrac{161}{254}}{2}\\\\d=\dfrac{1855}{3048}$

5 0

2 years ago

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 3

viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

$\triangle ABC$ represents the 1st angle of elevation of sun i.e. 58°

$\triangle ABD$ represents the 2nd angle of elevation of sun i.e. 36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = $h$ m

Let side BC = $x$ m

Now, let us apply tangent rules in $\triangle ABC, \triangle ABD$ one by one:

$tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)$

$tan36^\circ = \dfrac{h}{x+90}$

Putting value of $x$ using equation (1):

$tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}$

119.45 m is the height of pole.

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2 years ago

Leonel runs on different trails near his home for exercise. uses of positioning device to record how far from home he is when he

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Answer:

Step-by-step explanation:

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1 year ago

Which expression is equivalent to 6x2 – 19x – 55?

seraphim [82]

Answer, (6x + 11) (x - 5)

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2 years ago

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