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3 years ago

PLEASEEE HELP !! What is the value of x ?

Mathematics

1 answer:

Shtirlitz [24]3 years ago

4 0

Answer:

x = 20 cm

Step-by-step explanation:

The triangles given are similar triangles because they share the same angles. Because they are similar, their side lengths are in the same ratio, or proportion to one another. The left side of the larger triangle has a length of 121cm + 11cm = 132cm where the smaller triangle only has a length of 11 cm. We can put these lengths into a ratio:

$\frac{larger}{smaller}=\frac{132}{11}=\frac{12}{1}$

Since the other side of the triangle would have to be in the same proportion, or ratio, we can set up the following proportion:

$\frac{12}{1}=\frac{(5x+10)+10}{10}=\frac{5x+20}{10}$

Use cross-multiplication: 5x + 20 = (10)(12) or 5x + 20 = 120

Subtract 20 from each side: 5x + 20 - 20 = 120 - 20 or 5x = 100

Divide and solve for 'x': 5x/5 = 100/5 or x = 20 cm

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3 years ago

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Step-by-step explanation:

A = pi × r²

A = pi × 13²

A = 530.93 km²

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3 years ago

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8 0

4 years ago

If you rent a car for one day and drive 225 miles, the cost is $80. If you drive 350 miles in one day, the cost is $105. Let cm)

kolezko [41]

Answer:

a) $(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

b) For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

Step-by-step explanation:

For this case we can define the following notation:

m= represent the miles travelled

C= represent the cost

Part a

For this case we have the following two points given:

$(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

Part b

For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

6 0

3 years ago

1. Calculate the acceleration of riding her bicycle in a straight line that speeds up from 4 m/s to 12 m/s in 10 seconds. SOLUTI

valentina_108 [34]

<h3>✒️ACCELERATION</h3>

=================================

$\large\sf\underline{Problem:}$

Calculate the acceleration of riding her bicycle in a straight line that speeds up from 4 m/s to 12 m/s in 10 seconds.

=================================

$\large\sf\underline{Answer:}$

$\qquad \qquad \huge \rm = 0.8 \: m/s²$

=================================

$\large\sf\underline{Solution:}$

Here we have a given of,

$\tt{(12\:m/s) \:= \:V_f = (final\: velocity) }$
$\tt{(4\:m/s)\:=\:V_i = (initial \: velocity) }$
$\tt{(10\:sec) \:=\:T = (elapsed time) }$

$\bold{Formula\:||\: Acceleration = \frac{v\: - \:v_0}{t} = \frac{ΔV}{ΔT} }$

Because acceleration has a direction <u>(</u><u>riding her bicycle in a straight line</u><u>)</u>, it is important to always subtract the final velocity represented as $\bold{V_f}$ from your initial velocity also represented as $\bold{V_i}$ .

Now 'Work it out' and solve for Acceleration of riding her bicycle using the given formula.

$\large\rm{A = \frac{V_f \:- \:V_i}{T} }$
$\large\rm{A = \frac{(12\:m/s\:-\:4\:m/s) }{10\:sec}}$
$\large\rm{A = \frac{ 8\:m/s}{10\:sec} }$
$\large\rm{A = 0.8\:m/s²}$

Hence, The total acceleration of the girl riding her bicycle is 0.8 meters per second squared (m/s²).

=================================

૮₍´˶• . • ⑅ ₎ა

3 0

2 years ago