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3 years ago

AD is a common internal tangent to circles B and C. Find the length of the radius of circle B. Round to the nearest hundredth.

Mathematics

2 answers:

ycow [4]3 years ago

8 0

ΔABE ~ ΔDCE
AB=AE*DC/DE=18*4/6=12

ikadub [295]3 years ago

3 0

As AD is common tangent,

<BAE=90=<CDE

Also <BEA=<CED as they are opposite angles

By AAA, the two triangles, ABE and DCE, are similar

so AB/EA = DC/ED

AB = EA * DC/ED = 18 * 4/6

= 12

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12 divided by x = 50

olga2289 [7]

the answer to 12 divided by 50 calculated using Long Division is:

12 Remainder

7 0

3 years ago

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Jack is trying to make extra money on his summer vacation from school. He works two different jobs, earning $9 per hour washing

Sveta_85 [38]

Answer:

$57

$9w+6d$

Step-by-step explanation:

Given that:

Earnings per hour for washing cars = $9

Earnings per hour for walking dogs = $6

Number of hours for which car washing is done = $w$

Number of hours taken for walking dogs = $d$

Earnings for $w$ hours for washing cars = Per hour earnings multiplied by number of hours = $9 $w$

Earnings for $d$ hours for walking dogs = Per hour earnings multiplied by number of hours = $6 $d$

Total earnings by both = $( $9w+6d$ )

Now, given that

Number of hours spent washing cars = 5 hours

Number of hours spent walking dogs = 2 hours

Therefore, total earnings by both = 9 $\times$ 5 + 6 $\times$ 2 = <em>$57</em>

5 0

3 years ago

What is the equation for the plane illustrated below?

TiliK225 [7]

Answer:

Hence, none of the options presented are valid. The plane is represented by $3 \cdot x + 3\cdot y + 2\cdot z = 6$ .

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

$a\cdot x + b\cdot y + c\cdot z = d$

Where:

$x$ , $y$ , $z$ - Orthogonal inputs.

$a$ , $b$ , $c$ , $d$ - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

$y = m\cdot x + b$

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where:

$m$ - Slope, dimensionless.

$x_{1}$ , $x_{2}$ - Initial and final values for the independent variable, dimensionless.

$y_{1}$ , $y_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - x-Intercept, dimensionless.

If $x_{1} = 2$ , $y_{1} = 0$ , $x_{2} = 0$ and $y_{2} = 2$ , then:

Slope

$m = \frac{2-0}{0-2}$

$m = -1$

x-Intercept

$b = y_{1} - m\cdot x_{1}$

$b = 0 -(-1)\cdot (2)$

$b = 2$

The equation of the line in the xy-plane is $y = -x+2$ or $x + y = 2$ , which is equivalent to $3\cdot x + 3\cdot y = 6$ .

yz-plane (0, 2, 0) and (0, 0, 3)

$z = m\cdot y + b$

$m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}$

Where:

$m$ - Slope, dimensionless.

$y_{1}$ , $y_{2}$ - Initial and final values for the independent variable, dimensionless.

$z_{1}$ , $z_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - y-Intercept, dimensionless.

If $y_{1} = 2$ , $z_{1} = 0$ , $y_{2} = 0$ and $z_{2} = 3$ , then:

Slope

$m = \frac{3-0}{0-2}$

$m = -\frac{3}{2}$

y-Intercept

$b = z_{1} - m\cdot y_{1}$

$b = 0 -\left(-\frac{3}{2} \right)\cdot (2)$

$b = 3$

The equation of the line in the yz-plane is $z = -\frac{3}{2}\cdot y+3$ or $3\cdot y + 2\cdot z = 6$ .

xz-plane (2, 0, 0) and (0, 0, 3)

$z = m\cdot x + b$

$m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}$

Where:

$m$ - Slope, dimensionless.

$x_{1}$ , $x_{2}$ - Initial and final values for the independent variable, dimensionless.

$z_{1}$ , $z_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - z-Intercept, dimensionless.

If $x_{1} = 2$ , $z_{1} = 0$ , $x_{2} = 0$ and $z_{2} = 3$ , then:

Slope

$m = \frac{3-0}{0-2}$

$m = -\frac{3}{2}$

x-Intercept

$b = z_{1} - m\cdot x_{1}$

$b = 0 -\left(-\frac{3}{2} \right)\cdot (2)$

$b = 3$

The equation of the line in the xz-plane is $z = -\frac{3}{2}\cdot x+3$ or $3\cdot x + 2\cdot z = 6$

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

$a = 3$ , $b = 3$ , $c = 2$ , $d = 6$

Hence, none of the options presented are valid. The plane is represented by $3 \cdot x + 3\cdot y + 2\cdot z = 6$ .

8 0

3 years ago

"find the cost per ounce of a sunscreen made from 140 oz of lotion that cost $3.45 per ounce and 90 oz of lotion that cost $14.0

Olegator [25]

Sunscreen approx. 40.6 cents an oz
Lotion 6.4 cents an oz

5 0

3 years ago

How do I do this<br>plz help

WINSTONCH [101]

Answer:

Step-by-step explanation:

3 0

3 years ago

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