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2 years ago

Jalen inherited a collection of vintage comic books. An appraiser separated the comic

Mathematics

1 answer:

sladkih [1.3K]2 years ago

7 0

Jalen has total 63 comic books.

Step-by-step explanation:

Given,

Total value of comic books = $3135

Let,

Number of $45 comic books = x

Number of $65 comic books = y

According to given statement;

45x+65y=3135 Eqn 1

x=y+33 Eqn 2

Putting value of x from Eqn 2 in Eqn 1

$45(y+33)+65y=3135\\45y+1485+65y=3135\\110y=3135-1485\\110y=1650\\$

Dividing both sides by 110

$\frac{110y}{110}=\frac{1650}{110}\\y=15$

Putting y=15 in Eqn 2

$x=15+33\\x=48$

Total comic books = x+y

Total comic books = 48+15 = 63

Jalen has total 63 comic books.

Keywords: addition, elimination method

Learn more about elimination method at:

#LearnwithBrainly

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Line segments XY and ZY are tangent to circle O. Circle O is shown. Triangle X Y Z has points X and Z on the circle. Lines X Y a

pickupchik [31]

Answer:

The correct option is;

An isosceles triangle

Step-by-step explanation:

The parameters given are;

Line segments XY and ZY are tangents to circle O.

ΔXYZ has points X and Z on the circle.

XY and ZY are tangents that intersect at point Y outside the circle'

Therefore, given the circle has center O, then;

OY ≅ OZ = Radius of circle with center O

∠OXY ≅ ∠OZY = 90° (The radius line from the circle center to the tangent point is perpendicular)

OY ≅ OY (Reflexive property)

ΔOYX and ΔOYZ are right triangles (Triangle with one angle = 90°

ΔOYX ≅ ΔOYZ (Hypotenuse Leg, HL, rule of congruency)

Therefore;

XY = ZY (Corresponding Parts of Congruent Triangles are Congruent CPCTC)

Triangle XYZ is an isosceles triangle (Triangle with two equal sides).

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2 years ago

Cheryl wants to find the number of hours seventh-graders do homework each week. There are 297 boys and girls in seventh grade. I

Dafna1 [17]

There are a total of 297 students in the 7th grade. Rough estimates would say that about half of that number are boys and half are girls. Asking only 50 random girls would be biased because not only would it not be all of the girls (the number of girls would be around 148 or 149) but it would also be ignoring the roughly 148 to 149 boys there are on estimate. The sample would be biased because it would be ignoring the opinions of more than half the seventh grade.

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2 years ago

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We find the angle made at the opposite of the 45 yd side using the sine rule as follows.
$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} \\ \frac{\sin{25^o}}{20} = \frac{\sin{B}}{45} \\ \sin{B}= \frac{45\sin{25^o}}{20} = \frac{19.0178}{20} =0.9509 \\ B=\arcsin{(0.9509)}=71.97^o$

Thus, the third angle is given by 180 - 25 - 71.97 = 83.03 degrees.

We also use the sine rule to find the third side of the triangle as follows.
$\frac{\sin{A}}{a} = \frac{\sin{C}}{c} \\ \frac{\sin{25^o}}{20} = \frac{\sin{83.03^o}}{c} \\ c= \frac{20\sin{83.03^o}}{\sin{25^o}} = \frac{19.8522}{\sin{25^o}} =46.97 yds$

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2 years ago

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Answer: The distance between them is 230.65 miles.

Step-by-step explanation:

Since we have given that

Speed of plane A (b) = 200 miles per hour

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So,

We will use the "Cosine formula", we get

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So, distance between the two planes after one hour will be

$Distance=\frac{Speed}{time}=\frac{230.65}{1}=230.65\ miles$

So, the distance between them is 230.65 miles.

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Answer:

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