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valentina_108
14 days ago
7

Mai bought eleven 12-ounce bags of

Mathematics
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Which polynomial function could be represented by the graph below?
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According to the graph, which depicts a parabola, we can determine that the function will be quadratic. First, we identify the zeros as x=2 and x=4. Next, we can form the function using a point to solve for 'a'. For instance, at x=3 and y=-3, we can find 'a.' Plugging back into the equation, we can perform necessary multiplications to reach the final function.
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Danielle and Inder brought apples, bananas, and oranges to a fruit sale. The bananas were sold for $0.50 each, while the apples
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The answer is 10 apples.
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In isosceles △ABC (AC = BC) with base angle 30° CD is a median. How long is the leg of △ABC, if sum of the perimeters of △ACD an
Leona [12618]

Important details about isosceles triangle ABC:

  • The median CD, which is drawn to the base AB, also acts as an altitude to that base in the isosceles triangle (CD⊥AB). This indicates that triangles ACD and BCD are congruent right triangles, each with hypotenuses AC and BC.
  • In isosceles triangle ABC, the sides AB and BC are equal, meaning AC=BC.
  • The base angles at AB are equal, m∠A=m∠B=30°.

1. Consider the right triangle ACD. The angle adjacent to side AD is 30°, which dictates that the hypotenuse AC is double the length of the opposite side CD relating to angle A.

AC=2CD.

2. Now, for right triangle BCD, the angle next to side BD is also 30°, so hypotenuse BC is twice the opposite leg CD linked to angle B.

BC=2CD.

3. To calculate the perimeters of triangles ACD, BCD, and ABC:

P_{ACD}=AC+CD+AD=2CD+CD+AD=3CD+AD;

P_{BCD}=BC+CD+BD=2CD+CD+AD=3CD+AD;

P_{ABC}=AC+BC+AB=2CD+2CD+AD+BD=4CD+2AD.

4. If the total of the perimeters of triangles ACD and BCD is 20 cm greater than the perimeter of triangle ABC, then

P_{ACD}+P_{BCD}=P_{ABC}+20,\\ \\3CD+AD+3CD+AD=4CD+2AD+20,\\ \\6CD+2AD=4CD+2AD+20,\\ \\2CD=20.

5. Given that AC=BC=2CD, the lengths of legs AC and BC of the isosceles triangles are 20 cm.

Answer: 20 cm.

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2 months ago
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Millie has a box of 1 hundred cubes. She also has a bag of 70 cubes. How many trains of 10 cubes can she make?
Zina [12379]
100 plus 70 equals 170

170 divided by 10 equals 17

That makes 17 trains of 10 cubes
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