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Maslowich
3 years ago
15

Armando bought 45 baseball cards. of the 12 friends he invited to his cookout, half of them were able to attend. armando gave ea

ch of his friends at the cookout the same number of baseball cards and had 3 cards left for himself. how many baseball cards did each friend receive?
Mathematics
2 answers:
Ulleksa [173]3 years ago
6 0

Answer:

7 baseball cards

Step-by-step explanation:

Number of baseball cards = 45

Number of invited friends = 12

We are given that half of the friends were able to attend.

So, Number of friends attended the cookout = \frac{12}{2}

                                                                          = 6

Armando had 3 cards left for himself.

So, Number of cards distributed among 6 friends = 45-3 =42

So, number of cards for 6 friends = 42

So, number of cards for 1 friend = \frac{42}{6}

                                                    = 7

Hence each friend receive 7 baseball cards.

kumpel [21]3 years ago
5 0
If only 6 friends attended Armando's cookout, and he kept 3 cards for himself, then, 42 divided by 6 is 7.

Therefore, each friend received 7 cards.
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Tell whether the given value is a solution for the inequality. Then, justify your answer.
tatuchka [14]

Answer:

x=18 is not a solution

Step-by-step explanation:

18+9=27 but this is saying it has to be less than 27 so this is not a solution

4 0
2 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
Which triangle is it ?
coldgirl [10]
The answer is: The first triangle. The reasons are shown below:

 1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:

 Tan(α)^-1= opposite leg/adjacent leg

 Opposite leg=5
 Adjacent leg=5√3

 Tan(α)^-1= 5/5√3
 Tan(α)^-1=30°

 2. Let's calculate the other angle:

 Tan(α)^-1= opposite leg/adjacent leg

 Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:

 Tan(α)^-1= 5√3/5
 Tan(α)^-1=60°

 As you can see, the angles of first triangle are: 30°,60° and 90°. 
5 0
3 years ago
In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
Kitty [74]
So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100  so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
5 0
3 years ago
The product of two and x plus the quotient of w and five
Nataly [62]

Answer:

2x+w/5

Step-by-step explanation:

(2*x)+(w/5)

2x +w/5

8 0
3 years ago
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