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Taya2010 [7]
3 years ago
15

A gym instructor has a total of 60 hand weight in her studio. Some of the hand weights are 3 pound weights and the rest are 5 po

und weights. If there are 10 more 5-lb weights than 3-lb weights, then how many of each kind does she have?
Mathematics
1 answer:
Elden [556K]3 years ago
8 0

Answer:

  • 35 5-lb weights
  • 25 3-lb weights

Step-by-step explanation:

Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...

  f + t = 60

  f - t = 10

Adding these two equations, we get ...

  (f +t) +(f -t) = (60) +(10)

  2f = 70 . . . . . eliminate parentheses

  f = 35 . . . . . . divide by 2

She has 35 5-lb weights, and 25 3-lb weights.

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valkas [14]

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{

3x+5y=2

9x+11y=14

∣⋅(−3)

−9x−15y=−6

9x+11y=14

add both sides of equations

. −4y=8 ∣:(=4)

. y=−2

substitute the value of y to the first equation

3x+5⋅(−2)=2

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3x=12 ∣:3

x=4

Answer: x=4; y=−2→(4; −2)

5 0
3 years ago
Find the equation in standard form of the line passing through the points 3,-4 and 5,1
aliina [53]

Answer:

5x - 2y - 23 = 0

Step-by-step explanation:

Line is passing through the points (3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2)

Equation of line in two point form is given as:

\frac{y -y_1 }{y_1 -y_2 }  =  \frac{x -x_1 }{x_1 -x_2 } \\  \\  \therefore \:  \frac{y -( - 4) }{ - 4 -1}  =  \frac{x -3 }{3 -5 } \\  \\  \therefore \:\frac{y  +  4 }{ - 5}  =  \frac{x -3 }{ - 2 } \\  \\  \therefore \: \frac{y  +  4 }{  5}  =  \frac{x -3 }{  2 } \\  \\  \therefore \:  2(y + 4) = 5(x - 3) \\ \therefore \:  2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\  \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \:  \\ standard \: form.

7 0
3 years ago
Okay I know I suck at math and I really don't understand math that well so can you help me on this??? Thank you!
Alja [10]
W - width
l - length
p - perimeter

The perimeter is 72 cm (p=72).
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p=72 \\
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2w+2l=p \\
2w+2 \cdot 2w=72 \\
2w+4w=72 \\
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l=2w=2 \cdot 12 =24

Check the answer:
2 \cdot 12 + 2 \cdot 24 \stackrel{?}{=} 72 \\
24+48 \stackrel{?}{=} 72 \\
72 \stackrel{?}{=} 72 \\ \hbox{true}

The length of the photo is 24 cm, the width of the photo is 12 cm.
8 0
3 years ago
Y greater than or equal to x + 4
tatiyna

See the attached files

<h2>Explanation:</h2>

Here we have the following inequality:

y>x+4

In order to graph the shaded region, we have to graph the equation of the line y=x+4 whose slope is m=1 and y-intercept b=4.  So the graph of the line is shown in the First Figure below.

To find the shaded region we need to have a look at the symbol > that indicates that the shaded region is above the graph of the line and. Since this doesn't include the symbol =, then the line is dotted. Therefore, the resulting region is shown in the second Figure.

<h2>Learn more:</h2>

Shaded regions: brainly.com/question/9611462

#LearnWithBrainly

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It's a reflection :) look up colin Dodds geometric transformations that's how I learned it it's a fun song
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3 years ago
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