if 3 shirts and 4 caps cost $96, and 2 shirts and 5 caps cost $99, how much did each cap and each shirt cost?

Answers

Answer 1

Answer: hmmm..... let us try again...but this time with a different strategy,.... by the graph method.

The system is

3x + 4y =96
2x + 5y = 99.

We find solutions of each system and then plot them on a graph.

Solutions for equation 1 = (2, 22.5) and (30, 0)
Solutions for equation 2 = (49.5 , 0) and (1, 19.4)

Now, we plot both the equations on a graph paper and note its intersecting point.

Experimentally, we find the intersecting point is (12,15)

Thus, the solution for the system is x = 12 , y = 15.

Thus, we arrive at the conclusion 1 shirt costs 12$
1 cap costs 15$

Answer 2

Answer: $x-cost\ of\ one\ shirt\ny-cost\ of\ one\ cap\n \n3x+4y=\$96\ \ \ and\ \ \ 2x+5y=\$99\n \n \left \{ {{3x+4y=96\ /\cdot(-2)} \atop {2x+5y=99\ /\cdot(3)}} \right. \n \n \left \{ {{-6x-8y=-192} \atop {6x+15y=297} \right. \n --------\n7y=105\ /:7\n\ny=15\ \ \Rightarrow\ \ 3x+4\cdot15=96\ \ \Rightarrow\ \ 3x=36\ /:3\ \ \Rightarrow\ \ x=12\n \nAns.\ one\ shirt\ cost\ \$12,\ \ one\ cap\ cost\ \$15$

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Please help me with this ! Write a short explanation if it can but not necessary.

Answers

Unfortunately, we can't draw it for you, as the diagram is in your book! To create the line, simply find some points on the line and connect them, extending the line past each point in the same direction (you can use a ruler to help with this). To find points on the line, plug in values for x to the equation and find the corresponding y-value.

what is the slope of

1.)13x-11y=-12

2.)9x-7y=-7

Answers

$the \ slope \ intercept \ form \ is : \n \n y= mx +b \n \n1)\n \n 13x-11y=-12 \ \ -13x\n \n-11y=-13x -12 \ \ /:(-11)\n \ny=(13)/(11)x+(12)/(11) \n \n m=(13)/(11)$

$2.)\n \n9x-7y=-7 \ \ -9x \n \n -7y=-9x-7 \ \ /: (-7) \n \n y= (9)/(7) +1 \n \n m=(9)/(7)$

$Ax+By=C\n\nslope:m=-(A)/(B)\n\n\n1)\ 13x-11y=-12\n\nA=13;\ B=-11\n\nm=-(13)/(-11)=(13)/(11)\n\n\n2)\ 9x-7y=-7\n\nA=9;\ B=-7\n\nslope:m=-(9)/(-7)=(9)/(7)$

When two lines intersect they form two pairs of opposite angles called?

Answers

Hello, Katrina7!

Vertical angles are when two lines intersect they form two pairs of opposite angles.

I really hope this helps;)

What's the answer witch ones r composite 14 15
16 17 18 19
20
21

Answers

A composite number is a number with more than 2 factors and 16, 18, 20, and 21 are composite.

14 and 15 are also composite:

14 - 1×14, 2×7
15 - 1×15, 3×5

the first person probably didn't see the first row of numbers

The base of a square pyramid has a side length of 6 inches. The height of the pyramid is 12 inches. What is the volume of the pyramid? A. 108 in3 B. 36 in3 C. 72 in3 D. 144 in3

Answers

$a=6 \ in ,\ \ h= 12 \ in \n \nVolume = (1)/(3) B \cdot h \n \nB \ is \ the \ area \ of \ the \ base \nh \ is \ the \ height \n \n B =a^2 \n \nV =(1)/(3)\cdot a^2\cdot h =(1)/(3)\cdot 6^2 \cdot 12=36\cdot 4 = 144 \ in^3 \n \nAnswer : \ D. 144 in^3$

How do you find the center of dilation and scale factor in geometry?

Answers

Answer:

See below

Step-by-step explanation:

Centre of dilation

Dilation gives you a new shape that is either larger or smaller than the original.

In either case, every ray that passes through corresponding points of the two shapes will converge at the centre of dilation (Point O in the diagram).

Scale factor

To get the scale factor, you measure the ratio of lengths of corresponding sides in the shapes.

For example, a line in the red figure below may be four times as long as the corresponding line in the other.

If the dilation converts the blue shape into the red one, the scale factor is 4:1.

If the dilation converts the red shape into the blue one, the scale factor is 1:4.

Answer:Dilation scale factor 2: Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilation with scale factor 2, multiply by 2.

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