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Ivanshal [37]
3 years ago
12

Noah has $50. He wants to buy a cell phone case for $20 and some accessories. Each accessory costs $8. How many accessories (x)

can Noah buy if he wants to have more than $8 left after he buys everything? Use the equation editor to enter the missing part of the inequality that answers the question. The inequality answer must be a whole number.
Mathematics
1 answer:
levacccp [35]3 years ago
8 0

Answer:

Noah can buy 2 accessories.

Step-by-step explanation:

Given:

Money Noah has = $50

Cost of Cell phone case = $20

Cost of each accessory =$8

Amount he wants to be left = $8

So Total Amount he he wants to spend on accessories and Cell phone case will be equal to Money Noah has minus Amount he wants to be left.

framing in equation form we get;

Total Amount he he wants to spend on accessories and Cell phone case = \$50-\$8 =\$42

No we need to find the number of accessories Noah can buy.

Let the number of accessories be 'x'.

Now we can say that;

Cost of Cell phone case plus Cost of each accessory multiplied by number of accessories should be less than or equal to Total Amount he he wants to spend on accessories and Cell phone case.

framing in equation form we get;

20+8x\leq 42

Subtracting both side by 20 we get using Subtraction property of Inequality.

20+8x-20\leq 42-20\\\\8x\leq 22

Now Dividing both side by 8 using Division property of Inequality we get;

\frac{8x}{8}\leq \frac{22}{8}\\\\x\leq 2.75

Now rounding to whole number we get ;

x\leq 2

Hence Noah can buy 2 accessories.

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igor_vitrenko [27]
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4 years ago
42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor
jasenka [17]

The second matrix \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right] represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right]

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]

This is the second option.

4 0
3 years ago
Three vertices of parallelogram ABCD are A(2,-6),B(-1,2),C(5,3).find the coordinates of vertex D
salantis [7]

Check the first picture below.


for a parallelogram, it has to have two pairs of parallel sides, so BC || AD and AB || CD.

if two lines are parallel, they have the same slope, namely the <u>same rise and run</u>.

notice, the line BC has a run of 6 and a rise of 1, <u>arrows in red</u>, therefore, AD must also have a run of 6 and a rise of 1, so if we move from A 6 units over and 1 up, we'd end up at point D.


now, for part atop

Check the 2nd picture, in a parallelogram, opposite sides are parallel and opposite angles are equal, so if WLP is 144°, then PNW is also 144°.

in a parallelogram, diagonals bisect each other, so each cut the other in halves, so if PM is 9 then MW is also 9 and thus PW is just 9+9=18.


now, about QRST.

notice what we said about a parallelogram above, thus


\bf 8x+13=11x-23\implies 8x+36=11x\implies 36=3x \\\\\\ \cfrac{36}{3}=x\implies \boxed{12=x} \\\\[-0.35em] ~\dotfill\\\\ 2y+12=4y-4\implies 2y+16=4y\implies 16=2y \\\\\\ \cfrac{16}{2}=y\implies \boxed{8=y}


so then TQ ==> 2(8) + 12 ==> 16 + 12 ==> 28.

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and since in a parallelogram, adjacent interior angles add up to 180°, then ∡Q + ∡T = 180°.

∡T ==> 180 - 109 ==> 71°.

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