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Alexus [3.1K]
3 years ago
7

Joanna went school supply shopping. She spent $21.45 on notebooks and pencils. Notebooks cost $1.97 each and pencils cost $1.16

each. She bought a total of 15 notebooks and pencils. How many of each did she buy?
A.
5 notebooks; 10 pencils
B.
3 notebooks; 12 pencils
C.
8 notebooks; 7 pencils
D.
10 notebooks; 5 pencils
Mathematics
1 answer:
GarryVolchara [31]3 years ago
5 0

Answer:

A) 5 notebooks, 10 pencils

Step-by-step explanation:

n = notebook

p = pencil

1.97n + 1.16p = 21.45

A)✅

1.97(5) + 1.16(10) = 21.45

9.85 + 11.6 = 21.45

21.45 = 21.45

B) ❌

1.97(3) + 1.16(12) = 21.45

5.91 + 13.92 = 21.45

19.83 = 21.45

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Naomi is still not sure how many boxes of each type of candy to order. Her dad explains that he needs to do a little more mathem
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Answer:

how much does each box cost?

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6 0
3 years ago
Simplify the expression. Use standard polynomial format.<br> x(2x + 3) + (x - 3)(x - 4)
timofeeve [1]

Answer:

x(2x + 3) + (x - 3) (x - 4) = 3x²- 4x + 12

Step-by-step explanation:

<em>Expand:</em>

x(2x + 3): 2x² + 3x

2x² + 3x + (x - 3) (x - 4)

<em>Expand</em>:

(x - 3) (x - 4):  x²- 7x + 12

2x² + 3x + x²- 7x + 12

<em>Simplify:</em>

2x² + 3x + x² - 7x + 12:  3x² - 4x + 12

= 3x² - 4x +12

5 0
3 years ago
Help is needed please help
Anna007 [38]

You have to do Pythagorean theorem:

a^{2} +b^{2}  = c^{2}

"a" and "b" are the legs. In this case 7 is a leg and x is a leg

"c" is the hypotenuses, which is 19 here

so...

a = 7

b = x

c = 19

Plug the numbers above into the equation:

7^{2} + x^{2} = 19^{2}

49 +x^{2} = 361

Isolate x by subtracting 49 to both sides:

(49-49) + x^{2} = 361 - 49

x^{2} = 312

To solve for x you have to take the square root to both sides of the equation:

\sqrt{x^{2} } = \sqrt{312}

x = 17.6635

x = 17.7

Hope this helped!

6 0
3 years ago
Determine the number of solutions that exist to the equation below 8(j-4)=2(4j-16)
Firdavs [7]
Hello :
<span>8(j-4)=2(4j-16)
</span><span>2(4j-16)= 2(4(j-4))=8(j-4)
</span>8(j-4)= 8(j-4)....(identity : infinty solutions)

5 0
3 years ago
I surveyed students in my Math II classes to see how many hours of television they watched the night before our big test on tria
Oduvanchick [21]
Given the table below representing the number of hours of television nine Math II class students watched the night before a big test on triangles along with the grades they each earned on that test.

\begin{center}&#10;\begin{tabular}&#10;{|c|c|}&#10;Hours Spent Watching TV & Grade on Test (out of 100)  \\ [1ex]&#10;4 & 71 \\ &#10;2 & 81 \\ &#10;4 & 62 \\ &#10;1 & 86 \\ &#10;3 & 77 \\ &#10;1 & 93 \\ &#10;2 & 84 \\ &#10;3 & 80 \\ &#10;2 & 85&#10;\end{tabular}&#10;\end{center}

Let the number the number of hours of television each of the students watched the night before the test be x while the grades they each earned on that test be y.

We use the following table to find the equation of the line of best fit of the regression analysis of the data.

\begin{center} \begin{tabular} {|c|c|c|c|} x & y & x^2 & xy \\ [1ex] 4 & 71 & 16 & 284 \\ 2 & 81 & 4 & 162 \\ 4 & 62 & 16 & 248 \\ 1 & 86 & 1 & 86 \\ 3 & 77 & 9 & 231 \\ 1 & 93 & 1 & 93 \\ 2 & 84 & 4 & 168 \\ 3 & 80 & 9 & 240 \\ 2 & 85 & 4 & 170 \\ [1ex]\Sigma x=22 & \Sigma y=719 & \Sigma x^2=64 & \Sigma xy=1,682 \end{tabular} \end{center}

Recall that the equation of the line of best fit of a regression analysis is given by
y=a+bx
where:
a= \frac{(\Sigma y)(\Sigma x^2)-(\Sigma x)(\Sigma xy)}{n(\Sigma x^2)-(\Sigma x)^2}
and
b= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{n(\Sigma x^2)-(\Sigma x)^2}

y=\frac{(719)(64)-(22)(1,682)}{9(64)-(22)^2}+\frac{9(1,682)-(22)(719)}{9(64)-(22)^2}x \\  \\ = \frac{46,016-37,004}{576-484} + \frac{15,138-15,818}{576-484} x \\  \\ = \frac{9,012}{92} + \frac{-680}{92} x \\  \\ =97.95-7.391x

Thus, the equation of the line of best fit is given by y = 97.95 - 7.391x

<span>A student that watched 1.5 hours of TV will have a score given by
y = 97.95 - 7.391(1.5) = 97.95 - 11.0865 = 86.8635

Therefore, </span><span>a student’s score if he/she watched 1.5 hours of TV to the nearest whole number is 87.</span>
6 0
3 years ago
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