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Ivanshal [37]
4 years ago
15

Tom packed 12 identical textbooks and 8 identical notebooks ina box and found it's weight as 42 Ib. After he put 1 more textbook

and 10 more notebooks in the same box, the total mass was 59.5 Ib.
Write a system of equations to determine the mass m in pounds, of one textbook and one notebook.

Solve the system of equations and find the mass of each.
Mathematics
1 answer:
kvasek [131]4 years ago
5 0
You can find the answers by thes two systems of equation
(x is number of textbooks and y is number of notebooks)
12x + 8y = 42 \\ 1x + 10y = 17.5 \\  or \\  12x + 8y = 42 \\ 13x + 18y = 59.5

so the answers are
\\ x =  \frac{5}{2 }  \\  \\ y =  \frac{3}{2}  \\





good luck
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Solve T=L(2+RS) for R
True [87]

Answer:

Step-by-step explanation:

I would begin by distributing the L. It will be easier in the end to do it this way. There are a couple of ways you can do this, but distribution is the easiest. After you distribute the L you have

T = 2L + LRS

Next subtract the 2L to get

T - 2L = LRS. Lastly, to isolate the R, divide away the LS to get

\frac{T}{LS}-\frac{2L}{LS} = R  In that second term, the L's cancel each other out, leaving us with

\frac{T}{LS}-\frac{2}{S} = R

4 0
3 years ago
Given the diagram below, find X. The diagram IS<br> 40°<br> x - 15°<br> X =<br> degrees.
Crank

Answer:

X=65°

Step-by-step explanation:

Both angles combined is a right angle as indicated by the small square drawn on it, a right angle is always 90° therefore

(x-15°)+40°=90°

combine like terms

x+25°=90°

subtract 25° from each side

x=65°

6 0
3 years ago
Toy Emporium is having its annual sale. All items are marked with a 40 percent discount. Find the discounted price for each item
dezoksy [38]

Answer:

$9.99

$12 99

$5.69

Step-by-step explanation:

the answer there is not any number in hundred place value

7 0
4 years ago
In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg
siniylev [52]

Answer:

\dfrac{AP}{PC}=\dfrac{3}{5}

\dfrac{BN}{CN}=\dfrac{3}{5}

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

  • angle A is the common angle, so \angle MAP\cong \angle DAC by reflexive property;
  • angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,

so

\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}

Consider triangles ACB and PCN. In these triangles,

  • angle C is the common angle, so \angle ACB\cong \angle PCN by reflexive property;
  • angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,

so

\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}

4 0
3 years ago
PLEASE HELP SOMONE.
navik [9.2K]

Answer:

So here is the answer to your question by using the formulae of compound amount.

Initial price( P) = $5000

Interest rate( R) = 2% pa

Time ( T) = 30 years

Compound amount (CA)=?

We have

CA=P(1+R/100)^T

=5000(1+2/100)^30

=$9056.807921

=$9057(Approx)

Thus, the money will be $9057 after 30 years.

6 0
3 years ago
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