All categories

2 years ago

A pen and a ruler cost $2.10. 2 such pens and 3 such rulers cost $4.90. Find the cost of one ruler.

Mathematics

1 answer:

hammer [34]2 years ago

3 0

The cost of one ruler is $0.70

<h3>Applications of simultaneous equations </h3>

From the question, we are to determine the cost of one ruler

Let x represent the cost of a ruler

and

y represent the cost of a pen

From the given information, we can write that

y + x = $2.10 ----------- (1)

2y + 3x = $4.90 ----- (2)

From equation (1),

y + x = $2.10

Then,

y = $2.10 - x

Substitute this into equation (2)

2y + 3x = $4.90

2($2.10 - x) + 3x = $4.90

$4.20 - 2x + 3x = $4.90

$4.20 +x = $4.90

x = $4.90 - $4.20

x = $0.70

Hence, the cost of one ruler is $0.70

Learn more on Simultaneous equations here: brainly.com/question/26310043

#SPJ1

You might be interested in

Does anybody know the answer to these questions?

san4es73 [151]

Answer:

1. 625,000 J

2. 100 J

4. 5 kg

5. √5 ≈ 2.236 m/s

Step-by-step explanation:

You should be aware that the SI derived units of Joules are equivalent to kg·m²/s².

To reduce confusion between m for mass and m for meters, we'll use an italic m for mass.

In each case, the "find" variable is what's left after we put the numbers into the formula. It is what the question is asking for. The "given" values are the ones in the problem statement and are the values we put into the formula. The formula is the same in every case.

1. KE = (1/2)mv² = (1/2)(2000 kg)(25 m/s)² = 625,000 kg·m²/s² = 625,000 J

2. KE = (1/2)mv² = (1/2)(0.5 kg)(20 m/s)² = 100 kg·m²/s² = 100 J

4. KE = (1/2)mv²

250 J = (1/2)m(10 m/s)² = 50 m²/s²

(250 kg·m²/s²)/(50 m²/s²) = m = 5 kg

5. KE = (1/2)mv²

2000 kg·m²/s² = (1/2)(800 kg)v²

(2000 kg·m²/s²)/(400 kg) = v² = 5 m²/s²

v = √5 m/s ≈ 2.236 m/s

7 0

3 years ago

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

3 0

3 years ago

Solve the system of equation below by graphing them y= 2x-3 y=-2x+5

MatroZZZ [7]

Answer:

Step-by-step explanation:

3 0

3 years ago

Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary

sashaice [31]

Danielle earned $951.25

Step-by-step explanation:

Multiply her commission by her sales and add her base rate

x=7.25%($4500)+625 or x=0.0725(4500)+625

distribute

x=326.25+625

simplify

x=951.25

8 0

3 years ago

Ms. Ruiz bought 12 packages of plates for the party. Each package contains 15 plates. She bought 10 packages of small plates and

RideAnS [48]

Answer:

a) 150 plates

b) 30 plates

c) 180 plates

Step-by-step explanation:

Given that:

She bought twelve (12) packages of plates for the party in which each package contains 15 plates.

Out of the 12 packages;

10packages are small plates & 2 packages are large plates.

a) The number of small plates she bought = 10 × 15 = 150 plates

b) The number of large plates she bought = 2 × 15 = 30 plates

c) The total number of plates she bought all together is:

= number of small plates bought + = number of large plates bought

= (150 +30) plates

The total number of plates she bought all together = 180 plates

7 0

3 years ago