Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?

Answers

Answer 1

Answer: Let,
pencils be "x"
pens be "y"

According to the question,
17x + 18y = 61.50 ----------> equation (1)
10x + 21y = 57 -----------------> equation (2)

Now,
Taking equation (1),
17x + 18y = 61.50
18y = 61.50 - 17x
y = (61.50 - 17x ) / 18 -----> equation (3)

Now, substituting the value of "y" in equation (2), we get,

$10x+21( (61.50-17x)/(18) )=57$

$10x+7( (61.50-17x)/(6) )=57$

$10x+ (430.50-119x)/(6)=57$

$10x* (6)/(6) + (430.50-119x)/(6)=57$

$(60x)/(6) + (430.50-119x)/(6)=57$

$(430.50+60x-119x)/(6)=57$

$430.50-59x=57*6$

$430.50-59x=342$

$59x=430.50-342$

$x=(88.5)/(59)$

$x=1.5$

Now,
Substituting the value of "x" in equation (3), we get,

$y =(61.50-17x)/(18)$

$y =(61.50-17(1.5))/(18)$

$y =(61.50-22.5)/(18)$

$y =(39)/(18)$

$y =2.17$

$y =2$ approx. (rounded)

So, Each pencil costs $1.5 and each pen costs $2.

Answer 2

Answer:

Answer:

Each pencil costs $1.50 and each pen costs $2.00

Step-by-step explanation:

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The steps below show the incomplete solution to find the value of y for the equation 6y − 3y − 5 = −3 + 23:Step 1: 6y − 3y − 5 = −3 + 23
Step 2: 6y − 3y − 5 = 20
Step 3: 3y − 5 = 20

Which of these is most likely the next step?
3y = 4

3y = 15

3y = 25

3y = 5

Answers

Answer with Step-by-step explanation:

We have to find the value of y for the equation:

6y − 3y − 5 = −3 + 23:

Step 1: 6y − 3y − 5 = −3 + 23

Solving the right hand side of the equation gives Step 2

Step 2: 6y − 3y − 5 = 20

combining the terms of y on left hand side gives step 3

Step 3: 3y − 5 = 20

Now, Adding 5 on both sides, we get

3y-5+5=20+5

⇒ 3y=25

Hence, most likely the next step is:

3y=25

3y=25

final answer y=25/3

Himpunan penyelesaian dari pertidaksamaan | 2x + 1| ≤ 3 adalah.....a. { -1 ≤ x ≤3 }
b. { -2 ≤ x ≤ 2}
c. { -2 ≤ x ≤ 1 }
d. { -1 ≤ x ≤ 1 }
e. { 0 ≤ x ≤ 1 }
Tolong caranya...

Answers

$| 2x + 1| \leq3 \n2x+1\leq3\wedge2x+1\geq-3\n2x\leq2 \wedge 2x\geq-4\nx\leq1 \wedge x\geq-2\n-2\leq x \leq1 \Rightarrow C$

Final answer:

The solution to the given inequality, |2x + 1| ≤ 3, is the set { -2 ≤ x ≤ 1 }, which corresponds to answer choice (c). This is achieved by solving two separate inequalities, 2x + 1 ≤ 3 and - (2x + 1) ≤ 3.

Explanation:

The subject of the question is Mathematics, specifically a High School algebra topic on solving absolute inequalities. The student's question is asking us to solve the inequality |2x + 1| ≤ 3. To do this, we need to create and solve two separate inequalities: 2x + 1 ≤ 3 and - (2x + 1) ≤ 3.

Solving 2x + 1 ≤ 3 gives us 2x ≤ 2 and x ≤ 1 . Solving - (2x + 1) ≤ 3 gives us -2x - 1 ≤ 3 , then -2x ≤ 4 , and finally x ≥ -2 . Combining these answers gives us the solution set { -2 ≤ x ≤ 1 }, which corresponds to answer choice (c).

Learn more about Absolute Inequalities here:

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The line that divides a parabola in half is..?

Answers

The line of symmetry that divides a parabola in half as "The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola".

What is parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form. A parabola's general equation is written as y = a(x - h)² + k or x = a(y - k)²+ h. Vertex here is indicated by (h, k).

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The line of symmetry.

It divides the parabola into to halves that are exactly the same.

Find the volume of the pyramid. 100 points