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14 days ago

a student says that if 5x2 = 20, then x must be equal to 2. do you agree or disagree with the student? justify your answer.

2 answers:

5 0

I disagree. Dividing both sides by 5 gives x2 = 4. Taking square roots yields x = -2 or x = 2, so x could be -2 as well as 2.

Zina [3.9K]14 days ago

5 0

We'll verify the student's claim by solving the equation step by step.

Step 1 Divide both sides of the equation by 5:

$5x^2=20$

$\frac{5x^2}{5} =\frac{20}{5}$

$x^2=4$

Step 2 Apply the square root to both sides:

$\sqrt{x^2} =(+/-)\sqrt{4}$

$x=(+/-)\sqrt{4}$

$x=2$ or $x=-2$

The equation has two solutions, $x=2$ and $x=-2$ .

I disagree with the student because $x=2$ is only one root, not the sole solution; $x=-2$ also satisfies the equation.

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A bag holds 12 red marbles, 11 green marbles, 17 blue marbles, and 5 yellow marbles. What is the probability that you will not c

Zina [3914]

¡Hola! Bienvenido a!

Vamos a sumar cuántas canicas tenemos en total.

12+11+17+5=45

Queremos hallar la probabilidad de elegir una canica que no sea azul. Observemos cuántas canicas no son azules.

12+11+5=28

Tendremos esta probabilidad sobre 48.

28/48

Al simplificar, obtenemos 7/12 o alrededor de 58.33%.

¡Espero que esto ayude!

7 0

3 days ago

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Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He h

Svet_ta [4321]

To find the maximum number of identical packs we see we have 72 pencils and 24 calculators.

This involves discovering the largest number that divides both 72 and 24 evenly,
which is known as the GCM or greatest common multiplier.

To determine the GCM, factor 72 into primes and group them:
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
Thus, the common grouping is 2 times 2 times 2 times 3, equating to 24.
Therefore, the maximum number of packs is 24.

For pencils:
72 divided by 24=3
Resulting in 3 pencils per pack.

For calculators:
24 divided by 24=1
So, 1 calculator per pack.

The outcome is 3 pencils and 1 calculator in each pack.

6 0

22 hours ago

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A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b

PIT_PIT [3919]

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

$P=\frac{1}{10}x(300-x)$

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10:

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

Next, factor the quadratic:

$(x-70)(x-230)=0$

Solving for x gives:

$x=70,x=230$

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.

7 0

14 days ago

Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract

tester [3916]

Answer:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Detailed solution:

Given:

The problem to solve is:

$x^2=-5x+8$

Convert the equation into the standard quadratic form $ax^2+bx +c =0$ , where $a,\ b,\ and\ c$ represent constants.

So, by adding $5x-8$ to both sides, we get:

$x^2+5x-8=0$

Note that $a=1,b=5,c=-8$ .

The roots of this quadratic are found by applying the quadratic formula given as:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute $a=1,b=5,c=-8$ into the formula and calculate for $x$ .

$x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Hence, the roots are:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

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tester [3916]

You might have better success by searching for answers individually:)

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