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3 years ago

7 x 0.04=7 x 4 x Write a decimal to complete the equation

1 answer:

6 0

Solution:

1) Cancel 7 on both sides
x\times 0.04=x\times 4x

2) Regroup terms
0.04x=x\times 4x

3) Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}

0.04x={x}^{2}\times 4

4) Regroup terms
0.04x=4{x}^{2}

5) Move all terms to one side
0.04x-4{x}^{2}=0

6) Factor out the common term xx
x(0.04-4x)=0

7) Solve for x
x=0,0.01

Done!

You might be interested in

Bonjour pourriez vous m'aider avec cette équation du second degré? j'ai du mal à comprendre le concept. merci

olga_2 [115]

If a quadratic equation has solutions, the standard procedure will always work: given an equation like

$ax^2+bx+c=0$

The solutions (if any) are given by

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

In your case, you have

$a=-9,\ b=0,\ c=1$

So the formula becomes

$x_{1,2} = \dfrac{\pm\sqrt{36}}{18}= \pm\dfrac{6}{18}=\pm\dfrac{1}{3}$

Anyway, this is quite a special case, because you're missing the linear term (since $b=0$ )

This means that you can solve equations like these more easily: rearrange the equation to make it look like $ax^2=c$ . In your case, it becomes

$9x^2=1$

Divide both sides by 9:

$x^2=\dfrac{1}{9}$

Now, you know that the square of a number equals 1/9. By definition, it means that this number is the square root of 1/9. Nevertheless, both the square root and its opposite are solutions of the equation, because the minus sign will cancel out when squaring.

So, in general, you have

$ax^2=c \iff x^2 = \dfrac{c}{a} \iff x=\pm\sqrt{\dfrac{c}{a}$

which of course makes sense, if you're using real numbers, only if c/a>0.

In your case, this becomes

$9x^2=1 \iff x^2 = \dfrac{1}{9} \iff x=\pm\sqrt{\dfrac{1}{9}} = \pm\dfrac{1}{3}$

3 0

3 years ago

Cv0627

kari74 [83]

Answer:

dr. potter provides 54 vaccinations TOTAL (including both measles and polio).

p+m=54

since there are 4 doses of polio and of measles, you have to use a variable to distinguish how many doses were given for measles and polio out of 142 given doses.

4p+2m=142

p+m=54

4p+2m=142

^^system of equation

p+m=54

4p+2m=142

p=54-m

4p+2m=142

(substitute 54-m to the equation)

4(54-m)+2m=142

m=37

(collect like terms, then substitute the value of m into the first equation)

p=54-37

p=17

(m, p)=(37, 17)

Step-by-step explanation:

i hope this helps, sorry for the wait

5 0

3 years ago

Find the equation of the directrix of the parabola found in part A.

elena-s [515]

The specific equation of the parabola can be found by plugging the given

values of the variables of the general equation.

<h3>Correct Response;</h3>

$\displaystyle The \ equation \ of \ the \ parabolic \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

<h3>Method used to obtain the above equation;</h3><h3 /><h3>Given parameters;</h3>

The vertex of the parabola is at the origin with coordinates (0, 0)

The location of the focus = 3 cm from the vertex

<h3>Required:</h3>

The equation that models the parabola.

<h3>Solution:</h3>

The vertex form of the equation of a parabola is y = a·(x - h)² + k

The above equation can be expressed as (x - h)² = 4·p·(y - k)

Where in a vertical parabola;

(h + p, k) = The coordinates of the focus

(h, k) = The coordinates of the vertex = (0, 0)

p = 3 = The distance of the focus from the vertex

Therefore, the coordinates of the focus = (0 + 3, 0) = (3, 0)

The equation of the parabola is therefore;

(x - 0)² = 4×3 × (y - 0) = 12·y

x² = 12·y

$\displaystyle The \ equation \ of \ the \ parabola \ that \ models \ the \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

Learn more about the equation of a parabola here:

brainly.com/question/2131669

5 0

3 years ago

PLS HELPPP ASAP MATH

HACTEHA [7]

Answer:

B. 2x + 4y

Step-by-step explanation:

If x = 4, and y = 7, let's substitute these values for x and y in the equations!

For A, the equation is 2xy. Substitute the values and you have 2(4)(7) which equals 56. This expression is incorrect since the expression doesn't equal 36.

For B, the equation is 2x + 4y. Substitute and you get the equation

2(4) + 4(7) → 8 + 28 = 36.

36 is your desired value, and you get that with the expression 2x + 4y.

6 0

3 years ago

Read 2 more answers

Karina rode her bike up a mountain trail at an average of 4 mph. Then she rode it back down the trail at an average of 20 mph. T

earnstyle [38]

Answer:

36 miles.

Step-by-step explanation:

We have been given that Karina rode her bike up a mountain trail at an average of 4 mph. Then she rode it back down the trail at an average of 20 mph. The entire trip took 3 hours.

$\text{Distance}=\text{Speed}\times \text{Time}$