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2 years ago

Which equation has the same solution as x2 - 6x – 14 = 0?how i do this

Mathematics

1 answer:

Stells [14]2 years ago

5 0

Answer: 1.79

Step-by-step explanation: x2−6x−14=0

For this equation: a=1, b=-6, c=-14

1x2+−6x+−14=0

Step 1: Use quadratic formula with a=1, b=-6, c=-14.

−b±√b2−4ac

−(−6)±√(−6)2−4(1)(−14)

2(1)

6±√92

x=3+√23 or x=3−√23

Answer:

x=3+√23 or x=3−√23= 1.79

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Drag the values to order them from least to greatest, with the least at the top. Item 2 moved to position 3. 79 − − √ + 63 − − √

Nonamiya [84]

$\sqrt{63} \\ \\ \sqrt{79} \\ \\ \sqrt{143} \\ \\ 4\pi$

<h2>Explanation:</h2>

As I understand, in this exercise, we have the following numbers:

$\text{Number 1}=\sqrt{79} \\ \\ \text{Number 2}=\sqrt{63} \\ \\ \text{Number 3}=\sqrt{143} \\ \\ \text{Number 4}=4\pi$

By using calculator, let's convert those numbers into decimal form:

$\text{Number 1} \approx 8.88\\ \\ \text{Number 2} \approx 7.93 \\ \\ \text{Number 3} \approx 11.96 \\ \\ \text{Number 4} \approx 12.56$

So arranging from least to greatest we have:

$\text{Number 2} \\ \\ \text{Number 1} \\ \\ \text{Number 3} \\ \\ \text{Number 2}$

Put another way:

$\sqrt{63} \\ \\ \sqrt{79} \\ \\ \sqrt{143} \\ \\ 4\pi$

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2 years ago

Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15

Digiron [165]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$2x-5y=-13, \: 3x+4y=15$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

$2x=5y-13$

Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right) \\$

Multiply $\frac{1}{2}\\$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2} \\$

Substitute $\frac{5y-13}{2}\\$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\$

Multiply 3 times $\frac{5y-13}{2}\\$ .

$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15 \\$

Add $\frac{39}{2}\\$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2} \\$

Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.