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3 years ago

Solve the equation 4x^2 + 24x + 13 = 2x^2+ 6x to the nearest tenth.

Mathematics

1 answer:

Licemer1 [7]3 years ago

6 0

Answer:

-0.8 and -8.2

Step-by-step explanation:

To solve a quadratic you first need to have one side of the equation equal to zero (because x-intercepts are when y is zero).

4x^2 + 24x + 13 = 2x^2 + 6x

2x^2 + 18x + 13 = 0

Then you can use the quadratic formula to solve for x. You will then come to

-18 ± sqrt(220) / 4

This will simplify out (rounding to the nearest tenth) to -0.8 and -8.2

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Which of the following represents the set of integers greater than or equal to -5?

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Can you please help me find the area? Thank you. :)))

Phoenix [80]

The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.

The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

$A=w\cdot l$

For our rectangle w=12 in and l=20 in, the area is:

$\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}$

The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

You can determine the value of x as follows:

$\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}$

x=4 in → this means that the base of the triangle is 4in long.

The area of the triangle is equal to half the product of the base by the height, following the formula:

$A=\frac{b\cdot h}{2}$

For our triangle, the base is b=4in and the height is h=6in, then the area is:

$\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}$

Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:

$\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}$

The area of the figure is 228in²

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1 year ago

Evaluate −12(−2). 14 −14 −24 24

bixtya [17]

The answer would be positive 24. The reason being is because of the fact that two negatives when multiplied cancel the negative. Also 12 * 2 is 24 so yeah

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3 years ago

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Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and x + 7y = 8

goblinko [34]

$\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y = \frac{17}{14} } \atop {x+7y=8}} \right.$

To solve this system by substitution, first isolate x in the second equation.

$x+7y=8$
$x+7y-7y=8-7y$
$x=8-7y$

Now, plug this expression ( $8-7y$ ) for x in the top equation to solve for y.

$\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}$
$3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}$
$72-63y+8y=17$
$72-55y=17$
$-55y=17-72$
$-55y=-55$
$y=1$

Now that you have y, plug it into the second equation and solve for x.

$x+7y=8$
$x+7(1)=8$
$x+7=8$
$x=1$

Last step is to plug your x- and y-values in to both equations to check your work.

$\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}$

$\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ; \frac{1}{3} * \frac{8}{8} = \frac{8}{24}$

$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$ <--True

$1+7(1)=8$
$1+7=8$ <--True

Answer:
$x=1 \\ y=1$

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3 years ago