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3 years ago

9

Alice bought of a pound of grapes and ate of a pound. How many pounds were left?

2 answers:

vivado [14]3 years ago

7 0

None. She ate the pound she bought.

IRINA_888 [86]3 years ago

4 0

Alice bought a pound then she ate a pound. This is simple like:

+1 pound bought

-1 pound eaten

= <em>0 pounds left</em>

<em>The answer there was no pounds left.</em>

Hope this helps :)

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Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects

Yuri [45]

Answer:

Area of triangle ADC is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be $x$ ; hence, DC will be $14-x$

and AD be $y$

To, find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

= $\frac{1}{2}(14-x)(y)$

We will have to determine $x$ and $y$

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

$Area =\sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

For the given triangle ABC

Let $a$ = AB, $b$ = BC, and $c$ = CA

Hence, $a = 13, b= 14,$ and $c = 15$

∴ $s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21$

Then,

Area of triangle ABC = $\sqrt{(21)(21-13)(21-14)(21-15)}$

Area of triangle ABC = $\sqrt{(21)(8)(7)(6)}$ = $\sqrt{7056}$

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = $\frac{1}{2} (BD)(AD)$

Area of triangle ADB = $\frac{1}{2}(x)(y)$

Hence,

Area of triangle ABC = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

84 = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

∴ $84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)$

$84 = 7y\\y = \frac{84}{7}$

∴ $y = 12$

Hence, $y =$ AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = $\sqrt{25}$

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

Area of triangle ADC = $\frac{1}{2} (9)(12)$

Area of triangle ADC = 9 × 6

Area of triangle ADC = 54 square unit

Hence, Area of triangle ADC is 54 square unit.

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MissTica

Answer:

Scale factor = 7

Step-by-step explanation:

Dilation with scale factor to map HEFG to DABC will be,

Scale factor = $\frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}$

= $\frac{\text{Length of CD}}{\text{Length of GH}}$

Length of CD = Distance between two points C(0, -7) and D(-7, 0)

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

= $\sqrt{(-7-0)^2+(0+7)^2}$

= $\sqrt{98}$

= $7\sqrt{2}$

Length of GH = Distance between G(0, -1) and H(-1, 0)

= $\sqrt{(-1-0)^2+(0+1)^2}$

= $\sqrt{2}$

Scale factor = $\frac{7\sqrt{2} }{\sqrt{2} }$

= 7

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What is -6 divided by 3/7x

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Step-by-step explanation:

$- 6 \div \frac{3}{7x} \\ \\ = - 6 \times \frac{7x}{3} \\ \\ = - 2 \times 7x \\ \\ = - 14x$

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