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3 years ago

If BC = 6.5, CD = 7.8, and AD = 12.2, find AB to the nearest tenth.

Mathematics

1 answer:

Sladkaya [172]3 years ago

6 0

This can be solved using the angle bisector theorem. Note that line segment AD is the angle bisector of triangle DAB from angle DAB. Therefore, we know that the ratios $\frac{\text{AD}}{\text{CD}}$ and $\frac{\text{AB}}{\text{CB}}$ are equal. Solving, we get $\frac{\text{12.2}}{\text{7.8}}=\frac{\text{AB}}{\text{6.5}}$ . Cross multiplying, we get $79.3 = 7.8x$ , and solving this equation we get $x = 10.1666... \approx 10.2$ . 10.2 is your answer.

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mother divided the money among jan, jane and jello , in the ratio 4:9:6. If Jan got $200, find the total amount and money receiv

Kay [80]

Step-by-step explanation:

Let,

Money received by Jan = 4x
Money received by Jane = 9x
Money received by Jello = 6x

According to the question,

→ Money received by Jan = $200

→ 4x = $200

→ x = $200 ÷ 4

→ x = 50 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀… ( 1 )

Now,

→ Money received by Jane = 9x

→ Money received by Jane = 9($50)

→ <u>Money received by Jane = $450</u> [Ans]

And,

→ Money received by Jello = 6x

→ Money received by Jello = 6($50)

→ <u>Money received by Jello = $300</u> [Ans]

6 0

2 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

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2 years ago

Read 2 more answers

Carbon-14 has a half-life of 5,700 years. Scientists use this fact to determine the age of things made of organic material. Supp

kumpel [21]

I think it’s b! hearts

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2 years ago

Cannon balls for an antique cannon are stacked next to it in four layers to form a square pyramid. How many cannon balls are in

labwork [276]

The amount of balls in a given layer can be found by squaring the layer it is in

4 layers
top layer (1st) is 1
2nd is 4
3rd layer is 9
4th is 16

add them up
1+4+9+16=30

30 in that pyramid

7 0

2 years ago

Determine whether each of the following LTIC systems is i) BIBO stable, ii) asymptotically stable, and iii) marginally stable. E

nata0808 [166]

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

5 0

2 years ago