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3 years ago

What are the values of a and b number 8

Mathematics

1 answer:

puteri [66]3 years ago

5 0

Answer:

$\large\boxed{C.\ a=\dfrac{400}{21},\ b=\dfrac{580}{21}}$

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔABC, ΔDBA and ΔDAC are similar (AAA). Therefore the corresponding sides are in proportion:

$\dfrac{AB}{AD}=\dfrac{AC}{DC}$

We have AB = b, AD = 20, AC = 29 and DC = 21. Substitute:

$\dfrac{b}{20}=\dfrac{29}{21}$ cross multiply

$21b=(20)(29)$

$21b=580$ divide both sides by 21

$b=\dfrac{580}{21}$

and in proportion:

$\dfrac{BD}{AD}=\dfrac{AD}{DC}$

We have BD = a, AD = 20 and DC = 21. Substitute:

$\dfrac{a}{20}=\dfrac{20}{21}$ cross multiply

$21a=(20)(20)$

$21a=400$ divide both sides by 21

$a=\dfrac{400}{21}$

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The ratio of the bake time for a pepperoni pizza (P) and a cheese pizza (C) is modeled by the equation: P = 3C - 2. A.) If a sma

Elena L [17]

Answer:

34 minutes

Step-by-step explanation:

Given:

Ratio of time for which Pepperoni pizza and cheese pizza should be baked is given as:

$P = 3C - 2$

Where $P$ is the time for which pepperoni pizza should be baked and

$C$ is the time for which Cheese pizza should be baked.

Also, it is given that a small Cheese pizza should be baked for 12 minutes.

In other words, we are given that: $C=12\ min$

To find:

For how long small pepperoni pizza should be baked ?

In other words,

$P=?$

Solution:

Let us put the value of $C$ in the equation of the model.

$P = 3C - 2$

$\Rightarrow P = 3\times 12 - 2\\\Rightarrow P = 36 - 2\\\Rightarrow P = \bold{34\ min}$

Therefore, a small pepperoni pizza should be baked for 34 minutes.

5 0

3 years ago

The n term of a geometric sequence is denoted by Tn and the sum of the first n terms is denoted by Sn.Given T6-T4=5/2 and S5-S3=

Leno4ka [110]

1 step: $S_{5}=T_{1}+T_{2}+T_{3}+T_{4}+T_{5}$ , $S_{3}=T_{1}+T_{2}+T_{3}$ , then
$S_{5}-S_{3}=T_{4}+T_{5}=5$ .

2 step: $T_{n}=T_{1}*q^{n-1}$ , then
$T_{6}=T_{1}*q^{5}$
$T_{5}=T_{1}*q^{4}$
$T_{4}=T_{1}*q^{3}$
$T_{3}=T_{1}*q^{2}$
and $\left \{ {{T_{6}-T_{4}= \frac{5}{2} } \atop {T_{5}+T_{4}=5}} \right.$ will have form $\left \{ {{T_1*q^{5}-T_{1}*q^{3}= \frac{5}{2} } \atop {T_{1}*q^{4}+T_{1}*q^{3}=5} \right.$ .

3 step: Solve this system $\left \{ {{T_1*q^{3}*(q^{2}-1)= \frac{5}{2} } \atop {T_{1}*q^{3}*(q+1)=5} \right.$ and dividing first equation on second we obtain $\frac{q^{2}-1}{q+1}= \frac{ \frac{5}{2} }{5}$ . So, $\frac{(q-1)(q+1)}{q+1} = \frac{1}{2}$ and $q-1= \frac{1}{2}$ , $q= \frac{3}{2}$ - the common ratio.

4 step: Insert $q= \frac{3}{2}$ into equation $T_{1}*q^{3}*(q+1)=5$ and obtain $T_{1}* \frac{27}{8}*( \frac{3}{2}+1 ) =5$ , from where $T_{1}= \frac{16}{27}$ .

5 0

3 years ago

A 16-oz package of rice is $0.79. A 32-oz package is $3.49. Which has the lower unit cost?

soldier1979 [14.2K]

16 ounce bag of rice for $0.04 per unit

5 0

3 years ago

Read 2 more answers

Please help me I need help

dimulka [17.4K]

I think it would be 3x-4 because you could subtract WE and PE. Hope this helps!

8 0

3 years ago

A baseball team had 70 players show up for tryouts last year and this year had 85 players show up for tryouts. Find the percent

Mashutka [201]

Answer:percent increase in players from last year to this year= 7.14%

Step-by-step explanation:

percent increase = (Increase in number of players /Initial value of players Last year) x 100

value of players for tryouts last year = 70

value of players for tryouts this year = 85

Increase in tryouts = 85-70 =5

percent increase = 5/70 x 100

= 7.14%

3 0

3 years ago

What are the values of a and b number 8​

What are the values of a and b number 8