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3 years ago

Find the value of x if B is between A and C, AB=4x-9, BC= 3x+ 5, and AC=7

1 answer:

4 0

AB = 4 x - 9
BC = 3 x + 5
AC = 7

B is in between A and C. So AB + BC = AC

4x - 9 + 3 x + 5 = 7
7 x - 4 = 7 take -4 from LHS to the R H S (right hand side) it becomes +4
7 x = 7 + 4 = 11
x = 11/7 = 1.571

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In triangle ABC, AD is a median. FE is a straight line parallel to BC cutting the remaining sides AB at F and AC at E and cuttin

daser333 [38]

Answer:

Step-by-step explanation:

since AD is a median it implies that triangle ABC is bisected to two equal right angled triangle which are ADB and ADC.

FE is parrallel to BC and cuts AB at F and AC at E shows that there are two similar triangles formed which are AFE and ABC.

Recall that ADC is a right angled triangle, ED bisects a right angled triangle the the ADE = $45^{o}$ .

Now, Let FD bisect angle ADB,

then ADF = $45^{o}$ too.

Since AFX is similar to Triangle ABD and that Triangle AEX is similar to Triangle ACD, then EDX is similar to FDX

FDE = ADF + ADE = $90^{o}$

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3 years ago

Which of the ratio equivalent to 1:3 select all that apply

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Answer:

4:12

6:18

8:24

Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number.

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2 years ago

Plz answer then explain how did you did it

Stella [2.4K]

Answer:

subtract the exponents:

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Step-by-step explanation:

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3 years ago

You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows an even number.

NNADVOKAT [17]

Answer:

1/6

Step-by-step explanation:

If you're asking for the probability that the coin is heads and the die is even. Hope this helps :)

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6 0

3 years ago

Read 2 more answers

10 black balls and 5 white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the

Alex787 [66]

Answer:

The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is $\frac{1}{3}$ or 0.3333

Step-by-step explanation:

Probability is the greater or lesser possibility that a certain event will occur. In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law:

$P(A)\frac{number of favorable cases of A}{total number of possible cases}$

Each of the results obtained when conducting an experiment is called an elementary event. The set of all elementary events obtained is called the sample space, so that every subset of the sample space is an event.

The total number of possible cases is 15 (10 black balls added to the 5 white balls).

As each extraction is without replacement, the events are dependent. For that, the dependent probabilities are defined first

Two events are dependent on each other when the fact that one of them is verified influences the probability of the other being verified. In other words, the probability of A happening is affected because B has happened or not.

The probability of two events A and B of two successive simple experiments in a dependent compound experiment is:

A and B are dependent ⇔ P (A ∩ B) = P (A) · P (B / A)

P (A ∩ B) = P (B) · P (B / A)

As the color of the first ball that is extracted is unknown, there are two cases: that the ball is black or that the ball is white.

It will be assumed first that the first ball drawn is black. Then the probability of this happening is $\frac{10}{15}$ since the number of black balls in the urn is 10 and the total number of cases is 15. It is now known that the second ball extracted will be white. Then the number of favorable cases will be 5 (number of white balls inside the ballot urn), but now the number of total cases is 14, because a ball was previously removed that was not replaced. So the probability of this happening is $\frac{5}{14}$

So the probability that the first ball is black and the second white is:

$\frac{10}{15} *\frac{5}{14} =\frac{5}{21}$

It will now be assumed first that the first ball that is drawn is white. Then the probability of this happening is $\frac{5}{15}$ since the number of white balls in the urn is 5 and the total number of cases is 15. And it is known that the second ball drawn will be white. Then, the number of favorable cases will be 4 (number of white balls inside the urn, because when removing a white ball and not replacing it, its quantity will decrease), and the total number of cases is 14, same as in the previous case So, the probability of this happening is $\frac{4}{14}$

So the probability that the first ball is white and the second white is:

$\frac{5}{15} *\frac{4}{14} =\frac{2}{21}$

If A and B are two incompatible events, that is, they cannot occur at the same time, the probability of occurrence A or of occurrence B will be the sum of the probabilities of each event occurring separately.

These are events are incompatible, since I cannot, in a first extraction, extract a black and white ball at the same time. So:

$\frac{5}{21} +\frac{2}{21} =\frac{7}{21}=\frac{1}{3} =0.3333$

Finally, the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is $\frac{1}{3}$ or 0.3333

3 0

3 years ago