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2 years ago

The diagram shows a pentagon. It has one line of symmetry.

Mathematics

1 answer:

Nina [5.8K]2 years ago

7 0

Answer:

A) 10x + 8 = 21

B) x = 1.3

Step-by-step explanation:

2(2x + 3) + 2(x + 1) + 4x = 21

4x + 6 + 2x + 2 + 4x = 21

10x + 8 = 21

10x = 13

x = 1.3 cm

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A publishing company prints newspapers and magazines. Let NNN represent the number of newspapers and MMM represent the number of

adelina 88 [10]

Answer:

At most 800 magazines the company can print daily with the remaining number of ink cartridges.

Step-by-step explanation:

We are given the following in the question:

$0.5N+2.5M \leq 6000$

The above inequality gives the relation for daily supply of ink cartridges where N is the number of newspaper and M is the number of magazines.

Number of newspaper to be printed daily,N = 8000

We have to find the number of magazines at most can the company print daily with the remaining number of ink cartridges.

Puting the value in the given inequality,

$0.5(8000)+2.5M \leq 6000\\\Rightarrow 4000+2.5M \leq 6000\\\Rightarrow 2.5M \leq 2000\\\\\Rightarrow M \leq \dfrac{2000}{2.5}\\\\\Rightarrow M \leq 800$

Thus, at most 800 magazines the company can print daily with the remaining number of ink cartridges.

6 0

2 years ago

Point T, the midpoint of segment RS, can be found using the formulas x = (6 – 2) + 2 and y = (4 – 6) + 6. What are the coordinat

Fiesta28 [93]

Question:

Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?

Answer:

$T(4,5)$

Step-by-step explanation:

Given

$x = \frac{1}{2}(6 - 2) + 2$

$y = \frac{1}{2}(4 - 6) + 6$

Required

Determine the coordinates of T

The coordinates of T can be represented as $T(x,y)$

To do this, we simply solve for x and y

$x = \frac{1}{2}(6 - 2) + 2$

Solve 6 - 2

$x = \frac{1}{2}*4 + 2$

Solve 1/2 * 4

$x = 2 + 2$

$x = 4$

$y = \frac{1}{2}(4 - 6) + 6$

Solve 4 - 6

$y = \frac{1}{2}*-2 + 6$

Solve 1/2 * -2

$y = -1 + 6$

$y = 5$

Hence, the coordinates of T(x,y) is:

$T(x,y) = T(4,5)$

5 0

2 years ago

Read 2 more answers

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well

laiz [17]

Answer:

The value is $P(A) = 0.133617$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 7.5$

The standard deviation is $\sigma = 0.2$

The safest water level is between 7.2 and 7.8

Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as

$P(A) = 1 - P(7.2 \le X \le 7.8 )$

Here

$P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } < \frac{X - \mu }{ \sigma }$

Generally $\frac{X - \mu }{ \sigma } = Z (The \ standardized \ value \ of X )$

$P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - 7.5 }{0.2 } < Z$

$P(7.2 < X < 7.8 ) = P(-1.5 < Z$

=> $P(7.2 < X < 7.8 ) = P(Z < 1.5) - P( Z < - 1.5)$

From the z-table the probability of (Z < -1.5) and ( Z <1.5) are

$P(Z < 1.5) = 0.93319$

and

$P(Z < -1.5) = 0.066807$

$P(7.2 < X < 7.8 ) =0.93319 - 0.066807$

$P(7.2 < X < 7.8 ) =0.0866383$

$P(A) = 1 - 0.0866383$

=> $P(A) = 0.133617$

5 0

2 years ago

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours. At this rate of growth, how many bacteria will

Alik [6]

The number of bacteria grown in 32 hours is 15771

<u>Step-by-step explanation:</u>

It is given that,

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours.

Therefore, the bacteria has grown from 100 to 7000 in 14 hours.

<u> To calculate number of bacteria grown in 14 hours :</u>

⇒ 7000 - 100 = 6900

6900 bacteria grows in 14 hours. We need to find out the growth of bacteria in 1 hour in order to calculate its growth in 32 hours.

<u>To calculate number of bacteria grown in 1 hour :</u>

⇒ Total bacteria growth in 14 hours / 14

⇒ 6900 / 14

⇒ 492.85

<u>To calculate number of bacteria grown in 32 hours :</u>

⇒ 492.85 × 32

⇒ 15771.2

⇒ 15771 (rounded to nearest whole number)

∴ The number of bacteria grown in 32 hours is 15771

6 0

2 years ago

Read 2 more answers

Rationalize the denominator of $\frac{2}{3\sqrt{5} + 2\sqrt{11}}$ and write your answer in the form $\displaystyle \frac{A\sqrt{

vlada-n [284]

Answer:

Step-by-step explanation:

Given the surdic expression $\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\$ , to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;

$= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}$

Comparing the result $\frac{6\sqrt{5} - 4\sqrt{11} }{1}$ with the expression $\frac{A\sqrt{B} + C\sqrt{D}}{E}$ , it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1

A+B+C+D+E = 6+5+(-4)+11+1

A+B+C+D+E = 11-4+12

A+B+C+D+E = 19

Hence the value of A+B+C+D+E is 19

4 0

2 years ago