A consistent system of equations is a system with __________.



Select one:

a. the same line

b. parallel lines

c. intersecting lines and lines that have the same slope

d. intersecting lines and lines that have the same equation

Step-by-step explanation:

here's the answer to your question

Answer:

Step-by-step explanation:

Concept:

Here, we need to know the idea of a special triangle 30-60-90.

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.

The ratio between the corresponding side of each angle is 1 : √3 : 2

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

30-60-90 ⇔ 1 : √3 : 2

Given the side corresponding to 90° is 20

30° : 90° = 1 : 2

30° : 20 = 1 : 2

30° = 10

30° : 60° = 1 : √3

10 : 60° = 1 : √3

60° = 10√3

Hope this helps!! :)

Please let me know if you have any questions

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Answer:

  (a)  ΔWZY ~ ΔWXZ ~ ΔZXY

Step-by-step explanation:

In order for the similarity statement to be correct, the corresponding sides need to be listed in the same order.

A: ΔWZY lists sides in order short leg (WZ), long leg (ZY).

  ΔWXZ lists sides in order short leg (WX), long leg (XZ).

  ΔZXY lists sides in order short leg (ZX), long leg (XY).

The first similarity statement is correct.

__

You can compare this to an incorrect one, the last one, for example.

ΔYZW lists sides in order long leg (YZ), short leg (ZW).

ΔXZW lists sides in order long leg (XZ), hypotenuse (ZW). Hypotenuse and short leg are not corresponding sides, so the similarity statement is incorrect.

Answer:

g(-3) = 1

Step-by-step explanation:

The x-value -3 lies within the given interval x ≤ -3, and so the correct piecewise function is x + 4, not -4 or -1.  Evaluating x + 4 at x = -3 yields 1.

Thus, g(-3) = 1

The required value of the function g(x) at x = -3 , g(-3) is +1.

Given that,
A function is given with their domain,
g(x) = x + 4 when x≤
g(x) = 4 when -3 < x < 3
g(x) = - 1 when x ≥ 3

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here, Function has been given with their respective limit in which the function is defined,
For the value of g(-3) the value of x = -3 lies in the limit x ≤ -3
So for this limit, we have a function,
g(x) = x + 4
g(-3) = - 3 + 4
g(-3) = +1

The required value of the function g(x) at x = -3 , g(-3) is +1.

learn more about function here:

brainly.com/question/21145944

#SPJ5

Answer:

The correct answer is d.

Answer:

Step-by-step explanation:

Arranging the data in the ascending order:

108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4

The median is the middle value of the data set:

a)

Hence,

median = 117.4

b)

When the value of blood pressure is 117.7 instead of 117.4 then the median will be:

Median = 117.7

c)

This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.

Answer:

465/1178 = .395 = 39.5%

Step-by-step explanation:

        224 + 245

224+ 387 + 245 + 322

465/1178 = .395 = 39.5%

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Answer:

  78.5 km

Step-by-step explanation:

Measured at the airport, the angle between the two planes is ...

  180° -60° -50° = 70°

The law of cosines tells us the distance between the planes is ...

  d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km

The planes are about 78.5 km apart.

Answer:

n = .25

Step-by-step explanation:

For the equation to be true, both sides must be equal.

20 * 4 * 3 * n = 5 * 12

240 * n = 60

n = 60/240

n = .25

Answer:

1/4

Step-by-step explanation:

20×n×4×3=5×12

or, 240n=60

or, n=60/240

or, n=1/4

Answered by GAUTHMATH

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Answer:

  (a)  2

Step-by-step explanation:

Each inch is 2.54 cm, so 5.08 cm is ...

  x / (5.08 cm) = (1 in) / (2.54 cm)

  x = (1 in)(5.08/2.54) = (1 in)(2)

  x = 2 in

5.08 cm equals 2 inches.

Answer: Yes, but only if he houses 37, 38, 39, or 40 fish

Anything larger than 40 and he'll need more room.

==========================================================

Explanation:

The tank is 30 cm by 30 cm by 100 cm. The volume is 30*30*100 = 90,000 cm^3 which is shorthand for "cubic centimeters".

We're told that 1000 cm^3 = 1 liter, which means the 90,000 cm^3 converts to (90,000)/(1000) = 90 liters.

The fish tank is 90 liters.

Since 1 gallon = 4.5 liters, this means the 90 liter tank converts to 90/(4.5) = 20 gallons

----------------------------

Your teacher mentions "He can keep 2 small fish for every 1 gallon".

Since the tank is 20 gallons, that means he can keep 20*2 = 40 fish. This value is larger than 36, so Matt is correct to a point. If Matt is thinking 37, 38, 39, or 40 fish then he would be correct. If Matt is wanting more than 40 fish, then he'll need a bigger tank.

In short, he can't have any number over 36 and can only have 4 specific values (the four values mentioned earlier).

So technically, Matt is correct, but strong clarification is needed.

Answer:

a) About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of​ earbuds.

b) About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received ​$5 off their first​ purchase.

Step-by-step explanation:

a. About how many shoppers received a free set of​ earbuds?

21% out of 230. So

[tex]230\frac{21}{100} = 2.3(21) = 48.3[/tex]

About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of​ earbuds.

b. About how many shoppers received ​$5 off their first​ purchase?

25% out of 230, so:

[tex]230\frac{25}{100} = 230\frac{1}{4} = \frac{230}{4} = 57.5[/tex]

About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received ​$5 off their first​ purchase.

Answer:

4:5

Step-by-step explanation:

A pair of complementary add up to 90, given that one of them is 50, we can do this: x + 50 = 90

solve it and we get x = 40

40 + 50 = 90, so 40 and 50 are the pair of complementary angles.

As for it's Ratio, we can just get the pair and have it as 40:50 but we can reduce it to 4:5

Answer:

v<1 23/25

Step-by-step explanation:

The inequality simplifies to 48/25, which is equivalent to 1 23/25.

Answer:

b. 0.0228

Step-by-step explanation:

We are given that

n=40

Mean,[tex]\mu=402.7 g[/tex]

Standard deviation, [tex]\sigma=8.8[/tex]g

We have to find the probability hat the mean weight for a sample of 40 summer squash exceeds 405.5 grams.

[tex]P(x>405.5)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}>\frac{405.5-402.7}{\frac{8.8}{\sqrt{40}}})[/tex]

[tex]P(x>405.5)=P(Z>\frac{2.8}{\frac{8.8}{\sqrt{40}}})[/tex]

[tex]P(x>405.5)=P(Z>2.01)[/tex]

[tex]P(x>405.5)=1-P(Z\leq 2.01)[/tex]

[tex]P(x>405.5)=1-0.977784[/tex]

[tex]P(x>405.5)=0.022216[/tex]

Hence, option b is correct.

Answer:

-40

Step-by-step explanation:

-55 + 15 = x

-40 =x

Answer:  9 gallons

Work Shown:

(15 gallons)/(10 minutes) = (x gallons)/(6 minutes)

15/10 = x/6

15*6 = 10*x ... cross multiplication

90 = 10x

10x = 90

x = 90/10

x = 9

The camel can drink 9 gallons in 6 minutes. This is assuming that the unit rate is kept the same.

Answer:

The answer must be between 20 and 5000 characters

Step-by-step explanation:

Amount of acid = 14.9% of 331 mL solution

= 0.149×(331 mL)

= 49.3 mL acid

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Answer:

 14

Step-by-step explanation:

  [tex]7\log_7(49)=7\log_7(7^2)=7\cdot2=\boxed{14}[/tex]

Answer:

C. 4

Step-by-step explanation:

ln(4) = the power of e to get 4.

and then we put e to the power of that answer, so the result must be 4.

Write each equation in standard form:

3x + y + 3z = 11

x + 2y + z = 7

-x + y + z = 0

In matrix form, this is

[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]

and in augmented matrix form,

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]

Now for the row operations:

• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]

• Multiply row 2 by -1/5:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]

• Add -4 (row 2) to row 3:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]

• Multiply row 3 by 1/6:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Add -1 (row 2) and -3 (row 3) to row 1:

[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Mutiply row 1 by 1/3:

[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).

Answer:

There are 2,598,960 ways to receive 5 cards from a deck of 52.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

a. How many ways are there to receive 5 cards from a deck of 52?

[tex]C_{52,5} = \frac{52!}{5!(47)!} = 2598960[/tex]

There are 2,598,960 ways to receive 5 cards from a deck of 52.

Answer:

C. [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

Fifty percent of the data values lies between 34 and 46.

It is unlikely that there are any outliers.

Step-by-step explanation:

drawing out this box plot and looking online for a picture of the same plot:

From the box plot:

median=46

Q1=42

Q3=70

Q3-Q1= IQR=70-42=28

max=76

min=34

Range=max-min=76-34=42

no outliers seen from boxplot

Answer:

that person is right

Step-by-step explanation:

so

82-(-2)

=84

then ur answer is 84