Tell whether the ordered pair is a solution to the system.
(-1, -2) 3x + 5y = 3
-9x - 8y = -9
no
yes

If sec(A) = 4/3, then the value cot(A) is [tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]

The given trigonometric identity is:

[tex]sec(A)=\frac{4}{3}[/tex].........................(*)

Note that:

[tex]sec(A)=\frac{Hypotenuse}{Adjacent}[/tex].........................(**)

Comparing (*)  and (**)

Hypotenuse = 4

Adjacent = 3

Find the opposite using the Pythagoras theorem

Hypotenuse²  =  Opposite²  +  Adjacent²

4²   =  Opposite²  +  3²

Opposite² = 4²  -  3²

Opposite²  =  16 - 9

Opposite² = 7

Opposite = √7

cot(A) = Adjacent/Opposite

cot(A) = 3/√7

Rationalize the expression

[tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]

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Answer

1A=B 1B=tan 2=B 3=A

Step-by-step explanation:

Answer:

Step 1: Given

Step 2: Add 6 on both sides

Step 3: Multiply 7 on both sides

Step 4: Divide by 4 on both sides

The value of x for the given linear equation is -24.5.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

We have, a linear equation in one variable

[tex]\frac{4x}{7} -6=-20[/tex]

We solve the above equation in following steps

Step I : Adding 6 both the sides

[tex]\frac{4x}{7} = -20 + 6[/tex]  

⇒[tex]\frac{4x}{7} = -14[/tex]

Step II:  Multiply 7 both the sides

⇒ [tex]4x = -14[/tex] ×[tex]7[/tex]

⇒ [tex]4x = -98[/tex]

Step III: Dividing both the sides by 4

⇒ [tex]\frac{4x}{4} = -\frac{98}{4}[/tex]

⇒ [tex]x = -24.5[/tex]

Therefore, the value of x for the given linear equation is -24.5

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Answer:

a, h and k have values 1, -5 and -10 respectively

Answer:

y = 3x + 18

Here's how I got that:

- You first assign the points -

     (-9, -9) → x1 = -9, y1 = -9

     (-6, 0) → x2 = -6, y2 = 0

- Now you plug those points into slope formula and solve-

                          [tex]s=\frac{y2-y1}{x2-x1}[/tex]

                                   ↓

                       (0 - (-9))/((-6) - (-9))

                                   ↓

                                  9/3

                                   ↓

                           slope = 3

- Now we plug the numbers we got into intercept formula -

                            b = y1 − s ⋅ x1

                                      ↓

                             -9 - (3) · (-9)

                                      ↓

                           y-intercept = 18

           - Put everything together and you get.. -

                                 y = 3x + 18

~That's all folks~

-Siascon

Answer:

y = 3x + 18

Step-by-step explanation:

Using it's concept, it is found that the probabilities are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 400 moviegoers.

From the table, 74 are adults who prefer comedies, hence:

P(C ∩ D) = 74/400 = 0.185.

2 + 48 + 19 + 74 = 143 are adults, while 24 + 64 = 88 are not adults but prefer comedies, hence the "or probability" is given by:

P(C ∪ D) = (143 + 88)/400 = 0.5775.

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Answer:

0.3575

0.405

Step-by-step explanation:

Answer:

Question 10.

Length of the side of the square = [tex]\sqrt{441} = 21[/tex]

By Pythagoras' Theorem,

Hypotenuse = [tex]\sqrt{21^{2} + 20^{2} }[/tex] (H > 0)

                     = 29 m

Ans: 29 m

Question 11.

By Pythagoras' Theorem,

Length of longer side of 42 km = 42- [tex]\sqrt{18^{2} - 15^{2} }[/tex] (L > 0)

                                                                     = 32.050 km (5 s.f.)

By Pythagoras' Theorem,

Length of the unknown side = [tex]\sqrt{32.050^{2} + 15^{2} }[/tex] (L > 0)

                                               = 35.4 km (3 s.f.)

Ans: 35 km

Answer:

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.

Answer: 0.71429

Step-by-step explanation:

Answer:

1 and 3/4

Step-by-step explanation:

7×1/4 (the / symbolizes ÷)

(7×1) ÷4

7/4 ( divide by 4)

=1 and 3/4

Answer:

Step-by-step explanation:

Y -.-

Answer:

Point Y is the answer to this

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

Explanation:

Ignore the stems. We count out the number of leaves

So we have a total of 3+5+4+3 = 15 leaves which correspond to 15 data values.

Answer:

y = -3x + 7

Step-by-step explanation:

Answer:

y = -3x + 7 (above)

Step-by-step explanation:

To add on, the person above me is correct. The equation of the line is in mx + b, where m is slope and b is the y-intercept.

We see the line intercepts the y axis at (0,7). Therefore the equation is y= mx +7

Now we look for m, the slope. If you may remember slope is also change in y over change in x, or rise/run. If you look at the graph, for each unit to the right, the line drops 3 units(it goes down, so negative). Therefore the slipe would be -3/1, or -3.

Plugging that in,

y = -3x + 7

Answer:

x (Fancy Gold fish) = 3

y (Common goldfish) = 29

Step-by-step explanation:

Fancy goldfish x cost $3 each

common goldfish y cost $1 each

Graph: y  = 20 +  3x (I'm hoping this is the correct line equation, please do leave a comment below if it's not)

Thus, we graph it by subtitude either the x or y values. (Or you can use just X = 1,2,3).

Now, to find how many of each type of goldfish Tasha can buy. We subtitude the line equation by either using x = 3 or y = 1

Using either values to solve the equation, we get:

x = 3

y = 29

Hope this helps!

Answer:

8×10^5

Step-by-step explanation:

Perimeter= 2( length + width)

= 2(34.5 × 10⁴ + 5.5 × 10⁴)

= 2(40 × 10⁴)

= 80 × 10⁴

= 8 × 10^5 feet

Hope you could get an idea from here.

Doubt clarification - use comment section

Answer:

y = 1/3x

Step-by-step explanation:

Alright, so we have an equation with two variables (y and x) and I need to solve for y in terms of x. That is, I need to isolate y one one side with all the other terms on the other side.

First, let's distribute the 1/3 on the right side of the equation onto the x and 6 inside the parentheses.

y + 2 = 1/3(x + 6)

y + 2 = 1/3(x) + 1/3(6)

y + 2 = 1/3x + 2

Now, let's isolate y on the left side by removing 2 from both sides.

y + 2 = 1/3x + 2

y + 2 - 2 = 1/3x + 2 - 2

y = 1/3x

So, y is equal to 1/3x. Hopefully that's helpful! :)

Answer:

6432)10 = (1100100100000)2

Step-by-step explanation:

Step 1: Divide (6432)10 successively by 2 until the quotient is 0:

6432/2 = 3216, remainder is 0

3216/2 = 1608, remainder is 0

1608/2 = 804, remainder is 0

804/2 = 402, remainder is 0

402/2 = 201, remainder is 0

201/2 = 100, remainder is 1

100/2 = 50, remainder is 0

50/2 = 25, remainder is 0

25/2 = 12, remainder is 1

12/2 = 6, remainder is 0

6/2 = 3, remainder is 0

3/2 = 1, remainder is 1

1/2 = 0, remainder is 1

Step 2: Read from the bottom (MSB) to top (LSB) as 1100100100000. This is the binary equivalent of decimal number 6432 (Answer).

Hopes that it will help u...☺

[tex]\huge \bf༆ Answer ༄[/tex]

The method to convert the number from Decimal to binary number system is simple ~

Now let's solve the given question ~

Now, write the numbers from bottom to top ~

[tex] \sf{1100100100000}[/tex]

I hope it helps ~

The value of k to the nearest integer is 21

If the number of international tourist arrivals in Russia in 2012 was 13.5% greater than in 2011 will be expressed as:

k = 24.7 - (13% of 24.7)

k = 24.7 - (0.135 * 24.7)

k = 24.7 - 3.3345

k = 21.3655

Hence the value of k to the nearest integer is 21

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Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

In this problem:

The percentages associated with getting the flu are:

Hence:

[tex]P(A) = 0.2(0.3) + 0.65(0.7) = 0.515[/tex]

The probability of both having the flu and getting the shot is:

[tex]P(A \cap B) = 0.2(0.3) = 0.06[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165[/tex]

0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

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Answer:

flu shot

flu

no flu

.30

.20

Step-by-step explanation:

trust

Answer:

C) -5

Step-by-step explanation:

-5 is an integer but not a whole number or a natural number.

Answer:

[tex]\huge\color{purple}\boxed{\colorbox{black}{Answer♡}}[/tex]

[tex] \frac{2}{ \sqrt{7} - 1} \\ = > \frac{2}{ \sqrt{7} - 1} \times \frac{ \sqrt{7} + 1}{ \sqrt{7} + 1} \\ = > \frac{2( \sqrt{7} + 1)}{ \sqrt{7} {}^{2} - 1 {}^{2} } \\ = > \frac{2 \sqrt{7} + 2}{7 - 1} \\ = > \frac{2( \sqrt{7} + 1)}{6} \\ = > \frac{ \sqrt{7} + 1}{3} [/tex]

[tex]\color{red}\boxed{\colorbox{skyblue}{Additional Information~}}[/tex]

( a + b ) × ( a - b ) = a² - b²

we earlier had 2 multiplied to rest of the numerator and 6 in the denominator..

we simply divided both the numerator as well as denominator by 2 and hence got the result obtained.

‎ ‎

‎ ‎

‎ ‎

hope helpful~

Answer:

a) 335

b) 344

Step-by-step explanation:

If 310 is 30% of some number x, then

0.30x = 310

⇒   x = 310/0.30

⇒   x = 310/(3/10)

⇒   x = 310 × 10/3

⇒   x = 3100/3 ≈ 1033.33

Answer:

b = (a/16) - 4

Step-by-step explanation:

a = 16(b + 4)

a = 16b + 64

16b + 64 = a

16b = a - 64

16b/16 = (a/16) - 64/16

b = (a/16) - 4

Answer:

b = a/16 - 4.

Step-by-step explanation:

a=16(b+4)

b+4 = a/16

b = a/16 - 4.

Answer:

0.85

Step-by-step explanation:

HOPE THIS HELPS :)

Answer:

I don't know

Step-by-step explanation:

Gloria will knit 1 scarf in 3 hours.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Gloria likes to knit scarves to give as gifts to her friends and family.

She can knit 1 over 4 of a scarf in 3 over 4 of an hour.

Simplifying,

She can knit 1/4 of a scarf in 3/4 of an hour.

To find the time:

1/4 of a scarf in 3/4 of an hour.

Multiply by 4,

4 x 1/4 of a scarf in 4 x 3/4 of an hour.

1 scarf in 3 hours.

Therefore, she will take 3 hours to knit 1 scarf.

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Answer:

The difference between the maximum and the minimum temperature on that day is [tex]18^0C[/tex]

Step-by-step explanation:

The maximum temperature of an island was recorded [tex]15.5^0C[/tex]

The minimum temperature was recorded [tex]-2.5^0C[/tex]

Difference in temperature

[tex]=15.5--2.5\\\\=18^0C[/tex]

Answer:

the difference between 15.5 and -2.5 is 18

Step-by-step explanation: