How many solutions does the system have? 13x + 4y = 33 26y + 8x =66

Answer:

A

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1

Divide all terms by sin²x

[tex]\frac{sin^2x}{sin^2x}[/tex] + [tex]\frac{cos^2x}{sin^2x}[/tex] = [tex]\frac{1}{sin^2x}[/tex] , that is

1 + cot²x = csc²x

Thus

cot²θ + 1 = csc²θ → A

Answer:

A)

1.

Statement is - Vegetables are good for your health.

Let P - There are Vegetables , Q - they are good for health

Conditional statement is -If there are Vegetables , then they are good for the health.

Inverse Statement is - If there are no Vegetables, then they are not good for health.

Converse statement - If they are good for health , then they are vegetables.

Contra-positive statement - If they are not good for health , then they are not vegetables.

2.

Statement is - 3x + 8 = 14, x = 2

Let P - 3x + 8 = 14 , Q - x = 2

Conditional statement is -If 3x + 8 = 14 , then x = 2.

Inverse Statement is - If 3x + 8 ≠ 14 , then x ≠ 2.

Converse statement - If x = 2 , then 3x + 8 = 14

Contra-positive statement - If x ≠ 2 , then 3x + 8 ≠ 14

3.

Statement is - A right triangle has a 90° angle.

Let P - Triangle has a 90° angle , Q - It is right triangle .

Conditional statement is -If Triangle has a 90° angle , then It is right triangle.

Inverse Statement is - If Triangle has not a 90° angle , then It is not right triangle.

Converse statement - If It is right triangle , then Triangle has a 90° angle.

Contra-positive statement - If It is not a right triangle  , then Triangle has not a 90° angle.

4.

Statement is - An eagle is a bird .

Let P - It is an eagle  , Q - It is a bird

Conditional Statement - If it is an eagle , then it is a bird.

Inverse statement - If it is not eagle , then it is not bird.

Converse statement - If it is a bird , then it is an eagle.

Contra-positive statement - If it is not a bird , then it is not an eagle.

5.

Statement is - A whale is a mammal

Let  P - It is a whale , Q - It is a mammal

Conditional Statement - If it is a whale , then it is a mammal.

Inverse statement - If it is not whale , then it is not mammal.

Converse statement - If it is a mammal , then it is a whale.

Contra-positive statement - If it is not a mammal , then it is not a whale.

6.

Statement is - Two circle with equal diameters are congruent

Let  P - Two circles have equal diameters , Q - They are congruent

Conditional Statement - If Two circles have equal diameters , then they are congruent.

Inverse statement - If two circles have not equal diameters , then they are not congruent.

Converse statement - If two circles are congruent , then they have equal diameters.

Contra-positive statement - If two circles are not congruent , then they have not equal diameters.

7.

Statement is - An angle that measures between 90 and 180 degrees is obtuse  angle

Let  P - An angle that measures between 90 and 180 degrees , Q - They are obtuse angle.

Conditional Statement - If An angle that measures between 90 and 180 degrees , then they are obtuse angle.

Inverse statement - If An angle that does not measures between 90 and 180 degrees , then they are not obtuse angle.

Converse statement - If an angle is obtuse angle , then that angle measures between 90 and 180 degrees.

Contra-positive statement - If an angle is not an obtuse angle , then that angle does not measures between 90 and 180 degrees.

8.

Statement is - Two planes with no common point are parallel.

Let P - Two planes have no common point , Q - they are parallel.

Conditional Statement - If Two planes have no common point , then they are parallel.

Inverse statement - If two planes have common point , then they are not parallel.

Converse statement - If two planes are parallel, then they have no common point.

Contra-positive statement - If two planes are not parallel, then they have common point.

9.

Statement is - Carrot is rich in Vitamin A.

Let P -  There are carrots , Q - they are rich in Vitamin A

Conditional statement is -If There are carrots , then they are rich in Vitamin A.

Inverse Statement is - If there are no carrots , then they are not rich in Vitamin A.

Converse statement - If they are rich in Vitamin A , then they are carrots

Contra-positive statement - If they are not rich in Vitamin A , then they are not carrots.

10.

Statement is - All reptiles have scales.

Let  P - All are reptiles , Q - they all have scales.

Conditional statement - If all are reptiles , then they all have scales.

Inverse statement - If all are not reptiles , they have no scales.

Converse statement - If all have scales , then all are reptiles.

Contra-positive statement - If all have no scales , then they all are not reptiles.

B)

1. Both the conditional and converse  statements are true.

Bi-conditional statement - There are vegetables if and only if they are good in health.

3. Both the conditional and converse  statements are true.

Bi-conditional statement - A triangle has a 90° angle if and only if it is a right triangle.

6. Both the conditional and converse  statements are true.

Bi-conditional statement - Two circle are equal diameter if and only if they are congruent.

7. Both the conditional and converse  statements are true.

Bi-conditional statement - An angle that measures between 90 and 180 degrees if and only if it is an  obtuse  angle.

8. Both the conditional and converse  statements are true.

Bi-conditional statement - Two planes has no common point if and only if they are parallel.

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Answer:

[tex]3(x - 5) \leqslant 24 \\ 3x - 15 \leqslant 24 \\ 3x \leqslant 24 + 15 \\ 3x \leqslant 39 \\ x \leqslant \frac{39}{3} \\ x \leqslant 13[/tex]

Answer:

x ≤ 13

Step-by-step explanation:

Let's sort out the brackets first, expand them.

3(x-5) --> 3x - 15

Now our equation looks like this.

3x - 15 ≤ 24

Since we are solving the inequality, let's get the x on its own. Add the 15 to remove it from one side.

3x - 15 ≤ 24

     +15   +15

3x ≤ 39

We are still trying to get x on its own so let's divide the 3, to remove it.

3x ≤ 39

 ÷3  ÷3

x ≤ 13

And that is the final answer!

Answer:

Average price = $3.185

Step-by-step explanation:

Given:

12 notepads = $4.20 each

25 folders = $0.80 each

3 calculators =  $19.00 each

Find:

Average price

Computation:

Average price = Total cost / Total number of item

Average price = [(12)(4.20) + (25)(0.80) + (3)(19)] / [12 + 25 + 3]

Average price = [(50.4) + (20) + (57)] / [40]

Average price = [127.4] / [40]

Average price = $3.185

Answer:

[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]

Step-by-step explanation:

C = (0, 7)

Since, point A lies in y-axis, so it's x coordinate will be zero. Line y = 2x + 1 passes through point A.

Therefore, plug x = 0 in y = 2x +1, we find:

y = 2*0 + 1 = 0 + 1 = 1

Hence, coordinates of point A are (0, 1).

Now, by distance formula:

[tex] AC= \sqrt{(0-0)^2 +(7-1)^2} [/tex]

[tex] AC= \sqrt{(0)^2 +(6)^2 }[/tex]

[tex] AC= \sqrt{0 +36 }[/tex]

[tex] AC= \sqrt{36 }[/tex]

[tex] AC= 6\: units[/tex]

Length of perpendicular CB dropped from point C (0, 7) to line y = 2x + 1 or 2x - y + 1 = 0 can be obtained as given below:

[tex] CB =\frac{|2\times 0+(-1)\times 7+1|}{\sqrt {2^2 +(-1)^2} } [/tex]

[tex] CB =\frac{|0-7+1|}{\sqrt {4 +1} } [/tex]

[tex] CB =\frac{|-6|}{\sqrt {5} } [/tex]

[tex] CB =\frac{6}{2.24} [/tex]

[tex] CB =2.68\: units [/tex]

By Pythagoras Theorem:

[tex] AB=\sqrt{AC^2 - CB^2} [/tex]

[tex] AB=\sqrt{6^2 - (2.68)^2} [/tex]

[tex] AB=\sqrt{36 - 7.18} [/tex]

[tex] AB=\sqrt{28.82} [/tex]

[tex] AB=5.36842621\: units [/tex]

[tex] AB\approx 5.37\: units [/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times AB\times CB[/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times 5.37\times 2.68[/tex]

[tex] A(\triangle ABC) = \frac{1}{2} \times 14.3916[/tex]

[tex] A(\triangle ABC) = 7.1958[/tex]

[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]

Answer:

-4/3

Step-by-step explanation:

it says to find the slope you do y2 - y1 / x2 - x1.

From the points, you have x1 = -3, x2 = 0, y1 = 3, y2 = -1.

Plug those in:

-1 - 3 / 0 - (-3) = -4 / 3 = -4/3

Answer:

-1-3/0-(-3)= -4/3

Step-by-step explanation:

since m=y2-y1/x2-x1 the equation would be -1-3/0-(-3) which equals to -4/0+3 which equals -4/3. since it's slope you do not simplify.

Answer: 800 ft if im right

Step-by-step explanation:

Answer:

To stay within budget, she must use 4.4 gigabytes.

Step-by-step explanation:

Giving the following information:

Fixed cost= $57.50 per month

Variable cost= $4 per gigabyte.

She wants to keep her bill at $75.10 per month.

First, we need to establish the total cost formula:

Total cost= 57.5 + 4*x

x= number of gigabytes

Now, we isolate x:

75.1= 57.5 + 4x

17.6/4= x

4.4= x

To stay within budget, she must use 4.4 gigabytes.

Answer:

she has to use 4.4 gigabytes

Step-by-step explanation:

Answer:

4 x -11 = 12x

Step-by-step explanation:

4 x -11 = 12x

1. Subtract 4 by itself and -11

-15 = 12x

2. Divide 12 by itself and -15

x = -1.25

The resulting equation to fulfill this requirement would be:

y = 54x

When x = 4, y = 216

Answer:

9 / 14 for a brown , 3 / 14 for a blue

Step-by-step explanation:

1) summarize all cards 9 (brown) + 2 (yellow) + 3 (blue)= 14 cards.

2) probability depends on how many cards of a particular color, how more cards, then more probability.  

3) 9 brown cards, so probability = 9 brown cards to divide all cards 14.  

Answer:

-5.3

Step-by-step explanation:

-2.8+(-2.5)=-2.8-2.5=-5.3

Answer:

-5.3

Step-by-step explanation:

Answer:

C- 4f less than or equal to 36

Step-by-step explanation:

The fish are 4 dollars each so how many fish you buy, you will multiply 4. Example- I will buy 5 fish so 5×4=20.

You can only spend less than 36 or you can spend exactly 36 dollars.

In my example I spent less than 36 dollars. I don't know if you understand but tell me if you need help.

Answer:

the answer is center mark happy to help ya :)

Step-by-step explanation:

Answer:

2$+(1.29$ x 30)=40.70$

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

D the answer is zero that is as low as you can get

Answer:

Attached

Step-by-step explanation:

Answer:

true false false true

Step-by-step explanation:

Answer:

C) 10, 14, 13

the sum of the lengths of the two shorter legs must be greater than the length of the third leg.   note: not equal to either like "B".

Answer:

145) A

146) C

147) B

148) D

Answer:

The answer is number four(4).

5n+2n+6=4n-21 group like terms on left side

7n+6=4n-21subtract 6 from both sides

7n=4n-27 subtract 4n from both sides

3n=27 divide both sides by 3

n=9

Answer:

1  1/2 eggs

1/2 almond paste

1/8 vanilla

3/8 sugar

Step-by-step explanation:

Answer:

72.18

Step-by-step explanation:

The hundreth place is the second to the right of the decimal. So the number in the hundreths place is 72.178. When rounding, you look at the number behind the number you are rounding to. In this case, you want to look at the 8. If the number is 5 or above, you round up. 8 is above 5 so you round the 7 to an 8.

Answer: 72.18

Step-by-step explanation:

hope this helps

it would partially ionize....................

Answer:

it would partially ionize

Answer:

2+2=4

Step-by-step explanation:

If You Have 2 Circles And 2 Sqaures Add Them Together so 2+2+__

Now Add Them 2+2=4

OO+■■=4

Answer:

See Explanation

Step-by-step explanation:

The question has missing details; as the radius or an attachment of the hemisphere is not given.

However, I'll solve on a general terms.

The volume of a hemisphere is: [tex]V = \frac{2}{3}\pi r^3[/tex]

Take for instance

[tex]r = 14.9cm[/tex]

The volume becomes:

[tex]V = \frac{2}{3} * 3.142 * 14.9^3[/tex]

[tex]V = \frac{2 * 3.142 * 14.9^3}{3}[/tex]

[tex]V = \frac{20787.151516}{3}[/tex]

[tex]V = 6929.051cm^3[/tex]

So, all you need to do is plug in the value of radius in the formula.