9) If two lines intersect and form equal, adjacent
angles, then the lines are
1) perpendicular 2) collinear
3) parallel
4) complementary

In the equation given 2[(4m * 3.5) / 400] = 171.5, m has a value of 2450.

Equations are mathematical statements containing two algebraic expressions on both sides of an equal to sign. This can be expressed as the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

We can find the value of m by applying changing the subject of formula

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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The speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

It is given that a plane traveled 3900 miles in 6.5 hours with wind and 3250 miles in 6.5 hours against wind.

We have to find out the speed of plane in still air and speed of wind.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

Distance travelled with wind in 6.5 hours = 3900 miles

Distance travelled against wind in 6.5 hours = 3250 miles

Let's assume speed of plane in still air be P and speed of wind be W.

So;

The total rate with the wind is the plane speed plus the wind speed and against the wind is speed of plane minus speed of wind.

i.e.,

d = rt

⇒ 6.5 ( P + W ) = 3900 miles  --- ---- --- --- -- ------- ----- --- Equation 1

and

⇒ 6.5 ( P - W ) = 3250 miles  --- ---- --- --- -- ------- ----- --- Equation 2

Let's solve the equations to get value of P and W ;

i.e.,

P + W = 3900 / 6.5

or

P + W = 600

and

P - W = 3250 / 6.5

or

P - W = 500

adding both equations ; we get ;

2P = 1100

or

P = 550 miles / hour

And

W = 50 miles / hour

Thus , the speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

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The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer:

y = 3x + 5 option A

Step-by-step explanation:

For 2 lines that are parallel with slopes m1 and m2, the slopes are equal. Hence

m1 = m2

Given the line y = 3x - 5 Comparing with the general equation of a line

y = mx + c where m is the slope of the line

m = 3

hence m1 = m2 = m = 3

For the line that passes through the given point (2,11) Using

y - y1 = m (x - x1)

y - 11 = 3(x - 2)

y - 11 = 3x - 6

Add 11 to both sides

y = 3x - 6 + 11

y = 3x + 5

Answer:

\( \int \: e {}^{x {}^{2} } dx \\ y = {e}^{ {x}^{2} } \\ ln(y) = {x}^{2} \\ \frac{dy}{y} = 2xdx \\ dy/2x = {e}^{ {x}^{2} } dx \\ \int \: d( {e}^{ {x}^{2} } ) = \int {e}^{ {x}^{2} } .2xdx \\ \frac{{e}^{ {x}^{2} } }{2x} = \int \: {e}^{ {x}^{2} } dx \\ \int \: {e}^{ {x}^{2} } dx \: = \frac{1}{2x} {e}^{ {x}^{2} } + c\)

Answer:

Well plz dont delete my question  I need points to get mine out

Step-by-step explanation:

Answer: y = - 2/3x + 4

Altitude (AB) = 9cm

Base (BC) = 12cm

Hypotenuse (AC) = ?

\( \fbox \text{According To Pythagoras Theorem = }\)

\( \text{(Hypotenuse)² = (Altitude)² + (Base)²}\)

Inserting The Values

\( \text{(Hypotenuse)²} =( {9})^{2} + (12) {}^{2} \\ \\ \implies \text{(AC)} {}^{2} = 81 + 144 \\ \\ \implies \text{(AC}) {}^{2} = 225 \\ \\ \implies \text{AC} = \sqrt{225} \\ \\ \implies \text{AC} = 15\)

\( \therefore \text{Hypotenuse \: (AC)} = 15 \text{cm}\)

Option B= 15cm is the correct answer

All the functions which are bounded below and bounded above are,

⇒ Absolute value function.

⇒ sine function function

⇒ cosine function

We have to given that;

To check all the functions which are bounded below and bounded above.

Here, All the functions are,

⇒ Absolute value function.

⇒ sine function function

⇒ cosine function

⇒ Square root function

⇒ natural logarithmic function

Since, The Absolute value function is defined as;

⇒ | f (x) |

And,

⇒ | f (x) | ≤ M ; for M > 0

⇒ - M ≤ f (x) ≤ M

Hence, It is a bounded function.

Since, Sine and cosine function are defined in between 1 and - 1.

Hence, Both are bounded below by - 1 and bounded above by 1.

So, Both function are bounded.

Since, Square root function is defined as,

⇒ √ f (x) ≥ 0

Hence, It is only bounded below.

Since, When the base of the logarithm is greater than 1, log(x) approaches negative infinity as x approaches 0.

Hence, It is not bounded.

Thus, All the functions which are bounded below and bounded above are,

⇒ Absolute value function.

⇒ sine function function

⇒ cosine function

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Answer:

4m

Step-by-step explanation:

Expressions do not have equal signs,  So for the product of 2 things we just multiply them together.

4m

Answer:

4 × M = P

Explanation:

A product is the result of a multiplication expression, so in this case, We're using variables to represent numbers.

P = Product

We're multiplying 4 and M, so lets rewrite this.

4 × M

This is an incomplete expression, but what will we use for our product We can use a variable. Our variable is P. So lets complete this expression.

4 × m = p.

Or, we can put it in a less complex way.

4m.

This also is a incomplete expression, but it means 4 × m.

Answer:

a

\(P(A_1)  =  0.007\)

b

\(P(A_2) = 0.016\)

c

\(P(A_3) =  0.008\)

d

\(P(A_4) =  0.004\)

e

\(P(A_5) =  0.0002\)

Step-by-step explanation:

From the question we are told that

   The number of cards selected is  n = 7

Generally in a standard deck of cards

   The total  number of cards is  N  =  52

    The number of  hearts is  h = 13  

    The  number of diamonds is  d = 13

    The number of  spade is  s  =  13

    The number of  Ace is  a = 4

    The number of kings is  k =  4

Considering question a

   The number of ways to selected 5 hearts out of the  13 hearts is mathematically represented as

      \(G  =  ^{13}C_5\)

Here C means combination so  

The number of cards that is not hearts  is  52 -  13  =  39

Generally the number of ways of selecting the reaming 2 cards is  

    \(H  =  ^{39}C_2\)

Generally the number of ways to select the 7  cards from the 52 deck of cards is  

        \(V  =  ^{52}C_7\)

Generally the probability that exactly 5 of the 7 cards  are hearts is mathematically represented as

     \(P(A_1)  =  \frac{G  *  H}{V}\)

=>  \(P(A_1)  =  \frac{^{13}C_5  *  ^{39}C_2}{^{52}C_7}\)

=>   \(P(A_1)  =  0.007\)

Considering question b

     The number of ways to selected 3 diamonds out of the  13 diamonds is mathematically represented as

      \( B =  ^{13} C_3 \)

The number of ways to selected 3 hearts out of the  13 hearts is mathematically represented as

      \(K  =  ^{13}C_3\)

The number of cards that is not hearts or diamond  is  52 -  (13 +13)  =  26

Generally the number of ways of selecting the reaming 1 cards is  

    \(M  =  ^{26}C_1\)

Generally the probability that there are 3 hearts and 3 diamonds is

    \(P(A_2) =  \frac{B  *  K *  M}{V}\)

=> \(P(A_2) =  \frac{^{13}C_3  *  ^{13}C_3 *  ^{26}C_1}{^{52}C_7}\)

=>  \(P(A_2) = 0.016\)

Considering question c

The number of ways to selected 1 spade out of the  13 spade is mathematically represented as

     \(J = ^{13}C_1\)

Generally the probability that there are 3 hearts, 3 diamonds and 1 spade is

   \(P(A_3) =  \frac{B *  K  *  J}{V}\)

=> \(P(A_3) =  \frac{^{13}C_3 *  ^{13}C_3   *  ^{13}C_1}{^{52}C_7}\)

=>  \(P(A_3) =  0.008\)

Considering question d

The number of ways to selected 2 Aces out of the  4 Aces is mathematically represented a

     \(U = ^{4}C_2\)

The number of ways to selected 2 Kings out of the  4 Kings is mathematically represented a

       \(R = ^{4}C_2\)

The number of cards that is not Aces or Kings  is  52 -  (4 +4)  =  44

Generally the number of ways of selecting the reaming 3 cards is  

     \(S = ^{44}C_3\)

Generally the probability that there are 2 Aces and 2 Kings is

    \(P(A_4) =  \frac{U *  R  *  S}{ V}\)

=>  \(P(A_4) =  \frac{ ^{4}C_2 *  ^{4}C_2  *  ^{44}C_3}{ ^{52}C_7}\)

=>\(P(A_4) =  0.004\)

Considering question e

The number of ways to selected 3 Kings out of the  4 Kings is mathematically represented a

     \(P = ^{4}C_3\)

Generally the number of ways of selecting the reaming 2 cards is  

      \(Q = ^{44}C_2\)

Generally the probability that there are 2 Aces and 3 Kings is

     \(P(A_5) =  \frac{U  *  P  *  Q }{V}\)

=>  \(P(A_5) =  \frac{ ^{4}C_2  *  ^{4}C_3  *  ^{44}C_2 }{^{52}C_7}\)

=>  \(P(A_5) =  0.0002\)

Answer:

I also believe it is -4.9 but I may be mistaken

Step-by-step explanation:

Answer:

84.26° in the south west direction.

Step-by-step explanation:

I've attached an image showing the triangle formed by the motion of the plane and the wind.

I've depicted the plane being pushed west and the wind moving south west.

Thus, the direction of motion of the plane will be angle θ.

Using trigonometric ratios;

25/250 = cos θ

cos θ = 0.1

θ = cos^(-1) 0.1

θ = 84.26°

Thus will be in the south west direction.

Answer:

Explanation:

Here, we want to know the amount of water the bucket can hold when full

Let us have the volume as x liters

Mathematically:

The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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The center and the radius are (2, -5) and  3

From the question, we have the following parameters that can be used in our computation:

x² + y² - 4x + 10y = -20

Express the equation in factored form

So, we have the following representation

(x - 2)^2 + (y + 5)^2 = 3^2

The equation of a circle is represented as

(x - a)^2 + (y - b)^2 = r^2

Where

Center = (a, b)

Radius = r

So, we have

Center = (2, -5) and radius is 3

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Answer:

If you choose for C you'll get the wright answer,

This is because V26 is more towards V25. This has the outcome of a little bit more than the squarerooth of 25, if you have V34 it is more towards V36 which is 6. Since V30 is in between them it is the right answer +- 5.48 as an outcome

Step-by-step explanation:

Answer:

Your answer is 1, look below please

Step-by-step explanation:

ASSUMING that the x is a variable your equation is -1x=3+4 which would be...

-1x=7, then divide by -1 which gives us -7

Answer:

Step-by-step explanation:

The difference of a number and fifteen is two. Write and Algebra Sentence then solve the number.

x - 15 = 2

x = 2 + 15

x = 17

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

check

17 - 15 = 2

2 = 2

the answer is good

Answer:

$24

Step-by-step explanation:

Fist, you will multiply the percent, 15, and the total money amount, 160, which you would get 2,400. Then, divide 2,400 by 100, and there you will get the tip, $24. I hope this helps :)

Answer:

Elements in third column = - (elements in the first column) + 8(elements in the second column)

Step-by-step explanation:

A matrix is a rectangular array in which elements are arranged in a rows and columns.

Order of a matrix = Number of rows × Number of columns

Given matrix is \(\left[\begin{array}{ccc}1&2&15\\7&8&57\\6&5&34\end{array}\right]\)

Here,

\(15=-1+8(2)\\57=-7+8(8)\\\34=-6+8(5)\)

So,

Elements in third column = - (elements in the first column) + 8(elements in the second column)

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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The equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

According to the question,

We have the following information:

Slope of the line = 1/3

We know that the slope of the line is denoted by m.

y-intercept of the line = -1

We know that the y-intercept is denoted by b.

We have the following equation for the line in slope-intercept form:

y = mx+b

Putting the above values in this equation:

y = x/3-1

Hence, the equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

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