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Answer:

10.8 units or [tex]2\sqrt{29}[/tex] units

Step-by-step explanation:

The line drawn connecting two points on a graph is known as a line segment.

The formula used to calculate the length of a line segment is derived from the Pythagorean Theorem

Length of a line segment: [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2}}[/tex]

                                         = [tex]\sqrt{[2-(-2)]^{2} + (2-12)^{2} }[/tex]

                                         = [tex]\sqrt{(2+2)^{2} +(-10)^{2} }[/tex]

                                         = [tex]\sqrt{4^{2} + 100}[/tex]

                                         = [tex]\sqrt{16 +100}[/tex]

                                         = [tex]\sqrt{116}[/tex]

                                         = [tex]\sqrt{4}[/tex]×[tex]\sqrt{29}[/tex]

                                        = [tex]2\sqrt{29}[/tex] units

       Diagonal distance = 10.8 units (Rounded to 3 significant figures)

The solution to the logarithmic equation is; x = 81/4

We want to solve the logarithmic equation;

log₃x + log₃4 - 2log3 = 2

From property of logarithms, we know that;

logₐ4 = log 4/log a

Similarly we know that;

log a + log b = log (ab)

log a - log b = log (a/b)

Thus;

log₃x + log₃4 - 2log₃3 = 2 is;

(log₃4x) - 2log₃3 = 2

(log₃4x) - log₃3² = 2

log₃(4x/3² ) = 2

3² = 4x/9

4x = 9 * 9

4x = 81

x = 81/4

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Step-by-step explanation:

The given figure consists of some rectangles and square making up a bigger square.

As we know that,

area of rectangle= length*breadth, so

Area of rectangle A :-

A = lb

A = (6x+1)(x+2)

A = 6x(x+2)+1(x+2)

A = 6x² + 12x + x + 2

A = 6x² + 13x + 2

Area of rectangle B :-

A = (2x+2)(3x+1)

A = 2x(3x+1)+2(3x+1)

A = 6x² + 2x + 6x + 2

A = 6x² + 8x + 2

Area of rectangle C :-

A = (x+1)(x+2+2x+2)

A = (x+1)(3x+4)

A = 3x² + 4x + 3x + 4

A = 3x² + 7x + 4

Area of rectangle D :-

A = (3x+1)(3x+1)

A = 9x² + 3x + 3x + 1

A = 9x² + 6x + 1

Area of rectangle E :-

A = (6x+1-3x-1 )(2x+2+3x+1)

A = 3x(5x+3)

A = 15x² + 9x

Hence these are the simplified expressions making up the area of the whole square .

And we are done!

increase=(30/100)*50

=15

so,

value after increase

=50+15

=65

The factored form of the polynomial is x³( x + 2 ) - 1 ( 2x + 1 ).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial is (x⁴)+(2x³)-2x-1. The expression will be factorized as below:-

E =  (x⁴)+(2x³)-2x-1.

E = x² ( x² + 2 ) -1 ( 2x + 1 )

Hence, the factorized form of the polynomial is x² ( x² + 2 ) -1 ( 2x + 1 ).

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Answer:

16

Step-by-step explanation:

we need to find how many servings can be made out of 12cups of lemonade if each serving is 3/4th of a cup . For that you just need to divide the total quantity of lemonade with each serving as ,

= 12 ÷ 3/4

= 12 * 4/3

= 4*4

= 16

And we are done!

Answer: 11 1/2 cm or 11.5 cm

Step-by-step explanation:

       To see how much taller the woman is than her son, we will subtract the son's height from the woman's height. We can convert these fractions into decimals to make it easier to subtract.

159 1/4 - 147 6/8 = 159.25 - 147.75 = 11.5 = 11 1/2 cm

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

In which:

For this problem, the function is given as follows:

y = 20000(1.14)^t.

In which the parameters are given as follows:

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Step 1: Solve the equation V(t) = 4 for t. To solve the equation V(t) = 4 for t, divide both sides of the equation by 11, which gives us t = 4/11.

Step 2: Interpret the result. The value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Therefore, the value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Since there are more molecules in larger volumes than smaller ones, the pace of cooling will be slower if the water's volume is increased. Losing the heat energy from all the molecules will therefore take longer.

The question is incomplete and requires further explanation. For the mentioned part, the information is not significant to determine volume of water in the cooler.

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The sum of ages of P & Q before 4 years is 42 years.

Let present age of P is 4x years and the present age of Q is 6x years.

According to the problem, the sum of the present ages of P and Q is 50 years, so we have:

4x + 6x = 50

10x = 50

then, x = 5

So the present age of P is 4 * 5 = 20 years and the present age of Q is 6 * 5 = 30 years.

To find the sum of their ages before 4 years, we subtract 4 from each of their present ages:

20 - 4 = 16 years (for P)

30 - 4 = 26 years (for Q)

hence, sum of their ages before 4 years is 16 + 26 = 42 years.

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When the value of c is 13 and d = 2, then the value of the expression

0. 5c -2. 7d is 1.1

It is given that the expression for the given value of the variables is

0. 5c -2. 7d

If the value  of c is 13 and the value of d is 2, then the value of expression is

0. 5c -2. 7d

putting the value of 'c' and 'd'

0. 5c -2. 7d = 0.5(13) - 2.7(2)

0. 5c -2. 7d = 6.5 - 5.4

0. 5c -2. 7d = 1.1

so, the value of the expressions for the given value of the variables  i.e., c = 13 and d = 2 is 1.1

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Answer:

x=5

Step-by-step explanation:

distribute: 6x-12=4x-2

subtract 4x and add 12 on both sides: 2x=10

An old book was bought for Rs 1520 and sold for Rs 1444. The loss percent is 5.263%

Given,

Cost price = 1520

Selling price = 1444

Loss = C.P - S.P

        = 1520 - 1444

        = 76

Now, percentage of loss = [tex]\frac{Loss}{C.P}[/tex] × 100

                                         = [tex]\frac{76}{1444}[/tex] × 100

                                         = 5.263

Hence, the loss percent is 5.263%  

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Answer:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Step-by-step explanation:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Explanation: You can simplify the numbers to smaller numbers and make the denominator the same, or else just use a calculator.

The graph of the given quadratic function, y = -0.5(x + 5)(x - 3), is shown below

From the question, we are to draw the graph of the given quadratic function.

The given quadratic function is

y = -0.5(x + 5)(x - 3)

To plot the graph of the given quadratic function, we will determine the value pairs that satisfy the equation

When x = -5

y = -0.5(-5 + 5)(-5 - 3)

y = -0.5(0)(-8)

y = 0

When x = -2

y = -0.5(-2 + 5)(-2 - 3)

y = -0.5(3)(-5)

y = 7.5

When x = 0

y = -0.5(0 + 5)(0 - 3)

y = -0.5(5)(-3)

y = 7.5

When x = 2

y = -0.5(2 + 5)(2 - 3)

y = -0.5(7)(-1)

y = 3.5

When x = 3

y = -0.5(3 + 5)(3 - 3)

y = -0.5(8)(0)

y = 0

When x = -5

y = -0.5(5 + 5)(5 - 3)

y = -0.5(10)(2)

y = -10

Using the value pairs above, the graph of the given function is shown below

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he value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

According to the trigonometry identity

tan Ф = opposite/adjacent

sin Ф = opposite/hypotenuse

cos Ф = adjacent/hypotenuse

From the given triangle;

AC = 7

AB = 17

BC = 4√15

Determine the following trigonometry given

cos B = BC/AB

cos B = 4√15/17

sinB = AC/AB

sin B = 7/17

sinA = cos B = 4√15/17

tan B = AC/BC

tan B = 7/4√15

tan A = BC/AC

tan A = 4√15/7

The value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

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The probability of a female student studying abroad is 9.5%. 60% of those who study abroad are female, while 49% of those who do not study abroad are female.

P(Female studying abroad) = P(Female and Studying Abroad) / P(Female)

P(Female and Studying Abroad) = 0.095 × 0.60 = 0.057

P(Female) = 0.095 × 0.60 + 0.905 × 0.49 = 0.902

P(Female studying abroad) = 0.057 / 0.902 = 0.063

Therefore, the probability of a female student studying abroad is 0.063.

The probability of a female student studying abroad is 9.5%. This means that out of all the undergraduate students, 9.5% of them are female and are studying abroad. It is also important to note that out of those who study abroad, 60% are female, while 49% of those who do not study abroad are female. This means that more female students are likely to study abroad than male students, as the percentage of female students studying abroad is higher than the percentage of male students studying abroad. It is also important to note that the overall percentage of female students studying abroad is lower than the overall percentage of male students studying abroad, as the number of female students who study abroad is lower than the number of male students who study abroad. Therefore, the probability of a female student studying abroad is 9.5%.

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The function f(8)=4 defines that it will take x/2 hrs to complete the work and "x being No of workers".

The given data is as follows:

There are x people working in the crew at the racetrack, it takes f(x) hrs to get the track ready.

Let us assume that there is x worker at the racetrack,

f(x) is the function that is going to define the working hours required to get the track ready,

The function will depend on workers as it is mentioned as "f(x)".

Now,

function f(x)=?

But given that f(8)=4

It means when  x=8 that means when are there 8 workers working at the racetrack and it took  4 hours to complete the work.

Now,

we have written a function that gives the relation between a given worker as 8 and time as 4 hrs.

so 8 workers complete work in 4 hrs,

then x worker will complete in y hrs i.e.f(x).

=4x=8*f(x)

=4x/8

=x/2.

Hence the function will be f(x)=x/2

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The complete question is -

max works as a groundskeeper at a racetrack, where he is part of a bigger crew. when x people are working on the crew, it takes them f(x) hours to get the track ready for a day of racing. what does f(8)=4 tells us?

The equation of the graphed line is expressed as: A. y + 5 = -3/2(x - 4).

The equation that represents a line can be written in point-slope form as y - b = m(x - a), where a point on the line is (a, b) and the slope is m.

Slope (m) = rise/run = -3/2

Substitute a point on the line (a, b) = (4, -5) and m = -3/2 into y - b = m(x - a):

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

The equation is: A. y + 5 = -3/2(x - 4).

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Answer:

Step-by-step explanation: the answer would be 60.

The part 6 kobo as required in the task content represents 1% of the whole, 6 naira.

It follows from the task content that the percentage of 6 naira which 6 kobo represents is to be determined.

On this note, it follows from currency conversion that 1 naira is equivalent to 100 kobo.

Hence , 6 naira = 600 kobo

The percent as required to be determined can be evaluated as follows;

6 / 600 = percent / 100.

Percent = 1%.

Ultimately, the fraction of 6 naira which 6 kobo represents is; 1%.

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The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.

The number of different combinations of shirts he can wear is 5.

The number of different combinations of ties he can wear is 3.

The number of different combinations of jackets he can wear is 6.

To find the total number of different outfits, we multiply the number of combinations of each item:

8 * 5 * 3 * 6 = 8 * 90 = 720

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Answer:

69.

im not kidding, haha, good luck!

Answer:

[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-6x+4y=-28\\6x+7y=11\end{cases}[/tex]

To solve by the method of elimination, add the equations together to eliminate the terms in x.

[tex]\begin{array}{crcccl}&-6x & + & 4y & = & -28\\+&(6x & +&7y&=&\;\;\:11)\\\cline{2-6}\vphantom{\dfrac12}&&&11y&=&-17\\\cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies y=-\dfrac{17}{11}[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 6x+7\left(-\dfrac{17}{11}\right)=11[/tex]

[tex]\implies 6x-\dfrac{119}{11}=11[/tex]

[tex]\implies 6x=\dfrac{240}{11}[/tex]

[tex]\implies x=\dfrac{240}{11\cdot 6}[/tex]

[tex]\implies x=\dfrac{40 \cdot \diagup\!\!\!\!\!6}{11\cdot \diagup\!\!\!\!\!6}[/tex]

[tex]\implies x=\dfrac{40}{11}[/tex]

Therefore, the solution is:

[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]

The number of cakes (x) and cookies (y) are 15 and 60 respectively.

Given the system of equation in the question;

To solve for x and y, plug y = 4x into the first equation and solve for x.

x + y = 75

Plug in y = 4x

x + 4x = 75

5x = 75

Divide both sides by 5

5x/5 = 75/5

x = 75/5

x = 15

Now, plug x = 15 into the second equation and solve for y.

y = 4x

Plug in x = 15

y = 4( 15 )

y = 60.

Therefore, the value of x and y are 15 and 60 respectively.

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Converting the value from meters/second to kilometers/hour is 105 m/s =378 km/h

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used

We have to convert the meters per second into kilometers per hour.

1m /sec = (1/1000)/ (1/3600) km/h = 3600/1000 km /h

So, we have to divide 105 by 1000, and multiply it by 3600.

Mathematically speaking

Hence, converting One kilometer is equal to 1,000 meters, and 1 hour is equal to 3,600 seconds is 378 km/h

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A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

First, we need to solve for a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To get the common denominator between [tex]\frac{18}{7}[/tex] and [tex]\frac{5}{6}[/tex], we multiply their denominators.

Now, we know the fractions would look like this:

To solve for the numerators, we can use these equations:

Now, the fractions look like this:

Adding them together:

Now, we can convert this into a mixed number.

Now that we have this, we can subtract that from 6 to get the missing value.

Therefore, the third fraction is [tex]2\frac{25}{42}[/tex].

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