Which of these equations does NOT have any solutions?

10
−
3
�
−
1
=
7
+
3
�
+
2
10−3x−1=7+3x+2

12
−
7
�
−
10
=
�
−
8
�
+
2
12−7x−10=x−8x+2

13
−
4
�
+
2
=
3
�
−
7
�
+
2
13−4x+2=3x−7x+2

15
−
2
�
−
2
=
10
�
+
3
�
+
2
15−2x−2=10x+3x+2

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 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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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!

Answer:

x=5

Step-by-step explanation:

distribute: 6x-12=4x-2

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

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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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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Based on the information in the graph, it can be inferred that the perimeter of the room is 44 feet.

To find the perimeter of the room in the graph we must apply the following formula:

According to the above, if each of the sides is 11 feet long we have two alternatives

In both operations the result would be 44.

Based on the above, the perimeter of the room would be 44 feet.

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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 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:

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:

Below

Step-by-step explanation:

51÷6= 51/6 = 8 3/6 = 8 1/2  = 8.5

6

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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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 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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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: 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

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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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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increase=(30/100)*50

=15

so,

value after increase

=50+15

=65

After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (x² - 4y²) ÷ (5x - 10y) / x

Now, We an simplify as;

⇒ (x² - 4y²) ÷ (5x - 10y) / x

⇒ (x² - (2y)²) ÷ (5x - 10y) / x

⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x

⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)

⇒ x (x + 2y) / 5

Thus, The solution of the expression is,

⇒ x (x + 2y) / 5

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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.

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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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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Answer:

69.

im not kidding, haha, good luck!

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].

Answer:

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