4. Determine the root of the following equation. x-6/4-4= 3x/2+2x+1/5​

As we Know that, ΔTUV[tex]\sim[/tex] ΔXWV

So, for the given proportion TV(y) = 21.

What is Proportion?

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

What is Ratio?

The link between two or more things in terms of quantity, amount, or size.

Given that,

ΔTUV[tex]\sim[/tex] ΔXWV

∠T = ∠X

∠U = ∠W

∠TUV = ∠XWV

So, TU/WX = TV/WV

10/10 = TV/21

1 = TV/21

TV = 21

So, for the given proportion the value for the side TV(y) = 21

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-4Answer:

Step-by-step explanation:

Answer:

-7 + 3 = -4

Step-by-step explanation:

May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The value of u is -5/3 < u < 5/3

We need to calculate the value of u

-2|3u| +5 > -5

-2(3u) + 5 > -5

-6u + 5 > -5

-6u > -10

6u < 10

3u < 5

u < 5/3

-2(-3u) + 5 > -5

6u + 5 > -5

6u > -10

3u > -5

u > -5/3

Therefore, the value of u is -5/3 < u < 5/3

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The difference between the two investments after 35yrs is $4700 and  Bank of America is offering higher interest than 5/3rd banks.

Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.

For the given question,

5/3rd bank offers continuous interest:

For continuous interest, A = P[tex]e^{rt}[/tex]

where,

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant where e ≈ 2.7183.

A = 10000 × [tex]2.71^{0.042*35}[/tex]

A =  10000 × 4.04

A = $40400 approximately

Interest = Amount - Principle

Interest = 40400 - 10,000

Interest = $30400

Bank of America offers compound interest:

For compound interest:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

A = 10000 × 4.51

A = $45100

Interest = Amount - Principle

Interest = 45100 - 10,000

Interest = $35100

The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700

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Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

Answer:

563.7

Step-by-step explanation:

add 79 + 14.95 and multiply that by 6

The slope-intercept form of the equation of a straight line is given to be:

where m is the slope and b is the intercept on the y-axis.

The slope is calculated using two points on the line by the formula:

Therefore, for this line, the slope will be:

Therefore, this value for the slope is substituted back into the equation for the line:

At the point (6, 0), we can calculate the value of b to be:

Therefore, the equation is:

Answer:

Square footage

Step-by-step explanation:

What percent of 120 is 180

we know that

120 represent the 100%

so

Applying proportion

100/120=x/180

solve for x

x=(100/120)*180

x=150%

When we reflect a point over y = x, the x and y coordinates become swapped and switch places, that is why (x,y) results to (y,x).

Therefore, the answer is true.

The number of advance and same day tickets sold are 25 and 35 respectively.

let

x + y = 65

25x + 30y = 1800

From (1)

x = 65 - y

Substitute x = 65 - y into (2)

25x + 30y = 1800

25(65 - y) + 30y = 1800

1625 - 25y + 30y = 1800

5y = 1800 - 1625

5y = 175

y = 175/5

y = 35

Substitute y = 35 into (1)

x + y = 65

x + 35 = 65

x = 65 - 35

x = 25

Therefore, Simultaneous equation is used to determine the number of advance and same day tickets sold.

25 advance tickets and 35 same day tickets were sold.

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A Point-Slope equation of a straight line models this scenario: y -50,000 = -3,000(x -10).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

We can recognize any points of the graph.

(0,80000) ; (10,50000)

Given that;

y -50,000 =______(x -10)

We need to find the slope.

Slope = Change in y / Change in x

Slope = 80,000 - 50,000 / 0 - 10 = 30,000 / -10

= -3,000

The slope is equal to -3000 that is Choice A; y -50,000 = -3,000(x -10)

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The complete question is;

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario.

Answer:

Step-by-step explanation:

This is a sketch graph of y= sin x° for 0 ≤ x ≤360.

It is called as Sine curve. A mathematical curve described in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.

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The values of c and d that would make that the given expression represent a real number are c = –3, d = –2.

For the given question;

The expression is given as;

= i(2 + 3i)(c + di)

Simplify the expression;

= i(2c + 2di + 3ci + 3di²)

= 2ci + 2di² + 2ci² + 3di³

= (2c - 3d)i - 2d - 3c

In order is for expression to yield a real number, the coefficient of must now be zero.

Check the values from option;

2c - 3d = 2 x 2 - 3x 3 = -5

2c - 3d = 2 x -2 - 3 x -3 = -13

2c - 3d = 2 x 3 + 3 x -2 = -1

2c - 3d = 2 x -3 -3 x - 2 = 0

Thus, the correct values for the expression to becomes real number is

c = –3, d = –2.

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Answer:

= 4.875 × 105

(scientific notation)

= 4.875e5

(scientific e notation)

= 487.5 × 103

(engineering notation)

(thousand; prefix kilo- (k))

A is the equation representing proportional relationship .

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

If the y intercept is anything but 0, then the linear function is not proportional. So C is not proportional (2 is the y intercept)

B is a quadratic and it will not give proportional results. y/x is not a constant.

D has no x value and is not going to give a proportional result. y/x is undefined.

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Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be w. Then, the length is w+2.

[tex]w(w+2)=32\\\\w^2 +2w=32\\\\w^2 +2w-32=0\\ \\ w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7\\\\\implies w+2 \approx 6.7[/tex]

The given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -

[tex]{\displaystyle i^{2}=-1}[/tex]

Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers

We have the following statement -

3 and one-tenth times negative 6 times seven-twelfths

We can write -

3 (1/10 x - 6) × 7/12

- 3 [tex]\frac{3}{5}[/tex] × 7/12

-18/5 × 7/12

-3/5 x 7/2

- 21/10

- 2 [tex]\frac{1}{10}[/tex]

Therefore, the given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].

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SOLUTION:

Step 1:

we are to find the measure of minor arc cut off by one of the diagonals;

The sum of interior angles in a pentagon is:

Each interior angle of a regular pentagon is

So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.

Then recall,

Step 2:

We are to find the length of the same minor arc in problem;

Where our angle (titan) is 144 and radius is 10

So the length of the minor arc, given that the radius is 10 cm is 8 pi

Answer: I am pretty sure that the answer is flipping a coin twice and recording the result

Step-by-step explanation: my reasoning is you can compare the results unlike the rest

67 is a prime number and 1 is neither prime nor composite number.

What is prime number and composite number?

A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.

The given two numbers are 1 and 67.

Since, the prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

67 has exactly two factors i.e. 1 and the number 67 itself.

Therefore, 67 is a prime number.

Due to the fact that it only has one factor, 1, number is not a prime.

Hence, 67 is a prime number and 1 is neither prime number nor composite number.

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5 + 3 = 8

3 + 5 = 8

The represent the same expression

Answer: Inequality form: x is less then or equal to 6 or xis greater then or equal to 8

Interval Notation: (-infinity,6] u [8,infinity)

Answer:

x ≤ 6 ∨ x ≥ 8

Step-by-step explanation:

x-7 ≥ 0

when

x≥7

if x≥7

x-7≥ 1

x ≥ 7 + 1

x ≥ 8

if x < 7

-x + 7 ≥ 1

-x ≥ -7 + 1

-x ≥ -6

x ≤ 6

Final solution

x≤ 6 ∨ x ≥ 8

the initial expression is:

so to rest them we want to have the same radical so we can rewrite the root of 20 so:

To find the new coordinates, we just have to use the given rule

Let's apply it to each vertex

The zero of the function m = 25p - 200 is, p = 8 represents her break even.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  He sells each painting for $25, and he spent $200 on supplies to make the paintings.

The function m = 25p - 200 represents the profit m that Julio earns after selling p paintings.

The zeroes of the function is when she break even,

At p = 8 means after selling 8 paintings she will have break even as,

m = 25(8) - 200.

m = 200 - 200.

m = 0.

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The probability of all four women being on the search committee as members in it is 1/273.

We have 15 people in total out of which there are 10 men and 5 women. We need four people on the committee out of these 15.

The probability of that happening can be calculated using the formula -

= Probability of all four women getting selected/Probability of all getting selected

= (5!/4!.1!) / (15!/4!11!)

= (5!/4!1!) * (4!11!/15!)

= (5*4*3*2*1) / (15*14*13*12)

= 1/273

From this, we know that if we need to have all four women as members of the search committee, the probability of that happening is 1/273.

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A line in slope-intercept form is represented by the following equation:

Parallel lines have the same slope, then if the line is parallel to the line y=-2x+5, the slope of the parallel line would be -2 too.

Now, by the given point (2,1) and knowing the slope of the line, we can use the slope-point form of the line equation to get the slope-intercept form:

Substituting:

Notice that the parallel line would be the same original line, y=-2x+5.

Answer:

the sum of an even whole number and odd whole number is always odd ,

True

Given:

Surveyed Sample = 500 students

Number of students who listen to music = 300

The probability of students that listens to music is given by the formula:

In a sample of 1500 students, to find the probable number of students that will listen to music

we will multiply the probability we obtained initially by the sample space

=>

It is likely that 900 students will listen to music while studying