Help me please!! Ill rate 5/5 for whoever answers first

The  proportion that is equivalent to the original equation  [tex]\frac{x+1}{2x} =\frac{x^{2} -7x+10}{4x}[/tex]

The true solution to the equation [tex]x_{1} =1, x_{2}=8[/tex]

The extraneous solution to the equation.x=0

You are given the equation

[tex]\frac{1}{2} + \frac{1}{2x}=\frac{x^{2} -7x+10}{4x}[/tex]

we will note that

[tex]\frac{1}{2} + \frac{1}{2x}=\frac{x+1}{2x}[/tex]

this equation can now be rewritten as proportions as

[tex]\frac{x+1}{2x}=\frac{x^{2} -7x+10}{4x}[/tex]

Solving this equation using the main property of proportion:

[tex]4x. (x+1) =2x.(x^{2} -7x+10.\\[/tex]

[tex]2x(2x+2-x^{2} +7x-10) =0,[/tex]

[tex]2x(-x^{2} +9x-8) =0[/tex]

x cannot be equal to 0 (it is placed in the denominator of the initial equation and the denominator cannot be 0), so x=0 is the extraneous solution to the equation.

This will hence translate to

[tex]-x^{2} +9x-8=0[/tex]

[tex]x^{2} +9x+8=0,[/tex]

[tex]x_{1,2} = \frac{\sqrt{(-9)^2-4 . 8} }{2} =[/tex] 9±7/2

=1, 8

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The correct answers on Edge are explained and shown below.

Solve 1/2 + 1/2x = x^2 − 7x+10/4x by rewriting the equation as a proportion.

Q1: Which proportion is equivalent to the original equation?  

Answer:  C.  [tex]\frac{x +1}{2x} = \frac{x^{2} -7x + 10}{4x}[/tex]  

or

Option 3. x + 1/2x = x^2 - 7x + 10/4x

Q2: Name the true solution(s) to the equation:  

Answer: x = 1, x = 8.

Q3: Name the extraneous solution(s) to the equation:

Answer: x = 0.

You are all welcome. Hope this helps. Have a nice day. :)  

A line beginning at point (0, 0) and continuing through the point (28, 7) describes the graph of the proportional relationship. 2nd option is the answer

Given: the proportional relationship

x 12 16 28

y  3  4   7

In order to know the beginning of the line, we need to find the y-intercept.

The equation of a line is of the form

y = mx + c

where m is the slope and c is the y-intercept.

m = y2-y1 /x2-x1

m = 4-3 / 16-12 = 1/4

y = mx + c

3 = 1/4(12) + c

3 = 3 + c

c = 0

Thus, the beginning of the line is (0, 0).

The coordinate of a line or graph is written in the form (x, y). Therefore, the line begins at point (0, 0) and continues through point (28, 7).

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x/3-10=8

Add 10 to each side x/3=18 Multiply by 3

Answer:

x/3 - 10 = 8

Step-by-step explanation:

It seems like you want me to provide an equation, so here it is:

10 less equates to "minus 10", or "10 minus". [-10]

Quotient refers to division, and "a number" can be replaced with a variable: x. This is our numerator. Our denominator is "3", as it states, "and 3". Finally, the "is" statement refers to equality, and we can replace this with the equal sign.

Putting these all together, you get the equation, x/3 - 10 = 8.

Answer:

It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 ​by the alternate interior angles theorem, and m∠1=m∠2 ​by the transitive property. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the definition of complementary angles. By substitution, m∠2+ m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.

Since the customers were surveyed to see which type of service they had during their visit and their age, the data type which best describes this data set is: C. categorical and bivariate.

A categorical data can be defined as a type of statistical data that is typically used to group information that are having the same attributes or characteristics.

In Science, some examples of a categorical data include the following:

A bivariate data can be defined as a data set which comprises information that are based on two (2) variables, usually two types of related data.

In conclusion we can reasonably infer and logically deduce that the data set above would result in data that are categorical and bivariate.

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The effect on the gravitational force if:

a. Both masses are multipled by 3:  the gravitational force becomes 9 times.

b. The distance between centers is X4:  the gravitational force gets reduced by 16 times.

c. One mass is X2 and the other X3 :  the gravitational force becomes 6 times.

d. The distance is divided by 2:  the gravitational force becomes 4 times.

e. The distance is divided by 2 and one mass X3:  the gravitational force becomes 12 times.

We know that the gravitational force between two objects is given by,

F = Gm1m2 / r²                  ...........(1)

We need to find the effect on the gravitational force if

a.  Both masses are multipled by 3

F1 = G(3m1)(3m2) / r²

F1 = 9 Gm1m2 / r²

F1 = 9F                      ...........(from equation (1))

Thus the gravitational force becomes 9 times.

b. The distance between centers is X4

F2 =  Gm1m2 / (4r)²

F2 =  Gm1m2 / 16r²

F2 = 1/16 ( Gm1m2 / r²)

F2 = 1/16 * F                     ...........(from equation (1))

Thus the gravitational force gets reduced by 16 times.

c. One mass is X2 and the other X3

F3 = G(2m1)(3m2) / r²

F3 = 6 * Gm1m2 / r²

F3 = 6F                     ...........(from equation (1))

Thus the gravitational force becomes 6 times.

d. The distance is divided by 2

F4 =  Gm1m2 / (r/2)²

F4 =  Gm1m2 / (r²/4)

F4 = 4 ( Gm1m2 / r²)

F4 = 4F                     ...........(from equation (1))

Thus the gravitational force becomes 4 times.

e. The distance is divided by 2 and one mass X3

F5 =  G(3m1)m2 / (r/2)²

F2 =  3Gm1m2 / (r²/4)

F2 = (3*4) ( Gm1m2 / r²)

F2 = 12 F                     ...........(from equation (1))

Thus the gravitational force becomes 12 times.

Therefore, The effect on the gravitational force if:

a. the gravitational force becomes 9 times.

b. the gravitational force gets reduced by 16 times.

c. the gravitational force becomes 6 times.

d. the gravitational force becomes 4 times.

e. the gravitational force becomes 12 times.

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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By using substitution method the values of x and y are, x = -1/7 and y = -32/7.

What is substitution method?

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Consider, the given equations

-8x = 5y + 24       ..(1)

-9y = 40 - 8x        ..(2)

From equation (1),

x = -(5y + 24)/8

x = -5/8y - 3            ..(3)

Plug value of x in equation (2),

-9y = 40 - 8(-5/8y - 3)

-9y = 40 + 5y + 24

-14y = 64

y = -64/14

y = -32/7

Plug y = -32/7 in equation (3)

x = -5/8(-32/7) - 3

x = -1/7

Hence, by using substitution method the values of x and y are, x = -1/7 and y = -32/7.

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Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction and y-intercept of a line is the point at which the line crosses the y-axis.

Slope: Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b.

Example: A line with a slope of 2 would mean that for every increase of 1 in the x-direction, the y-value would increase by 2.

Y-intercept: The y-intercept of a line is the point at which the line crosses the y-axis. It is typically represented by the b in the equation y = mx + b.

Example: A line with a y-intercept of 4 would cross the y-axis at y = 4.

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Answer:

Since the number of calories burned is proportional to the number of minutes jogged, we can represent this relationship using the equation y = kx, where y is the number of calories burned, x is the number of minutes jogged, and k is the constant of proportionality.

To find the value of k, we can use one of the given data points. For example, if x = 10 and y = 95, we have 95 = k * 10. Solving for k, we find that k = 9.5.

The constant of proportionality, k, has the meaning of the number of calories burned per minute of jogging. In this case, k = 9.5 calories/minute, so for every minute of jogging, the person burns 9.5 calories.

Step-by-step explanation:

Splitting strategy is one of the technique in mathematics  which help to add  the larger number , two-digit and three digit and so on.

Explanation:

Splitting strategy is one of the mathematical technique :

Therefore, the splitting strategy is mathematical technique to make out work effortless.

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The rules of the scale factor has been explained

The scale factor is the ratio of the dimension of the new figure to the dimensions of the original figure.

The equation will be

Th scale factor = The dimensions of new figure ÷ Dimensions of the original figure

The values of the scale factor can be divided into three cases

When, scale factor greater than 1

The size of the new figure will be greater than original figure

When scale factor between 0 and 1

The size of the new figure will be less than original figure

When scale factor is equal to 1

The size of the new figure and original figure are same

Therefore, these are the rules of scale factor

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Answer:

a lot

960

Step-by-step explanation:

Since there are 4 woman in total, there are 14-4=10 men.

Part 1

They can choose either 2 women, 3 women, or 4 woman.

If they choose 2 out of the 4 woman, they can have 6 different combinations.

4!/(2!(4-2)!)

=24/(2(2!))

=24/4=6

There are 8 remaining men to be chosen on the committee (because 10-2=8).

There are 10 total men and 8 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(8!(10-8)!)

=10!/(8!(2!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 8! from both the numerator and denominator to simplify it. This leaves the numerator with 9x10, which is 90, and the denominator with 2!, which is just 2.

90/2=45

Now we need to multiply 45 (number of combinations to choose 8 men from 10 men) and 6 (number of combinations to choose 2 women from 4 woman).

45x6=270 combinations if 2 woman are chosen

Part 2

Next we need to find out how many combinations there are if they choose 3 women for the committee.

If they choose 3 out of the 4 woman, they can have 4 different combinations.

4!/(3!(4-3)!)

=24/(6(1!))

=24/6=4

There are 7 remaining men to be chosen on the committee (because 10-3=7).

There are 10 total men and 7 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(7!(10-7)!)

=10!/(7!(3!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 7! from both the numerator and denominator to simplify it. This leaves the numerator with 8x9x10, which is 720, and the denominator with 3!, which is 6.

720/6=120

Now we need to multiply 120 (number of combinations to choose 7 men from 10 men) and 4 (number of combinations to choose 3 women from 4 woman).

120x4=480 total combinations if 3 women are chosen

Part 3

If 4 women out of 4 women are chosen for the committee, then obviously, there will only be 1 combination for that, since all the women will be chosen.

This leaves us with 10-4=6 spots for men in the committee.

There are 10 total men and 6 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(6!(10-6)!)

=10!/(6!(4!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 6! from both the numerator and denominator to simplify it. This leaves the numerator with 7x8x9x10, which is 5040, and the denominator with 4!, which is 24.

5040/24=210

Now we need to multiply 210 (number of combinations to choose 6 men from 10 men) and 1 (number of combinations to choose 4 women from 4 woman).

210x1=210 total combinations if 3 women are chosen

Part 4

Finally, we need to add all the final answers from the previous parts.

270+480+210=960 total combinations if at least 2 women were chosen for the committee

Please let me know if you find any errors

The height of the tree is 2.25 m. The problem is related to quantitative comparison.

A quantitative comparison is a problem with two objects having different quantities but they can be increasing by the same factor.

Kayla is 1.85 m tall and she stands 23.1 m away from the tree. At the same time, a tree's shadow near her is 28.15 high. Determine the height of the tree!

We have:

If the tree's shadow is longer than Kayla's shadow, the tree's height is also higher that Kayla's tall. The tree's height is

Kayla's tall/tree's tall = Kayla's shadow/tree's shadow

1.85/tree's tall = 23.1/28.15

Tree's tall = (28.15 × 1.85)/23.1

Tree's tall = 2.25 m

Hence, the height of the tree that has a shadow of 28.15 meters is 2.25 m.

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a) The hypothesis are given as follows:

b) The test is classified as a right-tailed test.

The claim is given as follows:

"The mean weight of the fish in this reservoir is greater than 40 pounds".

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean is greater than 40 pounds, hence:

[tex]H_0: \mu \leq 40[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, hence:

[tex]H_1: \mu > 40[/tex]

We are testing if the mean is greater than a value, hence this is a right-tailed test.

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The average speed of the car if it travels 150 km in 2 hours is 75 kilometres per hour.

The average speed of the car will be calculated by the formula -

Average speed = total distance covered ÷ time taken

Keep the values from question in the above mentioned formula to calculate the average speed of the car

Average speed of the car = 150/2

Performing division on Right Hand Side of the equation to find the average speed of the car

Average speed of the car = 75 km/hr

Thus, the average speed of the car is 75 kilometres per hour.

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Answer:

The answer is 1.52.

Step-by-step explanation:

I don't know why it's not 1.52 no matter how I calculate it's 1.52

Answer:

the answer is letter B

Step-by-step explanation:

All you do is remove to parentheses

Answer:

-4

Step-by-step explanation:

I hope this helps

Answer:

y = [tex]-\frac{1}{2}[/tex]x + 1

Step-by-step explanation:

y = mx + c

Find the reciprocal and change the sign of the gradient (m), which is -[tex]\frac{1}{2}[/tex]

so

y = [tex]-\frac{1}{2}[/tex]x + c

Put in your point that you want it to intersect (4,-1):

-1 =   [tex]-\frac{1}{2}[/tex](4) + c

-1 = -2 + c

-1 + 2 = c

1 = c

y = [tex]-\frac{1}{2}[/tex]x + 1

The value of the variable x when the distance between two points is 10 is equal to 13 or 1.

As given in the question,

Given two points (7, 5) and (x, -3)

Distance between two points  (7, 5) and (x, -3) is equal to 10 units

Distance = √ ( y₂ - y₁ )² + ( x₂ - x₁ )²

⇒ (10)     = √ ( -3 -5 )² + ( x - 7 )²

⇒ 10      = √ ( -8 )² + x² - 14x + 49

⇒ 10²    =  64 + x² - 14x   + 49

⇒ 100   = 113 +  x² - 14x

⇒ x² -14x + 13 = 0

⇒ x² -13x -x + 13 =0

⇒ ( x - 13) ( x - 1) = 0

⇒ x = 13 or 1

Therefore, the value of the variable x for the given distance and points is equal to 13 or 1.

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The side x of the right angle triangle is 6√3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sides of a right triangle is named according to the position of the angle. The side of a right triangle are as follows:

The hypotenuse side is the longest side of a right triangle.

Therefore, let's find the x side of the right triangle using trigonometric ratios.

tan 60 = opposite / adjacent

opposite side = x

adjacent side = 6

tan 60 = x / 6

cross multiply

x = 6 tan 60

x = 6 × √3

x = 6√3

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Answer:

Step-by-step explanation: Simple plug x in.

x=1

(Square root) 4 -1=1

x=6

(square root) 9 -1=2

x=13

(square root ) 16-1=3

x=1 Y=1

x=6  Y=2

x=13  Y=3

The solutions for a and b are given below by using probability:

According to the central limit theorem, regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independently distributed variables will be roughly normal. According to the central limit theorem, if you take sufficiently large random samples from a population with mean and standard deviation and replace some of the individuals in the samples, the sample means will be distributed about normally. The central limit theorem in probability theory proves that, even when independent random variables are added together, their correctly normalized sum frequently tends toward a normal distribution.

As a result, the sampling distribution of the sample mean of 22 passengers is normally distributed, with a mean weight of 190 pounds that is the same as the population's mean σ/√n.

=35/√22

=7.46

Now, for X=4500, z=(μ)/σ

=(4500-190)/7.46

=577.74

P(X>577.4)

=1-P(X<577.4)=0

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Step-by-step explanation:

Given the angle 10 let's add 360 and see if the angle is in the interval.

[tex]10 + 360 = 370[/tex]

However,

[tex]10 - 360 = - 350[/tex]

So the coterminal angle is

-350

For question 2, subtract 360

[tex]180 - 360 = - 180[/tex]

Answer:

-35

Step-by-step explanation:

Knowledge Needed

This notation is called sigma notation (or summation). It is used later on in Calculus too.

The number on top of the sigma sign is called the top index.

The number on bottom of the sigma sign is called the lower index.

To the right of the sigma sign is an expression.

I will give you an example to help.

3

Σ n^2

n = 1

To start, look at the bottom number. Then, plug all numbers from the lower index to the top index (including the top index) into the expression.

n^2

(1) ^ 2

(2) ^ 2

(3) ^ 2

We stop at 3 because 3 is the top index.

Simplify.

1 ^ 2 = 1

2 ^ 2 = 4

3 ^ 2 = 9

Add the numbers.

9 + 4 + 1

14

The answer is 14.

Question

Start at 1 and go to 5.

-2n-1

-2(1)-1

-2(2)-1

-2(3)-1

-2(4)-1

-2(5)-1

Stop at the 5, the top index.

Simplify.

-2 - 1 = -3

-4 - 1 = -5

-6 - 1 = -7

-8 - 1 = -9

-10 - 1 = -11

Add.

-3 + -5 + -7 + -9 + -11

-35

Answer:

96

Step-by-step explanation:

25% of what is 24?

25% of X is 24

To find X we do 24/25%.

Converting percent to decimal:

25%/100 = 0.25

X = 24/0.25

X = 96

It takes about 16 years to reach the population size of 22000.

Population growth is the term used to describe changes in population size over time, which can be either positive or negative. The population growth formula is [tex]P=P_0\times e^{rt}[/tex]. Here, P is the total population size after time t, P₀ is the initial population size, r is the rate of growth, and e is Euler's number (e=2.72).

Given the total population, after time t is 22000, the initial population is 10000, and the rate is  5%.

Then, the time is calculated as,

[tex]\begin{aligned}22000&=10000\times e^{(0.05\times t)}\\\frac{22000}{10000}&=e^{(0.05\times t)}\\\ln(2.2)&=0.05\times t\\t&=\frac{0.788}{0.05}\\&=15.76\\&\approx16\end{aligned}[/tex]

The time it takes to reach a population size of 22000 is 16 years.

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Answer: Depends if AB and CD are equal, as they both have M in the same spot that can be eliminated, look at the quadrilateral and make a guess based off the information that AB and CD have to be equal

Step-by-step explanation:

What is a slope in math?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

To find the correct answer, we need to look at the formula for a straight line: y=mx+b where m= the slope of the line and b= the y intercept. We know from the problem that the slope must be equal to -4, leaving us with y= -4x +b. From here you can substitute the given point in the equation and solve for b.

-3= -4(4) +b

-3= -16+b

+16  +16

13= b

This tells us that b=13, now we simply substitute that into the formula.

The solution to your question is y=-4x+13

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