The sum of 3 consecutive odd numbers is 51.
What is the second number in this sequence?

Answer:

(3,5)

Step-by-step explanation:

5x+3y=15

5(0)+3y=15

3y=15

divide both sides by 3 and you get y=5

5x+3(0)=15

5x=15

divide both sides by 5 and get x= 3

So then the y-int is 5 and the x-int is 3.

Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

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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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.

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. :)  

Answer:

The dimensions of the rectangle are 10 meters (L) and 7 meters (W).

Step-by-step explanation:

please give brainliest

Answer:

Green Graph:  y = x - 6

Red Graph: y = -3/2 + 7

Step-by-step explanation:

Slope intercept form is represented by the formula:

y = mx + b

m is your slope

b is the y intercept

Another thing to note is that, when m is negative, the graph will point to the left, while when m is positive in will point in the right

For the green graph, the line intercepts at -6, so that will be your b value.

the slope is positive 1 because if your count up from -6 and count across to point (1,-5) you get 1/1

Put these pieces of information in your formula and you get

y = x - 6

You can use the same process to find the equation of the red line. However, the slope will be negative since the graph is pointing to the left side of the coordinate plane.

Answer:

Graph 1:  y = x - 6

Graph 2: y = -3/2 + 7

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:

x = 4 ;  y = 3

Step-by-step explanation:

2x - 3(x-1) = -1

2x - 3x + 3 = -1

- x = -1 - 3

- x = -4

x = 4

y = 4-1

y = 3

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:

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

Answer:

Point-slope form:

A. y - 9 = -6(x - 9)

B. y + 6 = -3/2(x + 8)

Slope-intercept form:

A. y = -6x + 63

B. y = -3/2x - 27/2

Standard form:

A. -6x + y - 63 = 0

B. -3/2x - y + 27/2 = 0

The probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against is given as follows:

31/88.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes in this problem is given as follows:

176 people.

The desired outcomes are given as follows:

(these outcomes are both calculated from the data given by the table).

Hence the probability is calculated as follows:

p = (41 + 21)/176 = 62/176 = 31/88.

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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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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: 1/6 as a number is 0.1666, with the sixes repeating infinitely, which makes it a rational number. 1/6 = 0.1666 repeating.

Step-by-step explanation: math

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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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 speed or fastness based on the data of distance and time is 0.02 kilometres per second.

The intensity of fastness is measured by the speed. Concerning this, using the formula of speed to find the how fast the mentioned data indicates.The formula to calculate the speed is -

Speed = distance covered ÷ total time

The distance covered is 150 kilometres and time taken in 7200 seconds. So, the answer will state the speed in kilometres per second. Keep the values in formula to find the speed.

Speed = 150/7200

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

Speed = 0.02 kilometres per second.

The mentioned value indicates the object covers 0.02 kilometres in one second.

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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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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.

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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The caffeine per ounce in the final mixture of green and instant tea is 40.08 mg.

Based on the data we know quantity of caffeine in an ounce of instant tea is 1368 mg and in green tea is 480.96 mg. So, calculating amount of caffeine in instant and green tea.

Amount of caffeine in instant tea = 24 × 57

Amount of caffeine in instant tea = 1368 mg

Amount of caffeine in green tea = 12 × 6.25

Amount of caffeine in green tea = 75 mg

Total caffeine in the mixture = 1368 + 75

Total caffeine in the mixture = 1443 mg

Total amount of mixture = 12 + 24

Total amount of mixture = 36

Amount of caffeine per ounce in the mixture = 1443/36

Amount of caffeine per ounce in the mixture = 40.08 mg

Hence, the caffeine in mixture is 40.08 mg.

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Angles ∠1 and ∠7 are alternate interior angles and angle ∠4 and ∠8 are adjacent angles.

Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and equivalent angles.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

When a transversal connects two coplanar lines, alternate interior angles are generated. They are on the inside of the parallel lines, but on the outside of the transversal.

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The three forms of split are as follow: splitting , split and splits.

Explanation :

Therefore, the three forms of the split are splitting , split and splits.

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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 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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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

If you failed to pay the minimum payment by the due date and are now being charged the penalty APR of 28.99%, your monthly interest charge on a balance of $1800 would be approximately $518.82. This is calculated as follows:

However, it is important to note that this calculation is an estimate and the actual amount of interest you would owe in one month could be different, depending on factors such as the number of days in the billing period and the daily interest rate. It is also worth noting that you were charged $6.31 in interest for purchases, which is separate from the interest charged on your unpaid balance.

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The slope of a line through the two points is (y2-y1) / (x2 - x1).

The slope of a line:

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

Here we have to find the slope of the line.

Data given:

Point one has the coordinate = (x1, y1)

Point two has the coordinate = (x2, y2)

So the slope of the line(m) =( y2 - y1) / (x2 - x1)

Therefore the slope of the line is (y2- y1) / ) (x2-x1)

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