Find y for 0.5y-2 2/5=1/2y+2.4

60 students out of 210 in a school went both roller skating and water park.

What is algebraic equation ?

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Have given ,

Total students = 210

Let x = The number of students who went only to the roller skating

and y = The number of students who went to the water park and roller skating

x + 4x + y = 210  ⇒ 5x + y = 210 ......(i)

x + y + 2y = 210 ⇒ x + 3y = 210 ⇒ x = 210 - 3y

Put the value of x in equation no. (i),

5(210 - 3y) + y = 210 ⇒ 1050 - 14y = 210 ⇒ 14y = 1050 - 210

14y = 840 ⇒ y = 60

Hence , 60 students out of 210 in a school went both roller skating and water park.

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Yes Jerome's sister is correct.

The answer to the table is given below.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here:

Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio of water to drink mix the same and still increase the total amount of energy drink.

Drink mix     3  6    9   12   15

water cups   8  16   24  32  40 

we know this is true because to find a ratio equivalent to another we have to multiply the two quantities, by the same number.

Hence, The complete table is shown above.

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The factors of given quadratic expression are (4a+3) and (a+6).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given quadratic expression is 4a²+27a+18.

By splitting middle term method, we get

4a²+3a+24a+18

= a(4a+3)+6(4a+3)

= (4a+3)(a+6)

Therefore, the factors of given quadratic expression are (4a+3) and (a+6).

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The employee who receives the largest percentage of their gross pay in employee benefits is Employee D.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviation "pct". For instance, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentage can be used to express part-to-whole relationships, such as "25% of the students in the class". It can also be used to compare two or more values, such as "the temperature rose by 3% over the course of the day". In some cases, percentage can be used to calculate a quantity from a given value, such as finding the percentage increase from one number to another.

This is because they have the highest total job benefits ($34,700) when compared to their gross pay ($33,700). This results in a percentage of 103.3%, which is the highest of the four employee options.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]

let's firstly convert the mixed fraction to an improper fraction, and then let's multiply both sides by the LCD of all denominators

[tex]\stackrel{mixed}{83\frac{1}{3}}\implies \cfrac{83\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{250}{3}} \\\\[-0.35em] ~\dotfill\\\\ 12x-\cfrac{2}{3}=\cfrac{250}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 12x-\cfrac{2}{3} \right)=3\left( \cfrac{250}{3} \right)}\implies 36x-2=250 \\\\\\ 36x=252\implies x=\cfrac{252}{36}\implies x=7[/tex]

The Given quadratic equation has two solutions: 1 and 3/2. A quadratic problem was solved by utilizing the factoring method.

A quadratic equation is defined.

At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. ax^2 + b*x + c = 0 is the quadratic equation's general form.

where x is the unknown variable and a, b, and c are constant terms.

In this case, I'm solving a quadratic problem by factoring.

The following quadratic equation is

2x^2 - 5x + 3 = 0.

2x^2 - (3+2)x + 3 = 0

2x^2 -3x -2x + 3 = 0.

x(2x-3) -1(2x -3) = 0.

(2x-3)(x-1) = 0.

2x - 3 =0 or x -1 =0

x = 3/2 or x =1

So the solutions of a quadratic equation are 3/2 and 1.

Given Question is incomplete complete question here:

What are the solutions of the quadratic equation 2x^2-5x+3 =  0?

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Answer:

? = 74°

Step-by-step explanation:

• in a parallelogram, consecutive angles sum to 180° , that is

? + 106° = 180° ( subtract 106° from both sides )

? ( ∠ G ) = 74°

Answer:

A) Angle 2, Angle M

B) Angle M

C) Angle NM (or MN), Angle QM (or MQ)

Step-by-step explanation:

A) So M is the vertex of angle QMP, and the picture tells you that it's angle 2

B) M is the middle angle

C) The diagram shows you the answer

The log function with base 10 is called the “common logarithmic functions” and the log with base e is called the “natural logarithmic function”. The logarithmic function is defined by, if logab = x, then ax = b.

The log with a base "e" (log e) is the same thing as In

The natural logarithmic function log e  refers to its logarithmic function of the base of the constant e. For this equation to be equivalent in logarithm;

We can say that:

log e = ln

Logarithm may alternatively be defined as the exponent power to which a base must be raised in order to produce a given number.

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Answer:

To construct a 98% confidence interval with a maximum error of 0.09 pounds and assuming a variance of 1 pound, the minimum sample size can be calculated using the formula:

n = (2 * standard error of the mean / margin of error)^2

Plugging in the values, we get:

n = (2 * (1 / sqrt(n)) / 0.09)^2

Solving for n, we get n = 832.6. Rounding up to the next integer, the minimum number of males over age 27 they must include in their sample is 833.

Step-by-step explanation:

The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

A) It is stated that Maci once earned $170 by grooming dogs.

For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;

170 = 60x + 50

the number of appointments is x.

B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;

210 = 75x + 35 - 10x

the number of appointments is x.

C) The quantity of tips they will receive even without an appointment varies between the formulae.

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The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

The range refers to all potential values of y, while the domain refers to all conceivable values of x.

The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

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The distance Issa travelled from school to his house is 9.6 km.

The actual length covered by the body is defined as distance travelled, whereas displacement is the straight path between the initial and final points.

Here,

Let the total distance between school and home be 'x' meters.

Issa jogged two-thirds of x = 2x/3

So the total distance between school and home is = 2x/3 + 3200

However, the total distance from school to home = x

= 2x/3 + 3200 = x

= 3200 = x/3

= 9600 = x

As a result, the total distance from school to home is 9600 meters.

We're now converting it to kilometers.

We know that 1000 meters equals one kilometer.

9600 meters = 1/1000 x 9600

= 9.6 kilometers

Therefore the distance travelled will be 9.6 km.

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Answer:

yes

Step-by-step explanation:

yes

yes

yes

yes

yeyed

yes

To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

minuscule temperature. There are a number of tales of how he initially created his scale, but the original publication states that the lower Fahrenheit  defining point, 0 °F, was set as the freezing temperature of a brine solution made from a combination of water, ice, and ammonium chloride (a salt).

Thus, the difference between Celsius and Fahrenheit is 1.8 times. In other words, 1 degree Fahrenheit is equivalent to 5/9 degree Celsius. These two temperature scales overlap at -40 degrees, which means that -40 degrees Fahrenheit is equivalent to -40 degrees Celsius despite their quite significant discrepancies.

°C) is a different unit of measurement for temperature. Except for the United States, most nations use Celsius as their unit of measurement. 0 degrees Celsius is really chilly. 40 degrees is a scorching temperature!

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On solving the provided question we cans ay thatVertical Angles: TZU, XZW Adjacent Angles: TZU, UZV are Vertical angle and adjacent angle.

What is Vertical angle and adjacent angle,?

Vertical angles are two angles that share the same vertex and are formed by two intersecting lines. They are congruent (i.e. have the same measure) and are opposite each other

Adjacent angles are two angles that share a common vertex and side, but do not overlap. They are also called "next to" or "sharing an arm" angles.

Fig 1:

Vertical Angles: NMJ, LMK

Adjacent Angles: NMJ, JMK

Fig 2:

Vertical Angles: DEA, CEB

Adjacent Angles: DEA, AEB

Fig 3:

Vertical Angles: LQM, PQN

Adjacent Angles: LQM, MQN

Fig 4:

Vertical Angles: TZU, XZW

Adjacent Angles: TZU, UZV

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Therefore , the solution of the given problem of linear equation comes out to be the plan will be equal at 21 visits.

The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.

Here,

Given :

Case 1: flat rate of $201 a month and you get unlimited visits.

and

Case 2:pay only $33 per month, but must pay $8 for each visit to the club.

Thus,

To find at what number of visits both plan be equal is

Let x be the number of visit,

We get,

Case 1: 201

Case 2: 33 + 8x

For equlaity:

=>33+ 8x =201

=>8x =168

=> x =168/8

=> x =21

Therefore , the solution of the given problem of linear equation comes out to be the plan will be equal at 21 visits.

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The best approximate average (arithmetic mean) number of calories per bag is equal to: D) 2,500.

In Mathematics, an arithmetic average is sometimes referred to as arithmetic mean and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the arithmetic average for the number of calories per bag can be calculated by using the following formula:

Arithmetic average = [F(x)]/n

Next, we would determine the total number of calories and then convert to ounces:

Total number of calories, F(x) = 198 + 80 + 159 + 166 + 185

Total number of calories, F(x) = 788 calories.

Note: 1 pound = 16 ounces.

Total number of calories, F(x) = 788 calories × 16 ounces

Total number of calories, F(x) = 12,608 calories.

Now, we can calculate the arithmetic average for the number of calories per bag:

Arithmetic average = [F(x)]/n

Arithmetic average = 12,608/5

Arithmetic average = 2,521.6 ≈ 2,500.

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Answer:

The answer is 679

Step-by-step explanation:

A significant figure is a number greater than zero so to 3 significant figures just count 3 from the front then round up 9 and it becomes 1 then add it to 8 to become 9 which equals 679

Hope it helps

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The number of chairs that should be removed, for there to be as few empty seats as possible but for all rows of chairs to be complete, is 33 chairs.

The number of chairs that make up a row is 11 chairs and there are to be 70 students in attendance. The number of rows that would take the students is therefore:

= Number of students / Number of rows

= 70 / 11

= 6. 36

= 7 rows rounded up

The number of rows needed is 7 rows which means the number of chairs would be:

= 7 rows x 11 chairs per row

= 77 chairs

The number of chairs to be removed is:

= Total chairs - Chairs needed

= 110 - 77

= 33 chairs

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The answer is 4cd/3b

hope it's correct

When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a scatter-plot or scatter-gram.

Scatter-plot: A scatter-plot is a form of mathematical diagram or plot that employs Cartesian coordinates to illustrate distinct values associated to two variables for a specific set of data. It is also known as a scatter-gram, scatter-graph, scatter-chatter, or scatter-diagram.

It is being utilized to determine how one variable influences the other.

The supplied statement in the question above represents the scatter plot.

Here,

When you observe a graphed cluster of dots reflecting the values and relationship of two separate variables, you are looking at a scatter-plot or scatter-gram, which is a visual explanation of relatedness.

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No, a TV with a 60 inch diagonal would not fit in an entertainment center that is 52 inches wide and 40 inches high.

Diagonal is a line connecting two or more points that are not in a straight line. It is used to describe the shape of a polygon and also used in mathematics to refer to lines, angles, and shapes. It can also refer to a line, or direction, that is not parallel or perpendicular to something else. In geometry, diagonal lines are used to divide shapes into equal parts, and are used in the construction of polygons. In linear algebra, diagonal lines are used to calculate the determinant of a matrix.

The diagonal measurement of a TV is the length of a line drawn between the opposite corners of the TV. For a 60 inch diagonal TV, the width of the TV would be around 52 inches and the height would be around 33 inches. As the entertainment center is only 40 inches high, the TV would not fit in it.

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Answer:119

Step-by-step explanation:

because it's on oppisite sides on the outside

Answer:

------------------------------

The two given two angles are alternate exterior angles and therefore  congruent according to alternate exterior angles theorem:

Definition:

The inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number is: B. negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Note: Let the variable y represent the unknown number.

Next, we would translate the word problem "negative one third is greater than or equal to the product of negative two fifths and a number" into an algebraic inequality as follows;

-1/3 ≥ -2/5 × y

-1/3 ≥ -2y/5

Multiplying both sides of the algebraic inequality by -5/2, we have:

-1/3 × -5/2 ≥ -2y/5 × -5/2

5/6 ≤ y

y ≥ 5/6.

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Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

Step 1: Multiply both sides of the equation by de:

a/b * de = bc/ef * de

Step 2: Simplify the left side of the equation:

ade = bcde

Step 3: Divide both sides of the equation by ad:

a/d = b/e

Step 4: Multiply both sides of the equation by be:

ab/d = be/e

Step 5: Simplify the left side of the equation:

ab = be

Step 6: Divide both sides of the equation by be:

a/b = 1/e

Step 7: Multiply both sides of the equation by ef:

a/b * ef = 1/e * ef

Step 8: Simplify the left side of the equation:

aef = ef

Step 9: Divide both sides of the equation by ef:

a/b = 1/e

Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

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Answer:

perpendicular

b and e

congruent

For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

For a=-1/2 and b=6, the expression with the largest value is a+b, which is equal to 5.5. The expression with the smallest value is a-b, which is equal to -7.5. The expression closest to zero is a+b, which is equal to 5.5.

For a=12 and b=-6, the expression with the largest value is a+b, which is equal to 6. The expression with the smallest value is a-b, which is equal to 18. The expression closest to zero is a-b, which is equal to 18.

For a=-6 and b=-12, the expression with the largest value is a+b, which is equal to -18. The expression with the smallest value is a-b, which is equal to 6. The expression closest to zero is a+b, which is equal to -18.

For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

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Answer:

Step-by-step explanation:

Perimeter is the addition of all the sides.

So in this question, if you add up all the sides :

14x + 8x +7x +12

Simplify by adding all terms with x :

29x + 12  

(As you can not add a number constant to a variable )