For each ordered pair, determine whether it is a solution to the system of equations. -18x+2y=8 and y=9x+4

well, if we use the vertex form of a parabola, we can pretty much see the parabolas all pretty much have a vertext at the origin, (0,0), now, let's take a look of a point they go by, Check the picture below.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=4 \end{cases} \\\\\\ 4=a(4-0)^2 + 0\implies 4=16a\implies \cfrac{4}{16}=a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}x^2}[/tex]

now let's do D

[tex]\begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=-1\\ y=-3 \end{cases} \\\\\\ -3=a(-1-0)^2+0\implies -3=a\hspace{5em}\boxed{y=-3x^2}[/tex]

The resulting sum function if x is equivalent to 2 is 18

Composite functions are known as function of a function

Given the following functions

f(x) = 3x + 5 and;

g(x) = 4x - 1.

(f+g)(x) = f(x) + g(x)

(f+g)(x) = 3x + 5 + 4x - 1

(f+g)(x) = 7x + 4

Substitute x = 2 into the result

(f+g)(2) = 7(2) + 4

(f+g)(2) = 18

Hence the value of the sum of the function when x = 2 is 18

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The sum of expression is 8a + 5b - 9.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(8a + 2b -4) and (3b-5)

Now, adding the above expression we get

(8a + 2b -4) + (3b-5)

= 8a + 2b - 4 + 3b - 5

= 8a + 2b + 3b -4 - 5

= 8a + b(2+ 3) - 9

= 8a + b(5) -9

= 8a + 5b - 9

Hence, the simplified expression is 8a + 5b - 9.

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Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08  .  

We use the formula for compound interest to find the final amount  :

that is ⇒  A = P(1 + r)ˣ  ;

where:  A = the amount of money in the account after "x years"  ;

P(initial amount) = $4400 ;   r (interest rate) = 0.0825  ;

⇒ x(time) = 22 years

we get ;

⇒ A = 4400×(1 + 0.0825)²²  ;

⇒ A =  4400×(1.0825)²²  ;

⇒ A =  4400×6.018028  ;

⇒ A = 26480.08  ;

Therefore , the amount in the account after 22 years is $26480.08  .

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The occupant load of a one room daycare that is 20' by 30' is 17 people.

The occupant load of the daycare room can be determined by using the formula:

Occupant load = Area of room / Occupant load factor

From the case, we know that the area of the room is 20' x 30', then:

Room area = 600 square feet.

The occupant load factor for a daycare is typically 35 square feet per person. This means that each person in the daycare should have at least 35 square feet of space.

Using the formula, the occupant load of the one room daycare is:

Occupant load = 600 square feet / 35 square feet per person = 17.14 people

Therefore, the occupant load of the one room daycare is 17 people. This means that the daycare can safely accommodate 17 people at one time.

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Answer:

Step-by-step explanation:

9 times

6,7,8,9 (4 times starting at 5)

Answer: 1.25

Step-by-step explanation:

you divide/combine 5 and 4 to get Ur anwser 1.25.  Yet it's the same thing as asking ,"How much is 5 divided by 4?" just think of it to yourself as how many times you can fit 4 into 5. One tip you can use is 4(x) = 5 and x will equal 1.25.

The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.

Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.

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Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.

According to the question a  factory has two smokestacks:

Let first smokestack take x  number of hours per day

and second smokestack take y number of hours per day

The rate of particle pollution produced is 12 kg/h for the first smokestack

and rate of particle pollution produced is 32 kg/h for the second.

A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.

so, equation becomes 12x + 32y = 374

also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.

so, x = 2 + 1.5y

putting value of x in other equation

12(2 + 1.5y) + 32y = 374

24 + 18y + 32y = 374

50y = 350

y = 7 hours

x = 2 + 1.5(7) = 12.5 hours

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The expression is constant for b = -7.5, and the constant is 49.5.

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that, The expression 3(5x - 1) + b(2x - 7) is constant

It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.

The co-efficient of the 'x' should be '0'.

3(5x - 1) + b(2x - 7)

= 15x - 3 + 2bx - 7b

= (15 + 2b)x - 3 - 7b

Now, 15 + 2b = 0

2b = -15

b = -7.5

On substituting the value of 'b' in the expression,

= -3 - 7 * (-7.5)

= 52.5 - 3

= 49.5

Therefore, The expression is constant for b = -7.5, and the constant is 49.5

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a) 0 kg of sugar is in the tank at the beginning., b) ds/dt = 0.08-(S/1120)*4, c) 0.32 kg of sugar is in the tank after 1 minute., d) 2.59 kg of sugar is in the tank after 84 minutes.

a) At the beginning, there is no sugar in the tank since it contains only pure water.

b) Let S(t) be the amount of sugar in the tank at time t (in minutes). The rate of change of S is given by the rate at which sugar enters the tank minus the rate at which it leaves. Since the solution enters at a rate of 4 L/min, and contains 0.08 kg of sugar per liter, the rate at which sugar enters is 0.08 kg/L * 4 L/min = 0.32 kg/min. Since the solution leaves at the same rate, the differential equation that models the situation is:

dS/dt = 0.32 - (S/1120) * 4

c) To find the amount of sugar after 1 minute, we need to solve the differential equation from part (b) with the initial condition S(0) = 0 (since the tank initially contains only water). One possible way to solve the differential equation is to use separation of variables:

dS/dt + (4/1120) S = 0.32

Multiplying both sides by dt and dividing by (0.32 - (4/1120) S), we get:

(1/S) dS = (4/0.32 - (1120/4)) dt

Integrating both sides from t = 0 to t = 1 and from S = 0 to S = S(1), we get:

ln(S(1)) - ln(0) = (1.25 - 280) * 1

S(1) = [tex]e^{0.25} * 1120[/tex] ≈ 300.92 kg

Therefore, after 1 minute, there is approximately 300.92 kg of sugar in the tank.

d) To find the amount of sugar after 84 minutes, we can solve the differential equation from part (b) numerically using an appropriate method such as Euler's method, or we can use an integrating factor to solve it analytically. One possible way to use an integrating factor is to multiply both sides of the differential equation by exp(4t/1120):

exp(4t/1120) dS/dt + (S/280) exp(4t/1120) = 0.32 exp(4t/1120)

This can be written as:

d/dt [S exp(4t/1120)] = 0.32 exp(4t/1120)

Integrating both sides from t = 0 to t = 84, we get:

[S(84) exp(4/1120 * 84)] - [S(0) exp(4/1120 * 0)] = ∫(0 to 84) 0.32 exp(4t/1120) dt

Since S(0) = 0 and exp(4/1120 * 84) is a constant, we can simplify this to:

S(84) = (1/exp(4/1120 * 84)) ∫(0 to 84) 0.32 exp(4t/1120) dt

Using integration by substitution with u = 4t/1120, we get:

S(84) = (1/exp(4/1120 * 84)) * (1120/4) * (0.32/4) * [exp(4/1120 * 84) - 1]

S(84) ≈ 301.53 kg

Therefore, after 84 minutes, there is approximately 301.53 kg of sugar in the tank.

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The complete question is:

A tank contains 1120 L of pure water. At a rate of 4 L/min, a solution that contains 0.08 kilogramme of sugar per litre enters the tank. At the same rate that it drains from the tank, the solution is mixed.

a) How much sugar is in the tank when it first starts?

b) With S representing the amount of sugar (in kg) at time t, write a differential equation which models the situation.

c) After 1 minute, calculate the sugar content (in kilogramme).

d) After 84 minutes, calculate the sugar content (in kg).

The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.

The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:

Kinetic Energy = (1/2) * mass * velocity^2

In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:

Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]

Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]

Kinetic Energy = 6 J

So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.

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The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Sin θ = Opposite Side to θ/Hypotenuse

Cos θ = Adjacent Side to θ/Hypotenuse

Tan θ = Opposite Side/Adjacent Side

Cot θ = Adjacent Side/Opposite Side

Sec θ = Hypotenuse/Adjacent Side

Cosec θ = Hypotenuse/Opposite Side

where, Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle)

The inverse ratios start with the ratio and then find the angle that produces this ratio.

(a) x=cos−1(a/c)

(b) x=sin−1(c/b)

(c) x=tan−1(c/a)

(d) y=sin−1(a/c)

(e)y=cos−1(c/b)

The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).

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The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.

A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.

Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:

Therefore,

n = numbers of floors in the building.

h = total height of the building

Hence, the function is as follows

h = 6.8n + 13.5

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The probability of spinning green and then rolling an even number is 1/36

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability of spinning green is 1/6 because there are 6 equally likely outcomes and 1 of them is green.

The probability of rolling an even number is 3/6 because there are 6 equally likely outcomes and 3 of them are even numbers (2, 4, and 6).

The probability of spinning green and then rolling an even number is the product of the probabilities of each event. To find this, we multiply the probability of spinning green (1/6) by the probability of rolling an even number (3/6):

(1/6) * (3/6) = 1/36

So, the probability of spinning green and then rolling an even number is 1/36.

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Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.

There are several ways to obtain a sample in research. The most common sampling methods in research are the following:

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Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

It is given that Gwen has a £5 note and a £2 coin.

Therefore, she has a total of £(5 + 2) = £7

A liter of cola costs £1.25.

Therefore, (7 ÷ 1.25) = 5.6

Therefore, Gwen can buy a total of 5 liters of cola.

Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75

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Complete question is:

Gwen has a £5 note and a £2 coin

a litre of cola cost £1.25

gwen buys as many liter bottles of cola as she can

how much money will she have left over

Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

The letter grades (A, B, C, D, F) for business analysis students are categories that represent different levels of achievement, so the variable's classification is (b) Categorical Data.

The Categorical data are defined as the variables that represent characteristics or attributes, and they are often expressed as labels or categories.

The Quantitative data, on the other hand, are  the numerical values which  represent measurements or quantities.

Since the letter grades are not numerical values and do not represent a measurement or quantity, they cannot be classified as quantitative data.

Therefore , the letter grades represents a Categorical Variables .

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The given question is incomplete , the complete question is

The letter grades (A, B, C, D, F) of business analysis students are recorded by a professor. this variable's classification .

(a) is time series data

(b) is categorical data

(c) is quantitative data

(d) cannot be determined

The area of the sidewalk in terms of x would be 3 x ² + x + 2

The area of the sidewalk would be :

= Area of rectangular area - Area of rectangular garden

Area of rectangular area = 2 x ( 2x + 1 )

Area of rectangular garden = x ( x + 1 )

The area of the sidewalk in terms of x is therefore :

= ( 2 x ( 2x + 1 ) ) - ( x ( x + 1 ) )

= ( 4 x ² + 2 ) - ( x ² + x )

= 4 x ² + 2 -  x ² + x

= 4 x ² - x ² + x + 2

= 3 x ² + x + 2

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A graph which represents the solution to this system of inequalities include the following: graph D.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

y ≤ 3x - 4     .....equation 1.

4x + 2y < 6    .....equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region below the solid and dashed line, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (1.4, 0.2).

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Answer: 25 sessions

Step-by-step explanation:

Set up an equation.

50+10x=12x

50=2x

x=25

She will have to take 25 sessions for both gym costs to be the same.

You can check this too. 50 plus 10*25 is $300, and 12*25 is $300.

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Hope this helps.

MM4343

Answer: We can start by setting the cost of the two gyms equal to each other and then solving for the number of sessions. Let's call the number of sessions Macy takes x. The cost of Avery's gym is 50 + 10x, and the cost of Gabe's gym is 12x. Setting these two equal to each other, we have:

50 + 10x = 12x

Subtracting 12x from both sides:

50 = -2x + 10x

Simplifying:

50 = 8x

Dividing both sides by 8:

x = 6.25

So, Macy would need to take 6.25 sessions for the cost of both gyms to be the same. However, since she can only take whole number of sessions, she would need to take 7 sessions to make both gyms cost the same.

Step-by-step explanation:

The method for addressing inequality 2v + 12 ≥ 16 is v ≥ 2. This indicates that any value of v larger than or equal to 2 will fulfil the inequality.

The idea of inequality—the state of not being equal, particularly in status, rights, and opportunities1—is one that is central to social justice theories. However, because it frequently has diverse meanings to different people, it can become confusing in public discourse.

The equation-like appearance of the phrase 5x 4 > 2x + 3 is altered by the arrowhead in place of the equals sign. It serves as an illustration of inequity. This shows that the section on the left, 5x 4, is bigger than the part on the right.

Subtract 12 from both sides of the inequality:

2v + 12 - 12 ≥ 16 - 12

Simplifying, we get:

2v ≥ 4

Divide both sides of the inequality by 2:

2v/2 ≥ 4/2

Simplifying, we get:

v ≥ 2.

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[tex]\cfrac{\sqrt[3]{27xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{\sqrt[3]{3^3 xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{(3^3 xy^3)^{\frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3^{3\cdot \frac{1}{3}}x^{\frac{1}{3}}y^{3\cdot \frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3x^{\frac{1}{3}}y}{5x^{\frac{4}{3}}y^2}[/tex]

[tex]\cfrac{3}{5}\cdot \cfrac{x^{\frac{1}{3}}y}{x^{\frac{4}{3}}y^2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}yx^{-\frac{4}{3}}y^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}x^{-\frac{4}{3}}yy^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}-\frac{4}{3}} y^{1-2} \\\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{a ~~~~ b ~~ ~~ c}{0.6 x^{-1}y^{-1}} \end{array}}~\hfill[/tex]

The apothem is perpendicular distance from the center of a regular polygon to any one of it sides.

The Apothem is defined as a term that used in geometry to describe a characteristic feature of a regular polygon.

A Regular Polygon is a polygon that has all sides of equal length and all angles of equal measure.

The Apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to any one of its sides.

The Center of circle is also the center of polygon. So , apothem is the distance from the center of the circle to the midpoint of any side of the polygon .

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The given question is incomplete , the complete question is

The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.

The translation of a function and coordinates are given below..

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The following functions:

y = x²

y = 2x

The transformation is:

Translate two units to the left.

So,

y = (x - 2)²

y = 2(x - 2)

Translation 5 units up.

y = x² + 5

y = 2x + 5

The following coordinates:

Translate 2 units to the right.

(1, 4) = (1 + 2, 4) = (3, 4)

(5, 8) = (5 + 2, 8) = (7, 8)

Translation 5 units down.

(1, 4) = (1, 4 - 5) = (1, -1)

(5, 8) = (5, 8 - 5) = (5, 3)

Thus,

The translation of a function and coordinates are given above.

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The value of t* would use for this interval is 1.699 to compute a 90% confidence interval.

It is given that the confidence = 90% or 0.9

also, the sample size (n) = 30

The degrees of freedom is the sample size decreased by 1:

df = n - 1

df   = 30 - 1

df = 29

The critical value t* can then be found in the row with df = 29 and in the column with c = 90% (or upper tail probability p = 0.05) using table B.

t* = 1.699

The image attached is t* table

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We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

So, as we have the equation:

12x + 3 = 3(5x + 9)

Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.

Which gave her the value of x as -8.

Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.

He also got -8 as the value of x.

Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.

Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

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Answer:

Howard's pencil is 750 millimeters

Step-by-step explanation:

[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]

Step-by-step:

75 cm = 75 × 10 mm

75 cm = 750 mm