A designer wants to
place a fountain at the intersection of the
shortest paths from each side to the opposite
vertex. What mistake is made on her model?
At what point of concurrency should the
fountain be located?

The function h(t) models the height of a ball thrown into the air, so it makes sense for the range of the function to be all non-negative values. This means that the range of the function will be all non-negative values up until the point where the ball reaches its maximum height, and then it will decrease to zero as the ball hits the ground.

To determine when the ball reaches its maximum height, we can find the vertex of the parabola. The vertex is found by taking the average of the x-coordinates of the roots of the quadratic. In this case, the roots of the quadratic are found by setting h(t) = 0 and solving for t:

-16t^2 + 48t - 36 = 0

By factoring the quadratic, we get:

(t-9)(-16t+4) = 0

So the roots of the quadratic are t = 9 and t = -0.25. The average of these two values is (9 - 0.25)/2 = 4.375. Therefore, the vertex of the parabola is at (4.375, h(4.375)).

To find the y-coordinate of the vertex, we can plug in 4.375 for t in the function h(t):

h(4.375) = -16(4.375)^2 + 48(4.375) - 36 = -16(19.140625) + 195 - 36 = -307.5 + 159 = -148.5

So the vertex of the parabola is at (4.375, -148.5). This means that the maximum height of the ball is -148.5 feet. Since the ball can't go below ground level, the range of the function h(t) is all non-negative values less than or equal to -148.5. Therefore, a reasonable range for the function is [-148.5, ∞).

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The sum of the two polynomials 6s^2t^2 + 2st^2 + 4s^2t + 3st^2 is

6s^2t^2 + 2st^2 + 4s^2t + 3st^2 = (6+4)s^2t^2 + (2+3)st^2 = 10s^2t^2 + 5st^2

The polynomials are being added term by term, and the coefficient of each term is being added.

The coefficient of s^2t^2 in the sum is 10, which is the sum of the coefficients of s^2t^2 in the original polynomials (6 and 4).

The coefficient of st^2 in the sum is 5, which is the sum of the coefficients of st^2 in the original polynomials (2 and 3).

So the sum of the polynomials is 10s^2t^2 + 5st^2, this is the final result.

It's important to note that the polynomials have to be in the same order of terms (same exponent) to obtain the correct result when adding them.

The remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

Every hour, the cow's body will break down 50% of the initial amount of 9,724 milligrams of the antibiotic. So in the first hour, 50% * 9,724 milligrams = 4,862 milligrams will break down.

The remaining amount of antibiotic in the cow's body after the first hour will be 9,724 milligrams - 4,862 milligrams = 4,862 milligrams.

In the next hour, 50% * 4,862 milligrams = 2,431 milligrams will break down. So the remaining amount will be 4,862 milligrams - 2,431 milligrams = 2,431 milligrams.

This process will repeat for 6 hours, the remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

The concept used here to solve this is called the half-life, which is the amount of time required for half of the amount of a substance to decay or be used up. In this case, the antibiotic has a half-life of 1 hour, meaning that every hour, half of the initial amount of 9,724 milligrams will be broken down in the cow's body.

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Answer:

So the final solution is q < 9 and the inequality is False.

Step-by-step explanation:

To solve the given inequality, you first need to simplify the left-hand side of the inequality:

9 + 8 = 17

so the inequality becomes:

17 > 20 or 2q - 5 < 13

Since 17 is not greater than 20, this inequality is false.

Next, we need to solve the other inequality:

2q - 5 < 13

To isolate the variable on one side of the inequality, we need to add 5 to both sides:

2q < 18

Then, we divide both sides by 2:

q < 9

So the solution is q < 9

So the final solution is q < 9 and the inequality is False.

x² + y = 55 ---1

y=6---2

subs 2 in 1

x²+ 6 = 55

x² = 55-6

x² = 49

x =√49

x = 7

25 equal pieces of lenth 7 inch is possible and 5 inch remains after the cutting string.

An inequality is a statement that compares the value of one expression to another, using one of the symbols: <, >, ≤, ≥, ≠. It shows a relationship between two expressions that are not equal. It can be represented in a graph as a boundary line, with a specific region representing the solution set of the inequality.

Convert value of  foot to inches:

we know that 1 foot = 12 inches

15 feet ⇒  15 feet × 12 inches/ft = 180 inches

now the let the number of peice be x

so 7*x<=180

=> x<=180/7

=> x<=25.71

solving the inequality we get

so there is 25 equal pieces of string of length 7 is possible.

remaining piece = 180 - 25*7

=> 180 - 175

=> 5

so 5 inch remains after  cutting the string

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Reason: It's the coefficient to the left of the input variable.

The degree of the polynomial 2x² 5x² 7 is 4.

The biggest sum of all the exponents for all of variables in a term is the polynomial's degree. Any polynomial's degree is determined solely by its variables; coefficients are to be disregarded. The highest exponential power in a polynomial equation is called the polynomial's degree.

When x is the variable with the highest power n in an nth degree polynomial function with real coefficients, where n can take whole number values.

One of the key ideas in mathematics is the degree of polynomials, which establishes the maximum number of possible solutions and the frequency with which a function will cross the x-axis on a graph.

A polynomial with many variables is of a certain degree: Find the term with the highest degree by averaging the exponents of all the variables in each phrase. That will be regarded as the polynomial's degree.

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Answer:

I also don't know good luck girly

There are various methods by which you can solve a quadratic equation such as:

In algebra, a quadratic equation is any equation that can be rearranged in standard shape wherein x represents an unknown cost, and a, b, and c represent acknowledged numbers, in which a ≠ 0. Quadratic equations are in detail related to issues about squares and quadrangles (every other name for rectangles). In reality, the word quadratic is derived from the Latin word quadratus for square.

The general shape of the quadratic equation is ax² + bx + c = 0. for instance, x² + 2x +1 is a quadratic or quadratic equation. A quadratic feature is a characteristic of the form f(x) = ax² +bx+c, in which a, b, and c are constants and a = 0. The term ax² is called the quadratic time period (therefore the call given to the feature), the term box is known as the linear term, and the time period c is known as the steady term.

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The equation system contains: No Solution.

A mathematical statement proving the equality of two mathematical expressions is what is meant by the term equation.

When two or more components of a situation must be taken into account in order to comprehend or describe the entire situation, this is known as an equation.

The equation in a new order:60x + 2y = 50

y+80x = 50​

On both sides of the equation, lessen the most prevalent factor:

80x + y =25

80x + y = 50

Remove the two equations:

80x + y - (80x + y) = 25-50

Take the parentheses out.

80x + y - 80x - y = 25 - 50

One variable is canceled: 0 = 25 - 50

Make a difference or total calculation: 0 = -25

The equation system contains: No Solution.

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The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

How do you tell the difference between domain and range on a graph?

A function's range is all of its y values, which are its outputs, and all of its x values, which are its inputs. The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

Every potential value of y is included in a function's range. A function's range can be determined using the formula y = f. (x). Only if every x value in a relation has a unique y value can it be considered a function.

The various output values are displayed on the y-axis and make up the range. Remember that the domain and range may be larger than the observable values if the graph extends beyond the area that we can view.

Without evaluating or graphing the functions, it is not possible to determine the exact ranges of g(x) and h(x). However, we can see that both functions are linear and have the same slope (2), so their ranges will be in the same direction.

Since the y-intercept of g(x) is 1 and the y-intercept of h(x) is 2, it can be inferred that the range of h(x) will be greater than the range of g(x) for all values of x in the given domain (0 < x < 5).

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There is a points of multiply a 3 digit number :

Now, According to the question:

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

If we need to multiply 123 × 3, we place them as shown below where 123 is the multiplicand and 3 is the multiplier. After multiplying these numbers we get the product as 269

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The additive inverse of 7 is -7.

The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

7

So, the additive inverse of 7:

⇒7 + Additive inverse = 0

⇒Additive inverse = -7

Thus the additive inverse of is 7 is -7.

--The given question is incorrect; the correct question is

"What is the additive inverse of 7?"--

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Answer:

42 feet

Step-by-step explanation:

p = 2l + 2w

232 - 2(74) =

232 - 148 = 84

84/2 = 42

Check

232 = 2(42) + 2( 74)

232 = 84 + 148

232 = 232

Improper fraction is greater than 1, their product is also greater than 1.

Now, According to the question:

A fraction is called a proper fraction if its numerator is less than its denominator. The value of a proper fraction is always less than 1. Whereas, in an improper fraction, the numerator is equal to or greater than the denominator. Its value is always one or greater than one. Consider 1/3 and 3/2. Their product is 1/3 × 3/2 = 3/6 = 1/2

Therefore, according to the definition, the product of a proper and improper fraction is less than the improper fraction.

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By applying the future values, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is $2,529.09

A current asset's future value, abbreviated as FV, is the value that asset is expected to have at some point in the future, based on a projected rate of growth. The future value is essential for investors and financial planners because they use it to estimate how much money an investment made now will be worth in the future.

To find the future values, we can use this following formula:

FV = I x (1 + R)^T

Where:

I = investment amount

R = interest rate

T = number of years

In this case, we are given that:

Future values (FV) = $8,250

The periodic rate = 12% : 4 = 0.03 (compounded quarterly)

Number of period = 10 years x 4 = 40

Hence, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is:

8,250 = I x (1 + 0.03)⁴⁰

I = 8,250: ((1 + 0.03)⁴⁰)

I = $2,529.09

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The value of P(F or G) using the general addition rule be 8/12.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.

We have that

F∪G = {5, 6, 7, 8, 9, 10, 11, 12}

P(FG) = 0.667

P(F or G) = 5/12 + 4/12 - (1/12)

P(F or G) = 5/12 + 1/4

From the question we are told

S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},

F = [5, 6, 7, 8, 9]

G = {9, 10, 11, 12}

Generally

The P(F or G) by counting the number of outcomes in F or G exists

[tex]$F \& G=\{5,6,7,8,9,10,11,12\}$$[/tex]

P(F or G) using the general addition rule

[tex]$& P(F G)=\frac{N_f}{N_g} \\[/tex]

substitute the values in the above equation, we get

[tex]$& P(F G)=\frac{8}{12} \\[/tex]

simplifying the equation, we get

P(F G) = 0.667

Using addition Rue to attain P(F or G) we get

P(F or G) = PF + PG - P(F + G)

substitute the values in the above equation, we get

[tex]$& P(\text { For } G)=5 / 12+4 / 12-(1 / 12) \\[/tex]

simplifying the equation, we get

[tex]$ P({For} G)=5 / 12+1 / 4 \\[/tex]

[tex]$& P(\text { For } G)=\frac{8}{12}[/tex]

Therefore, the value of P(F or G) using the general addition rule be 8/12.

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The list  below that  shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots List 2

the statement states that the school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.

List 1 mentions that there is "Ham, Carrots, celery". We know that students can only have either carrots or celery, but the list shows that the students have both. Therefore, list 2 is correct.

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To compare the unit rates, we need to find the cost per ounce for each bottle of water.

For the 16-ounce bottle, the unit rate is:

$2.40 / 16 ounces = $0.15 per ounce

For the 28-ounce bottle, the unit rate is:

$2.80 / 28 ounces = $0.10 per ounce

From the unit rate we can see that the 28 ounce bottle of water is a better deal because it cost $0.10 per ounce while the 16 ounce bottle cost $0.15 per ounce.

It's important to know that as the amount of water increases the price decreases making the 28 ounce bottle cheaper than the 16 ounce bottle.

For the given set of information, the inequality 25 - 1 ≤' temperature ≤' 25 + 1

Linear inequalities in two variables are statements containing symbols such as "'<'(less than), '>' (greater than), '≤''(less than or equal to), '≥' (greater than or equal to) and two separate variables.

Linear inequalities are defined as an inequality (expressed by inequality symbols) that holds a linear function.

A linear function is any function with a straight line as its graph.

The inequality representing the situation is:

25 - 1 <= temperature <= 25 + 1

So the temperature must be greater than or equal to 24°C and less than or equal to 26°C.

The highest possible temperature is 26°C.

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Answer:

80 students received a flu vaccine

Step-by-step explanation:

1. graph the equation.

2. Go to 65 on the y-axis.

3. Go to 80 on the x-axis.

4. If the line stops at the point (80,65) then for the 65 cases of the flu at school, 80 students received the vaccine.

Answer: d=0.5

Step-by-step explanation: 4.8d=2.4

Divide 4.8 form both sides to isolate d.

[tex]\frac{4.8d}{4.8} =\frac{2.4}{4.8}[/tex]

Then, just do 2.4 divided by 4.8 to get d=0.5.

Answer:

9

Step-by-step explanation:

exterior angle=x⁰

interior angle=3x⁰+20⁰

3x⁰+20⁰+x⁰=180⁰

4x=160⁰

x=40⁰

number of sides = 360⁰/exterior angle

360⁰/40⁰= 9sides

Answer:

by helping some one fast

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔPQR and ΔPQS,

∠P=∠P (Reflex property)

PQ=PQ (Reflex property)

∠PQR=∠PSQ=90°

By AA similarity, ΔPQR ~ ΔPQS

So, PQ/PR = PS/PQ

x/45 = 25/x

x²=45×25

x=15√5 units

Therefore, the value of x from the given figure is 15√5 units.

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Answer:

c

Step-by-step explanation:

V=a2h

3=14.22·3.9

3=262.132cm³

Answer: y=2x²+3x-5

Step-by-step explanation:

Solve 4x²+6x-2y=10

1. subtract 4x² and 6x from both sides

(you do this to leave y by itself)

-2y=10-4x²-6x

2. divide -2 on both sides

y= -5+2x²+3x

This is technically the right answer but you still need to put the numbers and variables in the right order.

y=2x²+3x-5

(variables w/ exponents go first, then the variable, then the number)

Hope this helps! Good luck!

The algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

These algebraic identities basically carry variable equations in such a way, that the Left-hand side (L.H.S) of the equation is equal to its Right-hand side(R.H.S).

What is the use of algebraic identities?

Algebraic Identities help in simplification. Algebraic Identities play a major role in solving quadratic equations and higher power equations.

The algebraic identities are also used to calculate products of numbers and other things.

Let us consider x, y and z are variables.

Algebraic Identities for Two Variables x and y :

(x + y)² = x² + y² + 2xy

(x – y)² = x² + y² – 2xy

x² – y² = (x + y) (x – y)

(x + a) (x + b) = x² + (a + b)x + ab ; a and b are two constant values

(x + y)³ = x³ + y³ + 3xy(x + y)

(x – y)³ = x³ – y³ – 3xy(x – y)

Algebraic Identities for Three Variables x, y and z :

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)

So, the algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

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