what is 155x60cm into square inches

Answer: [tex]\Large\boxed{f(-9)=-189}[/tex]

Step-by-step explanation:

f(x) = -3x² - 6x

Requirements of the question

Find the value of f(-9)

Substitute values into the given function

f(x) = -3x² - 6x

f(9) = -3 (-9)² - 6 (-9)

Simplify the exponent

f(9) = -3 (81) - 6 (-9)

Simplify by multiplication

f(-9) = (-243) - (-54)

Simplify by subtraction

[tex]\Large\boxed{f(-9)=-189}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Based on the calculations, the depth of tent is equal to 12 feet.

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

AD² = AC² - DC²

AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

Where:

Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

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The equation of the halfpipe is  Option A , (0, 20); Y equals one over eighty times x squared plus 20.

The equation of the halfpipe is  Y = X²/80 +20.

What is parabola ?

The equation of parabola is given by  

(X-h)² = 4p(Y-k)²

In this case h = 0

So we get  

Y = X²/4P +k

Focus point is (h, p+k) , (p+k) = 40

Hence h, k = (0,20)

P = 40-k = 20

Equation Y = X²/80 +20

Therefore, the equation of the halfpipe is  Y = X²/80 +20

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The complete question is -

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 20); y equals one over eighty times x squared plus 20

(0, 20); y equals one over eighty times x squared minus 20

(0, 10); y equals one over forty times x squared plus 10

(0, 10); y equals one over forty times x squared minus 10

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).

Given: [tex]$y=\frac{1}{8} (x^{2} -4x-12)[/tex]

[tex]$y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$[/tex]

Use the form [tex]$a x^{2}+b x+c$[/tex] to find the values of a, b, and c.

[tex]$a=\frac{1}{8}$[/tex], [tex]$b=-\frac{1}{2}$[/tex] and [tex]$c=-\frac{3}{2}$[/tex]

Consider the vertex form of a parabola [tex]$a(x+d)^{2}+e$[/tex]

To estimate the value of d using the formula [tex]$d=\frac{b}{2 a}$[/tex].

Substitute the values of a and b into the formula

[tex]$d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

Cancel the common factor 2 and 8.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$[/tex]

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

equating, we get

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

[tex]$d=-\frac{1}{2} \cdot 4$$[/tex]

The value of [tex]$d=-2$[/tex]

Find the value of e using the formula [tex]$e=c-\frac{b^{2}}{4 a}$[/tex].

Substitute the values of c, b and a into the above formula, and we get

[tex]$e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$[/tex]

simplifying the equation, we get

[tex]$e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$[/tex]

Apply the product rule to [tex]$\frac{1}{2}$[/tex].

[tex]$e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$[/tex]

simplifying the above equation, we get

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$[/tex]

[tex]$e=\frac{-3-1}{2}$$[/tex]

[tex]$e=\frac{-4}{2}=2$[/tex]

Substitute the values of [tex]$a, d_{t}$[/tex] and e into the vertex form [tex]$\frac{1}{8}(x-2)^{2}-2$[/tex].

Set y equal to the new right side.

[tex]$y=\frac{1}{8} \cdot(x-2)^{2}-2$[/tex]

Use the vertex form, [tex]$y=a(x-h)^{2}+k$[/tex], to determine the values of a, h, and k.

[tex]$a=\frac{1}{8}$[/tex]

[tex]$h=2$[/tex]

[tex]$k=-2$[/tex]

Find the vertex [tex]$(h, k)$[/tex]

[tex]$(2,-2)$[/tex]

Find [tex]$\boldsymbol{p}$[/tex], the distance from the vertex to the focus.

To estimate the distance from the vertex to a focus of the parabola [tex]$\frac{1}{4 a}$[/tex]

Substitute the value of a into the formula

[tex]$\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$[/tex]

[tex]$\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$[/tex]

[tex]$\frac{1}{\frac{1}{2}}=2$[/tex]

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)

Substitute the known values of h, p, and k into the formula, we get

(2,0).

Therefore, the correct answer is (2,0).

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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

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The interpretation of x in the equation 75•x + 19•y = T, used by the geographer, based on the land area of Aruba, 75 m², and Bermuda, 19 m², is the population in a square mile of Aruba

The land area of Aruba = 75 m²

Land area of Bermuda = 19 m²

The total number of residents is given in the question by the equation;

75•x + 19•y = T

Therefore;

x = The number of people in a square mile in Aruba

y = The number of people in a square mile in Bermuda

Which gives;

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Answer:

The scale factor is 1/5.

Step-by-step explanation:

You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached.  I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15.  What do I need to multiple 3 by to get 15?  5.  That is the scale factor from the little triangle to the big triangle.  If I go the other way, the scale factor is the reciprocal of 5 or 1.5

Using the Laplace transform, the value of y' + y = (t − 1), y(0) = 5 is y(t) = 5e ^ -t + u (t - 1)e^(1-t)

Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in  regions of physics, electrical engineering, control optics, arithmetic and sign processing.

y' + y = (t − 1)

y (0) = 5

Taking the Laplace transformation of the differential equation

⇒sY(s) - y (0) + Y(s) = e-s

⇒(s + 1)Y(s) = (5+ e^-s)/s + 1

⇒y(t) = L^-1{5/s+1} + {e ^-s/s + 1}

⇒y(t) = 5 e^-t + u(t -1)e^1-t

The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.

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Answer:

mass of a clay pot = 4.95 kg

Kindly award branliest

Step-by-step explanation:

Let the mass of a clay pot be x

Let the mass of a metal pot be y

Thus; 2x + 2y = 13.2

And ;

x = 3 times y

x = 3y

2x + 2y = 13.2

2(3y) + 2y = 13.2

6y + 2y = 13.2

8y = 13.2

y = 13.2/8 = 1.65

x = 3y = 3(1.65) = 4.95

mass of a clay pot = 4.95 kg

The verbal expression for the mathematical expression 5(x - 4) + 2 is the number 5 times the difference between an unknown x and the number 4 and plus 2.

It is defined as the combination of constants and variables with mathematical operators.

It is given that a mathematical expression as below:

= 5(x - 4) + 2

Here x is the unknown number

The number

Number 5 times the difference between an unknown x and number 4 and plus 2

Thus, the verbal expression for the mathematical expression 5(x - 4) + 2 is number 5 times the difference between an unknown x and number 4 and plus 2.

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Step-by-step explanation:

Use the Factor Theorem,

" if x-a is a factor of f(x), then f(a) =0,

So here, since x-3 is a factor then f(3)=0,

So first step, plug in 3 for x for the serperate equations.

[tex] {3}^{2} + ( p + q)3 - q = 0[/tex]

[tex]2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0[/tex]

Simplify both equations,

[tex]9 + 3p + 2q = 0[/tex]

[tex]15 + 4 p + 2q = 0[/tex]

Isolate the constants,

[tex]3p + 2q = - 9[/tex]

[tex]4p + 2q = - 15[/tex]

We have a system of equations so let eliminate a variable, by subtracting the two equations.

[tex] - p = 6[/tex]

[tex]p = - 6[/tex]

Plug p back in for any one of the equations to find q.

[tex]3( - 6) + 2q = - 9[/tex]

[tex] - 18 + 2q = - 9[/tex]

[tex]2q = 4.5[/tex]

So p is -6

q is 4.5

Answer:

cashier needed to divide by 1000, not 3.

Step-by-step explanation:

there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36

The value of c, the constant of the function y = ax² + bx + c, exists -3.

An equation exists as an expression that indicates the relationship between two or more numbers and variables.

Given that: y = ax² + bx + c

At point (4, 21)

21 = a(4²) + 4b + c .......(1)

At point (5, 32)

32 = a(5²) + 5b + c .........(2)

At points (6, 45)

45 = a(6²) + 6b + c .......(3)

Therefore, the value of a = 1, b = 2 and c = -3.

The value of c, the constant of the function y = ax² + bx + c, exists -3.

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Answer:

Book 3

Step-by-step explanation:

So we have four statements:

1: Book 1 or Book 2

2: Book 3 or Book 4

3: Book 4

4: Not Book 3

We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.

So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.

If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.

Let's look at why assuming any other statement to be true, leads to contradictions.

So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.

Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true

Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has  no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.

The correct  option (D).

There are infinitely many intersection points.

a two-variable equation that, when plotted on a graph, results in a straight line.

The term "point of intersection" refers to the intersection of two lines.

Russ is attempting to solve an equation whose two sides are both linear expressions.

He graphs the system and finds that they are on the same line after setting the expressions to y.

Since both lines are the same, there are an endless number of junction places.

Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.

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I understand that the question you are looking for is:

Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?

A. There are no intersection points.

B. There is exactly one intersection point.

C. There are exactly two intersection points.

D. There are infinitely many intersection points

The regression equation of this group of data is given as ŷ = 0.0108X - 1.98123.

ŷ = 0.0108X - 1.98123

x = 610

= 0.0108*610 - 1.98123

=  4.61 million dollars

2. the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.

7.65= 0.0108x-1.98123

take like terms

x = 892

2. correlation coefficient of X and Y is r = -0.987

This shows a negative relationship

b)Linear Regression Equation =

Y = 313309 - 34740x

c) Y = 313309 - 34740x

Y = 313309 - 34740 * 3

209089

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The range of the function f(x) is (-∝, 3]

The function definition is given as:

[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]

There are two sub-functions and the domains in the above definition.

Each function would be plotted alongside its domain.

See attachment for the graph of the function f(x)

From the graph of the function, we have the following range of f(x)

Minimum = Negative Infinity

Maximum = 5

Hence, the range of the function f(x) is (-∝, 3]

We have the domains to be

x <= 3 and x > 3

This means that the asymptote of f(x) is x = 3

From the graph, we have:

This means that the end behavior of f(x) is as x approaches +∝, the function approaches +∝ and as x approaches -∝, the function approaches -∝

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Complete question

A piecewise function f (x) is defined by

[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]

Answer:

6.75

Step-by-step explanation:

         Distance in Miles

MPH -------------------------

         Time in Hours

27/2 = 13.5. That is 1 hour. Half that and you get 6.75 MP1/2H

The exponential growth rate is obtained as 0.1099.

Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.

When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt

Po = initial number

P(t) = number at time t

r = rate of growth

t = time taken

Thus;

270=90e^10r

270/90 = e^10r

3 = e^10r

ln3 = 10r

r = ln3/10

r = 0.1099

After 13 hours;

P(t) = 90e^(0.1099 * 13)

P(t) = 376

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The dot product associated to sides AB and BC is 0.

In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:

Side BA

BA = (5, 3) - (0, 0)

BA = (5, 3)

Side BC

BC = (- 3, 5) - (0, 0)

BC = (- 3, 5)

By definition of dot product, the result associated to the two sides of the triangle is:

BA • BC = (5, 3) • (- 3, 5)

BA • BC = (5) · (- 3) + (3) · (5)

BA • BC = - 15 + 15

BA • BC = 0

The dot product associated to sides AB and BC is 0.

The statement is poorly formatted, the correct form is shown below:

If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:

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Answer:

  (a)  The two triangles are similar by AA

Step-by-step explanation:

Similar triangles have congruent corresponding angles and proportional corresponding side lengths.

The third angle in triangle ABC is found using the fact that the sum of angles is 180°.

  ∠C = 180° -∠A -∠B

  ∠C = 180° -97° -46° = 37°

Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...

  ∠A = ∠D = 97°

  ∠C = ∠F = 37°

The two triangles are similar by AA.

__

Additional comment

The similarity statement can be ΔABC ~ ΔDEF.

The smallest possible value of m according to the task is; 1/1540.

Since it follows from the task content that the product of 1540 and m is a square number and the smallest possible small number is; 1.

The equation which holds true is; 1540 × m = 1

Consequently, m = 1/1540.

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Answer:

3/4 or 75%

Step-by-step explanation:

Falcons scored 3 and Hawks scored 1, so in total 4 points were scored during the game. Falcons scored 3 out of 4 points, so they scored 3/4 of the points scored in the game.

To convert 3/4 to percentage, divide 3 by 4, multiply the quotient (result after division calculation) by 100, and add % sign after the number.

3/4 = 0.75

Therefore 3/4 is equivalent to 75%.

Answer:

[tex] \frac{3}{4} [/tex]

[tex]75\%[/tex]

Step-by-step explanation:

From the information given from the question, we can deduce:

Total goals scored by both teams = 3 + 1 = 4

Fraction of Goals Scored by Falcons =

[tex] \frac{goals \: scored \: by \: falcons}{total \: goals \: scored \: by \: both \: teams} \\ = \frac{3}{4} [/tex]

To get the percentage, we have to make sure the denominator is 100.

[tex] \frac{3}{4} \\ = \frac{3 \times 25}{4 \times 25} \\ = \frac{75}{100} \\ = 75\%[/tex]

Answer:

x = 99°

y = 91°

Step-by-step explanation:

For Cyclic quadrilateral, the sum of the opposite angles = 180°

Let's find x :-

x + 81° = 180°

x = 180 - 81

x = 99°

Let's find y :-

y + 89° = 180°

y = 180 - 89

y = 91°

Hope this helps you !

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Given ,

[tex]2x = 100[/tex]

To find ,

value of x

Now ,

[tex]\longrightarrow{2x = 20}[/tex]

Dividing both sides by 2 , we get

[tex] \frac{2x}{2} = \frac{100}{2} \\ \\ \longrightarrow\boxed{ \: x = 50} [/tex]

nikal -,- xD

Answer:

Step-by-step explanation:

[tex]\bf 2x=100[/tex]

Divide both sides by 2:-

[tex]\bf \cfrac{2x}{2}=\cfrac{100}{2}[/tex]

Simplify:-

[tex]\bf x=50[/tex]

___________________

Answer:

[tex]y = -\frac{2}{3}x + 490[/tex]

gradient = = [tex]-\frac{2}{3}[/tex]

y-intercept = [tex]490[/tex]

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope,

c = y-intercept.

• We are given the equation:

[tex]2x + 3y = 1470[/tex]

To change this into the slope-intercept form, we must make y the subject:

[tex]3y = -2x + 1470[/tex]          [subtract [tex]2x[/tex] from both sides]

⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex]        [divide both sides by 3]

⇒ [tex]y = -\frac{2}{3}x + 490[/tex]

• Comparing this equation with the general form equation, we see that:

m = [tex]-\frac{2}{3}[/tex]

c = [tex]490[/tex].

This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].

The plastic containers should be used by the company to minimize the cost because it will cost $5.40 more to use the wooden containers.

A mathematical word problem is a question that is stated as one or more sentences and calls on students to use their understanding of arithmetic operations to solve a "real-life" problem.

As you are aware, word problems can include almost any operation, including addition, subtraction, division, and even many operations at once.

From the given information:

If the company uses a wooden container shaped-liked rectangular prism, the will need to use (7560/180) containers.

= 42 containers of wooden containers.

If the company uses a plastic cylindrical container, they will need to use (7560/126) containers.

= 60 containers of plastic containers.

To determine the container that the company should use that will minimize the cost:

Therefore, we can conclude that the company should use plastic containers because it will cost $5.40 more to use wooden containers.

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Answer:

B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

Step-by-step explanation:

Answer:

A 90°

B 90°

C 62°

D 118°

Hopefully this helps u

Answer:

1. 16

2. 24

3. 75

Step-by-step explanation:

Answer:

28 DVDs

Step-by-step explanation:

Given information from the question, we can deduce:

2 weeks = 4 DVDs

1 week =

[tex] \frac{4}{2} \\ = 2[/tex]

2 DVDs on average.

Which means,

14 weeks = 2 × 14 = 28 DVDs

Therefore, Katy will buy 28 DVDs in 14 weeks.