im not supposed to be doing this stuff yet but yeee plz help :)
f(x)=3x^2-40x+180

The value of x from the expression is 4

Algebraic expressions are known a s mathematical expressions comprised of constants and variables.

These expressions are made up of algebraic operations such as addition, subtraction, division, multiplications and well as other operations.

From the information given, we have that;

\( \sqrt{2x - 7} = 1\)

To solve for x, we start by finding the square fo both sides, this would give;

\( { \sqrt{2x - 7} }^{2} = {1}^{2} \)

The square removes the square, we then have;

2x - 7 = 1

collect like terms

2x = 1 + 7

2x = 8

Make 'x' the subject

x = 8/2

x = 4

The value of x is 4

Thus, the value of x from the expression is 4

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Answer:

It's D

Step-by-step explanation:

When you add the 19-50 and over 50 then you get the highest answer

Answer:

the number that is halfway between 250 and 300 is 275

Step-by-step explanation:

250+300= 550/2= 275

The number i,e halfway is 275.

\(= (250 + 300) \div 2\\\\= 550 \div 2\)

= 275

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Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

Compute the gradient of \(f\).

\(\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle\)

Set this equal to the zero vector and solve for the critical points.

\(3x^2-6y = 0 \implies x^2 = 2y\)

\(-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}\)

\(\implies x^2 = \pm2\sqrt{2x}\)

\(\implies x^4 = 8x\)

\(\implies x^4 - 8x = 0\)

\(\implies x (x-2) (x^2 + 2x + 4) = 0\)

\(\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0\)

\(\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0\)

The last case has no real solution, so we can ignore it.

Now,

\(x=0 \implies 0^2 = 2y \implies y=0\)

\(x=2 \implies 2^2 = 2y \implies y=2\)

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

\(H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}\)

Check the sign of the determinant of the Hessian at each of the critical points.

\(\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0\)

which indicates a saddle point at (0, 0);

\(\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0\)

We also have \(f_{xx}(2,2) = 12 > 0\), which together indicate a local minimum at (2, 2).

Calculating the volume of a rectangular prism is a simple process that involves multiplying the length, width, and height.

Calculating the volume of a rectangular prism is a straightforward process. A rectangular prism is a three-dimensional shape that has a length, width, and height. To find its volume, you simply multiply the length by the width by the height. The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
For example, if a rectangular prism has a length of 5 cm, a width of 4 cm, and a height of 3 cm, its volume would be:
Volume = 5 cm x 4 cm x 3 cm
Volume = 60 cubic centimeters (cm³)
It's important to ensure that all measurements are in the same unit before calculating the volume. For instance, if the length is in meters and the width and height are in centimeters, you would need to convert the length to centimeters to ensure that all measurements are in the same unit before calculating the volume.
In conclusion, calculating the volume of a rectangular prism is a simple process that involves multiplying the length, width, and height. This formula can be used for any rectangular prism regardless of its size or shape.

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The domain of a function is all the possible input values for which the function is defined.

Function is a block of code that performs a specific task. It is a reusable piece of code that can be called from other parts of the code, reducing the amount of code that needs to be written and making the code easier to read and maintain. Functions can take in parameters and return values, allowing for increased flexibility and reusability. Functions can also be used to break up large programs into smaller, more manageable pieces.

In this case, the reasonable domain for the function f(x) = 4x³-50x²+150x would be all real numbers. This is because the function is a polynomial, which is continuous, meaning that it is defined for all real numbers.

The input of the function is a width, and the output is a volume. Therefore, the domain of the function should include all reasonable widths that could produce a volume. This means that the domain should include all positive real numbers, as any negative value would produce a negative volume, which is not reasonable. Thus, the reasonable domain for the function f(x) = 4x³-50x²+150x is all positive real numbers.

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Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

Answer:

3:2

Step-by-step explanation:

can also be written as 3/2 as a fraction!

Answer:

Blue paint to red paint - 3:2

Red paint to blue paint 2:3

Step-by-step explanation:

For every 3 cups of blue paint there is 2 cups of red paint

For every 2 cups of red paint there is 3 cups of blue paint

Fraction Mode: 3/2 or 2/3

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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Answer:

C, D, F

Step-by-step explanation:

Shape A is not a polygon; it has a line that doesn't connect anywhere. Even if it is a polygon, it would be concave. Shape B is a concave polygon, shape E is also a concave polygon, shape G and H are also concave polygons. Only shapes C, D, and F are convex polygons. Concave polygons are shapes that cave in, and convex polygons are caves that don't cave in.

Answer::2,075,673,600 batting orders may occur.

Step-by-step explanation: A baseball team has 4 pitchers, who only pitch, and 12 other players, all of whom can play any position other then pitcher.

\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

The chances that Liliana will pick a purple marble, replace it, and then pick a yellow marble is B. 6 / 25.

The fact that there are 18 purple marbles and 12 yellow marbles implies that the total marbles will be:

= 18 + 12

= 30 marbles

The probability will be:

= P(Purple) × P(yellow)

= 12/30 × 18/30

= 2/5 × 3/5

= 6/25

The probability is 6/25.

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Answer: The answer is C.

Step-by-step explanation:

It is definitely not B because the average of the numbers compared to what that shows don't make sense.

The biggest number that you gave us is 34 but on option A, it looks like its 30 or 31. So that's not correct.

Finally, it can't be D because the biggest number shown there is 35 when it actually is 34.

I hope I was able to help!

Good luck and have a great day :)

Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

The equation of the perpendicular line is y = -1/3x

From the question, we have the following parameters that can be used in our computation:

y = 3x + 2

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 2

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/3

The equation of the line is then calculated as

y = mx

Where

m = -1/3

So, we have

y = -1/3x

Hence, the line has an equation of y = -1/3x

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Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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Answer:r+(2r+7)

Step-by-step explanation:

By applying the congruent triangles concept, it can be concluded ΔGHI is congruent to ΔJKL.

Congruent triangles are two or more triangles that are exactly the same shape and size as one another. So, the triangles will remain exactly the same when rotated, reversed, or even folded.

The properties of congruent triangles:

if ΔABC ≅ ΔEFG then:

AB = EF

BC = FG

∠A = ∠E

∠B = ∠F

Now we look at the attached image:

Because GH ≠ MN, we don't need to check the other properties to conclude that ΔGHI and ΔMNP are not congruent.

Because GH = JK, HI = KL, ∠G = ∠J, and ∠H = ∠K, then we can conclude that ΔGHI ≅ ΔJKL

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The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Answer:

The answer is Ahope this helps

Answer:

Vertex: (-2, 3)

Step-by-step explanation:

We first have to find the x - variable of the vertex point.

The formula to find the x - variable is x = -b/ 2a.

\(3x^{2} + 12x + 15\)

a        b        c

Substitute the values into the formula.

x = - 12 / 2(3)

x = - 12 / 6

x = - 2       < - This is the x - variable

Now we have to find the y - variable of the vertex point.

To find the y - variable, we have to substitute the x value into the original equation (\(3x^{2} + 12x + 15\)).

g(x) = y    

\(y = 3(-2)^{2} + 12(-2) + 15\\\)

\(y = 3(4) - 24 + 15\)

\(y = 12 - 24 + 15\)

\(y = - 12 + 15\)

\(y = 3\)

So, now that we have the x and y values, we can find the vertex which is (-2, 3).

Hope this helps!

Answer:

QUART IS A LITTLE LESS THAN A LITER

Step-by-step explanation:

hope this helps :))

Answer:

279

Step-by-step explanation:

First, you plug in 500 for " x " because it says P( 500 ).

P( 500 ) = 0.75 (500) -96

Then, you multiply / simplify

P ( 500 ) = (375) - 96

P ( 500 ) = 279

Finally, it gives you your answer for selling 500 pretzels

279

When we look closely at the three triangles, we will observe the following:

This gives us sufficient proof that the three triangles are congruent. Hence, the correct answer is all three triangles are congruent