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The change from y = 2x + 7 to y = 1/2 x + 7 alters the slope, making the new function's graph less steep. The y-intercept remains at y = 7, ensuring the graphs coincide at this point.

The question asks how the graph of the function y = 1/2 x + 7 would compare to the graph of the original function y = 2x + 7. The key difference between these two functions is the slope part, which is the coefficient of x. In the original function, the slope is 2 indicating a rise of 2 on the vertical (y) axis for every increase of 1 on the horizontal (x) axis. But in the new function, the slope is 1/2, indicating a rise of only 1/2 on the y-axis for each increase of 1 on the x-axis. So, the new function's graph would be less steep than the original's. The y-intercept for both functions remains the same, at y = 7. These changes illustrate how the slope and y-intercept of the line equation (y = mx + b) determine the shape and position of the line on the graph.

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The direction of fastest increase is along the line \(y = x + 1\).

Given that [tex]\(y\)[/tex] varies directly as the square root of [tex]\(x\)[/tex], we can express this relationship as:

[tex]\[ y = k \sqrt{x} \][/tex]

where [tex]\(k\)[/tex] is the constant of variation.

We are given that when [tex]\(x = 16\), \(y = 12\)[/tex]. Let's find the constant of variation:

[tex]\[ 12 = k \sqrt{16} \][/tex]

[tex]\[ 12 = 4k \][/tex]

[tex]\[ k = 3 \][/tex]

Now we can write the equation of variation:

[tex]\[ y = 3 \sqrt{x} \][/tex]

To find [tex]\(x\)[/tex] when [tex]\(y = 15\)[/tex], we can solve for [tex]\(x\):[/tex]

[tex]\[ 15 = 3 \sqrt{x} \][/tex]

[tex]\[ \sqrt{x} = \frac{15}{3} \][/tex]

[tex]\[ \sqrt{x} = 5 \][/tex]

[tex]\[ x = 5^2 \][/tex]

[tex]\[ x = 25 \][/tex]

Therefore, when [tex]\(y = 15\)[/tex], the corresponding value of [tex]\(x\)[/tex] is 25.

Answer:

126

Step-by-step explanation:

Answer:

The correct answer is D. 126

Step-by-step explanation:

In order to solve this exercise, we need to know that two straight triangles that are sharing a vertex like in this picture are considered similar triangles. One property of the similar triangles is that exist a linear relationship between its sides. In this exercise, one triangle is ABC and the other CDE.

The relationship that we can write is between the length of its sides.

The relationship is a division between the length of the sides :

[tex]\frac{AC}{AB}=\frac{CE}{DE}[/tex] ⇒

[tex]\frac{140-x}{81}=\frac{x}{9}[/tex]

Solving the equation

[tex]x=\frac{(140-x)}{81}.(9)[/tex]

[tex]x=\frac{(140-x)}{9}[/tex]

[tex]9x=140-x[/tex]

[tex]10x=140[/tex]

[tex]x=14[/tex] ⇒

If the side AC is [tex]140-x[/tex] the length is

[tex]140-14=126[/tex]

The correct option is D. 126

Answer:

11.4 there now mark that person brainliest

Step-by-step explanation:

The component form of a vector represents it as the sum of its scalar components along the coordinate axes. It is used to describe a vector's individual directional effects in a Cartesian coordinate system, often denoted by Axi + Ayj for 2D vectors, and an additional Azk for 3D vectors.

The component form of a vector refers to its representation as the sum of its separate parts along the coordinate axes. In a two-dimensional system, a vector can be broken down into the x and y components. Each component is essentially the projection of the vector along one of the coordinate axes. For example, in a rectangular (Cartesian) coordinate system, a two-dimensional vector A with an initial point and a terminal point can be represented by the difference in the x-coordinates (horizontal component) and the difference in the y-coordinates (vertical component).

The formula to represent a two-dimensional vector in component form is A = Axi + Ayj, where Ax and Ay are the scalar components of the vector along the x-axis and y-axis, respectively, and i and j are the unit vectors in the direction of the x-axis and y-axis. In three-dimensional space, an additional z-component is included, resulting in the component form A = Axi + Ayj + Azk, with k being the unit vector along the z-axis.

The business will pay $506.99 on the loan in the sixth month, after making monthly payments of 12% of the remaining balance on an $8000 loan.

To determine how much the business will pay in the sixth month on a loan where they pay off 12% of the remaining balance each month, we need to use a decay formula. This is a type of exponential decay since the amount owed is decreasing by a fixed percentage each month. The formula to find the remaining balance after each payment is:

Balance after n payments = Initial amount * (1 - rate)^n

Starting with an initial loan amount of $8000 and a monthly payment rate of 12% (or 0.12 in decimal form), we calculate the remaining balance each month until the sixth month:

Now we can find out how much will be paid in the sixth month by calculating 12% of the balance at the end of the fifth month:

Sixth month payment = 12% of 4224.96
Sixth month payment = 0.12 * 4224.96
Sixth month payment = $506.99
The business will pay $506.99 in the sixth month.

Answer:

Option A is correct

x= -2 is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex]

Step-by-step explanation:

As per the statement:

Fran graphs the equations

[tex]y=2x^2-2[/tex] and

[tex]y = -0.5x + 4[/tex]

Equate these two equations:

[tex]2x^2-2 = -0.5x+4[/tex]

You can see the graph for these equations as shown.

Since, the line and the parabola intersects at x = -2 and x = 1.5.

From the given options:

x = -2 is the solution for these equations.

Therefore, the value is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex] is, x = -2

table A from 2-3 minutes it rose 64.9-61.3 = 3.6

from 3-7 it rose 79.3 -64.9 = 14.4 = 3.6 degrees per minute

 Table B needs to raise faster than 3.6 per minute

64.4 -61 = 3.4

64.6 - 61 = 3.6

64.3 -60.6 = 3.7

 so the 3rd table is correct

Answer:

3rd one

Step-by-step explanation: