Ralphie has 23 more toys than his little brother Joey. If they were to get all of their toys out and lay them on the floor, there would be 384 toys on the floor.

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.

Answer:

11=h

Step-by-step explanation:

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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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

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:

There is no solution.

Step-by-step explanation:

Answer:

11.4 there now mark that person brainliest

Step-by-step explanation:

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

To find y when x = 5, you can substitute x = 5 into the given equation. Let's substitute x = 5 into the equation y = -173.5 + 4.83x - 2(16.4) to find y = -182.15.

To find y when x = 5, we can substitute x = 5 into the given equation. Given that y = 5/17 when x = 10, we can find the value of y when x = 5. Let's substitute x = 5 into the equation y = -173.5 + 4.83x - 2(16.4):

y = -173.5 + 4.83(5) - 2(16.4)
y = -173.5 + 24.15 - 32.8
y = -182.15

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Answer:

[tex]2^{3}=x[/tex]

Step-by-step explanation:

We have to express the log in exponential form

The given expression is [tex]log_{2}(x)=3[/tex]

As we know, if  [tex]log_{b}a=c[/tex] then [tex]b^{c}=a[/tex]

So [tex]2^{3}=x[/tex] will be the esponential form of  [tex]log_{2}(x)=3[/tex]

Answer:

3rd one

Step-by-step explanation:

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