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cestrela7 [59]
3 years ago
5

What value for the constant,h, in the equation shown below will result in an onfinite number of solutions? Equation: 6x+18=h(3x+

9) Answer choices: a. -2 b.-3 c.2 d.3
Mathematics
1 answer:
o-na [289]3 years ago
4 0

Answer:

c.2

Step-by-step explanation:

6x+18=h(3x+9)

To have an infinite number of solutions, the left and right side must be equal

Distribute the h

6x+18 = 3xh +9h

6x = 3xh

Divide by x

6x/x = 3xh/x

6 = 3h

Divide by 3

6/3 =3h/3

2 =h

Lets verify

18 = 9h

Divide by 9

18/9 = 9h/9

2 =h

h must be 2

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10 yd<br> 5 yd<br> What’s the surface area of the cylinder
Thepotemich [5.8K]

Answer:

471.24 yd²

Step-by-step explanation:

The formula for the surface area of the cylinder

= 2πr(r + h)

Height = 10 yd

Radius = 5 yd

Surface area =

2 × π × 5(5 + 10)

= 471.24 yd²

The surface area of the cylinder = 471.24 yd²

4 0
3 years ago
The first group collected 238 cans. The second group collected 345 cans. How many cans did the two groups collect?​
True [87]

Answer:

The two groups collected 573.

Step-by-step explanation:

238

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4 years ago
Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid
Gnom [1K]

Answer:

The area of the triangle is A=\sqrt{\frac{4027}{2}}

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

A=\frac{1}{2}||{\bf u} \times {\bf v} ||

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

{\bf AB} and {\bf AC}

The vector {\bf AB} is the difference of point B minus point A

{\bf AB}=(5-3,5-5,0-9)=(2,0,-9)

and the vector {\bf AC} is the difference of point C minus point A

{\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)

Next we need to find the cross product of this vectors.

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

This is the definition of cross product of two vectors in space:

Let {\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k} and {\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k} be vectors in space. The cross product of {\bf u} and {\bf v} is the vector

{\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}

Applying this definition we get

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}

||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}

The area of the triangle is

A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}

7 0
4 years ago
What is: (x - 4)2 <br> Help
Marina86 [1]

Answer:

2x−8

Step-by-step explanation:

I will recommend you a website that is free, solves it for you and gives you a step by step explanation.

It is called MathPapa

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Y_Kistochka [10]

One side of the sandbox will be about 3.75 feet

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3 years ago
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