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3 years ago

Suppose y varies directly with x. When x is 2, y is 20. What is x when y is 50

Mathematics

1 answer:

yuradex [85]3 years ago

5 0

Answer:

Step-by-step explanation:

x = 2 >>> (Multiply by 10) >>> y = 20

x = ? >>> (Multiply by 10) >>> y = 50

50 ÷ 10 = 5

x = 5 when y is 50

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A jellyfish travels 3/5 mile in 1/6 hour and a walrus travels 5/6 mile in 3/10 hour.

emmasim [6.3K]

Answer:

The jellyfish travels faster than the walrus

Step-by-step explanation:

Given data

A jellyfish travels 3/5 mile in 1/6 hour

Distance= 3/5 mile

time= 1/6 hour

speed= distance/time

speed= 3/5/1/6

speed= 3/5*6/1

speed= 18 mile per hour

a walrus travels 5/6 mile in 3/10 hour.

Distance= 5/6 mile

time= 3/10 hour.

speed= distance/time

speed= 5/6/3/10

speed= 5/6*10/3

speed= 50/18 mile per hour

3 0

3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term $2x^2$ , which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression:

$x_v=\frac{-b}{2a}$

Since in our case $a=2$ and $b=-3$ , we get that the x-position of the vertex is:

$x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

$y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}$

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

$f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6$

See the graph produced in the attached image.

4 0

3 years ago

Two dice are rolled. What is the probability of getting a sum equals 5?

Ugo [173]

Ruuehshsnsnybsby. Xhdjdjsnsjjejsbx dhdjidsnbdbd hdhdhdbdsh

3 0

2 years ago

Find the Perimeter & Area for the following circle.

Feliz [49]

Answer:

A = 28.3 cubic inches; P = 20.1 inches

Step-by-step explanation:

Looks like 3/4 of a full circle

The area of a circle is calculated with the formula: $\pi r^{2}$

Since the problem wants pi = 3.14, we use 3.14 instead of pi in the equation.

The radius is given as 3 inches

Area = $3.14*3^{2} = 3.14*9 = 28.26$ cubic inches = 28.3 cubic inches

------------------------

Perimeter is calculated with $2\pi r$ .

But this is 3/4 of a circle with an additional two 3-inch sides

Perimeter = $\frac{3}{4}*2\pi r$ + 2(3) = 14.1 + 6 = 20.1 inches

6 0

3 years ago

Read 2 more answers

Find the surface area of a square prism with a side measure of 6.

Vesnalui [34]

The surface area of any solid is the summation of all the areas of its faces. For a square prism, the surface area is therefore calculated through the equation,
A = 6e²
where A is area and e is the measure of the side.

From the given above, it is stated that the edge of the prism measures 6. Substituting this value to the equation above,
A = (6)(6²)
A = 216
Therefore, the surface area of the given prism is equal to 216 square units.

3 0

3 years ago