Examine the diagram of circle C.

amanda ran 4 laps around the school track. Clifford ran half as many laps as brian ran. Together the 3 friends ran 13 laps. How

Mariulka [41]

Answer: 6 laps

Step-by-step explanation:

13 - 4= 9 left 6 and half would be three

7 0

3 years ago

A sphere rolls up an inclined plane of inclination angle 30 degree. At the bottom of the incline the center of mass of the spher

Zigmanuir [339]

Answer: The sphere is 0.002548 cm travel up the plane.

Step-by-step explanation:

Since we have given that

Inclination angle = 30°

Translational speed = 0.25 m/s

As we know that

$KE=0.5\times lw^2=PE$

and

Length of solid sphere is given by

$l=\dfrac{2Mr^2}{5}$

So, it becomes,

$KE=0.5\times \dfrac{2Mr^2}{5}w^2=Mgd\sin \theta$

And $0.25\ m/sv=rw$

So, it becomes,

$1\times (0.25)^2=5\times d\times 9.81\times \sin 30^\circ\\\\0.0625=49.05d\times \dfrac{1}{2}\\\\\dfrac{0.125}{49.05}=d\\\\d=0.002548$

Hence, the sphere is 0.002548 cm travel up the plane.

5 0

4 years ago

Find the measure of ZM

vfiekz [6]

the answer is

In AKLM, the measure of ZM=90°

7 0

3 years ago

Explain why the equation 5(2x+1)-2=6x+5 has only one solution. Then find the solution.

netineya [11]

Answer:

10x + 3 = 6x + 5

Based on this, we have the lines y=10x+3 and y=6x+5. Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.

Solution:

x = 1/2

y = 8

(1/2 , 8)

Step-by-step explanation:

Start by expanding with the distributive property, then simplify by collecting like terms.

5(2x + 1) - 2 = 6x + 5 Multiply "5" with each term in the brackets.

10x + 5 - 2 = 6x + 5 Collect left side's like terms (5 - 2 = 3)

10x + 3 = 6x + 5

Based on this, we have the lines <u>y=10x+3 and y=6x+5</u>. A solution is the same as the POI (point of intersection). Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.

Some linear systems might have no solutions (when the lines are parallel) or infinite solutions (when the lines are equivalent, the same).

To find the solution, continue with the equation and isolate "x". This will give you the x-coordinate of the point of intersection.

To isolate 'x', move everything to the other side of 'x'. To move something, you do its reverse operation to both sides in reverse BEDMAS order.

10x + 3 = 6x + 5

10x - 6x + 3 = 6x - 6x + 5 Subtract 6x from both sides

4x + 3 = 5 "6x" cancelled out on the right. Simplified left (10x-6x=4x)

4x + 3 - 3 = 5 - 3 Subtract 3 on both sides. "3" on the left will cancel out

4x = 2 The right side was simplified (5 - 3 = 2).

4x/4 = 2/4 Divide both sides by 4 to isolate 'x'. Simplify right side.

x = 1/2 Solution's x-coordinate

Substitute what you found for 'x' into any equation that has 'y' (either <u>y=10x+3 or y=6x+5</u>). I will choose the first equation.

y = 10x + 3

y = 10(1/2) + 3 Multiply 1/2 and 10

y = 5 + 3 Add

y = 8 Solution's y-coordinate

Therefore the solution is when x=1/2 and y=8, or as an ordered pair, (1/2 , 8).

8 0

3 years ago

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, an

Ratling [72]

Answer:

The first graph picture

Step-by-step explanation:

A polynomials is an equation with many terms whose leading term is the highest exponent known as degree. The degree or exponent tells how many roots exist. These roots are the x-intercepts.

This polynomial has roots -3, 0, 1, and 3. This means the graph must touch or cross through the x-axis at these x-values. What determines if it crosses the x-axis or the simple touch it and bounce back? The even or odd multiplicity - how many times the root occurs.

In this polynomial:

Root -3 has even multiplicity of 2 so it only touches and does not cross through.

Root 0 has odd multiplicity of 1 so crosses through.

Root 1 has odd multiplicity of 1 so crosses through.

Root 3 has even multiplicity of 3 so it only touches and does not cross through.

Knowing this, only the first and second graphs are possible answers.

Lastly, what determines the facing of the graph (up or down) is the leading coefficient. If positive, the graph ends point up. If negative, the graph ends point down. All even degree graphs will have this shape.

Only graph 1 matches the features of this polynomial.

8 0

3 years ago

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