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2 years ago

How many solutions does this equation have? 6x+5=4x+5

Mathematics

1 answer:

Travka [436]2 years ago

3 0

$:\implies \sf 6x +5 = 4x +5$

$: \implies \sf 6x +5 -4x = 5$

$:\implies \sf 2x = 5-5$

$:\implies \sf 2x = 0$

$:\implies \sf x = 0$

Seems like "6x+5=4x+5" has only one solution that's 0.

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Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

3 years ago

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

TiliK225 [7]

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

$(x-2)\\ (x-3)\\ (x-5)$

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

$x=2\\ x=3\\ x=5$

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

$(x-2)*(x-3)*(x-5)=0\\ (x^{2} -3x-2x+6)*(x-5)=0\\ (x^{2} -5x+6)*(x-5)=0\\ x^{3} -5x^{2} -5x^{2} +25x+6x-30=0\\ x^{3}-10x^{2} +31x-30=0$

therefore

the answer Part b) is

the cubic polynomial function is equal to

$x^{3}-10x^{2} +31x-30=0$

7 0

3 years ago

Read 2 more answers

What side is the shortest in the picture? A. GF B. DG C. EF D. GE F. DE

igor_vitrenko [27]

Answer:

A. GF

Step-by-step explanation:

The shortest side in a triangle is opposite the smallest angle

<d = 180 -52 -61 =67

The smallest angle is 52 so the smallest side is DG

<f = 180 - 48-85 =50

The smallest angle is 48 so the smallest side is FG

The smallest angle is 48 so the smallest side overall is FG (GF)

4 0

3 years ago

HELP PLEASE REEEEEEEEEEEE!! Note: Enter your answer and show all the steps that you use to solve this problem in the space provi

Fynjy0 [20]

Answer:

Step-by-step explanation:

480 = 100%

72 = ? you can find it doing (72(100))/480

72(100)= 7200

7200/480= 15

the answer is 15%

have a nice day :)

8 0

3 years ago

∠A and \angle B∠B are complementary angles. If m\angle A=(8x-28)^{\circ}∠A=(8x−28) and measure of angle B=(8x+22) ∠B=(8x+22) ,th

Afina-wow [57]

Answer:

Step-by-step explanation:

Basically we want to find x and then plug that in for angle B. How do we find x? Well, we know the angles are complimentary, which means theya dd to 90, so let's start with that.

A + B = 90

8x - 28 + 8x + 22 = 90

16x -6 = 90

16x = 96

x = 6

So there we go. Now to find B

8x+22

8(6)+22

48 + 22

3 0

3 years ago