HELP. Use the grouping method to factor the polynomial below completely.
x^3 – 5x^2 + 3x - 15
A. (x^2 + 5)(x-3)
B. (x^2 - 3)(x+5)
C. (x^2 - 5)(x+3)
D. (x^2 + 3)(x - 5)

Step-by-step explanation:

At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.

Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.

Then that's your answer.

9514 1404 393

Answer:

  544 square units

Step-by-step explanation:

The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...

  A = 1/2bh . . . . area of a triangle with base b and height h

  A = LW . . . . . are of a rectangle of length L and width W

__

  SA = 2(1/2)(12)(8) + (10 +10 +12)(14)

  SA = 96 +448 = 544 . . . square units

Answer:

B

Step-by-step explanation:

hope it is well understood

Answer:

15.5⁰ or approximately 16⁰

Step-by-step explanation:

let unknown side be x

cos x= 53/55

cos x= 0.9636

x=cos inverse of 0.9636

x=15.5⁰

Answer:

[tex]cosx = \frac{53}{55} \\ x = {cos}^{ - 1} ( \frac{53}{55} ) \\ x = 15.4987[/tex]

Answer:

155 women must be randomly selected.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation is known to be 28 lbs.

This means that [tex]\sigma = 28[/tex]

We want 90% confidence that the sample mean is within 3.7 lbs of the populations mean. How many women must be sampled?

This is n for which M = 3.7. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]3.7 = 1.645\frac{28}{\sqrt{n}}[/tex]

[tex]3.7\sqrt{n} = 1.645*28[/tex]

[tex]\sqrt{n} = \frac{1.645*28}{3.7}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*28}{3.7})^2[/tex]

[tex]n = 154.97[/tex]

Rounding up:

155 women must be randomly selected.

Answer:

a

Step-by-step explanation:

Answer:

I really can't read this

Step-by-step explanation:

if the formula is [tex]\frac{(B+b)}{2} .h[/tex] we just need to plug in the values

21/2 = 10.5 x 5 = 52.5

hope it helps :)

Answer:

A = 52.5 in^2

Step-by-step explanation:

The area of a trapezoid is

A = 1/2 (b1+b2)h

where b1 and b2 are the bases and h is the height

A = 1/2 ( 14+7)*5

A = 105/2

A = 52.5 in^2

Answer:

Let's assume the number be 100.

According to the problem , 100 is increased by 100%.

So, new number will be 100+100=200

Now 200 will decreased by 20%.

So, 20% of 200= 0.20*200= 40.

So, again the number has been changed into 200+40=240.

So, x=240

Step-by-step explanation:

9514 1404 393

Answer:

  x/1.6

Step-by-step explanation:

Let n represent the number. When n is increased by 100%, its new value is ...

  n(1 +100%) = n(1 +1) = 2n

When this value is decreased by 20%, its new value is ...

  (2n)(1 -20%) = (2n)(0.8) = 1.6n

This value is x, so the number is ...

  1.6n = x

  n = x/1.6 . . . . . . . divide both sides by 1.6

Answer:

954 passengers

Step-by-step explanation:

(Assuming I read the question correctly)

1 bus can carry in 1 trip = 53 passengers

1 bus can carry in 2 trips : 106 passsengers

9 busses can carry in 2 trips = 106 x 9 = 954

Answred by Gauthmath

Answer:

A

Step-by-step explanation:

They are different exponents but they have the same bas so you add them up.

4x^5+3 = 4x^8

[tex] \pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: as \: we \: know \: that \\ \\ \bf\: \: \rightarrow \: {(xy)}^{n} = {x}^{n} . {y}^{n} \\ \\ \bf \rightarrow \: {( {a}^{m} })^{n} = {a}^{m \times n} \\ \\ \bf \: now \\ \: \\ \blue{ {\boxed{\begin{array}{cc} \maltese \bf\: \: \: {(4 {x}^{5} })^{3} \\ \bf = {4}^{3} \times ({x}^{5} )^{3} \\ \bf = {4}^{3} \times {x}^{5 \times 3} \end{array}}}}\end{array}}}}[/tex]

So option D) is the correct answer

Answer:

[tex]c =\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Required

Shorten

We have:

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Rationalize

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]

Expand

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]

Take positive square roots

[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]

Take LCM

[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]

Collect like terms

[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]

[tex]c =\frac{8}{3}[/tex]

I strongly believe the answer is 2, if it isnt that it must be 3.

"Rotated around the origin", as the question actually says, puts it in Quadrant-II (2).

But the way you put the question, just saying the triangle is rotated 90°, leaves it right where it is, in Quadrant-I, with vertex-H on the bottom.

Answer:

VW ≈ 4.0

Step-by-step explanation:

Using the sine ratio in the right triangle

sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{VW}{VX}[/tex] = [tex]\frac{VW}{7}[/tex] ( multiply both sides by 7 )

7 × sin35° = VW , then

VW ≈ 4.0 ( to the nearest tenth )

Answer:

x + (4/ x-2) + (2/ x-1)

Step-by-step explanation:

x + (6x/ x^2 + 2x - x -2)

x + (6x/ (x + 2) X (x - 1))

(6x/ (x + 2) X (x - 1))

(A/ x+2) + (B/ x-1)

(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)

6x = Ax + Bx - A + 2B

6x = (A+B)x + (-A+2b)

{0 = -A+2B

{6 = A+B

(A,B) = (4, 2)

(4/ x+2) + (2/ x-1)

x + (4/ x-2) + (2/ x-1)

Answer:

Step-by-step explanation:

Answer:

Option B, 1

Step-by-step explanation:

tan 45° = 1/1 = 1

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the hypotenuse. Therefore, we should use the sine function.

sin(54) = 16/AB

AB = 16/sin(54)

AB = 19.78 units

Hope this helps!

Answer:

The expected flight time is 2 hours 10 minutes

Step-by-step explanation:

Given

[tex]a = 2\ hours[/tex]

[tex]b = 2\ hours\ 20\ mins[/tex]

Required

The expected flight time

To do this, we simply calculate the mean using:

[tex]Mean = \frac{a + b}{2}[/tex]

So, we have:

[tex]Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}[/tex]

[tex]Mean = \frac{4\ hours\ 20\ mins}{2}[/tex]

[tex]Mean = 2\ hours\ 10\ mins[/tex]

Answer:

the ratio of lengths of the two rods, Aluminum to Invar is 11.27

Step-by-step explanation:

coefficient of linear expansion of aluminum, [tex]\alpha _{Al} = 23 \times 10^{-6} /K[/tex]

Coefficient of linear expansion of Invar, [tex]\alpha _{Iv} = 1.2 \times 10^{-6}/K[/tex]

Linear thermal expansion is given as;

[tex]\Delta L = L_0 \times \alpha\times \Delta T\\\\where;\\\\L_0 \ is \ the \ original \ length \ of \ the \ metal\\\\\Delta L \ is \ the \ increase \ in \ length[/tex]

The increase in length of Invar is given as;

[tex]\Delta L_{Iv} = L_0_{Iv} \times \alpha _{Iv}\times \Delta T_{Iv}[/tex]

The increase in length of the Aluminum;

[tex]\Delta L_{ Al} = L_0_{Al} \times \alpha _{Al} \times \Delta T_{Al}\\\\from \ the\ given \ question, \ the \ relationship \ between \ the \ rods \ is \ given \ as\\\\ L_0_{Al} \times \alpha _{Al} \times \frac{1}{3} \Delta T_{Iv}= 2( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv}= 6( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv} = 6L_0_{Iv} \times 6\alpha _{Iv} \times 6 \Delta T_{Iv}\\\\[/tex]

[tex]\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6 \Delta T_{Iv}}{\alpha _{Al} \ \times \ \Delta T_{Iv}} \\\\\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6}{\alpha _{Al} \ } \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{\alpha _{Iv} }{\alpha _{Al} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2 \times 10^{-6} }{23\times 10^{-6} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2}{23} )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = \frac{259.2}{23} \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 11.27[/tex]

Therefore, the ratio of lengths of the two rods, Aluminum to Invar is 11.27

The ratio of the lengths of the two rods which is length of aluminum to length of Invar rod is; 11.27

Formula for linear thermal expansion is;

ΔL = L × α × ΔT

Where;

ΔL is change in original length

L is original length

α is coefficient of linear expansion

ΔT is change in temperature

We are told that increase in length of aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase.

Thus;

ΔL = 2ΔL

ΔT for the aluminum rod = ⅓ΔT for the Invar rod.

Thus, we have;

L_al × α_al × ⅓ΔT = 2L_in × 2α_in × 2ΔT

ΔT will cancel out to give;

⅓(L_al × α_al) = 2L_in × 2α_in × 2

Multiply both sides by 3 to get;

(L_al × α_al) = 6L_in × 6α_in × 6

From online tables, the linear coefficient of expansion of aluminum is 23 × 10^(-6) C¯¹

While the coefficient of thermal expansion for Invar rod is 1.2 × 10^(-6) K¯¹

Thus;

L_al × 23 × 10^(-6) = 6L_in × (6 × 1.2 × 10^(-6)) × 6

L_al/L_in = (6 × 6 × 1.2 × 10^(-6) × 6)/(23 × 10^(-6))

L_al/L_in = 11.27

Read more on coefficient of linear expansion at; https://brainly.com/question/6985348

Step-by-step explanation:

Excuse me! Who r u? where r u frm? tell me tht frst.

Answer:

Oop

Step-by-step explanation:

I’m bored

Answer:

a. In first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on subjects.

Step-by-step explanation:

In the first study, observation are made on 300 adults who eat 3 servings of vegetables a day on average. The second study has further intensified the research which imposed treatment on the subjects. The random samples of adults are observed in both studies.

Answer:

Step-by-step explanation:

If the 2s are exponents, you need to indicate this with "^":  

x^2 = 144^2 means x² = 144²

x = ±√144² = ±144

Answer:

Step-by-step explanation:

f the 2s are exponents, you need to indicate this with "^":  

x^2 = 144^2 means x² = 144²

x = ±√144² = ±144

c.write the fact,organize your thoughts and define your strategy.

Answer:

c

Step-by-step explanation:

Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.

BA / ED = AC / CD

42 / 6 = (64 - x) / (x)

6(64 - x) = 42(x)

384 - 6x = 42x

384 = 48x

x = 8

Hope this helps!