Which of the following are best described as lines that meet to form a right
angle?
A. Parallel lines
B. Lines that are coplanar
C. Perpendicular lines
D. Intersecting lines

Let y = x + 22 and dy = dx, so the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]

Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]

Expand the integrand into partial fractions:

[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]

Then we have

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]

Answer:

I believe it is 2/5 fraction

Answer:

-2/5

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 18-8)/(-15-10)

    = 10/-25

   = -2/5

Answer:

16818165

Step-by-step explanation:

12 guests equal 555 liters

total guests 363636

divide 363636 by 12

result is 30303

multiply 30303 times 555

total is 16818165

Answer:

C

Step-by-step explanation:

[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]

Answer:

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Step-by-step explanation:

The point estimate is the sample proportion.

Sample proportion:

103 out of 249, so:

[tex]p = \frac{103}{249} = 0.4137[/tex]

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Answer:

2x, a linear pair

Step-by-step explanation:

2/5x/3/4 = 7/4 = 1 3/4

Answer: (x+4) ( x-4i)(x+4i)

Discussion:

Factor the polynomial:

x^3+4x^2+16x+64 =  (x +4 ) ( x^2 + 16)     (*)

Factor x^2 +1 6 over the complex numbers:

x^2 + 16 = (x -4i)(x+4i)                               (**)

Combing (*) and (**) gives the full factorization

(x+4) ( x-4i)(x+4i)

Answer:

c

Step-by-step explanation:

cheese is rotten milk

Answer:

The ocean absorbs heat energy from the sun

Step-by-step explanation:

Yw :)

Answer:

The ocean absorbs heat energy from the sun.

Step-by-step explanation:

Answer:

[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{128x^8y^3}[/tex] --- the complete expression

Required

The equivalent expression

We have:

[tex]\sqrt{128x^8y^3}[/tex]

Expand

[tex]\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}[/tex]

Further expand

[tex]\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}[/tex]

Rewrite as:

[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}[/tex]

Split

[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}[/tex]

Express as:

[tex]\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}[/tex]

Remove bracket

[tex]\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}[/tex]

[tex]\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}[/tex]

[tex]\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}[/tex]

[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]

Answer:

1. 24

2. 4.444... (or 4 rounded to the nearest whole number)

Step-by-step explanation:

1. 80/100 = x/30

cross-multiply

100 × x = 100x

80 × 30 = 2400

divide

100x/100 = x

2400/100 = 24

answer

x = 24

2. 90/100 = 4/x

cross-multiply

90 × x = 90x

100 × 4 = 400

divide

90x/90 = x

400/90 = 4.444...

answer

x = 4.444...

Answer:

B

Step-by-step explanation:

side Ac is the opposite of angle B, therefore use the sin ratio to find ac since the hypotenuse is also given

sin B=opposite/hypotenuse

sin 27=ac/15

ac=sin27×15

=6.81

I hope this helps

Answer:

AC = 6.81

Step-by-step explanation:

∠BAC = 90° - 27° = 63°

Cos 63° =[tex]\frac{AC}{AB}[/tex] = 0.454

AC = cos 63° * AB = 0,454 * 15 = 6.81

Answer:

34.5p-2.75

Step-by-step explanation:

First add -0.5p and 12p together which is 11.5p, then add 23p with 11.5p which is 34.5p And -2.75 remains the same

So the answer is 34.5p-2.75

Answer:

34.5p-2.75

Step-by-step explanation:

-0.5p+12p-2.75+23p=34.5p-2.75

Answer:

0.25 = 25% probability that the two brothers will end up in the starting line up

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

Matthew plus another forward from a set of 3.

Tony plus another two guards from a set of 5.

So

[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]

Total outcomes:

Two forwards from a set of 4.

Three guards from a set of 6.

So

[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]

What is the probability that the two brothers will end up in the starting line up?

[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]

0.25 = 25% probability that the two brothers will end up in the starting line up

Answer:

This question is mainly about pythagorean theorm as if we just analyse this question we see the information given to us are

Now it is said to find out the length of ladder as because the ladder is resting against the buiding so it will generally form an acute angle with the ground and as we can take the ladder to be as the hypotenuse of a right angled triangle in which the length of the perpendicular building forms one of the leg and the distance of the building from the point where the ladder is kept is said to be another leg

Now we get the measure of the vertical leg = height of the buiding = 11 ft

and another leg = distance in between the fence and the point on which the ladder is kept + the distance in between the fence and building

= (8+1)ft =9ft

Now we know hypotenuse = √base^2+√height^2

= √9^2+√11^2

= √81+√121

= √ 202

= 14.21 ft

Therefore the length of the ladder = 14.21 ft

Hope it helps you

The length of the ladder should be 11.1 feet long.

Let's denote the length of the ladder as L.

According to the given information:

The distance from the building to the fence = 1 ft.

The height of the window = 11 ft.

The distance from the ladder to the fence = 8 ft.

Using the Pythagorean theorem, we can set up the equation:

[tex]L^2 = (1^2) + (11^2)[/tex]

Simplifying:

[tex]L^2 = 1 + 121[/tex]

[tex]L^2 = 122[/tex]

Taking the square root of both sides:

[tex]L = \sqrt{122}[/tex]

[tex]L = 11.05 ft[/tex]

Therefore, the worker will need a ladder approximately 11.1 feet long.

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Answer:

(4−3i)x^2

=4x^2 - 3ix^2

Answer:

Step-by-step explanation:

Mean: sum of terms/ number of terms

4 + 2 + 3 + 1 + 1 + 5  = 16

Numbr of terms = 6

16/6 = 2.66

Answered by g a u t h m a th

Answer:

2 2/3

Step-by-step explanation:

The mean is the average of the values

The values on the graph are 4, 2, 3, 1, 1, and 5

Average is sum/number of values

4+2+3+1+1+5=16

16/6=2 2/3

Answer:

x = 10

Step-by-step explanation:

[tex]x = 3 \times 2 + 4[/tex]

[tex]x = 6 + 4[/tex]

[tex]x = 10[/tex]

Answer:

22

Step-by-step explanation:

(5x2) + (3x2) + (3x2)

22 square units

Answer from Gauthmath

Here we have the quadratic function:

f(x) = -16*x^2 + 60*x + 16

We can see that it is in standard form:

y = a*x^2 + b*x + c

a) First we want to completely factorize the function f(x).

To do it, we first need to find the roots of f(x).

Remember that for a generic quadratic equation:

a*x^2 + b*x + c = 0

whit roots x₁ and x₂, the factorized form is:

a*(x - x₁)*(x - x₂)

And the roots are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:

[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]

So the two roots are:

x₁ = (-60 + 68)/-32 = -0.25

x₂ = (-60 - 68)/-32 = 4

Then the factorized form is:

f(x) = -16*(x - 4)*(x + 0.25)

B) We already found the roots, which are:

x₁ =  -0.25

x₂ =  4

These are the x-intercepts:

(-0.25, 0) and (4, 0)

C) We can see that the leading coefficient is negative.

This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.

D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.

If you want to learn more about this topic, you can read:

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Answer:

327680

Step-by-step explanation:

The general formula of the formula for the sequence is 5*(-4)^(n-1). The 9th term will be 5*(-4)^8=327680

The actual labor cost is $600 over the targeted labor cost.

Given that,

Work done by each person per week = 40 hours

Required labor hours per week = 600 hours

No. of workers in the team = 13

To find,

Actual weekly labor cost = ?

Procedure:

Actual weekly labor cost = No. of workers * no. of hours performed by them

[tex]= 13 * 40[/tex]

[tex]= 520 hours[/tex]

Given that,

[tex]Regular rate = $ 15.00 per hour[/tex]

[tex]Overtime rate = $ 22.50 per hour[/tex]

Thus,

Actual labor cost = (regular hours worked * regular rate) + (overtime * overtime rate)

[tex]= (520 * 15) + ([600 - 520] * 22.50)[/tex]

[tex]= $ 7,800 + $ 1,800[/tex]

[tex]= $ 9600[/tex]

Targeted Labor cost = $ 9,000 per week

Thus, option C i.e. the actual labor cost is $ 600 over the targeted labor cost.

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Answer:

40 years old

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]

[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]

[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]

[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]

[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]

[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]

[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]

[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

[tex] {4x}^{2} (x + 1) - 6x(x + 1) \\ = (x + 1)(4 {x}^{2} - 6 x ) \\ = (x + 1)(2x)(2x - 3)[/tex]

explanation:

first choose the common factor by observation, it is (x + 1):

factorise it out:

= (x + 1)(4x² - 6x)

by observation in (4x² - 6x), common factor is 2x.

Factorise 2x out:

= (x + 1)[2x(2x - 3)]

Answer:

(4x2-6x) (x+1)

now common factor is (x+1) ,so,(4x2-6x) (x+1)

Answer: Yes you are correct. The answer is choice A

============================================================

Explanation:

If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.

So by symmetry, P(Z > -1) = 0.84 approximately as well.

We'll convert the z score z = -1 into its corresponding x score

z = (x-mu)/sigma

-1 = (x-180)/15

-15 = x-180

x-180 = -15

x = -15+180

x = 165

We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.

I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.

Answer:

194.9

Step-by-step explanation:

ON EDG

9514 1404 393

Answer:

  90°, 60°, 30°

Step-by-step explanation:

The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.

The first angle is 3 ratio units, or 90°.

The second angle is 2 ratio units, or 60°.

The third angle is half that, or 30°.

The three angles are 90°, 60°, 30°.

Answer:

((c)).g(x) = 3 × 2^x +2..