Evaluate the given equation for the indicated function values. pls help

Answer:

[tex]y =112[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find y

The attached triangle is isosceles; so:

[tex]x - 5=34[/tex]

Also, we have:

[tex]y + x - 5 + 34=180[/tex] --- angles in a triangle

Substitute: [tex]x - 5=34[/tex]

[tex]y + 34 + 34=180[/tex]

Collect like terms

[tex]y =- 34 - 34+180[/tex]

[tex]y =112[/tex]

Answer:

640

Step-by-step explanation:

pleas check my answer

Answer:

112

Step-by-step explanation:

If you add all the triangle faces and the square.

Answer:

6000

Step-by-step explanation:

7500x4/5=6000

or

7500/5=1500

1500x4=6000

Answer:

-3/2

Step-by-step explanation:

Additive inverse of 2 = -2

Multiplicative inverse of 2 = ½

→ Sum = -2 + ½

→ Sum = (-4 + 1)/2

→ Sum = -3/2

Answer:

if you put that equation into a graphing calculator the answer is 4188.37

Answer:

1 hour 56 minutes

Step-by-step explanation:

Given :

Time taken by Lucy = 3 hours 15 minutes = 3.25 hours

Time taken by brother = 4 hours 45 minutes = 4.75 hours

Rate = 1 / time taken

Lucy's rate = 1 / 3.25

Brother's rate = 1 / 4.75

Combined rate = Lucy's rate + brother's rate

Combined rate = 1/3.25 + 1/4.75

Combined rate = 0.5182186

Time taken if they work together = 1/ combined rate

= 1 / 0.5182186

= 1.9296 hours

= 1 hour (0.9296 * 60) minutes

= 1 hour 56 minutes (approximately)

Answer:

79

100

0.79%

76

100

0.76%

Answer:

[tex]252[/tex] cubic yards

Step-by-step explanation:

[tex]V=lwh[/tex]

Volume = length * width * height

[tex]V=7*4*9[/tex]

[tex]V=252[/tex]

Answer:

252 yd³

Step-by-step explanation:

Volume of rectangular prism = length * width * height

= 9 * 7 * 4 yd³

= 252 yd³

Answer:

5

Step-by-step explanation:

[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]

Answer:

false

Step-by-step explanation:

The function given in the table is a linear function:

f(x) = 3x+2

Answer:

Step-by-step explanation:

Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]

Answer:

[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]

Explanation is attached to the picture

Hope this helps you.

Answer:

1448

Step-by-step explanation:

24 × 63-64

Multiply 24 and 63 to get 1512.

1512-64

Subtract 64 from 1512 to get 1448.

answer

1448

Answer:

[tex]a \frac{x}{n} = \sqrt[n]{a}^x .

\sqrt[3]{x}^4 \sqrt[3]{y} \sqrt[5]{z}^2 [/tex]

Answer:

No , it is not a right angle triangle

Step-by-step explanation:

according to the pythagoras theorem in right angled triangle sum of square of two sides is equal to the square of it's hypotenuse.

using pythagoras theorem

a^2 + b^2 = c^2

9^2 + 16^2 = 25^2

81 + 256 = 625

337 = 625

since sum of square of two smallest sides of a triangle is not equal to the square of it's hypotenuse it can be concluded that the given figure does not form right angle triangle.

9514 1404 393

Answer:

  J. 2085

Step-by-step explanation:

Fill in the desired value for y and solve for x.

  1500 = 50(1.05^x)

  30 = 1.05^x . . . . . . . divide by 50

  log(30) = x·log(1.05) . . . . . take logarithms

  x = log(30)/log(1.05) ≈ 69.71

Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.

Answer: A

Step-by-step explanation:

Step-by-step explanation:

the answer is in the above image

Answer:

314.2 cubic meters

Step-by-step explanation:

Volume of cone = 1/3 × pi × radius² × height

To find the radius we divide the diameter by two = 5 inches

1 × 3.142 × 25 × 12

               3

Ans= 314.2 cubic meters

I hope this helps u

Answer:

split the other three in half

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The product of the slopes of  and the line perpendicular to  through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.

Step-by-step explanation:

its correct

Answer:

N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)

Step-by-step explanation:

To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.

The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the square be represented as KLMN

Now , the coordinates of the square KLMN is

K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )

Now , let the translated square be represented as K'L'M'N'

When translating the square to three units to the left , the x coordinate of the square gets reduced by 3

So , the new coordinate of the square will be ( x - 3 , y )

Substituting the values in the equation , we get

K' = K ( -5 - 3 , 3 )

L' = L ( 1 - 3 , 3 )

M' = M ( 1 - 3 , 9 )

N' = N ( -5 - 3 , 9 )

So , on simplifying the equation , we get

The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )

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Answer:

The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]

Step-by-step explanation:

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.

At the null hypothesis, we test if the mean is of 8 hours, that is:

[tex]H_0: \mu = 8[/tex]

At the alternative hypothesis, we test if the mean is different of 8 hours, that is:

[tex]H_1: \mu \neq 8[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

8 is tested at the null hypothesis:

This means that [tex]\mu = 8[/tex]

From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.

This means that [tex]n = 101, X = 7.3, s = 2.6[/tex]

What is the t-statistic that Jacob calculates?

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]

[tex]t = -2.71[/tex]

The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]

The solution of the inequality will be;

⇒ x ≤ 9

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 15 + x ≤ 24

Now,

Since, The inequality is,

⇒ 15 + x ≤ 24

Solve the inequality as;

⇒ 15 + x ≤ 24

Subtract 15, we get;

⇒ 15 + x - 15 ≤ 24 - 15

⇒ x ≤ 9

Thus, The solution of the inequality will be;

⇒ x ≤ 9

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Answer:

C. reflection across the x-axis, translation 6 units left

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

[tex]a=b=c=0,p=5[/tex]

That is, the equation of the sphere in cartesian coordinates is,

[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]

[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]

Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]

The relation between cartesian and cylindrical coordinates is given by,

[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]

[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

[tex]r^{2}+z^{2}=25[/tex]

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]

Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,

[tex]x^{2}+y^{2}=1[/tex]

Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]

The relation between cartesian and spherical coordinates is given by,

[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])

Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.

Thus, we can square root both sides and only consider the positive root as,

[tex]\Rightarrow \rho sin\phi=1[/tex]

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]

(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]

Answer:

[tex](f+g)(x) = x^2 + 4x - 4[/tex]

Step-by-step explanation:

We are given these following functions:

[tex]f(x) = 4x + 2[/tex]

[tex]g(x) = x^2 - 6[/tex]

(f+g)(x)

We add the common terms. Thus:

[tex](f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4[/tex]

Thus:

[tex](f+g)(x) = x^2 + 4x - 4[/tex]

Answer:

3a)1680

b)2620

4a)2130

b)13300

c)460

d)7540

Step-by-step explanation:

3a)1500+180

b)2800-170

4a)1800+330

b)7300+6000

c)670-210

d)8000-460

Answer:

a) 1600

b) 2600

c) 2200

d) 13200

e) 500

Step-by-step explanation:

a) 1463 + 179

1400 + 200

1600

b) 2806 - 176

2800 - 200

2600

c) 1831 + 329

1900 + 300

2200

d) 7345 + 5893

7300 + 5900

13200

e) 665 - 213

700 - 200

500

Answer:

17degrees

Step-by-step explanation:

The sum of two supplementary angles is equation 180degrees. Hence:

5x+95 = 180

5x = 180-95

5x = 85

x = 85/5

x = 17

Hence the value of x is 17

Answer:

60 kg of 40% and 90 kg of 60%

Step-by-step explanation:

Let the amount of 40% chocolate be x.

Let the amount of 60% chocolate be y.

x + y = 150

0.4x + 0.6y = 0.52 * 150

x + y = 150

4x + 6y = 780

     -4x - 4y = -600

(+)   4x + 6y = 780

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

               2y = 180

y = 90

x + y = 150

x + 90 = 150

x = 60

Answer: 60 kg of 40% and 90 kg of 60%

Answer:

Miguel's account

Step-by-step explanation:

Miguel's account savings are doubled every month. Hence, they will eventually surpass the savings of Anita, even though Anita's account has more money atm.

Answer:

Miguel's account

Step-by-step explanation:

Even though Anita had more money at first compared to Miguel, Miguel savings will double each month while Anita will get only $200 each month. As a result, Miguel's account will grow faster compared to Anita's.