One angle of a right triangle measures 60°. The side opposite this angle measures 21 inches.

What is the length of the hypotenuse of the triangle?

Enter your answer, in simplest radical form, in the box.

Answer:

Step-by-step explanation:

Notice that the dividend has tree terms with , , c

Now, to divided our dividend by the monomial (single term) , the easiest thing to do is divide each term of the dividend by the monomial:

÷ =

After performing the division we get that now and

We can conclude that the correct answer is a = 2y and b = –3

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = 2x - 1 ← equation of line

Answer:

The answer is -8/3.

Step-by-step explanation:

First, you have to make y the subject :

8x + 3y = 9

3y = -8x + 9

y = (-8/3)x + 3

In a linear equation, y = mx + b, m represent gradient (slope). So in this equation the slope is -8/3.

Answer: true

Step-by-step explanation:

Answer:

it is A

Step-by-step explanation:

i remember doing this in middle school.

Step-by-step explanation:

\( \frac{3}{2} + \frac{x}{3} = \frac{11}{6} \)

\( \frac{x}{3} = \frac{11}{6} - \frac{3}{2} \)

\( \frac{x}{3} = \frac{11 - 3 \times 3}{6} \)

\( \frac{x}{3} = \frac{11 - 9}{6} \)

\( \frac{x}{3} = \frac{2}{6} \)

\( \frac{x}{3} = \frac{1}{3} \)

\(x = \frac{3 \times 1}{3} \)

\(x = 1\)

Answer:

x = 1

Step-by-step explanation:

3/ 2 + x/ 3 = 11/ 6

taking LCM

(9 + 2x)/ 6 = 11/ 6

multpiying both sides by 6

9 + 2x = 11

subtracting btih sides by 9

2x = 11 - 9

2x = 2

dividing both by 2

x = 1

Answer:

it takes 3 days for the crew to make one house

The sum of the first 7 terms of the series −8 16−32 64−... is 1,016.

The given series is an alternating geometric series with a first term of -8 and a common ratio of -2.

To find the sum of the first 7 terms, we can use the formula for the sum of an alternating geometric series:

S = a(1 - rⁿ) / (1 + r)

where:

S is the sum of the series,

a is the first term,

r is the common ratio,

and n is the number of terms.

In this case, a = -8, r = -2, and n = 7.

Plugging in the values:

S = (-8)(1 - (-2)⁷) / (1 + (-2))

= (-8)(1 - 128) / (-1)

= (-8)(-127) / (-1)

= 1016

Therefore, the sum of the first 7 terms of the series is 1016.

To learn more about geometric series

https://brainly.com/question/15415793

#SPJ11

Step-by-step explanation:

Isolate x.

7

−

8

x

>

19

−

7

Add

7

to

−

7

to cancel it out because it is the lowest number here.

But you do to one side what you do to the other, so add

7

to the positive

7

on the other side. You should now have:

14

−

8

x

>

19

Now, subtract

14

from

14

to cancel it out and do the same to the other side

(

19

)

. Now, you should have:

−

8

x

>

5

Now, to isolate

x

,

divide by

−

8

.

But remember when you divide or multiply an inequality by a negative value, the sign changes around.

−

8

x

−

8

<

5

−

8

Because you divided by a negative, the sign flips:

x

<

−

5

8

Answer:  x \(\geq\) -5

Step-by-step explanation:

-3x - 7 \(\leq\) 8

add 7 to both sides

-3x \(\leq\) 15

divide both sides by -3, you also have to flip the inequality sign because you are dividing by a negative.

x \(\geq\) -5

In ΔRST, the measure of ∠T=90°, the measure of ∠R=29°, and ST = 6.7 feet. Find the length of TR to the nearest tenth of a foot.

We will draw the rectangle triangle:

We can use the trigonometry property where the sine of an angle (∠R) is equal to the ratio between the opposite side (ST) and the hypotenuse (RS).

Also, the cosine of ∠R is equal to the ratio between the adyacent side (RT) and the hypotenuse (RS).

We can express this as:

The length of TR is 12 feet.

Answer:

5(3)² - 4

5x9-4

the answer is 41

Answer:

41

Step-by-step explanation:

5(9) - 4

45-4

41

Answer:

d

Step-by-step explanation:

The simplified value of the triple integral \(\int{\int{ \int{(xyz/18) },dz }\,dy}\, dx\) over the given limits of integration is 1/324.

The coordinates of the center of mass of the solid can be found using the triple integral formula for the center of mass. Given the density function p(x, y, z) = xyz/18, we can determine the coordinates (\(x^-, y^-, z^-\)). of the center of mass using the following formulas:

\(x^- = (1/M) \int{\int{ \int{x p(x,y,z) } }}\, dV\\y^- = (1/M) \int{\int{ \int{y p(x,y,z) } }}\, dV\\z^- = (1/M) \int{\int{ \int{zp(x,y,z) } }}\, dV\)

where M is the total mass of the solid and ∭ represents the triple integral.

To find the total mass M, we integrate the density function over the volume of the solid. The limits of integration for each variable are determined by the given constraints. In this case, the solid is a cube in the first octant formed by the planes x = 1, y = 1, and z = 1.

Using these limits, the triple integral becomes:

\(M =\int{\int{ \int{x p(x,y,z) } }}\,dV\\\int_0^1{ \int_0^1{\int_0^1{(xyz/18) }\, dz }\, dy}\, dx\)

Evaluating this integral will give us the total mass M of the solid.

After finding the total mass M, we can substitute it into the formulas for \(x^-, y^-, z^-\) to calculate the coordinates of the center of mass (\(x^-, y^-, z^-\)).

\(\int_0^1{ \int_0^1{\int_0^1{(xyz/18) }\, dz }\, dy}\, dx \\= \int_0^1{\int_0^1{ (z^2/36)_0^1}\, dy}\, dx \\= \int_0^1{(1/108) x^2 }\,dx\\= (1/108) [(1/3)x^3]_ 0^ 1\\= (1/108) [(1/3) - 0]\\= 1/324\)

Therefore, the simplified value of the triple integral\(\int{\int{ \int{(xyz/18) },dz }\,dy}\, dx\) over the given limits of integration is 1/324.

Learn more about  triple integration here:

https://brainly.com/question/32510822

#SPJ4

Answer:

y=3x-5

Step-by-step explanation:

Everytime x increases by 1 y increases by 3

Therefore the slope is 3

To find b plug in a coordinate

(1,-2) for example

-2= 3*1+b

-2=3+b

-5=b

Therefore the equation is

y=3x-5

We have been able to prove the converse of the triangle proportionality theorem that; YW ║ XV

The converse of the triangle proportionality theorem states that if a line intersects two sides of a triangle and cuts off segments’ proportionality, it is parallel to the third. In △WZV, let X and Y be points on line WZ and VZ, respectively, such that ZY/YW = ZX/XV. Now, prove that line YX is parallel to line WV.

Statement 1: WV ║ YX ∩ V’

Reason 1: Consider WV as a line through W parallel to line YX, intersecting side ZV at V’.

Statement 2: ZY/YW = ZX/XV’

Reason 2: Basic Triangle Proportionality Theorem

Statement 3: ZX/XV’ = ZX/XV & XV’ = XV & V= V’

Reason 3: By hypothesis

Statement 4: YW ║ XV

Reason 4: The Converse of the Triangle Proportionality Theorem

Read more about converse of the triangle proportionality theorem at; https://brainly.com/question/30584591

#SPJ1

Answer:

- 10

Step-by-step explanation:

g(x) = - x² + 2x

g(3) - 7 = - (3)² + 2(3) - 7 = - 10

Answer:

439 foot

Step-by-step explanation:

x/205=x+150/275

275x=205x+30750

70x=30750

x=439 foot

Answer:

33.3%

Step-by-step explanation:

10/ 30= 0.3(3 would be a reoccurring decimal)

0.3*100=33.3

10% of students take the bus

integral solutions to the equation \($y_1+y_2+y_3+y_4+y_5=24$\).We can use the method of generating functions to find the number of solutions.

The problem requires us to find the number of solutions of the given equation \($x_1+x_2+x_3+x_4+x_5=39$\), such that each \($x_i\geq3$\).

This is a typical problem of finding the number of non-negative The generating function for each\($y_i$ is$$(1+x+x^2+x^3+....)$$\)

The generating function for \($y_1+y_2+y_3+y_4+y_5$\) is the product of the individual generating functions.

\($$(1+x+x^2+x^3+....)^5=\frac{1}{(1-x)^5}$$\)

We can use the formula for the coefficient of\($x^{24}$\) in the above generating function to get the number of non-negative integral solutions to the equation.

To know more about equation visit :

https://brainly.com/question/29657983

#SPJ11

Two triangles with three pairs of corresponding congruent angles are congruent: Always TRUE

So, the statement says that:

Therefore, "two triangles with three pairs of corresponding congruent angles are congruent" is Always TRUE.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

#SPJ4

(C)

Given data:

The given inequalities.

The graph of the given inequalities is shown below.

The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.

let

Number of small bowl = x

Number of large bowl = y

x + y = 63

2.25x + 3y = 159

From (1)

x = 63 - y

Substitute into (2)

2.25x + 3y = 159

2.25(63 - y) + 3y = 159

141.75 - 2.25y + 3y = 159

- 2.25y + 3y = 159 - 141.75

0.75y = 17.25

divide both sides by 0.75

y = 17.25 / 0.75

y = 23

Substitute y = 23 into (1)

x + y = 63

x + 23 = 63

subtract 23 from both sides

x = 63 - 23

x = 40

In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

Answer:

D

Step-by-step explanation:

Its D because integers and whole numbers cannot be fractions, while a rational number can. A, B, C, and D can all be simplified into whole numbers while 7/11 cant

Vì tam giác ABC cân tại A (gt) mà AM là đg trung tuyến nên AM đồng thời là đg cao của t/giác đó:

AM là trung tuyến của t/giác ABC nên M là trung điểm BC:

=> BM =BC/2 =6:2=3(cm)

Xét tam giác AMB vuông tại M

AB^2 =AM^2+BM^2 ( theo định lý Py-ta -go)