In the right triangle, the altitude is 5 units and the longest segment of the hypotenuse of 7 units. Find the length of the hypotenuse.

Answer:

x = 3/2 or 1.5

Step-by-step explanation:

distribute 3 to the 2x and -1 by multiplying

6x - 3 = 6

add 3 to both sides to get 6x by itself and it keeps both sides equal

6x = 9

divide by 6

x = 9/6 = 3/2

x = 3/2

Answer:

[tex]\mathbf{- 20 \pi + \dfrac{40}{3}}[/tex]

Step-by-step explanation:

Given that:

[tex]\int\limits_c {F} \, dr[/tex]

where;

[tex]F(x,y) = \langle\sqrt{x} + 10y^3+10y^2 + \sqrt{y} \rangle[/tex] and C consist of the arc of the curve, This shows that C is a closed curve.

Thus, using Green's theorem for clockwise orientation.

[tex]\int \limits_CF. dr = \iint_D \Biggl \langle \dfrac{\partial Q}{\partial X} - \dfrac{\partial P }{\partial Y} \Biggl \rangle dA[/tex]

Then;

[tex]F(P,Q) = \langle\sqrt{x} + 10y^3+10y^2 + \sqrt{y} \rangle[/tex]

[tex]\int \limits _CF. dr = -\iint_D \Biggl \langle \dfrac{\partial}{\partial} ( 10x^2 + \sqrt{y} -\dfrac{\partial}{\partial y } ( \sqrt{x} + 10y^3) \Biggl \rangle dA[/tex]

[tex]\int \limits _CF. dr = -\iint_D \Biggl \langle 10(2x)-10(3y^2) \Biggl \rangle dA[/tex]

[tex]\int \limits _CF. dr = \iint_D \Big \langle -20x+30y^2 \Big \rangle dA[/tex]

y → 0 to sin (x)        x → 0 to π

[tex]\int \limits _CF. dr = \int \limits ^{\pi}_{0} \int \limits ^{sin \ x }_{0} \Big \langle -20x+30y^2 \Big \rangle dydx[/tex]

[tex]\int \limits _CF. dr = \int \limits ^{\pi}_{0} \Biggl [ -20xy + \dfrac{30 \ y^3}{3} \Biggl ] ^{sin\ x}_{0} \ dx[/tex]

[tex]\int \limits _CF. dr = \int \limits ^{\pi}_{0} \Big [ -20x \ sin x + 10 \ sin^3x \Big ] \ dx[/tex]

replace [tex]sin^3 x = \dfrac{3}{4} \ sin x - \dfrac{1}{4} \ sin (3x)[/tex]

[tex]= \int \limits ^{\pi}_{0} -20 x sin x dx + \int \limits ^{\pi}_{0} 10(\dfrac{3}{4} sin x - \dfrac{1}{4} sin (3x) ) \ dx[/tex]

By applying integration by posits

[tex]\int (u)(v') \ dx = (u)(v) - \int (u') (v) \ dx \\ \\ u = -20x \ \ \ \ \ \ \ v'= sin \ x \\ \\ u' = -20 \ \ \ \ \ \ \ v = - cos \ x[/tex]

[tex]= (-20x) (-cos x) - \int (-20)(-cos x) \ dx + 10 \Big [\dfrac{3}{4} \ cos x + \dfrac{1}{12}\ cos (3x) \Big ][/tex]

[tex]= 20x \ cos x - 20 \ sin x- \dfrac{15}{2} \ cos \ x + \dfrac{5}{6} \ cos (3x) \Biggl |^{\pi}_{0}[/tex]

[tex]= ( -20 \pi -0 +\dfrac{15}{2}-\dfrac{5}{6}) - (0-0-\dfrac{15}{2}+\dfrac{5}{6})[/tex]

[tex]= - 20 \pi + \dfrac{15}{2}-\dfrac{5}{6}+\dfrac{15}{2}-\dfrac{5}{6}[/tex]

[tex]\mathbf{= - 20 \pi + \dfrac{40}{3}}[/tex]

Answer:

{1,3,4,5,6,7}

Step-by-step explanation:

Here , U represents the universal set

L’ = {2,4,6}

L’ is what we have in the universal set but not present in set L

(m n L’)

This is the set that contains the elements that are present in both set ONLY

So this is;

{2}

(M n L’)’ = {1,3,4,5,6,7}

N’ = {1,7}

So the union of both would be;

= {1,3,4,5,6,7}

Answer:

8x

Step-by-step explanation:

Hope this helps:)

9514 1404 393

Answer:

  see below

Step-by-step explanation:

We have elected to use a table, so that the rows and columns have labels that identify the table content. A matrix can be made from the data in the table.

Answer: When an object accelerates, it changes it velocity over time.

Answer:

A is the answer

Step-by-step explanation:

Answer:

C.

The relative frequency is 0.3. It is likely that most ducks are yellow.

Step-by-step explanation:

Are you trying to write this from word form and convert it into an equation? If you could provide more details, I would be more than happy to help. Thanks!

Answer: it is 29.36

Step-by-step explanation:

Answer:

(b = 23 + a) and (a = 23 + b) = ab = 23 + ba

Step-by-step explanation:

Answer:

-1.67539

Step-by-step explanation:

There are many answer choices one of them could be...

-1.67550

Answer:A. slope: 7, y-intercept: 10

Step-by-step explanation:

Transform the equation into slope intercept form, y=7x+10. In the form y=mx+b, m = slope and b = y-intercept

Answer:

I cant see anything

Step-by-step explanation:

Answer:

Hope this helps

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

y=0 looks like |  and x=0 looks like -----  . This means that they are and not parallel

Answer:

?

Step-by-step explanation:

you have to find a ratio and multiply 8 by something to get the demensions

Step-by-step explanation:

Y = 3 X-6

... . .... ... ...

Answer: A

Step-by-step explanation: I did this on paper so its hard for me to write it done, like I cant copy and paste lol.

Answer:

It’s b I think

Step-by-step explanation:I is big dumb

Answer:

[tex]b=24[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}b-16=-4[/tex]

First, start by adding [tex]16[/tex] to both sides of the equation:

[tex]\frac{1}{2} b=12[/tex]

To make this problem easier, it would be a good idea to identify [tex]0.5[/tex] as the decimal equivalent of the fraction [tex]\frac{1}{2}[/tex]:

[tex]0.5b=12[/tex]

Divide both sides of the equation by the coefficient of [tex]b[/tex], which is [tex]0.5[/tex].

(**Tip: Dividing by a half is the same as multiplying by [tex]2[/tex]):

[tex]b=24[/tex]

-

To check our work and solution, substitute the solved value of [tex]b[/tex], ([tex]24[/tex]), into the initial equation:

[tex]\frac{1}{2}b-16=-4[/tex]

[tex]\frac{1}{2}(24)-16=-4[/tex]

[tex]12-16=-4[/tex]

[tex]-4=-4[/tex]

Since both sides of the equation are equal, our solution is correct!

Answer:

b = 24

Step-by-step explanation:

[tex]\sf \dfrac{1}{2}b-16=-4[/tex]

Add 16 to both sides.

[tex]\sf \dfrac{1}{2}b=-4+16\\\\ \sf \dfrac{1}{2}b=12[/tex]

Multiply both sides by 2.

[tex]\sf2* \dfrac{1}{2}b=12*2\\\\1b=24[/tex]

Divide both sides by 1.

[tex]\sf b = \dfrac{24}{1} \\\\b =24[/tex]

Answer:

27.9

Step-by-step explanation:

6.35+6.2+1.9+3.8+9.65=27.9

Answer:

w = 4

Step-by-step explanation:

distribute 10(w+3)=70

10w + 30 = 70

subtract 30

10w = 40

divide by 10

w = 4

Answer: w=7

Step-by-step explanation: 10 times what equals 70? 10 times 7 equals 10. So 3 plus 4 equals 7.

10(7+3)=70

Answer:

[tex]*+24x+9 = 16x^2 + 24x + 9[/tex]

Step-by-step explanation:

Given

[tex]* + 24x + 9[/tex]

Required

Fill in the gap

[tex]* + 24x + 9[/tex]

Express 24x as a sum of equal halves

[tex]* + 12x + 12x + 9[/tex]

Group into two

[tex](* + 12x) + (12x + 9)[/tex]

Factorize 12x + 9

[tex](* + 12x) + 3(4x + 3)[/tex]

Ignore the incomplete part and focus on (4x + 3)

Since the binomial is a square, then the factors of the binomial are :

(4x + 3) and (4x + 3)

So, we have:

[tex](* + 12x) + 3(4x + 3) = (4x + 3)(4x + 3)[/tex]

Expand

[tex](* + 12x) + 3(4x + 3) = 16x^2 + 12x + 12x + 9[/tex]

[tex](* + 12x) + 3(4x + 3) = 16x^2 + 24x + 9[/tex]

Hence:

[tex]*+24x+9 = 16x^2 + 24x + 9[/tex]

Answer:

c??

Step-by-step explanation:

The coordinates of B are (1,2).

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

Given that, Point C (3, 4) is the midpoint of AB If the coordinates of A are (7, 6),

Formula of midpoint coordinates = (x1+y1)/2, (x2+y2)/2

Therefore, (7+x)/2, (6+y)/2 = (3,4)

Comparing both side, we get,

(7+x)/2 = 3

x = 1

And, (6+y)/2 = 4

y = 2

Hence, The coordinates of B are (1,2).

For more references on Midpoints, click;

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Answer:

x = 70° ; y = 67°

Step-by-step explanation:

1) The triangle given in the picture is an isosceles triangle. So, the base angles will be equal to each other. (People do get confused and assume that x is a base angle. But in the figure , the triangle is rotated anticlockwise. So x is not a base angle).

Using angle sum property of triangles,

[tex]x+55+55=180[/tex]

[tex]=> x + 110 = 180\\[/tex]

[tex]=>x = 180-110=70[/tex]

2) Both the lines are parallel to each other and there's a transversal intersecting both the lines at 2 specific points. So ,

y = 67° (∵ Alternative Interior Angles are equal to each other when two lines are parallel and there's a transversal intersecting them)

Answer:

∠C = 70°

Step-by-step explanation:

When dealing with similar triangles, the angles of both triangles are equal. With that being said, the letters of those angles typically corralete as well. In this case, we have ΔABC and ΔDEF. Based on the way those letters are arranged, we can assume the following:

∠A = ∠D

∠B = ∠E

∠C = ∠F

The question tells us ∠A = 36°. Since we know that ∠A is equal to ∠D, we know that ∠D also equals 36°. The question also tells us ∠E = 74°. Once again, since we know that ∠E is equal to ∠B, we know that ∠B is 74° as well.

Now we use that information to solve for ∠C. The sum of the angles of a triangle always adds up to 180°. Because we know that, we can solve easily:

180 - (36 + 74) = 70

∴ ∠C = 70°

No , because the total distance of 31 miles is repeated in the table

Answer:

35

Step-by-step explanation:

I got you the answer is 35.

Answer:

35

Step-by-step explanation:

Answer:

-3.5

Step-by-step explanation:

-3 1/2 is the same as -3.5

-3.5 is negative, so it means that is below sea level, so it will be below the zero. if you don’t have the exact mark for -3.5, it will go betwee -3 and -4.

Answer:

X=21.21

Step-by-step explanation:

Cos(45)=15\x

0.707=15\x

15\0.707 =x

X= 21.21

The missing side length of the right triangle is 20.51.

"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively."

Given,

Perpendicular of the triangle is 15

Hypotenuse of triangle is x

And the adjacent angle will be 180°-133° = 47°

Now, [tex]sin(47 degree) = Perpendicular/hypotenuse = 15/x[/tex]

[tex]x = 15/0.731 = 20.51[/tex]

In the to get to the answer we use sine of the triangle.

Because sin is the ratio of the perpendicular to the hypotenuse.

Hence, The missing side of the right triangle is 20.51.

To know more about trigonometric ratios here

https://brainly.com/question/26719838

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Answer:

Option B

Step-by-step explanation:

The circumference of a circle changes from (pre-image)20 to 4(image) after a dilation.

[tex]Scale\ Factor=\frac{Circumference\ of\ image}{Circumference\ of\ pre-image} \\\\Scale\ Factor=\frac{4}{20}\\\\Scale\ Factor=\frac{1}{5}[/tex]