Please solve these radical equations and show the steps so that I can understand them. In my notes, it says the steps are to Isolate the radical, square both sides, solve for the variable, and check for the extraneous solutions so if this is what you are supposed to do please show these steps in action. Thank you for your time.

Answer:

[tex]58.99[/tex]

Step-by-step explanation:

[tex] \tan(61) = \frac{o}{a} \\3.74 = \frac{x}{17} \\ x = 17 \times 3.74 \\ = 58.99[/tex]

Answer:

y=-4x+16

Step-by-step explanation:

Okay, so a perpendicular line has an opposite reciprocal slope.

The slope for the first line is x/4, but I like to write it as 1/4x, since it's easier to look at.

The opposite reciprocal for 1/4x is -4x

So far, we have y=-4x+ [  ]

To find the remaining b value, we can use the given point intersection.

plug in the x and y values given (4, -1) and solve for b.

The equation for the perpendicular line is y=-4x+16

[tex]\\ \sf\longmapsto 41sin\Theta=40[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{40}{41}[/tex]

Now

[tex]\boxed{\sf cos\Theta=\sqrt{1-sin^2\Theta}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{1-\left(\dfrac{40}{41}\right)^2}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{1-\dfrac{1600}{1682}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{\dfrac{1681-1600}{1681}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{\dfrac{81}{1681}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\dfrac{9}{41}[/tex]

We know

[tex]\boxed{\sf tan\Theta=\dfrac{Sin\theta}{Cos\Theta}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{tan\Theta}{1-tan^2\Theta}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{sin\Theta}{cos\Theta}}{1-\dfrac{sin^2\Theta}{cos^2\Theta}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{\left(\dfrac{40}{41}\right)}{\left(\dfrac{9}{41}\right)}}{1-\dfrac{\left(\dfrac{40}{41}\right)^2}{\left(\dfrac{9}{41}\right)^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{{40}}{{9}}}{1-\dfrac{{40}^2}{{9}^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{9^2-40^2}{9^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{81-1600}{81}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{-1519}{81}}[/tex]

[tex]\\ \sf\longmapsto {\dfrac{40}{\cancel{9}}}\times \dfrac{\cancel{81}}{(-1519)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{40\times 9}{(-1519)}[/tex]

[tex]\\ \sf\longmapsto - \dfrac{360}{1519}[/tex]

Answer:

Y = 8 + 2d

Step-by-step explanation:

Y = 8 + 2d where d is miles traveled

Answer:

y = 2d + 8

Brainliest, please!

Step-by-step explanation:

y = mx + b

m = slope, b = y-intercept

The flat rate of $8 is the y-intercept, and the slope is $2.

y = 2x + 8

We can change x to d to match the context of this problem.

y = 2d + 8

Answer:

impossible

Step-by-step explanation:

The sum of the internal angles of the regular polygon and the theorem n-sided polygon is equal to: (n-2)×180° (n is greater than or equal to 3 and n is an integer)

when n=3，The internal angle sum is 180°

The order of Rotational symmetry is 2 (option B) for the given figure.

It is basically the number of times we obtain the initial(or same) figure in a single rotation of 360°.

The rotational symmetry of a shape demonstrates that when an object is rotated on its axis, the form of the object examines the same. Many geometrical shapes emerge to be symmetrical when they exist rotated 180 degrees or with some angles, clockwise or anticlockwise. Some of the examples exist as squares, circles, hexagons, etc.

If we rotate the picture by 90°or 270°, then it wont match the initial figure.

If we rotate the picture by 180° from initial, it will match the figure.

If we further rotate it by 180°( full 360° completed) , it will again match.

Hence, it matches 2 times in a single rotation.

Therefore it has rotational symmetry of order 2.

To solve more questions about rotational symmetry refer:

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Answer:

(1, 3)

Step-by-step explanation:

Since up and down are opposites, the point didn't move at all.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

(2, 0) and (0, 4) are coordinates in the form of (x, y)

(2, 0) -> x = 2, y = 0

(0, 4) -> x = 0, y = 4

Answer: 290

Step-by-step explanation:

[tex]First\ integer\ on\ line\ n\ is:\ \dfrac{n^2}{2}-\dfrac{n}{2}+1 \\\\For \ line\ 17\ : \dfrac{17^2}{2}-\dfrac{17}{2}+1 =137\\\\\\Last \ integer\ on\ line\ n\ is:\ \dfrac{n*(n+1)}{2} \\\\For\ line\ 17:\ \dfrac{17*(17+1)}{2} =153\\\\Sum=137+153=290[/tex]

I have not say the equation in u(n+3) for the recurrence,

the resolution of the equation caracteristic and the resolution of a system of 3 equations with 3 variables.

Answer:

b^27

Step-by-step explanation:

Answer:

A. b^27

You multiply 9x3 and you get 27 with the base "b"

Step-by-step explanation:

Answer:

The slope of AB is - 2,

Slope of BC is \frac{1}{2}

2

1

Slope of CD is -\frac{3}{4}−

4

3

Slope of AD is \frac{1}{2}

2

1

,

ABCD is trapezoid because one pair of opposite sides is parallel.

Step-by-step explanation:

Given vertices of quadrilateral ABCD,

A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2),

∵ Slope of a line passes through two points (x_1, y_1)(x

1

,y

1

) and (x_2, y_2)(x

2

,y

2

) is,

m=\frac{y_2-y_1}{xc_2-x_1}m=

xc

2

−x

1

y

2

−y

1

Thus, the slope of AB = \frac{3+1}{-3+1}=\frac{4}{-2}=-2

−3+1

3+1

=

−2

4

=−2

Slope of BC = \frac{5-3}{1+3}=\frac{2}{4}=\frac{1}{2}

1+3

5−3

=

4

2

=

2

1

Slope of CD = \frac{2-5}{5-1}=-\frac{3}{4}

5−1

2−5

=−

4

3

Slope of DA = \frac{-1-2}{-1-5}=\frac{-3}{-6}=\frac{1}{2}

−1−5

−1−2

=

−6

−3

=

2

1

Since, when two line segment having the same slope then they are parallel to each other.

∴ BC ║ DA

A quadrilateral only having two parallel sides is called trapezoid,

Hence, ABCD is a trapezoid.

Given the graph of quadrilateral ABCD, the coordinates of A, B, C and D are (-3,-4), (1,4), (4,0) and (1,-4) respectively. The length of DA using distance formula is 4 units.

The coordinates of the points in the graph is given in the form of (x,y) where x is the abscissa and y is the ordinate.

The distance formula is used to find the length of the line given the endpoints of the line.

Given endpoints as [tex](x_1, y_1) \ and \ (x_2, y_2)[/tex],

[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The coordinates of vertices are given by:

A = (-3,-4)

B = (1,4)

C = (4,0)

D = (1,-4)

The length of DA can be found by distance formula :

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

Learn more about distance formula here

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Answer:

126

Step-by-step explanation:

Answer:

126°

Step-by-step explanation:

x = (87+165)/2

x = 252/2

x = 126

Answered by GAUTHMATH

Answer:

[tex]\frac{1}{10} * \frac{1}{100} = \frac{1}{1000}[/tex]

1000 times

Step-by-step explanation:

Answer:

0.1% = 1 spin then

100% = ( 100×1) ÷0.1 = 1000

we are using 100% because its a sure bet it will happen but not logically

the answer is 1000

Use the Pythagorean theorem

? = sqrt(52^2 + 19^2)

? = sqrt(2704 + 361)

? = sqrt(3065)

Answer: sqrt(3065)

Answer:

5*2 +2*2 = s*2

s = 5.38

s = 5.4

Answer:

Does the answer help you?

Answer:

1 / 5

Step-by-step explanation:

Given the outcome of number cube spin : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6

The experimental probability of an event, A is given as :

P(A) = number of times A occurs / total number of trials

Therefore, the experimental probability of getting 2 ;

P(getting 2) = Number of times 2 occurs / total number of trials

P(getting 2) = 2 / 10 = 1/5

6.18000 x 10 5

This is the standard form of 618,000

Thanks , Please mark me brainliest

TyrantMC

Answer:

see below

Step-by-step explanation:

y = x^2 +2x - 8

Factor

y = ( x+4)(x-2)

The zeros are

x+4 = 0  x-2 = 0    

x= -4    x= 2

(-4,0)  (2,0)

The axis of symmetry is 1/2 way between the zeros

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

x = -1

The x coordinate of the vertex is at the axis of symmetry

The y value is found by substituting x=-1

y = (-1+4) (-1-2)= 3*-3 = -9

Vertex ( -1,-9)

The domain is all real numbers

The range is from -9 up

y≥ -9  since it opens upward

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = [tex]3^{x + 2}[/tex]

The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = [tex]3^{0 + 2}[/tex] = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = [tex]5^{1 - x}[/tex]

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = [tex]2^{x + 3}[/tex] - 1

The asymptote is [tex]2^{x + 3}[/tex]  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  [tex]2^{0 + 3}[/tex] - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0

[tex]2^{x + 3}[/tex] = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]

The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]

The y-intercept is (0, 6)

Answer:

Step-by-step explanation:

peter can buy pack of nine pencils

6 divided by 1.68 =3.5

9 divided by 2.34=3.8

package 2 is just 0.3 more

it give 3 more pencils for 0.3

Answer:

m=4

Step-by-step explanation:

m = y2 - y1/x2 - x1

(y2=8, y1=0, x2= 2, x1=0)

m = y2 -y1/x2 - x1

= 8 - 0/2 - 0

= 8/2

=4

Answer:

804.2 km³

Step-by-step explanation:

Volume of a cylinder: πr²h

r = radius, h = height

[tex]\pi r^2h\\\pi(8)^2(4)\\\pi(64)(4)\\\pi(256)\\804.2[/tex]

Answer:

see image

Step-by-step explanation:

Answer:

Part 1

The number of baseball players that are to split the profits = 9 baseball payers

The amount of money each player earned = $326

Let x represent the total amount of money raised, and given that each baseball player received equal amount of the profits we have the following division equation;

[tex]The \ division \ equation \ is , \dfrac{x}{9} = \$ \, 326[/tex]

Part 2

Solving for the variable, gives;

x = 9 × $ 326 = $2,934

The amount of profits from the fundraiser, x = $2,934

Part 3

The amount, A, each of the 9 players will earn from the profit of $2,934 raised in the fund raiser is given as follows;

A = $2,934/9 = $326

∴ The amount each of the 9 players will earn, A = $326, therefore the answer corresponds to the value in the question and is therefore, correct

Step-by-step explanation:

Answer:

122

Step-by-step explanation:

The exterior angle of a triangle is the sum of the opposite interior agnles

32+90 =x

122 =x

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex] \bf \large \hookrightarrow \: \: x \: = \: 32 \degree \: + \: 90 \degree [/tex]

[tex]\bf \large \hookrightarrow \: \: x \: = \: 122 \degree[/tex]

find the square root and of 1+i√3​  

Answer:

0 is the answer . The explanation is in the attachment .