Solve for x:
( x - 6 ) ^ 2 = 7

Answer:

Step-by-step explanation:

The reference angle is given as 63 degrees. The sides in question, x and 1, are adjacent to and opposite of this angle, respectively. The trig ratio that utilizes the sides adjacent to and opposite of angles is the tangent ratio; namely:

[tex]tan(63)=\frac{1}{x}[/tex] and rearrange algebraically to get

[tex]x=\frac{1}{tan(63)}[/tex] to get

x = .5

Answer:

x = 46.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin  54 = x / 58

58 sin 54 =x

x=46.92298

To the nearest tenth

x = 46.9

A,12/15=4/5

B,20/25=4/5

C,25/30=5/6

D,28/35=4/5

=> C

Answer:

[tex]\frac{\sqrt{3}}{6} a^{3}[/tex] và [tex]\frac{a^{3} }{6}[/tex]

Step-by-step explanation:

Câu 1: V = 1/3.2a.[tex]\frac{\sqrt{3}}{4}[/tex][tex]a^{2}[/tex] = [tex]\frac{\sqrt{3}}{6} a^{3}[/tex]

câu 2: Theo đề bài ta có SA là chiều cao và tam giác đáy SBC vuông tại S (hình chóp S.ABC đổi thành chóp A.SBC)

=> V = 1/3 SA.(diện tích tam giác SBC) = 1/3a.[tex]\frac{a^{2} }{2}[/tex] = [tex]\frac{a^{3} }{6}[/tex]

Answer:

x=7

Step-by-step explanation:

The sum of the arc of a circle is 360 degrees

85+5x+5+10x+5+-7+6x+6+17x = 360

Combine like terms

38x+94=360

Subtract 94 from each side

38x+94-94 = 360-94

38x = 266

Divide each side by 38

38x/28 = 266/38

x = 7

Answer:

Graph A

Step-by-step explanation:

Answer:

[tex]f(x) = e^x[/tex]

Step-by-step explanation:

Given

Options (a) to (d)

Required

Which is a parent function

A parent function is such that has a single term without coefficients

From the list of given options

[tex]f(x) = e^x[/tex] suits the above definition

Other options (b) to (d) either have coefficients, or have multiple terms

Step-by-step explanation:

Step 1:  Write the equation using point-slope form

Point-Slope Form:  [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

[tex]y-0=m(x-3)[/tex]

[tex]y = m(x-3)[/tex]

Step 2:  Find the slope

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-2-0}{-2-(-3)}[/tex]

[tex]m=\frac{-2}{1}[/tex]

[tex]m=-2[/tex]

Step 3:  Combine them together

[tex]y = m(x - 3)[/tex]

y = -2(x - 3)

IF NEEDED:  Completely factor

[tex]y = (-2 * x) + (-2 * -3)[/tex]

y = -2x + 6

[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]

Answer:

24aprtment3

Step-by-step explanation:

Answer:

x = [tex]\frac{5}{2}[/tex] , y = [tex]\frac{27}{4}[/tex]

Step-by-step explanation:

Equate the first 2 parts of the ratios on both sides of the equation and solve for x.

Expressing the ratios in fractional form, then

[tex]\frac{x}{3}[/tex] = [tex]\frac{\frac{15}{4} }{\frac{9}{2} }[/tex] = [tex]\frac{15}{4}[/tex] × [tex]\frac{2}{9}[/tex] = [tex]\frac{5}{6}[/tex] ( cross- multiply )

6x = 15 ( divide both sides by 6 )

x = [tex]\frac{15}{6}[/tex] = [tex]\frac{5}{2}[/tex]

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

Equate the last 2 parts of the ratios on both sides and solve for y

[tex]\frac{\frac{9}{2} }{y}[/tex] = [tex]\frac{3}{\frac{9}{2} }[/tex] = 3 × [tex]\frac{2}{9}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2y = [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex] ( divide both sides by 2 )

y = [tex]\frac{27}{4}[/tex]

Answer:

A = x + 15

B = 1 + 2

Step-by-step explanation:

x 2 + 17x + 30

x2 + 15 x + 2x + 30

1 ( x + 15 ) + 2 ( x + 15 )

 ( x + 15 ) ( 1 + 2 )

Hope this  answer helps you :)

Have a great day

Mark brainliest

Answer:

[tex]x = 10\\y = 5[/tex]

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to use the side ratios in a special right triangle. One should start by proving that the triangle is a (30 - 60 - 90) triangle. Since the problem gives on the information that one of the sides has a measure of ([tex]5\sqrt{3}[/tex]), one can use this combination with the ratio of the sides in a special right triangle, to find the unknown side lengths.

2. Prove this triangle is a (30 - 60 - 90) triangle

One is given a right triangle. This means the triangle has a (90) degree or right angle in it. This is indicated by a box around one of the angles. One is given that the other angle in this triangle has an angle measure of (30) degrees. The problem asks for one to find the third angle measure. A property of any triangle is that the sum of angle measures in the triangle is (180) degrees. One can use this to their advantage by stating the following:

[tex](90) + (30) + (unknown) = 180\\[/tex]

Simplify,

[tex](90) + (30) + (unknown) = 180[/tex]

[tex]120 + unknown = 180\\[/tex]

Inverse operations,

[tex]120 + unknown = 180\\[/tex]

[tex]unknown = 60[/tex]

Thus, this triangle is a (30 - 60 - 90) triangle, as its angles have the measures of (30 - 60 - 90).

3. Solve for (y)

The sides ratio in a (30 - 60 - 90) triangle is the following:

[tex]n - n\sqrt{3} - 2n[/tex]

Where (n) is the side opposite the (30) degree angle, ([tex]n\sqrt{3}[/tex]) is the side opposite the (60) degree angle and finally (2n) is the side opposite the (90) degree angle. The side (y) is opposite the (30) degree angle. This means that it is equal to the side opposite the (60) degree angle divided by ([tex]\sqrt{3}[/tex]). Therefore, one can state the following:

[tex]\frac{5\sqrt{3}}{\sqrt{3}}=y\\5=y[/tex]

4. Solve for (x)

Using the same thought process one used to solve for side (y), one can solve for side (x). The side (x) is opposite the (90) degree angle, hence, one can conclude that it is twice the length of the side with the length of (y). Therefore, one can state the following:

[tex]x = 2y\\x = 2(5)\\x = 10[/tex]

Answer:

-1

Step-by-step explanation:

Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.

This means we are looking for a vertical line.

Instead of lambda, I'm going to use u.

So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.

So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.

So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.

The value of λ is -1 and is perpendicular to vector a.

A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

We have,

Vector a = (1, 0) and b = (1, 1).

Here the vector is visualized as line is horizontal and has equation y=0.

Now, we have a + λb is perpendicular to vector a.

So, a + λb = (1, 0) + λ(1, 1)

                 = (1 + λ, 1)

Now, to get the vertical component we must have λ= -1.

Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.

Learn more about Vector here:

https://brainly.com/question/29740341

#SPJ3

Answer:

c. false (it should always be neg.)

d. false

Step-by-step explanation:

Answer:

(c) True, (d) False

Step-by-step explanation:

Answer:

24units

Step-by-step explanation:

From the parallelogram given, we can see that the line FH bisects EG at V. Hence;

GE = 2GV.

Given that

GV = 12

GE = 2(12)

GE = 24

Hence the measure of the length GE is 24units

Answer:

42

Step-by-step explanation:

30+25+10=65%

bus=35%

35/100×120=42

BUS=42

[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]

[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]

Answer:

19. 11

21. 119

Step-by-step explanation:

19.

(-5)² - [4(-3 ∙ 2 + 4)² + 3] + 5 =

= (-5)² - [4(-6 + 4)² + 3] + 5

= (-5)² - [4(-2)² + 3] + 5

= (-5)² - [4(4) + 3] + 5

= (-5)² - [16 + 3] + 5

= 25 - 19 + 5

= 6 + 5

= 11

21.

5 - 8[6 - (3 ∙ 2 - 8 + 2|4 ÷ -2 + (-3)| - 4) - 7 · 2] - 3² · (-2) =

= 5 - 8[6 - (3 ∙ 2 - 8 + 2|-2 + (-3)| - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (3 ∙ 2 - 8 + 2|-5| - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (3 ∙ 2 - 8 + 2(5) - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (6 - 8 + 10 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (-2 + 10 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (8 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - 4 - 7 · 2] - 3² · (-2)

= 5 - 8[6 - 4 - 14] - 3² · (-2)

= 5 - 8[2 - 14] - 3² · (-2)

= 5 - 8[-12] - 3² · (-2)

= 5 - (-96) - 9 · (-2)

= 5 + 96 + 18

= 101 + 18

= 119

Answer:

An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.

Step-by-step explanation:

Linear growth:

The number by which it increases is constant.

Exponential growth:

The rate which it increases is constant, that is, a proportion of population.

Annual increase of 1,000.

An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.

Answer:

(5-2z)(5+2z)

Step-by-step explanation:

25 -4z^2

Rewriting

5^2 - (2z)^2

This is the difference of squares  a^2 - b^2 = (a-b)(a+b)

(5-2z)(5+2z)

[tex] \\ \tt \longmapsto2x + 15 + 7 - 8x + 3x - 41 = 30 \\ \\ \tt \longmapsto 2x - 8x + 3x + 15 + 7 - 41 = 30 \\ \\ \tt \longmapsto - 3x - 19 = 30 \\ \\ \tt \longmapsto 3x + 19 = - 30 \\ \\ \tt \longmapsto 3x = - 30 -19 \\ \\ \tt \longmapsto 3x = - 49 \\ \\ \tt \longmapsto x = - \frac{49}{3}[/tex]

Answer:

Step-by-step explanation:

2x + 15 + 7 - 8x + 3x - 41 = 30

2x  - 8x + 3x + 15 + 7 - 41 = 30

Combine like terms

-3x - 19 = 30

Add 19 to both sides

-3x = 30 + 19

-3x = 49

Divide both sides by (-3)

x = 49/-3

x = -[tex]16\frac{1}{3}[/tex]

Answer:

sorry I could not help you but I wish you luck

Answer:

or,

3/4×2/3=6/8

or, 3/4×3/3=9/12

Answer:

Step-by-step explanation:

1/3×2/8=2/24

1/2×5/12=5/42

5/6×3/4=15/24

Hope it is helpful to you

Answer:

Pls give me the answers as soon as possible and make sure that the answers are correct.

Answer:

do you have any images with the questions?

Step-by-step explanation:

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{13}{15}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{-13}{15})²}[/tex]

Solving numerical

[tex]Sin\theta_{1}=\sqrt{1-(\frac{169}{225})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{56}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{56}}{\sqrt{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*14}}{\sqrt{15*15}}[/tex]

[tex]Sin\theta_{1}=\frac{2\sqrt{14}}{15}[/tex]

Since

In III quadrant sin angle is negative

Answer:

Step-by-step explanation:

In the quadrant III both the sine and cosine get negative value.

Use the identity:

And consider negative value as mentioned above:

9514 1404 393

Answer:

  7. d. l = 6.48 cm, w = 6.48 cm

  8. d. square

Step-by-step explanation:

For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.

__

7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.

__

8. In light of the above, the shape is a square.

_____

The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.

6,3:y=4,2:2,4

y=3,6

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