Find the slope of each line.

Answer:

[tex]\sqrt3[/tex]

Step-by-step explanation:

To find:

The value of [tex]tan60^\circ[/tex] = ?

Solution:

Kindly consider the equilateral [tex]\triangle ABC[/tex] as attached in the answer area.

Let the side of triangle = [tex]a[/tex] units

Let us draw the perpendicular from vertex A to side BC.

It will divide the side BC in two equal parts.

i.e. BD = DC = [tex]\frac{a}{2}[/tex]

Using Pythagorean Theorem in [tex]\triangle ABD[/tex]:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]

Side AD = [tex]\frac{\sqrt3}{2}a[/tex]

Using Trigonometric ratio:

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tanB = \dfrac{AD}{BD}[/tex]

Putting the values of AD and BD:

[tex]tan60^\circ=\dfrac{\frac{\sqrt3}{2}a}{\frac{1}{2}a}\\\Rightarrow tan60^\circ = \bold{\sqrt3}[/tex]

8 months

Step-by-step explanation:

Answer:

2x-y=-10

Step-by-step explanation:

I'm assuming by standard form you mean

Ax+By=C

Ax⇒2x

By⇒-y

C=-10

2x-y=-10

Answer:

The unknown value is being subtracted from 226 is 160

Step-by-step explanation:

Long division setup showing an incomplete calculation

so,

The dividend = 3426

 The divisor = 16

2 hundreds means 200 and 1 tens means 10

∵ The quotient = 200 + 10 + x

∵ Dividend = divisor × quotient

∴ (16 × 200) + (16 × 10) + (16 × x) +remainder  = 3426  

∵ 16 × 200 = 3200

Subtract 3200 from the dividend  

∴ 3426 - 3200 = 226

∵ 16 × 10 = 160

∴ 226- 160 = 66

⇒160is the unknown value

∵ 16 × x = 16x  

∵ 66 - 16x = 0

∴ 66 = 16x

- Divide both sides by 16

∴ x = 4  and remainder = 2

∴ 3426 ÷ 16 = 200 + 10 + 4

∴ 3426 ÷ 16 = 214  

∴ From the steps above the missing number subtracted from

  226 is 160

The unknown value is being subtracted from 226 is 160

Answer:

8.25

Step-by-step explanation:

8 1/4= 8 25/100=8.25

Hey there!

8 1/4

= (8 * 4 + 1)/ 4

= (32 + 1)/4

= 33/4

= 33 ÷ 4

= 8.25

Therefore, your answer is: 8.25

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

area a=lxb

48=(x+10)x(x-3)

48=x2-3x+10x-30

0=x2+7x-30-48

0=x2+7x-78

hence it is proved

The requried, we have shown that x satisfies the equation x² + 7x - 78 = 0.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
The area of the rectangle is given by the formula:

Area = length x width

Substituting the given expressions for length and width, we have:

Area = (x + 10)(x - 3)

We are also told that the area of the rectangle is 48 cm², so we can set up the equation:

(x + 10)(x - 3) = 48

Expanding the left side using the FOIL method:

x² - 3x + 10x - 30 = 48

Simplifying:

x² + 7x - 78 = 0

Therefore, we have shown that x satisfies the equation x² + 7x - 78 = 0.

Learn more about equations here:

brainly.com/question/10413253

#SPJ7

Answer: 1, 3, and 4 can form triangles. The rest can not.

Step-by-step explanation:

on triangles 1, 3, and 4, the 2 smaller sides added together are greater than the longer side.

Answer:

y= -1/3x-7

Step-by-step explanation:

Answer:

The area of the trapezium is [tex]74.8\ cm^2[/tex]

Step-by-step explanation:

Area of a trapezium:

[tex]\displaystyle A=\frac{b1+b2}{2}h[/tex]

This formula is valid if b1 and b2 are parallel and h is perpendicular to both.

Since the trapezium given in the problem satisfies those conditions, we use the formula with:

b1=15 cm

b2=7 cm

h=6.8 cm

[tex]\displaystyle A=\frac{15+7}{2}\cdot 6.8[/tex]

[tex]A=74.8\ cm^2[/tex]

The area of the trapezium is [tex]74.8\ cm^2[/tex]

Answer:

Step-by-step explanation:

i would say d

Answer:

55 adult tickets were sold on Friday.

Step-by-step explanation:

A linear system will be used to model the system.

Let c be the number of child tickets and a be the number of adult tickets

Then according to given statements

[tex]a+c = 133\ \ \ \ Eqn\ 1\\9.50a+5.20c = 928.10\ \ \ Eqn\ 2[/tex]

From equation 1

[tex]a = 133-c[/tex]

Putting this in equation 2

[tex]9.50(133-c)+5.20c = 928.10\\1263.5-9.50c+5.20c=928.10\\1263.5-4.3c = 928.10\\-4.3c = 928.10-1263.5\\-4.3c=-335.4\\\frac{-4.3c}{-4.3} = \frac{-335.4}{-4.3}\\c = 78[/tex]

Putting c = 78 in equation 1

[tex]a+78 = 133\\a = 133-78\\a = 55[/tex]

Hence,

55 adult tickets were sold on Friday.

Answer:

Search it up on utube

Step-by-step explanation:

Answer:

b) No solutions

Step-by-step explanation:

y=2x+1

y= 2(x+3)

Substitute the y in y=2x+1 with 2(x+3)

2(x+3)=2x+1

Then distribute the 2.

2x+6=2x+1

Subtract 2x from both sides to isolate the variable.

6=1

this statement is false, meaning the system of equations has no solutions.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

C

The change of the frequency of people waking up with respect to the sound level, 9% per 8 decibels.

Linear function is the function in which the highest power of the unknown variable is one. Linear functions used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

[tex]y=mx +c[/tex]

Here, (m) is the slope of the function and (c) is the y intercept.

The slope can be found out as,

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The sound level is plotted on x-axis and frequency of people walking up (%) is plotted on y-axis. The slope of the line given the rate of change of y values with respect to x value.

In the graph given, the frequency of people walking up is 10 at 55 decibels and 55 at 95 decibels. The point, we get for this line are (55, 10) and (95, 55). Therefore the slope or the change of rate is,

[tex]\dfrac{dy}{dx}=\dfrac{55-10}{95-55}\\\dfrac{dy}{dx}=\dfrac{45}{40}\\\dfrac{dy}{dx}=\dfrac{9}{8}[/tex]

Hence, the change of the frequency of people waking up with respect to the sound level, 9% per 8 decibels.

Learn more about the linear function here;

https://brainly.com/question/15602982

Answer:

Step-by-step explanation:

Original equation:

7/2x - 3(5x - 1/2) = ?

Use distributive property for the parentheses

-3 · 5x = -15x

-3 · (-1/2) = 3/2 or 1.5

Plug these values into the equation

7/2x - 15x + 1.5 = ?

Combine like factors

-11.5x + 1.5 = a (a = answer)

The equation with fractions:

-11 1/2 + 1 1/2 = a

Hope this helps :)

Answer:

3/4

Step-by-step explanation:

15/20 is 3/4. therefore, according to the previous data, it is 3/4.

P.S. I looked at your answers and you cannot just spam random answers. thats rude and it violated the honor code. how would you feel if you posted a question and the answer was just random letters. and then you failed your test. thats not nice. and you are on canvas, because i use it too, and i know what it looks like. you cannot cheat on a test, as this is not what Brainly is for. im just so dissapointed because you disrespect others.

Answer:

1) 33/36 = 11/12

2) 22/24 = 11/12

Step-by-step explanation:

Hope it helps you! Please give me Brainlest!

Step-by-step explanation:

As a decimal you divide 11 by 12 which is 0,916 (6 repeating)

now as a percent you multiply this decimal by 100 which is 91.6 (6 repeating)%

Answer:

its 120 your supposed to divide 120 ÷ 100% and ur answer will be 120

Answer: 15

Step-by-step explanation: 3:4 5x4=20 5x3=15 15:20

Answer:

there are 15

men in the dance recital

Step-by-step explanation:

Answer:

the slope is-7/11

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=3-(-4)/(-2)-9

m=7/-11

m=-7/11

Answer:

735x0.01

Step-by-step explanation:

Answer:

Step-by-step explanation:

I looked this up on google. There is an answer key if u look up this exact question the 1st link is the answer key!

Answer:

0

Step-by-step explanation:

Since it is a flat, horizontal line, it has a slope of 0.

If the line was straight up and down, it would be undefined.

Answer:

=5xy−9x−9y+7

Step-by-step explanation:

Let's simplify step-by-step.

−6x+5xy−9y−3x+7

=−6x+5xy+−9y+−3x+7

Combine Like Terms:

=−6x+5xy+−9y+−3x+7

=(5xy)+(−6x+−3x)+(−9y)+(7)

=5xy+−9x+−9y+7

Answer:

=5xy−9x−9y+7

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Let : A = ( - 2 , - 6 ) & B = ( 3 , 9 )

[tex]d = distance \: \: between \: \: points \\ [/tex]

[tex]d = \sqrt{ ( \: {y(B) - y(A) } \: )^{2} + ( \: { x(B) - x(A) } \: )^{2} } \\ [/tex]

[tex]d = \sqrt{ ( \: {9 - ( - 6)} \: )^{2} + ( \: {3 - ( - 2)} \: )^{2} } \\ [/tex]

[tex]d = \sqrt{ ( \: {9 + 6} \: )^{2} + ( \: {3 + 2} \: )^{2} } \\ [/tex]

[tex]d = \sqrt{ {15}^{2} + {5}^{2} } [/tex]

[tex]d = \sqrt{225 + 25} [/tex]

[tex]d = \sqrt{250} [/tex]

[tex]d = \sqrt{25 \times 10} [/tex]

[tex]d = \sqrt{ {5}^{2} \times 10 } [/tex]

[tex]d = 5 \sqrt{10} [/tex]

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Thus Steve draws a line which has a length of 5√10 .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

=-3471 is the answer this may help you.

Step-by-step explanation:

=3.471×10^-3

=3.471×-1000

=-3471

Answer: For which item was he charged twice? 42.25 – 29.50 = 12.75, so he was charged twice for the hat.

It may be incorrect! This is in my math book and it was this answer. Please forgive me if it’s incorrect!