What is the slope of the line represented​

Answer:

[tex]{ \underline{ \sf{6y = x + 1 }}}[/tex]

Step-by-step explanation:

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

m is slope

c is y intercept.

at x-intercept, y = 0

[tex]0 =( \frac{1}{6} \times - 1 )+ c \\ \\ c = \frac{1}{6} [/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is 6y=x+1.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

Given that the slope of the equation of the line is 1/6, while the x-intercept is at -1. Therefore, if we substitute the coordinate of the intercept and the slope in the equation in the general equation of the line. We will see,

y = mx + c

0 = (1/6)(-1) + c

0 = -1/6 + c

c = 1/6

Now, the equation of the line can be written as,

y = (1/6)x + (1/6)

y = (x/6) + (1/6)

y = (x+1)/6

6y = x + 1

Hence, the equation of the given line is 6y=x+1.

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Answer:

40+x+5 = 3x +15

2x= 30

x=15

Their present ages are 15 and 55

Answer:

true

Step-by-step explanation:

Answer:

<CAB =30°

Step-by-step explanation:

<DAB=80°

<DAC=50°

<DAB=<DAC+<CAB

<CAB=<DAB-<DAC

=80°-50°

=30°

Answer:

Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.

Step-by-step explanation:

Let the average rate (in miles per hour) at which Anthony travels by car be c and by bike be b.

His average rate of speed by car is 24 miles per hour faster than his average rate of speed on bike. In other words:

[tex]c = b + 24[/tex]

Anthony travels 48 miles by car in the same amount of time it takes him to travel 12 miles by bike.

Recall that distance is given by the rate multiplied by the time t.

Hence, c multiplied by time t equals 48 miles:

[tex]\displaystyle ct = 48[/tex]

Likewise, b multiplied by the same time t equals 12 miles:

[tex]bt = 12[/tex]

Solve. We can multiply the second equation by four:

[tex]4bt = 48[/tex]

Substitute:

[tex]ct = 4bt[/tex]

Divide:

[tex]c = 4b[/tex]

Since c = b + 24:

[tex](b + 24) = 4b[/tex]

Solve for b. Subtract:

[tex]24 = 3b[/tex]

And divide:

[tex]b = 8\text{ miles per hour}[/tex]

Hence, Anthony bikes at an average rate of 8 miles per hour.

Since his average speed by car is 24 miles per hour faster, his average speed by car is 32 miles per hour.

In conclusion, Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.

Answer:

Step-by-step explanation:

In x², here the 2 is exponent while x is base.

Answer:

an exponent

Step-by-step explanation:

hope it helps:)

Answer: $4.50

Step-by-step explanation:

48-21=27

27 divided by 6= 4.50

Therefore each case costs 4.50

Answer:

$4.50

Step-by-step explanation:

48 - 21

27

divide by 6

4.50

Answer:

Hope it helped

Step-by-step explanation:

The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

An inverse function or an anti function is defined as a function, which can reverse into another function.

Now the given quadtratic function is,

f(x) = x² + 2

Now vertex of the given quadratic function is (0,2)

Thus the range of the function is [2,∞)

If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.

Now the inverse function is given as,

y = x² + 2

Upon interchanging x and y, we get:

x = y² + 2

⇒ y² = x - 2

or, y = ±[tex]\sqrt{x-2}[/tex]

Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

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Answer:

[tex]\frac{(a+b)}{a^{2} -b^{2} }[/tex] + [tex]\frac{(a-b)}{a^{2} -b^{2} }[/tex] = [tex]\frac{2a}{a^{2} -b^{2} }[/tex]

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{ \sqrt{a + b} }{ \sqrt{a - b} } + \frac{ \sqrt{a - b} }{ \sqrt{a + b} } \\ squaring \: on \: both \: sides \\ \frac{a + b}{a - b} + \frac{a - b}{a + b} \\ \frac{(a + b) \times (a + b) + (a - b)(a - b)}{(a - b)(a + b)} \\ \frac{ {(a + b)}^{2} + {(a - b)}^{2} }{ {a}^{2} - {b}^{2} } \\ remaining \: in \: attachment[/tex]

[tex]thank \: you[/tex]

Answer:

The correct choice is option B. (5, 2)

Step-by-step explanation:

The rotation rule of 180° is = (x ,y) -> ( -x , -y) .

Coordinates of C before the rotation are ( -5 , -2) so according to the rule above they will now be = C'( 5 , 2 ) .

Therefore, the ordered pair for C' is (5, 2) after the 180 degrees rotation.

Answer:

1/23

Step-by-step explanation:

5/23 - 4/23 would be 1/23. When the denominators of the fractions are the same, you can just subtract the numerators.

Answer:

Below.

Step-by-step explanation:

The GCF of 9 , 27 and 45 = 9.

GCF of the d terms is d^2.

So the GCF of the whole expression is 9d^2.

Factors are 9d^2( 1 - 3d^3 + 5d)

Answer:

40% increase

Step-by-step explanation:

c = final value - initial value

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

                initial value

112 - 80 = 32

32 / 80 = 0.4

0.4 = 40%

Answer:

its still 34 bcs there were 18 new members and 2 left they were new not old so we didn't exactly touch the number 34 so yeah hope i'm correct

Step-by-step explanation:

Answer:

[tex] \sqrt{2.2.3.3.5} [/tex]

[tex]\sqrt{2.2.3.3.5}[/tex] is equivalent to [tex]\sqrt{180}[/tex]. Correct option is 1. First, we look for perfect square factors within 180. We can factor 180 as follows: [tex]\(180 = 2^2 \times 3^2 \times 5\)[/tex]

Next, we can group the perfect square factors together:

[tex]\(180 = (2 \times 3)^2 \times 5\)[/tex]

Since we are taking the square root of 180, we can rewrite it as the square root of its perfect square factors multiplied by the remaining non-perfect square factor:[tex]\(\sqrt{180} = \sqrt{(2 \times 3)^2 \times 5}\)[/tex]

The square root of a perfect square is just the value of the number itself:

[tex]\(\sqrt{180} = 2 \times 3 \times \sqrt{5}\)[/tex]

Finally, we can simplify the expression by multiplying the numbers outside the square root [tex]\(\sqrt{180} = 6\sqrt{5}\)[/tex]

So, the expression [tex]\(6\sqrt{5}\)[/tex] is equivalent to [tex]\(\sqrt{180}\)[/tex], and it represents the positive square root of 180 with any perfect square factors taken outside the square root sign.

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Answer:

Step-by-step explanation:

[tex] \frac{3}{5} xy \: \times ( - 25 {x}^{2} y)[/tex]

[tex] = \frac{3}{5} \times ( - 25) \times x \times {x}^{2} \times y \times y[/tex]

[tex] = - 15 \times {x}^{3} \times {y}^{2} [/tex]

[tex] = - 15 {x}^{3} {y}^{2} (ans)[/tex]

Answer:

4x + x^2 + 3

Step-by-step explanation:

First you are gonna drop the parenthesis. Then you are gonna combine -1 and +3 which gives you +2.

Answer:

Step-by-step explanation:

[tex]U=\{(x,y)\ \zeta\ y=|x+1| \ and\ x \in \{-2,-1,0,1,2\}\ \}\\\\\begin{array}{|c|c|}x&y\\---&---\\-2&2\\-1&0\\0&2\\1 & 4\\2&6\\---&---\\\end{array}\\\\U=\{(-2,2),(-1,0),(0,2),(1,4),(2,6)\}\\[/tex]

Answer:

2 / (-2,2)

Step-by-step explanation:

Answer:

Get all the terms with x on the left. Get all the terms without x on the right. Simplify by adding and subtracting the terms without x and adding and subtracting the terms with x. Finally divide to get the value of x.

Step-by-step explanation:

6x+6 =- 5+3x+17

6x+6 -6 =- 5+3x+17 -6

6x = 5+3x+11

6x = 3x + 16

6x - 3x = 3x + 16 -3x

3x = 16

3x / 3 = 16 / 3

x = 15/3 + 1/3

x = 5 1/3

x = 5.33333...

Assuming 120 is a base 10 numeral, then

120 = 100 + 20 = 4×5² + 4×5¹

so you have

120₁₀ = 440₅

Answer:

65 kph

Step-by-step explanation:

There were a total of 7 hours. So two hours were at 70 and the other 5 hours at 63: the equation would be: (70+70+63+63+63+63+63)/7=65

(f–g)(x)= (3x-13) – (2x²–4x–5)= –2x²+7x-8

(f–h)(x)= (3x-13) – ( 4^x –7) = 3x – 4^x–6

(f+g)(x)= (3x-13) + (2x²–4x–5) = 2x²–x – 18

I hope I helped you^_^

Answer:

7, 11, 15, 19, 23, ... To get the terms in the original sequence, we need to add on 3 to each of the terms in the 4n sequence. Hence, the general formula for the nth term of the original sequence is 4n + 3.

hope this helped!!!

Answer:

x = 17°

m∠MKL = 116°

m∠JKL = 159°

Step-by-step explanation:

JKM = 43

MKL = 8x - 20

JKL = 10x - 11

Since JKL is the whole angle, JKM + MKL = JKL

43 + 8x - 20 = 10x - 11

Add 20 to both sides:

43 + 8x = 10x + 9

Subtract 8x from both sides:

43 = 2x + 9

Subtract 9 from both sides:

34 = 2x

x = 17°

MKL = 8(17) - 20

MKL = 116°

JKL = 10(17) - 11

JKL = 159°

And to check 159 - 116 = 43

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

all of the above

Step-by-step explanation:

Answer:

It gives heat and light on the earth.

plants makes food with the help of sunlight.

Animals take warmth by sunlight.etc.

Hi ;-)

[tex]y-4=3\\\\y=3+4\\\\\boxed{y=7}[/tex]

Answer:  7  

.....7-4=3

Area=50m^2

Let side be a

[tex]\\ \rm\Rrightarrow Area=a^2[/tex]

[tex]\\ \rm\Rrightarrow a^2=50[/tex]

[tex]\\ \rm\Rrightarrow a=\sqrt{50}[/tex]

[tex]\\ \rm\Rrightarrow a=7.1m[/tex]

Answer:

[tex]\displaystyle 5\sqrt{2}\:m.[/tex]

Step-by-step explanation:

Sinse squares are equal in length all around, this formula applies:

[tex]\displaystyle s^2 = A → \sqrt{50} = \sqrt{s^2} \\ \\ 5\sqrt{2} = s[/tex]

Therefore, the length of the playground is [tex]\displaystyle 5\sqrt{2}[/tex] metres.

* Just in case you could not figure out how to find the square root of fifty, here is how using perfect squares:

[tex]\displaystyle \sqrt{50} → \sqrt{2 \times 25} \\ \\ 5\sqrt{2}[/tex]

Sinse we are dealing with measurements, we only want the NON-NEGATIVE root.

I am joyous to assist you at any time.