After Lois picks a value for b, Clark must solve the equation 2x + 7 - x = 4x + 2b – 3x - 3b.

Clark uses Lois's b, then tries to solve the equation by repeatedly guessing values of x until he guesses
the right one. However, for every x he picks, the left side is always 3 more than the right side. What
value of b did Lois give Clark?

Answer:

[tex]y=3x-15[/tex]

Step-by-step explanation:

[tex]Slope=m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-9-(-3)}{2-4}=\frac{-6}{-2}=3[/tex]

[tex]y=3x+b[/tex]

[tex]-3=3(4)+b[/tex]

[tex]-3=12+b[/tex]

[tex]-15=b[/tex]

[tex]y=3x-15[/tex]

[tex]\text{Given that,}\\\\(x_1,y_1) = (4,-3),~\text{and}~ (x_2,y_2) = (2,-9)\\\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-9+3}{2-4} = \dfrac{-6}{-2} = 3\\\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y -(-3) = 3(x-4)\\\\\implies y+3 = 3x -12\\\\\implies y = 3x -12 -3 \\\\\implies y = 3x -15\\\\\textbf{This is the slope - intercept form(y = mx +b), where m =3 and b =-15.}[/tex]

Answer:

3 < r

Step-by-step explanation:

167<6+7(2+7r)

distribute the 7 to the 2 and 7r

7 * 2 = 14 and 7 * 7r = 49r

167 < 6 + 14 + 49r

combine like terms: 6 + 14 = 20

167  < 20 + 49r

subtract 20 from both sides

147 < 49r

divide both sides by 49

3 < r

Answer:

ngee hirap Naman niyan sayang

Using inverse function concepts, it is found that:

The function given is:

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

To find the inverse, we exchange x and y, and isolate y, then:

[tex]y = (x + 1)^2 - 3[/tex]

[tex]x = (y + 1)^2 - 3[/tex]

[tex](y + 1)^2 = x + 3[/tex]

[tex]\sqrt{(y + 1)^2} = \sqrt{x + 3}[/tex]

[tex]y + 1 = \sqrt{x + 3}[/tex]

[tex]y = \sqrt{x + 3} - 1[/tex]

The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].

A similar problem is given at https://brainly.com/question/13160937

Answer:

Step-by-step explanation:

No, Poppy did not answer the problem correctly.

The mistake I see is that she did not include the exponent on the first 3. She also forgot to keep the -8.

The correct answer would be -7. (see attachment)

Have a nice day :)

Answer:

27

Step-by-step explanation:

The triangle shown is a right triangle, indicated by the little square at the bottom right. When trying to find the length of a missing leg of a right triangle we can use the Pythagorean theorem.

Pythagorean theorem : a² + b² = c²

Where a and b = legs and c = hypotenuse ( longest side )

We are given the length of the hypotenuse as well as a leg and we need to find the other leg.

Hypotenuse (c) = 45

Leg (a) = 36

To find the length of the other leg we can plug in the given values of the hypotenuse and the leg into the Pythagorean theorem and solve for b

Recall the Pythagorean theorem : a² + b² = c²

a = 36 and c = 45

(36)² + b² = (45)²

simplify exponents : 36² = 1296 and 45² = 2025

1296 + b² = 2025

subtract 1296 from both sides: 1296 - 1296 cancels out and 2025 - 1296 = 729

b² = 729

take the square root of both sides: √(b)² = b and √729 = 27

We're left with b = 27 meaning that the length of the other leg ( or missing side ) is 27

Answer:

you should take notes

Step-by-step explanation:

why you should know this your teacher probally already taught you this already you should go back and take notes = )

Answer:

y = 10x + 6.

Step-by-step explanation:

y = mx + c

Here  the slope m = 10 and c = 6 ( the y-intercept)

It's 6 because the point (0, 6) lies on the y-axis (where x = 0).

Answer:

Step-by-step explanation:

[tex]3- \dfrac 12 x >10\\\\\implies - \dfrac x 2> 10 -3\\\\\implies -\dfrac x 2 >7\\\\\implies -x > 14\\\\\implies x<-14\\\\\text{Interval solution,}~ (-\infty,-14)[/tex]

Answer:

D) 3x + 33

Step-by-step explanation:

3(x + 11)

3x + 33

Hope this helps! Pls give brainliest!

Answer:

slope:1

y-intercept:(0,0

Answer:

x = -1 and x = 8.1

See image

Step-by-step explanation:

If you are allowed to use your graphing calculator, the directions "solve by graphing" means to graph the equations and look for the points where the two graphs intersect (cross) or if allowed, use an online graphing utility such as Desmos. It is really useful. If you may not use a calculator or desmos, then sketch a graph of the functions. Using transformations can help you sketch a graph fairly quickly. You should be memorizing the shape of the graph in its simplest form

y=sqrt x

And

y=|x|

Transformations then reflect, shrink or stretch, and shift sideways or up or down the graph. This is only if you're not allowed to graph it using technology. Remember that the solution is where the graphs cross. ...a little bit tricky: the answers only give the x value instead if two ordered pairs.

Step-by-step explanation:

let's consider BA and CD as one pair of sides, and CB and DA as the second pair of sides.

the slope BA = -1

as x changes +4 (from 0 to 4), and y changes -4 (from 4 to 0).

the slope of CD = -1

as x changes +4 (from -4 to 0) and y changes -4 (from 0 to -4).

so, both lines are indeed parallel.

the slope CB = +1

as x changes +4 (from -4 to 0) and y changes +4 (from 0 to 4)

the slope of DA = +1

as x changes +4 (from 0 to 4) and y changes +4 (from -4 to 0)

so, these 2 lines are also parallel to each other and perpendicular to the first 2 lines (x and y in the slope ratio upside-down, and the sign is flipped).

therefore, we have only 90° angles here.

and the sums of the x and y coordinate differences are the same for every side, so all sides are equally long.

therefore, this is a square.

and with that it is automatically also a rectangle and a rhombus.

Answer:

-8

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Evaluate f(- 2) then substitute the value obtained into g(x)

f(- 2) = 3(- 2)² + 2(- 2) - 1 = 3(4) - 4 - 1 = 12 - 5 = 7 , then

g(7) = 4(7) - 5 = 28 - 5 = 23

[tex]\text{Given that,}\\\\f(x) = 3x^2 +2x -1\\\\f(-2)=3(-2)^2 +2(-2) -1 = 12-4-1=7\\\\g(x) = 4x -5\\\\\text{Now,}\\\\(g \circ f) (-2)\\\\=g(f(-2))\\\\=g(7)\\\\=4(7)-5\\\\=28-5\\\\=23[/tex]

Answer:

84 and 144

Step-by-step explanation:

If the two numbers are  a  and  b  and their LCM is  x  and their HCF is  y  then there is a rule that is  a×b=x×y

in this case:

a×b=x×y

a×b=(504)×(24)

a×b=12096

when finding factors of 12096 that are between 60 and 160, we can see that 84 and 144 is the best pair.

hope this helps! :D

have a miraculous day!! <3

Answer:

x=6

Step-by-step explanation:

x/-2=-3

*-2    *-2

x=6

-hope it helps

Answer:

None of the bowls

Step-by-step explanation:

It's because the amount of chocolate and vanilla in the pudding is the same,

which is why both are chocolatey; none are more chocolatey

Answer:

none

Step-by-step explanation:

Answer:

1,081

[tex]f( - 4) = 9( - 4 - 7) {}^{2} - 8 \\ f( - 4) = 9( - 11 {)}^{2} - 8 \\ f( - 4) = 1081[/tex]

Answer:

y = 7

Step-by-step explanation:

0.3y+0.6 = 9.7 - y

0.3y+y = 9.7 -0.6

1.3y = 9.1

y= 7

sorry it had an error

Answer:

so first you add something and then subtract and then divide then you er butf then youcan see toplod ej

Answer:

Larger angle: 104 degrees

Smaller angle: 76 degrees

Step-by-step explanation:

(9x+5) + (6x+10) = 180

x = 11

Answer:I hope it helps to you it's so important to you right♡

The identity could be the missing step to verify the identity

(cosФ)(cscФ) = cotФis, (cosФ)(1/sinФ) = cotФ.

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f(x), with all x being real values, is said to be periodic.

We know, sin/cos = tan = 1/cot = cos/sin.

Given, (cosФ)(cscФ) = cotФ.

We know, sin = 1/csc.

Therefore,

(cosФ)(cscФ) = cotФ.

cosФ×1/sinФ = cotФ.

cosФ/sinФ = cotФ.

learn more about trigonometric identities here :

https://brainly.com/question/3785172

#SPJ7

Answer:

8-r/-2

8-12/-2

-4/-2

2

This is the answer

I think this will help you

[tex]\huge \rm༆ Answer ༄[/tex]

In the given question, the two sides of the given triangles are parallel, so the the two corresponding angles of the Triangles are equal to one another.

Therefore, the Triangles are similar by AA similarity criteria ~

And since they are similar, the ratio of sides of one Triangle will be equal to ratio of corresponding sides of the other Triangle.

that is ~

Hence, value of l = 15.4 units ~

Answer:

3.02

Step-by-step explanation:

Find the difference:

17 - (-10) = 27

So the distance between 17 and -10 is 27.

Answer: 27

Step-by-step explanation: