SOMEONE HELP MEEEEEE 75 POINTS TO THE PERSON THAT HELPS

1. Indicate the equation of the given line in standard form.

The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).


2. Indicate the equation of the given line in standard form.

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).


3. Indicate the equation of the given line in standard form.

The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.


4. Indicate the equation of the given line in standard form.

The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.


5. Indicate the equation of the given line in standard form.

The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).


6. Indicate the equation of the given line in standard form.

The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).

7. Indicate the equation of the given line in standard form.

The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).

8. Indicate the equation of the given line in standard form.

The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.

Answer:

The measure of angle BCD is [tex]68.5\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

In this problem

[tex]m<ABD+m<BCD+m<EDF=180\°[/tex] -----> is a straight line

substitute the values

[tex](3x+4)+(6x-8)+(7x-20)=180\°[/tex]

[tex](16x-24)=180\°[/tex]

[tex]16x=180\°+24\°[/tex]

[tex]x=12.75\°[/tex]

step 2

Find the measure of angle BCD

[tex]m<BCD+=(6x-8)\°[/tex]

substitute the value of x

[tex]m<BCD+=(6(12.75)-8)=68.5\°[/tex]

Answer:

slope=-1/4

Step-by-step explanation:

point 1: -4,-1

point 2: 0,-2

y1-y2/x1-x2

1/-4

-1/4

Answer:

Step-by-step explanation:

A

The vertex form: f(x) = a(x-h)^2 + k

f(x) = x^2 + 16x + 60 = (x^2 + 16x) + 60

We want to get a perfect square in the brackets, so we solve for our b^2 coefficient.

b^2 = (16/2)^2 = 64

f(x) = (x^2 + 16x + 64 - 64) + 60. Note we subtracted 60 right away to end up with an equivalent expression and not some other function.

f(x) = (x+8)^2 - 4, as you can see it matches the general vertex form.

The vertex form shows when the profit is minimal. The point (h, k) or f(h).

B. The x-intercepts or when the function is equal to 0, or the profit is 0 in the context of the problem.

f(x) = x^2 + 16x + 60 set = 0

x^2 + 16x + 60 = 0

[tex]x_{12} = \frac{-16 \pm \sqrt{256 - 4(1)(60)}}{2} = \frac{-16 \pm \sqrt{16}}{2} = \frac{-16 \pm 4}{2} = -8 \pm 2[/tex]

Answer:

the vertex is either the maximum or minimum value

since the leading coefinet is negative (the number in front of the x² term), the parabola opens down and is a maximum

so

A.

a hack version is to use the -b/(2a) form

if  you have f(x)=ax²+bx+c, then the x value of the vertex is -b/(2a)

so

given

f(x)=-1x²+16x-60

the x value of the vertex is -16/(2*-1)=-16/-2=8

the y value is f(8)=-1(8)²+16(8)-60=

-1(64)+128-60=

4

the vertex is (8,4)

so you selll 8 candels to make the max profit which is $4

B.

x intercepts are where the line crosses the x axis or where f(x)=0

solve

0=-x²+16x-60

0=-1(x²-16x+60)

factor

what 2 numbers multiply to get 60 and add to get -16

-6 and -10

0=-1(x-6)(x-10)

set each factor to 0

0=x-6

x=6

0=x-10

10=x

x intercepts are at x=6 and 10

that is where you make 0 profit

I hope u get what ur looking for and I wish u give me brainlist But I know u won't cuz everyone say that . But thank you so much if u put for me and It would be a very appreciated from you and again thank you so much

Thank you

sincerely caitlin

4x➕6(503-x)=2296

Distribute the 6 into the parentheses

Let x represent the students

503-x will represent the non-students

4x➕3018➖6x=2296

Then combine like terms

-2x➕3018=2296

Now since you move your constant your sign has to change as well,

-2x=2296➖3018

Then subtract

-2x=-722

Then divide both sides by -2

You are left with x=361

This represents the students

503➖361= 142 which equal the non-students

Therefore your answer is:

361=students

142=non-students

Hope this helps! :3

Answer:

361 students and 503-361=142 non students

Step-by-step explanation:

Let x = number of students. And 503-x = the number of non students. Therefore, 4x+6(503-x)=2296

Do what? I can't see a question

repost and let me know once it’s up because I can’t see the picture

Good luck,

:)

Answer:

4a + 2b + 1/4 c.

Step-by-step explanation:

1/4(16a+8b+c)

= 1/4 * 16a + 1/4 * 8b + 1/4 * c

= 4a + 2b + 1/4 c.

Final answer:

To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses and simplify the expression.

Explanation:

To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses. This means multiplying 1/4 by 16a, 1/4 by 8b, and 1/4 by c. The distributive property states that a (b + c) = ab + ac. So, the expression becomes:

1/4(16a) + 1/4(8b) + 1/4(c)

Since 1/4 times any number equals the number divided by 4, we can simplify further:

(16a/4) + (8b/4) + (c/4)

Which simplifies to:

4a + 2b + c/4

ANSWER

D. 13

EXPLANATION

The given function is:

[tex]f(x) = \frac{2x + 1}{x -4} [/tex]

Let

[tex]y = \frac{2x + 1}{x -4} [/tex]

Interchange x and y.

[tex]x= \frac{2y + 1}{y-4} [/tex]

Solve for y.

[tex]x(y - 4)=2y + 1[/tex]

[tex]xy - 4x=2y + 1[/tex]

[tex]xy - 2y = 1 + 4x[/tex]

[tex](x - 2)y = 1 + 4x[/tex]

[tex]y = \frac{1 + 4x}{x - 2} [/tex]

[tex] {f}^{ - 1}(x) = \frac{1 + 4x}{x - 2} [/tex]

We put x=3,

[tex]{f}^{ - 1}(3) = \frac{1 + 4 \times 3}{3- 2}[/tex]

[tex]{f}^{ - 1}(3) = \frac{13}{1} = 13[/tex]

Answer:

D

Step-by-step explanation:

Substitute x = g(x) into f(x)

f(2x + 3) = (2x + 3)² ← expand factors

f(g(x)) = (2x)² + 6x + 6x + 3² = 4x² + 12x + 9 → D

Answer:

  B) x^2/12 +y^2/16 = 1

Step-by-step explanation:

The distance from focus to covertex is the same as the distance from the center to the vertex: 4. So, the Pythagorean theorem tells you ...

  a^2 + 2^2 = b^2

  a^2 +4 = 4^2 = 16

  a^2 = 16 -4 = 12

So, the standard-form equation ...

  x^2/a^2 +y^2/b^2 = 1

looks like this when the values are filled in:

  x^2/12 +y^2/16 = 1

The last ones answer is six

Answer:

[tex]4w^4-7z^4+6w^2z^2[/tex]

Step-by-step explanation:

We can reformat this equation so we can vertically add.

Then, we can just add down.

Since all the degrees and the variables are the same, we only have to worry about the coefficients.

5 - 1 = 4 --> [tex]4w^4[/tex]

-7 + 13 = 6 --> [tex]6w^2z^2[/tex]

-3 - 4 = -7 --> [tex]-7z^4[/tex]

Now let's rewrite this.

[tex]4w^4-7z^4+6w^2z^2[/tex]

A function assigns the values. The temperature that will model most accurately predict the time spent cooling will be 300.

A function assigns the value of each element of one set to the other specific element of another set.

For the given function [tex]f(t)=349.2 (0.98)^t[/tex], the value of t which will lie within the given function range will be the value function that will model most accurately predict the time spent on cooling. Therefore, let's substitute the values and check,

A.) t = 0

[tex]f(t)=349.2 (0.98)^t\\\\0=349.2 (0.98)^t[/tex]

As the value of t will lie at infinite, therefore, this will not give an accurate prediction of the model.

B.) f(t) = 100

When the value of the function will be 100 then the value of t will be 61.6, therefore, this can not be the most accurate prediction.

C.) f(t) =300

When the value of the function will be 300 then the value of t will be 7.5, therefore, this is the most accurate prediction.

D) f(t) = 400

When the value of the function will be 400 then the value of t will be -6.724, therefore, this can not be the most accurate prediction.

Thus, the temperature that will model most accurately predict the time spent cooling will be 300.

Learn more about Function:

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The value of ∑n=14[100(−4)n−1] is -5368709100

The sequence is given as:

∑n=14[100(−4)n−1]

The above sequence is a geometric sequence, with the following properties

The sum of n terms of a geometric series is:

[tex]S_n = \frac{a* (r^n - 1)}{r - 1}[/tex]

So, we have:

[tex]S_n = \frac{100* ((-4)^{14} - 1)}{-4 - 1}[/tex]

Evaluate

[tex]S_{14} = -5368709100[/tex]

Hence, the value of ∑n=14[100(−4)n−1] is -5368709100

Read more about geometric series at:

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The sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\)[/tex] is [tex]\[\boxed{-5100}\][/tex]

To find the sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\),[/tex] we will calculate the individual terms of the sequence and then sum them up.

The general term of the sequence is [tex]\(100(-4)^{n-1}\)[/tex]. Let's compute the terms from [tex]\(n = 1\) to \(n = 4\):[/tex]

1. For [tex]\(n = 1\):[/tex]

[tex]\[ 100(-4)^{1-1} = 100(-4)^0 = 100 \cdot 1 = 100 \][/tex]

2. For [tex]\(n = 2\):[/tex]

[tex]\[ 100(-4)^{2-1} = 100(-4)^1 = 100 \cdot (-4) = -400 \][/tex]

3. For [tex]\(n = 3\):[/tex]

[tex]\[ 100(-4)^{3-1} = 100(-4)^2 = 100 \cdot 16 = 1600 \][/tex]

4. For [tex]\(n = 4\):[/tex]

[tex]\[ 100(-4)^{4-1} = 100(-4)^3 = 100 \cdot (-64) = -6400 \][/tex]

Now, let's sum these terms:

[tex]\[100 + (-400) + 1600 + (-6400)\][/tex]

Perform the calculations step-by-step:

1. [tex]\(100 - 400 = -300\)[/tex]

2. [tex]\(-300 + 1600 = 1300\)[/tex]

3. [tex]\(1300 - 6400 = -5100\)[/tex]

Answer:

[tex]f(x)=3^x[/tex]

Step-by-step explanation:

Given that the function is represented by the graph below, which  begins in the second quadrant near the x−axis and increases slowly while crossing the ordered pair 0, 1. When the graph enters the first quadrant, it begins to increase quickly throughout the graph

Because it passes through (0,1) it is of the form

[tex]y=a^x[/tex]

Also for negative x large it is very near x axis, So a must be positive then only it increases faster in the I quadrant.  Range is only posiitve real numbers

So the function is

[tex]f(x) =3^x[/tex]

Answer:

the person above me is correct

Step-by-step explanation:

by the way its 8 because 24 words divided by 4 weeks is 8.

The unit rate describing Alan's vocabulary acquisition is 6 words per week.

The unit rate that describes the situation where Alan learned 24 new vocabulary words in 4 weeks is 6 words per week.

To find the unit rate, divide the total number of words learned by the total number of weeks. In this case, 24 words / 4 weeks = 6 words per week.

Answer: 47+B(.85) = A

Step-by-step explanation:

One bagel = $0.85

Sold 47 today

One bagel(.85) = profit

A = profit

B = additional bagels

47+B(.85) = A

answer for this question is (d)3x2-x+6

This is the answer:)

Answer:

The length of QS and TV is 8 units

Step-by-step explanation:

we know that

If triangle QRS is congruent with triangle TUV

then

QS=TV

QR=TU

RS=UV

In this problem

we have

QS=3v+2

TV=7v-6

so

QS=TV

3v+2=7v-6

Solve for v

7v-3v=2+6

4v=8

v=2

Find the length of QS

substitute the value of v

QS=3(2)+2=8 units

so

TS=8 units

Final answer:

Triangle QRS is congruent to triangle TUV, so side QS is equal to side TV. By setting the expressions for QS and TV equal and solving for 'v', we find that both lengths are 8 units.

Explanation:

To solve the problem of finding the length of QS and TV given that triangle QRS is congruent to triangle TUV, and being given the expressions QS = 3v + 2 and TV = 7v - 6, we must recognize that congruent triangles have corresponding sides of equal length. Thus, we can set the expressions for QS and TV equal to each other:

3v + 2 = 7v - 6

We then solve for 'v' by subtracting 3v from both sides:

2 = 4v - 6

Next, we add 6 to both sides:

8 = 4v

Divide both sides by 4 to find 'v':

v = 2

Now that we have the value of 'v', we can substitute it back into the expressions for QS and TV to find their lengths:

QS = 3(2) + 2 = 8

TV = 7(2) - 6 = 8

Therefore, the length of QS and TV is 8 units each.

Answer:

c. 1 and 3

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph s

The equations are:

1) y = sin (3x + π/6)

2) y = cos (3x - π/6)

3) y = cos (3x - π/3)

Looking at the graphs, we can see that the identical ones

are equations one and three

Correct option:

c. 1 and 3

The correct option is:

             option: c     c.   1 and 3

The first trignometric function is given by:

     [tex]y=\sin (3x+\dfrac{\pi}{6})[/tex]

and also we know that:

[tex]\sin \theta=\cos(\dfrac{\pi}{2}-\theta)[/tex]

This means that:

[tex]\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-(3x+\dfrac{\pi}{6})\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-3x-\dfrac{\pi}{6})\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{2}-\dfrac{\pi}{6}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{2\pi}{6}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=\cos (\dfrac{\pi}{3}-3x)\\\\\\\sin (3x+\dfrac{\pi}{6})=cos (-(3x-\dfrac{\pi}{3}))[/tex]

As we know that:

[tex]\cos (-\theta)=cos(\theta)[/tex]

Hence, we have:

[tex]\sin (3x+\dfrac{\pi}{6})=\cos (3x-\dfrac{\pi}{3})[/tex]

Also,  by the graph we may see that the graph of 1 and 2 function do not match.

Hence, they are not equivalent.

Answer:

Domain = Range =  All real numbers

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=2x+cos x

From the plot, we can see the answer is

Option a.

Domain = Range = (-∞,∞)

Answer: a

Step-by-step explanation:

right on edg

Answer:

The answer is -8.

Step-by-step explanation:

Answer:

The x intercepts are x=-4 and x=2

axis of symmetry x=-1

vertex (-1,-9)

D: {x: all real numbers}

R: {y: y≥ -9}

Step-by-step explanation:

f(x) = x^2+2x-8

y= x^2+2x-8

Factor the equation

What 2 numbers multiply to -8 and add to 2

4*-2 = -8

4+-2 =2

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

The x intercepts are found when we set y =0

0=  (x+4) (x-2)

Using the zero product property

x+4=0   x-2 =0

x=-4 and x=2

The x intercepts are x=-4 and x=2

The axis of symmetry is halfway between the x intercepts.  It is symmetric must be in the middle of the x intercepts

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

The axis of symmetry is at x=-1

To find the vertex, it is along the axis of symmetry.  Substitute x=-1 into the equation

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

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

  =3*-3

  =-9

The vertex is (-1,-9)

The domain is the values that x can take

x can be any number

D: {x: all real numbers}

The range is the values that y can take

since the parabola opens upward, the vertex is the minimum,Y must be greater than or equal to -9

R: {y: y≥ -9}

The mathematical expectation for the number of spaces moved in one turn is:

           A.    3 spaces forward.

Th result or the sample space on spinning a spinner twice is:

           (1,1)    (1,4)    (1,6)    (1,8)

           (4,1)   (4,4)    (4,6)  (4,8)

           (6,1)   (6,4)    (6,6)  (6,8)

           (8,1)   (8,4)    (8,6)   (8,8)

Total number of outcomes= 16

The number of outcomes whose sum is even= 10

( Since the outcomes are: {(1,1) , (4,4) , (4,6) , (4,8) , (6,4) , (6,6) , (6,8) , (8,4) , (8,6) , (8,8)}  )

The number of outcomes whose sum is odd= 6

( Since, the outcomes are: { (1,4) , (1,6) , (1,8) , (4,1) , (6,1) , (8,1) }

Probability(sum even)=10/16

Probability(sum odd)=6/16

Hence, the expectation is:

 [tex]E(X)=\dfrac{10}{16}\times (+6)+\dfrac{6}{16}\times (-2)\\\\\\E(X)=\dfrac{60-12}{16}\\\\\\E(X)=\dfrac{48}{16}\\\\\\E(X)=+3[/tex]

                 Hence, the answer is:

              A.  3 spaces forward.

Answer:

983497

step-by-step explanation:

The sum formula of arithmetic sequence is given by:

[tex]S_n = \frac{n}{2}(2a_1 +(n - 1)d[/tex]

a_1 is the first term, n is the nth term and d is the common difference

From the given information

[tex]d = - 1 -( - 5) = - 1 + 5 = 4[/tex]

[tex]a_1 = - 5 \: and \: n = 703[/tex]

By substitution we obtain:

[tex]S_{703}= \frac{703}{2}(2( - 5) +(703- 1)4)[/tex]

[tex]S_{703}= \frac{703}{2}( - 10 + 2808)[/tex]

[tex]S_{703}= \frac{703}{2}(2798)[/tex]

[tex]S_{703}=98397[/tex]

Answer:

S = 983,497

Step-by-step explanation:

We are given the following sequence and we are to find the sum of the first 703 terms of this sequence:

[tex]-5, -1, 3, 7, ...[/tex]

Finding the common difference [tex]d[/tex] = [tex]-1-(-5)[/tex] = [tex]4[/tex]

[tex]a_1=-5[/tex]

[tex]a_n=?[/tex]

[tex]a_n=a_1+(n-1)d[/tex]

[tex] a_n = - 5 + ( 7 0 3 - 1 ) 4 [/tex]

[tex] a _ n = 2803 [/tex]

Finding the sum using the formula [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex].

[tex]S_n = \frac{703}{2}(-5+2803)[/tex]

S = 983,497

Answer:

B) 3/4

Step-by-step explanation:

3 /4

Set A interquartile range = 4

Difference between medians is 3.

Therefore,  3 /4

The difference between the median of set A and set B as a multiple of interquartile range of set A is 3/4.

Set A interquartile range is 4

Difference between their medians is 3

The interquartile range is a measure of the “middle fifty” in a data set in which a range is a measure of the beginning and end are in a set, an interquartile range is a measure of the bulk of the values lie.

Difference between the median = Median / Interquartile range of A

                                                       = 3/4

Thus, the difference between the median set A and set B as multiple of interquartile range is 3/4.

Learn more about the Interquartile range from:

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#SPJ2

Answer:

option B

Step-by-step explanation:

Step 1

A + B = C

[tex]A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right][/tex][tex]+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right][/tex]

=

[tex]C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 2

[tex]\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 3

4 equations are form

Equation 1

8 + 3x = x

8 = -2x

x = -4

Equation 2

-3 + z + 4 = 2z

1 + z = 2z

1 = z

z = 1

Equation 3

3 + w = 4

w = 1

Equation 4

y + 2 + y/2 = y

2 + y/2 = 0

4 + y = 0

y = -4

Step 4

[tex]\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right][/tex]

Answer:

B

Step-by-step explanation:

I got 100% on EDGE 2020 Unit test

Answer:

Option A

Option C

Step-by-step explanation:

A relationship is defined as a function if and only if each element of the "domain" set is assigned only one element of the "range" set. That is, there is only one output value y assigned to each input value x.

The relation x = 3 is not a function because there are infinite output values y, assigned to the same input element x.

(3, 2), (3, 5) (3, 9) (3,10000)

Then the option A is true

Option C is also true, the equation of the line shown is

[tex]x = 3[/tex]

The rest of the options are false because x = 3 is not a function

Answer:

Explanation:

To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:

1) To graph the equation 1 you can use these features of logarithmfunctions:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

2) Graphing the equation 2 is easier because it is a line: y = - 1 - x

3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:

Answer:

x = -2.1

& .2

Step-by-step explanation:

Answer:

Sanjay watched television last weekend for 180 minutes.

Step-by-step explanation:

Sanjay watched 3 television shows and one movie on television last week.

Time duration of 1 television shows = 30 mins

Time duration of 3 television shows = 3* 30 = 90 mins

Time duration of movie = 90 mins

Total number of minutes Sanjay watched television last weekend = Time duration of 3 television shows + Time duration of movie

= 90 + 90

= 180 min

So, Sanjay watched television last weekend for 180 minutes.

That is 99 degrees if you have the triangle facing the other way

the measure of angle KJL is [tex]\( 40^\circ \)[/tex].

Given information

[tex]\( m(KP) = 2 \cdot m(IP) \)\\\( m(IVK) = 120^\circ \)[/tex]

Using the fact that the sum of angles in a circle is [tex]\( 360^\circ \)[/tex], we have:

[tex]\[ m(KP) + m(IP) + m(IVK) = 360^\circ \][/tex]

Substituting the given values:

[tex]\[ 2 \cdot m(IP) + m(IP) + 120^\circ = 360^\circ \][/tex]

Solving for [tex]\( m(IP) \)[/tex]:

[tex]\[ 3 \cdot m(IP) = 360^\circ - 120^\circ \]\[ 3 \cdot m(IP) = 240^\circ \]\[ m(IP) = \frac{240^\circ}{3} \]\[ m(IP) = 80^\circ \][/tex]

Finding [tex]\( m(KP) \)[/tex]:

[tex]\[ m(KP) = 2 \cdot m(IP) = 2 \cdot 80^\circ = 160^\circ \][/tex]

Using the angle formed by a tangent and a secant theorem, we can find [tex]\( m(\angle KJL) \)[/tex]:

[tex]\[ m(\angle KJL) = \frac{1}{2} (m(KP) - m(IP)) \][/tex]

Substituting the known values:

[tex]\[ m(\angle KJL) = \frac{1}{2} (160^\circ - 80^\circ) \]\[ m(\angle KJL) = \frac{1}{2} (80^\circ) \]\[ m(\angle KJL) = 40^\circ \][/tex]

Therefore, the measure of angle KJL is [tex]\( 40^\circ \)[/tex].

The complete question is:

given:  [tex]\( m(KP) = 2 \cdot m(IP) \)\\[/tex] and [tex]\( m(IVK) = 120^\circ \)[/tex]

find: m∠KJL.