If 3+k,18-k,5k+1 are in A.P, then find k​

Answers

Answer 1
Given:

• 3 + k , 18 - k and 5k + 1 are in AP .

To find :

• The value of K .

Solution :

• As we know that, In AP common difference is same :

• b - a = c - b

=> 2b = a + c

Here ,

• a = 3 + k

• b = 18 - k

• c = 5k + 1

=> 2 ( 18 - k ) = 3 + k + 5k + 1.

=> 36 - 2k = 4 + 6k

=> 36 - 4 = 6k + 2k

=> 32 = 8k

=> k = 32/8

=> k = 4

Hence , the value of k is 4.

Answer 2

Answer:

k=4

Step-by-step explanation:

Since the given terms are in A.P., the common difference will be the same

So, 18-k-3-k = 5k+1-18+k

15-2k = 6k-17

6k+2k = 17+15

8k = 32

k = 4


Related Questions

A vet measured the mass of two birds. The mass of the robin was 76.58 grams. The mass of the blue jay was 81.05 grams.

Estimate the difference in the masses of the birds.

The estimated difference in masses of the two birds is grams.

Answers

Answer:

a) 4.47

b) 4.47 g

Step-by-step explanation:

The masses of the birds are given as;

The mass of the robin =76.58 grams.

The mass of the blue jay = 81.05 grams.

Difference in the masses of the birds is : 81.05 - 76.58 =4.47

Difference in masses of the two birds is grams is : 81.05g - 76.58g =4.47g

Directions: Graph the lines in standard form.
5. 3x + 2y = 6

Answers

Answer:

x=2 y=3

Step-by-step explanation:

3x=6

2y=6

x=2

y=3

Round 23,487 to the nearest ten. PLEASE HELP I WILL BRAINEST ASAP

Answers

Answer:

23,490

Step-by-step explanation:

a company packages fruit baskets of different weights and ships them to customers. the company charges a flat fee for packaging the baskets. the total packaging and shipping cost in dollars, y, of a fruit basket weighing x pounds is represented by the line on the graph below. (1 point at (3, 10) another at (6, 16))
what is the y intercept of the line on the graph​

Answers

Answer:

4

Step-by-step explanation:

The y-intercept of any given graph is always the value of the y of the point where the line of the graph intercepts or cut across the y-axis. It is the value of y when x = 0.

In this case, the y-intercept of the line of the graph above is y = 4. At y = 4, x = 0.

It represents the flat fee the company charges for packaging the baskets = $4.

how many solutions does a quadratic equation that can be written as the difference of squares have?

Answers

Answer:

there are teo solutions that can be written as tge difference of square have.

There are two possible solutions for the quadratic equation that can be written as the difference of squares.

What is a quadratic equation?

A quadratic equation is of the form -

y = f(x) = ax² + bx + c

Given is a quadratic equation that can be written as the difference of squares.

A quadratic equation that can be written as the difference of squares is of the form -

(x² - a²)

For the roots, we can write the equation as -

(x² - a²) = 0

x² = a²

x  = ± a

Therefore, there are two possible solutions for the quadratic equation that can be written as the difference of squares.

To solve more questions on quadratic equation, visit the link below -

brainly.com/question/1041084

#SPJ3

7r - 15/s

When r = 3 and s = 5

Answers

Answer:

18

Step-by-step explanation:

7r - 15/s

First step: Substitute

7(3) - 15/5

21 - 3

21 - 3 = 18

Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support your answer​

Answers

Answer:

10.6 hours

Step-by-step explanation:

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
48 yd : 56 yd

Answers

Answer:

4/6

Step-by-step explanation:

please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

10

Step-by-step explanation:

During a soccer game, a goalie kicks a ball upward from the ground. The equation h(t)=-10t^2+40 represents the height of the ball above the ground in feet as a function of time in seconds. When the ball begins moving downward toward the ground, a player from the other team intercepts the ball with his chest 11 feet above the ground. How long after the goalie kicks the ball does the player intercept the ball?

Answers

Answer:

3.98 seconds

Step-by-step explanation:

The given relationship between height, in feet, and the time, in seconds, is

[tex]h(t)=-10t^2+40[/tex]

[tex]\Rightarrow t^2=\frac{40-h(t)}{10}[/tex]

[tex]\Rightarrow t= \pm\sqrt{4-0.1h(t)}\cdots(i)[/tex]

Let at time [tex]t_1[/tex], the ball was at the goalie, so, [tex]h(t_1)=0[/tex], and at the time [tex]t_2[/tex], the ball was intercepted, so, [tex]h(t_2)=11[/tex].

Now, the time to reach the player after the goalie kicks the ball

[tex]\Delta t=t_2-t_1[/tex]

By using equation (i)

[tex]\Delta t=(\pm\sqrt{4-0.1h(t_2)})-\left(\pm\sqrt{4-0.1h(t_1)}\right)\cdots(ii)[/tex]

Now, at the highest point, the slope of the graph must be zero.

So, [tex]\frac {dh(t)}{dt}=0[/tex]

[tex]\Rightarrow -20t=0[/tex]

[tex]\Rightarrow t=0[/tex]

As at the highest point, the time is zero, to before reaching the highest point ( when kikes by the goalie, [tex]t_1[/tex]) take the time with the negative sign and after the highest point (when the ball intercepted, [tex]t_2[/tex]) take the positive sign.

So, from equation (ii) become.

[tex]\Delta t=\sqrt{4-0.1\times 11}-\left(-\sqrt{4-0.1\times 0} \right)[/tex]

[tex]=\sqrt{3.9}-(-\sqrt 4)[/tex]

[tex]=1.98+2[/tex]

= 3.98 seconds

Hence, the time to reach the ball to the player after the goalie kicks the ball is 3.98 seconds.

Jacinth is 4 years older than her sister Naomi. The sum of their ages is 30. How old are the sisters?

Answers

Answer:

Jacinth = 17

Naomi = 13

Step-by-step explanation:

they add up to 30 and follow the criteria

Jacinth is 17 years old, and Naomi is 13 years old as per the linear equation method.

Let's assume Naomi's age is x. According to the given information, Jacinth is 4 years older than Naomi, so Jacinth's age would be x + 4.

The sum of their ages is given as 30, so we can write the equation: x + (x + 4) = 30.

Combining like terms, we have 2x + 4 = 30.

Subtracting 4 from both sides, we get 2x = 26.

Dividing both sides by 2, we find x = 13.

Therefore, Naomi's age (x) is 13 years old.

To find Jacinth's age, we substitute the value of x into the equation for Jacinth's age: Jacinth's age = x + 4 = 13 + 4 = 17 years old.

So, Jacinth is 17 years old, and Naomi is 13 years old.

To learn more about the linear equation;

https://brainly.com/question/29739212

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i am too unmotivated to do any math even if its easy please help :)

Answers

Answer:

40% increase

Step-by-step explanation:

First, find the difference:

161-115=46

Then divide by the past price to get the percent increase:

46/115=.4=40%

Help please!!!

Question 6
5 pts
Factor the variable expression:
36X + 8X
0419x-4)
4X (9+2)
9(4X+2x)
8(X+X)

Answers

Answer:

4x (9+2)

Step-by-step explanation:

36x+8x

36 and 8 can be divided by 4 and they both have an x

[tex]36x + 8x = 4x(9 + 2)[/tex]

[tex]44x = 36x + 8 x[/tex]

[tex]44x = 44x[/tex]

The Answer is

[tex] \green {\boxed{4x(9+2)}}[/tex]

#IfWrongPleaseReport

#StudyTogetherWithMe

#ILoveMath

Evaluate the following expression when a = -3, b = 2,c=5, and
d= -4.
5ac - 26

Answers

Answer:

-101

Step-by-step explanation:

5ac - 26

5 × -3 × 5 - 26 (since a = -3 & c = 5, you substitute them)

-15 × 5 - 26

- 75 - 26

- 101

I hope this is helpful.

anya bought 1.3 pounds of apples. She used 0.28 pound in a pie. How much is​ left? Use the bar diagram to help you

Answers

Answer:

1.02 pounds left

Step-by-step explanation:

Skip the bar graph, just subtract .28 from .30 and voila!

which is the following solution to
x-13<18

Answers

Answer:

X < 31

Step-by-step explanation:

Answer: X<31

Hope this helps!

Find the distance between the two points in simplest radical form.
n.
(6, -9) and (1,3)
Help?

Answers

[tex]\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}[/tex]

Given to points to us are :-

( 6 , -9)( 1 , 3 )

Now , we can use Distance Formula , which is :-

[tex]\boxed{\purple{\tt Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}[/tex]

Here ,

x1 = 6 .x2 = 1.y1 = (-9)y2 = 3.

→ Substituting the respective values ,

⇒ Distance = √ [ ( 6 - 1)² + ( 3 +9)² ] .

⇒ Distance = √ 5² + 12²

⇒ Distance = √ 25 + 144

⇒ Distance = √ 169 .

⇒ Distance = 13 units .

Hence the distance between two points is 13u.

Write , or = to make the statement true. 9.008 ___ 9.08

Answers

Answer:

9.008 < 9.08

Step-by-step explanation:

9.08 is greater because you compare the number 9 and 9 are the same, 0 and 0 still the same, but then 0 and 8 you know eight is greater. was this helpful enough

can you ou guys please help me with the first two questions?

Answers

number one: multiply by 2
number two: multiply by 5.2 or 5 1/5

HELP ME PLEASE!!! this is the recipe.

Answers

Answer:

Ok... hmmmmm

So im going to assume that this is an adding fractions question so for a half batch it would be 1 1/4 + 2 2/4 which is 3 3/4 cups and for a double batch it would be 15 cups because 10 + 5 is 15.

The first blank probably is 3 3/4

The second blank probably is 15

<3 I already answered this on the other question but I want points so tysm.

Please help me solve this problem!

Answers

Answer:

The line would be a diagonal line that is negative(pointing down).

You can use Desmos Graphing Calculator to help you even more! :)

Name the subset(s) of real numbers to which the number belongs.
−1.57

A. integer only
B. rational only
C. irrational and rational
D. rational and integer

Answers

it’s b- rational (i think)



The figure shown is reflected over the x-axis, then reflected
over the y-axis, and then translated 3 units right.
Which graph best represents the new position of the figure
after the three transformations?
Select one:

Answers

Answer:

grapgh?????

Step-by-step explanation:

please help asapppppppppppppp

Answers

If we perform the vertical line test, we can see that every line touches the graph once. This means that the graph is a graph of a function.

Answer choice b is correct.

Tommy and Arnold are playing with water balloons. Arnold is standing by a bush that is 20 feet from where Tommy is standing. Tommy released a water balloon at 5 feet above the ground and hits Arnold’s chest- which is also 5 feet above the ground. The balloon reached a maximum height of 15 feet off the ground. using Tommy’s location as the starting point, help Tommy write an equation that describes the path of the water from the point of release to Arnold's chest. Using the equation y=a(x-h)^2+k

Answers

Answer:

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Step-by-step explanation:

The motion of the water balloon is represented by quadratic functions. Tommy launches a water balloon from [tex]A(x,y) = (0\,ft, 5\,ft)[/tex] and hits Arnold at [tex]B(x,y) = (20\,ft, 5\,ft)[/tex]. Given the property of symmetry of quadratic function, water ballon reaches its maximum at [tex]C(x,y) = (10\,ft,15\,ft)[/tex], which corresponds to the vertex of the standard equation of the parabola, whose form is:

[tex]y = a\cdot (x-h)^{2}+k[/tex] (Eq. 1)

Where:

[tex]a[/tex] - Vertex parameter, measured in [tex]\frac{1}{ft}[/tex].

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, measured in feet.

[tex]x[/tex], [tex]y[/tex] - Horizontal and vertical location of the ball, measured in feet.

If we know that [tex]x = 0\,ft[/tex], [tex]y = 5\,ft[/tex], [tex]h = 10\,ft[/tex] and [tex]k = 15\,ft[/tex], the vertex parameter is:

[tex]5\,ft = a\cdot (0\,ft-10\,ft)^{2}+15\,ft[/tex]

[tex]a = \frac{5\,ft-15\,ft}{(0\,ft-10\,ft)^{2}}[/tex]

[tex]a = - \frac{1}{10}\,\frac{1}{ft}[/tex]

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Segment KJ = 8, JI = x+6 and KI = 2x+8.
8
X + 6
K.
1
J
2x + 8
Find the values below. Be sure to show all your work.
a. Find x. [Respond Here]
b. Find the length of KI. [Respond Here]

Answers

Answer:

a). x = 6

b). Length of KI = 20 units

Step-by-step explanation:

From the picture attached,

a). Length of KI = length of KJ + length of JI

    By substituting lengths of the segments given in the picture,

    (2x + 8) = 8 + (x + 6)

    2x + 8 = x + 14

    2x - x = 14 - 8

    x = 6

b). Length of KI = (2x + 8)

   By substituting x = 6 in the expression,

   Length of KI = 2(6) + 8

                        = 12 + 8

                        = 20 units

find three points that solve the equation then plot on the graph -x-2y=8

Answers

i gotchu: (-8,0) (0,-4) (4,-6)

Answer:

(-8,0) (0,-4) (4,-6)

Step-by-step explanation:

Brainliest who wants it?? 15 x 15 - 31 + 46 - 5 + 12 =______

Answers

Answer:

247

Step-by-step explanation:

Answer: 247

Step-by-step explanation: 247

What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2

Answers

Answer:

(2, 4, 3)

Step-by-step explanation:

Range = Y

luke paid 30 percent less for a used car than its original price of $3,500. how much did luke pay for the car?​

Answers

Answer:

Im not sure ok

Step-by-step explanation:

Im trying to solve too

Answer:

2450

Step-by-step explanation:

30% of 3500

30÷100×3500

=30×35

=1050

3500-1050

=2450

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