The point (3 , k) is a distance of 5 units from (0 , 1). Find the two possible values of k.

Answers

Answer 1
d =√(x2-x1)^2 + (y2-y1)^2
......._____________
5 =√(3-0)^2 + (k-1)^2
.......__________
5 =√3^2 + (k-1)^2

25 = 9 + (k-1)^2

16 = k^2 - 2k + 1

k^2 -2k - 15 = 0

(k - 5)(k + 3) = 0

k - 5 = 0.....or.......(k + 3) = 0

k = 5.........or.......k = -3

Related Questions

8x6=(8x_)+(8x_)
Complete the question to fine 8x6

Answers

Answer:

8 multiply 6 =(8 multiply 3)+(8 multiply 3)=4

The ordered pairs show amounts y​ (in inches) of rainfall equivalent to x​ inches of snow.(16, 1.5), (12, 1.3), (18, 1.8), (15, 1.5), (20, 2.1),(23, 2.4)​ About how many inches of rainfall are equivalent to 6 inches of snow? Round your answer to the nearest hundredth, if necessary.

Answers

Answer:

0.57 inches of rainfall is equivalent to 6 inches of snow

Step-by-step explanation:

The given data are presented here as follows;

[tex]\begin{array}{cc}x&y\\16&1.5\\12&1.3\\18&1.8\\15&1.5\\20&2.1\\23&2.4\\\end{array}[/tex]

The data points are approximately linear

From the the trend line of the plotted points of the graph, created with Microsoft Excel, with Forecasting, when there is 6 inches of snow the rainfall is 0.575 inches

By linear regression, we have;

Y = a + b·X

Where;

[tex]b = \dfrac{n \cdot \sum XY - \left (\sum X \right ) \cdot \left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}[/tex]

[tex]a = \dfrac{\sum Y - b \cdot \sum X}{n}[/tex]

∑x = 104

∑y = 10.6

∑(x·y) = 191.7

(∑x)·(∑y) = 1102.4

(∑x)² = 10816

n = 6

SigX^2 = 1878

Plugging in the values, gives;

[tex]b = \dfrac{6 \times191.7 - 1102.4}{6 \times 1878 - 10816} \approx 0.10575[/tex]

[tex]a = \dfrac{10.6 - 0.10575 \times 104}{6} \approx -0.06637[/tex]

Therefore;

Y = 0.10575·x - 0.06637

When x = 6 inches, we have;

Y = 0.10575 × 6 - 0.06637 = 0.56813

Y = 0.56813 inches ≈ 0.57 inches of rainfall

Therefore;

0.57 inches of rainfall is equivalent to 6 inches of snow

What's 2/5 divided by 1/10?
Please help

Answers

Answer:

4

Step-by-step explanation:

That's the answer......

Answer:

2/5 ÷ 1/10 = 4

Hope this helped!

Enter the next 3 terms from the geometric sequence below.

2
,
1
,

1
2
,
.

Answers

Answer:

The next 3 terms from the geometric sequence below.

3

2

,

1

,

0

1

2

,

3

.

Step-by-step explanation:

The next 3 terms of the geometric sequence are [tex]\frac{1}{4} , -\frac{1}{8}, \frac{1}{16}[/tex].

What is a Geometric Sequence?

'A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.'

According to the given problem,

The terms are, -2 , 1 , - [tex]\frac{1}{2}[/tex] ....

Now, geometric sequence means that there is a common ratio between the numbers in the sequence.

Common ratio can also be denoted as r.

so, from -2, the next term is -2 × r and the one after this is -2 × r × r and so on.

If we compare, -2 × - [tex]\frac{1}{2}[/tex] = 1

                           1 × -[tex]\frac{1}{2}[/tex] = -[tex]\frac{1}{2}[/tex]

                           -[tex]\frac{1}{2}[/tex] × -[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

                            [tex]\frac{1}{4}[/tex] × -[tex]\frac{1}{2}[/tex] = -[tex]\frac{1}{8}[/tex]

                           -[tex]\frac{1}{8}[/tex] × -[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{16}[/tex]

Hence, we can conclude that the next three terms are, [tex]\frac{1}{4}[/tex] , -[tex]\frac{1}{8}[/tex] ,  [tex]\frac{1}{16}[/tex].

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What is the expression that means the same as 7 less than the square of a number? A. 7-2x B. 7-2× C. 7-x2 D. x2-7 ​

Answers

answer d is correct!!!!!

Answer:

D

Step-by-step explanation:

7 less than the square of the number means a number squared subtracted by 7, which would be D.

A. Find the product. Rewrite +
5.67 X 1.25

Answers

Answer:

Multiply

5.67 by 1.25.

7.0875

a taxi charges $2 per mile and $1 per person. If a ride for 2 people costs $12, how many miles was the ride?

Answers

Answer:

5 miles

Step-by-step explanation:

$12 = ($2 per mile) (2 people)

$12 = $2 + $2m (m = mile)

subtract 2 on both sides to eliminate

$12 - $2 = $2 - $2 + 2m

$10 = 2m

divide both sides by 2 to eleminate m

$10 / 2 = 2m / 2

m = 5

O A
Rx) = 3(x + 1)2 = 2
B.
(x) = -3(x + 1)2 + 2
OC.
Ax) = -3(x + 1)2 - 2
D.
(x) = 3(x - 1)2 + 2
Reset

Answers

It is B hope this helps!!

Write an equation that relates the angles in a triangle. The measures of angles X and Y are the same, x degrees. The measure of angle Z is twice the measure of angle Y.

Answers

Answer:

4x = 180

Step-by-step explanation:

angle x = angle y so we can say both angles are 'x + x' or '2x'

angle z = twice angle y (or twice angle x because they're equal) so we can say angle z = 2x

2x + 2x = 180

The ratio of plates to cups is 10:14. If
there are 7 cups, how many plates
are there?
(Help)

Answers

x PLATES ... 10

7 CUPS ... 14

Cross multiply and et' violá:

[tex]14x=70\implies x=70/14=5[/tex]

Find the length of side x in simplest radical form with a rational

denominator.

45°

V5

45°

X

Answers

Answer: 10/2

Step-by-step explanation:

HELPPPPPPPP!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

4

Step-by-step explanation:

- 14 + 30 / 4

16 / 4

16 ÷ 4

= 4

^-^

Answer:

4

Step-by-step explanation:

-2×7=-14

-2×15=-30

-14--30=16

16÷4=4

Find the solution to the system of equations.
You can use the interactive graph below to find the
solution.
–2x + 2y = -4
3x + 3y = -18

Answers

No solution it’s infinite

Which point below is not on the graph of px) = 36-X?
(-13, 7)
(-35, 1)
(11,5)
(27,3)​

Answers

Answer: B

The square root of 71 does not equal 1

There are 5 pens in a container on your desk. Among them, 3 will write well but 2 have defective ink cartridges. You will select 2 pens (without replacement) to take to a business appointment. Select the most appropriate statement for each part (a-e) when considering calculating the probability that both pens are defective.
a. Let X: the number of defective pens selected. X is a random variable. [Select ]
b. For each pen chosen from the container, we can consider "Defective" as the success and "Working" as the failure since we are interested in both pens being defective. [ Select] -
c. X is well approximated by a Binomial Random Variable X-Bin(n=2. pi=2/5) True
d. If the first pen was replaced before the second pen was selected (sampling with replacement), then X would be very well approximated by a Binomial Random Variable X-Bin(n=2, pi=2/5) True
e. Had you been drawing 2 pens (without replacement) from a container of 25 pens, X would be better approximated by a Binomial Random Variable.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Total Number of pens = 5

Number of defective pens = 2

Number of non-defective pens = 3

A.) number of defective pens selected :

X : {0, 1, 2}

It is possible that no defective pen will be selected ; 1 defective will be chosen or both pens are defective.

2.)

Defective as Success (since selecting a defective pen is the point of interest.

3.)

Since selection is done without replacement

Probability of success per selection is different for each selection ;

Number of defective = 2

Number of observations = 5

P(success on first selection) = 2/5

P(success on second selection) = 1/4

Hence, X is not well approximated by a binomial random variable.

4.) if selection is done with replacement ; then then the probability of success per selection will be the Same for each selection made. Hence, X will be well approximated by a binomial Random variable.

5.) If sampling is done without replacement, then the the hypergeometric function will be a more effective approximation.

Which graph shows dilation?

Answers

Answer:

The First Image

Step-by-step explanation:

A dilation is a type of transformation that enlarges or reduces a figure, therefore in the first Image we see an increase in scale factor of 2.  

The first image because a dilation is either a re-education of enlargement of an image

For the quadratic function shown below, find (a) the direction of the opening, (b) the vertex, and (c) the axis of symmetry.
y=-3(x-3)^2+5

Answers

Answer:

honestly I don't know the answer

I need help fast i apericiate it my guy

Answers

Answer: 59

Step-by-step explanation:

Answer:

I think it's letter b.29

Rhombus
b= 14 in.
h=9 in.


Paralelogram
b= 12ft
h= 8.5ft


A rhombus has an area of 375 mm2 and a base of 25 mm. What is its height?

Answers

Answer:

Step-by-step explanation:

The solution is, The area of Rhombus B is 9 times bigger than the area of Rhombus A.  The reason is that 2 dimensions were tripled, so x3 x3 = 9 times bigger.

What is area ?

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

Rhombus A:

Area = 35 square inches

base = 7 inches

height = 5 inches

Rhombus B:

Area = 315 square inches

base = 21 inches (7 x 3)

height = 15 inches (5 x 3)

A = 21 x 15

so, we get,

The area of Rhombus B is 9 times bigger than the area of Rhombus A.  The reason is that 2 dimensions were tripled, so x3 x3 = 9 times bigger.

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complete question:

Rhombus A has base of 7 inches and an area of 35 square inches. Rhombus B has a Base and Height that are three times the base and height of Rhombus A. Find the area of Rhombus b and compare it to the area of rhombus A Explain

helppppp ahhhh!!

At the library there is a four hour span of time to use a computer. The time slots are 1/3 hour long. How many time slots are there?

Answers

Answer:
12 slots
Step-by-step explanation:
1/3 of an hour = 20 minutes
4 hours * 60 =240mins/20mins=12

Step-by-step explanation:

[tex] \frac{4 \: hours}{computer} \times \frac{1 \: slot}{ \frac{1}{3} hour } = 12 \: \frac{slots}{computer} [/tex]

Write the vertex form equation of a parabola that has been translated right of the origin by 5 units, translated down from the origin by 15 units, reflected over the x-axis, and stretched vertically by a factor of
6

Answers

Answer:

90x+8202727

Step-by-step explanation:

90x70+8090#* 77

10 % of what number is 29?

Answers

Answer:

290

Step-by-step explanation:

To solve this problem you multiply 29 by 100 and then divide the total by 10 as follows:

(29 x 100) / 10

Therefore, you can derive that 10 percent of 290 equals 29.

Note that the answer provided is rounded to the nearest two decimals if necessary.

Kimberly has $120 to spend at the bookstore. Kimberly buys a hardcover book for $36, as well as some gift cards for her family and friends. Each gift card is $15. How many gift cards can Kimberly buy

Answers

Answer:

she can buy 5 more

Step-by-step explanation:

5.6 but she can’t buy half a gift card so 5 gift cards is your answer :)

Please help me nowww
I need this right away!!

Answers

there is not enough information to complete the answer

6 less than the number y

Answers

Answer:

6 less a number y can be represented by the expression 6 - y

Three sets of data are given below. What is the
median of the ranges?
Data A: -3,2,-5,6,8
Data B: 4,9,6,2
Data C: 8,3,0,4
A) 2
B) 5
C) 7
D) 8

Answers

the answer is C. 7
1.) take 8-(-3)
2.) 9-2
3.) 8-0
Then list the number in order least to greatest
-13 7 8
Find the middle number
Get 7

The Coners family are going on a 250 mile road trip. The first day they drive 100 miles. Write an equation with a variable that can be used to find the number of miles remaining.​

Answers

Answer:

100+x=250 or 250-x=100

Step-by-step explanation:

You invested $7000 in two accounts paying 7% and 8% annual interest, respectively. If the total interest earned for the year was $536, how much was invested at each rate?

Answers

Answer: $4,600 was invested in the 8% account and $2,400 was invested in the 7% account.

Step-by-step explanation:

Let's break this down into simpler terms so you can understand.

You invested $7000 in a 7% and 8% account (always remember: the 'x' variable is always given to the biggest percentage)

Total of interest: 536 (this always goes at the end of the equation, after the equal sign)

Step 1: Let's set up the equation:

Here are how percents are written: (7% = 0.07, 8% = 0.08, other examples: 50% = 0.50)

0.08x + 0.07(7,000-x)=536

You're adding both because you want to see how much each account paid together.

Step 2: Distribute the 0.07 to everything in the parenthesis

0.08x + 0.07(7,000-x)=536

0.08x + 490 - 0.07x =536

Step 3: Combine like terms

0.08x + 490 - 0.07x =536

0.01x + 490 =536

Step 4: Continue combining like terms

0.01x + 490 =536

0.01x = 46

Step 5: Divide both sides by 0.01 to get the 'x' by itself

0.01x = 46

x = 4,600

This answer, x = 4,600, says to us that $4,600 was invested in the 8% account.

To find out how much was invested in the 7% account, just replace the x = 4,600 back into this part of the original equation: 7,000-x

7,000-x

7,000-4,600

2,400

So.. $4,600 was invested in the 8% account and $2,400 was invested in the 7% account.

Explain how to solve the problem y = (xz)/ x for y when x = 3 and z = 2.

Answers

Answer:

y=6

standard form

Does anyone know?? I'll give a brainliest For the correct answer.​

Answers

Answer:

its 14

Step-by-step explanation:

because you have 40 bucks then you minus 18 then you divide then u get 14.

Answer:

$14

Step-by-step explanation:

20*2=40

40-12=28

28/2=14

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