Given (11,6)
and (x,−9)
, find all x
such that the distance between these two points is 17
. Separate multiple answers with a comma.

Answers

Answer 1

All possible values of 'x' such that the distance between the points is 17 is, x = 19 or x = 3.

What is the distance formula between two points?

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, (x₁, y₁) = (11, 6) and (x₂, y₂) = (x,- 9) and the distance between them

is 17 units.

Therefore, The equation can be constructed as,

[tex]17 = \sqrt{(x - 11)^2 + (- 9 - 6)^2[/tex].

[tex]17 = \sqrt{(x - 11)^2 + 225[/tex].

Taking squares on both sides to remove the square root we have,

289 = (x - 11)² + 225.

289 = x² - 22x + 121 + 225.

x² - 22x + 57 = 0.

x² - 19x - 3x + 57 = 0.

x(x - 19) - 3(x + 19) =0.

x = 19 or x = 3 are the two possible points.

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Related Questions

Question number 10 I need help with please

Answers

Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

what is ratio ?

In algebra, ratios display how infrequently one figure is contained in another. For instance, if there are 8- oranges and 6 citrus in a fruit dish, the percentage of oranges to oranges is 8 to 6. In a similar vein, lemons to whole fruit ratio is 8 to 1, whereas lemons to oranges rate is 6 to 8. A ratio is a non-zero ordered pair of numbers, x and y b, that is stated as a / b. A ratio is really an equation that joins two ratio. The ratio can be written as 1:3, signifying that if there 1 boy and (3) girls (she has 3 girls for every boy), 3/4 of the population is female and 1/4 is male.

given

the ratio of sans , gravel and sand is 6:3:2

total pounds needed = 3300

so 6x + 3x + 2x = 3300

11x = 3300

x = 300

6x = 6 * 300 = 1800

3x = 3* 300 = 900

2x = 2* 300 = 600

Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

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Diane asked 12 students how many courses they have taken so far at her college. Here is the list of answers. 14, 3, 22, 10, 3, 5, 23, 18, 16, 9, 1, 26 What is the percentage of these students who have taken fewer than 4 courses? ​

Answers

25%
There are 3 numbers listed that are less than 4 so 3/12= .25 and move two places to the right or x100 and get 25%

what is 1777771 plus 8999907

Answers

Answer: 10777678

ywyw

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (2, 5, 0) and perpendicular to both i+j and j k x(t), y(t), z(t)) The symmetric equations are given by O x+2=-(y + 5), z = 0. O x+2=-(y + 5) = z.

Answers

X(t) = 2-t, Y(t) = 5-t, and Z(t) = 0 are the parametric equations for the line passing through (2, 5, 0) and being perpendicular to both i+j and j k. The line has symmetric equations x+2 = -(y + 5) and z = 0, or x+2 = -(y + 5) = z.

As x(t) = 2-t, y(t) = 5-t, and z(t) = 0, the parametric equations of the line passing through (2, 5, 0) and perpendicular to both i+j and j k can be written. The x, y, and z coordinates of the line are defined by these equations in terms of the parameter t. It is possible to write the line's symmetric equations as x+2 = -(y + 5) and z = 0, or as x+2 = -(y + 5) = z. These equations define the line as the collection of all points (x, y, and z) that concurrently meet both equations. The line goes through the point and is perpendicular to both i+j and j k. (2, 5, 0).

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why does m1 x m2 = -1

Answers

Answer:

By Thales' Rule (aka "the angle in a semicircle is a right angle"), since PR is a diameter,angle PQR is 90 degrees, i.e. PQ is perpendicular to QR, so their gradients multiply to -1.Thus 8/12 * -6/(a-9) = -1, so 12(a-9) = 48, so a-9 = 4, so a=13, as required.

Step-by-step explanation:

Tanner is 2 years younger than his brother. Tanners age t in years is 2 years less than his brothers age b

Answers

Answer:is his brother 4 or 8

Step-by-step explanation:

I don't know for sure

ANSWER -

The relationship between Tanner's age and his brother's age can be represented by the equation:

t = b - 2

This equation states that Tanner's age (t) is equal to his brother's age (b) minus 2 years.

I need help with these questions Pls

Answers

Fractions of smallest to largest

Smallest to largest: 1/4, 1/3, 2/5, 2/3, 3/4

Smallest to largest: 1/5, 2/7, 3/5, 5/7, 31/35

Smallest to largest:  31/30, 23/20, 6/5, 13/10, 7/5

Smallest to largest:   13/10, 13/6, 11/5, 25/6, 21/5

What is fraction?

An element of a whole is a fraction. The number is mathematically expressed as just a fraction, where the numerator and denominator are split. Both are integers in a simple fraction. A simple fraction contains a fraction in either the numerator or the denominator. A fraction consists of two components. The numerator seems to be the number which goes just at top of the line. 

Smallest to largest: 0.25, 0.33, 0.4, 0.67, 0.75

Smallest to largest: 0.2, 0.29, 0.6, 0.71, 0.89

Smallest to largest:  1.03, 1.15, 1.2, 1.3, 1.4

Smallest to largest:  1.3, 2.16, 2.2, 4.17, 4.2

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(I’ll give 10 points help meee) Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure
A*B'C D'E using a series of two different transformations. They give two different
answers.
Answer the questions to investigate ways to transform ABCDE.
Olivia finds a combination of two different transformations that moves ABCDE
onto A'B'C'D'E'. What is one way she might have done this?

Answers

Answer: One way that Olivia might have found a combination of two transformations to move figure ABCDE onto figure A'B'C'D'E' is by using a combination of translations and rotations.

A translation is a type of transformation that moves a figure a certain distance in a specified direction, without changing its size or orientation. A rotation is a type of transformation that turns a figure about a fixed point, called the center of rotation, by a certain angle.

Olivia might have first translated figure ABCDE to a new location and then rotated it about a point to match the orientation of A'B'C'D'E'. For example, she could have translated figure ABCDE so that one vertex coincides with a corresponding vertex in A'B'C'D'E', and then rotated it about that common vertex so that the sides match up.

Alternatively, Olivia might have first rotated figure ABCDE to a new orientation and then translated it to the final position. The sequence of transformations could have been different, but the end result would still be figure ABCDE matching the orientation and position of A'B'C'D'E'.

Step-by-step explanation:

Select all that apply.


Given the points (-6, 8) and (-3, 4), which of the following are true about the line passing through these points?


The line represents a direct variation function.

The line has a slope of - 3/4.

The point (9, -12) is also on the line.

The line has a slope of 3/4 .

Answers

Answer:

The line has a slope of - 3/4.

The line has a slope of 3/4.

Step-by-step explanation:

To determine the slope of a line passing through two points, you can use the formula:

Slope = (y2 - y1) / (x2 - x1)

Using the points (-6, 8) and (-3, 4), the slope would be:

Slope = (4 - 8) / (-3 - (-6)) = -4 / 3 = -4/3

So, the line has a slope of -4/3. The other statements in the list are not necessarily true based on the given information.

The monthly dues for a premium membership at a health club is $15 more than the cost of a standard membership.

The premium membership is $40 per month.

What is the cost of a standard membership?

please explain how you got the answer

Answers

Answer:

To find the cost of a standard membership, we need to subtract the $15 premium from the monthly premium membership cost of $40.

$40 - $15 = $25

Therefore, the cost of a standard membership is $25 per month.

Are the two triangles similar? If so, state the reason and the similarity statement.

A) Impossible to determine
B) The triangles are not similar.
C) Yes, SSS;VWX ~ YZX
D)Yes, SAS; VWX~YZX

Answers

The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides are given as,

YX / XV = ZX / XW

3 / 9 = 2 / 8

1 / 3 ≠ 1 / 4

The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.

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What is the scale factor, without units, of 1 in : 14 ft and 1 in : 30 yard

Answers

The scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1: 168 and 1: 1080 respectively.

What is scale factor

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

For the ratio 1 in : 14 feet, we convert to the same unit in inches:

1 foot = 12 inches

14 feet = 12 × 14 inches

14 feet = 168 inches

1 in = 168 in

1 : 168

For the ratio 1 in : 30 yards, we convert to the same unit in inches:

1 yard = 36 inches

30 yards = 36 × 30 inches

30 yards = 1080 inches

1 in = 1080 in

1 : 1080

Therefore, the scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1 : 168 and 1 : 1080 respectively.

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A $9070 investment earns interest at
3.3% per year compounded
semiannually over 17 years. Use the
compound interest formula to
calculate the value of this investment
to the nearest cent.

Answers

Answer:

The investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Step-by-step explanation:

The compound interest formula is:

A = P * (1 + (r/n))^(nt)

where

A is the amount of the investment after t years,

P is the principal amount (9070),

r is the annual interest rate (3.3%),

n is the number of times the interest is compounded per year (2),

t is the number of years (17).

Using the formula:

A = 9070 * (1 + (0.033/2))^(2 * 17)

A = 9070 * (1.0165)^34

A = 9070 * 1.882611

A = 16898.67 to the nearest cent.

So the investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Answer: $3660.96 or $3661.0

Step-by-step explanation:

The diagonals of EFGH intersect at point M. if HM =37

Answers

Answer:

If HM = 37, then ML = 37 as the diagonals of EFGH intersect at point M.

Step-by-step explanation:

To solve the diagonals of EFGH intersecting at point M, if HM = 37, first graph the points on a coordinate grid and draw the diagonals. Then use the Pythagorean Theorem to calculate the length of HM. Finally, use trigonometry to calculate the angle measure of FHG.

Convert the number to scientific notation.
120,000,000,000,000

Answers

Answer:

1.2 x [tex]10^{14}[/tex]

Step-by-step explanation:

Scientific notation OR standard form:

This is expressed in powers of 10 (i.e [tex]10^{x}[/tex])

If the decimal point cannot be visibly seen, you can deduce that the decimal point is currently located after the last digit (i.e0).

For the number to be expressed in scientific notation, the decimal point has to be placed right after the first digit (which is NOT a zero) in the left most direction.


For this number, the decimal point has to be placed right after the ‘1’.  Therefore, the decimal point will be moving 14 places to the left. In addition, this 14 is considered as the positive power of 10.

Answer:

1.2 × 10¹⁴

Step-by-step explanation:

Scientific notation is written in the form [tex]a \times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one non-zero digit to the left of the decimal point.

The number of times you have moved the decimal point is the power of 10 (the value of n).

If the decimal point has moved to the left, n is positive.If the decimal point has moved to the right, n is negative.

Therefore, to convert 120,000,000,000,000 to scientific notation, move the decimal point 14 places to the left so that [tex]a[/tex] is 1.2.

As the decimal point has been moved 14 places the left, we need to multiply 1.2 by 10¹⁴.

Therefore,  120,000,000,000,000 = 1.2 × 10¹⁴.

How much has the value of y changed between the points (-8,4) and (8,-4)?

Answers

By 8 (down).
Look at the y value only (x,y).
4 and -4. That’s a total of 8 units down

An obtuse angle has a measure of 150°. The angle was bisected. Each of those angles was then trisected. Finally, each of those angles was divided into 5 equal parts. How large is the smallest angle?

Answers

The smallest angle is 5° when each of those angles was divided into 5 equal parts.

What is an Angle ?

In Geometry, an angle is a figure which is produced by two rays, which share a common point called a vertex. The two rays stand in for the angle's two sides. The Roman word "Angulus," which means "corner," is where the term "angle" originates. The intersection of two curves in this plane results in the angles. Angles of several kinds can be generated on a planar surface. As follows:

Acute Angle

Obtuse Angle

Right Angle

Reflex Angle

Straight Angle

Full Angle

Obtuse Angle :

An angle greater than 90° but less than 180°  is referred to as a "obtuse angle."  An obtuse angle is between a right angle and a straight angle.

Now in this question,

Starting with an obtuse angle of 150°, bisecting it gives two angles of 75° each.

Trisecting each of these angles gives three angles of 25° each.

Dividing each of these angles into 5 equal parts gives angles of 5° each.

Therefore, the smallest angle is 5°.

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Eli and Pierre wanted to buy $40 of breakfast rolls for guests. Bagels B are $1.25, and Crossiants C are $2 each. With the extra guests coming, they later increased their budget to $55.

The difference between the vertical intercepts is ________

Answers

Answer:

The difference between the vertical intercept is a ratio of 20$ so the difference in intercepts is about 2.50$ or 20 spaces.

Hope this helps

equation for (3,3) and (3,-3)

Answers

Answer:

x = 3

Step-by-step explanation:

A vertical line is drawn on a graph paper, which passes through points (3, 3) and (3, -3).  For a vertical line, slope or gradient is undefined.
Therefore, the equation of vertical line is the common x-coordinate of the points along the line. In this case, the common x-coordinate is 3


∴Equation of line

        x = 3

Question 19). TPRS is a parallelogram. Identify mZR.
P
R

(4x+1)
T

(3x+4)
S

Answers

( 4x + 1 ) ° = ( 3x + 4 )°

Opposite side of parallelogram are always equal ...

4x + 1° = 3x + 4°

4x - 3x = 4° - 1°

x = 3°

The measure of angle R from the given parallelogram TPRS is 101°.

What is parallelogram?

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, TPRS is a parallelogram.

Here, ∠T=(4x+1)° and ∠S=(3x+4)°

The sum of adjacent angles of a parallelogram is 180°.

∠T+∠S=180°

(4x+1)°+(3x+4)°=180°

7x+5=180

7x=175

x=175/7

x=25°

So, ∠T=(4x+1)°=4×25+1=101°

∠T=∠R=101° (Opposite angles of parallelogram are equal)

Therefore, the measure of angle R is 101°.

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Determine the amplitude, midline, period, and an equation involving the sine function for the graph shown below.

Answers

The features of the sine function in this problem are given as follows:

Amplitude: 2.Midline: y = -4.Period: 3 units.

The equation is given as follows:

y = 2sin(2πx/3) - 4.

How to define the sine function?

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.

The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:

2A = 4.

A = 2.

Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:

D = -4.

The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:

2π/B = 3

B = 2π/3.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 2sin(2πx/3) - 4.

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it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable

Answers

The correlational hypothesis is a type of research hypothesis that proposes a relation between two variables.

Hypothesis proposes that there is a relationship or association between two variables, known as the independent and dependent variables.

The relation between the two variables can be positive or negative. A positive relation means that as the independent variable increases, the dependent variable also increases.

On the other hand, a negative relation means that as the independent variable increases, the dependent variable decreases.

The strength of the relation can be determined by calculating the correlation coefficient, which is a numerical representation of the strength of the relation between two variables.

In the mathematical representation of a correlational hypothesis, the equation

=> Y = mX + b

is used, where m represents the slope of the line and b represents the intercept. The slope of the line reflects the strength of the relation between the independent and dependent variables, while the intercept reflects the starting point of the relation.

Complete Question:

What is meant by the thing that it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable?

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Sharks can swim 45 miles per hour. How long would it take for the shark to swim 1 mile?

Answers

Answer:

Below

Step-by-step explanation:

distance / rate = time

1 mi / (45 mi/hr)  = 1/45 hr = .02222 hr = 1 1/3 min

11.3 min

...............

Which is a sum of cubes? A^3+18, a^6+9, a^9+16, a^16+8

Answers

The sum of cubes expression is a^3 + 8

How to determine which is a sum of cubes?

From the question, we have the following parameters that can be used in our computation:

The list of options

A sum of cube expression can be represented as

a^3 + b^3

From the list of options, we have

a^3 + 8

This can be expressed as

a^3 + 2^3

Hence, teh expression is a^3 + 8

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Edna has been keeping an eye on an emerald ring she likes. She just noticed that it has been marked down to $28,394.70, which is 27.1% less than its original price. What was the original price of the ring?
Round your answer to the nearest cent.

Answers

Answer:

36089.66

Step-by-step explanation:

First you have to change the percent to a decimal (0.271) then you multiply the number by $28,394.70 and get (7,694.96) last you add ($7,694.96)+  ($28,394.70) to get your answer

Find (fog)(-4)!!!!!!!

Answers

Answer:

23

Step-by-step explanation:

We can think of (f o g)(-4) as f(g(-4)).

As you can see, we start with the inner function and the output of the inner function becomes the output of the outer function.

So we'll plug in -4 for x in g(x) and then the output of this becomes the input of f(x):

[tex]f(x)=2x-1\\g(x)=x^2-4\\f(g(-4))\\\\g(-4)=(-4)^2-4=12\\\\f(12)=2(12)-1=23[/tex]

Suppose you purchased a shirt for $16.51​ using a coupon. If the shirt originally costs $25.40​, what was the percent discount from the coupon? Simplify your answer completely.

Answers

The discount can be found by subtracting the sale price from the original price:

$25.40 - $16.51 = $8.89

So the discount was $8.89.

To find the percent discount, we can divide the discount by the original price and multiply by 100:

$8.89 / $25.40 * 100% = 35%

Therefore, the percent discount from the coupon was 35%.

A particular fruit's weights are normally distributed, with a mean of 796 grams and a standard deviation of 28 grams. The heaviest 2% of fruits weigh more than how many grams?

Answer =
(Give your answer to the nearest gram.)

Answers

Answer:

325888899998898897879

If h(x) =x+2 , g(x) =x² and f(x) =-x , find the values of x for which gh(x) =f(x)

Answers

The values of x for which gh(x) = f(x) are -1 and -4.

As a result, we have gh(x) = g(h(x)) = g(x + 2). ² = x² + 4x + 4 f(x) = -x

The equation must be solved in order to determine the range of x values for which gh(x) = f(x):

x² + 4x + 4 = -x

When all the phrases are moved to the left, we obtain:

x² + 5x + 4 = 0

This quadratic equation has the following factors:

(x + 1)(x + 4) = 0

Thus, either x + 1 = 0 or x + 4 = 0 is the answer.

We obtain x = -1 or x = -4 after solving for x.

Hence, -1 and -4 are the values of x for which gh(x) = f(x).

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Help please! Easy points!

Answers

angle CAB = 23
angle ACB = 80
Other Questions
Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAh 2gh , where c (0 < c < 1) is an empirical constant. A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (Assume the removed apex of the cone is of negligible height and volume.) (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = 5 6h3/2 . In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be 32 ft/s2. See the figure below. If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.) 14.31 Correct: Your answer is correct. minutes (b) Suppose the tank has a vertex angle of 60 and the circular hole has radius 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 and g = 32 ft/s2. dh dt = If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) min I need help with this question. I cant figure out how to find revenue with just the cost function. the amount of interest earned on $k for one year is $3, 990.00. the quantity $2, 290.00 is the amount of discount paid on a one-year loan for $k transacted at a discount rate that is equivalent to the interest rate of the first transaction. find $k. Find the area of $\triangle DEF$ with vertices $D\left(2,\ 5\right)$ , $E\left(3,\ -1\right)$ , and $F\left(-2,\ -1\right)$ . The area of $\triangle DEF$ is In a circle with radius 8, an angle intercepts an arc of length 16pi/3. Find the angle in radians in simplest form. which parental statement would the nurse recognize as indicating a need for further education about protecting a preschooler from lead exposure? select all that apply. one, some, or all responses may be correct. How many base units are there in the code for one amino acid? the nurse is assessing a client in active labor and notes a small, rounded mass above the symphysis pubis that is distended but nontender. which action should the nurse prioritize? the code to display the search results relies on many variables. which of these variables are storing a string data type? Why were these two events, the war with the Barbary Pirates and the War of 1812, so significant to American relations with the rest of the world? What did they show? when journaling a correcting entry, what do you debit in the transaction that incorrectly debited electric expense instead of utilities expense? question 17 options: utilities expense miscellaneous expense electric expense cash can someone please help me with the question at the bottom?? The mechanism by which testosterone alters cell function is by:_________ Find the value of x.Give your answer in degrees.(hint: form an equation, then solve it to find x) if the frequencies are significantly different, then one of the assumptions of the hardy-weinberg principle was probably violated. explain which one was violated in your answer. if none were violated, explain why this is the case. Solving Linear Equations (px + q = r) Ava had $28.50 to spend at the farmer's market. After buying 3 pumpkins Ava, has $12 left. Question 1 Which equation could you use to find the price of one pumpkin (x)? Responses A 28.50/3 = xB x + 12 = 28.50C 3x 12 = 28.50D 3x + 12 = 28.50 Question 2 How much did Ava pay for each pumpkin? Responses A $5.25B $5.50C $6.30D $4.75 Why did the United States fight a war in the Philippines after the Spanish-American War? scientists trying to calculate the half-life (the time it takes for half of a sample to decay) of phosphorus-32, took measurements of the sample once every day for five days. on what day should about half of the original amount of p-32 remain? (round answer to the nearest day.) according to the u.s. census bureau, 5% of americans age 25 or older had completed a bachelor's degree or higher in 1940. write this percent as a ratio and do not simplify. before the civil war, how were free african americans limited in their freedom and job opportunities?