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.
learn more about the distance between two points here :
https://brainly.com/question/29163759
#SPJ1
Question number 10 I need help with please
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.
To know more about ratio visit:
https://brainly.com/question/29467965
#SPJ1
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?
what is 1777771 plus 8999907
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.
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).
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
why does m1 x m2 = -1
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
Answer:is his brother 4 or 8
Step-by-step explanation:
I don't know for sure
I need help with these questions Pls
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
To know more about fractions refer to:
https://brainly.com/question/78672
#SPJ1
(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?
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 .
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
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
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.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
What is the scale factor, without units, of 1 in : 14 ft and 1 in : 30 yard
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 factorScale 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.
Know more about scale factor here: https://brainly.com/question/2826496
#SPJ1
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.
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
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
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.e ‘0’).
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)?
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?
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°.
Learn more about Obtuse Angles visit:
https://brainly.com/question/1581660
#SPJ1
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 $55.
The difference between the vertical intercepts is ________
Answer:
The difference between the vertical intercept is a ratio of 20$ so the difference in intercepts is about 2.50$ or 20 spaces.
Hope this helps
equation for (3,3) and (3,-3)
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
( 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°.
Learn more about the parallelogram here:
https://brainly.com/question/19187448.
#SPJ5
Determine the amplitude, midline, period, and an equation involving the sine function for the graph shown below.
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.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ1
it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable
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?
To know more about relation here,
https://brainly.com/question/13088885
#SPJ4
Sharks can swim 45 miles per hour. How long would it take for the shark to swim 1 mile?
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
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
Read mre about expression at
https://brainly.com/question/15775046
#SPJ1
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.
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)!!!!!!!
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.
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.)
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)
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).
To know more similar question visit:
https://brainly.com/question/23286212
#SPJ1
Help please! Easy points!