Applying the midpoint formula, the coordinates of point M are: (-3, -4).
How to Apply the Midpoint Formula?The midpoint formula is given as, (x, y) = [(x2 + x1)/2, (y2 + y1)/2].
Given the following:
N(x, y) = (1.5, 2.5)
P(x1, y1) = (6, 9)
M(x2, y2) = (?, ?)
Plug in the values into the midpoint formula
N(1.5, 2.5) = [(x2 + 6)/2, (y2 + 9)/2]
Isolate each coordinate
1.5 = (x2 + 6)/2
2(1.5) = x2 + 6
3 = x2 + 6
3 - 6 = x2
x2 = -3
2.5 = (y2 + 9)/2
5 = y2 + 9
5 - 9 = y2
y2 = -4
Therefore, applying the midpoint formula, the coordinates of point M are: (-3, -4).
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please help im foundation maths and don’t understand:(
The coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).
Given that the coordinates of the triangle be (-5,5), (-5,-1) and (3,-1)
We are required to find the coordinates of the new triangle.
Scale Factor is basically used to scale shapes in different dimensions.
Coordinates are the points that lie on the plane surface.
As we can see in the picture, the coordination of the vertices of the triangle be A(-5,5), B(-5,-1) and C (-3,-1).
=1/2 [tex]\left[\begin{array}{ccc}-5+3&-5+3&-3+3\\5+1&-1+1&-1+1\\\end{array}\right][/tex]
=1/2 [tex]\left[\begin{array}{ccc}-2&-2&0\\6&0&0\\\end{array}\right][/tex]
=[tex]\left[\begin{array}{ccc}-1&-1&0\\3&0&0\\\end{array}\right][/tex]
Hence the coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).
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the product of two irrational numbers is rational? true/false
Answer:True
Step-by- by step
Irrational numbers are square roots of numbers , when two irrational numbers are multiply together, it is called rationalization and this gives a rational value, So the answer is true.
What step would you perform first to solve the
following equation? Explain your reasoning.
1/4(12 – 8x) = 2/3(6x)
Answer: x = 3/4
Step-by-step explanation:
The first step to solve this equation would be to simplify both sides of the equation by multiplying
1/4*12 - 1/4*8x = 2/3*6x
3 - 2x = 2x
3= 2x+2x
3=4x
x=3/4
Answer:
Step-by-step explanation:
AS THERE ARE 2 fractions 1/4 and 2/3, one way would be to first get rid of these by multiplying through by the LCM 12, giving:
12*1/4(12 – 8x) = 12*2/3(6x)
3(12 - 8x) = 8(6x)
36 - 24x = 48x
36 = 72x
x = 1/2.
Write an equation of each line.slope = 5/6 ; through (22,12)
The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5/6 and (x1 , y1) = (22 , 12)
(y - 12) = 5/6(x - 22)
In slope-intercept form, the equation of the line is:
(y - 12) = 5/6(x - 22)
y - 12 = 5/6 x - 110/6
y = 5/6 x - 19/3
In standard form, the equation of the line is:
y = 5/6 x - 19/3
5/6 x - y = 19/3
Multiplying both sides by 6,
5x - 6y = 38
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In the equation |x| = b, if b>0, then how many solutions are there for x?
O Zero
O Two
O Can't be determined without more information
O One
The value of b (real number) can be anything greater than zero so we cannot be determined with the given information so option (C) will be correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
Given the absolute equation,
|x| = b for b >0
b is a set of all positive real numbers and we know that real number goes 0 to infinite means,
b could be 1,2,3... anything.
It means the corresponding solution will also be 1,2,3... anything.
Therefore we cannot determine the solution.
Hence "We cannot predict the number of solutions of the given mode function |x| = b, such that b>0 without more information".
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A Florida orange juice plant started producing a juice blend, it must be within 0.78 fluid ounces of the advertised 32 fluid ounces on the label. If x represents the volume, write an equation to model the maximum and minimum volumes and determine the minimum volume in a bottle.
|x - 32| = 0.78
|x + 32| = 0.78
|x - 0.78| = 32
|x + 0.78| = 32
The correct equation is:
|x - 32| = 0.78
In this case, x represents both the maximum and minimum accepted volumes.
How to writhe an equation that models the maximum and minimum volumes?We know that the mean volume is 32 fluid ounces, and the acceptable error is 0.78 fluid ounces.
Then the maximum acceptable volume is 32 + 0.78 fluid ounces, and the minimum acceptable volume is 32 - 0.78 fluid ounces.
This means that the absolute value of the difference between x, the volume, and 32, must be equal to 0.78
This is written as:
|x - 32| = 0.78
In this case, x represents both the maximum and minimum accepted volumes.
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PLEASE HELP ASAPPPPPP
Write an equation for each boat rental company that gives the cost in dollars y of renting a kayak for x hours. What is the difference in cost between the company that charges the most and the one that charges the least for 4 hours?
A table titled Company A with two columns and five rows is shown. The first column is the number of hours. The second column is the total cost in dollars. For two hours, the cost is thirty-three dollars. For three hours, the cost is forty-nine dollars and fifty cents. For four hours, the cost is sixty-six dollars. For five hours, the cost is eighty-two dollars and fifty cents.
Company B The cost y of renting a kayak for x hours is $9.00 for each half hour.
Company C The cost y of renting a kayak is $14.25 per hour.
Using linear functions, the costs are given as follows:
A(x) = 16x + 1.B(x) = 18x.C(x) = 14.25x.For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:
A(x) = 16x + b.
When x = 2, A(x) = 33, hence we use it to find b as follows:
33 = 16(2) + b
b = 1.
Hence:
A(x) = 16x + 1.
Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:
B(x) = 18x -> 9 for each half hour = 18 for an hour.C(x) = 14.25x.For 4 hours, the costs are given as follows:
A(4) = 16(4) + 1 = 65.B(4) = 18(4) = 72.C(4) = 14.25(4) = 57.The difference is:
72 - 57 = 15.
For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.
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In triangle △ABC, ∠C is a right angle and CD is the altitude to AB . Find the angles in △CBD and △CAD if
Applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°
In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°
What is the Triangle Sum Theorem?All interior angles of a triangle have a total sum of 180 degrees when added together, according to the triangle sum theorem.
Given:
Measure of angle C = 90 degrees
In △CAD, we have the following angle measures:
m∠A = 65° (given)
m∠ADC = 90° [right angle]
m∠ACD = 180 - 90 - 65 [triangle sum theorem]
m∠ACD = 25°
In △CBD, we have the following angle measures:
m∠CDB = 90° [right angle]
m∠BCD = 90 - m<ACD [complementary angle]
m∠BCD = 90 - 25
m∠BCD = 65°
m∠CBD = 180 - m∠BCD - m∠CDB [triangle sum theorem]
m∠CBD = 180 - 65 - 90
m∠CBD = 25°
In summary, applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°
In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°
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chuck cut an entire length of rope into 28 peices each 1 1/2 feet long what was the length of the rope before chuck cut it ?
Answer:
42 feet
Step-by-step explanation:
1 1/2 * 28 = 42
hi can you help woth this question
Answer:
The point of intersection is the number of gigabytes and the total cost when the two plans cost the same.
Step-by-step explanation:
Company A doesn't charge a fee "per gigabyte", there's just a flat fee and it is $100. Company B only charges a flat fee of $20, BUT there IS a "per gigabyte" charge. These two plans actually cost exactly the same when the customer uses 16 gigabytes.
Write an explicit formula for each geometric sequence. Then find the first three terms. a₁ =-1, r=-1
FA recursive formula allows us to find each term in the geometric sequence using the previous term. Each new term is the product of the common ratio for that sequence and the previous term of that unknown or to-be-found term. If the common ratio is 9, each term is nine times the previous term.
The general term for the geometric sequence is,
an= a1 * r ^ (n-1)
Where "an" refers to the nth term of the sequence, a1 is the first term known as the sequence, and r is the common ratio, n is its position or the number.
Now the given values are,
a₁ = -1 and r = -1
Sequence: -1, 1, -1, 1, -1, 1, -1, 1, -1 ...
We can easily identify the first three terms from the above sequence.
3rd value: -1
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MATH
-2 1/3 + ( -1 3/4) =
Calculate the electric flux through the cube face in the plane z = 0 and the cube face in the plane z=l. for each face the normal points out of the cube.
Ф2 = E2 L² is the electric flux through the cube face in the plane z = 0.
What exactly are electric flux and unit?
The SI unit for electric flux is newton-meters squared per coulomb (N m 2 /C N m 2 /C), and it is a scalar quantity. It is important to note that N E A 1 N E A 1 can also be represented as N N , proving that the number of field lines crossing a surface is what determines how much electric flux there is.given ,
edge length = L
Area of each surface = L²
Ф = E . A
= E . A Cos θ
Φ1 = E1 A Cosθ
Φ1 = E1 L²
Similarly we get
Ф2 = E2 L²
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Brandon and Nestor are participating in a bicycle race on a circular track with a radius of 200 feet.
a. If the race starts at (200,0) and both complete one rotation in 30 seconds, what are their coordinates after 5 seconds?
The coordinates are (100, 173.2) after 5 seconds.
What are examples of coordination?
Being able to move and use your body efficiently as well as several individuals or things operating well together are the definitions of coordination. When a gymnast walks on a tightrope without falling, that's coordination in action. When two people collaborate to arrange or coordinate a party, that is an example of coordination.Let x represent the angle of rotation in 5 seconds.
[tex]\frac{Irotation }{time} = \frac{current position}{time}[/tex]
360° / 30 = x°/ 5
30x = 1800
x = 60°
To find the coordinates, use sine and cosine ratios.
Sin60 = opposite/ hypotenuse
sin60 = y / 200
y = 200sin60
y ≈ 173.2
cos60 = adjancent/ hypotenuse
cos60 = x / 200
x = 200cos60
x = 100
The coordinates are (100, 173.2).
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PLEASE HELPPP !! URGENT :3 THANKS
Answer:
no 1 answer is asia
no 2 answer is europe
9 - 2x <= - 5 or 1/2 * x + 13 < 15
4. Find the product. (4.0 × 10^-2) × (5.2 × 10^8) (1 point)
20.8 x 10^8
2.08 x 10^7
2.08 x 10^6
20.8 x 10^7
Answer:
2.08 × [tex]10^{7}[/tex]
Step-by-step explanation:
Multiply 4 × 5.4 to get 20.8. Then multiply [tex]10^{-2}[/tex] × [tex]10^{8}[/tex] = [tex]10^{6}[/tex]
However, that is not an answer. So, you can divide 20.8 by 10 and multiply [tex]10^{6}[/tex] × 10.
Then you get 2.08 × [tex]10^{7}[/tex]
What is the value of -32+(-4+7)(2)?
O-28
O-3
03
O 15
Answer:
-26Step-by-step explanation:
the answer is -26 but it is not in the choices
-32+(-4+7)*(2)=
-32+3*2=
-32+6=
-26
Hello!
Solve this Quadratic Equation: [tex]x^2 + 4x + 3 = 0[/tex]
Use factoring to solve, then double-check using the Quadratic Formula.
Include all steps and show your work in detail. The best answer gets Brainliest.
Answer:
[tex]x = -1, -3[/tex]
Solve by FactoringTo solve by factoring, we will split up the equation using our factoring rules.
In this particular instance, we will factor out common variables.
We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.
[tex]x^2 + 4x + 3 = 0[/tex]
[tex](x+3)(x+1)=0[/tex]
Set each factor equal to zero and solve.
Root 1
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
Root 2
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
The final answer is [tex]\boxed{x = -1, -3}[/tex].
As requested in the question, we must now check with the quadratic formula.
What is the quadratic formula?To solve this quadratic equation, we will utilize the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].
We will define our variables:
a: 1b: 4c: 3Now, we will plug these into the equation and solve the equation.
Solve[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]
Root 1
[tex]\displaystyle x=\frac{-4+2}{2}[/tex]
[tex]\displaystyle x=\frac{-2}{2}[/tex]
[tex]\boxed{x=-1}[/tex]
Root 2
[tex]\displaystyle x=\frac{-4-2}{2}[/tex]
[tex]\displaystyle x=\frac{-6}{2}[/tex]
[tex]\boxed{x=-3}[/tex]
Final AnswerThe final answer is [tex]\boxed{x = -1, -3}[/tex].
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Given the equation, we can start by rewriting:
x^2 + 4x + 3 = 0
Now, let’s write in factored form:
(x + 1) (x + 3) = 0
since x is the only variable and there are 2 numbers, we can make 2 equations:
x + 1 = 0
x + 3 = 0
This forms:
(X + 1) (x + 3) = 0
Now, we can solve:
? + 1 = 0
? + 3 = 0
-1 + 1 = 0 and -3 + 3 = 0
x = -1 AND -3
The points (-3,2),(-1,3),(0,0),(-2,-1) represent a function. What are the domain and range?
The domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}
The given relation is {(-3,2), (-1,3), (0,0), (-2,-1)}. Here, the relation is given as a set of ordered pairs. Domain in mathematics is defined as the all the inputs that are possible to be part of functions. Range refers to the values assumed by function and these are the output values.
The domain of the function is the set of x- coordinates.
∴ The domain is {0, -1, -2, -3}
The Range of the function is the set of y- coordinates.
∴The Range is {0, -1, 2, 3}
Hence, the domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}.
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A rectangualr field has a perimeter of 150m The field is 15 metres longer than it is wide . The width of the field is x metres
The required width of the rectangle is 10 meters.
Given that,
A rectangular field has a perimeter of 150m The field is 15 meters longer than it is wide. The width of the field is x meters.
The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
The area of the rectangle = length * width
150 = 15 * x
x = 150 / 15
x = 10
Thus, the required width of the rectangle is 10 meters.
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Choose the letter of the word or phrase that best completes each statement.
a. ratio
b. proportion
c. means
d. extremes
e. similar
f. scale factor
g. AA Similarity Post.
h. SSS Similarity Theorem
i. SAS Similarity Theorem
j. midsegment
k. dilation
I. enlargement
m. reductionIf
∠ A ≅ ∠ X and ∠ C ≅ ∠Z , then ΔA B C ∼ ΔX Y Z by the ____?_____.
If ∠A ≅ ∠X and ∠C ≅ ∠Z , then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.
Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.
example:
If ΔABC ∼ ΔXYZ, then ∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z, and
AB/XY = BC/YZ = AC/XZ
AA (or AAA) or Angle-Angle Similarity Postulate states that if any two angles of a triangle are congruent to any two angles of another triangle, then the two triangles are similar to each other.
So, given that ∠A ≅ ∠X and ∠C ≅ ∠Z, then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.
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Please find the answer for me asap
Write an equation in point-slope form of the line having the given slope that contains the given point.
m: 1/4,(3,-1)
The equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]
Given,
The slope m= [tex]\frac{1}{4}[/tex]
The point = (3,-1)
We know the point-slope form,
[tex]y-y_{1}=m(x-x_{1})[/tex]
Substitute the values in the equation
[tex]y-(-1)=\frac{1}{4} (x-3)\\y+1=\frac{1}{4}(x-3)[/tex]
Hence, the equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]
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Refer to ®A .Name a chord that is not. a diameter.
Referring to the circle ED is the chord that is not a diameter.
The circle is one of the shapes with consists of all points with identical distances from its center. A particular circle is named by its center.Here diameter of the circle is the distance across the circle through the center, whereas a chord is a line segment that joins two points on a curve on the circle since the diameter is satisfieding the points of a chord but a chord is not a diameter, as diameter are the line that just passes through the center of the circle, whereas the chord doesn't cross from the center of the circle, thus it can be quoted that, every diameter is a chord, but not every chord is a diameter.
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Find the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n}.
The mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is and .
For Discrete Uniform Distribution the probability mass function (pmf) is denoted by P(x)=1/n , where x=1,2,3,...,n.
in the given question
The mean of the Discrete Uniform Distribution is given by [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]
By substituting the value of P(x)=1/n
[tex]E(x)=\[\sum_{x=1}^{n}\frac{1}{n} *x\][/tex]
[tex]=\frac{1}{n}\[\sum_{x=1}^{n}x\][/tex]
[tex]=\frac{1}{n} (1+2+3+4+...n)[/tex]
[tex]=\frac{1}{n} *\frac{n(n+1)}{2}[/tex] ( as we know that sum of n terms is [tex]\frac{n(n+1)}{2}[/tex] )
=[tex]\frac{n+1}{2}[/tex]
hence , [tex]\mu=\frac{n+1}{2}[/tex] ....(i)
The Variance of the Discrete Uniform Distribution is denoted by Var(x) and is given by [tex]Var(x)=E[(x-\mu)^{2}][/tex]
As we know that [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex] similarly for E[(x-μ)²] we get
[tex]E[(x-\mu)^{2}]=E[x^{2} ]-\mu^{2}[/tex]
[tex]=E[x^{2}]-(\frac{n+1}{2} ) ^{2}[/tex] ( we have found [tex]\mu=\frac{n+1}{2}[/tex] ) ....(ii)
For E[x²]
[tex]E(x^{2} )=\[\sum_{x=1}^{n}\frac{1}{n} *x^{2} \][/tex]
[tex]=\frac{1}{n}\[\sum_{x=1}^{n} x^{2} \][/tex]
[tex]=\frac{1}{n} (1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} )[/tex]
We know that [tex]1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} =\frac{n(n+1)(2n+1)}{6}[/tex]
Substituting the value in above equation we get we get
[tex]E[x^{2} ]=\frac{1}{n} *\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]E[x^{2} ]=\frac{(n+1)(2n+1)}{6}[/tex]
Substituting the value of E[x²] back in equation (ii)
We get
[tex]Var[x]=\frac{(n+1)(2n+1)}{6} -( \frac{n+1}{2})^{2}[/tex]
[tex]=\frac{(n+1)(2n+1)}{6} -\frac{(n+1)^{2} }{4}[/tex]
[tex]=(n+1)(\frac{(2n+1)}{6} -\frac{(n+1) }{4})[/tex]
taking LCM as 12 and solving further we get
[tex]=(n+1)(\frac{4n+2-3n-3}{12} )[/tex]
[tex]=\frac{(n+1)(n-1)}{12}[/tex]
[tex]=\frac{n^{2}-1 }{12}[/tex] (using identity of (a+b)(a-b) )
Therefore , the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is [tex]\frac{n+1}{2}[/tex] and [tex]\frac{n^{2}-1 }{12}[/tex] .
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295+39x=350+33x
This is based off of solving equations with variables!
.ALGEBRA 1
Answer: x=55 over 6
Step-by-step explanation:
Do the following side lengths form a right triangle?
51, 68, 85
Answer: Yes
Step-by-step explanation:
If these lengths were to form a right triangle, then 51 and 68 would be the legs and 85 would be the hypotenuse.
[tex]51^2 +68^2 =7225\\\\85^2 =7225\\\\\therefore 51^2 +68^2 =85^2[/tex]
So, the side lengths form a right triangle.
A classmate uses the formula for the sum of an infinite geometric series to evaluate 1+1.1+1.21+1.331+ . . . and gets -10 . What error did your classmate make?
What error did your classmate make? This series is divergent so does not have a sum.
How is the divergence of the series proved?
Given:
[tex]a(\text{ the first term })=1\\\\r(\text{ the common difference })=1.1[/tex]
Since, [tex]\vert r \vert > 1[/tex] the infinite series diverges.
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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A survey found the following number of children in various neighborhoods around town. {3, 49, 16, 70, 21, 0, 7, 123} What is the mean absolute deviation for these numbers? Round to the hundredths place (two digits after the decimal). MAD =
