Answers
The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.
What are the properties of a rhombus?The properties of a rhombus are:
All the sides of a rhombus are congruent and equalOpposite sides are parallelOpposite angles are equalThe adjacent angles add up to 180°Diagonals perpendicularly bisect each otherDiagonals bisect opposite anglesCalculation:The given rhombus BCDE has B(n, p) and E(0, 0).
Since the diagonals of a rhombus are perpendicular bisectors,
EO = OC or BO = OD
Where O is the midpoint of EC and BD.
In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.
So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).
Thus, we have B(n, p), D(n, -p), and E(0, 0)
Consider the coordinates of C as (x, y).
The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])
⇒ coordinates of O = (n, 0)
So,
The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])
⇒ coordinates of O = (x/2, y/2)
⇒ (n, 0) = (x/2, y/2)
∴ x = 2n and y = 0
Then, the coordinates of C are (2n, o)
Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).
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Related Questions
Maths Questions box 51.The function f: R→ R is twice differentiable and for any x ER we have g(x) = f(4-x²), if f'(1) = -5 and f" (1) = -1 than what is g" (√3)?
Answers
By the chain rule,
[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]
Observe that
[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]
Then
[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]
Write 636,000 in scientific notation.
HELP ME PLEASE
Answers
Explanation: You have to move the decimal to change the number between 1 to 10. Then, the 10 would be the power of how many times you moved the decimal.
2. The product of two consecutive even numbers is 168. What are the numbers?
Answers
Answer:
12 and 14
Step-by-step explanation:
12 * 14 = 168
Answer:
12 & 14
Step-by-step explanation:
the work: x = first even number, (x+2) = second even number
The equation
[tex]x(x+2)=168[/tex]
[tex]x^{2} +2x=168[/tex]
[tex]x^{2} +2x-168=0[/tex]
Factoring
[tex](x-12)(x+14)=0[/tex]
first factor
[tex]x-12=0\\x=12[/tex]
Second factor
[tex]x+14=0\\x=-14[/tex]
The solution is the positive number
x = 12 is the first even number
x + 2 = 12 + 2 = 14 is the second even number
Hope this helps
Please see the attached photo. I do not know how to calculate any of this using my TI 84+ CE calculator and the answers I am getting when trying to calculate by hand are not correct.
Answers
The decision is to fail to reject the null given that p value is not ≤ 0.05.
How to solve for the z statistical testThe hypothesis
H0 = p = 0.63
H1 = p < 0.63
α = 0.05
sample proportion = 71/125 = 0.568
x = 71
n = 125
standard error of the proportion
√0.63(1-0.63)/125
= 0.0431
The null hypothesis follows a standard normal distribution. This is a left tailed test.
We are to reject the null if the p value is less than 0.05
p < 0.05
This probability test is a z probability test.
Z test = 0.568 - 0.63 / 0.0431
test statistic = -1.436
-Z0.05 =
Critical value = -1.645
p(z < -1.436)
p value = 0.0755
The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.
P-value is not ≤ α 0.05
0.0755 > 0.05
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Ms. Callahan had 250 sheets of paper. She used 6 sheets of paper. She then gave each student 3 sheets of paper. Which expression represents the number of sheets of paper Ms. Callahan had left after she gave paper to n students?
Answers
Answer:
250 - 6 - 3n
Step-by-step explanation:
Let n equal the number of students.
45.7 kilometers =
meters
Answers
Answer:
45.7 kilometers = 45,700 meters
Explanation:
Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.
Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).
Hope this helps!
To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.
Convert 45.7 kilometers to meters:
Knowing that 1000 m = 1 km.[tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]
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Simplify [tex]\frac{6a^2 b^-^2}{8a^-^3 b^3}[/tex] Assume a≠0 and b≠0
Answers
Answer:
sorry i thought i knew it
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
someone please help me in this question i need step by step sol with explaination
Answers
Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.
How to Compare Percentage, Decimals, and Fractions?The bigger the digit that is close to the decimal point, the bigger the number given.
Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.
Fractions can also be converted to decimals by simply dividing the numerator by the denominator.
To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.
Converting 25/36 to decimal, we have: 0.694 (3rd grade)
Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)
From the rest of the portions given, 0.694 is greater than the others.
Therefore, the grade that has the greatest portion of students is: 3rd grade.
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the width of a large butterfly is about 0.08. What is the width when it is written in scientific notation
Answers
Answer: 8 x 10^2
Step-by-step explanation:
scientific notation has to be greater than 1, less than 10
therefore:
0.08 = 8 x 10^2
PLEASE HELP
Determine which quadratic equation reveals its maximum or minimum value without changing the form of the equation.
y=x² + 4x-3
y = -3(x+4)² + 1
y=(x-9)(x + 7)
y=2x²-5x+4-10
Answers
y=x²+(3+1)x-3
y=x²+3x+1x-3
y=x(x+3)-1(x+3)
y=(x-1)(x+3)
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
Answers
When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).
We are required to divide the first expression by second expression.
Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.
Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.
We know that relationship between quotient, divisor, divident and remainder is as under:
Dividend=Divisor*Quotient+Remainder
[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39
Quotient=[tex]x^{2} +8x+19[/tex]
Remainder=39
Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
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The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
Drag each function to show whether it has roots at x=−2 and x=3, roots at x=2 and x=−3, or neither.
Answers
The following classification of quadratic equations is presented below:
x = - 2 and x = 3: h(x) = (x + 2) · (x - 3), k(x) = - 3 · (x + 2) · (x - 3). x = 2 and x = - 3: g(x) = 8 · (x + 3) · (x - 2), m(x) = (x + 3) · (x - 2). Neither: j(x) = (x - 2) · (x - 3)How to classify quadratic equations in terms of its roots
In this problem we have quadratic equations in factored form, whose form is presented below:
y = a · (x - r₁) · (x - r₂) (1)
Where r₁ and r₂ are the roots of the equation and a is the leading coefficient. A value of x is a root if and only if y is zero. Besides, we must located all the quadratic equations according to their roots.
x = - 2 and x = 3
h(x) = (x + 2) · (x - 3)
k(x) = - 3 · (x + 2) · (x - 3)
x = 2 and x = - 3
g(x) = 8 · (x + 3) · (x - 2)
m(x) = (x + 3) · (x - 2)
Neither
f(x) = 3 · (x - 1) · (x + 2)
j(x) = (x - 2) · (x - 3)
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A town has a population of 1.23 x 10 and grows at a rate of 6.7% every year. Which
equation represents the town's population after 4 years?
Answers
At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
What is the formula for the population?The growth rate of a population is a measure of how fast a population increases.If the initial population is [tex]P[/tex] and the growth rate is [tex]r\%[/tex] every year, then the population after [tex]t[/tex] years will be given by the following formula: [tex]A=P(1+\frac{r}{100})^t[/tex].Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].
So the population after [tex]t=4[/tex] years will be:
[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]
Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
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13
Company A has 800 employees, and it decides to grant each of the employees 50 share options as
part of its new rewards plan. The options are exercisable over 5 years and subject to a 3-year
service condition. The fair value of each option at the grant date is $16. The company estimates
that 80% of its employees will meet the service condition required for receiving the options.
Calculate the total share-based payment expense for Company A assuming that 80% of the
employees actually meet the service condition.
$512,000
$853,333
$341,333
$170,667
Answers
Option A. The total share expense that the company would share would be given as 512,000
What is meant by share expense?These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.
How to solve for the share expenseThe total number of the employees that are knwon to satistfy condition are given as
800 * 0.8
= 640
The options that are estmated that would be exercised
This is given as the employees * share option
= 640×50
=32000.
The total shae for the company would be gotten as
= 32000× $16
This gives us $512,000.
Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.
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add the two equations, 0.75x+1.5y=40 and −1.5x−1.5y=−60 , to find the value of x .
Answers
The value of x in the equation is 26.7
How to solve an equation?0.75x + 1.5y = 40
−1.5x − 1.5y = −60
add both equation to eliminate y .
Therefore,
−1.5x + 0.75x = -0.75x
1.5y + (- 1.5y) = 0
40 + (-60) = -20
Hence,
-0.75x = - 20
divide both sides by -0.75
-0.75x / -0/75 = - 20 / -0.75
x = - 20 / -0.75
x = 26.6666666667
x = 26.7
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En la final de un concurso escolar de
matemática participan 6 alumnos de los
cuales 3 son alumnos del colegio A. Si se
premia a los dos primeros con regalos
diferentes, entonces la probabilidad de que
los alumnos del colegio A obtengan los dos
premios (no hay empates), es:
Answers
Usando la distribución hipergeométrica, la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.
¿Qué es la fórmula de distribución hipergeométrica?La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 6, k = 3, n = 2.
La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]
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√2n +6=6
n =
Answer?
Answers
Answer:
your question is not correct i can not find the answer
help answer this please
Answers
Answer:
Step-by-step explanation:
2x + 5y = 8
-5 -5
2x = 8 - 5y
divide both sides by 2
[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]
divide by 2 undoes the multiplication by 2
x = [tex]\frac{8- 5y}{2}[/tex]
divide 8 - 5y by 2
x = - [tex]\frac{5}{2}[/tex] y + 4
What is the equation of the line in standard form of the graph below?
Answers
Answer:
Step-by-step explanation:
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
Answers
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
How to determine the linear inequality represented by the graph?The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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Find the value of z.
X
7
Y
3
Z
Z = √[?]
Answers
Answer:
z = [tex]\sqrt{30}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )
z = [tex]\sqrt{30}[/tex]
Do companies that provide mobile wifi hotspots see your history?
Answers
Yes, companies that provide mobile wifi hotspots can see your history.
What is a Wi-Fi hotspots?A Wi-Fi hotspots can be defined as the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.
For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .
Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.
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How to solve these questions?
(with work)
Answers
The angles and length of the triangle area as follows:
∠CBD = 61°∠A = 35°AD = 32.77 unitsBD = 22.94 unitsBC = 11.12 unitsCD = 9.73 unitsHow to find the sides and angle of a triangle?The sum of angles in a triangle is 180 degree.
Therefore,
∠DBC = 180 - 29 - 90 = 61°
Hence,
∠A = 180 - 29 - 61 - 55 = 35°
∠CBD = 61°
Using trigonometric ratios,
sin 55 = opposite / hypotenuse
sin 55 = AD / 40
AD = 40 sin 55
AD = 32.7660817716
AD = 32.77 units
cos 55 = adjacent / hypotenuse
cos 55 = BD / 40
BD = 40 cos 55
BD = 22.943057454
BD = 22.94 units
sin 29 = 22.94 / BC
BC = 22.94 sin 29
BC = 11.1215326885
BC = 11.12 units
cos 29 = CD / 11.12
CD = 11.12 cos 29
CD = 9.72577114339
CD = 9.73 units
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PLWASW HELP ALOT OF POINTS Charlie used construction paper, scissors and a ruler to construct an
isosceles triangle with a pair of sides each 3 inches long and an acute
angle on top. He drew an altitude from the acute angle to the base and
wrote down his observations. He then created another isosceles triangle
with a pair of sides of 7 inches long with an obtuse angle on top, drew a
altitude to the base, and recorded his observations.
Which of these is the best conjecture for Charlie to develop?
Answers
The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
What is conjecture?It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.
From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.
Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
Answers
The equation 15x + 5y = 0 is a direct variation and the constant of variation is -3 while the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
How to categorize the type of each equation?As a general rule, we have the following forms of equation:
Direct variation: y =kx
Inverse variation: y = k/x
Where k represents the constant of variation
The equations 15x + 5y = 0 can be rewritten as:
5y = -15x
Divide by 5
y = -3x
The above equation take the form y = kx
This means that k = -3
Hence, the equation 15x + 5y = 0 is a direct variation and the constant of variation is -3
However, the equation -5x + 8y = 3 do not take any of the given forms
Hence, the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
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WILL GIVE BRAINLIEST
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Answers
Factorization refers to the process by which the terms that are common in an expression are obtained.
What is factorization?Factorization refers to the process by which the terms that are common in an expression are obtained.
Given the trinomials, the correct binomial factors are;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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Stopyra Incorporated makes a single product—a cooling coil used in commercial refrigerators. The company has a standard cost system in which it applies overhead to this product based on the standard labor-hours allowed for the actual output of the period. Data concerning the most recent year appear below:
Budgeted variable manufacturing overhead $ 28,200
Budgeted fixed manufacturing overhead $ 89,280
Budgeted hours 12,000 labor-hours
Actual production (a) 16,000 units
Standard hours per unit (b) 0.60 labor-hours
Standard hours allowed for the actual production (a) × (b) 9,600 labor-hours
Actual variable manufacturing overhead $ 26,967
Actual fixed manufacturing overhead $ 74,280
Actual hours 8,900 labor-hours
The variable overhead rate variance is:
$6,528 U
$6,528 F
$6,052 U
$6,052 F
Answers
The variable overhead rate variance is: c. $6,052 U.
Variable overhead rate varianceFirst step is to calculate variable component of the predetermined overhead rate using this formula
Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours
Let plug in the formula
Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours
Variable component of the predetermined overhead rate=$2.35 per labor-hour
Second step is to calculate variable overhead rate variance using this formula
Variable overhead rate variance=(AH×AR)-(AH×SR)
Let plug in the formula
Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)
Variable overhead rate variance= $ 26,967- $20,915
Variable overhead rate variance= $6,052 U (Unfavorable)
Therefore the variable overhead rate variance is: c. $6,052 U.
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Consider the parametric equations below.
x = t^2 − 3, y = t + 2, −3 ≤ t ≤ 3
Eliminate the parameter to find a Cartesian equation of the curve.
for
−1 ≤ y ≤ 5
Answers
Solve the second equation for [tex]t[/tex], then substitute it into the first equation.
[tex]y = t + 2 \implies t = y-2[/tex]
[tex]x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}[/tex]
A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?
Answers
Answer:
3 hours
Step-by-step explanation:
When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.
Distance = Speed * Time
So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:
Distance travelled of 1st ship = Distance travelled of 2nd ship
30x = 40(x-1)
30x = 40x - 40
-10x = - 40
x = [tex]\frac{-40}{-10}[/tex]
= 4
Since we are calculating based on the 2nd ship,
Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.
Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}
Answers
Answer: 8.7 the mean is 20
Step-by-step explanation:
