In triangle ABC, AC = 21, BC = 28, and ∠ACB = 90◦
. The bisector of ∠ACB meets AB at D.
Find the length BD and CD
Sorry don't have image
The length of BD and CD are 15 units and 20 units respectively
How to find the length BD and CD?By the Angle Bisector Theorem, we have:
BD/DC = AC/BC = 21/28
We can use the Pythagorean Theorem to find AC:
AC² + BC² = AB²
21² + 28² = AB²
AB = 35 units
Now we can use the Angle Bisector Theorem to find BD:
BD/DC = 21/28
BD + DC = AB
BD = (21/49) × AB
BD = (21/49) × 35
BD = 15 units
To find CD, we can use the fact that BD + DC = AB:
CD = AB - BD
CD = 35 - 15
CD = 20 units
Therefore, the length are BD = 15 and CD = 20 units.
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The survey found that women's Heights are normally distributed with a mean of 63. 9 in and standard deviation 2. 2 in the survey also found that men's Heights are normally distributed with mean 67. 6 in. And standard deviation 3. 5 in considered and executed jet that seats 6 with a doorway height of 56. 4 in.
a)what percentage of adult men can fit through the door without bending?
b) what's a doorway height would allow 40% of men to fit without bending
Using the given information, we can calculate the z-score as z = (56.4 - 67.6) / 3.5, which gives us a z-score of -2.3. This means that 2.3 standard deviations below the mean of adult men's heights is the doorway height of 56.4 inches. Since the area under the normal curve from -∞ to -2.3 is 16%, this means that 84% of adult men can fit through the door without bending.
Using the given information and the desired percentage, we can calculate the z-score as z = (x - 67.6) / 3.5, where x is the doorway height. Solving for x, we get x = 57.6 inches. Therefore, a doorway height of 57.6 inches would allow 40% of adult men to fit through without bending.
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Is this function linear, quadratic, or exponential?
X 2 3 4 5 6 Y 40 90 160 250 360
Answer:
Step-by-step explanation:
It is Linear
Find m/G.
F
150°
H
G
The measure of angle G is 121 degrees and this can be determined by using the sum of interior angle properties.
What is sum of interior angles?
Sum of interior angles is calculated using the formula (n 2) 180, where is the total number of sides. In a regular polygon, each inside angle is the same. Interior angle of a polygon is equal to the sum of interior angles divided by the number of sides, according to the following formula. One of the first things we all learned about triangles was that the sum of the internal angles is 180 degrees.
Given :
Triangle FHG
Angle F = (x - 5) degreesAngle G = (3x + 25) degreesAngle H = (x) degreesApplying the sum of interior angles property on the triangle FHG. According to the sum of interior angles property:
[tex]$$\angle \mathrm{F}+\angle \mathrm{H}+\angle \mathrm{G}=180^{\circ}$$[/tex]
Now, substitute the values of the known terms in the above equation.
[tex]$$(x-5)+(x)+(3 x+25)=180$$[/tex]
Simplify the above equation In order to determine the value of ' $x$ '.
[tex]& 5 x+20=180 \\[/tex]
[tex]& 5 x=160 \\[/tex]
[tex]& \mathbf{x}=\mathbf{3 2} \text { degrees }[/tex]
So the angle[tex]$\mathbf{G}$[/tex] is given by:
[tex]& \angle \mathrm{G}=3(32)+25 \\[/tex]
[tex]& \angle \mathrm{G}=121^{\circ}[/tex]
The complete question is,
What is m∠G ?
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Are the following triangles congruent? Why or why not? Yes, AAS Yes, SAS Yes, SSS No, there is not enough information
The following triangles are congurent
Yes SAS
What is the type of polynomial 2x2 3x 9 expressing area of the garden?.
The expression 2x2 3x 9 area of the garden is a quadratic polynomial.
2x2 contains a power value and 3x contains the constant x and 9 is the integer so this is the Quadratic Polynomial. When a variable term in the polynomial expression has a highest power of 2, the polynomial is said to be quadratic.
Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is.
A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the name given to the solutions of such an equation.
The capability to derive a number of significant inferences from the analysis of the discriminant is an additional advantage of this approach.
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Full Question: What is the type of polynomial 2x^2-3x-9 expressing area of the garden?
(a) linear polynomial
(b)Quadratic polynomial
(c) cubic polynomial
(d) constant polynomial
Write the equation of a line in slope intercept form that meets these two criteria
1. It does not pass through quadrant 1
2. It contains the point (-3,1)
How to solve 2 equations with 2 variables using calculator?.
You can solve 2 equations with 2 variables using calculator in equation mode.
To solve a system of two equations with two variables using a scientific calculator, you can use the following steps (based on CASIO fx-991ES PLUS):
First press the 'mode' button and then press '5' corresponding to equations.
Now press '1' corresponding to a linear equation in two variables of format anX + bnY = cn. Now a matrix appears, each row correspond to each equation. The first column represent the coefficient of X, second column represent the coefficient of Y and third column, the coefficient. Note that the equation should be of the format mentioned before.
Now press '=' to get the solution. On the first press you get X and on second press, you get the value of 'Y'.
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what is the correct inequality
Answer:
Step-by-step explanation:
Trigonometric Ratios
Answer:Hi there the answer is in quizlet is another page :) flashcards TRIGONOMETRIC RATIOS
*URGENT*
I’ve been doing this problem over and over but i have a feeling i’m wrong, please help!!
[tex]\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m[/tex]
Direction:Solve for the meaning term to form equivalent
1)2:3=N:21
2)5:2=20:N
3)2:7=12:N
4)6:7=30:N
5)N:10=15:55
The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio and the value of the meaning term can be found.
1)2:3=N:21
N=21*2/3
N=14
2)5:2=20:N
N=20*5/2
N=50
3)2:7=12:N
N=12*2/7
N=4.57
4)6:7=30:N
N=30*7/6
N=35
5)N:10=15:55
N=15*10/55
N=2.73
The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio. To do this, the numerator and denominator of the first equation can be multiplied or divided by the same number to get the same ratio as the second equation. When the ratio is the same, the meaning term can be found by dividing the numerator of the second equation by the denominator of the first equation. For example, the equation 2:3 = N:21 can be solved by multiplying 3 and 21 by 2, giving 6:42 = N:42, which has the same ratio. The meaning term is then found by dividing 42 by 3, giving N = 14. This process can be applied to all equations to find the meaning term.
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What percent of the 8th graders estimated they spend less than an hour a day on social media? Round your answer to the nearest whole number percent.
43% of eighth graders claim to spend more than an hour every day on social media.
What is the percentage?A ratio written as a fraction of 100 is what is referred to as a percentage.
Students were asked in a survey if they thought they used social media more or less than an hour every day.
Added to Less
7th 12 14
8th 20 26
The number of students who responded "more" must be divided by the total number of 8th-grade students polled, and the result must then be multiplied by 100 to get the percentage of students who said they spend more than an hour a day on social media.
20 out of 46 students (20+26) responded "more," or roughly 43.48%.
As a result, 43% of eighth graders believe they spend more than an hour every day on social media.
The Complete Question.
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a quadratic function with vertex (1,3) and passes through the point (3,5). its an equation is f(x)=a(x-1)^2+3 what ls the value of a?
The value for a in quadratic function a(x-1)²+3 is obtained as a = 2.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The vertex of the quadratic function is (1,3).
The line passes through the points (3,5).
The equation is in the form - a(x-1)²+3
It is known that the vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola.
So it can be written -
f(x) = a(x-1)² + 3
Substitute the value of (1,3).
f(1) = a(1-1)² + 3 = 3
And for the point (3,5) the equation will be -
f(3) = a(3-1)² + 3 = 5
Set up a system of equations -
a(1-1)² + 3 = 3
a(3-1)² + 3 = 5
Solving for a in these equations -
a = 2
Therefore, the value of a is obtained as 2.
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Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded annually. How much money will be in her account at the
end of the 12 years? (Remember to round your answer to the nearest cent.)
Answer:
$800.516
Step-by-step explanation:
We use the equation
A = P(1 + [tex]\frac{r}{n}[/tex])^nt
P = principal
r = rate of interest
t = times
Now let's solve
P = $500
r = 4% = 0.04
t = 12 years
A = $500(1 + [tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516
Alex ran 4 1/2 kilometers in 3/4 of an hour. How many kilometers he ran per hour?
How many kilometers he ran per hour?
Alex ran 6 kilometers per hour.
The ratio can be calculated as follows:
The first is to convert mixed fractions to improper fraction
4 [tex]\frac{1}{2}[/tex] km = [tex]\frac{(4x2)+1}{2}[/tex] km
= [tex]\frac{8+1}{2}[/tex] km
= [tex]\frac{9}{2}[/tex] km
The next step is to compare worth comparison
[tex]\frac{a1}{b1}[/tex] = [tex]\frac{a2}{b2}[/tex]
[tex]a_{1}[/tex] = 4 [tex]\frac{1}{2}[/tex] km = [tex]\frac{9}{2}[/tex] km
[tex]a_{2}[/tex] = X
[tex]b_{1}[/tex] = [tex]\frac{3}{4}[/tex] hour
[tex]b_{2}[/tex] = 1 hour
So,
[tex]\frac{9/2}{3/4}[/tex] = [tex]\frac{X}{1}[/tex]
X = [tex]\frac{(9/2)x1}{3/4}[/tex]
X = [tex]\frac{9/2}{3/4}[/tex]
X = [tex]\frac{9}{2}[/tex] × [tex]\frac{4}{3}[/tex]
X = [tex]\frac{36}{6}[/tex] kilometers
X = 6 kilometers
Alex ran 6 kilometers per hour.
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What are the 4 conditions of a binomial distribution?.
The four conditions of a binomial distribution are: independence, normality, symmetry, and rarity.
Independence: Each trial in a binomial distribution is independent of the other trials, meaning that the outcome of one trial does not affect the outcome of any other trial.
Normality: The distribution of the data follows a normal distribution, meaning that it is bell-shaped and symmetrical.
Symmetry: The binomial distribution is symmetrical around the mean, meaning that the probability of the outcome being above the mean is the same as the probability of the outcome being below the mean.
Rarity: The binomial distribution is characterized by rare events, meaning that the probability of an event occurring is relatively low. This is because the outcomes of each trial are determined by a random process.
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Hanon opened a aving account and depoited $800. 00 a principal. The account earn 4% interet, compounded annually. What i the balance after 9 year?
Ue the formula A=P1
r
n
nt, where A i the balance (final amount), P i the principal (tarting amount), r i the interet rate expreed a a decimal, n i the number of time per year that the interet i compounded, and t i the time in year. Round your anwer to the nearet cent
The balance after 9 years is $1139.94 rounded to the nearest cent.
The formula to use in this case is A = P(1 + r)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given the information in the problem, we know that:
P = $800.00 (the principal or starting amount)
r = 0.04 (the interest rate as a decimal)
n = 1 (the interest is compounded annually)
t = 9 (the number of years)
Plugging these values into the formula, we get:
A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
So the balance after 9 years is $1139.94 rounded to the nearest cent.
Therefore, The balance after 9 years is $1139.94 rounded to the nearest cent.
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A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
the zeros of my parabola are (-6,0) and (-2,0)
what am i?
You are a parabola with vertex at (x,y) = (-4,0) and a focus at (x,y) = (-4,3).
What is parabola?A parabola is a mathematical curve that is symmetrical in shape and is often described as an upside-down U. It is a two-dimensional, closed curve and is an important part of conic section geometry. A parabola has a single vertex, which is the highest or lowest point of the parabola. It can also be thought of as the focus of the parabola.
The zeros you have listed are the x-intercepts, which means that your equation is of the form y = ax^2 + bx + c, and your a value is negative because your parabola opens downwards. You can determine the other coefficients by looking at the vertex and focus coordinates.
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someone help solve this pls
Using SAS, property of triangle congruency, ΔRTV ≅ ΔRTS.
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
The five congruent triangle theorems are therefore SSS, SAS, AAS, HL, and ASA.
Given,
Two triangles,
ΔRTV and ΔRTS,
RT = RT (Side) [Common side]
∠RTV = ∠RTS (Angle) [Both are 90°]
VT = TS (Side) [As T is the mid - point of VS ]
Using SAS, property of triangle congruency,
ΔRTV ≅ ΔRTS
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a popsicle tray has 6 cone-shaped popsicle molds. each popsicle mold has a diameter of 5.4 cm and a height of 12.9 cm. how many cubic centimeters will one tray hold
One tray will hold 590.877 cubic centimeters.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
We have to find the volume of a cone-shaped popsicle mold and then multiply it with 6 to find the required answer.
Volume of a cone = [tex]\frac{1}{3}[/tex] π r² h
Given,
Diameter = 5.4 cm
Radius = Diameter / 2 = 5.4 / 2 = 2.7 cm
Height = 12.9 cm
Volume of the cone = [tex]\frac{1}{3}[/tex] π × (2.7)² × 12.9
= [tex]\frac{1}{3}[/tex] π × 94.041
= 98.4795
Total volume of 6 molds in the tray = 98.4795 × 6
= 590.877 cubic centimeters
Hence the volume of the molds that the tray hold is 590.877 cubic centimeters.
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The question is in the photo for you to answer.
Answer:50
Step-by-step explanation:
Bruna i comparing the pay for advertied job. Which 2 way could Bruna find the bet paying job? ( choo 2 anwr)
1. She can look at similar job postings online to compare the salary range offered.
2. She can contact the average employer and ask directly what salary range they offer for the job.
There are two ways Bruna can compare the pay for advertised jobs. First, she can research the salary range of similar job postings. This can be done through job search websites, social networks, and other online resources. She can look at the salary range offered for similar jobs to get an idea of the pay she can expect from an employer.
The second way she can find out the best paying job for her is to ask the employer directly about the salary range. She can contact the employer and ask directly what salary range they offer for the job. This will give her an accurate picture of the salary range that the employer is offering, so she can make an informed decision on which job to apply for. By using these two methods, Bruna can compare the pay for advertised jobs and find the one that offers the best salary.
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3. The circle is circumscribed by the pentagon as shown (not drawn to scale). If QZ = 10, IX = 9, XT = 9, UW = 17, and SU = 10, find the perimeter of the pentagon and show work.
The perimeter of the pentagon is 76 units. The solution is obtained using tangent to circle.
What is tangent to a circle?
A line that touches a circle only once is said to be tangent to it. A point to circle can only have one tangent.
In the figure, the circle is circumscribed by the pentagon.
We are given QZ = 10, YX = 9, WX = 9, UW = 17, and US = 10
VW = WX = 9 (tangent of circle)
So, VU = UW - VW
VU = 17-9= 8
Since, VU and UT are tangents of circle, therefore
UT = 8
US = UT + TS
⇒10 = 8 + TS
⇒TS = 2
Now, TS and SR being tangents, therefore
TS = SR = 2
Also, RQ and QZ are tangents, therefore
RQ = QZ = 10
Similarly, ZY and YX are tangents, therefore
ZY = YX= 9
Thus, Perimeter = SQ + QY + YW + WU + US
⇒Perimeter = SR+ RQ+ QZ+ ZY+ YX+ XW+ UW+ US
⇒Perimeter = 2+ 10+ 10+ 9+ 9+ 9+ 17+ 10
⇒Perimeter = 76 units
Hence, the perimeter of the pentagon is 76 units.
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What is the value of k if the system of equations kx 5y 2 6x 2y 7 has no solution?.
So, the value of k that makes the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution is -1.
A system of linear equations has no solution when the equations are inconsistent, which means that there is no set of values for the variables that would make both equations true at the same time.
In the case of the system of equations kx - 5y = 2, 6x + 2y = 7, we can check for consistency by trying to find a unique solution for the system. We can use different methods such as elimination, substitution or Gaussian elimination.
If we use elimination method, we try to eliminate one of the variable from one equation and substitute it in another equation. By adding the two equations, we get: (k + 6)x = 9, which implies that the value of x is x = 9/(k+6).
Now by substituting this value into the first equation we get k*9/(k+6) - 5y = 2
And we can find the value of y by dividing both sides by -5/1: y = (2*(k+6))/(5*k)
Now if we substitute this value of x and y into the second equation:
6x + 2y = 7
We get: 6*(9/(k+6)) + 2*((2*(k+6))/(5*k)) = 7
And if we simplify this equation we get: 9 + 4/(5*k) = 7(k+6)/(k+6)
And that gives us k = -1, which means the system has no solution.
Therefore, the value of k that makes the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution is -1.
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What is an example of a linear equation in two variables in standard form?.
The example of a linear equation in two variables in standard form is 3x + 2y = 6
A linear equation in two variables in standard form is of the form:
Ax + By = C
where A, B, and C are constants and x and y are variables.
An example of a linear equation in two variables in standard form is:
3x + 2y = 6
This equation can be written in standard form by first subtracting 6 from both sides,
3x + 2y -6 = 0
and then dividing both sides by the greatest common factor of the coefficients,
(3/1)x + (2/1)y = 6/1
This gives the standard form of the equation:
3x + 2y = 6.
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An element with a ma of 300 gram decay by 5. 4% per minute. To the nearet tenth of a minute, how long will it be until there i 110 element remaking
The element will be gone in approximately 10.9 minutes.
We can calculate this by using the formula:
Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))
Time = (log(300 / 110)) / (log(1 - 0.054))
Time = 10.9 (rounded to the nearest tenth of a minute)
Therefore, The element will be gone in approximately 10.9 minutes.
A logarithmic function is a mathematical function that relates the logarithm of a number to its argument. The logarithm of a number (base 10) is represented by the log symbol (log 10) and the number being used as the argument. The inverse of this function is an exponential function, which relates the exponential of a number to its argument. Logarithmic functions are often used in mathematics and science to simplify and solve equations involving large exponents. They are also commonly used in finance, engineering, and other fields that involve large numbers.
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Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))
Time = (log(300 / 110)) / (log(1 - 0.054))
Time = 10.9 (rounded to the nearest tenth of a minute)
Un equipo de cuatro personas participó en una carrera de revelo de 400 yardas cada miembro del equipo corrió la misma distancia el equipo completo a la carrera en 53.2 segundos cuál es el tiempo promedio que corrió cada persona
Un equipo de cuatro personas participó en una carrera de relevo de 400 yardas, lo que significa que cada miembro del equipo corrió una distancia de 400 yardas. El equipo completo completó la carrera en 53.2 segundos. Para calcular el tiempo promedio que cada persona corrió, debemos dividir el tiempo total de la carrera entre el número de personas en el equipo. En este caso, se divide 53.2 segundos entre 4 personas, lo que da un tiempo promedio de 13.3 segundos por persona.
What is the solution to the equation x^2 - 5x + 8 = -2?
For what value of k the following pair of linear equations has infinitely many solutions 10x 5y?.
The 2 equations will have infinitely many solutions if k equals 10.
Here we have
10x + 5y − (k−5) = 0 and 20x + 10y − k = 0
Since these 2 are already in the standard form
a₁x + b₁y + c₁ = 0
and
a₂x + b₂y + c₂ = 0
we don't have to make any changes to them
According to the law, an equation has infinitely many solutions if
a₁/a₂ = b₁/b₂ = c₁/c₂
here,
a₁ = 10, b₁ = 5, and c₁ = - k + 5
and,
a₂ = 20, b₂ = 10, and c₂ = - k
Hence, we get
10/20 = 5/10 = ( - k + 5)/(-k)
or, (k - 5)/k = 1/2
or, 2k - 10 = k
or, k = 10
Hence the 2 equations will have infinitely many solutions if k is equal to 10.
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Complete Question
For what value of k does the following pair of linear equations have infinitely many solutions?
10x + 5y − (k−5) = 0 and 20x + 10y − k = 0
