Answer:
[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
Step-by-step explanation:
Given
Let the two triangles be A and B
Sides of A: 4, 6 and 8.5
Sides of B: 6, 9 and 12.5
Required
Which set of ratio determines the dilation
To determine the dilation of a triangle over another;
We simply divide the side of a triangle by a similar side on the other triangle;
From the given parameters,
A ------------------B
4 is similar to 6
6 is similar to 9
8.5 is similar to 12.5
Ratio of dilation is as follows;
[tex]Dilation = \frac{4}{6}[/tex]
[tex]Dilation = \frac{6}{9}[/tex]
[tex]Dilation = \frac{8.5}{12.5}[/tex]
Combining the above ratios;
[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
From the list of given options, the correct option is A,
Answer:
a
Step-by-step explanation:
This recipe makes 6 portions of fajitas. Carly has 900 g of chicken, 1200 g of peppers, 150 g of onion, 60 g of spice mix and 30 tortillas. How much more of each ingredient will she need to make 18 portions by following this recipe? Recipe: Serves 6 500 g chicken 600 g peppers 90 g onion 25 g spice mix 12 tortillas
Answer:
600 g chicken
600 g peppers
120 g onion
15 g spice mix
6 tortillas
Step-by-step explanation:
To make 18 portions, Carly needs to make 3 times the original recipe.
1. Solve for how much of each ingredient is needed.
500 · 3 = 1500 g chicken
600 · 3 = 1800 g peppers
90 · 3 = 270 g onion
25 · 3 = 75 g spice mix
12 · 3 = 36 tortillas
2. Subtract how much of each ingredient Carly already has from how much is needed to find how much more she needs.
1500 - 900 = 600 g chicken
1800 - 1200 = 600 g peppers
270 - 150 = 120 g onion
75 - 60 = 15 g spice mix
36 - 30 = 6 tortillas
Answer:
hjvjhee
Step-by-step explanation:ejbfkwej
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Determine the money factor for a lease with an interest rate of 9%
Answer:
0.00375
Step-by-step explanation:
The money factor for a lease is used to determine how much is charged monthly on a lease payment. If the money factor is low, the lease payment is low making it a good transaction but if the money factor is high, the lease payment is also high and this is not desirable. The money factor is given by:
Money factor = Interest rate / 2400
Given an interest rate of 9%, the money factor is calculated as:
Money factor = Interest rate / 2400 = 9% / 2400 = 0.00375
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32 (3, 5) (6, 2) (8, –1) (14, –18)
Answer:
work is shown and pictured
The solution to the system of linear equation is (x, y) = (6, 2)
3x - 2y = 14 (1)
3x - 2y = 14 (1)5x + y = 32 (2)
From (2)
y = 32 - 5x
Substitute y = 32 - 5x into (1)
3x - 2y = 14 (1)
3x - 2(32 - 5x) = 14
3x - 64 + 10x = 14
13x = 14 + 64
13x = 78
x = 78/13
x = 6
Substitute x = 6 into (2)
5x + y = 32 (2)
5(6) + y = 32
30 + y = 32
y = 32 - 30
y = 2
(x, y) = (6, 2)
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Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 40º. Then Jill goes to the roof of her apartment building, directly above her previous position, and measures the angle of elevation to the top of the same tower to be 30°. If the height of the tower is 100 meters, the height of Jill's apartment building is meters.
Answer:
1) From the measure of 40°, you can write:
tan(40°) = 100/x, where x is the base from the building to the tower
⇒x=100/tan(40°) = 119,18 m
2) From the measure of 30°, you can write
tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.
Then, y = tan(30°) * 119,18 = 68,81 m
3) The height of Jill's building is 100 - 68,81 = 31,19 m
When the height of the tower is 100 meters, the height of Jill's apartment building is 31.19m
How to calculate the height?Let the base from the building to the Rowe be represented by x. Based on the information given, the value will be:
x = 100/tan 40°
x = 119.18m
The height can be represented as:
= 100 - [tan30° × 119.18]
= 100 - 68.81
= 31.19m
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A set of five integers has unique mode 7, median 9, and arithmetic mean 11. What is the greatest possible value in the set?
Answer:
22
Step-by-step explanation:
Since the mean of the set is 11, the sum of the integers in the set must be 11 * 5 = 55. The median must be the 3rd integer, therefore the 3rd integer is 9. Since 9 > 7 and there are only 2 integers less than the median, the 1st and 2nd integers must be 7 and 7 because 7 is the mode. This leaves the last two integers to have a sum of 55 - (9 + 7 + 7) = 32. In order for the last integer (the greatest one) to have the largest value, the fourth integer must be as small as possible. Therefore, the fourth integer is 10 (it can't be 9 because 7 is the only mode) which makes the answer 32 - 10 = 22.
write down as decimal.
Answer:
iii) 5.7
iv) 27.85
vii) 0.609
viii) 40.0709
Step-by-step explanation:
hope this helps
Please help me with this. I am really struggling...
The sand used for sanding icy roads in the winter is stored in a conical-shaped structure with a radius of 10 m and a height of 16 m. Calculate the maximum amount of sand which can be stored in this structure.
Answer:
1,675.516
Step-by-step explanation:
The formula for a cone is V = pi r^2 h/3.
Plugging in the values of the radius and height, V = pi 10^2 16/3
Solving, you get:
V = pi 100 5.3333333
V = 1,675.516
What the answer question now
Answer:
UW=41
Step-by-step explanation:
the tangent line and the radius always meet at a right angle(90 degrees)
UWV is a right angle triangle, apply the Pythagorean theorem:
a²+b²=c² (a=40, b=9, c=UW)
40²+9²=c²
c=√40²+9²=√1600+81=√1681
c= 41
discriminant of xsqaure - 1/2x +1/2=0
Answer:
[tex]\boxed{D = 15/8}[/tex]
Step-by-step explanation:
=> [tex]x^2-\frac{1}{2} x +\frac{1}{2} = 0[/tex]
Comparing it with the standard form of quadratic equation [tex]ax^2+bx+c = 0,[/tex] we get
a = 1, b = -1/2 and c = 1/2
Discriminant = [tex]b^2-4ac[/tex]
[tex]D = (-1/2)^3+4(1)(1/2)\\D = -1/8 + 2\\D = \frac{-1+16}{8} \\D = \frac{15}{8}[/tex]
Which equation is modeled below?
4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.
2 x + (negative 2) = negative 2 x + 6
4 x + (negative 2) = negative 2 x + 6
2 x + 4 = 6 x + 2
Negative 2 x + 4 = 6 x + (negative 2)
(Ignore the filled in bubble)
Answer:
B
Step-by-step explanation:
4 (x) + 2 (-1) = 2 (-x) + 6(1)
4x + -2 = -2x + 6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure,
x+x+x+x+(-1-1)=(-x-x)+(1+1+1+1+1+1)
⇒ 4x-2=-2x+6
So, equation modeled as 4x-2=-2x+6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
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Will give BRAINLIEST to best answer One way to explore a career opportunity is to work as a trainee in your field of interest to gain practical experience. In this experience you would be known as a(n). A intern B. mentor C. tutor D. volunteer
Answer:
A. Intern
Step-by-step explanation:
Usually as a intern, you go around gaining experience about something. For example, if your a fresh graduate , you would first be hired as an intern to gain experience in the job you want.
Answer:
B:Mentor
Step-by-step explanation:
Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[tex]Solve for $x$, where $x \ \textgreater \ 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[/tex]
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The solutions are, for a positive discriminant:
[tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]
Here, we have a = -21, b = -11, c = 40, so it gives:
[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]
So, we have two solutions:
[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]
We only want x > 0 so the solution is
[tex]\dfrac{8}{7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which equations represents inverse variation? Check all that apply
An inverse variation can be represented by the equation xy=k or y=kx . That is, y varies inversely as x if there is some nonzero constant k such that, xy=k or y=kx where x≠0,y≠0
The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level?
Answer:
We reject the students claim because the P-value is less than the significance level.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = 25,235
Alternative hypothesis;Ha; μ > 25,235
Now, let's find the test statistic. Formula is;
t = (x' - μ)/(σ/√n)
We are given;
x' = 27,524
μ = 25,235
σ = 6000
n = 100
Thus;
t = (27524 - 25235)/(6000/√100)
t = 2289/600
t = 3.815
So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.
The p-value is less than the significance level of 0.05. Thus,we reject the students claim.
A city has a population of 220,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 13 years?
Answer: 546496.76
Step-by-step explanation:
Given the following :
Current population = 220,000
Population growth rate per year = 7.25%
Population size after 13 years =?
Using the compounding formula :
A = P(1 + r)^t
Where ;
A = final population size
P = current population size
r = growth rate
t = time or period
A = P(1 + r)^t
A = 220,000 ( 1 + 7.25/100)^13
A = 220,000 ( 1 + 0.0725)^13
A = 220,000 (1.0725)^13
A = 220,000(2.484076)
A = 546496.760
The population will be about 546,497 people
What is the simplified expression for
2^2 • 2^3 over
24
O 20
O 21
O 22
O 23
Answer:
(B)[tex]2^1[/tex]
Step-by-step explanation:
We are to simplify the given expression: [tex]\dfrac{2^2 \cdot 2^3}{2^4}[/tex]
Step 1: Apply the addition law of indices to simplify the numerator.
[tex]\text{Addition Law: }a^x \cdot a^y=a^{x+y}[/tex]
Therefore:
[tex]\dfrac{2^2 \cdot 2^3}{2^4} \\\\=\dfrac{2^{2+3}}{2^4}\\\\=\dfrac{2^5}{2^4}[/tex]
Step 2: Apply the Subtraction law of indices to simplify the expression
[tex]\text{Subtraction Law: }a^x \div a^y=a^{x-y}\\\\\implies \dfrac{2^5}{2^4} =2^{5-4}\\\\=2^1[/tex]
The correct option is B.
LeBron buys 500 shares of Tiger Corporation for $10 a share. The corporation’s president is caught committing fraud and the stock drops to $3 a share. LeBron sells all his shares. How much can he take off his income as a capital loss this year?
Answer:
$3,500
Step-by-step explanation:
First, Lets analyze the problem.
LeBron buys 500 shares for $10 a share. So he buys 500 shares for $5,000.
Now the price drops to $3, he had 500 stocks, the stocks are now only worth $1500.
5000-1500=3,500
He has lost $3,500 in the Tiger Corporation shares.
The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (nk). True or false.
Answer:
The correct option is;
False
Step-by-step explanation:
The coefficient of x^k·y^(n-k) is nk, False
The kth coefficient of the binomial expansion, (x + y)ⁿ is [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]
Where;
k = r - 1
r = The term in the series
For an example the expansion of (x + y)⁵, we have;
(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵
The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15
Therefore, the coefficient of x^k·y^(n-k) for the expansion (x + y)ⁿ = [tex]C(n,k)[/tex] not nk
Answer:
True
Step-by-step explanation:
apec
11. Which of the following lines is perpendicular to the line 3x-9y = 17?
A) 12x + y = 4
B) 9x - 3y = 11
C) 6x + 2y = 8
D) 3x - y = 5
Step-by-step explanation:
When using the equation of a line, one calculates the value of
y
in terms of
x
, say
y
=
m
x
+
c
, then
m
is the slope of the line and
c
is its intercept on
y
-axis.
As
3
x
−
9
y
=
15
can be written as
3
x
−
15
=
9
y
or
y
=
3
9
x
−
15
9
or
y
=
1
3
x
−
5
3
Hence slope of
3
x
−
9
y
=
15
is
1
3
Product of slopes of two perpendicular lines is
−
1
Hence, the slope of the line that is perpendicular to the line
3
x
−
9
y
=
15
is
−
1
1
3
=
−
1
×
3
1
=
−
3
graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}
Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2 What is the other solution to the equation? x=−6 x=−4 x=2 x=4
Answer:
x = - 4
Step-by-step explanation:
Given
3 - 2 |0.5x + 1.5 | = 2 ( subtract 3 from both sides )
- 2 |0.5x + 1.5 | = - 1 ( divide both sides by - 2 )
|0.5x + 1.5 | = 0.5
The absolute value function always gives a positive value, however, the expression inside can be positive or negative, thus
0.5x + 1.5 = 0.5 ( subtract 1.5 from both sides )
0.5x = - 1 ( divide both sides by 0.5 )
x = - 2 ← solution Manuela obtained
OR
-(0.5x + 1.5) = 0.5 ← distribute parenthesis on left side by - 1
- 0.5x - 1.5 = 0.5 ( add 1.5 to both sides )
- 0.5x = 2 ( divide both sides by - 0.5 )
x = - 4 ← other solution to the equation
Based on the information given, it can be noted that the solution to the equation will be x = -4.
Solving an equation.From the equation given, 0.5x + 1.5 = 0.5
Subtract 1.5 from both sides
0.5x + 1.5 - 1.5 = 0.5 - 1.5
0.5x = - 1
Divide both side by 0.5
0.5x/0.5 = 1/0.5
x = 2
Also, the other solution will be:
-0.5x - 1.5 = 0.5
-0.5x = 0.5 + 1.5
-0.5x = 2
x = 2/-0.5
x = -4.
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Classify the following expression by degree and term: x^3y + 5xyz A: 3rd degree trinomial B: 4th degree binomial C: 3rd degree binomial D: 5th degree binomial
Answer:
4th degree binomial
Step-by-step explanation:
x^3y + 5xyz
Add the exponents on each term
3+1 = 4 1+1+1 =3
The highest power is the degree, so it is a 4th degree
It also has 2 terms so it is a binomial
4th degree binomial
Answer:
B: 4th degree binomial
Step-by-step explanation:
I took the test flvs
se tiene que embaldosar el patio interior de un edificio con baldosas cuadradas de 30 cm de lado. El patio es rectangular y sus medidas son 10 m por 12 m. ¿cuantas baldosas se necesitaran?
Answer:
40,000 baldosas
Step-by-step explanation:
Lo primero que debemos hacer aquí es calcular el área del patio rectangular.
El mejor enfoque para esto es convertir primero sus medidas a centímetros
Matemáticamente, 100 cm = 1 m, entonces 10 m se convierten en 1000 cm y 12 m se convierten en 1200 m.
El área de un rectángulo es L * B y, por lo tanto, tenemos 1200 * 1000 = 1,200,000 cm ^ 2
Ahora, para saber la cantidad de azulejos que tendrá el patio, necesitaremos dividir el área del patio por el área de los azulejos
Matemáticamente, eso sería 1,200,000 / 30 = 40,000 fichas
Un estanque tiene 13/2 litros de leche y se le agregan 87/10. ¿Cuánta leche quedó en el estanque? ¿Sí en el estanque caben 65/4 litros, cuántos litros más se pueden agregar?
Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.
Answer:
a(1)= -3
a(n)=a(n-1) (-3)
Step-by-step explanation:
hope this helps
Recursive formula of the given sequence -3, 9, -27, 81, -243, ... , is (-3)^n ; where n = 1,2,3, ...
What is recursive formula?A recursive formula defines any term of sequence with its preceding term.
The given sequence is -3, 9, -27, 81, -243, ... ,
First term = -3
Second term = (-3)^2 = 9
Third term = (-3)^3 = -27
Fourth term = (-3)^4 = 81
Fifth term = (-3)^5 = -243
Hence, the recursive formula of the given sequence -3, 9, -27, 81, -243, ... , is (-3)^n ; where n = 1,2,3, ...
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Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuántas preguntas
Complete question:
Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuantas preguntas respondió bien?
Responder:
número de respuestas correctas = 22
Explicación paso a paso:
Dado lo siguiente:
Número total de preguntas = 30
Deje respuestas correctas = y; Respuestas incorrectas = n
Marca otorgada por y = 5
Marca deducida por n = 2
Si el total de preguntas = 30; luego
y + n = 30 - - - - (1)
Puntuación total obtenida = 94; luego
5y - 2n = 94 - - - (2)
De 1),
y + n = 30
y = 30 - n
Sustituya y = 30 - n en equ (2)
5 (30 - n) - 2n = 94
150 - 5n - 2n = 94
150 - 7n = 94
-7n = 94-150
-7n = - 56
n = 56/7
n = 8
Sustituir n = 8 en (1)
y + n = 30
y + 8 = 30
y = 30 - 8
y = 22
y = número de respuestas correctas = 22
n = número de respuestas incorrectas = 8
Usando un sistema de ecuaciones, se encuentra que el participante obtuve 22 respuestas correctas.
En el sistema, x es el número de respuestas correctas, con y siendo el número de respuestas incorrectas.
Total de 30 preguntas, o sea:
[tex]x + y = 30 \rightarrow y = 30 - x[/tex]
5 puntos asignados por cada respuesta correcta, 2 restados por cada respuesta incorrecta. Puntaje de 94 puntos, o sea:
[tex]5x - 2y = 94[/tex]
Considerando [tex]y = 30 - x[/tex]
[tex]5x - 60 + 2x = 94[/tex]
[tex]7x = 154[/tex]
[tex]x = \frac{154}{7}[/tex]
[tex]x = 22[/tex]
El participante obtuve 22 respuestas correctas.
Un problema similar es dado en https://brainly.com/question/24646137
Complete the square to rewrite y = x2 + 8x+ 3 in vertex form, and then identify
the minimum y-value of the function.
Please answer ASAP!!!
====================================================
Work Shown:
y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3
It is in the form y = ax^2 + bx + c
a = 1
b = 8
c = 3
Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)
h = -b/(2a)
h = -8/(2*1)
h = -8/2
h = -4
Plug this into the original equation to get its paired y value. This will get us the value of k
y = x^2 + 8x + 3
y = (-4)^2 + 8(-4) + 3
y = 16 - 32 + 3
y = -13
This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)
We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.
given the equation below which of the following shows the quadratic formula correctly applied? 3x^2-4x-12=0
[tex] {3x}^{2} - 4x - 12 = 0[/tex]
[tex]a = 3[/tex]
[tex]b = - 4[/tex]
[tex]c = - 12[/tex]
Formula:
[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]
Replacing:
[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]
Option: C).
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
A. $16.34
B. $16.13
C. $5.37
D. $16.63
Answer: B. $16.13
Step-by-step explanation:
Formula : Sum of n observations = Mean x n
Given, 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student.
Total students = 82+74+96+99 =351
Sum of earnings of 82 seniors = $26.75 x 82= $2193.5
Sum of earnings of 74 juniors = $12.25 x 74 = $906.5
Sum of earnings of 96 sophomores = $15.50 x 96 = $1488
Sum of earnings of 99 freshmen = $10.85 x 99 = $1074.15
Total earnings = $2193.5 + $906.5+ $1488 +$1074.15
= $5662.15
Average collection = (Total earnings) ÷ (Total students )
= $5662.15÷ 351
≈ $16.13
Hence, the average collection for a student in this school = 16.31
So, the correct option is B.
What is total number of elements in 3 trials of rolling a 6-sided die?
Answer:
216 elements
Step-by-step explanation:
the total number of elements of a dice is :
6^n
6 stand for the 6 faces of the dice
n stands for the number trial
then total number of elements in 3 trials of rolling a 6-sided die is 6^3=216 elements
