Use Heron's formula to find the area of the triangle with side lengths 6, 9, and 12, as shown below.
Answers
Answer:
√(6 + 9 +12) = √27 = 3√3
√(-6 + 9 + 12) = √15 = √3√5
√(6 - 9 + 12) = √9 = 3
√(6 + 9 - 12) = √3
(1/4)(3√3)(√3√5)(3)(√3)
= (1/4)(27√3)(√5) = (27√15)/4 = 26.1
Answer:correct answer is 26.1
Step-by-step explanation:
Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, which is half the perimeter of the triangle:
s = (a + b + c) / 2
In this case, the side lengths are a = 6, b = 9, and c = 12. Therefore, the semiperimeter is:
s = (6 + 9 + 12) / 2 = 27 / 2
Using Heron's formula, we can now calculate the area of the triangle:
Related Questions
The volume of a sphere is 33.51032164 cubic meters. What is the radius of the sphere?
Answers
The radius of the sphere that has a volume of 33.51032164 cubic meters is approximately 2 meters.
What is the Radius of a Sphere?The radius of a sphere is the distance from the center of the sphere to any point around the circumference. The radius is half of the length of the diameter of a sphere.
The volume of a sphere = 4/3 * π * r³
Given that:
Volume ≈ 33.5 cubic meters
Use the formula to find the radius of the sphere:
33.5 = 4/3 * π * r³
33.5 = 4π/3 * r³
3 * 33.5 = 4π * r³
100.5/4π = r³
r³ = 7.998
r = ∛7.998
r ≈ 2 meters.
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Determine whether the pairs of vectors is orthogonal
Answers
No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.
What is the dot product of the pair of vectors?The dot product will help us to determine if the pair of vectors are orthogonal or not.
If the dot product is equal to zero, then the pair of vectors are orthogonal.
The dot product of the vectors is calculated as follows;
(3i - 8j).(8i - 3j)
= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)
= (24) - (0) - (0) + (24)
= 24 + 24
= 48
So the pairs of vectors are not orthogonal.
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Round to the nearest tenth, then find the sum. 35.26 + 8.32 + 6.78 i will give 12 points pleas help me in in a test
Answers
Answer:
Step-by-step explanation:
35.26 rounded to 35.3
8.32 rounded to 8.3
6.78 rounded to 6.8
35.3 + 8.3 = 43.6
43.6 + 6.8 = 50.4
The answer is 50.4.
39.26 rounds to 35.3
8.32 rounds to 8.3
6.78 rounds to 6.8
When you add them together, you get 50.4.
Which ordered pair is a solution to the system? X>4 Y≥12
Answers
Some solutions for the given system of inequalities are:
(5, 12)
(6, 12)
(7, 13)
And so on.
Which ordered pair is a solution for the system?Here we have the following system of inequalities:
x > 4
y ≥ 12
We want to see which ordered pair, of the form (x, y), is a solution for the system.
A solution is a pair that makes both inequalities true.
So, x must be larger than 4.
y can be equal to 12, or larger than 12.
Then some solutions are:
(5, 12)
(6, 12)
(7, 13)
And so on.
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La empresa clarisse dedicada al rubro de telefónica, está ampliando su cobertura, debido a esto está colocando postes, donde la séptima parte de un poste está enterrada, y sobresale del suelo 25 metros. Calcular la altura del poste aproximado a los centímetros.
Answers
The approximate height of the pole in centimeters is 17,500 centimeters.
We have,
Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.
We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.
25 = L/7
where L is the total length of the pole.
We can solve for L by multiplying both sides of the equation by 7:
L = 7 x 25
= 175 meters
Now we need to convert this length to centimeters.
Since 1 meter is equal to 100 centimeters,
175 meters x 100
= 17,500 centimeters
Therefore,
The approximate height of the pole in centimeters is 17,500 centimeters.
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The complete question.
The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.
Alma makes `5` cups of her favorite shade of purple paint by mixing `3` cups of blue paint, `1 & 1/2 cups of red paint, and 1/2 a cup of white paint.
Alma has `2` cups of white paint.
How much blue paint and red paint will Alma need to use with the `2` cups of white paint?
Answers
Alma need to use 6 cups of blue paint and 4 cups of red paint with the 2 cups of white paint.
Here, Alma makes 5 cups of her favorite shade of purple paint by mixing
3 cups of blue paint,
1 1/2 cups of red paint,
and 1/2 a cup of white paint.
Alma has 2 cups of white paint.
The ratio of blue to the white paint is:
3 : (1/2)
so, for 2 cups of white paint,
3 : (1/2) = x : 2
x = 6 cups of blue paint
The ratio of red to the white paint is,
3: (1 1/2)
3 : (3/2)
So, for 2 cups of white paint,
3 : (3/2) = y : 2
y = 4 cups of red paint
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Which description is most accurate for a Zero-Based Budget? Group of answer choices You put every dollar of your take-home pay into a budget category each month You pay every one of your debts down to $0 every month You spend your saving account balance down to $0 every month You spend your checking account balance down to $0 every month
Answers
The most accurate for a Zero-Based Budget is You put every dollar of your take-home pay into a budget category each month. Option A
What is a zero-based budgeting?
Zero-based budgeting (ZBB) is simply defined as a method of budgeting having that all expenses must be checked for each new period.
The process of zero-based budgeting is one that begins from a zero account
Note that the budgets are carried out when it is needed for the upcoming period, regardless of whether the budget is less or greater than the previous one.
It is important to note the following;
Zero -based and traditional budgeting are different methods that used by companies and firms to track expenditures.ZBB method helps managers in tackling lower costs in a company.Learn more about zero-based budget at: https://brainly.com/question/26195666
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The annual profits for a company are given in the following table, where x represents the number of years since 2012, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected profit (in thousands of dollars) for 2022, rounded to the nearest thousand dollars.
Answers
The linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
How to calculate the valueReplacing the means, the intercept a is given by:
108.8 = 22.6(2.5) + a.
a = 108.8 - 22.6(2.5)
a = 52.33
Therefore, the linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
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Answer:
Step-by-step explanation:
What are the coordinates of point A?
(4.5,1)
(4.5, 0.5)
(5, 0.5)
(5,1)
Answers
if $5700 is invested in a savings account for which interest is compounded annually, and if the $5700 turns into $6100 in 12 years, what is the interest rate of the savings account?
Answers
Answer:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the ending amount, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = $5700, A = $6100, n = 1 (since the interest is compounded annually), and t = 12. We can solve for r:
$6100 = $5700(1 + r/1)^(1*12)
$6100/$5700 = (1 + r)^12
1.0702 = (1 + r)^12
log(1.0702) = log[(1 + r)^12]
0.0291 = 12log(1 + r)
0.00243 = log(1 + r)
10^(0.00243) = 1 + r
r = 0.0059 or 0.59%
Therefore, the interest rate of the savings account is 0.59%.
Convert 300° to radians.
O A. 3T
7T
OB. T
O C.
11T
ike
O D. ST
3
Answers
A conversion of 300 degrees to radians is equal to 5.24 radians.
How to determine the angle in radians?In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = rθ
Where:
r represents the radius of a circle.θ represents the central angle measured in degrees.Next, we would convert degrees to radians;
300 = rads × 180/π
Radians = 300π/180 = 5.24 radians.
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Determine the measure of angle Q.
Not possible
20°
30°
25°
Answers
The angle that is marked as Q has a value of 30°
What is cosine rule?The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.
Cosine rule useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.
By the use of the cosine rule, we have that;
7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q
49 = 144 + 196 -336CosQ
49- 340 = -336CosQ
-291= -336CosQ
Q = Cos-1 (-291/-336)
Q = 30
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Suppose we wish to factor 13b2 + 23b - 8 by grouping. What is the key number, ac?
Answers
The key number, ac, is -104.
What is key number ?
Key number is the product of the coefficients of the first and last terms. The right binomial factors for a quadratic expression can be determined with its assistance.
We must multiply the coefficient of the quadratic term by the constant term to obtain the key value, ac, which results in:
ac = 13(-8) = -104
Therefore, The key number, ac, is -104.
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Suppose 217 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
Answers
There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
We have,
Based on a sample of 217 subjects, 53 of them developed nausea.
To test this claim, a hypothesis test is conducted using a significance level of 0.01.
The null hypothesis, denoted as H0, assumes that the true proportion of users who develop nausea is less than or equal to 20%, while the alternative hypothesis, denoted as Ha, assumes that the true proportion is greater than 20%.
If the test statistic, calculated from the sample data, falls in the rejection region, which is determined based on the significance level and the degrees of freedom, then the null hypothesis is rejected, and it can be concluded that there is sufficient evidence to support the alternative hypothesis.
In this case,
If the test statistic falls in the rejection region, it means that the evidence suggests that more than 20% of users of the pain drug develop nausea, and the claim that less than or equal to 20% of users develop nausea is not supported by the data.
Thus,
There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
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e desea estimar el gasto promedio mensual en dolares de una familia de cierta ciudad del pais gasta en embutidos.
a) Determine cuantas familias se debe tomar como muestra con una confianza del 95% y un error de 2 dolares . Un especialista a estimado una desviacion estandar de 9 dolares.
b) Haga el calculo para una nueva urbanizacion con 850 familias con un 99% de confianza y un error de 1.5 dolares considerando la desviacion estandar con un valor de 9 dolares.
Answers
Answer:
a) Utilizando la fórmula para el tamaño de muestra, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).
Sustituyendo los valores, obtenemos:
n = (1.96 * 9 / 2)^2 ≈ 77
Por lo tanto, se debe tomar una muestra de al menos 77 familias.
b) De manera similar, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).
Sustituyendo los valores, obtenemos:
n = (2.58 * 9 / 1.5)^2 ≈ 261
Por lo tanto, se debe tomar una muestra de al menos 261 familias.
Step-by-step explanation:
the graph of f(x)= 3 times 2x -3 is shown below. g(x) is a transformation of f(x).
Answers
The function of g(x) is 3 ([tex]2^x[/tex]) + 3.
We have,
f(x) = 3 ([tex]2^x[/tex]) -3
Now, the function f(x) have shifted by -3 unit to move 6 unit up.
This means that we have the shifting of
= -3 + 6
= +3 unit
Also, g(x) crosses the y-axis at about 5 or 6 when x=0.
Then, the function of g(x) is
= 3 ([tex]2^x[/tex]) + 3
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5.4 times 2 3/4 ???????????????????????????????????????????????????
Answers
Answer: In decimal form, 14.85
Answer in fraction form: 297/20
Step-by-step explanation:
Which type of relationship is indicated by the residual plot? Non-linear relationship. Linear relationship Exponential relationship
Answers
The type of relationship that is indicated by the residual plot is given as follows:
Non-linear relationship.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.
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Fill in the blanks using the available answers
I believe the first part is 2.2. But lost on the fill in the blanks. Help please.
Answers
Note that the estimated population mean is 2.2
The mean absolute deviation is 1
The average distance each data value is from the mean is 1 hours per night
The distribution has _Low_ variability
How did we reach the above conclusions?Where the data graphed is:
Hours Per Night Students
0.5 0
1 2
1.5 3
2 4
2.5 2
3 2
3.5 1
4 1
The estimate of the population mean is
0.5 (0 ) + 1 ( 2) + 1.5( 3) + 2(4) + 2.5(2) + 3( 2 ) + 3.5( 1) + 4( 1) =3 3
⇒ 33 / 15
population Mean = 2.2
To find the Mean Absolute Deviation:
0.5 - 2.2 = - 1.7
1 - 2.2 = -1 .2
1.5 - 2.2 = - 0.7
2 - 2.2 = - 0.2
2.5 - 2.2 =0.3
3 - 2.2 = 0.8
3.5 - 2.2 = 1.3
4 - 2.2 = 1.8
The absolute deviations from the sample mean are
1.7 , 1.2, 0.7, 0.2 , 0.3, 0.8 , 1.3,1.8
Thus
(1.7 + 1.2 + 0.7 + 0.2+0.3 + 0.8 + 1.3 +1.8) / 8 = 8/8 = 1
Therefore, the M.A. D is 1 hours per nigh
For average distance each data value is from the mean...
|(-1.7)| + |( -1.2) | + | ( -0.7)| + |( -0.2 | + | 0.3| + | 0.8| + | 1.3 | + | 1.8 | = 8
8/ 8 = 1
So average distance of each data value form the mean is 1 hours per night.
We discovered that the M.A. D in this scenario is 1hr/ night. We may claim that the distribution has low variability because this number is quite tiny.
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62 √ 632154
- with solution
Answers
The square root of 632154 is approximately 795.1 (rounded to one decimal place).
Multiplying 62 by 795.1 gives us:
62 x 795.1 = 49277.4
Therefore, the solution to the expression 62 √632154 is approximately 49277.4.
Hurry up please
State the domain and range and tell if the graph is a function yes or no
What’s the domain and range?
Answers
The graph is a function: yes
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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Help me please please please
Answers
Answer:
C you are so welcome I hope it helped you
Two forces act at a point in the plane. the angles between the two forces are given. fidn the magnitude of the resultant force
Answers
The resultant between the two vectors is 21.17 lb
What is parallelogram law of vectors?Parallelogram law of vectors says that if two vectors acts on a point, the resultant of this vectors can be represented by the diagonal from the point of intersection.
R² = x²+y2+2xycos (tetha)
where x and y are the vectors
When x = 20.6 and y = 17.4
R² = 20.6²+17.4²+2(20.6)(17.4)cos 112.9
R² = 727.12+716.88cos 112.9
R² = 727.12 -278.95
R² = 448.17
R = √448.17
R = 21.17 lb
Therefore the resultant is 21.17lb
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Peter has won the lottery. He will receive Kenya Shillings 87325 per month for the next 21 years, a total of Kenya Shillings 22.01
million.
What single deposit (in millions) should the lottery commission make now to fund Peter's annuity. Assume 10.7%
annual interest, compounded monthly
Answers
The requried lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.
To calculate the present value of Peter's annuity,
[tex]PV = PMT * (1 - (1 + r)^{-n}) / r[/tex]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
In this case, PMT = 87325, r = 0.107/12 = 0.008917, and n = 21*12 = 252.
Substitute the value in the formula given above:
[tex]PV = 87325 * (1 - (1 + 0.008917)^{-252} / 0.008917[/tex]
PV = 8747531.78
Thus, the lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.
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What is the volume of the shape below
Answers
The volume of the given figure is 1176 cubic cm.
The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).
The volume of the figure is calculated as,
Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )
Volume = 1176 Cubic cm
Hence, the volume of the figure will be equal to 1176 Cubic cm.
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Draw a net to represent the following 3d shape.
Don't forget your lebel where the 6cm and 4cm are on the net.
Answers
Answer: Discover how a 3D solid shape can be made up from a 2D net. Understand how nets are formed with examples of common 3D polygons and prisms.
Step-by-step explanation:
Pls tell me just the answer
Answers
The domain of the function g(x) is given as follows:
B. All values of x such that x ≥ 0.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
The function for this problem is defined as follows:
[tex]g(x) = \sqrt{8x}[/tex]
The square root function assumes values that are greater than or equals to zero, hence the domain of the function is obtained as follows:
8x ≥ 0.
x ≥ 0.
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Selena took a pizza out of the oven, and it started to cool to room temperature (68°F). She will serve the pizza when it reaches 130°F. She took the pizza out at 5:00 P.M. Use regression to find when she can serve it.
Answers
Selena can serve the pizza at around 6:40 P.M.
How to explain the regressionThe regression line should have the equation y = -1.7x + 300, where y is the temperature, x is the time in minutes since the pizza was taken out of the oven, -1.7 is the slope of the line, and 300 is the y-intercept.
Set y (the temperature) to 130°F, and solve for x (the time).
130 = -1.7x + 300
-170 = -1.7x
x ≈ 100
According to the regression model, the pizza will reach 130°F after about 100 minutes after it was taken out of the oven. Therefore, Selena can serve the pizza at around:
= 5 + 1:40
= 6:40 P.M.
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Linear or exponential interest
Answers
The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]
The fox population in 2008 is 9722.
What is the fox population in 2008?The equation that would represent the population of the foxes is an exponential equation.
The form of the exponential equation would be
Future population = present population x [tex](1 + r)^{t}[/tex]
Where:
r = interest rate = 6%t = number of years after 2000P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]
P(t) = 6100 x [tex]1.06^{t}[/tex]
Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722
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Which of the following scatterplots shows a correlation affected by an influential point?
Answers
Answer:
The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.
Step-by-step explanation:
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