Answer:
6x - 9
Step-by-step explanation:
18x -11 - (12x - 2) Can be written
18x -11 -1(12x -2) Distribute the -1
18x - 11 -1(12x) + (-1)(-2)
18x - 11 -12x +2 Combine like terms
6x -9
Ummm can y’all solve these problems I’ll give extra points for this
Pls solve step by step and label which is which
Find the surface area of the composite figure.
5 cm
10 cm
4 cm
5 cm
SA =
10 cm
-8 cm
4 cm
12 cm
[?] cm²
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Answer:
Step-by-step explanation:
5*10*2=100
8*10/2=40
12*4*2=96
12*5=60
4*5*2=40
100+40+40+96+60=336cm²
The surface area for the given composite figure is 442 cm²
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given is a composite figure, composed of a triangular prism and rectangular prism, attached to each other.
We will find the surface area of the composite figure by adding surface areas of both the solids and subtracting the common base area from it.
We know that, surface area of a triangular prism and rectangular prism, are S = bh+(b1+b2+b3)l and 2(lh+wh+lw) respectively.
Therefore, SA = 12(8)+(12+10+8)5 +2(12×5+4×5+12×4) - lw
= 96+150+2(60+20+48) - 12×5
= 246+256-60
= 442
Hence, The surface area for the given composite figure is 442 cm²
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ASAP GUYS PLEASE I NEED UR HELP THIS IS SO HARD
Solve: 5 − 7 ( z + 1 ) = 7 ( − 9 − 3 z )
Answer:
[tex]-\frac{61}{14}[/tex]
Step-by-step explanation:
Question: 5 - 7(z+1) = 7(-9-3z)
We multiply the number in front of the bracket first, since that is multiplication.
--> 5 -7z -7 = -63 - 21z
--> -7z -2 = -63 - 21z
Now, we move all the z and all the numbers to each side.
--> -7z +21z = -63 +2
--> 14z = -61
--> z = -61/14
This cannot be simplified further, so z is -61/14.
volume of a cone = r²h,
where r is the radius and h is the height.
A frustum is formed by removing a small cone from a similar, larger cone, as
shown below.
a) Calculate the radius of the original large cone.
b) Calculate the volume of the frustum to the nearest integer.
50 m height
10 m height of frustum
6m radius of frustum
Answer:
7.5 m 457.5[tex]\pi[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.
The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = [tex]\frac{1}{3} \pi r^{2}h[/tex].
Original Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *7.5^{2}*50[/tex] = 937.5[tex]\pi[/tex]
Smaller Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *6^{2}*40[/tex] = 480[tex]\pi[/tex]
Frustum = 937.5[tex]\pi[/tex] - 480[tex]\pi[/tex] = 457.5[tex]\pi[/tex]
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
Answer:
Step-by-step explanation:
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
Solve the equation 3x^2-2x-10=0
Show all your working and give your answers correct to 2 decimal place
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -2
C = -10
B2 - 4AC =
4 - (-120) =
= 124
Applying the quadratic formula :
2 ± √ 124
x = —————
6
√ 124 simplified
The prime factorization of 124 is
2•2•31
To be able to remove something from under the radical, there have to be 2 instances of it
√ 124 = √ 2•2•31 =
± 2 • √ 31
√ 31, rounded to 4 decimal digits, is 5.5678
So now we are looking at:
x = ( 2 ± 2 • 5.568 ) / 6
Two real solutions:
x =(2+√124)/6=(1+√ 31 )/3= 2.189
or:
x =(2-√124)/6=(1-√ 31 )/3= -1.523
Answer:
Step-by-step explanation:
3x^2-2x-10=0
This is a quadratic equation that can be solved using the quadratic formula where
a = 3, b = -2, and c = -10
x=−b±(b^2−4ac)^(1/2)/2a
x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))
x=2±(124)^(1/2)/6
Simplify the Radical:
x=((2/6) ±2(31)^(1/2))/6
x=26±231−−√6
Simplify fractions and/or signs:
x=1/3±√31/3
which becomes
x=2.18925
See the attached image for a more clear display of solving using the quadratic equation.
x=−1.52259
A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?
6.546
6.643
6.123
6.142
Answer:
Below in bold.
Step-by-step explanation:
P = 1.50(1.065)^t where P = population in millions and t = no. of years.
So we have
2.31 = 1.50(1.065)^t
(1.065)^t = 2.31/1.50
Taking logs:
t log 1.065 = log (2.31/1/50)
t = log (2.31/1/50) / log 1.065
= 6.856 years.
In the context of data models, relationships among records in a hierarchical model are called _____.
In the context of data models, relationships among records in a hierarchical model are called Branches. This is further explained below.
What are data models,?Generally, The act of generating a visual representation of either a whole information system or portions of it in order to express the linkages between different data points and structures is known as data modeling.
In conclusion, When discussing data models, the connections between different records in a hierarchical structure are referred to as "Branches."
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ucscout word problem define the variables. (see screenshot) please help
Integrated math 3
The exponential equation for the number of Bacterian Camels in Mongolia is:
[tex]P(t) = 600(0.982)^t[/tex]
The parameters can be described as follows:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.What is an exponential function?A decaying exponential function is modeled by:
[tex]P(t) = A(1 - r)^t[/tex]
In which:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.For this problem, the values of the parameters are given as follows:
A = 600, r = 0.018.
Then the equation is:
[tex]P(t) = A(1 - r)^t[/tex]
[tex]P(t) = 600(0.982)^t[/tex]
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PLEASE HELP 50 POINTS
I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS
*TIP: you can delete the answer the second person gave you to be able to recive more answers :)
Mr.jake and me. sebastian are business partners. they divided the ratio of 3:2 the profit is 24,000. how much did mr.jake receive ?
Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.
So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.
Thus, the total profit between them is 3x + 2x = 5x.
The total profit given is 24,000.
Thus, we get an equation:
5x = 24000,
or, x = 24000/5 = 4800.
Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.
Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
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[tex]\mathbb Question[/tex]
Attached above!!
Answer:
see explanation
Step-by-step explanation:
(a)
play ends at 9 : 55 pm
15 minutes to get to bus stop , then time is
9 : 55 + 15 min = 10 : 10 pm = 22 : 10
the earliest bus she can catch is 22 : 25
(b)
time to wait 22 : 10 → 22 : 25 = 15 minutes
What's the slope and y-intercept?
Answer:
Slope: 2; Y-Intercept: (0,3)
Step-by-step explanation:
As you can see from the graph, it rises 4 and runs 2. So, the slope is 2. It intersects the y axis at (0,3)
Answer:
Slope: 3/2
Y-intercept: 3
Step-by-step explanation:
The line passes the y-axis at 3, and to find the slope you use rise over run. Our rise (which is going up) is 3, and our run (which is going across) is 2 (and since it moves from left to right, it is positive). The slope would be 3/2.
I hope it helps! Have a great day!
bren~
The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Using a system of equations, it is found that 10,000 children attended the park that day.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable c: Number of children in the park.Variable a: Number of adults in the park.The attendance at the amusement park is 30,000 attendees, hence:
c + a = 30,000, which is the first equation in matrix form.
Then:
a = 30,000 - c
The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:
10c + 20a = 500,000, which is the second equation in matrix form.
Since a = 30,000 - c, we replace:
10c + 20a = 500,000
10c + 20(30000 - c) = 500,000
10c = 100,000
c = 10,000.
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what is the maximum number of relative extrema contained in the graph of this function ? F(x) = 3x^4 - x^2 + 4x - 2
The maximum number of relative extrema of the given polynomial is; 3
How to find the maxima of a Polynomial Function?When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;
Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.
We are given the Polynomial as;
f(x) = 3x⁴ - x² + 4x - 2
Now, the degree of the Polynomial would be 4. Thus;
Maximum number of relative extrema = 4 - 1
Maximum number of relative extrema = 3
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Finding a sunken submarine in the middle of the ocean using Bayes' theorem: the search for the Scorpion.
Finding a sunken submarine in the middle of the ocean using Bayes' theorem to the search for USS Scorpion.
In the event of a missing vessel or aircraft at sea, in this case a submarine, Bayes search theorem can be applied.
The ocean using Bayes' theorem: the search for the Scorpion.
In May 1968, the U.S. Navy's nuclear submarine USS Scorpion (SSN-589) failed to arrive as expected at her home port of Norfolk. The command officers of the U.S. Navy were nearly certain that the vessel had been lost off the Eastern Seaboard, but an extensive search there failed to discover the remains of Scorpion.Then John P. Craven, a Navy deep-water expert, proposed that Scorpion had sunk somewhere else. Based on a contentious approximation of hydrophone triangulation, Craven organized a search southwest of the Azores. He was only given one ship, Mizar, and to make the most of his resources, he sought help from a team of consulting mathematicians. A Bayesian search approach was used. To develop theories regarding what might have led to Scorpion's loss, veteran submarine commanders were questioned.What is Bayes' theorem?
Bayes' theorem is a theorem in probability theory. It is a trivial consequence of the definition of conditional probability.Bayesian search theory is the application of Bayesian statistics to the search for lost objects.Learn more about Bayes' theorem
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The segments shown below could form a triangle.
A
5
с
B
8
B
6
Based on the triangle inequality theorem, the statement that the given segments will form a triangle is TRUE.
What is the Triangle Inequality Theorem?If a, b, and c are lengths of a triangle, then,
a + b > c
a + c > b
b + c > a
Given the segments:
AC = 6
CB = 5
BA = 8
6 + 5 > 8 [true]
6 + 8 > 5 [true]
5 + 8 > 6 [true]
Therefore, it is true that the segments given could form a triangle.
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Escribe una ecuación de la recta que pasa por el punto (5, –8) con pendiente 5.
Considerando la expresión de una ecuación lineal, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.
Ecuación linealUna ecuación lineal o línea se puede expresar en la forma y = mx + b
donde
x y son coordenadas de un punto.m es la pendiente.b es la ordenada al origen y representa la coordenada del punto donde la línea cruza el eje y.La ecuación lineal se puede expresar también mediante la ecuación punto-pendiente de la recta, que se plantea si se conoce la pendiente de la recta y cualquiera de sus puntos. Con ello queda determinada la recta, conociendo la pendiente “m” y un punto (x1, y1) dado:
y - y1= m(x -x1)
Ecuación de la recta en este casoEn este caso, la recta que pasa por el punto (5, –8) con pendiente 5.
Reemplazando en la ecuación punto-pendiente de la recta:
y - (-8)= 5(x -5)
Resolviendo:
y + 8= 5(x -5)
Aplicando propiedad distributiva:
y + 8= 5x - 5×5
y + 8= 5x - 25
Aislando la variable "y":
y= 5x - 25 - 8
y= 5x - 33
Finalmente, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.
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You can approximate e by substituting large values for ninto the expression
You can approximate e by substituting large values for (1 + 1/n)^n into the expression.
How to illustrate the expression?It should be noted that an expression can simply be used to illustrate the information given in a data.
In this case, you can approximate e by substituting large values for (1 + 1/n)^n into the expression.
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She spent 18.62 in grosherys she has 43.55 left how much did she have before she bought grashery
Answer:
Step-by-step explanation:
43.55 + 18.62 = 62.17
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(0) = g(0) and f(2) = g(2)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer:
first option
Step-by-step explanation:
Always remember to graph a diagram :)
What makes this graph misleading?
Different bar widths
The bars should be horizontal
Inconsistent scale on the y-axis - Correct
Y-axis didn't start at zero
The reason the graph given is misleading is that there is an Inconsistent scale on the y-axis.
Why is the graph misleading?The y-axis is inconsistent because it went from 0 to 200 and instead of continuing to increase by 200, it begins to increase by 10.
This is misleading because the scale used has to be uniform or else it would be hard to read the data.
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Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been translated to produce figure 2.
Graph shows 2 quadrilaterals plotted on coordinate plane. Quadrilateral 1 in quadrant 2 has vertices at (minus 6, 3), (minus 5.5, 5), (minus 3.5, 5), (minus 3, 3). Quadrilateral 2 in quadrant 1 has vertices at (2, 1), (2.5, 3), (4.5, 3), (5, 1).
This translation can be described by
,
).
Answer:
A translation 8 units right and 2 units down
write an equation of a line perpendicular to y = 7 and passes through the point (3, -1).
Answer: x = 3
Step-by-step explanation:
The equation of the line perpendicular to a horizontal line is a vertical line, which has an equation of the form x=c.
For the function F defined by F(x)=x2−2x+4, find F(|−4|)
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
How to evaluate a quadratic equation with an absolute value
Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:
|x| = x, when x ≥ 0 or - x, when x < 0. (1)
Then, we apply (1) on the quadratic equation:
F(|x|) = |x|² - 2 · |x| + 4
As x < 0, by absolute value properties:
F(|x|) = x² + 2 · x + 4
F(|- 4|) = (- 4)² + 2 · (- 4) + 4
F(|- 4|) = 16 - 8 + 4
F(|- 4|) = 12
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
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The ________________ manages water resources in a 16-county region that stretches from Orlando to the Florida Keys, serving a population of 8.1 million (hint: Remember the water conservation calculator
South Florida Water Management
The South Florida Water Management District is a regional governmental agency that manages the water resources in the southern half of the state, covering 16 counties from Orlando to the Florida Keys and serving a population of 9 million residents.
Water management is the control and movement of water resources to minimize damage to life and property and to maximize efficient beneficial use. Good water management of dams and levees reduces the risk of harm due to flooding.
Water management is the activity of planning, developing, distributing and optimum use of water resources under defined water polices and regulations.
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the angle 01 is located in quadrant iii, and cos(01) = -13/15. what is the value of sin (01)?
The value of sin(∝) is -√56/15
How to evaluate the sine angle?The given parameter is:
cos(∝) = -13/15
To determine the sine, we use the following identity
sin^2(∝) = 1 - cos^2(∝)
So, we have:
sin^2(∝) = 1 - (-13/15)^2
This gives
sin^2(∝) = 1 - 169/225
Evaluate the difference
sin^2(∝) = 56/225
Take the square root of both sides
sin(∝) = ±√56/15
sin(∝) is negative in quadrant III.
So, we have:
sin(∝) = -√56/15
Hence, the value of sin(∝) is -√56/15
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Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The slope in question seven is 1. Below are the solutions to the remaining questions
In what means can Transformation occur ?Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.
Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise
2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.
3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2
4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.
5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0
6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.
7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be
Slope = Δy ÷ Δx
Slope = (5 - 4) ÷ (-10 + 11)
Slope = 1 ÷ 1
Slope = 1
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what is the distance between the points (23,-33) and (4,9) if necessary round your answer to two decimal places
The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
What is the distance between the points (23,-33) and (4,9)?The distance between two points on a graph can be determined using the equation;
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
Given that;
x₁ = 23x₂ = 4y₁ = -33y₂ = 9We substitute our values into the equation above.
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]
D = √[ ( -19 )² + ( 42 )² ]
D = √[ 361 + 1764 ]
D = √[ 2125 ]
D = 46.10
Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
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A certificate of deposit offers a nominal interest rate of 5.5 percent annually.If inflation is 2.5 percent, what is the real rate of return?
The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The real rate of return exists at 2.926%.
How to estimate the real rate of return?The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The formula for the real rate of return:
R = (1+N)/(1+i) - 1
Where, N exists the nominal rate and i exists the inflation rate, as decimals.
A certificate of deposit offers a nominal interest rate of 5.5 percent annually.
This means that N = 0.055
Inflation exists 2.5 percent
i = 0.025
Substitute the values in the above equation, we get
[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]
= [1.055/1.025] - 1
= 1.02926 - 1
= 0.02926
0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%
The real rate of return exists at 2.926%.
Therefore, the correct answer is option D. 3%.
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