Alex had $444.231 in the beginning.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let, x = the money Tierra had in the beginning
y = the money Nico had in the beginning
z = the money Alex had in the beginning
Tierra, Nico and Alex had $865 altogether
x + y + z = 865
Tierra spent 2/5 of her money and now she has: x - (2/5)x = 3x/5 left
Nico spent $40 and now has y - 40 left
Alex spent twice as much as Tierra and now has z - 2(2/5)x = z - 4x/5 left
the three friends had the same amount of money left
3x/5 = y - 40
y - 40 = z - 4x/5
by solving the system of equations
x + y + x = 865
3x/5 = y - 40
y - 40 = z - 4x/5
we find
x= $317.308
y = $230.385
z = $444.231
Alex had $444.231 in the beginning.
Hence, Alex had $444.231 in the beginning.
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Tommy starts walking from school to home at the same time that his Dad starts walking from home to school. They both depart at 3:00 p.m. Tommy is walking at a speed of 1.35 meters per second, and his Dad is walking at a speed of 1.65 meters per second. The distance between home and school is 720 meters. At what time will they meet?
Answer:
They will meet at 3:04 p.m
Step-by-step explanation:
Since they are walking towards each other , that means we should add their speed together:
speed = 1.35 m/s + 1.65 m/s
= 3 m/s
Now that we have found the speed, we can calculate the time:
time = 720 meters / 3 m/s
= 240 seconds
= 4 minutes ( 240 seconds is 4 minutes)
Which of the following is not in the domain of tan(x)? Select all correct answers.
The Domain and Range of tan(x) are mathematically given as
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
What is The Domain and Range of tan(x)?All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "[tex]\pi/2+\pi n[/tex]" for all integers n, which is the case when cos(x) = 0.
It follows that "[tex]\frac{-3 \pi }{2}[/tex]" is not in the domain of "tan (x)" among the possible values.
In conclusion,
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
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The plane 15x − 12y + 20z = 60 is represented by which graph below? Notice the z-axis.
Answer:
b
Step-by-step explanation:
I did it
what is the answer of:
[tex]2 \div 3 + \sqrt{5} [/tex]
Answer:
[tex]\frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]
Step-by-step explanation:
[tex] \frac{2}{3} + \sqrt{5} = [/tex]
[tex] = \frac{2}{3} + ( \sqrt{5} \times \frac{3}{3} )[/tex]
[tex]= \frac{2}{3} + \frac{3 \sqrt{5} }{3} [/tex]
[tex]= \frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]
How is the graph of g(x) = (x - 6)³ related to the
graph of f(x) = x³? (0.5 point)
A. The graph of g(x) is a translation of the
graph of f(x) down 6 units.
B.
The graph of g(x) is a translation of the
graph of f(x) right 6 units.
C.
The graph of g(x) is a translation of the
graph of f(x) left 6 units.
Answer:
B. )The graph of g(x) is a translation of the graph of f(x) right 6 units.
Step-by-step explanation:
When a positive number is directly added to an "x" variable (usually inside of parentheses), the graph is shifted to the left that many units.
When a negative number is directly added to an "x" variable, the graph is shifted to the right that many units.
A graph shifts up or down when a positive or negative number is added to the overall function. For example, if the -6 were outside of the parentheses, the graph would be translated 6 units downwards.
The graph of the function f(x)=log7(x) is stretched vertically by a factor of 4, shifted to the left by 5 units, and shifted down by 3 units.
The resulting function after all transformations have been carried out is; 4log7(x+5) + 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 4; Hence, we have; 4f(x) = 4log7(x).
Shifted to the left by 5 units; 4f(x) = 4log7(x +5).
Shifted down by 2 units; 4f(x) +2 = 4log7(x+5) + 2.
On this note, it follows that the resulting function upon all the Transformations is; = 4log7(x+5) + 2.
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6 in.
10 in.
15 in.
V = [?] in.³
area of base
Volume of Prism B.h
Answer:
300
Step-by-step explanation:
A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula:
Volume= 1/3 × Base area × Height
Question 6 of 10
What is the approximate value of x in the diagram below? (Hint: You will need
to use one of the trigonometric ratios given in the table.)
23
54°
90°
OA. 18.61
OB. 39.12
C. 31.64
36°
sin 36
cos 36
tan 36
0.588
≈ 0.809
0.727
Answer:
C. 31.64
Step-by-step explanation:
23 = sin(36) × Hypotenuse
Hypotenuse is the baseline between the angles 36° and 54°.
Hypotenuse = 23/sin(36)
x = cos(36) × Hypotenuse
x = cos(36) × 23/sin(36) = cos(36)/sin(36) × 23 =
= 1/tan(36) × 23 = 23/tan(36) = 31.63686382... ≈
≈ 31.64
The approximate value of x in the diagram is,
⇒ x = 31.5
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now, We can formulate;
⇒ tan 36° = 23 / x
⇒ 0.73 = 23/x
⇒ x = 23 / 0.73
⇒ x = 31.5
Thus, The approximate value of x in the diagram is,
⇒ x = 31.5
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AM and AN are tangent to circle C. If AM measures 2.5 cm, what is the measure of AN?
M
2.0 cm
O 5.0 cm
O 1.5 cm
2.5 cm
C
A
N
The measure of AN form the given figure is 2. 5cm. Option D
How to determine the length
It is important to note that if from one external point, two tangents are drawn to a circle then they have equal tangent segments.
We have that,
AM ≅ AN
so, if AM measures 2. 5cm
AN measures 2. 5cm
Thus, the measure of AN form the given figure is 2. 5cm. Option D
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can someone pls help find x and y
Answer:
x = 9 & y = 29
Step-by-step explanation:
Since we know that 7x is next to 117, that area will be equal to 180*,
7x + 117 = 180
7x = 180-117
7x=63
x=9
to find y, you can use the same method, just by finding the other angle inside. 53+7(9) + z = 180
53+63 = 180
116+z = 180
z = 180-116
z = 64.
Then we do
4y + 64 = 180
4y = 180-64
4y=116
y = 29
Compare and Contrast a square and an equilateral triangle? Be sure to communicate and discuss using mathematical language, ideas and concepts from this module.
The comparison and contrast between a square and an equilateral triangle are stated and explained below:
What is a square? A square is a plane shape with an equal length of sides. This implies that the measure of its length is the same as that of its breadth.
What is an equilateral triangle? A triangle is a plane shape with three sides, and a sum of its internal angles to equal [tex]180^{o}[/tex]. Thus an equilateral triangle is a type of triangle with equal lengths of sides, and therefore equal internal angles.
Comparison: i. The two shapes have equal lengths of sides.
ii. An equilateral triangle and a square are examples of plane shapes.
Contrast: i. An equilateral triangle has three sides, while a square has four sides.
ii. An equilateral triangle has three internal angles, while a square has four internal angles which are right angles.
iii. The sum of internal angles of an equilateral triangle is [tex]180^{o}[/tex], while that of a square is [tex]360^{o}[/tex].
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Kindly get 1-on-1 help from an expert tutor for more explanations if required.
Answer:
A square has degrees that add up to 360 but an equilateral triangle only adds up to 180
Step-by-step explanation:
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
3. Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.
Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
The key features of the function g(x) = (x + 3)(x + 2)(x − 3) are; Maximum Point at g(x) = 6.065; Minimum Point at g(x) = -0.879; 2.593 is the point of inflection
How to identify the features of a Polynomial?1) The Fundamental Theorem of Algebra states that a polynomial of degree "n" has at most "n" number of complex roots.
Since Kelsey argues the function can have as many as three zeros only, then we can say that Kelsey is correct.
2) The g(x) function that I will choose is;
g(x) = (x + 3)(x + 2)(x − 3)
Expanding this gives us;
g(x) = x³ - x² - 4x + 4
To find the key features which are critical points (maximum, minimum, point of Inflection), we will differentiate g(x) with respect to x to get;
g'(x) = 3x² - 2x - 4 = 0
Using quadratic formula gives;
x = 1.535 and Minimum Point; x = -0.869
Thus;
g(1.535) = -0.879 minimum point
g(-0.869) = 6.065 maximum point
Thus;
Maximum Point occurs at g(x) = 6.065
Minimum Point occurs at g(x) = -0.879
g"(x) = 6x -2
At g"(x) = 0, we will have the point of inflection which is at;
x = 1/3
g(1/3) = 2.593 which is the point of inflection
3) The graph of the Polynomial of the function g(x) = (x + 3)(x + 2)(x − 3) is as attached.
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QUESTION IS DOWN BELOW!
Answer:
The ratio of the widths is 3:16, the ratio of the volumes is 27:4096, and the ratio of the surface areas is 9:256.
Step-by-step explanation:
In Geometry, you'll learn that when the scale factor of similar figures is a:b, then the ratio of the perimeter is a:b, the ratio of the area is a*a:b*b and the ratio of volume is a*a*a:b*b*b.
Estimate the following quantities without using a calculator. Then find a more precise result, using a calculator if necessary. Discuss whether the approximation technique worked.
The approximate value of 63000 x 200 will be 12600000.
What is multiplication?
In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.
Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.
E = 63000 x 200
E = 12600000
Therefore the approximate value of 63000 x 200 will be 12600000.
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The voyage of the Mayflower took 8 months and 11 days. Convert the time to days.
Answer:
If i did it correctly the answer should be 255 days
Step-by-step explanation:
please mark brainliest
giving brainliest!!!!!!
Answer:
10.4
Step-by-step explanation:
So an exponential equation with a decay can be expressed as: [tex]f(x)=a(1-r)^t[/tex] where r is the decay rate. In this case is decreasing at 4% each year, this means that the r is equal to 0.04 (divide the percent by 100 to convert to decimal). So the equation is going to be: [tex]f(x)=a(0.96)^t[/tex]. The reason this works is because whenever you decrease by x%, the new value is (1-x)%, which is expressed in the formula. But the reason the exponent is there is because after 1 year it's going to be 0.96a, but after two years, it's going to be 0.96 the previous year which is 0.96a, so after two years it's going to be 0.96(0.96a), and then the next year it's 0.96 of the second year, which is then 0.96(0.96(0.96a))... and so on. So the amount of 0.96 increases as t increases. the a is going to be the initial amount, since then t=0, 0.96^0 will be equal to 1, which makes the expression a(1), which is just a. So this gives you the complete equation: [tex]p(x)=13000(0.96)^t[/tex]
Now to find when it's equal to 8,500 you need to start by setting it equal to 8,500 so I'll work through each step
Original Equation:
[tex]p(x)=13000(0.96)^t[/tex]
Set the equation equal to 8,500
[tex]8500=13000(0.96)^t[/tex]
Divide both sides by 13,000
[tex]0.653846\approx 0.96^t[/tex]
Rewrite in logarithmic form
[tex]log_{0.96}0.653846=t[/tex]
If you're calculator allows you to enter the base when calculating log, but this expression into your calculator to calculate the value of t, otherwise use the change of base formula
[tex]\text{change of base formula: }log_ba = \frac{log(a)}{log(b)}[/tex]
[tex]t=\frac{log0.653846}{log0.96}\\[/tex]
[tex]t\approx\frac{-0.1845}{-0.0177}[/tex]
[tex]t\approx10.4[/tex]
Joy is going to a sub shop for a sandwich. At the restaurant, she can choose either a roll (R), bread (B), or a wrap (W). There are two meat choices, ham (H) and turkey (T), and 2 kinds of cheese, Swiss (S) and American (A). Before she goes, Joy wants to make a list of her choices. If she chooses one item from each selection, which will be part of her list?
Answer:
so their are three kinds of breed 2 kinds of meet and 2 kinds of cheese here the list
roll, ham,swiss
roll, turkey,american
roll,ham,american
roll, turkey,swiss
bread, ham,swiss
bread, turkey,american
bread,ham,american
bread, turkey,swiss
wrap, ham,swiss
wrap, turkey,american
wrap,ham,american
wrap, turkey,swiss
Hope This Helps!!!
Suppose the theoretical probability of winning a prize at a carnival game is 0.18. Based on this probability how many more customers would you have expected to win a prize
Answer:
Could you please provide more context to the problem
Step-by-step explanation:
There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.
Sarah will ship packages for anyone. She charges $6 for her services and then $2.75 per item. How much would she charge to ship 8 items
Solve for the missing item in the following. (Do not round intermediate calculations. Round your answer to the nearest whole percent.)
Principal 5000 time 6 months simple interest $300
Rate?
Answer:
The answer is $0.36
Step-by-step explanation:
y = -2 f(3(x - 4)) - 1 Describe this transformation
The graph y = x^3 is compressed vertically by a factor of 1⁄2 , translated 4 units to the right, and translated 5 units upward.
Write the equation of the transformed function.
The equation of the transformed function is y = 1/2(x - 4)^3 + 5
How to describe the transformation?The parent function is given as:
y = x^3
When the function is vertically compressed by 1/2, the rule is:
(x, y) ⇒ (x, 1/2y)
So, we have
y = 1/2x^3
When translated 4 units right, we have:
y = 1/2(x - 4)^3
When translated 5 units up, we have:
y = 1/2(x - 4)^3 + 5
Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5
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Ralph chase plan to sell a piece of property for $160,000. He wants the money to be paid off in two ways- a short term note at 10% interest and a long term note at 7% interest. Find the amount of each note if the total annual interest paid is $13750.
$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of fund at 10% and y represent the amount of fund at 7% interest, hence:
x + y = 160000 (1)
Also:
0.1x + 0.07y = 13750 (2)
From both equations:
x = 85000 and y = 75000
$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.
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giving brainliest :)
Answer:
The last one - 256 people
Whats the correct answer answer asap
A line passes through the point (-2, 8) and has a slope of-5/2.
Write an equation in slope-intercept form for this line.
Answer:
[tex]y = -\frac{5}{2} x + 3[/tex]
Step-by-step explanation:
We are given that a line passes through (-2, 8) and has a slope of -5/2.
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of this line, we can immediately plug it into the equation.
Replace m with -5/2.
[tex]y = -\frac{5}{2} x+ b[/tex]
Now we need to find b.
As the equation passes through the point (-2, 8), we can use its values to help solve for b.
Substitute -2 as x and 8 as y.
[tex]8 = -\frac{5}{2} (-2) +b[/tex]
Multiply.
8 = 5 + b
Subtract 5 from both sides.
3 = b
Replace b with 3 in the equation.
[tex]y = -\frac{5}{2} x + 3[/tex]
Topic: finding the equation of the line (slope-intercept form)
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set x is made up of the possible ways five students, represented by a, B, C, D, and E, can be formed into groups of three. Says y is made up of the possible ways five students can be formed into groups of three if student a must be in all possible groups. which statements about the situation are true
The true statement about the set include:
Set X has 10 possible groupings. X Y Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} There are three ways to form a group if persons A and C must be in it.How to illustrate the information?If set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three, then the set X consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE}.
The set X totally contains 10 elements.
There are three ways to form a group if persons A and C must be in it. This statement is true and these groups are ABC, ACD, ACE.
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Simplify the following expression, and combine like terms: 15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x
Answer:
15x^2y+20xy^2+28xy-9x
Step-by-step explanation:
15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x
First distribute the -4 to all the terms in the parentheses
15x²y +8xy² + 36xy + 12xy² - 8xy - 9x
Now combine like terms
15x²y +8xy² + 12xy² + 36xy - 8xy - 9x
15x^2y+20xy^2+28xy-9x
For the function f(x) = -(x+6)(x+2), when is the function decreasing and when is it increasing?
Answer:
• The function f is increasing to the left of -4 (-∞ , -4]
• The function f is decreasing to the right of -4 [-4 , +∞)
Step-by-step explanation:
f(x) = -(x+6)(x+2)
= -(x² + 2x + 6x + 12)
= -(x² + 8x + 12)
= -x² - 8x - 12
The leading coefficient is -1 (the coefficient of the highest term -x² of the trinomial)
Then
The parabola opens downward.
………………………………………
[tex]-\frac{b}{2a} =-\frac{-8}{2\times \left( -1\right) } =-4[/tex]
Then
The function f is increasing to the left of -4 (-∞ , -4]
The function f is decreasing to the right of -4 [-4 , +∞)
1
Which expression is equivalent to [log9+ logx+log(x²+4)]-log6?
og 3√x (x² + 4)
2
O log-
3√√x (3x+4)
2
O log-
√9x(x³+4)
6
O log-
log9x(x³+4)
6
The equivalent expression to the given logarithm without tables is [tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]. Option A is correct.
What are equivalent expressions?Equivalent expressions are expressions that differ in appearance but when a value is being replaced for their unknown variable, gives an equivalent result.
From the given information:
[tex]\mathbf{(log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) )-log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) -log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9x)+ log_{10}(x^2+4) -log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) }[/tex]
Apply log rule: [tex]\mathbf{log_a(x)-log_a(y) =log_a(\dfrac{x}{y})}[/tex]
[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]
[tex]\mathbf{ =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]
[tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]
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Let v = leftanglebracket 3, negative 2 rightanglebracket. what is the approximate direction angle of v?
The approximate direction angle of v is 326°
Definition of Direction Angle
A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.
What is the direction angle of v?
Let θ be the direction angle of v or the angle mad by v with the horizontal line.
It is given that,
[tex]v = < 3, -2 >[/tex]
We know that,
θ = tan⁻¹([tex]\frac{y}{x}[/tex])
Here, we have y = -2 and x = 3. Hence, we get,
∴ θ = tan⁻¹[tex](\frac{-2}{3})[/tex]
⇒θ = tan⁻¹(0.66)
Hence the direction angle of v = 360 - tan⁻¹(0.66)
≈ 326°
Thus, the approximate direction angle of v is 326°.
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