Answer:
$10,000 invested at 5%
$20,000 invested at 8%
Step-by-step explanation:
1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.
x + y = 30,000 (the total amount invested)
0.05x + 0.08y = 2,100 (the total interest earned)
2. Solve the system by whatever method you choose.
Find two positive numbers whose difference is 20 and whose product is 429.
Graph the polygon with the given vertices and its image after a reflection in the line y = -x .
A(2, 0), B(3, 4), C(6, 4), D(5, 0)
As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.
Transformation:
Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Given,
Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.
Now we have to plot the graph with the given vertices and its image after a reflection in the line y = -x .
Here reflection refers flipping of a figure.
Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)
For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:
A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)
The image of the polygon is attached below.
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Birdseed costs $0.67 a pound and sunflower seeds cost $0.97 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.79 per pound. How many pounds of each type of seed should she use?
All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Birdseed that costs $0.67 a pound and sunflower seeds that cost $0.97 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.79 per pound.
Assume that she used [x] pound and [y] pound of each type. We can write -
0.67x + 0.97y = 0.79 x 30
0.67x + 0.97y = 23.7
Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
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log x + 5 log y -4 log z rewrite as a single logarithm
Solution :
[tex]\qquad \sf \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]
[tex]\qquad \sf \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]
( a log(x) = log(x^a) )
[tex]\qquad \sf \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]
( log (a) + log (b) = log (ab) )
[tex]\qquad \sf \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]
( log (a) - log (b) = log (a/b) )
why are 0.8 and 0.80 are equivalent?
0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.
The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.
It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.
Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
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Point-slope equation
y-6=3(x - 5)
y- 4 = -9(x+8)
y- 2 = 5x
Slope
-10
2
712
2
Point on
line
(1,4)
(5,-3)
(-7,-7)
The point slope equation and slope of some lines are given below
1) For y - 6 = 3(x - 5), slope = 3
2) For y - 4 = -9(x + 8), slope = -9
3) y - 2 = 5x, slope = 5
4) Point slope equation of line whose slope = -10 and passing through (1, 4)
y - 4 = -10(x - 1)
5) Point slope equation of line whose slope = 2 and passing through (5, -3)
y + 3 = 2(x - 5)
6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through (-7, -7)
[tex]y +7 = \frac{1}{2}(x +7)\\[/tex]
What is equation of line in point slope form?
The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line
Where m is the slope of the line
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
1) y - 6 = 3(x - 5)
y - 6 = 3x - 15
y = 3x - 15 + 6
y = 3x - 9
Slope = 3
If x = 0,
[tex]y = 3 \times 0 -9\\y = -9[/tex]
(0, -9) is a point on the line
2) y - 4 = -9(x + 8)
y - 4 = -9x - 72
y = -9x - 72 + 4
y = -9x - 68
Slope = -9
If x = 0
[tex]y = -9 \times 0 -68\\y = -68[/tex]
(0, -68) is a point on the line
3) y - 2 = 5x
y = 5x + 2
Slope = 5
Putting x = 0
[tex]y = 5 \times 0 + 2\\y = 2[/tex]
(0, 2) is a point on the line
4) Slope = - 10
The line passes through (1, 4)
Point slope equation
y - 4 = -10(x - 1)
5) Slope = 2
The line passes through (5, -3)
Point slope equation
y - (-3) = 2(x - 5)
y + 3 = 2(x - 5)
6) Slope = [tex]\frac{1}{2}[/tex]
The line passes through (5, -3)
Point slope equation
[tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]
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An Olympic-size swimming pool holds approximately 6×105 gallons of water. The capacity of this swimming pool is between which interval?
The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.
What is the capacity?Capacity refers to the product of the length, width, and height of a three-dimensional object or space.
The capacity of an object means the same as its volume.
Olympic-size swimming pools have the following standard dimensions:
Length = 50 m
Width = 25 m
Height = 2 m
Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)
= 660,000 gallons (2,500 x 1,000 ÷ 3.785)
An interval estimate shows the lower and upper limits.
6 x 105 gallons = 630 gallons
Thus, the capacity of the swimming pool is Option B.
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Question Completion with Answer Options:A. 100 gallons to 500 gallons
B. 500 gallons to 1,000 gallons
C. 1,000 gallons to 1,500 gallons
D. 1,500 gallons to 2,000 gallons
Use a graphing utility to approximate the solutions of the equation in the interval [0, 2). Find the exact solutions algebraically. (Enter your answers as a comma-separated list.)
3 tan(2x) − 3 cot(x) = 0
An integral graph with graph spectrum is the utility graph.The utility graph's adjacency, incidence, and graph distance matrices are displayed in the aforementioned graphs.
Find the exact solutions algebraically?These technologies enable users to mathematically represent their ideas, dynamically link several representations, form hypotheses, and finally create totally new concepts.
Use a graphing utility
See attached file
The value of X in the interval [0, 2π) are
X1=0
X2=π/2-----1.5708
X3=π------- 3.1416
Values of X (0,1.5708,3.1416)
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y2−5y=750
750 -y(y-5)=0750−y(y−5)=0 and (y+25)(y-30)=0
I need help! could someone help me with this? is from Imagine Math
Answer:
1st: One solution
2nd: Infinite many solutions
3rd: No solution
4th: No Solution
5th: One Solution
Step-by-step explanation:
1st:
The solution is (6,9)
x = 6 if a vertical line going though (6,0)
y = 9 is a horizontal line going through (0,9)
The two lines with intersect at (6,9)
2nd:
3y = 15x + 6 If you divide all the way through by 3, you get
y = 5x + 2
This is identical to the first equation given. Since it is the same line, the answer is infinite many solutions.
3rd:
3y = x + 2 Divide all the way through by 3
y = 1/3 x + 2/3
9y = 3x + 7 Divide all the way through by 9
y = 1/3 x + 7/9
Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.
4th:
Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.
5th:
2y = 3x Divide both sides by 2
y = 3/2
-5y = -10 Divide both sides by -5
y = 2x
These equations are proportional so they go through the origin. They both have a y intercept of zero, so they intersect at (0,0). The answer is one solution.
I need the answer fast please
(ASAP Please)
Find the area of the sector. Use 3.14 for the value of pi. Round your answer to the nearest tenth.
A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
The total sector of a circle is 360°
The area of the sector of 270° is 37.68 square meters.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
We have,
The radius of the circle = 4 m
The total sector of a circle is 360°
The area of the sector with 270°.
= (270°/360°) x πr²
= 0.75 x πr²
= 0.75 x 3.14 x 4²
= 37.68
= 37.7 square meters
Thus,
The area of the sector of 270° is 37.68 square meters.
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Classify the following number: 5√2. Choose all that apply.
Answer:
Real, Irrational
Step-by-step explanation:
5sqrt2 is NOT:
Natural (1,2,3...)
Whole (0,1,2,3...)
Integer (...-3,-2,-1,0,1,2,3...)
Rational (can be written like a ratio)
Imaginary (have the number i in it.)
It IS Irrational, will have neverending decimal with no repeating pattern.
5sqrt2 = 7.0710678119...
It IS REAL and IRRATIONAL.
A coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) are all dropped from a height of 10 meters. The coin and the hammer take
about the same amount of time to fall. Which statement describes the time it takes for the parachute to fall? (1 point)
O It takes less time to fall because it has the most surface area.
O It takes the same amount of time to fall because the effect of gravity is the same.
O It takes less time to fall because it has the least mass
O It takes longer to fall because it experiences greater air resistance.
Answer:
the last one= It takes longer to fall because it experiences greater air resistance.
also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall
Answer: It takes longer to fall because it experiences greater air resistance.
Parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n, what is true for the transformation that took place?
Line m was translated down 4 units.
Line m was translated up 4 units.
Line n was translated up 8 units.
Line l was translated down 8 units.
Line l was translated down 8 units, is true for the transformation that took place.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,
We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.
Hence, Line l was translated down 8 units, is true for the transformation that took place.
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In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 10 A (amperes), the resistance is 13 ohms. What is the resistance when the current is 26 A?
Answer:
33.8ohms
Step-by-step explanation:
10A : 13ohm
26A : 33.8ohm
5. Describe a relationship between the two variables shown in this graph. Be
sure to include a description that includes the whole pattern of what happens
to the money during the tone shown.
Time please help asap
The relationship between the variables is that an increase in the degree of slope cause an increase in the loss of soil
How to describe the relationship between the variables?The possible graph that completes the question is added as an attachment
From the attached graph, we have the variables represented to be
Degree of slope - on the x-axisLoss of soil - on the y-axisNext, we determine the relationship
To start with:
The relationship between the variables on a graph is simply the end bahavior of the graph
In this case, we can see that:
As the degree of the slope increases, the loss of soil also increase
However, the increase in the slope does not cause a constant increase in the loss of soil
The loss of soi starts by increasing slowly as the degree of slope increases, then the loss of soil increases sharply as the degree increases further
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Which of the following is a good point estimator for the population variance?
A good point estimator for the population variance is: s².
What is a two-tailed test?A two-tailed test can be defined as a type of hypothesis test in which a rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution.
In Statistics, the basis of an inference about the population is usually used to determine statistical inference based on all of the statistics that are calculated from samples.
This ultimately implies that, the sample mean should be close to the population mean, the sample proportion should be close to the population proportion, and the sample standard deviation should be close to the population standard deviation.
In this context, we can logically deduce that standard deviation (s²) is considered as a good point estimator for the population variance.
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Simplify
8(x + 3)^2/2(× + 3)
Answer:
[tex] = \frac{8(x + 3) {}^{2} }{2(x + 3)} = 4(x + 3) = 4x + 12[/tex]
Hopefully this will help u
Please Help
Find (f-g)(x) if f(x)--3x2+2x-3 and(x)=2x2-3x+4
The function operation (f - g)(x) of the functions f(x) = -3x² + 2x - 3 and g(x) = 2x² - 3x + 4 is -5x² + 5x - 7.
What is the function operation (f - g)(x) of the given functions?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = -3x² + 2x - 3g(x) = 2x² - 3x + 4(f - g)(x) = ?To determine the function operation (f - g)(x), replace the function designators with the real functions and simplify.
(f - g)(x) = f(x) - g(x)
(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )
Apply distributive property to eliminate the parenthesis.
(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )
(f - g)(x) = -3x² + 2x - 3 - 2x² + 3x - 4
Collect and add like terms
(f - g)(x) = -3x² - 2x² + 2x + 3x - 3 - 4
(f - g)(x) = -5x² + 5x - 7
Therefore, the function operation (f - g)(x) is -5x² + 5x - 7.
Option A is the correct answer.
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Evaluate (6x+3y)-z2 divided by (2x) when X = -3 , y=4 , z=-6
The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3
How to evaluate an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.
Therefore,
(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32
2x = 2(-3) = -6
Hence,
- 32 / -6 = 5.3
Therefore,
(6x+3y) - z² / 2x when x = -3, y = 4 and z = -6 is 5.3
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David and Vicky share £36 in the ratio 2:7. How much do they each
receive?
David share is £8
Vicky share is £28
From the question, we have
David and Vicky share £36 in the ratio 2:7.
David share = £36 *2/9 = £8
Vicky share = £36 *7/9 = £28
Multiplication:
The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.
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Write the number in 2 equivalent
forms as a fraction, decimal, or
percent.
20
20
What is the equivalent percent?
Step-by-step explanation:
Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.
The equation: -2(x - 5) = 4x is solved in several steps below. For each step, select the reason that best justifies it.
Equations:
2x + 10 = 4x
-2x + 10 + 2x = 4x + 2x
10 = 6x
10/6 = 6x/6
5/3=x
Options:
Simplifying
Subtraction Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Distributive Property
Division Property of Equality
The order of reasons that best justifies each step of the equation's solution is as follows;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).What are the reasons that justify the steps of the solution?It follows from the task content that the reasons which best justify each step of the solution be identified.
Therefore; Given the equation; -2(x - 5) = 4x; we have;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).Ultimately, the reasons which best justifies each of the steps as required are as provided above.
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Answer: Justification for each step is provided below.
Step-by-step explanation:
Original Equation: -2(x - 5) = 4x
-2x + 10 = 4x --> Distributive property - simplify the left side
-2x + 10 + 2x = 4x + 2x --> Addition property of Equality - add 2x to both sides
10 = 6x --> Simplifying
10/6 = 6x/6 --> Division Property of Equality - divide each side by 6
5/3 = x --> Simplifying
The monthly output at the Olek Carpet Mill is
Q(x) = 15,000 + 2x2 units, (40 ≤ x ≤ 60)
where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).
Q'(46) =
The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.
What is the instantaneous rate of change?The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.
In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.
Taking the derivate of the given function, we have:
Q(x) = 15,000 + 2x²
Q'(x) = d/dx(15,000) + d/dx(2x²)
Q'(x) = 0 + 2x(2)
Q'(x) = 4x.
At x = 46, we have:
Q'(x) = 4(46)
Q'(x) = 184.
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Complete Question:
The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).
Q'(46) =
Factor 64+ 60. Write your answer in the form a(b + c) where a is the GCF of 64 and 60
PLEASE SOMEONE HELP ME GIVING BRAINLIEST!!!
Answer:
23/5 > (sqrt(18)
Step-by-step explanation:
there are many ways you could go about this,
I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18
100 POINTS WILL GIVE BRAINLYEST AND EVERYTHING!!!! What is the distance from (−7, −24) to (−7, 8)?
−32 units
−16 units
16 units
32 units
Answer:
D) 32 units==============
Given Two endpoints (- 7, - 24) and (- 7, 8)Find the distance between themSince both points have same x-coordinate, the distance between them is the difference of y-coordinates:
d = 8 - (- 24) = 8 + 24 = 32 unitsCorrect choice is D
Answer:
32 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Define the two given points:
Let (x₁, y₁) = (-7, -24)Let (x₂, y₂) = (-7, 8)Substitute the two points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]
[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]
[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]
[tex]\implies d=\sqrt{32^2}[/tex]
[tex]\implies d=32[/tex]
Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:
[tex]\implies 8 - (-24) = 8+23=32[/tex]
If the area to the left of x in a normal distribution is 0.193, what is the area to the right of x?
The area to the right of x in the normal distribution is 0.807
What is the normal distribution?The normal distribution is the probability distribution that helps to find the probability for continuous variables.
For a probability x, for a normal distribution, we have that
P(X ≤ x) + P(X ≥ x) = 1
How to find the area to the right of x?Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.
Since P(X ≤ x) + P(X ≥ x) = 1 where
P(X ≤ x) = area to the left of x P(X ≥ x) = area to the right of xMaking P(X ≥ x) subject of the formula, we have that
P(X ≥ x) = 1 - P(X ≤ x)
Given that P(X ≤ x) = 0.193
Substituting this into the equation, we have
P(X ≥ x) = 1 - P(X ≤ x)
P(X ≥ x) = 1 - 0.193
P(X ≥ x) = 0.807
So, the area to the right of x is 0.807
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The numbers 1000, 1001, 1002, 2000 are all in base 10. Rewrite all of the
numbers in base 5 and find the base 5 number whose digits have the least sum. What
is this number written in decimal notation?
Rewriting all numbers in base 5
1000 = 13000
1001 = 13001
1002 = 13002
2000 = 31000
The base 5 number whose digits have least sum are 13000 and 31000
The decimal notation of the numbers are 1000 and 2000
Define unit number.
The rightmost point in a number or the number one are both acceptable definitions of the word "unit" in mathematics. A unit can also be an item or a person that is seen as distinct and whole but is actually a component of a whole or group. An identification number for a unit in a declaration is referred to as a unit number.
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