Answer:
d which implies m/3 + 5 = 9
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Step-by-step explanation:
continuation of the previous answer:
now, for the final step angie should use the change of base formula in order to make the logarithmic expression simpler to analyze.
[tex]x = \frac{ log(6) }{ log(23) } [/tex]
after applying this formula Angie has successfully solved her exponential equation.
Answer:
Angie should use the change of base formula to make this equation faster. Which would be x= log(6)/log(23). Then, after using this formula and just plugging it into your calculator, Angie should have successfully answered her question.
Step-by-step explanation:
I took the exam
help help help help help help help
The required point-slope form of the equation of the line is y - 20= -5(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-2,-20) and m=-5.
What is the slope of the line?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.To learn more about point-slope refer to:
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Freda bought a sandwich for $4. 00 and a drink for94$. Her grandson ordered a meal for$6. 35. What was the total price of all three items when 8% sales tax was added?Explain how touse estimation to check whether your answer is reasonable
The answer is $112.70 The Question is a simple Sales tax rate calculating problem.
How do you solve sales tax problems?Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.
Sales tax rate = Sales tax percent / 100.
Sales tax = List price x Sales tax rate.
Given,
Rate of sandwich is = $4. 00
Rate of drink is = 94$
The rate of a meal that Her grandson ordered is =$6. 35.
What was the total price of all three items when 8% sales tax was added?
Total price of all three items without tax = 4 + 94 + 6.35
= $104.35
Total price of all three items with tax = (100% + tax) * Price
= (100% + 8%) * 104.35 = 108% * 104.35
= 1.08 * 104.35 = 112.698
≅ $112.70
The estimation to check if the result is reasonable by putting the answer in the original equation.
E.g. x + 4 = 10; x = 10 - 4
We get that x = 6
Plug in x = 6 in x + 4 = 10.
6 + 4 = 10.
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The temperature was recorded at midnight for 5 consecutive days. The
recorded temperatures are: -2°, 4°, 5°, -6°, and 9°. What is the average
temperature?
A website lists homes for sale in a suburban town. The site provides information including neighborhood, selling price, number of bedrooms, and whether the home has a garage. What are the individuals in this setting?
homes
neighborhoods
selling prices
bedrooms
answer is homes
Based on the description above, the individuals in this setting is option A: homes.
Whys the setting home?The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.
In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.
Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.
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Which expression simplifies to
m-2
—— ?
m-1
3 times one number minus a second is 8 and the sum of the numbers is 12
Answer: 3x-y=8
Step-by-step explanation:
A rectangle has a perimeter represented by the expression 4x−8. Which expression also represents this perimeter? 4(x-8), 2(2x-8), 2(2x-4), 4(2x-4)
The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)
How to determine the perimeter expressionFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 4x - 8
Factor out 2 from the expression
So, we have the following representation
Perimeter = 2 * 2x - 2 * 4
So, we have
Perimeter = 2(2x - 4)
Hence, the perimeter is 2(2x - 4)
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Graph the system.
What is the estimated solution of the system?
Enter your answer in the blanks. Round each coordinate to the nearest integer.
The lines intersect closest to the integer coordinates
The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.
What is Graph of System of Linear EquationsA graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.
In the given problem, we have two linear equations which are
y = 3x - 6 ...eq(i)
y = 2/5x + 5 ...eq(ii)
Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.
The coordinates to the nearest integer are (x, y) 4 and 7
The value of x is 4 and y is 7
Kindly find attached graph below.
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If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the largest percentage of their gross pay in employee benefits?
Answer: the answer is the option
Employee B: gross pay $32,900, total job benefits $34,000
hope this helped you
John gains 5% by selling a book for 273. Find the cost price of the book
Answer:
$260
Step-by-step explanation:
$273 - 5% = $260
5% commission = $13
Answer:
260
Step-by-step explanation:
273-5%=260
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 293 students using Method 1 produces a testing average of 82.9. A sample of 282 students using Method 2 produces a testing average of 76.5. Assume that the population standard deviation for Method 1 is 7.97, while the population standard deviation for Method 2 is 6.66. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places. g
The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.
The confidence interval for the difference of the population mean is calculated as,
CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2
= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82
=6.4 ± 1.199
=(v5.201 , 7.599)
therefore , approximately 5.20 , 7.60 .
Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.
The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.
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y<3x+12, y≥5x+7
The solution of the system of linear inequalities.
Answer: nswer ; x , we can find ; y with the first equation :.
1 answer
·
We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−
Step-by-step explanation:
The table shows a linear function. What is the rate of change?
Hours
Pay
1
18
1.5
23
2
28
2.5
33
3
38
Answer:
rate of change = 5
Step-by-step explanation:
the slope m gives the measure of the rate of change of the function
calculate the slope m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]
with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table
m = [tex]\frac{18-38}{1-3}[/tex] = [tex]\frac{-20}{-2}[/tex] = 5
then rate of change = 5
the total cost of the airline ticket is $432, including an 8% tax. What was the cost of the ticket before the tax was added?
aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2. Aleris can spend no more than $24 on the gift. write an inequality that describes the situation
The inequality when apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift is 3a + 2o ≤ 24.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift.
Let apple = a
Let orange = o
Therefore, the inequality will be:
3a + 2o ≤ 24.
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Lily purchases 3 gallons and two quarts of ice cream. How much ice cream did she purchase, in QUARTS
Answer:
14 Quarts
Step-by-step explanation:
1 Gallon = 4 Quarts.
3x4 = 12 + 2 = 14 Quarts.
Need need help with it
Answer:
Step-by-step explanation:
This is pretty simple. To find the area of anything in square centimeters, you multiply the length by the height. You already have both of those number, so you just have to do 4.2 x 4.2 (or 4.2 to the second power). The answer is 21.84 square centimeters.
Answer: 21.84 square centimeters
2 of 10
x
Colin buys a car for £27900.
It depreciates at a rate of 3% per year.
How much will it be worth in 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
Below
Step-by-step explanation:
3% loss means 97% (.97 in decimal ) remains
after 2 years :
27 900 ( .97)^2 = £ 26251 .11
To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Therefore ,the result is. It means that there exist 17 units between the two points supplied as the answer to the given distance problem.
Specify the distance.An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the quickest route a moving object can travel. We frequently take into account the concepts of range and displacement.
Here,
6 and -3 are given (2, -2)
Points (a, b) and (c, d) are now separated by
d= √(c-a)² + ( d- b) ²
d= √(-3+2)² + (2-6)² as a result.
=>d = √ 1 + 16 = √17
The distance between the two places is therefore 17 units.
the result is. It follows there are 17 units between the two points supplied as the answer to the given distance problem.
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Sue has 18 sweets
Tony also has 18 sweets
Sue gives Tony × sweets
Sue then eats 5 of her sweets
Tony then eats half of his sweets
Write expressions for the amount of sweets Tony and Sue now have
The expressions for the number of sweets that Tony and Sue now have are:
Given:
Sue has 18 sweets
Sue = 18
Tony also has 18 sweets, that is:
Toney = 18
Sue gives Tony × sweets; that is
Sue = 18 - x; and
Tony = 18 + x
Sue then eats 5 of her sweets, Tony then eats half of his ⇒ Sweets:
that is ⇒
Sue = 18 - x - 5
Tony = (18 + x) / 2
Thus, simplifying the above, we have:
Sue = 13 - x
Tony = (18 + x) / 2
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can somebody please help me with this
The scale factor of the image is 1/4 or 0.25.
What is scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
To solve this question, use the coordinates of WX and W'X' as points of reference.
From the diagram, it can be obtained that -
W(-8,8) and X(8,0)
W'(-2,2) and X'(2,0)
First, calculate distance for WX -
Distance formula is -
d = √(x2-x1)^2+(y2-y1)^2
Distance for WX -
d1 = √(8+8)^2+(0-8)^2
d1 = √(16)^2+(-8)^2
d1 = √256+64
d1 = √320
d1 = 17.88
Distance for W'X' -
d2 = √(2+2)^2+(0-2)^2
d2 = √(4)^2+(-2)^2
d2 = √16+4
d2 = √20
The scale factor is then calculated using -
Scale = W'X'/WX
Scale = d2/d1
Substitute values of d1 and d2 -
Scale =√20/√320
Scale = √(20/320)
Scale = √1/16
Scale = 1/4
Therefore, the scale value is 0.25.
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Question 15 of 27
What are the zeros and x-intercepts of this quadratic function?
-5
A. Zeros: -2 and 1
5
-5
Select two answers: one for the zeros and one for the x-intercepts.
5
B. Zeros: -1 and 2
C. x-Intercepts: (-1,0) and (2,0)
D. x-Intercepts: (0, -1) and (0, 2)
E. Zeros: 1 and 2
OF. x-Intercepts: (-2, 0) and (1, 0)
Correct options are: A. Zeros: -2 and 1
E. x-Intercepts: (-2, 0) and (1, 0)
What are zeros & x-intercepts of quadratic function?
The zero of the function is where the y-value is zero.
The x-intercept is where the graph crosses the x-axis.
The zeros of a quadratic function are the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. For the given quadratic function, the zeros
are -2 and 1.
The x-intercepts of a function are the points at which the function crosses the x-axis. In other words, they are the solutions to the equation f(x) = 0 when y = 0. For the given function, the x-intercepts are (-2, 0) and (1, 0) which are the points on the x-axis where the function crosses it.
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The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water.
We want to make a very SMALL batch of the SAME shade of green water.
We need to know how much yellow water to mix with only 1 ml of blue water.
Help Me Out ASAP please
On solving the provided question, we can say that - here in this inequality 17[tex]\leq[/tex]2x - 3[tex]\leq[/tex]25
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
17[tex]\leq[/tex]2x - 3[tex]\leq[/tex]25
[tex]20\leq 2x\leq 28\\10\leq x\leq 14[/tex]
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Why is a 5th interval called perfect?
The 5th interval is called perfect
Interval notation is a method to represent an interval on a number line.
The 5th interval is called perfect
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.
Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.
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Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67. Write a system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y).
The system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -
8x + 9y = 117
3x + 8y = 67
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67.
We can write the system of equations as -
8x + 9y = 117
3x + 8y = 67
Where -
cost of gespils → (x)
cost of alabers → (y).
Therefore, the system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -
8x + 9y = 117
3x + 8y = 67
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Last year at a certain high school, there were 75 boys on the honor roll and 120 girls on the honor roll. This year, the number of boys on the honor roll increased by 24% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase
The total number of students on the honor roll increased by 20%.
Given that, 75 boys and 50 girls on the honor roll
=> boys increased by 24% = 75*24/100 = 18
So, the number of boys is increased by 18.
=> girls increased by 14% = 50*14/100 = 7
So, the number of girls is increased by 7.
After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.
Thus, the total number of students increased = 18+7 = 25
Therefore, the percentage increment in total = 25 / 125 * 100 = 20%
Hence, The total number of students on the honor roll increased by 20%.
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Donny is raising money for the school charity drive by mowing lawns for $9.75 per lawn. How much will he raise for the drive? its a liner equation.
Answer:
y = 9.75x
Step-by-step explanation:
y = the money earned
x = number of lawns.
What should be the value of a if the value of 2x² X − a 5 when x 0?
The value of a=0 in a given expression.
what are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
Define algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
If the value of 2x² - a*5 when x = 0 is 0, then we can substitute x = 0 into the equation and solve for a.
So,
[tex]2(0)² - a5 = 0[/tex]
[tex]-a5 = 0[/tex]
[tex]a = 0[/tex]
Therefore, the value of a should be 0.
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