Answer:
8 = 0 (this equation is always false)Step-by-step explanation:
5(1 − n) + 3n = 3(n − 1) – 5n
5 - 5n + 3n = 3n - 3 - 5n
5 + 3 = 5n - 3n + 3n - 5n
8 = 0
this equation is always false
7. You bought a Gatorade and 4 bags of apples for $5.50. Write the equation that determines how much
each bag of apples was if the Gatorade cost $2.50.
Answer: (5.50-2.50)/4 = 0.75. each bag of apples is $0.75
Step-by-step explanation:
first, you subtract $5.50 by $2.50 to get $3, the cost of the 4 bags of apples altogether ($5.50 - $2.50 = $3)
then you divide $3 by 4 to get the cost of each bag of apples. (3/4 = 75)
so each bag of apples is $0.75
i hope this helps!
Find the coordinates of the midpoint M
(-3, 2) and K(9, 2)
Answer:
(3,2)
Step-by-step explanation:
since -3 + 9 =6
6 ÷ 2 =3
2 + 2 = 4
4 ÷ 2 = 2
therefore (3,2)
Please answer the question
For given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
In this question, we have been given two functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x²
We need to find f(x) - g(x)
We need to subtract function g(x) from function f(x)
= f(x) - g(x)
= 3x² - 8 - (5 - 2x - 2x²)
= 3x² - 8 - 5 + 2x + 2x²
= 3x² + 2x² + 2x - 8 - 5
= (3 + 2)x² + 2x - (8 + 5)
= 5x² + 2x - 13
Therefore, for given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
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Write a rule to describe the transformation.
E(-1-3), F(0,1), G(3,-2)
E'(-1.5,-4.5), F'(0,1.5), G' (4.5.-3)
Answer:
x= x1.5 y = x1.5
E' = E dilated by 1.5
Step-by-step explanation:
-1 x 1.5 =-1.5 -3 x 1.5 = -4.5 (-1.5,-4.5)
0 x 1.5 =0 1 x 1.5 = 1.5 (0,1.5)
3 x 1.5 = 4.5 -2 x 1.5 =-2 (4.5.-3)
suppose that 75% of the applicants for a certain industrial job possess advanced training in computer programming. applicants are interviewed sequentially and are selected at random from the pool. find the probability that the first applicant with advanced training in programming is found on the third interview. (round your answer to four decimal places.)
The probability that the first applicant with advanced training in programming is found on the third interview is 0.0469
Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so
Geometric distribution is: (1-75%)
=0.75
The density function of geometric distribution is,
[tex]P(X=x)=p(1-p)^{x-1}[/tex], for all x = 1,2,3,....
Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:
P(X=3) =[tex]0.75(1-0.75)^{3-1}[/tex]
=[tex]0.75(1-0.75)^{2}[/tex]
=0.75×0.0625
=0.0469
Hence, the required probability is 0.0469
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Converting Units of Measure I - Item 35100
Ellie needs 24 cups of milk for a large recipe. How many gallons does she need?
2 c = 1 pint
(pt)
2 pt = 1
quart (qt)
4 qt = 1
gallon (gal)
Ellie needs 1.5 gallon of milk (that is 24 cups).
we are given 2 cup = 1 pint
we have 24 cup which will be equal to 24/2 i.e. 12 pint.
we are given 2 pint = 1 quart
we have 12 pint which will be equal to 12/2 i.e. 6 quart
we are given 4 quart = 1 gallon
we have 6 quart which will be equal to 6/4 i.e. 1.5 gallon.
Hence, we know 24 cups of milk is equivalent to 1.5 gallon of milk
what are conversions in maths?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. When a conversion is required, the right conversion factor to an equivalent value must be applied. For instance, 12 inches equals 1 foot when converting between inches and feet.
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PLEASE HELP ASAP this stuff doesn’t make sense ;-;
The system of Inequality for the given graph is;
2x + 3y ≥ 12
3x - 5y ≥ 15
How to Interpret Inequality graph?
Inequalities that use < or > symbols are always plotted with a dashed line while Inequalities that use ≤ or ≥ symbols are always plotted with a solid line.
Now, if the shaded portion is above a dashed line, the the symbol is > but if it is shaded above a solid line, then the symbol is ≥. In this question, a solid line is used for both equations and shaded above the lines and so we will use ≥.
Equation of Line 1;
x-intercept = 6
y intercept = 4
Slope = -2/3
Thus, using the general equation of slope of line, the equation of this inequality is; 2x + 3y ≥ 12
Similarly, the equation of the second line will be;
3x - 5y ≥ 15
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Solve for x -
[tex]\sf 6+4x+3=6x-21[/tex]
Answer:
x = 15
Step-by-step explanation:
Let's start by copying down the equation.
6 + 4x + 3 = 6x - 21
Let's simplify this equation and we get,
4x + 9 = 6x - 21
Now, we can add 21 to both sides to isolate 6x on one side. Then, we get...
4x + 30 = 6x
Now, we minus 4x from both sides to get rid of it.
Then we get...
2x = 30
Thus, x = 15
6 + 4x + 3 = 6x - 21
We minus (4x+3) on both side.
6 + 4x + 3 - (4x+3) = 6x - 21 - (4x + 3)
6 = 2x - 24
2x = 30
x = 15.
Recheck : 6 + 60 + 3 = 90 - 21
69 = 69 (nice.)
Sam creates a dot pattern using a rule. He starts with 2 dots and adds 2 dots for each term. The dot pattern continues for 50 terms. The first four terms in his dot pattern are shown below.
Answer:
That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.
If f(x)=2(x)^2 + 5 square root (x-2), complete the following statement
The domain for f(x) is all real numbers _____ than or equal to 2.
Answer:
Greater.
Step-by-step explanation:
The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.
Thus, the domain for f(x) is all real numbers greater than or equal to 2.
Answer:
The domain for f(x) is all real numbers greater than or equal to 2.
Step-by-step explanation:
Given function:
[tex]f(x)=2x^2+5 \sqrt{x-2}[/tex]
The domain of a function is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken:
[tex]\implies x-2\geq 0[/tex]
Therefore:
[tex]\implies x-2+2\geq 0+2[/tex]
[tex]\implies x\geq 2[/tex]
Therefore, the domain of the given function is greater than or equal to 2.
Which of the following best describes the graph below?
A. It is not a function.
B. It is a one-to-one function.
C. It is a many-to-one function.
D. It is a function, but it is not one-to-one.
The correct option B. It is a one-to-one function; for the given graph.
What is termed as the one-to-one function?Each element of one set, say Set (A), is mapped with such a unique element of another set, say Set (B), where A as well as B are two different sets. It can also be written 1-1. In terms of function, if f(x) = f(y) implies that x = y, after which f is one to one.An injective function is a one-to-one function that maps each element of one set to each element of some other set.For the given question;
As, in the given graph for the function, for each value of the domain (the value of x), there is only one value of range (y).
Thus, the given graph shows the one-to-one function.
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which rational is qvuivalent to 0.86
The rational equivalent to 0.86 can be written as 43/50.
A rational number may be defined as the number which can be expressed in the form of p/q where p and q are integers, and the term q cannot be equal to zero. It can be either positive or negative or both. We can also say that any fraction which does not have zero in the denominator is called a rational number. Zero can also be regarded as a rational number as it can also be represented as a fraction. For example, 0/2, 0/5. In order to write 0.86 as a rational number, we have to convert it in fraction form. In fraction form it can be written as
0.86 = 86/100
This is also a rational number, but we simplify it further and we get
86/100 = 43/50 which is a rational number.
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cami invested $6000 dollars into an account that ears 10% intrest compound annually. write an explicit equation for how much money she wil have after t years
Answer:
Below in bold.
Step-by-step explanation:
10% = 0.10 as a decimal fraction.
After t years:
Amount = 6000(1 + 0.10)^t
Long division synthetic remainder theorem and factor theorem
[tex](4n^3 - 18n + 21 - 8n^2) ÷ (2n - 6)[/tex]
answer step by step:
hope this helps
1. Given the sequence: {5, 7, 9, 11, ...}
Which explicit formula generates this sequence?
What’s the answer
Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.
Arithmetic Sequence formula.In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.
How are explicit formulas handled?Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same.
The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.
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All of the following are equivalent fractions except
04/12
07/21
O 5/20
O9/27
Answer:
05/20 is not an equivalent fraction
Step-by-step explanation:
1) Write each fraction in its simplest form. To do this divide the numerator by the denominator.
04/12 becomes 1/3
07/21 becomes 1/3
05/20 becomes 1/4
09/27 becomes 1/3
2) all the fractions simplify to the same number except 05/20. So, we can conclude that 05/20 is not an equivalent fraction
Brian is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Brian has 69 miles to his destination after 15 minutes of driving, and he has 58.8 miles to his destination after 27 minutes of driving. How many miles will he have to his destination after 41 minutes of driving?
Brian will have 46.90 miles to his destination after 41 minutes of driving.
In the question ,
it is given that
Brian has 69 miles left to his destination after 15 minutes of driving
let x denotes the driving time ( in minutes)
and y denote the remaining distance ( in miles )
so the point is represented by (15,69)
and given that
Brian has 58.8 miles to his destination after 27 minutes of driving
so the second point is (27,58.8).
Since the relationship is given to be linear , hence it will represent a line .
the equation of line passing through the two points (15,69) and (27,58.8) is given by
(y-69)=(58.8-69)/(27-15) * (x-15)
y-69 = -10.2/12 * (x-15)
y-69 = -0.85(x-15)
y-69= -0.85x+12.75
y = -0.85x + 81.75
So , the linear relationship between remining distance and driving time is given by y = -0.85x + 81.75 .
to find miles will he have to his destination after 41 minutes of driving
Substituting x=41 we get
y = -0.85(41) + 81.75
y = -34.85 + 81.75
y = 46.90 .
Therefore , Brian will have 46.90 miles to his destination after 41 minutes of driving.
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The arithemetic mean of 3,15, and my number is 40. What is my number?
_
Average of given n numbers X1,X2,.........,Xn is x= £xi/n
Let the my number be x
Given:- The average of 3,15,x is 40
£xi/n =40
3+15+x/3=40
Multiplying 3 both side
18+x=120
x=120-18
x=102
Hence, my number is 102
Find the odd one out
7142
2168
3248
7426
3211
8547
9455
9273
the time it takes me to wash the dishes is uniformly distributed between 12 minutes and 20 minutes. what is the probability that washing dishes tonight will take me between 14 and 16 minutes?
The probability that washing dishes will take time between 14 and 16 minutes is equal to 25%.
This type of probabilty can be termed a uniform probability in which all the outcomes or results are equally likely.
The lower limit can be represented as a and in this problem is 12 minutes and the upper limit can be considered b and in this problem is 20 minutes.
The equation to find probability, in this case, can be given as:
P ( c ≤ X ≤ d ) = d - c / b - a
Here c = 14 and d = 16 as we have to find the probability that washing dishes will take between 14 and 16 minutes.
Therefore;
P ( 14 ≤ X ≤ 16 ) = 16 - 14 / 20 - 12 = 2 / 8 = 0.25
Converting it into percentage:
0.25 = 0.25 × 100 = 25%
Therefore, the probability that washing dishes will take her between 14 and 16 minutes is calculated to be 25%.
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The area of a rectangle ABCD is 9cm².
Show that x² + 5x = 3
We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.
How to Find the Area of a Rectangle?To find the area of a rectangle, use the formula given below:
Area of a rectangle = (length)(width).
Given the parameters:
Area of rectangle ABCD = 9 cm²Length of the rectangle = BC = (x + 3) cmWidth of the rectangle = AB = (x + 2) cmTo show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:
(x + 3)(x + 2) = 9
Apply the distributive property of equality
x(x + 2) + 3(x + 2) = 9
x² + 2x + 3x + 6 = 9
Combine like terms:
x² + 5x + 6 = 9
Add -6 to both sides of the equation
x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]
x² + 5x = 3
Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.
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a. If p is an even number, then p + 12 is even.
Answer:
True???
Step-by-step explanation:
Is this a true or false question?
P+12=even number
Examples...
12+12=24
16+12=28
66+12=78
Answer:
YES
Step-by-step explanation:
even + even = even
always and forever
Skippy got his first paycheck and his gross pay was $1200. He noticed he paid the federal
government $180, FICA $91.44, and a state tax of $60.
a) How much did he pay in taxes?
b) What percentage of his gross income went to taxes?
c) What is his net pay?
Find the solutions to x² = 12. O A. x = +2√/6 OB. x = +2√3 O C. x = +6√2 O D. x = ±3√2
The solution for the expression x² = 12 will be x = ±2√3.
The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,
√x² = √12
x = √(2×2×3)
x = ±2√3
We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,
Thus, the value of x is ±2√3.
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Write down the order of rotational symmetry of this regular heptagon.
The order of the rotational pentagon is 6.
What is order of a polygon?The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.
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What is the result of converting 0.5 cups to fluid ounces? (Remember that 1
cup = 8 fluid ounces.)
O A. 16 fluid ounces
OB. 2 fluid ounces
OC. 4 fluid ounces
O D. 8 fluid ounces
SUBT
The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 9292 feet, find the value of the longest of the four side lengths.
The longest side of a quadrilateral with length of consecutive even integers is 26 feet.
How to find the side of a quadrilateral?The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers.
A quadrilateral is a polygon with 4 sides.
Therefore, the sides are consecutive even numbers.
Hence,
smallest side = x
Therefore, perimeter is the sum of the whole sides of the quadrilateral.
x + x + 2 + x + 4 + x + 6 = 92
4x + 12 = 92
4x = 92 - 12
4x = 80
x = 80 / 4
x = 20
Therefore, the longest side of the quadrilateral is 20 + 6 = 26 ft.
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Determine whether the graph represents a linear or non linear function and explain
Answer:
Non-linear
Step-by-step explanation:
Because the line is not straight.
Find the distance between points S(-2,4) and T(3,9). Round your answer to the nearest tenth.
Answer:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=[3-(-2)]^2+(9-4)^2
d^2=(5)^2+(5)^2
d^2=25+25
d^2=50
d= [tex]\sqrt{50}[/tex]
d=7.07 units
8th grade Mathematics
According to the trend line equations, which plants are growing at the same rate per day?
1 and 2
1 and 4
2 and 3
2 and 4
I appreciate you answers so much!
Have a great day! :)
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )
What is rate of change ?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]
because they have same slope(rate of change )
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