Answer:
5x + 1 = 4x
You can really put any letter for "a number":
5n + 1 = 4n
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (1,6), endpoint (-2,1)
Answer:
(4,11)Step-by-step explanation:
Given two coordinates (x₁, y₁) and (x₂,y₂), the midpoint of the coordinates is expressed as M(X,Y) = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] where;
[tex]X = \dfrac{x_1+x_2}{2}\ and \ Y = \dfrac{y_1+y_2}{2}[/tex]
Given the midpoint (X, Y) = (1,6) and one end point to be (-2,1), to get the unknown endpoint (x,y), we will apply the formula above. from the coordinates given X = 1, Y = 6, x₁ = -2 and y₁ = 1
[tex]Given \ X = \dfrac{x_1+x_2}{2}\\1 = \dfrac{-2+x}{2}\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4[/tex]
Similarly to get y;
[tex]Given \ Y = \dfrac{y_1+y}{2}\\6 = \dfrac{1+y}{2}\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11[/tex]
Hence the unknown endpoint (x,y) is (4,11)
Solve for x: −2(x + 3) = −2x − 6
Answer:
All real numbers
Step-by-step explanation:
Solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
What is equation?
" Equation is defined as when two algebraic expression which are related with the sign of equality."
According to the question,
Given,
-2(x + 3) = -2x - 6
Open the brackets of the equation we get,
-2(x) + (-2)(3) = -2x - 6
⇒ -2x - 6 = -2x - 6
Add 6 on both the sides of the equation we get,
-2x = -2x
Divide by -2 of the equation both sides
x = x _____(1)
Add (-x) both the sides we get,
0 = 0 _____(2)
From (1) and (2) we conclude ,
Solution is true for all the real values of x.
Hence, solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
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Each ounce of Food I contains 3 g of carbohydrate and 2 g of protein, and each ounce of Food II contains 5 g of carbohydrate and 3 g of protein. Suppose x ounces of Food I are mixed with y ounces of Food II. The foods are combined to produce a blend that contains exactly 73 g of carbohydrate and 46 g of protein.
a. Explain why there are 3x + 5y g of carbohydrate in the blend and why we must have 3x + 5y = 73. Find a similar equation for protein. Sketch the graphs of both equations.
b. Where do the two graphs in part (a) intersect? Interpret the significance of this point of intersection
Answer:
The answer is below
Step-by-step explanation:
a) Food I contains 3 g of carbohydrate and food II 5 g of carbohydrate. x is the number of ounce of food I while y is the number of ounce of food II.
Therefore, the amount of carbohydrate in food 1 is 3x while that of food II is 5y. Since the blend contains exactly 73 g of carbohydrate, the total number of carbohydrate in both food I and food II is 73 g. Hence:
3x + 5y = 73 (1)
Food I contains 2 g of protein and food II 3 g of carbohydrate. Therefore, the amount of protein in food 1 is 2x while that of food II is 3y. Since the blend contains exactly 46 g of protein, the total number of protein in both food I and food II is 46 g. Hence:
2x + 3y = 46 (2)
Using geogebra to Sketch the graphs of both equations.
b) The point of intersection is gotten from the graph, this gives x = 11, y = 8.
The point of intersection shows the amount of food I and food II that give the required amount of protein and carbohydrate.
11 ounce of food I and 8 ounce of food II would produce the required amount of protein and carbohydrate
A square calendar has sides that are 7 inches long. What is the calendar's area?
Answer:
49
Step-by-step explanation:
7x7=49
Answer:
49
Step-by-step explanation:
7x7=49
The function C(F) =5/9 (F - 32) is used to convert temperature from Fahrenheit (F) to Celsius (C).
The function K(C)= C + 273.15 is used to convert temperature from Celsius (C) to the Kelvin (K) scale. Write a function to convert 77°F to the Kelvin scale.
To express temperature in Kelvin as a function of Fahrenheit, compose the functions as(_*_)(_).
Now, derive the function described above and use it to express 77°F as ___K.
Answer:
K(F) = 5/9 (F - 32) + 273.15
K(F)=298.15k
Step-by-step explanation:
C(F) =5/9 (F - 32) is used to convert temperature from Fahrenheit (F) to Celsius (C).
C(F) =5/9 (F - 32)
The function K(C)= C + 273.15 is used to convert temperature from Celsius (C) to the Kelvin (K) scale.
K(C)= C + 273.15
K(c) - 273= C
Equating both values of C
K(F) - 273.15=5/9 (F - 32)
K(F) = 5/9 (F - 32) + 273.15
If F = 77°F
K(F) = 5/9 (F - 32) + 273.15
K(F) = 5/9(77-32) + 273.15
K(F) = 5/9(45) +273.15
K(F) = 25+273.15
K(F)=298.15k
Answer:
K
C
F
298.15
Step-by-step explanation:
Solve the equation x2 = 5.
±√5
Step-by-step explanation:x² = 5
x = ±√5
The solution to the equation [tex]x^2=5[/tex] is [tex]x = \pm \sqrt{5}[/tex].
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
[tex]x^2=5[/tex]
By taking the square root of both sides of the equation, we have:
[tex]x = \pm \sqrt{5}[/tex].
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What is the value of this expression?
6 + 24 % 3 x 4 %2
Answer:
22
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
6 + 24 ÷ 3 x 4 ÷ 2
Step 2: Divide
6 + 8 x 4 ÷ 2
Step 3: Multiply
6 + 32 ÷ 2
Step 4: Divide
6 + 16
Step 5: Add
22
Derrick and Samantha are selling tickets for their school musical. Floor seats cost $7.50 and balcony seats cost $5.00. Samantha sells 60 floor seats and 70 balcony seats, Derrick sells 50 floor seats and 90 balcony seats. Write an expression to show how much money Samantha and Derrick have collected for tickets.
Josiah subtracts 337 from 600 and writes the following
600 minus 300 is 300. Then I can subtract 40 more and get 260. But I should have only subtracted 37
more, so I'll add 3 back to my difference to get 263
Which montal math strategy did Josiah use?
Answer:
Associative property is the math strategy Josiah used
Find the value of the expression for the given values.
6x-2 for x = -2, x = 6, and x = -5
If x= - 2. then 6x - 2 =
If x = 6, then 6x - 2 =
If x= - 5. then 6x-2=
Answer:
If x= - 2. then 6x - 2 = -14
If x = 6, then 6x - 2 = 34
If x= - 5. then 6x-2= -32
Step-by-step explanation:
You have to substitute the value of x in the expression.
If x = -2,
6x-2 = 6*(-2) - 2 = -12-2 = -14
Fruit juice in 4/5 pint cartons is sold by the park in 5/6 pint mugs. How many mugs are in a carton?
Answer:
Number of mugs in cartoon = 24 / 25
Step-by-step explanation:
Given:
Pints of cartoon = 4/5
Pints of mugs = 5/6
Find:
Number of mugs in cartoon
Computation:
Number of mugs in cartoon = Pints of cartoon / Pints of mugs
Number of mugs in cartoon = (4/5) / (5/6)
Number of mugs in cartoon = 24 / 25
Techside Real Estate, Inc. is a research firm that tracks the cost of apartment rentals in Southwest Virginia. In mid-2002, the regional average apartment rental rate was $895 per month. Assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. In a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.
a. Do the sample data enable Techside Real Estate, Inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? The sample mean is $915 and the sample standard deviation is $227.50. Make your decision based on α=0.10.
b. What is the P-value?
Answer:
1) we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002
2) P - value = 0.116435
Step-by-step explanation:
We are given;
Population mean; μ = $895
Sample mean; x' = $915
Population standard deviation; σ = $225
Sample standard deviation; s = $227.50
Sample size; n = 180
Let's state the hypothesis;
Null hypothesis;H0: μ ≤ $895
Alternative hypothesis;Ha: μ > $895
Now, the z-score formula is;
z = (x' - μ)/(σ/√n)
Thus, we are making use of the population standard deviation
z = (915 - 895)/(225/√180)
z = 20/16.7705
z = 1.193
From online p-value from z-score calculator attached, with α = 0.10, one tail, we have;
The P-Value is 0.116435
This is more than the significance level of 0.1, thus we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002
If the length of rectangle is 8.26cm and its breadth is 5.5cm, the find the
area of the rectangle
Answer:
Area of a rectangle= L×B
=8.26cm×5.5cm
=45.43cm square
Answer:
45.43cm squared
Step-by-step explanation:
Length times breadth =
8.26cm x 5.5cm.
8.26cm x 5.5cm = 45.43cm squared.
Using an algorithm is a good way to figure out this question. There are useful websites to teach you about them :)
Please help. I’ll mark you as brainliest if correct!
Simplify the expression.
(2x^2y)^3
Answer:
=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6
Step-by-step explanation:
The sum of two even consecutive integers is 114. What is the smallest integer?
Answer:
56
Step-by-step explanation:
The sum of two even consecutive integers is 114.
Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.
So, this means that the second number is 2n+2.
Their sum is 114. In other words:
[tex](2n)+(2n+2)=114[/tex]
Solve for n.
Combine like terms:
[tex]4n+2=114[/tex]
Subtract 2 from both sides:
[tex]4n=112[/tex]
Divide both sides by 4:
[tex]n=28[/tex]
So, n is 28.
This means that the first number is 28(2) or 56.
And the second number is 58.
So, the smallest integer is 56.
And we're done!
The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70% of programmers remain in that position 20% are pro- moted to project manager and 10% are fired (state X). 95% of project managers remain in that position while 5% are fired. How long on the average does a programmer work before they are fired?
Answer:
it will take a programmer about 16.67 times to work before they are fired
Step-by-step explanation:
From the information given;
The transistion matrix for this study can be computed as:
P M X
P 0.7 0.2 0.1
M 0 0.95 0.05
X 0 0 1
where;
The probability that the programmer remains a programmer = [tex](P *P)[/tex]
The probability that the programmer turns out to be a manager = [tex](P*M)[/tex]
The probability that the programmer is being fired = [tex](P*X)[/tex]
Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;
[tex]y(P)=1+0.7y(P)+0.2y(M)[/tex]
[tex]y(M)=1+ 0.95y(M).[/tex]
[tex]0.05y(M)=1[/tex]
y(M) = [tex]\dfrac{1}{0.05}[/tex]
y(M) =20
y(P)=1+0.7y(P)+0.2y(M)
y(P) - 0.7y(P) = 1 + 0.2y(M)
0.3y(P) = 1 + 0.2(20)=1+4
0.3y(P) = 1 + 4
0.3y(P) = 5
[tex]y(P)=\dfrac{5}{0.3}[/tex]
[tex]y(P)=16.67[/tex]
Therefore, it will take a programmer about 16.67 times to work before they are fired
students surveyed about birthdays. How many more students were born on monday than friday?
a) 4 students
b) 1 students
c) 2 students
d) 3 students
Alan can do 2/3 part of his work and sam can do 3/4 part of her work .Who can do more work
Answer:
Sam can do more work.
Step-by-step explanation:
2/3 equals out to just over half of his work done. 0.66666667.
3/4 equals out to almost all of her work done. 0.75.
*hope this helps*
Answer:
Sam can do more work:)
Step-by-step explanation:
. Jessica went to the grocery store and purchased a box of cereal for $3.75, milk for $1.50, and bread for $2.25. She paid with a $20.00 bill. How much change did Jessica receive?
The temperature went from -6°F to -11°F. What was the change in temperature? 17°F -17°F -5°F 5°F
Answer:it got colder by more than 2 degrees
Answer:
well It would have been a change of -5ºF
Which statement is true about the two lines whose equations are given below?
y =
= 3x + 2
y = -4x + 9
A.
The lines are parallel.
B.
The lines are perpendicular.
The lines intersect but are not perpendicular.
C.
D.
The lines coincide.
Answer:
C. The lines intersect but are not perpendicular.
Step-by-step explanation:
The slopes (x-coefficients) of these lines are 3 and -4. They are different, but their product is not -1. Lines with different slopes are distinct lines that will intersect. If the product of their slopes is -1, they are perpendicular.
The lines intersect but are not perpendicular.
what is five added to twice a number
2x+5
Step-by-step explanation:
let the number be x
According to the question
2x+5
hope it whould help
what expression would be equivalent to 4+12? 6(8+6) 12(4+1) 4(44+3) 8(6+4)
Answer:
12(4+1) i think
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\large\textbf{4 + 12}[/tex]
[tex]\huge\textbf{Convert it to an easier way to}\\\huge\textbf{understand or keep it as it is:}[/tex]
[tex]\large\textbf{= 12 + 4}[/tex]
[tex]\huge\textbf{The answer:}[/tex]
[tex]\large\textbf{= 16}[/tex]
[tex]\huge\textbf{Now, let's see which one of your choices}\\\huge\textbf{are equivalent to your original equation.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\large\textbf{6(8 + 6)}[/tex]
[tex]\large\textbf{= 6(8) + 6(6)}[/tex]
[tex]\large\textbf{= 48 + 36}[/tex]
[tex]\large\textbf{= 84}[/tex]
[tex]\large\textsf{OR}[/tex]
[tex]\large\textbf{6(8 + 6)}[/tex]
[tex]\large\textbf{= 6(14)}[/tex]
[tex]\large\textbf{= 84}[/tex]
[tex]\large\textbf{84 }\boxed{\neq}\large\textbf{ 16}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\large\textbf{12(4 + 1)}[/tex]
[tex]\large\textbf{= 12(4) + 12(1)}[/tex]
[tex]\large\textbf{= 48 + 12}[/tex]
[tex]\large\textbf{= 60}[/tex]
[tex]\large\textsf{OR}[/tex]
[tex]\large\textbf{12(4 + 1)}[/tex]
[tex]\large\textbf{= 12(5)}[/tex]
[tex]\large\textbf{= 60}[/tex]
[tex]\large\textbf{60 }\boxed{\neq}\large\textbf{ 16}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\large\textbf{4(44 + 3)}[/tex]
[tex]\large\textbf{= 4(44) + 4(3)}[/tex]
[tex]\large\textbf{= 176 + 12}[/tex]
[tex]\large\textbf{= 188}[/tex]
[tex]\large\textsf{OR}[/tex]
[tex]\large\textbf{4(44 + 3)}[/tex]
[tex]\large\textbf{= 4(47)}[/tex]
[tex]\large\textbf{= 188}[/tex]
[tex]\large\textbf{188 }\boxed{\neq}\large\textbf{ 16}[/tex]
[tex]\huge\textsf{Option D.}[/tex]
[tex]\large\textbf{8(6 + 4)}[/tex]
[tex]\large\textbf{= 8(6) + 8(4)}[/tex]
[tex]\large\textbf{= 48 + 32}[/tex]
[tex]\large\textbf{= 80}[/tex]
[tex]\large\textsf{OR}[/tex]
[tex]\large\textbf{8(6 + 4)}[/tex]
[tex]\large\textbf{= 8(10)}[/tex]
[tex]\large\textbf{= 80}[/tex]
[tex]\large\textbf{80 }\boxed{\neq}\large\textbf{ 16}[/tex]
[tex]\huge\text{Therefore, your answer: \boxed{\textsf{None of the above}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?
2x- 6 is 5x + 3
your answwr
In the diagram,
AB =BC,AC = CD, and AD
12. Find the
lengths of all segments in the diagram. Suppose you
choose one of the segments at random. What is the
probability that the measure of the segment is greater
than 3? Explain your reasoning.
Answer:
Probability that the measure of a segment is greater than 3 = 0.6
Step-by-step explanation:
From the given attachment,
AB ≅ BC, AC ≅ CD and AD = 12
Therefore, AC ≅ CD = [tex]\frac{1}{2}(\text{AD})[/tex]
= 6 units
Since AC ≅ CD
AB + BC ≅ CD
2(AB) = 6
AB = 3 units
Now we have measurements of the segments as,
AB = BC = 3 units
AC = CD = 6 units
AD = 12 units
Total number of segments = 5
Length of segments more than 3 = 3
Probability to pick a segment measuring greater than 3,
= [tex]\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
What is the image point of
(−5,−3) after a translation right 4 units and down 1 unit?
Answer:
(-1,-4)
Step-by-step explanation:
(-5,-3) if we're moving four units right on the x axis, it would be a bigger number near the center. Think of it as adding -5 and 4, which would get you -1 for x (-1,x)
Now to get y, we would basically do the same thing except if it's going down, it would be a negative. We would add both -1 and -3 together to get -4, hence the answer, (-1,-4)
I suggest drawing a graph and doing it yourself, it'll really help you.
(3 + 4i) - (8 -5i) Write answer in standard form a +bi Group of answer choices
A:-5+9i
B:-5 + 9i
Answer:
[tex]A=-5+9i[/tex]
Step-by-step explanation:
[tex]\left(3+4i\right)-\left(8-5i\right)\\\\\mathrm{Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number}\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3-8\right)+\left(4+5\right)i\\3-8=-5\\4+5=9\\\\=-5+9i[/tex]
What is 12 raised to the first power?
Answer:
12^1 = 12
Step-by-step explanation:
Any number raised to the power of one equals the number itself.
Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.15%. They have 500 grams of substance B which decays at a rate of 0.37%. They are trying to determine how many years it will be before the substances have an equal mass.
Answer:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area
Step-by-step explanation:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area