Answer:
x = -2
Step-by-step explanation:
If m(x) = 4x + 15 and m(x) = 7, the we can substitute and get the equation:
4x + 15 = 7
x = -2
The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x-4, y-1), give the vertices of △A′B′C′.
Answer:
A' = (-2, -4)
B' = (-7, -6)
C' = (0, 0)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x - 4, y - 1)
This notation tells you that the x-coordinate is translated 4 units to the left, and the y-coordinate is translated 1 unit down.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 - 4, -3 - 1) = (-2, -4)
⇒ B' = (-3 - 4, -5 - 1) = (-7, -6)
⇒ C' = (4 - 4, 1 - 1) = (0, 0)
step by step explanation 6 divided by 396 show work
The value of 6 divided by 396 is 0.1515.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.
The steps include:
Step 1: Take the first digit of the dividend from the left.
Step 2: Divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and then write the difference below.
Step 4: Bring down the next digit of the dividend.
In this case, 6/396 will give the value illustrated above.
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A chemist is using 363 milliliters of a solution of acid and water. If 13.6% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
If 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
In the question;
it is given that
the total solution of acid and water is 363 milliliters .
and also it is given that 13.6% of the solution is acid ,
which means
the amount of acid in solution = 13.6% of total solution
Substituting the values , and
on solving further ,
we get
amount of acid in solution = 0.136×363 ......as 13.6% = 0.136
= 49.368
≈ 49.4 milliliter
Therefore , if 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
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Two angles are supplementary. The measure of one angle is 54 more than the measure of the other angle. What is the measure of the bigger angle?
The measure of the bigger angle is 117°
What are Supplementary Angles?
Two angles are said to be supplementary if their sums total 180 degrees.
Let, x be the angle
and, x + 54 other angle measure.
we know, sum of Supplementary angle is 180°
so, the equation will be
x + (x + 54) = 180°
2x + 54 = 180
2x = 180 - 54
2x = 126
x = 63°
x + 54 = 63 + 54 = 117°
Therefore, The measure of the bigger angle 117°
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Is the commutative or associative property being shown in the problem below?
(3 x 5) x 8 = 3 x (5 x 8)
Associative Property
Answer:
Associative
Step-by-step explanation:
simplify the following 22e- 5e- 8e- 4e
Answer:
5e?
Step-by-step explanation:
so if i help let me know this please
[tex]22e - 5e - 8e - 4e = 5e[/tex]
Give an example of a percent problem involving the simple interest formula. Then solve your problem.
The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?
What is simple interest?
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Solution for the above problem is:
The formula to calculate simple interest is:
[tex]S.I. = P \times I \times T[/tex]
Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time
Given in the question:
P = $2500
I = 6% = 0.06 (in decimals)
T = 2
Putting the value in the question:
S.I. = 2500(0.06)(2)
S.I. = 300
Therefore, the simple interest is $300.
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help battery 10% pls hurry
The solution to the simultaneous equation is y = 5.5 and x = 1.5
How to solve for the simultaneous equation'Simultaneous equations are the types of equations in mathematics that is made up of two equations where the equations would have to share variables.
we have
y = 3x + 1 - - - - 1
x + y = 7 - - - - 2
we have to put the value of y in equation 1 into equation 2
we would have
x + 3x + 1 = 7
4x + 1 = 7
4x = 7 - 1
4x = 6
x = 6 / 4
x = 1.5
put the value of x in equation 2 to get y
1. 5 + y = 7
y = 7 - 1.5
y = 5.5
Therefore the values of y is 5.5 while the value of x is 1.5
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The required solution of the given simultaneous equation is x = 1.5 and y = 5.5.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
y = 3x + 1 _ _ _ _ _ _ (1)
x + y = 7 _ _ _ _ _ _ (2)
From equation 2
y = 7 - x substitute this in equation 1
7 - x = 3x + 1
4x = 6
x = 6 / 4
x = 3 / 2
Now put this x in equation 2
3/2 + y = 7
y = 7 - 3/2
y = 11 / 2
Thus, the required solution of the given simultaneous equation is x = 1.5 and y = 5.5.
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Is the ordered pair a solution of the equation?
y = -6x - 14, (-5,16)
a. yes
b. no
Answer:
a. Yes
Step-by-step explanation:
If you plug in the ordered pairs, the -5 is x and 16 is y.
The equation would look like this:
16=30x-14
Add 14 on both sides
14+16=30
30=30x
divide by 30 on both sides
1=1
a. Yess
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution.
In the theory of probability, the central limit theorem states that the distribution of a sample mean approximates a normal distribution as the size of the sample increases. For the central limit theorem to hold, it is necessary that the sample size at least cross a margin of 30. Having a sufficiently larger sample size can predict the characteristics of the sample more accurately. The central limit theorem is applicable when we are analyzing large data sets.
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what is t - 18 = 6 can you help me
Answer:
[tex]\boxed{\sf{t=24}}[/tex]
Step-by-step explanation:
Find the value of t, to isolate on one side of the equation.
t-18=6
First, add by 18 from both sides.
[tex]\rightarrow \sf{t-18+18=6+18}[/tex]
Solve.
Add the numbers from left to right.
6+18=24
[tex]\Rightarrow \boxed{\sf{t=24}}[/tex]
Therefore, the final answer is t=24.
The answer should have a positive sign.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{t - 18 = 6}[/tex]
[tex]\large\text{ADD \boxed{\textsf{18}} to BOTH SIDES:}[/tex]
[tex]\mathsf{t - 18 + 18 = 6 + 18}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{-18 + 18}} because it gives you 0.}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{6 + 18}} because it gives you the answer of the t-value.}[/tex]
[tex]\large\text{New equation: }\mathsf{t = 6 + 18}[/tex]
[tex]\mathsf{t = 6 + 18}[/tex]
[tex]\mathsf{t = 24}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{t = 24}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Which subset of real numbers is the best one to use to describe discrete data?numbers of students in a school district, the number of home runs hit by a baseball team, etc..,
GIVEN
The subset that best describes discrete data.
SOLUTION
Discrete data is a count that involves integers — only a limited number of values is possible.
Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers. These data are usually prefixed by "the number of..."
Whole numbers are the best for describing discrete data.
ANSWER
Whole numbers are the best subset of real numbers to describe discrete data.
product of (-12)(-8)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{GUIDE TO FOLLOW: }[/tex]
• [tex]\large\textsf{2 negatives equal positive}[/tex]
• [tex]\large\textsf{2 positives equal positive}[/tex]
• [tex]\large\textsf{1 negative \& 1 positive equal negative}[/tex]
• [tex]\large\textsf{1 positive \& 1 positive equal negative}[/tex]
[tex]\large\textsf{SOME OPERATIONS MAY BE DIFFERENT THAN OTHERS!}[/tex]
[tex]\large\textsf{ANYWHO, LET US ANSWER THIS QUESTION, SHALL WE? }[/tex]
[tex]\mathsf{(-12)(-8)}[/tex]
[tex]\mathsf{= 12(8)}[/tex]
[tex]\mathsf{= 96}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{96}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A and B are supplementary angles. If mA = (3x - 28)° and
m/B = (x − 4)°, then find the measure of A.
Answer:
A = 131°
Step-by-step explanation:
Supplementary angles sum 180°
A + B = 180°
(3x - 28) + (x - 4) = 180
4x - 28 - 4 = 180
4x - 32 = 180
4x = 180 + 32
4x = 212
x = 212/4
x = 53
Then:
A = 3x - 28
A = 3*53 - 28
A = 159 - 28
A = 131°
B = x - 4
B = 53 - 4
B = 49°
Check:
131° + 49° = 180°
Answer:m∠A=33
Step-by-step explanation:
4/y+2 = 10/5y
solve for y
Answer:
y = - 1
Step-by-step explanation:
[tex]\frac{4}{y}[/tex] + 2 = [tex]\frac{10}{5y}[/tex]
multiply through by 5y to clear the fractions
20 + 10y = 10 ( subtract 20 from both sides )
10y = - 10 ( divide both sides by 10 )
y = - 1
(x^4/7^-8)^7
Solve asap pls
Answer: x=2
Step-by-step explanation: (x^4/7^-8 )^7
(4x/-56)^7 (7×8=56)
4x/-8
x/-2
x = 2
what is the slope of the line represented by the equation 4/5x -3
The slope of the line represented by the equation; 4/5x - 3 is; 4/5.
What is the slope of the line represented by the equation 4/5x - 3?It follows from the task content that the slope of the line represented by the equation; (4/5)x - 3 is to be determined.
Recall, from line geometry and equation of lines;
The slope-intercept form of the equation of a line, y is given as; y = mx + c.
Where, m is the slope and c is the y-intercept.
Therefore, by comparison of the equation defined as; 4/5x - 3; it follows that the slope of the equation is; 4/5.
Ultimately, the required slope is; 4/5.
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4560=12 ÷ y
What is y equal to?
Answer:y=1/380
Step-by-step explanation:
if you are trying to do y divided by 12 it would be 4560x12
Which graph represents data used in a linear regression that produces a correlation coefficient closest to -1?
What does the letter "L" stand for in the simulation?
Answer: d
Step-by-step explanation: ion know man but i looked it up and got it right
You deposit $200 each month into an account earning 4% interest compounded monthly.
a) How much will you have in the account in 25 years?
$
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
1. There will be $102, 826 in the account in 25 years.
2. The total amount of money you will put into the account is $60, 000
3. The total interest that you would have earned is $42,826.
How do you calculate total interest?For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)
When we insert the values, it will be
FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))
= 102, 825. 9. If we round this up, we should get
$102, 826
For us to calculate the total amount of money you put into the account, we should us the formula;
Total Deposits = Monthly Deposit x Number of Months
If we insert the values it wil be
200 x (25 x 12)
60,000
Lasty, if we are to find the total interest earned:
Total Interest = Future Value - Total Deposits
$102, 826 - 60,000
= $42,826
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According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29,
2005, the national debt was 4.974 x 10^12 dollars. Find the amount of increase in the national debt from September of 2005 to September of 2015.
Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.
What is scientific notation?Scientific notation simply means a way of expressing numbers that are either too large or too small.
The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,
2005, the national debt was 4.974 x 10^12 dollars.
The increase will be the difference between the two notations. This will be:
= 1.815 x 10^13 - 4.974 x 10^12
= 1.3176 × 10^13
The increase is 1.3176 × 10^13.
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The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.
Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.
So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³
Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
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Can you help me pls this was very hard for me
Given:
The equation is,
[tex]\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}[/tex]Explanation:
Simplify the right hand side of equation.
[tex]\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}[/tex]From left side and right side of equationn it can be observed that,
[tex]-8ax^2=24x^2\text{ and (-3a+16)x=}25x[/tex]Simplify the equation for a.
[tex]\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}[/tex]OR,
[tex]\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}[/tex]So value of a is -3.
Option B is correct.
84 minutes for 32 songs = 42 minutes for _____
songs
Answer: 84 minutes for 32 songs= 42 minutes for 16 songs.
Step-by-step explanation: All I had to do was divide 84 by two and divide 32 by 2.
84/2=42
32/2= 16 songs.
Answer: 16 songs.
84 dived by 2 equals 42.
Do 32 divided by 2 and it gives us 16.
a bakery uses 3 3/5 cups of oats to make 2 4/7 pounds of oatmeal cookies how many cups of oats are required per pound of cookies
Answer: 7/5 or 1 2/5
Step-by-step explanation:
Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.
You need to find the unit price.
So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7
You need to do the same thing to 3 3/5 cups.
3 3/5 as an improper fraction is 18/5
2 4/7 as an improper fraction is 18/7
Now to divide you need to keep, change, and flip
keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18
18/5*7/18=7/5
7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies
Find the measure of the missing arc (dont worry about the degree symbol)
The formula to calculate the missing arc is,
[tex]m\angle T=\frac{1}{2}\times m\angle arcTS[/tex]where,
[tex]m\angle arcTS=146^0[/tex]Therefore,
[tex]\begin{gathered} m\angle T=\frac{1}{2}\times146^0=73^0 \\ \therefore m\angle T=73^0 \end{gathered}[/tex]Hence, the answer is
[tex]\begin{equation*} m\angle T=73^0 \end{equation*}[/tex]can anyone please solve this 3 dimensional equation?
The solution for the system of equations of three variables is:
x = 4
y = -1
z = -3
Or (4, -1, -3) written as a point.
How to solve the system of equations?
Here we have a system of equations on 3 variables, the system is:
3x + 2y + z = 7
5x + 5y +4z = 3
3x + 2y + 3z = 1
Notice that the "x" and "y" coefficients in the first and last equation are the same ones, so we can take the difference between these to get:
(3x + 2y + 3z ) - (3x + 2y + z ) = 1 - 7
2z = -6
z = -6/2 = -3
So the value of z is -3.
Replacing that in the first and second equation we get:
3x + 2y - 3 = 7
5x + 5y + 4*(-3) = 3
Now we can simplify these:
3x + 2y = 10
5x + 5y = 15
We can divide the second one by 5 to get:
(5x + 5y)/5 = 15/5
x + y = 3
Isolating x, we get:
x = 3 - y
Now we replace that in the other equation:
3*(3 - y) + 2y = 10
9 - y = 10
9 - 10 = y
-1 = y
Now we know the value of y, finally with:
x = 3 - y
We can get the value of x:
x = 3 - (-1) = 4
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Paige makes bracelets and sells them online for $15 and $20. She buys all of her supplies in bulk. The table shows her sales for the last 3 months. During the 3-month period represented by the table, she ordered supplies twice. Each time, she spent $292.58 on supplies.
Paige's profit for the three-month period given the information provided in the question is $569.84.
What is the profit?
Profit is the difference between total revenue and total cost. Revenue is the product of total units sold and the price per output.
Profit = revenue - cost
Revenue from selling the $15 bracelet = total bracelets sold for the 3 months x price of the bracelet
(8 + 11 + 22) x 15
41 x $15 = $615
Revenue from selling the $20 bracelet = total bracelets sold for the 3 months x price of the bracelet
(7 + 6 + 14) x $20
27 x $20 = $540
Total revenue = $615 + $540 = $1,155
Total cost = $292.58 x 2 = $585.16
Profit = $1,155 - $585.16 = $569.84
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Jonathon's family is driving to a foot ball game. they have completed 40% of the trip they have traveled 20 miles how far is the trip
The total distance of the trip is 50 miles
How to determine the length of the trip?From the question, we have the following parameters
Distance completed = 40%
Distance travelled = 20 miles
Represent the total distance with x
So, we have the following equation
Distance travelled = Distance completed *Total distance
This gives
Distance travelled = Distance completed * x
So, we have
20 miles = 40% * x
Divide both sides by 40%
x = 50 miles
Hence. the length of the trip is 50 miles
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. based on a 19 bag sample where the mean is 437 grams and the varicance is 441, is there sufficent evidence at the 0.025 level that the bags are underfilled?
Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .
In the given question, we shall check the bag is underfilled at given level or not .
We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :
H₀ : u = 411 : the bags are not underfilled
Hₜ : u < 411 : the bags are underfilled
Check it now using statistic Z-test and the test Statistic formula is given by
= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .
From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21
Including all of the above variables in formula
Z = (437-411)/21/√19
= 26/21/√19
= 5.395
This is right -tail test in statistic Z -test
P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )
The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025
P- value >α , this implies that Null hypothesis is not Rejected .
There is sufficient evidence to suggest that bag is not underfilled.
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Suppose a ray of sunlight bounces off a window at a point P, and that
line mis perpendicular to the window at point P. Angles of inflection
and reflection are created as shown.
Write an equation and then solve for x.
m
-
(3x - 10)°
(2x + 5)°
P
By applying the law of reflection to the ray of sunlight, the value of x is equal to 5.
What is the law of reflection?The law of reflection is a theorem which states that the magnitude of the angle of incidence is equal to the magnitude of the angle of reflection when a ray of light is reflected off a surface such as a plane mirror.
Mathematically, law of reflection can be represented or modelled by this mathematical expression:
sinθi = sinθr
Where:
sinθi represents the angle of incidence.sinθr represents the angle of reflection.By applying the law of reflection to the ray of sunlight (see attachment), we have the following equation:
(3x - 10)° = (2x + 5)°
3x + 2x = 10 + 5
5x = 15
x = 15/3
x = 5.
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