By substitution; x = 4 and y = -31
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.
y=-6x-7 --- 1
7x+y=-3 --- 2
Substituting y as 6x - 7 in equation 2
7x + (-6x - 7) = -3
7x - 6x - 7 = -3
x - 7 = -3
x = -3 + 7
x = 4
Substitute x as 4 in equation 1
y = -6x - 7
y = -6(4) - 7
y = -24 - 7
y = -31
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find the slope of this line
Answer:
-3
Step-by-step explanation:
Select a point on the red line that crosses the graph at a corner like point (2,2). Start at the middle of the graph and go 2 spaces to the right on the x axis and then 2 spaces up. Now you will be a the point (2,2). Do you see how the right line is hitting at the top left corner of the square?
From this point, count how many spaces up and how many spaces to the left to get to the next spot that the red line touches a corner. If you go up 3 spaces and left 1, you have found the next corner. The slope is -3/1 or -3.
The slope is negative because the x and y's are going in different directions, as the x is getting bigger, the why is getting smaller, or another way of looking at it, is that I went up to the find slope and up is positive, but then I went left 1 and left is toward the negative numbers. A positive divided by a negative is a negative, so the slope is negative.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x2 – 3
y > –x2 + 2
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is an expression that shows the non equal comparison of two or more numbers and variables
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)
How to modify the graphsThe complete question is in the attached image (the first graph)
From the graph, we have:
f(x) = x^2 - 3 and g(x) = -x^2 + 2
To derive y ≤ x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.
To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than
How to identify the solution setThe inequalities of the graphs become
y ≤ x^2 - 3 and y > -x^2 + 2
From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)
Hence, the solution of the set of inequalities is (±1.581, -0.5)
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A metallurgist has one alloy containing 30% copper and another containing 62% copper. How many pounds of each alloy must be used to make 50 pounds of a third alloy containing 32% copper?
The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.
How to estimate proportions of ingredients for an alloy by weighted averages
In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:
(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)
32 · 50 = 30 · x + 62 · (50 - x)
32 · 50 = 30 · x + 62 · 50 - 62 · x
32 · x = 30 · 50
x = 46.875
The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.
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PLS I NEED HELP
2. Write the rule for the linear function. Remember a function rule is written using f(x).
Answer:
[tex]f(x) = \frac{1}{2}x + 5[/tex]
Step-by-step explanation:
So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.
The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]
The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.
We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run
[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]
So plugging this into the slope-intercept form you get the function
[tex]f(x) = \frac{1}{2}x + 5[/tex]
Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem
4. Which expression, the original expression or the expanded expression, involves finding the total cost first, then calculating the tax on that total?
Answer:
$4.50
Step-by-step explanation:
Okay so, first add both.
50+40 is 90, then multiply 90 by the tax percent which is
90x5%=4.5
If expression then,
x=money that they have to pay.
5%(50+40)=x (the original)
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16) Write the scientific notation.
5.5 billion
If f(x) = 3x +3, which of the following is the inverse of
f(x)?
Answer: [tex]f^{-1}(x)=\frac{x-3}{3}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=3y+3\\\\x-3=3y\\\\y=\frac{x-3}{3}\\\\\therefore f^{-1}(x)=\frac{x-3}{3}[/tex]
A preimage can never be congruent to Which of the following is the notation for a translation that moves a figure 2 units right and 2 units up?
(x, y) → (2x, 2x)
(x, y) → (x − 2, y − 2)
(x, y) →
(x, y) → (x + 2, y + 2)its image.
The notation for the translation is (x, y) → (x + 2, y + 2)
How to determine the translation?The translations are given as:
2 units right2 units upThe above implies that we add 2 to the x coordinate and 2 to the y coordinate.
So, we have:
(x, y) → (x + 2, y + 2)
Hence, the notation for the translation is (x, y) → (x + 2, y + 2)
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Prove: An odd plus an odd
equals an even.
(2m + 1) + (2n + 1) = [ ? ]m + [ ]n + [ ]
= 2(m+n+ [])
= even
[tex](2m+1)+(2n+1)=2m+2n+2\\\\=2(m+n+1)[/tex]
Simplify the problem
Answer:
B. 2√3+4
Step-by-step explanation:
3√3+4−√3
=2√3+4 (Decimal: 7.464102)
A boat travels 50 miles downstream in 2 hours and it takes 5 hours to travel back upstream. What is the speed of the boat if it were in still water and what is the speed of the river current?
The 50 mile distance traveled downstream and back that takes 2 hours and 5 hours respectively gives;
The speed of the boat in still water = 17.5 mphThe river current flows at 7.5 mphHow can the boat speed be calculated?Let v represent the speed of the boat and let u represent the speed of the river current.
Distance the boat travels downstream = 50 miles
Time taken to travel downstream by the boat = 2 hours
Time taken to travel back upstream = 5 hours
[tex]velocity = \frac{distance}{time} [/tex]
Therefore;
Which gives;
[tex]v + u = \frac{50}{2} = 25...(1)[/tex]
v + u = 25[tex]v - u = \frac{50}{5} = 10...(2)[/tex]
v - u = 10Adding equation (1) to equation (2) gives;
(v + u) + (v - u) = 2•v = 25 + 10 = 35
2•v = 35
v = 35 ÷ 2 = 17.5
The speed of the boat, v = 17.5 mphu = 25 - v
Which gives;
u = 25 - 17.5 = 7.5
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A ladder is 8 feet 2 inches tall. How tall is it in inches?
Answer:
The ladder is 98 inches tall in inches.
Step-by-step explanation:
1 foot = 12 inches.⇒ 8 (feet) × 12 (inches) = 96 inches
⇒ Add the extra 2 inches
⇒ 98 inches tall.
What is the Pythagorean theorem
Answer:
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Pythagoras Theorem Equation
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Answer:
The Pythagoras theorem states that:The sum of the squares on the edges of a right triangle angle is equal to the squareon the hypotenuse.Mathematically stated as: a² +b² = c²Hope this helps.Good luck ✅.Hellp please i need this super fast please
The surface area of the cone is 282.6 square centimeters.
How to get the surface area?
For a cone of radius R and height H, the surface area is given by:
[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]
Where pi = 3.14
In this case, we have:
R = 10cm/2 = 5cmH = 12 cm[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]
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A city mayor in Michigan is planning the number of new snow plows he must purchase to remove the snow next winter. The
average snowfall in the past 10 years has been normally distributed with a mean of 112 inches and a standard deviation of
14 inches. What amount, in inches, separates the lowest 20% of the means of yearly snowfall in the past 10 years from the
highest 80%?
The amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
Given mean of 112 inches, standard deviation of 14 inches.
We are required to find the amount that separates the lowest 20% ofthe means of yearly snowfall in the past 10 years from the highest 80%.
a) Bottom 20% would have a z score of -0.8416.
b) Top 80% would have a z score of 0.842.
Use the z formula to find the raw score.
z=(X-m)/sd
X=the raw score
m= mean
sd=standard deviation
Putting the value of low score.
-0.8416=(X-112)/14
X=-11.7824+112
=100.2176
Putting the values of high score.
0.842=(X-112)/14
X=123.788
The amount that seprates the lowest from highest is 123.788-100.2176
=23.57 inches.
Hence the amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
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Let m = X^2 + 3.
What is (x^2+3)^2+7x^2+21=-10 in terms of m?
OR
Let m=x^2+3m=x
2
+3m, equals, x, squared, plus, 3.
Which equation is equivalent to (x^2+3)^2+7x^2+21=-10(x
2
+3)
2
+7x
2
+21=−10left parenthesis, x, squared, plus, 3, right parenthesis, squared, plus, 7, x, squared, plus, 21, equals, minus, 10 in terms of mmm ?
The Equation in terms of m, m^2+7m+10=0
What is substituting in the equation ?
substituting means changing or replacing the values in the given equation.
Calculation:
Given equation is (x^2+3)^2+7x^2+21=-10
and m= X^2 + 3.
make the given equation in the form X^2 + 3,
now,
(x^2+3)^2+7x^2+21=-10
(x^2+3)^2+7(x^2+3)=-10
where,
X^2 + 3= m
after putting the value or replacing the values
we get, m^2+7m=-10
m^2+7m+10=0
the above equation is in the form of "m".
The Equation in terms of m, m^2+7m+10=0
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Answer:
m^2+7m+10=0
Step-by-step explanation:
Give brainly lol
What is the simple interest rate on a $2100 investment paying $1,559.46 interest in 15.8 years?
The simple interest rate is 4.7%
How to determine the simple interest rate?The given parameters are:
Principal = $2100
Interest = $1,559.46
Time = 15.8 years
The simple interest is calculated as:
I = PRT
Make R the subject
R = I/(PT)
So, we have:
R = 1559.46/(2100 * 15.8)
Evaluate
R = 0.047
Express as percentage
R = 4.7%
Hence, the simple interest rate is 4.7%
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In the binomial probability distribution function, nCx represents the number of ways of obtaining x successes in n trials. True or False?
In the binomial distribution for probability function, [tex]_{n}C_{x}[/tex] represents the number of ways of obtaining x successes in n trials: True
What is binomial distribution?The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
The underlying assumptions of the binomial distribution are that each trial has exactly one possible outcome, that each trial has the same success chance, and that each trial is either independent of or mutually exclusive with every other trial.
As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.
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How many three-digit positive integers have three different digits?
648 is the three-digit positive integers have three different digits
According to the statement
we have given that there are three positive digit number are formed with three distinct digits.
And we have to find that the how many words are formed with distinct numbers.
So, to solve this type of problem the Combination formula is best.
Because it provides the all possibilities that from how many ways numbers are formed.
So, from a combination formula
here we take 9 two times because first time when we let a number then remaining numbers are 9. and second time remaining numbers are also 9 because we let the distinct number but for third number there will be a probability that choosing number will be same.
So, Three digit positive number become from 9*9*8 =648
So, 648 is the three-digit positive integers have three different digits.
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Which of the following functions has a vertical asymptote at x=−1, a horizontal asymptote at f(x)=5, and a root at x=−3?
Answer:
Step-by-step explanation:
B :10/(x+1) +5
3
Seven students cut 5 inches of thread from a spool for a school project. What number represents the change in the
amount of the thread on the spool?
O-40 inches
3
O-35 inches
-29 inches
-26 inches
Answer:
35 inches
Step-by-step explanation:
7 x 5 = 35 lol
The number which represents a change in the amount of thread on the spool exists 35 inches.
What are mathematical operations?In mathematics, an operation exists as a process that takes zero or more input values to a well-defined output value.
Given: Length of thread a student cuts = 5 inches
Total number of students that cut thread = 7
Length of thread a student cuts = 5 inches
Length of thread 7 student cuts = 5 [tex]*[/tex] 7 = 35 inches
The negative length that 7 students cut from the spool exists the number that represents a change in the amount of thread.
The number which represents a change in the amount of thread on the spool exists 35 inches.
Therefore, the correct is option b) 35 inches.
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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.11 gallons. A previous study found that for an average family the standard deviation is 1.8 gallons and the mean is 16.2 gallons per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.
The sample size required is mathematically given as
n=1454
What is the Margin of error?Generally, the equation for Margin of error is mathematically given as
[tex]M=Z_{\alpha/2} > \frac{\sigma}{\sqrt{n}}[/tex]
Therefore
[tex]M= 0.11 \leq \frac{ 2.33*1.8}{\sqrt{n}}\\\\\sqrt{n} \leq 38.127[/tex]
n=1453.69.
In conclusion, The sample size required is mathematically given as
n=1454
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The following data depicts the relationship between the Amount spent on insurance and the amount of inventory loss.
X = Amt spent on protection
Y = Amt of inventory lost or stolen
The least squared regression line : Y = 86.43 – 38.47 X
How much will the amount of loss in inventory be if the amount of protection is $6.39? Leave your answer to 2 decimal places.
Using the given regression line, it is found that the amount of loss in inventory will be of $159.39.
What is the regression line?The regression line is:
Y = 86.43 - 38.47X
In which:
X is the amount spent on protection.Y is the amount of inventory lost.In this problem, we have that X = $6.39, hence:
Y = 86.43 - 38.47 x 6.39 = -$159.39.
The amount of loss in inventory will be of $159.39.
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Which point is a solution to the system?
Answer:
C. (2;9)
Step-by-step explanation:
for more details see the attachment.
solve this equation -1/2 ( -3y + 10)
Answer:
3/2y-5
Step-by-step explanation:
Nicky opened a savings account with a single deposit of R1 000 on 1 April 2011. She
then makes 18 inonthly deposits of R700 at the end of every month. Her first payment
is made on 30 April 2011 and her last payment on 30 September 2012. The account
earns interest at 15% per annum compounded monthly.
Determine the amount that should be in her savings account inmediately after her last
deposit is made (that is on 30 September 2012).
The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
What is the future value?The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.
The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.
Data and Caluclations:N (# of periods) = 18 months
I/Y (Interest per year) = 15%
PV (Present Value) = R1,000
PMT (Periodic Payment) = R 700
Results
FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)
Sum of all periodic payments = R12,600 (R700 x 18)
Total Interest = R1,682.91
Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
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An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotrips,” (1986, Vol. 292, pp. 879–882)] found that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. The traditional method was 78% effective.
(a) Is there evidence that the success rate for PN is greater than the historical success rate? Find the P-value.
(b) Explain how the question in part (a) could be answered with a confidence interval.
The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
According to the statement
we have given that the percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. And
The traditional method was 78% effective.
we have to show that the success rate for PN is greater than the historical success rate then
we use the percentage formula to find the success rate of the new method. So,
(a) Total patients = 350
Success rate in number of patient = 289
Percentage of success rate = (289/350)*100
Then after calculating
Percentage of success rate = 82.57%
It is clear that the outcome success rate is 82.57% which is greater than traditional method.
(b) we have a 95% confidence that the success rate of new method is higher than the older method from a confidence interval of 2.262 and 3.67
So, The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
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For f(x) = 2x + 1 and g(x) = x² - 7, find (f+ g)(x).
Answer:
(f + g)(x) = x² + 2x - 6
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 ← in standard form
Given: 3x+12=8x−18 algebraic proofs
Step Reason
3x+12=8x−18
12=5x−18
30=5x
6=x
x=6
The value of x comes out to be 6 from the algebraic equation.
Solving the Given Algebraic Equation for x:
Given algebraic equation is,
3x + 12 = 8x - 18
⇒ 12 = 8x - 3x -18
8x - 3x - 18 = 12
5x - 18 = 12
5x = 12 + 18
5x = 30
x = 30 / 5
x = 6
What is an algebraic equation?
A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.
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Which number line represents the solutions to |x + 4| = 2?
Answer: Option 1
Step-by-step explanation:
[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]
Solve Absolute Value.
| x + 4 | = 2
We know either x + 4 = 2 or x + 4 = −2
x + 4 = 2 (Possibility 1)
x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)
x = -2
x + 4 = −2 (Possibility 2)
x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)
x = -6
Answer: x = - 2 or x = -6
Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.