From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
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a plane, 50 miles away from its destination, is flying toward the airport at an altitude of 30,500 feet. later, this same plane is 20 miles from the airport and has descended to an altitude of 18,000 ft. how far has the plane flown?
Using the geometry from the question and using the Pythagorean theorem with the distance provided, The answer is 30.09 miles.
What is unit conversion?By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units.
What is Pythagorean theorem and it's formula?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
It's formula is:
[tex]h^{2} = p^{2} +b^{2}[/tex]
h1=30500 feet = 5.77 miles
d1= 50 miles
h2= 18000 feet = 3.4 miles
d2= 20 miles
for right angle triangle,
height = h1-h2 = 2.37 miles
distance = 50-20 = 30 miles
plane flown = [tex]\sqrt{2.37^{2}+30^{2}}[/tex]
=30.09 miles
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Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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a random sample of size 36 is taken from a population with mean 17 and standard deviation 6. the probability that the sample mean is greater than 18 is?
The probability that the sample mean is greater than 18 as calculated is 0.8413.
Given data,
n = 36, sample size
μ = 17, population mean
σ = 6, population standard deviation
when x = 18
z = (18 - 17)/1 = 1
P(x <18) = 0.8413
Therefore , the probability = 0.8413
A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.
While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.
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Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
question 5: on a given day, there is a car accident reported at the intersection of victory blvd and richmond avenue with a probability 0.05. what is the probability that there are at most 2 car accidents reported thoughout a month?
The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:
Cumulative probability is equal to (number of events * e)/(average number of events per time period).
(Number of events / (-average number of events per time period)!)
In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:
Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.
That amounts to:
Probability total = 1 + 0.05 + 0.0025
which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.
question in screenshot (need help ASAP)
Ma Baker's Pies charges $12 for a pumpkin pie and $14 for an apple pie. Last week, they sold a third as many pumpkin pies as apple pies, for a total of $5,400. How many pumpkin pies were sold last week?
20 POINTS!!!!
The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,
Who was the first American author of a recipe for pumpkin pie?This type of pie appears to have been made by some of the early colonists as well—but, by 1796, when Amelia Simmons' American Cookery, the first cookbook written by an American and published in America, appeared, pumpkin pie had evolved into a familiar form that we would recognize today.The cost of one apple pie = $6They stewed pumpkins or filled a hollowed out pumpkin shell with milk, honey and spices, and then baked it in hot ashes. Northeastern Native American tribes grew squash and pumpkins. The Native Americans brought pumpkins as gifts to the first settlers, and taught them the many uses for pumpkin.Types of squashes were first introduced to Europe in the form of Pumpkin seeds brought back from the Americas by Columbus himself. The introduction of pumpkins affected the way food was consumed in Europe. In both Italy and Spain, pumpkins were used in puddings and soups, making food much tastier and more enjoyable.And cost of one pumpkin pie = $8
Let the cost of one apple pie be $x
And cost of one pumpkin pie be $ y.
According to given problem,
For Lisa : sold 8 apple pies and 4 pumpkin pies for a total of $80
8x + 4y = 80 ------------(1)
For Shreya : sold 8 apple pies and 3 pumpkin pies for a total of $72
8x + 3y = 72 ---------------(2)
Solving equation (1) and (2), to get x and y.
Subtract equation (2) from equation (1)
i.e 8x + 4y - (8x +3y) = 80 - 72
or 8x - 8x + 4y - 3y = 8
or y = 8
And x = 6 { 8x + 4×8 = 80 or x = (80 - 32)/8 = 48/8 = 6 }
Hence, the cost of one apple pie = x = $6
And cost of one pumpkin pie = y =$8
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Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
Identify the slope and y-intercept of each linear function's equation. X -3=4 slope = 1; y-intercept at -3 y=1-3x slope =-3; y-intercept at 1 y = 3x. - 1 slope =-1; y-intercept at 3 -x+3=y slope = 3; y-intercept at -1
Using slope-intercept form, the slope and y-intercept of the equation are 1 and - 7 respectively
Slope and Y-interceptThe slope-intercept formula is often used to calculate or identify the slope, the y-intercept, the x-intercept, or the equation of a straight line in the equation.
The slope of the line is defined as the rate of change of the y - axis to the change in the x - axis.
The formula is represented as;
m = Δy / Δx
where Δ represent the change
The y-intercept of a line is the point at which the line touches the y-axis of the graph.
With these information, we can write a slope-intercept form of a straight line which is given as;
y = mx + c
m = slopec = y-interceptIn the given question;
x - 3 = 4
Let's collect like terms
x - 3 - 4 = x - 7
The equation can be rewritten as y = x - 7
In this case, the slope is 1 and the y-intercept is - 7
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STEP BY STEP please help me asap please !!!???
Answer:
(A) 19 times, 16 people.
Step-by-step explanation:
There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.
The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.
Since the Caterpillar cannot run a fraction of a time, it must run 19 times.
There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.
Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.
Tell me if this helped :)
Need help and fast please and thank you.
y= 0.141(15) + 0.842 =
y = 2.115 + 0.842
= 2.957
no explanation
suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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Round 24.07 to the nearest tenths. It’s for an app it got a number line
24.07 rounded to the nearest tenth is 24.1
one number is 431 more than the other, their sum is 679, find the two numbers
Answer:
Step-by-step explanation:
Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.
Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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k3-4j=12,wen k =8,j=2
With the Application of Arithmetic operators the value of given equation is 492.
what is Arithmetic operators?
an operator that works with groups and numbers in arithmetic. The prefix and the binary plus (+) and minus (-) symbols are the only arithmetic operators in AHDL that are supported for Boolean expressions.
solution:
sub k =8,j=2 in equation k^3-4j = 12
Therefore, (8)^3 - 4 (2) = 12
512 - 8 - 12 = 0
492 is the value.
Therefore the value of given equation is 492
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Complete Question:
What Is The Answer
k3 - 4j +12, when k=8, j=2
Hello can someone help me out with these two questions!?!?! This will help me a lot thank you! :D
The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The inequalities are,
2( x +6 ) > -6( x +1) +2
2x + 12 > -6x - 6 + 2
2x + 6x > -12 - 6 +2
8x > -16
x > -2
-3x - 1 ≥ 20
-3x ≥ 21
x ≥ -7
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Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The
area of the patio is 350 ft2. Find the base. Round your answer to the nearest foot.
Hint : Use A = bh.
We may calculate our answer using fractions and the fact that the base is 18.3 feet.
What are fraction ?The components of a whole or group of items are represented by fractions. A fraction consists of two components.
The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.
According to our question-
The patio is 280 square feet in size. locate the base.
Height = 5x Area = 280 feet square
Base = 6x
The parallelogram A's area can be expressed mathematically as;
Base + height equals area.
A = b×h
the values of area, base, and height are substituted.
280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)
Given that the base is 6x,
swapping out x's value.
Base = 6x = 6(√(280/30))
Base=18.3 feet
18.3 ft tall is the base
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Answer:
At short 18.7 ft is the answer
Using composition of functions, determine if the two functions are inverses of each other. A. No, because the functions contain different operations. B. Yes, for all values x ≥ 0. C. No, because the composition does not result in an answer of x. D. Yes, because F(x) is equal to –G(x).
Yes, for all values x ≥ 0. If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other.
What is composition of functions?Composition of functions is a mathematical operation that involves combining two functions to form a new function. To determine if two functions are inverses of each other using composition of functions, we need to first define the two functions and then determine if the composition of the two functions is equal to the identity function (f(x) = x).If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other. In this case, the correct answer is B: Yes, for all values x ≥ 0.To learn more about composite functions refer :
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Word Problems: (please write out the equations and solve it)
1. David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra
topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:
Independent variable:
Equation:
Use your equation to determine the total cost of the pizza with 3 extra
toppings.
The total cost of the pizza is
Dependent variable: t (total cost of the pizza)
Independent variable: x (number of extra toppings)
Equation: t = 10.50 + 1.50x
To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:
t = 10.50 + 1.50(3)
t = 10.50 + 4.50
t = 15.00
So the total cost of the pizza with 3 extra toppings is $15.00.
What is Dependent Variables?
The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.
What is Independent Variables?
Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.
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The median, or middle value, is 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The given set of numbers is in ascending order.
There are 15 numbers.
The middle number will be the 8th number.
8th number = 64
Thus,
The median is 64.
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yes Are these polygons congruent? 1.5 cm 4 cm 3 cm no 2 cm
Graph the inequality on the axes below.
3x + y ≤ -3
Answer:
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points. The inequality is ≤ that means the solutions are the points on the line and below the line. This is shown in the pink shading.
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y-axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points.
The inequality is ≤ which means the solutions are the points on the line and below the line. This is shown in the pink shading.
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Please help asap ill give brainlest
The solutions to the equation word problems are as follows;
1) Amount jane will have is 50 + 2d
2) Amount Elis will have = 24 + 6d
3) The equation is; 50 + 2d = 24 + 6d
4) Amount each has saved = $63
How to solve Algebra Word Problems?We are given that;
Amount Jane has = $50
Amount Elis has = $24
Amount saved by Jane each day = $2
Amount saved by Elis each day = $6
1) After d days of saving, amount jane will have is;
A = 50 + 2d
2) After d days of saving, amount Elis will have is;
A = 24 + 6d
3) The equation that will be used to show when Joan and Elis would have saved same amount is;
50 + 2d = 24 + 6d
4) 50 + 2d = 24 + 6d
26 = 4d
d = 26/4
d = 6.5 days
Amount each has saved = 50 + 2(6.5) = $63
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A cereal box says that now it contains 20% more originally it came with 18.5 ounces of cereal how much cereal does the box come with now
Answer:
Step-by-step explanation:
Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.
A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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write an equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4
An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.
What is Parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
12 = 4(9) + b
12 = 36 + b
b = -24
The equation will be y= 4x -24.
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r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
a car and a motorcycle leave at noon from the same location, heading in the same direction. the average speed of the car is mph slower than twice the speed of the motorcycle. in two hours, the car is miles ahead of the motorcycle. find the speed of both the car and the motorcycle, in miles per hour.
The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.
Let M = speed of the motorcycle.
Hence, speed of the car = 2M - 30.
Distance covered = Time taken x Speed.
Hence in 2 hours,
Distance covered by motorcycle = 2M
Distance covered by car = 2(2M-30).
Given, the car is 20 miles ahead of the motorcycle.
Hence,
2(2M-30) = 2M + 20
4M-60 = 2M + 20
2M = 80
M = 40
2M-30 = 2(40)-30 = 80-30 = 50
Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.
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Find the value of a if the line line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x +a
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.
To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:
y = -x + 4
f(x) = x^2 - 5x + a
Then, we can substitute the equation for the function into the equation for the line:
-x + 4 = x^2 - 5x + a
We can then solve this equation for a by moving all the terms to one side:
-x + 4 - x^2 + 5x = a
-x^2 + 6x - 4 = a
We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.
The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:
2x - 5 = -1
2x = -6
x = -3
Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:
f(-3) = (-3)^2 - 5(-3) + a
f(-3) = 9 + 15 + a
f(-3) = 24 + a
Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:
y = -(-3) + 4
y = 3 + 4
y = 7
Substituting this back into the equation for the function, we get:
f(-3) = 24 + a = 7
a = 7 - 24
a = -17
Therefore, the value of a is -17.
what do you mean by tangent?
A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.
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