Answer:
f[g(4)] = 4
Step-by-step explanation:
Given table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]
f[g(4)] is a composite function.
When calculating composite functions, always work from inside the brackets out.
Begin with g(4): g(4) is the value of function g(x) when x = 4.
From inspection of the given table, g(4) = -6
Therefore, f[g(4)] = f(-6)
f(-6) is the value of function f(x) when x = -6.
From inspection of the given table, f(-6) = 4
Therefore, f[g(4)] = 4
As we can see
g(4)=-6So
f(g(4))f(-6)4Write an equation of a line with a slope of 2/3 whose graph will cross the y-axis at the point (0, 12.65).
Therefore , the solution of the given problem of slope intercept comes out to be y = 0.66x +12.65.
What exactly is a slope-intercept form?The gradient intercept method can be used once you are satisfied that Y = mx + b holds true. The direction form can be used to illustrate a hypothesis for a line by focusing on a single point directly and its slope. The slope is determined by the increase across the run and is first represented by the point form (x,y). The slope can be determined using slope intercept method, which is y = mx + b. (0, b). The direct form is a method for formulating a prediction equation for a line by making just one precise declaration about a vector slope.
Here,
Given : slope = 2/3
and coordinates = (0 , 12.65)
Thus ,
the equation of the given line by using formula of slope intercept:
=> y- y1 = m(x-x1 ) + c
=> y - 12.65 = 2/3*x
=> y = 0.66x +12.65
Therefore , the solution of the given problem of slope intercept comes out to be y = 0.66x +12.65.
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The work shows the first steps of writing a partial fraction decomposition. Startfraction 3 x + 9 over (x + 1) (x minus 5) endfraction = startfraction a over x + 1 endfraction + startfraction b over x minus 5 endfraction 3 x + 9 = a (x minus 5) + b (x + 1) 3 x + 9 = a x minus 5 a + b x + b what is the partial fraction decomposition in terms of x?.
The partial fraction decomposition in terms of x for the given equation is:
3x + 9 = (a(x-5) + b(x+1))
To solve for a and b, we need to multiply both sides by (x+1)(x-5). This will give us:
3x² + 4x - 45 = ax - 5a + ax + b
Now we can move all the terms with an x to one side and all the terms without an x to the other side. This will give us:
3x² + 4x - ax + b = 45 - 5a - b
We can rearrange this equation to get the following:
3x² - ax + (4 + b) = (45 - 5a - b)
Now we can use the quadratic formula to solve for a and b:
a = (4 + b) + √(4²- 4×3×(45 - 5a - b))/ (2×3)
b = (45 - 5a - (3x² - ax)) / (4 + b)
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Answer:
It's C
Step-by-step explanation:
StartFraction 3 x + 9 Over (x + 1) (x minus 5) EndFraction = StartFraction negative 1 Over x + 1 EndFraction + StartFraction 4 Over x minus 5 EndFraction
In graphing a linear equation using the slope-intercept method, plot the y-intercept then use the x-intercept to locate the second point. (PLEASE HELP)
The slope-intercept method is a way to graph a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. This method allows you to find the slope and y-intercept of the line and use that information to graph the line.
An explanation graph is what?
A graph shows how two variables that are typically measured along one of a pair of axes at right angles relate to one another.
To graph a linear equation using the slope-intercept method, you can follow these steps:
Identify the y-intercept by looking for the constant term (b) in the equation. The y-intercept is the point where the line crosses the y-axis, so it will have an x-coordinate of 0.
Plot the y-intercept on the coordinate plane.
Identify the slope of the line by looking for the coefficient of the x-term (m) in the equation. The slope represents the steepness and direction of the line.
Using the slope and the y-intercept, pick a point on the x-axis and use the slope to find the corresponding point on the y-axis.
Plot the point found in step 4.
Plot the two spots and then draw a straight line through them.
Note that this method will work for any linear equation where y = mx + b, and can help you graph a line quickly.
Also note that there is another method to graph a linear equation, it's called the point-slope method which is starting from any point on the line and use the slope to locate the additional line points.
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How do you find the perpendicular distance between two lines in 3D?
To find the perpendicular distance between two lines in 3D, you can use the dot product of the vector joining the two lines and the cross product of the direction vectors of the two lines, divided by the length of the cross product vector.
To find the perpendicular distance between two lines in 3D, you can use the following method:
Write the parametric equations of the two lines: Line 1: x = x1 + tv, y = y1 + tw, z = z1 + tu and Line 2: x = x2 + sv, y = y2 + sw, z = z2 + su, where (x1,y1,z1), (x2,y2,z2) are the coordinates of the two lines, (v,w,u) and (s,t,r) is the direction vectors of the two lines respectively.Find the vector joining the two lines: (x2-x1, y2-y1, z2-z1)Find the cross product of the direction vectors of the two lines, this is the vector that is perpendicular to both lines.Take the dot product of the vector joining the two lines and the cross product of the direction vectors, and divide by the length of the cross product vector.The absolute value of the result obtained in step 4 is the perpendicular distance between the two lines.To learn more about 3-D Lines at
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(+6)-(-3) (+1)
That’s the first one then I have this one
(-3)-(-7)-(+8)
The integer value of both values is 10 and -4.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
A positive integer and a negative integer cannot be multiplied. A pair of positive integers have a positive product. Two negative integers add up to a positive number. A positive integer and a negative integer do not add up to a positive number.
Positive and negative numbers are used differently in everyday life. Although positive numbers are frequently employed everywhere, negative integers are also used to measure temperature because it is possible for a city's temperature to be either -4°C or -10°C.
(+6)-(-3) (+1)
⇒ 6 + 3 + 1 [using rules of integers, (-)(-) yields (+)]
⇒ 9 + 1
⇒ 10
(-3)-(-7)-(+8)
⇒ -3 + 7 - 8 [using rules of integers, (-)(+) yields (-)]
⇒ -3 - 8 + 7
⇒ -11 + 7
⇒ -4 [As -11 is greater than 7]
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Can all quadratic functions be written in factored form?
No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.
What are quadratic functions?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape. In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring." This terminology comes from the fact that a square's area is equal to its side length multiplied by itself. The Latin term quadratum, which means square, is where the word "quadratic" derives. No, factoring cannot be used to solve every quadratic problem. Because not all quadratic expressions, ax2 + bx + c, are factorable, this is the case.To learn more about quadratic functions refer to:
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WILL GIVE BRAINLIEST
Line segment MN joins the midpoints of two sides of the triangle below. The length of MN is half the length of the base of the triangle. What is the value of x in centimetres?
Answer:
48 centimeters
Step-by-step explanation:
This deals with the midline theorem.
The midline is defined by a seg that is joined by the midpoints of 2 sides.
The midline is half of the base, so if it is 10, the base is 20 cm.
You see that 26 cm is 1/2 of the hypotenuse because it is bisected, sot he whole thing is 26(2) or 52.
Now you have to solve for x using the Pythagorean theorem.
20^2 (400) + x^2 = 52^2 (2704)
Subtracted 400 from both sides to get x^2 by itself.
x^2 = 2304
Take the square root of both sides to isolate x (take the principle root)
x= 48 centimeters.
Hope this helps!
Identify the elements of the range of the function shown in the graph.
Responses
6
3
1
5
2
-6
The range of the relation on the graph is:
R: {1, 2, 6}
How to identify the range on the graph?For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).
Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:
(3, 6), (5, 2) and (6, 1)
The range is the set of the second values of each of these pairs, so the range in this case is:
R: {1, 2, 6}
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Write an equation of a line in slope-intercept form that goes through the points (-13,0) and (-1, -6).
Answer: m = -1/2
Step-by-step explanation:
Bing bang boomarang i have no idea
Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?
So, on solving the provided question, we cans ay that new slope interest equation is y = 3x +c
what is slope intercept?In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
given, x = 5, that is lope
coordinates = (1,0)
new slope interest equation is
y = 3x +c
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The correct question is -
Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?
How do you solve inequalities in 8th grade?
1. Add the same number to both sides.
2. Subtract the same number from both sides.
3. Multiply both sides by the same positive number.
4. Divide both sides by the same positive number.
5. Multiply both sides by the same negative number and reverse the sign.
Factor completely. Drag the expressions into the box if they are part of the factored form of the polynomial. If the polynomial is not factorable,
drag prime.
8c^3-27d^3
Answer: prime
Step-by-step explanation:
there is no greatest common factor (GCF) of the coefficients: 8 and -27. And the variables: c and d, are different so the polynomial is in its prime form.
Write the equation of a sine function that has the following characteristics.
1
Amplitude: 4 Period: 7pi Phase shift:
1/5
Answer:
[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]
Step-by-step explanation:
Period: [tex]7\pi=\frac{2\pi}{b}\rightarrow b=\frac{2}{7}[/tex]
Phase Shift:
[tex]\displaystyle \frac{c}{b}=\frac{1}{5}\\\\\rightarrow\frac{c}{\frac{2}{7}}=\frac{1}{5}\\\\\rightarrow \frac{2}{7}=5c\\ \\\rightarrow \frac{2}{35}=c[/tex]
Final equation:
[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]
Steve’s savings account has a balance of $1287. after 4 years, what will the amount of interest be at 6% compounded semiannually? a. $161.53 c. $308.88 b. $337.81 d. $343.33
Answer:
d. $343.33
Step-by-step explanation:
We use the equation
A = P(1 + r)^t
P = $1287
r = 6% = 0.06
t = 4 years
Let's solve
A = 1287( 1 + 0.06)^4
A = 1287(1.06)^4
A = $1630.33
$1630.33 - $1287 = $343.33
So, the answer is D
Is 7/8 greater than 2/5?
Answer:
Step-by-step explanation:
Yes 7/8= 0.875. 2/5 is equal to 0.40
Which expression simplifies to 5 radical 3?
The rational expression that simplifies to 5 square root of 3 is given as follows:
C. [tex]\sqrt{75}[/tex]
What is a rational expression?A rational expression is a term that involves a root in the expression.
The simplified rational expression for this problem is given as follows:
[tex]5\sqrt{3}[/tex]
The original expression, from which the simplified expression was obtained, can be obtained moving the number 5 back to the square root.
The number is moved back into the square root with an exponent of 2, hence the original expression is obtained as follows:
[tex]\sqrt{3 \times 5^2} = \sqrt{75}[/tex]
Which is the original expression, meaning that the correct option regarding which expression simplifies to five times the square root of three is given by option C.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Find the value of each variable in the following parallelogram
Answer:
x= 92 degrees
Y=44 degrees
HURRY PLEASE!!!!!!!!!!!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate 1/3 of an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, 2/3 an ounce per second.
What does the graph tell you about the situation? Specifically answer the following:
a.) How many solutions are there? (25 pts)
b.) Interpret the solution(s). (25 pts)
c.) Who finishes the milkshake first? (25 pts)
The solution is
a) The number of solutions to the equation is 1
b) Diego finishes the milkshake in 30 seconds and Lin finishes the milkshake in 36 seconds
c) Diego finishes the milkshake first
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the time to finish the milkshake by Lin and Diego be represented as A and B respectively
Now , the equation will be
The amount of milkshake with Lin = 12 ounce
The rate at which Lin finishes her milkshake = 1/3 milkshake per second
The time for Lin to finishes her milkshake A = amount of milkshake with Lin / rate at which Lin finishes her milkshake
Substituting the values in the equation , we get
The time for Lin to finishes her milkshake A = 12/ ( 1/3 )
The time for Lin to finishes her milkshake A = 36 seconds
Now ,
The amount of milkshake with Diego = 20 ounces
The rate at which Diego finishes his milkshake = 2/3
The time for Diego finishes his milkshake B = 20 / ( 2/3 )
The time for Diego finishes his milkshake B = 30 seconds
Hence , Diego finishes his milkshake faster
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What do you divide 41/8 by to get the most simplest form
Answer:
The simplest form would be 5 1/8
Step-by-step explanation:
You don't have a common factor with 41 and 8, so the real reduced answer would just be mixed, as 5 1/8.
Judy measured the lengths of her flowers, in inches. The lengths are shown below.
1/4
1/2
3/4
1/4
1/4
1
1/4
1/2
3/4
1/2
The total length of the flowers that Judy measures will be the 1 3/4 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, Judy measured the lengths of her flowers, in inches. The total length of the flowers will be the sum. This will be:
= 1/4 + 1/2 + 3/4 + 1/4
= 1 3/4 inches.
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Complete question
Judy measured the lengths of her flowers, in inches. The lengths are shown below.
1/4
1/2
3/4
1/4
What is the total length of the measurement?
Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Which of the following is not a pythagorean triplet a) 3,4,5 b) 6,8,10c) 5,12,13d) 2,3,4
D) 2, 3, 4 is not a pythagorean triplet.
Pythagoras theorem is in the form of;
a²+b²=c²
Applying this formula to the given options we get'
a) 3, 4, 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25 = 5^2
b) 6, 8, 10 is not a Pythagorean triplet because 6^2 + 8^2 = 36 + 64 = 100 = 10^2
c) 5, 12, 13 is a Pythagorean triplet because 5^2 + 12^2 = 25 + 144 = 169 = 13^2
d) 2, 3, 4 is not a Pythagorean triplet because 2^2 + 3^2 = 4 + 9 = 13 ≠ 4^2
In other words the pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is the sum of the squares of the other 2 sides.
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1.97x - 4.83x + 7.95x + 11.83 - 3.63x =
Answer:
13.29x
Step-by-step explanation:
1.97x - 4.83x = -2.86x
-2.86x + 7.95x = 5.09x
5.09x + 11.83x = 16.92x
16.92x - 3.63x = 13.29x
subtract -9x^2+4x from -8^2+8x-10
What is the domain and range for this function?
if you add Natalie's age and Fred's age, the result is 38. If you add Fred's age to 3 times Natalie's age, the result is 66. Write and solve a system of equations to find how old Fred and Natalie are.
a) The system of equations to find Fred and Natalie's ages are:
x + y = 383x + y = 66.b) Solving the system of equations shows that their respective ages are:
Fred = 24Natalie = 14.What is a system of equations?A system of equations is two or more equations simultaneously or concurrently solved.
We call this a system of equations or simultaneous equations because they are solved at the same time.
Let Natalie's age = x
Let Fred's age = y
The total ages of Natalie and Fred = 38
Equation 1:x + y = 38
Let Natalie's age = 3x
Let Fred's age = y
The total ages of Natalie and Fred = 66
Equation 2:3x + y = 66
Subtract Equation 1 from Equation 2:
3x + y = 66
-
x + y = 38
2x = 28
x = 14
y = 38 - 14
y = 24
Thus, Fred is 24 years old while Natalie is 14 years.
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Find the hypotenuse use simplest radical form if necessary
The triangle's third side will measure 6.71 units in length.
What is meant by Pythagoras theorem?Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle. Use the Pythagoras theorem to find the third side of a right-angled triangle.The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c² = a² + b², where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.According to the Pythagorean theorem, two squares added together equal the square of the longest side.
The Pythagoras theorem's equation is as follows:
H² = P² + B²
The triangle's third side will be the following length:
Let x represent the triangle's third side's length. Next, we have
9² = 6² + x²
81 = 36 + x²
x² = 45
x = 6.708
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12 Sketch the graphs of the following equations on the same Cartesian coordinate plane
a) 2y + 7 = 3x
b) 1/2x + 4y = 6
Answer:
Step-by-step explanation:
2y+7=3x
-3x+2y=-7
1/2x+4y=6
x+8y=12
Rosie enters the 120-step contest. She takes 6 jumps and overshoots the 120-step mark by 6 steps. How long was each of Rosie’s jumps?
The length of each of Rosie's jumps, given that she overshoots the 120 - step mark by 6 steps, is 21 steps.
How to find the length of the jumps?Rosie is involved in the 120 - step contest and when she took 6 jumps, she overshot the 120 - step mark by 6 steps. This simply meant that she took 6 more steps over the 120 mark, thanks to her jump length.
The number of steps she took in total is therefore :
= 120 + 6
= 126 steps
This then means that the length of each jump was :
= Number of steps in total / Number of jumps
= 126 / 6
= 21 steps
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Through the woods, hiker Eric comes upon a redwood tree. The sun casts shadows for both hiker Eric and the tree. Eric knows he is 6 feet tall and his shadow is 8 feet long. He is 496 feet away from the tree. How tall is the great redwood?
The height of the redwood has been calculated as 372 meters.
How to solve for the heightIn order to get the height of this tree, I would have to make use of the similar triangles method. The proportion is set as
tree height / tree shadow = Eric's height / Eric's shadow
Eric's height is 6 feet, his shadow is 8 feet
The proportion is 6 / 8
= 3 / 4
To get the height of the tree we have to multiply the proportion by the distance with which Eric is away from the tree
= 3 / 4 * 496
= 372 feet
The redwood is 372 feet
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