Answer:
f( g ( - 2 ) ) = - 14
Step-by-step explanation:
f(x) = - 2x + 4
g(x) = 3x² - x - 5
f( g ( - 2 ) ) = ?
g( - 2 ) = 3( - 2 )² - ( - 2 ) - 5 = 12 + 2 - 5 = 9
f(9) = - 2 × 9 + 4 = - 14
f( g ( - 2 ) ) = - 14
Is the relation represented by the graph a function? Why or why not?
Answer:
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Step-by-step explanation:
If a system of n linear equations in n unknowns has infinitely many solutions, then the rank of the matrix of coefficients is n − 1.
True or False
The statement "If a system of n linear equations in n unknowns has infinitely many solutions, then the rank of the matrix of coefficients is n − 1" is False.
In a system of linear equations, the rank of the matrix of coefficients can be determined by performing row operations to bring the matrix to row-echelon form or reduced row-echelon form. The number of non-zero rows in the row-echelon form or reduced row-echelon form corresponds to the rank of the matrix.
If a system has infinitely many solutions, it means that there are fewer equations than unknowns or there is a linear dependency among the equations. In such cases, the rank of the matrix of coefficients will be less than n, contradicting the statement that the rank is n − 1.
Therefore, the statement "If a system of n linear equations in n unknowns has infinitely many solutions, then the rank of the matrix of coefficients is n − 1" is False.
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You have quarters and nickels saved in a piggy bank. There is a total of $3.45 in the bank. If you have 70 cents in nickels, how many quarters do you have in your piggy bank?
Answer:
11 quarters
Step-by-step explanation:
First, I subtract : 3.45 - .70 = 2.75
Then, divide : 2.75 by 25 ( a quarter ) = .11
Check : 11 x 25 = 2.75 -------------> 2.75 + .70 = 3.45
Hope this helps :)
Answer:
if I got quarters and nickels saved in my piggy bank and $3.45 is in my bank then I know I have 9 quarters 29 nickels
Step-by-step explanation:
What is the answer to this question because I don’t know?
Answer:
B.
Step-by-step explanation:
To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.
HELP PLEASEEEEEEEE its almost due. omg.
Answer:
3 gallons i believe
Step-by-step explanation:
3 gals in 48 cups
Does an X or y-axis scale have to always start at zero?.
No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero
Define axis.A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.
Given,
No, X or y-axis scale does not have to always start at zero.
A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.
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In a right triangle, a and b are the lengths of the legs and c is the length
of the hypotenuse. If a = 9 centimeters and b = 3 centimeters, what is c? If
necessary, round to the nearest tenth.
4) c = ?
centimeters
Answer:
c=9.5 centimeters
Step-by-step explanation:
a^2+b^2=c^2
9^2+3^2=c^2
90=c^2
c=\(\sqrt{90}\)
c=9.487
c=9.5
help me im dying and i
Answer:
The better bar to buy is the Nutty Crunch
Step-by-step explanation:
4.74 / 6 = 0.79 per bar
7.80 / 10 = 0.78 per bar
:)
Answer:
Nutty Crunch is better
Step-by-step explanation:
A container in the shape of a right circular cylinder with no top has surface area 3 ft2. What height h and base radius r will maximize the volume of the cylinder?
The height of the cylinder is 0.682 feet and the radius of the base is 0.612 feet.
How to find the height and radius of cylinder that maximize its volume?Let's begin by identifying the variables in the problem:
- h: the height of the cylinder
- r: the radius of the base of the cylinder
We want to maximize the volume of the cylinder, which is given by the formula:
V = π\(r^2\)h
The surface area of the cylinder is given as \(3 ft^2\), which consists of the lateral surface area:
A = 2πrh
plus the area of the base:
A = π\(r^2\)
Since there is no top to the cylinder, we don't need to account for any additional surface area. We can use the first equation to solve for h in terms of r:
h = (3 - π\(r^2\)) / (2πr)
Substituting this expression for h into the formula for the volume, we get:
V = π\(r^2\)[(3 - π\(r^2\)) / (2πr)]
Simplifying this expression, we get:
V = (3/2)π\(r^2\) - (1/2)π\(r^4\)
To maximize the volume, we need to find the critical points of this function. We can do this by taking the derivative with respect to r and setting it equal to zero:
dV/dr = 3πr - 2π\(r^3\)= 0
Solving for r, we get:
r = √(3/2) / 2
To ensure that this critical point corresponds to a maximum, we need to take the second derivative of the volume function with respect to r:
\(d^2\)V/d\(r^2\) = 3π - 6π\(r^2\)
At the critical point, r = √(3/2) / 2, this expression evaluates to:
\(d^2\)V/d\(r^2\) = 3π - 6π(3/8) = -π/2
Since this is negative, we can conclude that the critical point corresponds to a maximum. Therefore, the optimal radius of the base of the cylinder is:
r = √(3/2) / 2 ≈ 0.612 ft
To find the corresponding height, we can use the expression we derived earlier for h in terms of r:
h = (3 - π\(r^2\)) / (2πr)
Substituting the value we found for r, we get:
h = (3 - π(3/8)) / (2π(√(3/2) / 2))
Simplifying this expression, we get:
h ≈ 0.682 ft
Therefore, the optimal height of the cylinder is approximately 0.682 feet and the optimal radius of the base is approximately 0.612 feet.
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Don’t know how to solve.
Answer:
$122.88
Step-by-step explanation:
the phone decreases by 20% each year , that is
(100 - 20)% = 80% = \(\frac{80}{100}\) = 0.8
the phone reduces by a factor of 0.8 each year , then after 4 years
value = $300 × \((0.8)^{4}\) = $122.88
Two places X and Y on the equator are on the longitude 67°E and 123°E respectively
a) What is the distance between them along the equator?
b)How far is X from the North Pole
(take π to be 22/7 and Earth to be 6400km).
i) Distance between X and Y along the equator ≊ 6258 km
ii) Distance of X from the North pole ≊ 10057 km
What is the equator ?
The Equator is a fictitious line that circles the globe's center. The line that separates the Northern Hemisphere from the Southern Hemisphere is located halfway between the North and South Poles.
The Longitude difference = 123° - 67° = 56°
(i) Distance between X and Y along the equator
= (56/360)×2×(22/7)×6400cos(0)
= (56/360)×2×(22/7)×6400
= 6257.78 km
≊ 6258 km
(ii) Latitude difference = 90°
Distance from the North pole
= (90/360)×2×(22/7)×6400
= 10057.14 km
≊10057 km
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find the area of the shaded region. the graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The shaded region is the area under the graph between -1.5 and 0. The area is 0.4332.
Φ(0) = 0.5
Φ(-1.5) = 0.0668
Area = 0.5 - 0.0668
= 0.4332
The area of a standard normal distribution refers to the amount of data within a certain range of values. The area is determined by calculating the difference between the cumulative probability at the upper limit and the cumulative probability at the lower limit. For example, the area between 0 and -1.5 on the standard normal distribution can be calculated to be 0.4332. This is determined by subtracting the cumulative probability at -1.5 (0.0668) from the cumulative probability at 0 (0.5). The result of this calculation is the area of the standard normal distribution between 0 and -1.5.
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Amelia tenía 1/3 de pliego de papel cartulina para hacer 6 tarjetas de felicitación ¿Que fracción del pliego utilizó para cada tarjeta
The fraction of the sheet that Amelia used for each card is 1/18 sheets.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
First of all, we would determine the total number of sheet of construction paper used as follows;
Total number of sheet of construction paper used = 6 × 3
Total number of sheet of construction paper used = 18 sheets.
Now, we can determine the fraction of the sheet used by Amelia as follows;
Fraction of sheet = 1/3 × 1/6
Fraction of sheet = 1/18 sheets.
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Complete Question:
Amelia had 1/3 of a sheet of construction paper to make 6 greeting cards. What fraction of the sheet did she use for each card?
A fence is to be built to enclose a rectangular area of square feet. The fence along three sides is to be made of material that costs $ per foot. The material for the fourth side costs $ per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.
Given in the question,
Area = 1250 ft²
The three sides cost $3 per foot, and the fourth side costs $9 per foot.
Let x and y be the length and width of the rectangle.
Because the area is 1250 ft², therefore
xy = 1250, or
y = 1250/x
Case 1: Three sides are (x,y,x) and the 4-th side is y.
The cost is
C = 3(2x +y) + 9y
= 6x + 12y
= 6x + 12(1250/x)
= 6x + 15000/x
For C to be minimum, C' = 0. That is
6 - 15000/x² = 0
x² = 15000/6
x = 50 ft, y = 1250/50 = 25 ft
C = 6(50) + 15000/(50²) = $600
Case 2: Three sides are (y,x,y) and the 4-th side is x.
The cost is
C = 3(x + 2y) + 9x
= 12x + 6y
= 12x + 6(1250/x)
= 12x + 7500/x
For C to be minimum, C' = 0.
12 - 7500/x² = 0
x² = 7500/12 = 625
x = 25 ft, y = 50ft
C = 12(25) + 7500/25 = $600
Thus, the Dimensions will be 25 feet and 50 feet.
Question:
A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs $3 per foot. the material for the fourth side costs $9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.
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WILL GIVE BRAINLIEST IF YOU SHOW WORK!PLZ QUICKLY!! What is the solution to the equation Negative 4 (2 x + 3) = 2 x + 6 minus (8 x + 2)? x = –10 x = –8 x = Negative five-halves x = Negative StartFraction 4 Over 7 EndFraction
Answer:
x = -8
Step-by-step explanation:
Step 1: Write out the equation
-4(2x + 3) = 2x + 6 - (8x + 2)
Step 2: Distribute
-8x - 12 = 2x + 6 - 8x - 2
Step 3: Combine like terms
-8x - 12 = -6x + 4
Step 4: Isolate x's
-2x -12 = 4
-2x = 16
Step 5: Divide both sides by -2
x = -8
Answer:
b) x = -8
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ -4(2x + 3) = (2x + 6) - (8x + 2)
Then the value of x will be,
→ -4(2x + 3) = (2x + 6) - (8x + 2)
→ -4(2x + 3) = 2x + 6 - 8x - 2
→ -8x - 12 = (2x - 8x) + (6 - 2)
→ -8x - 12 = -6x + 4
→ -8x + 6x = 4 + 12
→ -2x = 16
→ x = 16/-2
→ [ x = -8 ]
Hence, the value of x is -8.
Solve each equation for x 3х- 12у= 27
A football team tries to move the ball forward as many yards as possible on each play, but sometimes they end up behind where they started. The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25. A positive number indicates moving the ball forward, and a negative number indicates moving the ball backward. 1). Which number in the list is the greatest? 2). What is a better question to ask to find out which play went the farthest from where the team started? 3). The coach considers any play that moves the team more than 4 yards from where they started a "big play." Which play(s) are big plays?
Answer:
Given:
The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25.
Solved:
1. The greatest number is 25
2. If the moved distances are square, which one is largest?
3. The move which is greater than 4 is considered "big play"
=> 21 and 25 are big play (21 > 4, 25 > 4)
Hope this helps!
:)
Some say that a restaurant should charge its customers about 3. 5 times the cost of the ingredients. How much should a restaurant charge if the ingredients cost d dollars?
Answer:3.5d
Step-by-step explanation:
If you would multiply the cost(d) by 3.5, the answer is 3.5d.
Answer: 3.5d
Step-by-step explanation: All you do is multiply 3.5 times d (cost of the ingredients). No matter how d changes, the answer will be true because d is equivalent to just whatever the ingredients cost at that time.
soooooooooo no ones gonna help me with my paper? ight lol
Answer:
Which paper?...LOL...
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 8, negative 5, negative 1, 1, and 12 and another circle labeled y values containing values negative 4 and negative 2 and arrows from negative 8 to negative 4, negative 5 to negative 2, negative 1 to negative 2, 1 to negative 2, 12 to negative 4, and 12 to negative 2. Is the relation a function? Explain.
To determine whether the relation is a function, we need to check if each x-value is associated with only one y-value in the mapping diagram.
Identify the mapping diagram.A mapping diagram is a picture of two circles that shows the connection between input and output values. Illustration of a mapping diagram. The x-values (inputs) in the image are converted to the associated y-values by drawing an arrow from one x-value to its corresponding y-value (outputs).
From the given mapping diagram, we can see that the x-value -8 is associated with the y-value -4, the x-value -5 is associated with the y-value -2, the x-value -1 is associated with the y-value -2, the x-value 1 is associated with the y-value -2, the x-value 12 is associated with both the y-value -4 and -2.
Since the x-value 12 is associated with two different y-values, the given relation is not a function. To be a function, each x-value must be associated with only one y-value in the mapping diagram.
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Answer: I think its C lmk if I'm wrong
Explanation:
will give brainliest to quickest answer
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
Pls mark brainliest.
GIVING BRAINLIEST!! someone please help me with this
Answer:
Quesnel Lake:Lake Baikal=.31
Quesnel Lake:Great Slave Lake=.82
Step-by-step explanation:
1 foot = .3048 meters
Lake Baikal: 5369 ft. = 1636.4712 m
Great Slave Lake: 2015 ft. = 614.172 m
Quesnel Lake: 506 m
Quesnel Lake:Lake Baikal
\(506 \div 1636.472 = .31\)
Quesnel Lake:Great Slave Lake
\(506 \div 614.172 = .82\)
Janet bought 5 paperback books at a garage sale for $1.50 each and 3 lamps for $11.50.
Which equation could be used to find her total cost?
A. 5+$1.50+ $11.50 = C
B. 5+$1.50 - $11.50 = C
C. 5 ($1.50)+ $11.50 = C
D. $11.50-5 ($1.50) = C
A line includes the points (6,10) and (1,0) What is its equation in slope-intercept form?
Answer:
The slope-intercept is \(y = 2x -2\) .
Step-by-step explanation:
-First, you need to find the slope by using the slope formula:
\(m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
-Second, use both points (6, 10) and (1, 0) for the formula:
\(m =\frac{0-10}{1-6}\)
-Third, you solve:
\(m =\frac{0-10}{1-6}\)
\(m = 2\)
-Fourth, after you found the slope, you need to use the Point-slope form equation:
\(y - y_{1} = m (x -x_{1})\) (where \(m\) represents the slope, and \((x_{1},y_{1})\) represents the first coordinate or the first point).
-Fifth, use the slope 2 and the first point (6, 10) for the Point-slope form equation:
\(y - 10= 2 (x -6)\)
-Sixth, you solve the equation to get the slope-intercept form:
\(y - 10= 2 (x -6)\)
\(y -10 = 2x -12\)
\(y -10 +10 = 2x -12 +10\)
\(y = 2x -2\)
So, therefore, the slope-intercept is \(y = 2x -2\) .
pls help with you actually truly know this
Answer:
x= 72
Step-by-step explanation:
- move 9 to the right.
- when a number moves to the other side, their sign changes.
- in this case, 9 multiplies by 8.
- thus 9 x 8 equals to 72.
Answer:
x=0
Step-by-step explanation:
1.Subtract 8x from both sides
2.Simplify the expression
3.Divide both sides by the same factor
4.Cancel terms that are in both the numerator and denominator
Answer: x=0
a knitted hat pattern comes in styles with stitch options and sizes, and there are yarns appropriate for the hat. disregarding size, how many different hats can be made?
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.
To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.
There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.
For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.
Therefore, the total number of different hats that can be made, disregarding size, is:
16 (style and stitch combinations) x 7 (yarn choices) = 112
This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.
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Complete question is:
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?
In your initial ocular visit to the site, you measured the radius of the curved path that is 40 meters. Complete the table below.
The table for the coefficient of friction and velocity speed square when the radius of the curved path is 40 meters.
Coefficient of static friction 0.1 0.2 0.3 0.4 0.5
(Velocity speed)² ( m²/s² ) 40 80 120 140 200
The radius of the curved path is 40 meters.
To provide the friction force necessary for an automobile moving at speed v to navigate a flat curve of radius r, consider the coefficient of static friction of v² = μrg.
When the coefficient of static friction between tires and pavement is μ, the fastest curve of radius r can be traveled is at this speed.
Here g is the acceleration due to gravity g = 10 m/s².
When μ = 0.1,
v² = 0.1 × 40 × 10 = 40 m²/s²
When μ = 0.2,
v² = 0.2 × 40 × 10 = 80 m²/s²
When μ = 0.3,
v² = 0.3 × 40 × 10 = 120 m²/s²
When μ = 0.5,
v² = 0.5 × 40 × 10 = 200 m²/s²
Hence, the complete table is:
Coefficient of static friction 0.1 0.2 0.3 0.4 0.5
(Velocity speed)² ( m²/s² ) 40 80 120 140 200
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). find the 48 term 11,20,29
The 48th term of the sequence, 11, 20, 29, ...., is 434.
According to the question,
We have the following sequence:
11, 20, 29, ...
Now, we will first try to find which kind of sequence it is.
To check whether it is in arithmetic progression or not, we will subtract the two consecutive terms.
So, we have:
Second term - first term
20-11
9
Now, we have:
Third term - second term
29-20
9
Now, the difference is the same or it can be said that it is the common difference of A.P. (which is also denoted by d).
We know that the formula to find nth term of the A.P. is as follows:
an = a+(n-1)d
where an is the nth term of the sequence and a is the first term
Now, we have to find 48t term:
a48 = 11+(48-1)9
a48 = 11+(47*9)
a48 = 11+423
a48 = 434
Now, in this result, we do not need to round it to nearest thousandth.
Hence, the 48th term is 434.
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Jason knows that za + 2d + g = 180°. Which of the following observations will allow him to complete his proof?
The equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.
given that za + 2d + g = 180°, some observations that could potentially be useful to Jason include:
Identifying any relationships or constraints between the variables za, d, and g that might help him simplify or solve the equation. For example, if he knows that za and g are complementary angles (i.e., they add up to 90°), he could substitute 90 - za for g in the equation to get a new expression in terms of za and d.
Using additional information about the angles or the situation to derive new equations or constraints that could help him solve for one or more variables. For example, if he knows that za and d are equal (i.e., za = d), he could substitute za for d in the equation to get a new expression in terms of za and g.
Identifying any patterns or structures in the equation that might suggest a particular approach or technique for solving it. For example, if he notices that the equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.
Ultimately, the most effective observations for completing the proof will depend on the specific details of the problem and the approach that Jason is taking.
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The complete question:Jason knows that za + 2d + g = 180°. Which of the following observations, if true, would allow him to prove a statement or theorem related to the angles za, d, and g?
Subtract 10x + 7y from -15x+6y
Step-by-step explanation:
= -15x+6y-(10x+7y)
= -15x+6y-10x-7y
= -25x-y.
Answer: 4
Step-by-step explanation:
10 + 7 = 17
15 + 6 = 21
21 - 17 = 4
I don’t know but wanted to try it might not be right