Part 5
Is not a function, because for one value of x there are two values of y
Part 6
Is a function
Part 7
Is not a function, because for one value of x there are two values of y
Part 8
Is a function
A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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Please look at the pic and help!!
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
Amanda had 931 apples, Leonardo had 1096 apples, if Amanda and Leonardo combined their apples, what would the product be?
Answer:2027
Step-by-step explanation:
931+1096=2027
Determine the equation (picture).
The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.
How to find equation of a line?The equation of a line can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, lines that a perpendicular follows the rule below:
m₁m₂ = -1
Hence,
y + 6 = 3 / 4 (x - 2)
y + 6 = 3 / 4 x - 6 / 4
y = 3 / 4 x - 6 / 4 - 6
y = 3 / 4 x - 30 / 4
y = 3 / 4 x - 15 / 2
Hence,
3 / 4 m₂ = -1
m₂ = - 4 / 3
Therefore,
slope of the line is - 4 / 3
Let's find the y-intercept of the second line
4x + 5y -20 = 0
5y = -4x + 20
y = -4 / 5 x + 4
y-intercept = 4
Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.
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Question 2: Which statements about functions g(xx² - 4x +3 and f(x) = x² - 4x are true? Select all
that apply.
The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:
The functions have the same range.
The functions have the same domain.
The functions have the same x-intercepts.
Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.
Here are the options:
The functions have the same graph.
The functions have the same range.
The functions have the same domain.
The functions have the same vertex.
The functions have the same y-intercept.
The functions have the same x-intercepts.
The functions have the same graph:
This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).
Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).
The functions have the same range:
This statement is true.
Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.
The functions have the same domain:
This statement is true.
The domain of both functions, unless restricted by any other factors, is all real numbers.
Quadratic functions have a domain of (-∞, ∞).
The functions have the same vertex:
This statement is false.
The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).
Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).
The functions have the same y-intercept:
This statement is false.
The y-intercept of a function is the value of y when x = 0.
For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.
For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3
= 3.
Their y-intercepts are different.
The functions have the same x-intercepts:
This statement is true.
To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.
The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.
Both functions have the same x-intercepts.
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves x=√y, x=0, and y=4 about the x-axis.
The volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.
What is the formula for the volume of the cylinder?The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
According to given information :To find the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells, we need to follow these steps:
Sketch the region and the axis of rotation. The region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.
Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.
Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness \($\Delta x$\), height \($4 - x^2$\), and radius \($x$\).
The volume of this cylindrical shell is given by the formula \($V = 2\pi x(4-x^2)\Delta x$\).
To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:
\($V = \int_{0}^{2} 2\pi x(4-x^2) dx$\)
We can simplify this integral by expanding the expression inside the parentheses, which gives us:
\($V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$\)
We can then integrate each term separately to get:
\($V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$\)
\($V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$\)
\($V = 8\pi - 4\pi = 4\pi$\)
Therefore, the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.
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simplify the expression 8 + (7 + x)
Answer:
15 + x
Step-by-step explanation:
A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 1. Find the area of the square.
Answer:
2/9
Step-by-step explanation:
You want the area of a square inscribed in an isosceles right triangle with legs 1 unit.
RatiosReferring to the attached figure, we have right triangle ABC with sides AB = AC = 1. The ratio the side length to the hypotenuse of an isosceles right triangle is 1 : √2, so we have ...
FG/FA = √2/1 ⇒ FG = FA·√2
FH/FB = 1/√2 ⇒ FH = FB/√2
Since FG=FH, we have ...
FA·√2 = FB/√2
FB = 2·FA
Side lengthAB = 1 = FB +FA = (2FA) +FA = 3FA
This means FA = 1/3 and the side length of the square is √2/3.
The area of the square is ...
A = s² = (√2/3)² = 2/9
The area of the square is 2/9 square units.
__
Additional comments
The centroid of the square is the same as the centroid of the triangle. We constructed the figure using the triangle centroid to help divide the sides into thirds.
The figure can be divided into 9 congruent triangles of the size of ∆AGF. The square is comprised of 4 of those.
Graphing rational functions. I need help asap!!!!
Answer:
1.
Vert. asymptote: x = {-3, 2}
Horiz. asymptote: y = 0
x-int: None
Question 3.
a. There is no hole
b. Vert. asymptote: x = {-2, 2}
c. f(x) = 0: x = {0, -1/2}
d. The graph has no hole at (-2, 4)
Question 4.
a. Vert. asymptote: x = {-2, 2}
b. f(x) = 0: x = {0, -1/2}
c. Horizontal asymptote: y = 2
d. The graph has no hole
I'm a bit confused. Some of the things stated in the question aren't true like how there are holes in places where there aren't.
Let m = 3.
Enter >, <, or = to compare the expressions.
4m−145m−4
Answer:
=
Step-by-step explanation: Please mark brainliest
Substitute 3 in for m and solve
4m - 1 = 4(3) - 1 = 11
5m - 4 = 5(3) - 4 = 11
Answer:
Step-by-step explanation:
P&R3 model and solve
problems using linear
equations of the form:
ax = b *
x
a
= b, a ≠ 0*
ax + b = c *
x
a
+ b = c ,a ≠ 0*
a x( ) + b = c *
ax + b = cx + d *
* a bx ( ) + c = d ex ( ) + f
*where a, b, c, d, e, and f [C,
CN, PS, V]
1. Introduction to Solving Linear Equations (pg. 4-7)
• Model the solution of a given linear equation using concrete or
pictorial representations, and record the process.
Algebra stones and Algebra Tiles.
Solve x + 5 = 10 , x − 7 = 10 , 2x = 10 , x
3 = 10
2. Solving equations of the form ax+b=c and a/c +b=c (pg. 8-10)
• Solve a given linear equation symbolically.
• Solve a given problem using a linear equation and record the
process.
Solve. 4m+3=31 & 2
5
m − 5 = 3
3. Solving equations of the form a(x+b)=c and ax+b=cx+d(pg. 11-14)
• Determine, by substitution, whether a given rational number is a
solution to a given linear equation.
Solve. 4(m+3)=40 & 6m+3=2m+15
Is m=5 a solution to the equation 2(m + 2) = 14 ?
4. More practice with ax+b=cx+d (Pg. 15-18)
• Identify and correct an error in a given incorrect solution of a
linear equation
Solve. 2(m+1)+4m=4(m-2)+6.
5. Solve equation with fractions. (Pg. 19-23)
• Solve a given linear equation symbolically. Solve m
3 + 2m
5 − 1
2
= 2
6. Solve Linear equations without numbers. (Pg. 24-28)
• Solve a given linear equation symbolically.
Solve for m. )( =+ BnmA
P&R4 explain and illustrate
strategies to solve single
variable linear inequalities with
rational coefficients
within a problem-solving
context.
7. Introduction to linear inequalities (Pg. 29-33)
• Translate a given problem into a single variable linear inequality
using the symbols ≥, >, < , or ≤ .
• Determine if a given rational number is a possible solution of a
given linear inequality.
Write an expression to represent the following
statement: Melanie needs at least $280 for snow
boarding.
8. Inequalities that Include Addition and Subtraction (Pg. 34-37)
• Generalize and apply a rule for subtracting a positive or
negative number to determine the solution of a given inequality.
• Generalize and apply a rule for multiplying or dividing by a
positive or negative number to determine the solution of a given
inequality.
• Solve a given linear inequality algebraically and explain the
process orally or in written form.
• Verify the solution of a given linear inequality using
substitution for multiple elements in the solution.
Solve 2x + 5 < 25 and verify your solution.
True or False.
If −2x > −10 then x > 5 .
9. Solving Problems with Linear Inequalities (Pg. 38-41)
• Compare and explain the process for solving a given linear
equation to the process for solving a given linear inequality.
• Graph the solution of a given linear inequality on a number line.
• Compare and explain the solution of a given linear equation to
the solution of a given linear inequality.
• Solve a given problem involving a single variable linear
inequality and graph the solution.
Vertical Wireless charges $50/ month plus $0.25 for
all minutes above 400 minutes per month. Frue Gal has
decided that she does not want to pay more than $70
per month. Write an inequality to represent how many
minutes she can use per month without going over her
$70 limit. Approximate your solution on the number
line
10. Chapter Review and Practice Test
• Help students develop sound study habits.
• Many students will graduate high school saying they do not
know how to study for math tests.
11. Go over Practice Test
12. Unit Evaluation
need help with this ASAP
!!!!!!!!!!!!!!!!!!!!!!!!
The fence in dead center is about 399 feet from the third base.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For the triangle in this problem, we have that:
The sides are d ft and 90 ft.The hypotenuse is of 409 ft.Hence the distance is obtained as follows:
d² + 90² = 409²
\(d = \sqrt{409^2 - 90^2}\)
d = 399 ft.
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Evaluate p+(n-1) x3 for n=7 and p=9
Find the number of distinguishable permutations of the letters IOWA.
A.45
B.48
C.90
D.120
Answer:
4!/(1! 1! 1! 1!) = 24
Step-by-step explanation:
None of your answers are correct!
Choose one item to purchase. What is the greatest number of that item you can buy with a $10 bill and still receive change? How much change will you receive ? Explain.
Answer:
poster board
Step-by-step explanation:
2Conditions:
-greatest number of 1 item
-still receive change
If you go for the cheapest items like pencil or eraser you will pay with $10 for
$0.10* 100items= $10 yet no change
If you go for second most cheapest pen $0.25 you can by
if you buy 4 pencils and each with $0.25 you will pay $1
for $ 10 you can get 4*10 = 40 pencils yet no change
if you go for the third cheapest item is the poster board
$ 1.50*2= $3 so $1.50*6 =$9 and the change will be $10-9$ = $1
HELP MUST BE DONE BY 4:00
Wild animals from around the world wanted to hold an athletic competition, but no one would let them on an airplane. They decided to just measure how far each animal could sprint in one minute and send the results to you to decide the winner. Put them from fastest to slowest! Thanks!”
Answer:
the antelope is 5280 feet the cougar is 4224 feet the hare is 4136 feet the kangaroo is 3520 feet and the coyote is 3773 feet the ostrich is 3773 feet hope this helps the answer is the antelope
Before solving this system, Danielle noticed that the point of intersection is also the y-intercept of 5x-2y=4
Answer:
Because it is. The point of intersection is the y-intercept. Where the line crosses the y-axis that is your y-intercept.
Step-by-step explanation:
Answer:
(0,4)
Step-by-step explanation:
5x - 2y = 4 Subtract 5x from both sides
5x - 5x -2y = -5x + 4
-2y = -5x + 4 Divide all the way through by -2
y = \(\frac{5}{2}\) x + 4
The y-intercept is 4.
The point to intersection is (0,4)
Help me please and thank you..
Answer:
You will move each point of this shape 1 unit into the right. Then will move each point of this shape 2 units down. The draw line between each point.Overview
13
14
15
16
17
18
19
2
Question Progress
Homework Progress
22/44 Marks
Round the number 125.3546 to 1 decimal place.
Answer:
125.4
Step-by-step explanation:
Given
\(Number = 125.3546\)
Required
Round to 1 decimal place
Up till the first decimal place, the number is:
\(Number = 125.3\)
The digit after .3 is 5
The conditions for approximation are:
If n > 4, approximate to 1Else: approximate to 0In this case: 5 > 4, so we approximate to 1
Add this "1" to the last digit of 125.3. This becomes 125.4
Hence: when the number is approximated to 1 decimal place, the digit is 125.4
Choose the four factor pairs of 42.
A. 1 and 42
B. 2 and 21
C. 3 and 14
D. 4 and 12
E. 5 and 8
F. 6 and 7
Answer:
the factors of 42 in pairs are (1, 42), (2, 21), (3, 14) and (6, 7).
Step-by-step explanation:
May I get brainelist?
29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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In the table, which TWO relationships describe a function?
Name Tammy Allen Juan Keshia
Hair Color Red Brown Black Brown
Eye Color Hazel Brown Brown Blue
Responses
A Name as a function of hair colorName as a function of hair color
B Hair color as a function of eye colorHair color as a function of eye color
C Eye color as a function of nameEye color as a function of name
D Eye color as a function of hair colorEye color as a function of hair color
E Hair color as a function of nameHair color as a function of name
F Name as a function of eye color
The two relationships that describe a function in the table are A: Name as a function of hair color, and D: Eye color as a function of hair color.
A function is a relationship between two sets of values in which each element of the first set corresponds to exactly one element of the second set. In this table, for each hair color there is only one associated name, so the relationship between name and hair color is a function. Similarly, for each hair color there is only one associated eye color, so the relationship between eye color and hair color is also a function.
Note that the other relationships listed in the question (B, C, E and F) are not functions because they do not have a one-to-one correspondence between the two sets of values. For example, in the relationship between eye color and name, multiple people (Juan and Keshia) have the same eye color (brown), so this relationship does not describe a function.
Therefore, options A and D are the correct answer.
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PLS ANSWER CORRECTLY
The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. Which statements are true about the graph of f(x)? Select three options.
A. The axis of symmetry is the line x = 6.
B. The vertex of the graph is at (–6, –11).
C. The parabola has a minimum.
D. The parabola opens down.
E. The value of h, when the equation is written in vertex form, is positive.
Answer:
A. The axis of symmetry is the line x = 6.
D. The parabola opens down.
E. The value of h, when the equation is written in vertex form, is positive.
Step-by-step explanation:
f(x) = –3(x – 6)^2 – 11.
This is in vertex form
y = a( x-h)^2 +k
where ( h,k) is the vertex
(6,-11) is the vertex, so line line of symmetry is x=6
a =-3 so the parabola opens down and it has a maximum
The value of h is 6, which is the x coordinate of the vertex
Answer:
A, D, EStep-by-step explanation:
f(x) = –3x2 + 36x – 119 written in
vertex form is f(x) = –3(x – 6)2 – 11
Vertex form is y = a(x - h)² + k
vertex is (h,k) which is (6, -11)
axis of symmetry x = 6where a = -3 because a<0, the parabola opens down.value of h = 6 as the vertex on the x coordinatecan you please help me with this question
Answer:
-28
Step-by-step explanation:
-7 x 4 = -28 because 7 x 4 =28 then add negative so -28
Hope this helped ;) Have a good day :D
←statistics please help!
The true mean level of radon exposure in tombs in the region is
Upper limit: 4190.99;
Lower Limit: 2747.01
What is Assumed mean?
The assumed mean approach in statistics is used to determine the mean or arithmetic mean of a set of grouped data. This approach is advised over a direct method for determining the mean if the input data is huge. This technique aids in minimizing calculations and generates tiny numerical values. This approach relies on guessing the mean and rounding to a convenient result. Once more, this amount is deducted from each sample value. The calculations are carried out after selecting a central class and dividing the data into equal-sized ranges or class intervals.
Assumed Mean Formula:
Let f1, f2, f3,..., fn be the corresponding frequencies and x1, x2, x3,..., xn be the midpoints or class marks of n class intervals. The assumed mean method's formula is as follows:
\(\bar{x}=a+\frac{\sum f_i d_i}{\sum f_i}\)
In the given question:
\(\begin{aligned}&n=12 \\&\bar{x}=3469 \\&5=1135\end{aligned}\)
The 95% confidence interval for mean:
\(\begin{aligned}&\left(\bar{x} \pm t_{\alpha / 2, n-1} \frac{5}{\sqrt{n}}\right) \\\Rightarrow &\left(3469 \pm(2.2010) \frac{1135}{\sqrt{12}}\right) \\\Rightarrow &(3469 \pm(2.2010) 328.03) \\\Rightarrow &(3469 \pm 721.99) \\\Rightarrow &(2747.01,4190.99)\end{aligned}\)
The 95% confidence interval for mean:
Upper limit: 4190.99;
Lower Limit: 2747.01
Hence, for a given interval, we can conclude that the true mean lies beth 2747.01 & 4190.99. with 95% C.I.
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jose spent 6 hours in school. each school period is 3/4 hour long. how many period did jose spend in school?
Answer:
why are you asking me ask jose
I have a question for you guys
Answer:
what is the question?
Step-by-step explanation:
Is anyone able to check this for me?
Pyragtheom theory
8th grade math
Answer:
Those are both correct
Step-by-step explanation:
To solve for the triangle 12^2+10^2=c^2, and for the other question, you are correct because the hypotenuse is NEVER the shortest side.
please solve this ixl sucks
Filled box will be:
Box 1: Sum of angles on starlight line is 180°.
Box 2: m ∠LQR + m ∠MQR = 180°
Box 3: m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR
Box 4: m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR
Box 5: If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel.
From the given figure we have to prove that LM ∥ NP.
m ∠LQR + m ∠QRN = 180° [Given]
m ∠LQR + m ∠MQR = 180° [Sum of angles on starlight line is 180°]
m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR [Transitive property of Equality]
m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR [Subtraction property of Equality]
m ∠QRN = m ∠MQR [Definition of Congruence]
LM ∥ NP [If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel]
Hence it is proved that, LM ∥ NP.
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The diameter of a circle is 8 miles. What is the area?
Answer:
50.26548
Step-by-step explanation:
A=πr2
what is the values if 5 in 52105
Answer:
5 is equal to 50000 and 5 is equal to 5
Step-by-step explanation: