Answer:
The correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.
Step-by-step explanation:
Consider the provided information,
We need to identify the option which has no solution,
Consider the option A)
Six pizzas are shared equally among three people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 6/3 = 2
That means each person gets 2 pizza.
The problem has a solution.
Consider the option B)
Three pizzas are shared equally among two people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 3/2 = 1.5
That means each person gets 1.2 pizza.
The problem has a solution.
Consider the option C)
Zero pizzas are shared equally among three people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 0/3 = 0
That means each person gets 0 pizza.
The problem has a solution.
Consider the option D)
Two pizzas are shared equally among zero people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 2/0 = No solution
As we know any number divided by 0 has no solution.
Thus, the problem has no solution.
Hence, the correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.
Angela and Brian were measuring the length of each side of the same box, in order to find its volume. They both measured the sides to be 7.2, 3.5, and 8.7. Angela, to avoid mistakes in rounding, first found the volume and then rounded to the nearest whole number. Brian, on the other hand, decided to take the easy route and rounded the length of the sides to the nearest integers and then found the volume using the rounded lengths. What was the positive difference between Angela's and Brian's rounded volumes? (Note: The volume of a box is defined to be the product of its three sides.)
Answer:
33
Step-by-step explanation:
Using Angela's method, we first multiply, then round.
V = (7.2)(3.5)(8.7)
V = 219.24
V ≈ 219
Using Brian's method, we first round, then multiply.
V = (7.2)(3.5)(8.7)
V ≈ (7)(4)(9)
V ≈ 252
The positive difference between their answers is:
252 − 219 = 33
The positive difference between Angela's and Brian's rounded volumes is 33.
What is volume of cuboid?
The volume of a cuboid is equal to the product of length, width and height of a cuboid.
According to Angela's method,
V = (7.2)(3.5)(8.7)
V = 219.24
First found the volume, then round.
V ≈ 219
According to Brian's method,
V = (7.2)(3.5)(8.7)
First round, then found the volume,
V ≈ (7)(4)(9)
V ≈ 252
The positive difference between their answers = 252 − 219 = 33
Hence, the positive difference between Angela's and Brian's rounded volumes is 33
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What is the solution to the equation x + 9.5 = 27.5?
x = 2.9
x = 18
x = 20
x = 37
Answer:
x = 18.
Step-by-step explanation:
x + 9.5 = 27.5
Subtract 9.5 from both sides:
x = 27.5 - 9.5
x = 18 (answer).
wassup the answer is 18 have fun get that A+
Choose the expression that represents a quadratic expression.
a. 9x - 2
b. 5x^2 + 9x - 1
c. -2x^3 + 8x^2 - 7x + 1
d. x^4 - 12x^3 + 8x^2 - 7x + 1
Answer:
b. 5x^2 + 9x - 1
Step-by-step explanation:
A quadratic expression had the highest power of the variable at 2
x^2
b. 5x^2 + 9x - 1
a has the highest power as x
c and d goes higher than x^2
The expression that represents a quadratic expression is 5x^2 + 9x - 1 (option b), which is in the form ax^2 + bx + c, where a, b, and c are constants.
The expression that represents a quadratic expression is option (b), which is 5x^2 + 9x - 1. A quadratic expression is generally in the form ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero. This type of equation represents a parabola when graphed on a coordinate plane. The examples provided in the question show how various terms relate to the constants a, b, and c in the quadratic equation, and the use of the quadratic formula for solving such equations. Option (a) is linear, option (c) is cubic, and option (d) is quartic, as indicated by the highest powers of x.
What is the explicit formula for this sequence?
2, 10, 50,250, 1250....
Answer:
Explicit formula is 2(5)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio 10/2 = 50/10 = 250/50 = 5.
The nth term an = a1 r^(n - 1)
= 2(5)^(n-1).
Formula for sequence tells about getting its specific term by putting its index. The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]
What is a geometric sequence and how to find its nth terms?There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]
Then the sequence would look like
[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-1}[/tex]
For the given sequence, it can be seen that each previous term is multiplied by 5 to get the next term to that term.
Like, we got
[tex]10 = 2 \times 5\\50 = 10 \times 5[/tex] and so on.
This shows that there is single constant used which is multiplied to previous terms to get the next term. This is the property of a geometric sequence. Here, we got
[tex]a = 2\\d = 5[/tex]
Thus, sequence is
[tex]a, ad, ad^2, ad^3, ...\\\\or\\\\2, 2\times 5, 2 \times 5^2, 2 \times 5^3 ...\\\\or\\2, 10, 50, 250, 1250,...[/tex]
Its nth term is given as: [tex]T_n = ad^{n-1} = 2(5)^{n-1}[/tex]
A sequence with n terms, and its nth term formula being [tex]a_n[/tex] is written as [tex]\{a_i\}_{i=1}^n[/tex] (showing that put i = 1, 2, ... n) to get its terms.
Here, sequence is not limited, so infinite terms.
or, we get the formula for the sequence as: [tex]\{a_i\}_{i=1}^n = \{2(5)^{i-1}\}_{i=1}^\infty[/tex]
Thus, The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]
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Please please answer this correctly
Answer:
The answer is 31.83....
Step-by-step explanation:
If you divide 191 by 6 we get:
=31.8333333333
Rounding to the nearest hundredth:
Underline the hundredths place: 31.8333333333
Look to the right. If it is 5 or above 5 then we give it a shove.
If it is 4 or less than 4, we let it go.
In our case it is 3.
Round to 31.83
Therefore the answer is 31.83....
Which Platonic solid has twenty faces that are equilateral triangles?
Answer:
Icosahedron
Step-by-step explanation:
Icosahedron has 20 faces and all the faces are equilateral triangle. Also the faces are congruent and the Icosahedron is one of the five Platonic solids.
Icosahedron has twenty faces that are equilateral triangles.
What is Icosahedron?Icosahedron is one of the 5 Platonic solid which has 20 faces, 12 vertices, 30 edges.
All the faces of Icosahedron is an equilateral triangle at each vertex. also all the faces are congruent and are of the same size.
From the picture given below, it is also clear that
Icosahedron has twenty faces that are equilateral triangles.
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The slope of MN is −3. Which segments are parallel to MN ? Select each correct answer.
A= RS, where R is at (1, 3) and S is at (4, 2)
B= PQ, where P is at (5, 6) and Q is at (8, 7)
C= TU, where T is at (8, 1) and U is at (5, 10)
D= WX, where W is at (2, 6) and X is at (4, 0)
Report by TurtleAnderson
Answer:
Option C and D is correct
Step-by-step explanation:
We need to find the slopes of the given segments.
The lines are parallel if there slopes are equal.
A) = RS, where R is at (1, 3) and S is at (4, 2)
[tex]Slope\,\,of\,\,RS =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\Slope\,\,of\,\,RS=\frac{2-3}{4-1}\\Slope\,\,of\,\,RS=\frac{-1}{3}[/tex]
Option A is incorrect because Slope of MN = -3 while slope of RS = -1/3
B)= PQ, where P is at (5, 6) and Q is at (8, 7)
[tex]Slope\,\,of\,\,PQ =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,PQ=\frac{7-6}{8-5}\\Slope\,\,of\,\,PQ=\frac{1}{3}[/tex]
Option B is incorrect because Slope of MN = -3 while slope of PQ = 1/3
C)= TU, where T is at (8, 1) and U is at (5, 10)
[tex]Slope\,\,of\,\,TU=\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,TU\,\,=\frac{10-1}{5-8}\\Slope\,\,of\,\,TU\,\,=\frac{9}{-3} \\Slope\,\,of\,\,TU=-3[/tex]
Option C is correct because Slope of MN = -3 while slope of TU = -3
D)= WX, where W is at (2, 6) and X is at (4, 0)
[tex]Slope\,\,of\,\,WX\, =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,WX\,=\frac{0-6}{4-2}\\Slope\,\,of\,\,WX\,=\frac{-6}{2} \\Slope\,\,of\,\,WX\,=-3[/tex]
Option D is correct because Slope of MN = -3 while slope of WX = -3
Segments TU and WX have the slope -3, which is the same as line MN's slope, making them parallel to segment MN.
The question asks which line segments are parallel to a line MN with a slope of
-3. To determine if two segments are parallel, they must have the same slope. The slope of a line through two points (x1, y1) and (x2, y2) is calculated with the formula
m = (y2 - y1) / (x2 - x1).
Let's find the slopes for each segment:
For segment RS, slope m = (2 - 3) / (4 - 1) = -1 / 3. This is not equal to -3, so RS is not parallel to MN.For segment PQ, slope m = (7 - 6) / (8 - 5) = 1 / 3. This is not equal to -3, so PQ is not parallel to MN.For segment TU, slope m = (10 - 1) / (5 - 8) = 9 / -3 = -3. This slope is equal to -3, so TU is parallel to MN.For segment WX, slope m = (0 - 6) / (4 - 2) = -6 / 2 = -3. This slope is equal to -3, so WX is parallel to MN.Therefore, the segments parallel to MN are TU and WX.
The slope of a given line is -2. What is the slope of a line that is parallel to the given line?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given the slope of a line m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
I WILL GIVE BRAINLIST if I get enough answers how do i find the radius someone help me please
Answer:
r=7
Step-by-step explanation:
We have the equation
(x+5)^2 + (y+8)^2 =
We know that this is equal to the radius squares
(2+5)^2 + (-8+8)^2 = r^2
We know a point on the circle (2,-8)
Substitute this point into the equation
(2+5)^2 + (-8+8)^2 = r^2
(7)^2 + (0)^2 = r^2
7^2 = r^2
The radius is equal to 7
if [tex]f(x)=\frac{1}{3} - \frac{1}{2}x [/tex] and [tex]g(x) = 2x^{2} + x + 4[/tex] find [tex] (f+g)(x) [/tex]
Answer:
[tex]\large\boxed{(f+g)(x)=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\\text{We have}\\\\f(x)=\dfrac{1}{3}-\dfrac{1}{2}x,\ g(x)=2x^2+x+4.\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{3}-\dfrac{1}{2}x\right)+(2x^2+x+4)\\\\=\dfrac{1}{3}-\dfrac{1}{2}x+2x^2+x+4\qquad\text{combine like terms}\\\\=2x^2+\left(-\dfrac{1}{2}x+x\right)+\left(\dfrac{1}{3}+4\right)\\\\=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}[/tex]
Solve
-10 + 3x + 5 = 18 - 2
Answer:
x = 7
Step-by-step explanation:
-10 + 5 + 3x = 16
-5 + 3x = 16
3x = 21
x = 7
at the mall buying a pair of shoes and buying a book are independent events the probability that a shopper buys shoes is 0.12 the probability that a shopper buys a book is 0.10 what is the probability that a shopper buys shoes and a book
Answer: .012
Step-by-step explanation:
We know that when two events A and B are independent of each other , then the probability of their intersection is given by :-
[tex]P(A\cap B)=P(A)\ \cdot\ P(B)[/tex]
Given : The probability that a shopper buys shoes is 0.12
The probability that a shopper buys a book is 0.10
Since, both the events are independent , then the probability that a shopper buys shoes and a book is given by :-
[tex]0.12\times0.10=0.012[/tex]
Hence, the probability that a shopper buys shoes and a book is .012 .
Answer:
0.012 is the answer
What is the equation of a line that contains the point (2, 1) and is perpendicular to the line y= 3x - 4
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 4 ← is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], hence
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the line
To find c substitute (2, 1 ) into the partial equation
1 = - [tex]\frac{2}{3}[/tex] + c ⇒ c = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
What is the slope of a line perpendicular to line A?
Answer:
-7/4
Step-by-step explanation:
Line A is the blue one.
I see two points they have identified for me:
(-7,0) and (0,4).
To find the slope of the line A given two points we could use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We could also line up the points vertically and subtract, then put 2nd difference over 1st difference.
Like this:
(-7,0)
-(0,4)
-------
-7 -4
So the slope is -4/-7=4/7
So the slope of a line that is perpendicular will have opposite reciprocal slope. That is the opposite reciprocal of 4/7 is -7/4.
Therefore the slope of a line that is perpendicular to A will have slope -7/4.
Answer:
[tex] - \frac{7}{4} [/tex]
Step-by-step explanation:
We use the slope formula to fine the slope of line A.
[tex] m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Line A passes through (-7,0) and (0,4)
[tex]m = \frac{4 - 0}{0 - - 7} [/tex]
[tex]m = \frac{4}{7} [/tex]
The slope of a line that is perpendicular to line A is the negative reciprocal of the slope of line A
[tex] - \frac{7}{4} [/tex]
What Is the line of reflection between pentagons PQRST and P'Q'R'S'T' ?
A) x = 0
B) y = x
C) y = 0
D) x = 1
Answer:
A
Step-by-step explanation:
From the diagram:
P(-4,6)→P'(4,6);Q(-7,4)→Q'(7,4);R(-6,1)→R'(6,1);S(-2,1)→S'(2,1);T(-1,4)→T'(1,4).The general rule of this reflection is
(x,y)→(-x,y)
and this is reflection across the y-axis. The y-axis has the equation x=0.
How many degrees is angle b?
Answer:
b =45
Step-by-step explanation:
A full circle is 360 degrees
b+315 = 360
Subtract 315 from each side
b+315-315 = 360-315
b =45
Oatmeal is packaged in a right circular cylindrical container that has a
radius of 7 centimeters and a height of 16 centimeters.
What is the surface area of this container in terms of pi?
[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} h=height\\ r=radius\\ \cline{1-1} h=16\\ r=7 \end{cases}\implies SA=2\pi (7)(16+7) \\\\\\ SA=14\pi (23)\implies SA=322\pi[/tex]
The surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π. This is obtained by using the formula for surface area of cylinder.
What is the surface area ?
Surface area of cylinder is, S = 2πrh+2πr², where S is the surface area, r is the radius and h is the height of the cylinder.
Given that r =7 cm, h =16 cm,
S = 2πrh+2πr²
= 2π(7)(16)+2π(7)²
= 224π+98π
= 322π
Hence the surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π.
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Factor the expression.
15n−18
Enter your answers in the boxes to complete the factored expression.
(
n − 6)
Answer:
3(5n -6)
Step-by-step explanation:
15n -18
Both 15 and 18 can be divided by 3
Factor out a 3
3(5n -6)
Anwser
3(5n -6)
Step-by-step explanation:
15n -18
Both 15 and 18 can be divided by 3
Factor out a 3
3(5n -6)
Evaluate: (35 + 25)2 + 3
A) 123
B) 98
Answer:
[tex]\huge \boxed{123}[/tex]
Step-by-step explanation:
This question is about the order of operations. The order of operations stands for parenthesis, exponent, multiply, divide, add, and subtract.
Do parenthesis.
[tex]\displaystyle (35+25)=60[/tex]
[tex]\displaystyle 60*2+3[/tex]
Multiply from left to right.
[tex]\displaystyle 60*2=120[/tex]
Add numbers from left to right.
[tex]\displaystyle 120+3=123[/tex]
123 is the correct answer.
What elements are in A and B?
Answer:
Zack and bo
Step-by-step explanation:
A and B is where the circles intersect so zack and bo are the only names I see there.
The elements {Zack, Bo} are in A and B.
What is set A intersection set B?The element that is present in both set A and set B i.e. at the common area of set A and set B in Venn diagram is called set A intersection set B.
Here In Venn diagram set A is green colored which contains the element {Kalie, Noah, Zack, Bo}
Set B is orange colored which contains the element {Julia, Zack, Bo}.
The elements which are present in both A and B are the intersection of set A and set B.
These elements are available at the common joint area of set A and set B.
Here, dark color represents the area that contains the element present in A and B.
In that dark-colored region, the elements present are {Zack,Bo}.
Therefore The elements {Zack, Bo} are in A and B.
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Given:
BC⊥AC
m∠BAC = 32°
Use the given information to determine m∠CDE.
32°
58°
68°
90°
Answer: 32°
Step-by-step explanation:
m∠BAC = m∠CDE, therefore m∠CDE = 32°
Answer:
Option B, 58°
Step-by-step explanation:
In the given figure AB ║ CD and BC ║ DE ( given )
Since BC ║ DE and BC ⊥ AC
So DE will also be perpendicular to CE
m ∠ BAC = 32° [given]
Since AB ║ CD and line AE is transverse
Then ∠BAC ≅ ∠DCE ≅ 32°
Now in ΔDEC.
∠DCE + ∠CED + ∠EDC = 180°
32° + 90° + ∠EDC = 180°
122° + ∠EDC = 180°
∠EDC = 180 -122
= 58°
Option B, 58° is the answer.
What is the value of f-1(3)
Answer: C.
Step-by-step explanation:
The value of inverse function f⁻¹(3) is 13, option (D) is correct.
What is function?Function is a combination of different types of variable and constants.
A function is generally denoted by f(x).
The given function is,
f(x) = (2x+1)/(x-4)
To find the value of f⁻¹(3),
Let f⁻¹(3) = y
⇒3 = f(y)
⇒3 = (2y+1)/y-4
⇒3(y-4) = 2y+1
⇒3y-12 = 2y+1
⇒ y = 13
⇒ f⁻¹(3) = 13
Therefore, the value of f⁻¹(3) is 13.
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I’m giving all the points I have, plz help and get it right? Someone please help me
Answer:
The area (probability) is: 0.6864.
Step-by-step explanation:
According to the statement, we are in front of a normal distribution with the following parameters:
µ (mean) = 0
σ (Standard deviation) = 1.
Then we need to find the area of the shaded region, which is the area between the points -1.21 < z < 0.84.
And the area (probability) is: 0.6864.
Answer:
A. 0.6864
Step-by-step explanation:
The area of the shaded region between the two z-scores indicated in the diagram is 0.6864.
mean = 0
Standard deviation = 1
the inverse of f(x)=4x+5
To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.
Original equation:
y = 4x + 5
Switched:
x = 4y + 5
Solve for y by isolating it:
x - 5 = 4y + 5 - 5
x - 5 = 4y
(x - 5)/4 = 4y/4
[tex]\frac{1}{4}x-\frac{5}{4} = y[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Which of the following represents a function?
Answer:
a
Step-by-step explanation:
bc its the only one that makes sence to me heheh
Answer: Option D
Step-by-step explanation:
A relationship is a function if and only if for each input value x (domain) only one output value y is assigned (Range)
Option A.
Note that x represents the input values and y represents the output values.
When [tex]x = 3[/tex] then [tex]y = 14[/tex] and [tex]y = 19[/tex].
The input value [tex]x = 3[/tex] has two output values y assigned.
So the relationship is not a function
Option B.
Note that x represents the input values and y represents the output values.
When [tex]x = 3[/tex] then [tex]y = 0[/tex] and [tex]y = -5[/tex].
The input value [tex]x = 3[/tex] has two output values y assigned.
So the relationship is not a function
Option C
Note that x represents the input values and y represents the output values.
When [tex]x = -1[/tex] then [tex]y = -11[/tex] and [tex]y = 5[/tex].
[tex](-1,-11)[/tex] , [tex](-1, 5)[/tex]
The input value [tex]x = -1[/tex] has two output values y assigned.
So the relationship is not a function
Option D
Note that x represents the input values and y represents the output values and for each input value x (domain) only one output value y is assigned (Range)
[tex]\{(-5, 3), (-3, 1), (-1, -1), (1, -1), (3, 1), (5, 3)\}[/tex]
So the relationship is a function
You are a math superstar and have been assigned to be a math tutor to a third grade student. Your student has a homework assignment that requires measuring angles within a parallelogram. Explain to your student how to measure the angles within the shape.
To measure angles within a parallelogram, use a protractor. Align the protractor with the vertex of the angle and read the number where the other side crosses. Repeat for each angle.
Explanation:To measure the angles within a parallelogram, you can use a protractor. A protractor is a tool that helps measure angles. Here’s how you can use it:
Place the protractor on one side of the parallelogram, aligning the center hole with the vertex of the angle you want to measure.Read the number on the protractor where the other side of the angle crosses it. This number represents the measure of the angle in degrees.Repeat this process for each angle within the parallelogram.For example, if you want to measure one of the angles in a parallelogram and the protractor shows that the two sides of the angle cross at the 60° mark on the protractor, that means the angle has a measure of 60 degrees.
4^-x x=-3
i need to stretch this to 20 words and im struggling to come up with things.
So,
[tex]4^{-x}[/tex]
When [tex]x=-3[/tex]
Becomes,
[tex]4^{-(-3)}=4^3=\boxed{64}[/tex]
Hope this helps.
r3t40
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the expression below.
(- 6)(x+ 2)
For (x - 6)(x + 2) to equal ,either (X - 6) or (x+2) must equal____
The values of x that would result in the given expression being equal to 0, in order from least to greatest___are
and____
The values of x that make the expression (x - 6)(x + 2) equal to zero are -2 and 6. This is based on the Zero Product Property in Mathematics, which states that if the product of two factors is zero, then at least one of the factors must equal zero.
Explanation:In Mathematics, the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this property in the expression (x - 6)(x + 2) = 0, one can conclude that either (x - 6) = 0 or (x + 2) = 0.
The expression (x−6)(x+2) equals 0 when either (x−6)=0 or (x+2)=0. Solving each equation separately:
For (x−6)=0, add 6 to both sides to get x=6.
For (x+2)=0, subtract 2 from both sides to get x=−2.
So, the values of x that make (x−6)(x+2)=0 are x=−2 and x=6.
Solving both equations, we get two possible solutions, x = 6 or x = -2. So, the values of x that would result in the expression being equal to zero are -2 and 6, listed in order from least to greatest.
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which function has the greater maximum value f(x)=-2x^2+4x+3 or g(x), the function in the graph?
Answer:
A
Step-by-step explanation:
Alright so in the graph we can see the highest y that is reach is at x=3 which is y=6. The maximum of the graph g(x) is 6.
Now we have to be a bit more algebraic and messy when comes to finding a maximum (the vertex of the parabola) of f(x)=-2x^2+4x+3.
First step, I'm going to find the x-coordinate of the vertex. Once we do that we can find the y that corresponds to it by using y=-2x^2+4x+3.
So the x-coordinate of the vertex can be found by computing -b/(2a).
a=-2 and b=4 so we are going to plug that in giving us -4/(2*-2)=-4/-4=1.
So the x-coordinate of the vertex is 1 and we are going to find the y that corresponds to that using y=-2x^2+4x+3.
So let's plug in 1.
This gives us:
y=-2(1)^2+4(1)+3
y=-2(1)+4+3
y=-2+4+3
y=2+3
y=5
So the maximum of graph f is 5.
6 is higher than 5
So g has the higher maximum
So the answer is A.
Answer:
A.) g(x)
Step-by-step explanation:
:p
Find the area of triangle ABC.
A = 34.5°, b = 13.2 in., c = 5.3 in.
Answer:
=19.81 in²
Step-by-step explanation:
We use the sine formula to find the area of the triangle in question.
In this formula we find the product of two adjoined sides with the sine of the angle between them.
The sides b and c are bound by the angle A.
Therefore area=1/2bcSin A
A=1/2×13.2 in×5.3 in× Sin 34.5
=19.81 in²
Answer:19.812
Step-by-step explanation:
Given
angle A=34.5
b=13.2 in.
c=5.3 in.
Area of triangle when two sides and angle between them is given
[tex]A=\frac{1}{2}bcsina[/tex]
[tex]A=\frac{1}{2}\left ( 13.2\right )\left ( 5.3\right )sin\left ( 34.5\right )[/tex]
[tex]A=19.812 in.^2[/tex]