finding the slope
(-2,-2) , (11,-10)
What are the features of the quadratic function ƒ(x) = (x – 3)(x + 7)?
Question 8 options:
A)
Vertex = (2,25), y-intercept = (0,21), x-intercepts = (7,0) and (–3,0), axis of symmetry is x = 2
B)
Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = 2
C)
Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2
D)
Vertex = (–2,25), y-intercept = (0,21), x-intercepts = (7,0) and (3,0), axis of symmetry is x = –2
Answer:
Option C:Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2
Step-by-step explanation:
We are given the function;
f(x) = (x - 3)(x + 7)
The axis of symmetry in a quadratic equation is given by the formula;
x = -b/2a
Expanding the function given, we have;
f(x) = x² + 4x - 21
a = 1
b = 4
c = - 21
Thus;
Axis of symmetry is:
x = -(4)/(2 × 1)
x = -2
Now, y-intercept is when x = 0
Thus;
f(0) = (0 - 3)(0 + 7)
f(0) = - 3 × 7 = - 21
y - intercept is (0, - 21)
x-intercept is when f(x) = 0
Thus;
(x - 3)(x + 7) = 0
Thus;
x - 3 = 0 or x + 7 = 0
x = 3 or x = - 7
x - intercept is (-7, 0) and (3,0)
The y-coordinate of vertex will be at the line of axis of symmetry.
Thus, we will put x = -2 into the function to get;
y = (-2 - 3)(-2 + 7)
y = -5 × 5 = - 25
Vertex is at (-2, -25)
Correct Answer is option C
Answer:
Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2
Step-by-step explanation:
A one dimensional object with no endpoint is a?
A.ray
B.line segment
C.line
D.point
Answer:
its line fjfjfjjejjdjdj
As per the given condition, the required one dimensional object with no end point is a line.
What is a ray?"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.
On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "
What is a line segment?"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."
What is a line?"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "
What is a point?"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."
Given, a one dimensional object with no endpoint.
Therefore, the require object is a line.
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Estimate the square root of the imperfect square of 18.
Answer:
18 times four is 72
Step-by-step explanation:
If p = 5, q = 4, and r = 1, what is the value of p - r ?
a. 3
b. 4
c. 6
d. 1
Due today HELP PLEASEEEEE!!!
Answer:
Oiiiiio ka cha thik cha
Lines A and CD (if shown) are straight lines. Find x. Give reasons to justify your solutions.
Please Write in a form like the table below.
Answer/Step-by-step explanation:
STATEMENT ====> REASONS
1. m<AOB = 180° ==> 1. Definition of straight angle
2. m<AOF + m<FOG + m<GOB = m<AOB ==> 2. Angle Addition Postulate
3. (5x - 15)° + 90° + 2x = 180° ==> 3. Substitution
4. Solve as algebra to get x
5x - 15 + 90 + 2x = 180
Collect like terms
5x + 2x - 15 + 90 = 180
7x + 75 = 180
Subtract 75 from both sides
7x + 75 - 75= 180 - 75
7x = 105
Divide both sides by 7
7x/7 = 105/7
x = 15 ===> 4. Algebra
PRE CALC QUESTION
For the following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions.
The zeros are -3,-1, and 4. The leading coefficient is -5.
(type answer in standard form)
P(x)=
Answer:
-5[tex]x^{3}[/tex] + 65x + 60
Step-by-step explanation:What is the slope of (-7,-1) and (3,8)? Pls show your work
Answer:
[tex]m=\frac{9}{10}[/tex]
Step-by-step explanation:
To find the slope between any two points, we can use the following slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (-7, -1) be (x₁, y₁) and let (3, 8) be (x₂, y₂). Substitute them into the slope formula:
[tex]m=\frac{8-(-1)}{3-(-7)}[/tex]
Evaluate:
[tex]m=\frac{9}{10}[/tex]
Therefore, the slope between the two points is 9/10.
2
10x2 - 724
100x2 + 140xy + 4972 10x + 7y
Answer:
14xy/(10x+7y)^
Step-by-step explanation:
Plz answer 1st RIGHT gets BRAINLY!!!!! PLUS 10 POINTS!!!!
Answer: I think the answer is B.) 570
Find the value of the expression 2x^4–5x^3+x^2+3x+2 for: b x=−5
1.Find the product of 419 and 321.
Answer:
134499
Step-by-step explanation:
When someone asks for the product of something they are saying multiply the two values.
So,
419 x 321 = 134,499
Answer:
$134,499
Step-by-step explanation:
The product is the result of two numbers that are multiplied. In this case 419 and 321.
419 x 321 = 134,499
an equivalent ratio to the tape diagram shown is to
Answer:
it is 16 to 32
Step-by-step explanation:
if you divided 16 by 8 and 32 by eighth you get 2:4
if the airplane flew 40 miles, how many gallons of gas would be left in the tank
For the expression 5-5x to have a negative value, what must be true about the value of x?
Answer:
x>1
Step-by-step explanation:
let's make this an inequality.
5-5x<0
let's solve.
-5x<-5
x>1
therefore, the value of x must be larger than 1 for this statement to make sense.
The value of x has to be greater than 1 in order for the expression to make sense.
Let z = 1 + 3i and w = -3 - 4i.
Use the drop down menus to complete the statements.
The sum z + w is equal to - -i
The sum w + z is equal to - 2 - i
The result supports that complex number addition is
Step-by-step explanation:
z+w= 1+3i-3-4i = -2-i
w+z=-3-4i+1+3i = -2-i
So, z+w = w+z
So, complex number addition is commutative
If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.
What is commutativity property of addition?We are aware that the addition's commutative property states that altering the addends' order will not affect the sum.
How to solve it ?Here z = 1 + 3i and w = -3 - 4i.
Now, z + w = 1 + 3i - 3 - 4i = 1 - 3 + 3i - 4i = - 2 - i
and w + z = - 3 - 4i + 1 + 3i = - 3 + 1 - 4i + 3i = - 2 - i
i.e. z + w = w + z
Clearly, the addition obeys the commutative property.
Therefore we can conclude that If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.
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Combine Like Terms. -13x + 14a - 12x + 7x - 4x *
Answer:
4a - 22x
Step-by-step explanation:
-13x +14a - 12x + 7x - 4x = 4a - 22x
hope this helps :)
Natalie was given a box of assorted chocolates for her birthday. Each night, Natalie treats herself to some chocolates. Let C represent the number of chocolates remaining in the box t days after Natalie's birthday. A graph of C is shown below. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.
PLEASE HELP ME I NEED THE ANSWER NOW
Answer:
C= -5t+30
The slope of the function is -5 which reveals the number of chocolates Natalie eats each night.
Step-by-step explanation:
There is triangle one of the angles is 101 degrees and the other is 38 workout x
Angle sum property = Sum of the three angles of a triangle will be equal to 180° .
Using this let us find out the measure of x .
Measure of first angle = 101°
Measure of second angle = 38°
Measure of third angle = x
[tex]101 + 38 + x = 180[/tex]
[tex]139 + x = 180[/tex]
[tex]x = 180 - 139[/tex]
[tex] = x = 41[/tex]
[tex]∴ \: the \: value \: of \: x \: = 41°[/tex]
Write an example that is not an integer
Answer:
1/2, 1/4 3/72, .50, .25, etc.
Step-by-step explanation:
An INTEGER is a whole number, positive or negative. A number that ISN'T an integer is a fraction or decimal.
The Walt Disney Company, the production studio behind the Marvel Cinematic Universe, is trying to find the best release date for their new super hero movie. They are hesitating between the summer and winter holiday release, and they want to know if there is any difference between the earning potential during those seasons. The analytics division in the company examined a random sample of box-office data for movies released during the past 5 years in the USA and Canada and found that 52 out of 1258 movies with summer release date earned over 400 million dollars. They also counted that out of 545 movies released in the winter, 8 earned over 400 million dollars.
Over 4 million USD Under 4 million USD
Summer release 57 1251
Winter release 11 544
Total
1. We want to investigate whether there is a difference in the proportion of movies that eam over 400 million dollars for the two release seasons. Which hypotheses should we use?
2. Calculate the difference in the proportions of movies that eamed over 400 million dollars.
3. The paragraph below describes the set up for a randomization test, if we were to conduct a hypothesis test without using software. Fill in the blanks with a number.
We write Summer on_____cards and cards representing the movies with summer release date, and Winter on_____cards. Then, we shuffle these cards and split them into two groups one group of size_____representing the movies with box-office over 400 million dollars, and another group of size_____representing the rest of the movies. We calculate the difference in the proportions of movies that eaned over 400 million dollars during the two release seasons to get PSmmer PWinter. Finally, we build a histogram of these simulated dfterences.
Answer:
Step-by-step explanation:
Over 4 million USD Under 4 million USD Total
Summer release 57 1195 1251
Winter release 11 533 544
1)Let [tex]P_1[/tex] be the proportion of movies that earn over 400 million in summer and [tex]P_2[/tex] be the proportion of movies that earn over 400 million in winter.
Null hypothesis:[tex]H_0:P_1= P_2[/tex]
Alternate hypothesis : [tex]H_a: P_1 \neq P_2[/tex]
2)Calculate the difference in the proportions of movies that earned over 400 million dollars.
[tex]P_1=\frac{57}{1251}=0.045[/tex]
[tex]P_2=\frac{11}{544}=0.0202[/tex]
3)
[tex]P_{(Summer)}-P_{(winter)}=0.045-0.0202=0.0248[/tex]
We write Summer on 1251 cards and cards representing the movies with summer release date, and Winter on 544 cards. Then, we shuffle these cards and split them into two groups one group of size 68 representing the movies with box-office over 400 million dollars, and another group of size representing 1728 the rest of the movies.
16,1,0,1,16 input x and output y -2,-1,0,1,2
Answer:
what is the question?
Step-by-step explanation:
PLEASE HELP ME ASAP!!!! I WILL GOVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
try a none of them match because if you add 35 and 7 to each side none of them match up but the first is the closest
what is the coefficient of the term 12p in the expression 12p+9q
Answer:
12
Step-by-step explanation:
Answer:
The answer is 12,
Step-by-step explanation:
12 is the coefficient because it is the number multiplied by the variable p in the equation.
If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square. For the uniform electric field normal to the surface, the flux through the surface is____________the area of this surface. Therefore, Φsquare is ________ ϕcircle .
Answer:
The area of this circle is [tex](\frac{\pi}{2} )[/tex] the area of the square.
For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.
Therefore, Φsquare is [tex](\frac{2}{\pi} )[/tex] ϕcircle
Step-by-step explanation:
Area of the circle is given by;
[tex]A_c = \frac{\pi d^2}{4}[/tex]
Area of the square is given by;
[tex]A_s = L^2[/tex]
relationship between the edge length of the square, d, and length of its side, L,
[tex]d = \sqrt{L^2 + L^2} \\\\d = \sqrt{2L^2}[/tex]
But area of the square , [tex]A_s = L^2[/tex]
[tex]d = \sqrt{2A_s}[/tex]
Then, the area of the square in terms of the edge length is given by;
[tex]A_s = \frac{d^2}{2}[/tex]
Area of the circle in terms of area of the square is given by;
[tex]A_c = \frac{\pi d^2}{4} = \frac{\pi}{2}(\frac{d^2}{2} )\\\\But \ A_s = \frac{d^2}{2} \\\\A_c = \frac{\pi}{2}(\frac{d^2}{2} )\\\\A_c = \frac{\pi}{2}(A_s )[/tex]
For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.
Ф = E.A
Flux through the surface of the circle is given by;
[tex]\phi _{circle} = E.(\frac{\pi d^2}{4})[/tex]
Flux through the surface of the square is given by;
[tex]\phi _{square} = E.(\frac{d^2}{2} )\\\\\phi _{square} =E.(\frac{d^2}{2} ).(\frac{\pi}{2} ).(\frac{2}{\pi} )\\\\\phi _{square} =E.(\frac{\pi d^2}{4} ).(\frac{2}{\pi} )\\\\\phi _{square} =(\phi _{circle}).(\frac{2}{\pi} )[/tex]
Therefore, Φsquare is [tex](\frac{2}{\pi} )[/tex] ϕcircle
If the circle has the same diameter as the edge length of the square, then the area of this circle is [tex]\rm \dfrac{\pi }{2}[/tex] the area of the square
The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.
Φsquare is [tex]\dfrac{2}{\pi}[/tex] ϕcircle
Given
If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square
For the uniform electric field normal to the surface, the flux through the surface is____________the area of this surface.
Therefore, Φsquare is ________ ϕcircle .
1. If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square.
The area of the circle is;
[tex]\rm Area \ of \ circle = \dfrac{\pi d^2}{4}[/tex]
The area of the square is;
[tex]\rm Area \ of \ square = a^2[/tex]
The relationship between the edge length of the square, d, and length of its side a is;
[tex]\rm d = \sqrt{a^2+a^2}\\\\d = \sqrt{2a^2}\\\\d = \sqrt{2} a[/tex]
The area of the circle in terms of the area of the square is;
[tex]\rm Area \ of \ circle = \dfrac{\pi }{2} \ Area \ of \ square[/tex]
If the circle has the same diameter as the edge length of the square, then the area of this circle is [tex]\rm \dfrac{\pi }{2}[/tex] the area of the square.
2. The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.
Ф = E.A
3. Flux through the surface of the circle is given by;
[tex]= \rm E\dfrac{\pi d^2}{4}\\\\=\dfrac{2}{\pi }[/tex]
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What is the measure of angle b?
Answer: 53
Step-by-step explanation: I just woke up I’m too tired to explain
How is 5 represented in 6.75
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
Convert 2∘F to ∘C round to one decimal place
Answer:
-16.7
Step-by-step explanation:
(2°F − 32) × 5/9 = -16.7°C
List all subsets of the given set.
B = {Lennon, McCartney}
O {}, {Lennon}, {McCartney}
O {}, {Lennon}, {McCartney}, {Lennon, McCartney}
{}, {McCartney}, {Lennon, McCartney}
{ }, {Lennon}, {Lennon, McCartney}
{Lennon}, {McCartney}, {Lennon, McCartney}
please help!
Answer:
O {}, {Lennon}, {McCartney}, {Lennon, McCartney}
Step-by-step explanation:
Both the empty set and the total set are subsets of the given set.
Hence there are 4 subsets.
Answer:
O {}, {Lennon}, {McCartney}, {Lennon, McCartney}
Step-by-step explanation: