explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do they reveal about the graph or the quadratic?
Answer:
Summary:
Standard form allow us to quickly find the y-intercept.
Vertex form allow us to quickly locate the vertex.
And factored form allows us to quickly determine the roots/zeros.
Step-by-step explanation:
The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.
Standard Form:
The standard form of a quadratic is:
[tex]ax^2+bx+c[/tex]
There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.
The leading coefficient a will tell us if the parabola curves upwards or downwards.
And the constant c will give us the y-intercept.
Vertex Form:
The vertex form of a quadratic is:
[tex]a(x-h)^2+k[/tex]
There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient.
The leading coefficient is given by a. Again, this tells us the orientation of the parabola.
And the vertex is given by (h, k).
Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.
Factored Form:
The factored form of a quadratic is:
[tex]a(x-p)(x-q)[/tex]
Where p and q are the zeros/roots/solutions of the quadratic.
Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.
The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.
Summary:
Therefore, each form of a quadratic equation has its own benefits.
Standard form allow us to find the y-intercept.
Vertex form allow us to quickly locate the vertex.
And factored form allows us to quickly determine the roots/zeros.
Hence, depending on the question, each form can be useful in its own way.
can someone help me this is algebra 1
Jada is buying a car and the cost is c + 400 = 36,000 where c is the price of the car and 270 is the registration fee but in the end 36000 was paid.
c + 400 = 36,000
1. Avery multiplies both sides of the equation by 2 while her brother Jaxon adds 2,000 to both sides of the equation. Will both moves leads to the SAME solution for the equation? Ensure math evidence is shown or included in your response when you explain your reasoning.
2. What is the solution?
Answer:
hi do You have tiktok?mm
please help find the top angle
Answer:
130 degrees
Step-by-step explanation:
So u can see those little lines on two of the sides of the triangle, it means that it's congruent also meaning the same length, and if u didn't, the angles had to be the same in order for the sides to be the same length. So the other missing angle degree is also 25 degrees. A triangle is 180 degrees, so with this info:
25 + 25 + 4x + 2 = 180
4x + 52 = 180
4x = 128
x = 32, now we have x so replace the x in the equation with 32
4(32) + 2
128 + 2
130
.. help lol just find the answer
Determine the slope of the line that passes through these points (3,9) and (-7,11)
Answer:
-5
Step-by-step explanation:
To calculate the gradient of the slope, we have to calculate the [tex]\frac{rise}{run}[/tex].
[tex]\frac{3-(-7)}{9-11}[/tex] = [tex]\frac{3+7}{-2}[/tex]
[tex]\frac{3+7}{-2}[/tex] = [tex]\frac{10}{-2}[/tex]
[tex]\frac{10}{-2}[/tex] = -5
A weather station on the top of a mountain reports that the temperature is currently and has
been falling at a constant rate of per hour. Find each temperature. Explain or show your
reasoning.
What was the temperature?
D. An hour ago?
E. 3 hours ago?
F. 4.5 hours ago?
Answer:
1 hour ago-0*C3
hours ago-(-3*C)
4.5 hours ago- (-9*C
A gym is selling monthly memberships for $35 each and reusable water bottles for $9 each. The gym
needs to make $1188 by the end of the month.
Enter a linear equation that describes the problem.
An equation for the amount of money made by the gym is = $1188, where m is the number of
monthly memberships sold, and w is the number of reusable water bottles sold.
Answer:
x = gym memberships, and y = bottles of water
30x + 7y = 1050.....when x = 28
30(28) + 7y = 1050
840 + 7y = 1050
7y = 1050 - 840
7y = 210
y = 210/7
y = 30....so he would have to sell 30 water bottles
Step-by-step explanation:
Answer:
1188=35m+9w
Step-by-step explanation:
What is the factored form of the binomial expansion 81x2 + 144xy + 64y2?
(9x – 8y)2
(9x + 8y)2
(3x – 4y)2
(3x + 4y)2
what is the measure of <x
Answer:
x = 24°
General Formulas and Concepts:
Pre-Alg
Equality PropertiesGeometry
Definition of a Line: A line is 180°Step-by-step explanation:
Step 1: Set up equation
x + 156 = 180
Step 2: Solve for x
Subtract 156 on both sides: x = 24he length of a rectangle is five times its width.
If the perimeter of the rectangle is 120m , find its length and width.
Answer:
w = 10
l = 50
Step-by-step explanation:
Formula of Perimeter: w + w + l + l or 2w + 2l
l = 5w
2l + 2w = 120
2(5w) + 2w = 120
10w + 2w = 120
12w = 120
w = 10
l = 5(10)
l = 50
Check:
2l + 2w = 120
2(50) + 2(10) = 120
100 + 20 = 120
120 = 120
Hope This Helps!
Lets denote our variables as:
x the width of the rectangle5x the length of the rectangleThe formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length of the rectangle and W is the width of the rectangle. We know that the perimeter of the rectangle is 120m, so we can write:
2(x) + 2(5x) = 120
2x + 10x = 120
12x = 120
x = 120/12
x = 10 m → Width of the rectangle
Substituting in the length:
5x = 5(10) = 50 m → Length of the rectangle
The length of the rectangle is 50 m and its width is 10 m.
A building 78 feet tall casts a shadow 64 feet long. Find the measure of the angle of elevation of
the sun?. Draw a right triangle and round to the nearest tenth of a degree.
Answer:
50.6°
Step-by-step explanation:
The reference angle = angle of elevation [tex] (\theta) [/tex]
Side opposite to the reference angle = 78 ft
Adjacent side = 64 ft
Applying trigonometric ratios formula, we would have:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Plug in the values
[tex] tan(\theta) = \frac{78}{64} [/tex]
[tex] tan(\theta) = 1.21875 [/tex]
[tex] \theta = tan^{-1}(1.21875) [/tex]
[tex] \theta = 50.6 [/tex] (nearest tenth)
(2) A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purchase? Explain your reasoning. *
Answer:
$65
Step-by-step explanation:
Let
x = original price of the item
Mai buys one item and saves $13,
This means 20% of the original price of the item = $13
20% of x = 13
20/100 * x = 13
0.2 * x = 13
0.2x = 13
Divide both sides by 0.2
x = 13 / 0.2
= 65
x = $65
Therefore, the original price of the item is $65
(-4, 18) is a solution to:
y = 5x – 2
Mrs. Booker's meal at Chick-fil-A costs $16.78.
The tax on the meal is 6%. How much was her
total bill, including tax?
Answer:
17.79
Step-by-step explanation:
16.78*1.06=17.886
The sum of a number times 6 and 17 is at most 21.
Answer:
? that makes no sense
Step-by-step explanation:
Answer:
n × 6 + 17 ≤ 21
On a piece of paper graph, y < -2x
and then give me a picture of this paper so i can see what it looks like
Answer:
Step-by-step explanation:
This is a dotted line.
Please help me with this question! :)
Will mark brainliest
Answer:
10
Step-by-step explanation:
y = 3(5) - 5 multiply 3 and 5
y = 15 - 5 subtract 5 from 15
y = 10 10 is the output
hope this helps!
PLZ HELP WITH THIS QUESTION ASAP. 20 POINTS!!! Brainliest to best answer!! Please answer with detail and show ALL steps to how you completed this problem. I attached a picture of the problem below. THANKS!!! :)
Answer:
110
Step-by-step explanation:
It's only 10 points, but
33 Km
I used the perimeter, triangle area theorem, and angle theorem
If 1 cup has a 16 tablespoons,how many tablespoons are there in 2 1/2
Answer:
40 tablespoons
Step-by-step explanation:
What is 35% of 80? use the if/of formula
Answer:28
Step-by-step explanation:
10%= 8
35%/10%= 3.5
8 x 3.5 = 28
Answer:
28
Step-by-step explanation:
80/x=100/35
(80/x)*x=(100/35)*x - we multiply both sides of the equation by x
80=2.85714285714*x - we divide both sides of the equation by (2.85714285714) to get x
80/2.85714285714=x
28=x
x=28
now we have:
35% of 80=28
Solve the equation 5x+9=1
Answer:
x = -1.6
Step-by-step explanation:
Original equation:
5x + 9 = 1
Subtract 9 from both sides
5x = -8
Divide both sides by 5
x = -1.6
Hope this helps :)
Please consider Brainliest :)
For which values of x is the expression undefined?
x2 – 49
x2 – 16
You meant to say x^2 - 49 and the second binomial is x^2 - 16.
x^2 - 49 = (x - 7) (x + 7).
Set each factor to 0 and solve for x individually.
x - 7 = 0
x = 7
x + 7 = 0
x = -7
Do the same for x^2 - 16.
Here is the set up:
x^2 - 16 = (x - 4) (x + 4).
Take it from here.
please help, will give brainlist
(x-2)(x-1) use the distributive property
please explain as well!
Answer:
Step-by-step explanation:
(x-2)(x-1)
You need to take the first x and multiply by the other x. Then multiply the first x by the -1. Do this for the -2 also. -2 by the second x and -2 by the -1.
You get x^2-x-2x+2 then combine terms.
x^2-3x+2
Answer:
x² - 3x + 2
Step-by-step explanation:
(x-2)(x-1)
xx - x - 2x + 2
x² - 3x + 2
A twizzler factory makes regular 8in, king size 10in, extra long 16in, and snack size 3in twizzlers. Before packaging the candy, the size is checked and any pieces that have a percent error of 1.5% or more are rejected. Would every size of twizzler be rejected for being 0.14in too short? Why or why not?
Answer:
Step-by-step explanation:
fdsdfghjhgv njhgfghj nbhgvfgbh nhgvfbhg huygvbh huyvg hbv
Which lists all of the x-ontercept of the graphed function 0,6
Answer:
The answer is C, because those are the points that cross the x-axis.
Step-by-step explanation:
Answer: C
Step-by-step explanation:
When you look at the graph, you can see that all the points are listed where they should be
(x+1)(x+5)≤0
Solve and write solution in interval notation
Answer:
just multiply first x+1 to x+5 then add and subtract
Find the sum of the following nine products: 1 × (10 – 1), 2 × (10 – 2), 3 × (10 – 3), … , 9 × (10 – 9)
Answer:
9, 16, 21, 9
Step-by-step explanation:
I hope this help and it was going in order
Answer:
165
Step-by-step explanation:
We solve the first 5
1*(10-1)=9
2*(10-2)=16
3*(10-3)=21
4*(10-4)=24
5*(10-5)= 25
and notice
when you go from 6 on its getting the same number because say 3*(10-3) = 3*7 and 7*(10-7) = 7*3 and 7*3 = 3*7 so
You add the first 5 integer you solved up
9 16 21 24 25 = 95
and then you double it no extra 25
and then you get 165 = answer
The expression (x^3)(x^−17) is equivalent to xn. What is the value of n?
Answer:
-14Step-by-step explanation:
(x^3)(x^−17) =x^(3 - 17) =x^-14n = -14n = -14
(x^3)(x^−17) =
x^(3 - 17) =
x^-14
What’s the value of y ?
Please help!
Rewrite the rational exponent as a radical. (2 points)
Answer:
Answer: 3) [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Radical Form and Exponent Form
A radical can be expressed as a rational exponent following the identity:
[tex]\displaystyle \sqrt[m]{x^n}=x^\frac{n}{m}[/tex]
We should also recall that:
[tex](x^n)^m=x^{nm}[/tex]
We are given the expression:
[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}[/tex]
Applying the power of power:
[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\left(5^{\frac{3}{4}\cdot \frac{2}{3}}\right)[/tex]
Simplifying:
[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=5^{\frac{1}{2}}[/tex]
Converting to radical form:
[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\sqrt{5}[/tex]
Answer: 3) [tex]\sqrt{5}[/tex]