The three types of quadratic functions are as follows: We can quickly find the y-intercept using the standard form. We can quickly locate the vertex in vertex form, and we can quickly determine the roots/zeros in factored form.
What are the 3 forms of a quadratic function and their features?The three forms of quadratics are the standard form, the vertex form, and factored form. Each of them reveals a specific part of the quadratic.
A quadratic has the following standard form:
A quadratic in standard form can immediately convey only two details: (1) the leading coefficient a and (2) the y-intercept. The leading coefficient a determines whether the parabola curves upwards or downwards. The y-intercept will be given by the constant c.
Vertex Form: The vertex form of a quadratic is:
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. This tells us the orientation of the parabola. 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:
Where p and q are the zeros/roots/solutions of the quadratic. Factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros. The zeros tell us when the parabola crosses the x-axis, which can assist in graphing.
Therefore,
Each form of a quadratic equation has its own benefits.
The standard form allows us to find the y-intercept.
The vertex form allows us to quickly locate the vertex.
The factored form allows us to quickly determine the roots/zeros.
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At a real estate agency, an agent sold a house for $344,000. The commission rate is 4.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer:
Commission - $15,480 | Money the agency made - $86,000
Step-by-step explanation:
4.5% of $344,000 is $15,480
25% of $344,000 is $86,000
can you plsss help me due now
Answer:
D
Step-by-step explanation:
I'll try to be brief
Let's plug in our 'y' variable (2x)
2x + (2x) = 20
4x = 20
x = 5
Now, plug in our 'x' variable to get our 'y' variable:
y = 2(5)
y = 10
So, our answer in (5, 10)
Or, D
9 more than the quotient of a number and 6 is 3
The expression "a number" can be represented with any letter. Use, for instance, the letter n.
Then, the expression "The quotient of a number and 6" can be represented as:
[tex]\frac{n}{6}[/tex]9 more than the quotient of a number and 6 can be expressed as:
[tex]9+\frac{n}{6}[/tex]If that expression is equal to 3, then:
[tex]9+\frac{n}{6}=3[/tex]Which is an algebraic expression for "9 more than the quotient of a number and 6 is 3".
Consider the equation, x2 3x + 4, where x represents a real number.a. Are the expressions x2 and 3x + 4 algebraically equivalent?b. The following table shows how we might "sift” through various values to assign to the variable symbol x in the hunt for values that would make the equation true.
(a)
The expression are equivalent to each ohter if both expressions give same value for all assign values of x. From the table it can be observed that both expression do not give same value for all values of x. Thus expression
[tex]x^2[/tex]and 3x + 4 are not eqivalent to each other.
(b)
From the table, it can be observed that values of the expression are equal for x = 4. So equation
[tex]x^2=3x+4[/tex]holds true for x = 4.
A number n plus 4.1 is less than or equal to 7 . Write this word sentence as an inequality.
Answer:
The word sentence you are looking for is:
n + 4.1 ≤ 7
Step-by-step explanation:
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Solve the inequality for y. y+15 less than 14Simplify your answer as much as possible.
im in accelerated algebra
Answer:
y < - 1
Step-by-step explanation:
y + 15 < 14 ( isolate y by subtracting 15 from both sides )
y < - 1
Answer: y < - 1
Step-by-step explanation:
y + 15 < 14 (isolate y by subtracting 15 from both sides)
y < - 1
How much interest will Harley earn in 3 years if she deposits $1,200 into a savings account that pays 6% simple interest?
14 08.08LCChoose the brand of chips with the lowest price per ounce.Brand A 20 ounces for $2.50Brand 6 32 ounces for $3.25 (1 point)O Brand ABrandBoth brands have the same price per ounce.Not enough information is given
Brand 6
1) In this problem, we need to find the unit rate. So let's do it and then compare for both brands
2) Brand A
[tex]\begin{gathered} 20oz----2.5 \\ 1oz-----x \\ 20x=2.5 \\ \frac{20x}{20}=\frac{2.5}{20} \\ x=\$0.125 \end{gathered}[/tex]So for Brand A, 1 oz is approximately 13 cents ( rounding up to the nearest hundredth)
3) Brand 6
We can write out another proportion:
[tex]\begin{gathered} 32oz----3.25 \\ 1oz----y \\ 32y=3.25 \\ \frac{32y}{32}=\frac{3.25}{32} \\ y=\$0.101 \end{gathered}[/tex]So brand 6, 1 oz is approximately 10 cents.
Solve the system of linear equations using matrices.4y-z=-5X+ 5y +z=-32x-y + 3z =13
The given system expressed as a matrix would be
0 4 -1 -5
1 5 1 -3
2 -1 3 13
To solve this, first, we have to change the first row for the second
1 5 1 -3
0 4 -1 -5
2 -1 3 13
Now, we multiply the first row by 2, then subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 -11 1 19
Then, we multiple the second row with -11/4 to subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 0 -7/4 21/4
The resulting system would be
[tex]\mleft\{\begin{aligned}x+5y+z=-3 \\ 4y-z=-5 \\ -\frac{7}{4}z=\frac{21}{4}\end{aligned}\mright.[/tex]We solve for z
[tex]\begin{gathered} \frac{-7}{4}z=\frac{21}{4} \\ z=\frac{21}{-7}=-3 \end{gathered}[/tex]Therefore, z is equal to -3.
We use z to find y in the second equation.
[tex]\begin{gathered} 4y-(-3)=-5 \\ 4y+3=-5 \\ 4y=-5-3 \\ 4y=-8 \\ y=\frac{-8}{4}=-2 \end{gathered}[/tex]Therefore, y is equal to -2.
We use y and z to find x in the first equation.
[tex]\begin{gathered} x+5(-2)+(-3)=-3 \\ x-10-3=-3 \\ x=-3+10+3=10 \end{gathered}[/tex]Therefore, x is equal to 10.
A coordinate plane with a graphed system of inequalities. The x- and y-axes both scale by one. There is a dashed line representing an inequality that goes through the plotted points (0,5) and (3,1). The shaded region for the inequality is below the line. Find the inequality represented by the graph.
The linear inequality that represented by the graph is given as follows:
y < -4x/3 + 5.
How to obtain the inequality?The inequality is represented by a line, which has the following format:
y = mx + b.
In which the coefficients of the equation of the line are listed as follows:
m is the slope, representing the rate of change, that is, by how much y changes when x increases by one.b is the y-intercept, representing the value of y when x = 0.The two points of the line are given as follows:
(0,5) and (3,1).
Hence the intercept is:
b = 5.
The slope is given by the change in y divided by the change in x, hence it is of:
m = (1 - 5)/(3 - 0) = -4/3.
Hence the line is:
y = -4x/3 + 5.
The inequality is below the shaded line, hence it is:
y < -4x/3 + 5.
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Answer:
y < -4/3x + 5.
Step-by-step explanation:
soving equations variable on both sides 3x=2x+50
Answer:
x = 50
Step-by-step explanation:
Solve the equation:3x = 2x + 50
Subtract 2x from both sides,
3x - 2x = 2x -2x + 50
x = 50
In the word BALLOONS, the ratio of vowels to all letters is
3/5
5:3
8/5
3 to 8
Pls show me step by step
The ratio of vowels to all letters in the word is 3 to 8
Given,
The word BALLOONS
We have to find the ratio of vowels to all letters in this word.
Ratio;
Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
So,
The number of letters in BALLOONS = 8
The number of vowels = 3
The ratio of vowels to all letters in the word = 3 to 8
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1/3b+11/18 when b=1/6
To answer this question, we have that the expression is:
[tex]\frac{1}{3}b+\frac{1}{18}[/tex]Answer:
Solve for b by simplifying both sides of the equation, then isolating the variable. Exact Form:
b = 3/17 Decimal Form: b=0.17647058
Step-by-step explanation:
Marcus can choose between a monthly salary of $1,500 plus 5.5% of sales or $2,600 plus 2% of sales. He expects sales between $5,000 and $10,000 a month. Complete the explanation to show which salary option he should choose based on how much he could make.
Marcus should choose $2400 plus 3% of sales.
His salary is composed of a fixed salary and a variable salary.
Fixed Salary + Variable Salary = Monthly Salary
2400 150 (3% of 5k) = 2350 - minimum salary he'll receive
2400 300 (3% of 10k) = 2700 - maximum salary he'll receive
VS
Fixed Salary + Variable Salary = Monthly Salary
1500 275 (5.5% of 5k) = 1775 - minimum salary he'll receive
1500 550 (5.5% of 10k) = 2,050 - maximum salary he'll receive
As you can see, despite the high percentage of sales offered, it is not a good option because the fixed salary is low as compared to the other option. Even the maximum salary he'll receive under the option of $1500 is way lower than the minimum salary he'll receive under the option of $2400.
Fixed salary means that each employee receives exactly the same pay and fairness as any other employee in the same pay grade. The level is determined by years of experience and position. For example, all analysts are paid exactly the same all directors are paid the same and all executives are paid the same.
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what does this equal
-5/6+(-5/6)=
Answer:
-5/3
Step-by-step explanation:
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Answer:
Diagonal = 9m
Step-by-step explanation:
area of a rectangle=L×W.-----------(I)
L=2W---------------(ii)
from (1)
32=2W×W
32=2W²
W²=32/2
W²=16
W=√16
W=4
from (ii)
length(L)=2W=2(4)=8m
Width(W)=4m
ii)Diagonal of a rectangle involves the use of Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=8²+4²
Hyp²=64+16
Hyp²=80
Hyp=√80
Hyp=8.94427191
Hyp=9m
:-The diagonal =9m
For f(x)=2^x, find for for f(5) and f (-6)
It order to find f(5) and f ( -6 ) we just replace x on the equation with
x = 5 and x = -6
In the first case, x = 5
[tex]\begin{gathered} f(x)=2^x \\ f(5)=2^5 \\ =2\cdot2\cdot2\cdot2\cdot2 \\ =32 \end{gathered}[/tex]In the second case, x = -6
[tex]\begin{gathered} f(x)=2^x \\ f(-6)=2^{-6} \\ =\frac{1}{2^6} \\ =\frac{1}{2\cdot2\cdot2\cdot2\cdot2\cdot2} \\ =\frac{1}{64} \end{gathered}[/tex]Answer: f(5) = 32 and f(-6) = 1/641 print is equal to 2 cups or 16 fulid ounces how many fulid onces are in 4 prints 3 cups
Answer:
There would be 88 fluid ounces in 4 prints and 3 cups.
Step-by-step explanation:
So, if 1 print is equal to two cups, and we have 4 prints, that would mean we can multiply 4 x 2, which equals 8 cups. Now that the prints are out of the way, we add the 3 cups still remaining, to get 11 cups. Now, it wants us to find the fluid ounces, which 16 fluid ounces are in 2 cups, so, 11 divided by 2 = 5.5. So, 5.5 x 16 = 88 fluid ounces.
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Answer:
88
Step-by-step explanation:
16x4=64
8x3=24
64+24=88
Combined gas law
Please reply with the steps, I'm confused
Answer:
V₂ = 1.0 L
Step-by-step explanation:
Combined Gas Law
[tex]\sf \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]
where:
P₁ is the initial pressure.V₁ is the initial volume.T₁ is the initial temperature.P₂ is the final pressure.V₂ is the final volume.T₂ is the final temperature.Temperature must be in kelvins (K).
To convert Celsius to kelvins, add 273.15.
Volume can be in any unit.
Given values:
P₁ = 5 atmV₁ = 1 LT₁ = 300 KP₂ = 10 atmT₂ = 600 KRearrange the equation to isolate V₂:
[tex]\implies \sf V_2=\dfrac{P_1V_1T_2}{P_2T_1}[/tex]
Substitute the given values into the equation:
[tex]\sf \implies V_2=\dfrac{5 \cdot 1 \cdot 600}{10 \cdot 300}[/tex]
[tex]\sf \implies V_2=\dfrac{3000}{3000}[/tex]
[tex]\sf \implies V_2=1.0\;L[/tex]
Therefore, the volume of V₂ is 1.0 L.
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I need help with this and I need it explained to me how to do it
Answer:
14.42 feet
Explanation:
In the figure, we can see that the pole form a right triangle with legs equal to 12 feet and 8 feet, where 8 ft is half the wide or 16 ft/2 = 8 ft.
Then, by the Pythagorean theorem, the length of the slanted pole square is equal to the sum of the square of the legs, so
[tex]x^2=12^2+8^2[/tex]Where x is the minimum length of the slanted pole. Therefore, x is equal to
[tex]\begin{gathered} x^2=144+64 \\ x^2=208 \\ x=\sqrt[]{208} \\ x=14.42 \end{gathered}[/tex]Therefore, the answer is 14.42 feet.
find the area of this parallelogram in unit9yd13 yd10 yd
Given: A parallelogram with the dimension below
[tex]\begin{gathered} b=\text{base}=13yd \\ h=\text{height}=9yd \\ a=\text{slant side=10yd} \end{gathered}[/tex]To Determine: The area of the given parallelogram
The area of a paralleogram is given by the formula
[tex]A_{\text{PARALLELOGRAM}}=\text{base}\times height[/tex]Substitute the base and the height into the formula
[tex]\begin{gathered} A_{\text{PARALLELOGRAM}}=13yd\times9yd \\ A_{\text{PARALLELOGRAM}}=117yd^2 \end{gathered}[/tex]Hence, the area of the given parallelogram is 117yd²
х1451°Find the value of x. Round to the nearest tenth.x=
To solve this question, we employ the sine relation;
[tex]\begin{gathered} \frac{14}{x}=\sin 51 \\ \end{gathered}[/tex]Rearranging the equation, we obtain ;
[tex]x=\frac{14}{\sin 51}=20.88\approx20.9[/tex]Therefore, x = 20.9
Use the partial quotients strategy to solve the following equations. Show your work. 1. 70.4 ÷ 11 = 2. 43.2 ÷ 16 =
Answer:
70.4/11 = 6.4
Step-by-step explanation:
Given a line segment that contains the points A,B, & C in order, and given that B is the midpoint of AC, if AB = 3x + 6, and BC = X + 14,find x.
Since B is the midpoint of AC.
AB = BC
3x + 6 = x + 14
Solve for x :
3x - x = 14 - 6
2x = 8
x= 8/2
x= 4
3. (02.02 MC)
The beginning mean bi-weekly wage in a certain industry is $2,498.00. If the mean bi-weekly wage grows by 3.25%, what is the new mean annual wage? (4 points)
$62,903.63
$64,948.00
$67,058.81
$69,079.13
If the mean bi-weekly wage grows by 3.25%, the new mean annual wage is: C. $67,058.81.
What is annual wage?Annual wage can simply be defined as the amount a person is paid annually as wages . Wages can be paid daily or weekly.
Using this formula to find the new mean annual wage
New mean annual wage = [Beginning mean bi-weekly wage × ( 1+ mean bi-weekly wage ) ]× Number of weeks per year /2
Let plug in the formula
New mean annual wage = [$2,498.00 × (1+ 0.0325)] × 52 weeks /2
New mean annual wage = [$2,498.00 × (1.0325)] × 26 weeks
New mean annual wage = $2,579.185 × 26 weeks
New mean annual wage = $67,058.81
Therefore the correct option is C.
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Which number lines have a point that is equal to point
P? Check all that apply.
←
H
-
-60
-60
-60
-60
0
0
0
0
0
Answer:
Step-by-step explanation:
-60 -60 -60 0 0
Rey wrapped 6 presents every 10 hours. At that rate, how long, in hours, will it take to wrap 18 presents? label optional
Data
Rey wrapped 6 presents every 10 hours.
will it take to wrap 18 presents?
Procedure
[tex]18\text{ presents }\cdot\frac{10\text{ hours}}{6\text{ presents}}=30\text{ hours}[/tex]
It will take 30 hours
Answer: it will take 30 hours to wrap 18 gifts
Step-by-step explanation:
I cant really explain it so i will show you.
() = h (hours)
| = g (gifts)
( | | | | | | ) }-6
( | | | | | | ) }-6
( | | | | | | ) }-6
10h + 10h + 10h = 30h
6g + 6g + 6g = 18g
I hope this helped
What is the difference between, obtuse, right, and scalene angles?
Answer:
Obtuse angles are angles with a measure over 90 degrees.
Right angles are angles with a measure of exactly 90 degrees.
A scalene triangle can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.
Step-by-step explanation:
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guys can u help me with this question, please
The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
The x and y coordinate helps in identifying a point in the coordinate axis and it is written as a ordered pair (x,y) .
where x represents the position of point with reference to the x-axis
and y represents the position of point with reference to the y axis .
In the question ,
points are given , we have to plot them and mark a cross .
Part(a)
point is (-2.5 , -5)
So , the x coordinate is -2.5
means the point is 2.5 units left from the origin ,
and y coordinate is -5 .
means the point is 2.5 units down from the origin .
the cross mark on the point is shown below .
Part(b)
point is (0 , -1.5)
So , the x coordinate is -2.5
means the point is 0 units units from the origin ,
and y coordinate is -1.5 ,
means the point is 1.5 units down from the origin .
the cross mark on the point is shown below .
Therefore , The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
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Line f passes through 4, 0) and is parallel to a line that passes through (7, -3) and (-10. -2)
A straight line can be written in the form of a two variable linear equation.
The equation of line passing through point (4,0) is y = -1 / 17 x + 4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The line is passing through the point (4,0).
It is parallel to the line passing through (7, -3) and (-10. -2).
The slope of the line passing through (7, -3) and (-10. -2) is
m₁ = (-2-(-3)) / (-10 - 7)
m₁ = - 1 / 17
Since the slope of two lines parallel to each other is equal, the slope of the line passing through point (4,0) is - 1 / 17.
Thus, the equation of line passing through point (4,0) can be written as,
(y - 4) / (x - 0) = - 1 / 17
=> y = -1 / 17 x + 4
Hence, the equation of the given line is y = -1 / 17 x + 4.
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