a. In order to factor the equation, the vertex form needs to be expanded to the standard form first, to obtain the factors of the equation
b. The parabola is easily graphed with the information on the vertex given in the vertex form of the quadratic equation
c. The vertex, minimum or maximum of the parabola are easily obtained in the vertex form of the quadratic equation
d. The quadratic formula is defined based on the standard form of the quadratic equation
Answer:
[tex]\huge{\boxed{\text{A) Standard form}}}\\\huge{\boxed{\text{B) Vertex Form}}}\\\huge{\boxed{\text{C) Vertex Form}}}\\\huge{\boxed{\text{D) Standard Form}}}\\[/tex]
Step-by-step explanation:
Vertex form is represented as: [tex]f(x) = a(x-h)^2+k[/tex], where the vertex of the parabola is (h, k).
Standard form is represented as [tex]f(x) = ax^2+bx+c[/tex], where a, b, and c are constants.
A) When factoring an equation, the sum of the roots is equal to b and the sum of the roots is equal to c, meaning standard form is the beneficial.
B) When graphing a parabola, vertex form is extremely beneficial, as it provides the vertex of the parabola, and the direction in which it opens. If "a" is positive, the vertex opens upward, while when "a" is negative, the vertex opens downward. As such, graphing is greatly eased with this information.
C) As is evident from the name, vertex form is the best for identifying the vertex of a parabola, as it is explicitly shown via the constants h and k.
D) The quadratic formula directly uses the constants a, b, and c, so working in standard form is more beneficial, as it removes the effort of solving for each constant.
Hope it helps :) and let me know if you want me to elaborate.
Find the next two terms in this
sequence.
50, 40, 31, 23, 16, | ? ],[?]
Answer:
8, 0
Step-by-step explanation:
Evaluate x³-2xy² + y³ when x= -2 and y=3
Answer:
5
Step-by-step explanation:
[tex] {x}^{3} - {2xy}^{2} + {y}^{3} \\ {( - 2)}^{3} - 2( - 2)(3) {}^{2} + {3}^{3} \\ - 8 + 4 - 18 + 27 \\ 31 - 26 = 5[/tex]
Answer:
55
Step-by-step explanation:
1. Substitute in the values
-2^3 - ( 2 * -2 * 3^2 ) + 3^3
2. Simplify the powers
-8 - ( 2 * -2 * 9 ) + 27
3. Solve the brackets
-8 - ( -4 * 9 ) + 27
-8 - ( -36 ) + 27
-8 + 36 + 27
4. Solve
-8 + 63
55
I need help with my homework
Answer:
60
Step-by-step explanation1
135 = 2x+15 => corresponding angles
2x= 135-15
2x= 120
x= 60
Which equation is true?
Answer:
B
Step-by-step explanation:
Answer choice B would equal -3/4
A cyclist rode 3.75 miles in 0.3 hours
A. how fast was she going in miles per hour?
B. At that rate, how long will it take her to go 4.5 miles?
The cyclist takes 0.36 hours to travel 4.5 miles.
What is distance?The actual length covered by the body is defined as distance travelled, whereas displacement is the straight path between the initial and final points.The imperial and customary systems use the unit miles per hour (symbol: mph) to measure speed. It represents the number of statute miles traveled in one hour.Here given that,
The distance travelled by the cyclist 3.75 miles.
Time = 0.3 hour
Distance / Time = Speed
By substituting,
3.75 / 0.3
= 12.5 miles per hour is the speed.
2) Distance = 4.5 miles, speed = 12.5 miles per hour.
Distance / Speed = Time
Time = 4.5 / 12.5
=0.36 hours
Therefore it takes 0.36 hours to travel 4.5 miles.
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Erin is selling books for $12 each. She wants to make more than $180 in book sales. Write an inequality that can be used to determine the number of books, b, she must sell in order to meet her goal, then solve for b.
The inequality that can be used to determine the number of books, b, Erin must sell in order to meet her goal of making more than $180 in book sales is 12b ≥ 180.
2. The solution to the inequality 12b ≥ 180 is that b ≥ 15.
What is inequality?Inequality is a mathematical statement that two or more mathematical expressions are unequal because their solutions are not equivalent in value.
Inequalities are depicted as less than (<), more than (>), not equal to (≠), less than or equal to (≤), and more than or equal to (≥).
The selling price per book = $12
The total sales revenue expected is ≥ $180
The number of books = b
Inequality describing the situation = 12b ≥ 180
b ≥ 180 ÷ 12
b ≥ 15
Thus, we can conclude that Erin needs to sell 15 or more books to earn $180 or more from the book sales.
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What kind of transformation converts the graph of f(x)= – 7|x|+7 into the graph of g(x)=7|x|–7?
The transformation from f(x) = -7|x| + 7 to g(x) = 7|x|- 7 is-
The graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)
What is rotation?
The mathematical transformation which turns a geometrical figure about a fixed point is called rotation. The fixed point is called center of rotation.
f(x)= –7|x|+7
g(x) = 7|x|- 7
At first the graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)
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How would I solve this equation?
[tex]\sqrt{x}({x}+{1})=0[/tex]
Find the total snowfall for this year if it snowed 1/10 inch in November, 2 1/5 inches in December and 1 3/4 inches in January.
Answer: Just add them up. 5 1/20
Step-by-step explanation:
1+1+2=4. For the fractions, find the LCM. The LCM is 20 so you make all the fractions denominator 20. 2/20, 4/20, 15/20. Now you get 5 1/20 in the end
the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes. write an expression that shows how many sweatshirts were not adult sizes.
The expression that shows how many sweatshirts were not adult sizes is s - 19 .
Given :
the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes.
Expression :
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Expression = number of sold sweatshirts - number of adult sizes.
= s - 19.
This gives the number of sweatshirts that are not adult sizes
if s = 25
then not adult sizes sweatshirts = s - 19
= 25 - 19
= 6
Hence the expression is s - 19.
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The table below shows the temperature, in degrees Fahrenheit, in Boston, Massachusetts, over a 10-hour interval
Time
A
B
C
D
1 am to 5 a.m.
5 a.m. to 7 a.m.
7 am to 10 a.m.
1am.
10 am to 11 a.m.
29° F
5am
Temperature (Fahrenheit)
Over which interval does the temperature have the greatest average rate of change?
20° F
7 am
18 F
10 a.m.
25° F
11am.
28 F
Answer:i don’t know
Step-by-step explanation:
Need Help for this Answer on this screenshot
Answer:
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A
Step-by-step explanation:
a car is traveling at 50 mph due south at a point 1 mile north of an intersection. a police car is traveling at 40 mph due west at a point 1 mile east of the same intersection. at that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. what does the radar gun register?
If a car is traveling at 50 mph due south at a point 1 mile north of an intersection. the radar gun register at -62.6 mph.
What is distance?Distance can be defined as how far an object is from another object.
Distance of the first car north of the intersection point =y
Distance of the police car west of the intersection =x
Distance between the cars =s
s² =x² +y²
x=1.4 miles or 0.25 miles
y =1/2 miles or 0.50 miles
Pythagoreans theorem
Distance between cars
s =√x²+y²
s=√(0.25 miles)² +(0.50 miles)²
s =0.559 miles
Hence,
ds/dt = [0.25 miles/ 0.559 miles (-40 mph)] + [0.50 miles/0.559 miles (-50 mph)
ds/dt = -17.89 + -44.7
ds/dt = - 62.59mph
ds/dt =- 62.6 mph (Approximately)
Therefore the distance is 62.6 mph.
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Given: ΔPQR ≅ ΔPNM
What is the measure of PM?
Responses
A - b
B - c
C - a
D not enough information
Answer:
A
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent.
Δ PQR congruent to Δ PNM
PR and PM are corresponding sides , then
PM = PR = b
Convert 7π/21 to degrees.
Converting 7π/21 to degrees will be 60°.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.
Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.
It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.
This will be illustrated as:
= 7π / 21 × 180 / π
= 7/21 × 180
= 60°
The value is 60°.
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HELP MEE !! 45 points!!
Solve. What is “u” in the inequality? –11 < 6u+ 4u
Answer:
u > -11/10
Step-by-step explanation:
Select the equation of a line with a slope of 5 that passes through the point (2, –3).
Multiple choice question.
cross out
A)
y=5x – 13
cross out
B)
y=5x – 3
cross out
C)
y=5x+7
cross out
D)
y=5x+2
Answer: A) y = 5x – 13
Step-by-step explanation:
The equation is y=mx + b
We know the slope is 5 and the y-intercept is at ( 0, -13)
So our equation is y = 5x - 13
So, the answer is A
If the constant of Proportionality between X and Y is 2.5, Which equation represents their relationship
A) Y= 2.5X
B)2Y=5X
C)5Y=2X
D)Y=X divided by 2.5
Y= 2.5x equation represent their relationship .
What is equation?An equation is a formula that is express the equality of two expressions ,by the connecting them with the equal sign .
The process of equting one thing with another is called the equation of science with objective .
The equation is representing direct proportion is, by the connecting them with in the equal sign.
y = kx ← k is the constant of proportion
Here k = 2.5 , thus
y = 2.5x ← equation of proportion.
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Please help me out I really need this answer please please
Answer:
A. Imaginary Square is 1 so ye ignore
Tyler eat 6 crackers for a snack each weekday. On Friday, he drops 3 and only eats 3. What is the total number of crackers Tyler eats during the week?
Answer: 39 crackers
Step-by-step explanation:
There are seven days a week
Only Friday, he eats half, so 6 left
6 times 6 = 36
36+ 3= 39
What is the value of f(x) = 1/2x + 5 when x = 4?
Answer:
f(x)=7
Step-by-step explanation:
f(x)= 1/2x+5 ; x=4
f(4)= 1/2(4)+5
f(4)= 2+5
f(x)=7
Hope this helps, because I just did this lesson and I was confused at first, but with practice you will get it!
a candidate for political office wants to determine if there is a difference in his popularity between men and women. to test the claim of this difference, he conducts a survey of voters. the sample contains 250 men and 250 women, of which 44% of the men and 52% of the women favor his candidacy. do these values indicate a difference in popularity? use a 0.01 significance level.
Yes, these values indicate a difference in popularity. Using a 0.01 significance level, the p-value for this test is 0.0018, which is less than the significance level.
This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.
1. The candidate has a population of voters that he wishes to test to see if there is a difference in his popularity between men and women.
2. He conducts a survey of 250 men and 250 women, 44% of the men favoring his candidacy and 52% of the women favoring his candidacy.
3. To determine if there is a significant difference between the two samples, we first calculate the difference in proportions between the two groups:
52% - 44% = 8%.
4. We then use a 0.01 significance level to conduct a two-tailed z-test for proportions to determine if there is a statistically significant difference between the two groups.
5. The p-value for this test is 0.0018, which is less than the significance level of 0.01.
6. This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.
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Let point A be (2,7) and point B be (-6,-3). What point is on the segment connecting A and B such that the distance from the point to B is 4 times the distance from the point to A?
Answer:
The point on the segment connecting A and B that is 4 times as far from B as it is from A is (-8, 8).
Answer:
or the distance to be 4 times the distance from B as A the segment must be divided into (4+1) = 5 segments
so we want the point that is 1/5 of the way from A to B
x from A to B is 2 to - 6 = -8 units 1/5 * -8 + 2 = 0.4
y from A to B is 7 to -3 = -10 units 1/5 * -10 + 7 = 5
there are 10 students in the class. two th them should be selected as the best students in the class. how many different ways can be done
There are 45 different ways in which two of them can be selected as the best students in the class.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).
A k-combination of a set S is officially defined as a subset of S's k unique elements.
Total number of students = 10
Number of students to be selected = 2
No. of ways = 10C2
= (10*9)/2
= 5*9
= 45
Hence, there are 45 different ways in which two of them can be selected as the best students in the class.
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The first side of a triangle is 3cm longer than the second. The third side is twice as long as the second. The perimeter is 31cm. Find the length of each side.
Answer:
7 cm ; 10 cm ; 14 cm
Step-by-step explanation:
x = y + 3
z = 2y
x + y + z = 31
y + 3 + y + 2y = 31
4y = 31 -3
4y = 28
4/4 y = 28/4
y = 7
z = 7(2) = 14
x = 7 + 3 = 10
there are 25 animals on a farm. 10 of them are cows. what percentage of animals on the farm are cows?
Answer: 40%
Step-by-step explanation:
Take 10 divided by 25; then times 100 = 40%
C
10x + 12 = 2(5x+6)
WITH SOLUTION
Answer:
0
Step-by-step explanation:
10x + 12 = 2(5x+6)
or, 10x + 12 = 10x + 12
or, 10x - 10x = 12 - 12
or, 0 = 0
.
. . so, 0 is the answer.
Step-by-step explanation:
1st : distribute10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
2nd : subtract 12 from both sides10x + 12 = 10x + 12
10x + 12 - 12 = 10x + 12 - 12
3rd : simplify subtract the numbers 10x = 10x4: subtract 10x from both sides10x = 10x
10x - 10x = 10x - 10x
5: simplify combine like terms 0 = 0____________________________________________
hope it helps uh..!! ♥️A full box of cereal contains 12 1/2 cups. Each morning for breakfast Jules eats a serving of cereal that is 1 1/2 cups size. How many servings are in a full box of cereal?
Number of servings that are in a full box of cereal is 8.33 servings
Total quantity of cereal contains in the box = [tex]12\frac{1}{2}[/tex] cups
Convert the mixed fraction to simple fraction
[tex]12\frac{1}{2}[/tex] cups = 25/2 cups
Total quantity of cereal eats in each serving = [tex]1\frac{1}{2}[/tex] cups
Convert the mixed fraction to simple fraction
[tex]1\frac{1}{2}[/tex] cups = 3/2 cups
Number of servings in a full box of cereal = Total quantity of cereal contains in the box ÷ Total quantity of cereal eats in each serving
Here we have to use the division
Substitute the values in the equation
Number of servings in a full box of cereal = 25/2 ÷ 3/2
= 25/2 × 2/3
= 25/3
= 8.33
Therefore, a full box contains 8.33 servings
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The ratio r:h is 5:8 and the ratio h:u is 4:7. Work out the ratio r:h:u in its simplest form
The simplest form of the ratio r:h:u is 5 : 8 : 14.
What is the ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
We have,
r : h = 5 : 8 .........(i)
h : u = 4:7 ........(ii)
Multiplying the (i) and (ii) by numbers that will make 'h' have the same value in the ratios
Multiplying (i) by 1
(r : h)*1 = (5 : 8)*1
= r : h = 5 : 8
Multiplying (ii) by 2
(h : u)*2 = (4:7) *2
= 8 : 14
the ratio r : h : u in the simplest form = 5 : 8 : 14.
Hence, the simplest form of the ratio r:h:u is 5 : 8 : 14.
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5/6 X +3 equals 13 
Answer:
Step-by-step explanation:
The answer is 12
Answer:
x=12
Step-by-step explanation:
[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]