The x-intercepts of an equation are simply the zeros of the equation
The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts
The equation is given as:
[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]
Set the equation to 0; i.e. calculate the zeros
[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Divide both sides by constant b
[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Split the above equation, as follows
[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]
Solve for x in each of the equation
[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
Remove repeated solutions
[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
The count of solutions above is 4
Hence, the equation has 4 distinct x-intercepts
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Find x if mZPHI = 150º,
mZGHI = 15x – 5, and mZGHP = x + 13
PLEASE ANSWER Quickly!
Find the equation of the line
Y= __x + __
Answer:
y= -x+5
Step-by-step explanation:
→first you need to identify 2 points. I'm using (5,0) and (0,5)
→second you need to find the slope using y2-y1/x2-x1 as your formula
5-0/0-5= 5/-5=-1
→then you need to use y-y1=m(x-x1) formula
y-0=-1(x-5)
(distribute the -1)
y-0= -1x+5 (+5 because a negative times a negative is a positive)
(combine like terms)
y= -1x+5
→once you solve you get y= -x+5
image.......................
Answer:
10.75
Step-by-step explanation:
The cost of an adult ticket is £6 more than that of a child ticket, so will be shown by c+6.
Now, we are told that the cost of four child tickets and two adult tickets is £40.50, so we can put this in an equation and solve for c:
(c+6)+(c+6)+c+c+c+c=40.50
6c+12=40.50
6c=28.50
c=4.75
so, a childs ticket is 4.75
now to find the cost of an adult ticket you add 6,
4.75 + 6
= 10.75
Round 0.00208815 to 3 significant figures
Please help! I’ll mark as BRAINLIEST :))
If a conditional statement is true and its converse is also true, could the conditional statement be written in another way?
Step-by-step explanation:
could the conditional statement be written in another way
The ratio of collectible cards Kyle owns to cards that Zeona owns is 3:2. Zeona has 36 cards. How will the ratio of Kyle’s cards to Zeona’s cards change if they both sell half of their cards? Explain.
Answer:
It wouldn't.
Step-by-step explanation:
With the ratio, since Zeona has 36 cards, Kyle must have 54. If they each sold half, Kyle would have 27 and Zeona would have 18. So, the ratio would still be 3:2.
Let x represent any year. Write an inequality in terms of x and 1610
that is true only for values of x that represent years after the year the Mali Empire fell.
The year of the empire fell = 1610.
We are given x as a variable that represents the year after the given year 1610.
We need to setup an inequality for this situation.
Please note: The year after the year number 1610 will have a number that greater than 1610.
Let us make a statement for inequality to be written.
"The year after the 1610 is greater than 1610".
The year after the 1610 is x and gerater than symbol is >.
So, we can setup an inequality as:
x > 1610 : Read as x is greater than 1610.
Whitch of the following best represents a graph with a range that is less than -3?
The coffee shop also sells small bag of coffee beans. the bags come in two 4/5 kilogram and 7/12 kilogram. How much more coffee does the bigger bag have?
The bigger bag have 13/60 kilogram more coffee.
What is fraction?A fraction is defined as numerical representation for part of a whole which represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that the bags come in two 4/5 kilogram and 7/12 kilogram
⇒ 4/5
⇒ 7/12
We will first establish that there has a comparable denominator.
Multiply by (12/12) in the fraction 4/5
⇒ 4/5 (12/12)
⇒ 48/60
Multiply by (5/5) in the fraction 7/12
⇒ 7/12 (5/5)
⇒ 35/60
Determine the difference between fractions as :
⇒ 48/60 - 35/60
⇒ 13/60 kilogram
Hence, the bigger bag have 13/60 kilogram more coffee.
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What is an estimation strategy
This is for 6th grade math please help
Answer:
Estimation is a mental process of coming up with an answer that is relatively close, to allow decisions to be made. The types of estimation are quantity, computation and measurement.
An estimation strategy is simply coming up with a good estimate based on evidence and already known facts. Coming to a conclusion as close to the real answer as you can. It can also be called an educated guess.
In the late nineteenth century, the scientist Marie Curie performed experiments that led to the discovery of radioactive substances. A radioactive substance is a substance that gives off radiation as it decays. Scientists describe the rate at which a radioactive substance decays as its half-life. The half-life of a substance is the amount of time it takes for one-half of the substance to decay. Radium has a half-life of 1600 years. How much radium will be left from a 1000-gram sample after 1600 years?
Answer:
Step-by-step explanation:
Half life is the time taken by a radioactive substance to reduce of half of its original size
If the half life of radium is 1600, this means that the original radioactive substance N0 have reduced to N0/2 after 1600 years
if we are given N0 = 1000grams
The amount of the substance that will remain after 1600 years will be N0/2 i.e 1000/2 = 500g
Hence 500 grams of radium will be left after 600years
20 POINTS!!!! NUMBER 9 please
Answer:
Step-by-step explanation:
C
prime factorization of 45 expanded form
The prime factorization of 45 would be 5×9, and 9 is 3×3, so 45 would be 5×3^2.
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help me it's my homework
Answer:
2. Answer is 4 and for 3. P= 1/4s
Step-by-step explanation:
Simply divide the values of one another.
This results you with:
8/2 = 4
12/3 = 4
10/5 = 2 -> I think there was an error or typo here
40/10 = 4
The constant proportion would be 4 because it is constant in every situation for S and P.
The equation would be p= 1/4s because 1 value of p would equal 4 s.
What are two different decimals that when rounded to the nearest thousandth would give 5.24 as an answer
Answer: 5.2387 and 5.2437
Step-by-step explanation:
Explain or show that the point (5,-4) is a solution to this system of equation 3x-2y=23
Answer:
Step-by-step explanation:
3(5)-2(-4)=23
15+8=23
23=23
The system of equation 3x-2y=23 satisfies the point (5, -4) after plugging x = 5 and y = -4, the point is a solution to the equation.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation of linear equation is:
3x - 2y = 23
The point is (5, -4)
Plug x = 5 and y = -4
3(5) - 2(-4) = 23
15 + 8 = 23
Thus, the system of equation 3x-2y=23 satisfies the point (5, -4) after plugging x = 5 and y = -4, the point is a solution to the equation.
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6x+3<7-2x
I’m not sure if I’m doing it right so an explanation would be nice
Answer:
x<0.5
Step-by-step explanation:
this is just like simplifiying equations if you've done that before
first you want to isolate the variable, so you want to combine the values of x (in this case it's 6x and the -2x)
so you can either add 2x to both sides or you can subtract 6x on both sides, in this case ill just add 2x to both sides.
Then you subtract 3 from both sides to get 8x<4
after you get that, you want to divide both sides by 8, and you generally want to do that step last, it makes it easier, and you get x<1/2 or 0.5
just a reminder that with working with inequalities, you want to remember to flip the direction the inequality is whenever you divide by a negative number
what is (6x-5) + (8x-50)
Answer:
14x - 55
Step-by-step explanation:
6x - 5 = 8x - 50
6x + 8x = 14x -5-50
-5- 50 = -55
14x -55
[tex]6x + 8x - 5 - 50 \\ = > 14x - 55[/tex]
Bob owed S225 on his store credit card. Ile made a payment of S75. Ilow much does Bob owe on his credit card? 0 -150 O 150 O 300 -300
Help me pleasee !
The answer is -300 because he owes -225 and then when he spends they subtract the amount he spent so the equation would be -225-75= the answer of -300
Which of the following shows the greatest percent increase?
A. 50 increased to 75
B. 500 increased to 700
C. 5,000 increased to 7,000
D. 50,000 increased to 74,000
50 increased to 75 (option A) shows the greatest percent increase.
How to solve for percentage increase?To determine which of the given options shows the greatest percent increase, we can calculate the percent increase for each option using the following formula:
percent increase = (new value - old value) / old value x 100%
Using this formula, we can calculate the percent increase for each option as follows:
A. percent increase = (75 - 50) / 50 x 100% = 50%
B. percent increase = (700 - 500) / 500 x 100% = 40%
C. percent increase = (7,000 - 5,000) / 5,000 x 100% = 40%
D. percent increase = (74,000 - 50,000) / 50,000 x 100% = 48%
Therefore, the option that shows the greatest percent increase is option A, which increased from 40 to 75, a percent increase of 50%.
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Which mathematical concepts did Euler's legacy include? Check all that apply.
the notation for the imaginary unit
the idea of a functional relationship
the formalization of function notation
the definition of a circle's circumference
the notation for the base of the natural logarithm
Answer:
a)the notation for the imaginary unit
c) the formalization of a function notation
e) the notation for the base of the natural logarithm
Step-by-step explanation:
it said i was correct :P
the notation
the formalization of function notation
the notation for the base of natural logarithm
the function f(x) is shown in this graph
the function g(x) = -6x -5
Answer:
C.
Step-by-step explanation:
in a survey, 8 out of 32 students preferred vanilla ice cream if 252 students are surveyed how many should theoretically prefer ice cream
Answer:
63 people
Step-by-step explanation:
Given parameters:
Number of students survey = 32
Number of those that liked ice-cream = 8
Total population size = 252
Unknown:
How many people in the population should prefer ice cream = ?
Solution:
From the survey;
8 out of 32 students prefer ice cream;
8 : 32
1: 4
This shows that 1 out of 4 students will prefer ice cream
NOw to the total population;
If out of 4 students, 1 prefers ice-cream;
Out of 252 students y will prefer ice-cream
Number of students that prefers ice-cream = [tex]\frac{252}{4}[/tex] = 63people
Gianna earned $466.90 at her job when she worked for 23 hours. How much money did she earn each hour?
Answer:
About $20.30
Step-by-step explanation:
$466.90 divided by 23.
a game consists of placing seeds in 24 cups. a player puts two seeds in the first cup, four in the second, six in the third and so on. how many seeds will be required altogether if the player continues to the 24th cup in this way?
Step-by-step explanation:
The next cup will always have 2 more than the previous one. Continue the pattern of adding two seeds to each cup until you reach the 24th cup like so:
#s on left side = # of seed , #s on right side = # cup
6 | 3 8 | 4 10 | 5 12 | 6 14 | 7 16 | 8 18 | 9 20 | 10 22 | 11
24 | 12 26 | 13 28 | 14 30 | 15 32 | 16 34 | 17 36 | 18 38 | 19
40 | 20 42 | 21 44 | 22 46 | 23 48 | 24
What you want to know is the number of TOTAL SEEDS NEEDED TO PLAY THIS GAME. NOT how many seeds will be in the 24th cup. To find the TOTAL you need to add 2 + 4 + 6 and so on like so:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = 600 TOTAL SEEDS TO PLAY THIS GAME. (this is your answer)
In a lab, a substance was heated by 48 Degrees Celsius over a period of 8 hours at a constant rate. what was the change in temperature each hour?
Answer: The change in temperature each hour was 6 degrees celsius.
Step-by-step explanation: 48 divided by 8 = 6
A graph of a quadratic function is shown below.
What is the vertex of the parabola shown? (5 points)
A (10, 800)
B (800, 10)
C (30, 0)
D (0, 600)
Using it's concept, it is found that the vertex of the quadratic function is given by:
B (800, 10).
What is the vertex of a quadratic equation?It is the point in which the parabola changes from increasing to decreasing, or vice versa, that is, the point in which it turns.
In this problem, it turns at x = 10 and y = 800, hence option A is correct.
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Answer:
Step-by-step explanation:
I WILL GIVE BRAINLIEST! Rectangle A is a rectangle with area 24. Rectangle B is a scaled copy of Rectangle A with a scale factor of 2. What is the area of Rectangle B?
Answer:
12
Step-by-step explanation:
24/2=12
Encuentra la ecuación del siguiente enunciado. El profesor Rigoberto tiene cuatro hijos. Cada uno es un año mayor que el anterior. ¿Cuál es el total de años que acumulan los cuatro hijos de Rigoberto?
x+x+x+x
4x+6
6+x
4+x
Construyendo las ecuaciones, se encuentra que el total de años que acumulan los cuatro hijos de Rigoberto es dado por 4x + 6.
------------------------------------
No sabemos la edad de el menor, entonces, la llaremos de x.Cada uno es un anõ mayor que el anterior, puesto que las edades son: [tex]x + 1, x + 1 + 1 = x + 2, x + 2 + 1 = x + 3[/tex]El total de años es dado por:
[tex]x + x + 1 + x + 2 + x + 3 = 4x + 6[/tex]
4x + 6, segunda opción.
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Quinn posted a comment on a social media site. The table shows the number of new "likes" Quinn's comment receives each minute after the comment is posted. Write an equation of a line in standard form to represent the data. Then use the equation to find the amount of time it will take until Quinn's comment receives no new "likes".
mintues; liked:
1 8
2 6
3 4
A. x + 2y = 10; 5 minutes
B. 2x + y = 10; 5 minutes
C. x + 2y = 10; 6 minutes
D. 2x + y = 10; 6 minutes
Answer: B. 2x + y = 10; 5 minutes