The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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Which simplified ratio correctly compares 5 meters to 100 centimeters?
A. 5:1
B. 20:1
C. 1:5
D. 1:20
The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A
How to determine the ratioRatio is simply described as the non equal comparison of two numbers, variables, or events.
It shows how many times a number or variable contains another.
The comparison is also based on size.
From the information given, we have;
5 meter to 100 centimeters
It is important to note that;
100 centimeters = 1 meters
Also, 1 meter= 100 centimeters
5 meters = x centimeters
cross multiply
x = 100(5)
Multiply the values
x = 500 centimeters
Then,
5 meters = 1 meter
Hence, the ratio is 5:1
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In 2016 the population of North Carolina was approximately 1 × 10^7. The population of Raleigh was approximately 4.6 × 10^5. How many times larger was the population of North Carolina than the population of Raleigh, to the nearest whole number?
3 of 103 of 10 Item
04:59
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Quetion
Suppoe a plane flie 48 mile in 12 minute. The relationhip between mile flown, x, and minute flown, y, by the plane can repreented by the equation y = 14x. How far will the plane fly in 28 minute?
Repone
A 120 mile120 mile
B 116 mile116 mile
C 112 mile112 mile
D 124 mile
The plane will fly 392 miles in 28 minutes. Therefore, the answer is D) 124 miles.
What is the relationship between distance and time?
The important thing is that speed is always the ratio of the distance traveled to the time needed to travel that distance: distance/time.
To find out how far the plane will fly in 28 minutes, we need to substitute x = 28 into the equation y = 14x.
y = 14x represents the relationship between the distance flown (y) and time flown (x).
Substituting x = 28 into the equation:
y = 14 * 28 = 392
Hence, the plane will fly 392 miles in 28 minutes.
Therefore, the answer is D) 124 miles.
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A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?
1.5
2.25
3.0
4.5
The multiplicative rate of change of the exponential function represented in the table is 1.5.
Option A is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the multiplicative rate of change of the exponential function represented in the table, we need to look at the ratio of consecutive
y-values.
The first ratio is:
6.75 / 4.5 = 1.5
The second ratio is:
10.125 / 6.75 = 1.5
The third ratio is:
15.1875 / 10.125 = 1.5
Since all three ratios are the same, we can conclude that the function is exponential with a constant multiplicative rate of change equal to 1.5.
Therefore,
The multiplicative rate of change of the exponential function represented in the table is 1.5.
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A right triangle has two sides with lengths 10 and 10. What is the length of its third side?
Answer:
its C
Step-by-step explanation:
Gaya buys 2 oranges and 1 cauliflower she pays £2.00
Esteben buys 4 oranges and 1 cauliflower he pays £2.90
Work out the price of one orange
Answer:
Step-by-step explanation:6
Arjun is hiking from a mountain lodge to a nearby summit. The probability that he will take the longest trail is 59. The odds against Arjun taking the longest trail are _[blank]_.
What odds best complete the sentence?
Enter your answer as “m:n{}^{\prime\prime} where m and n are the smallest integers possible, like this: 3:2
The odds against Arjun taking the longest trail are 4 : 9 .
How to find the probability ?The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.
This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:
= 1 - 5 / 9
= 4 / 9
When given as a ratio, this would be:
= 4 : 9
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What is the degree of the polynomial √ 3?
The degree of the polynomial √3 is 1.
What is polynomial?Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents of variables. Polynomials are often used to solve problems in algebra, geometry, calculus and other branches of mathematics.
A polynomial is an expression made up of variables, constants, and exponents.
A polynomial is said to have a degree when the highest degree of any of its terms is known.
The degree of a polynomial is determined by the highest exponent of a given term. In the case of √3, the exponent is 1, making the degree 1.
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Which of the following is a perfect square trinomial?
(A) 5x2 - 5x + 1
(B) 5x2 - 10x + 5
(C) 10x2 - 20x + 5
(D) 25x2 - 20x + 3
(E) 25x2 + 20x + 4
Answer:
B is the perfect square
Step-by-step explanation:
You select a marble from a bag of yellow and green marbles and put it back. You record how many yellow marbles are selected in two attempts. The graph shows the theoretical probability distribution.
Which could be the contents of the bag?
A. 2 yellow, 2 green
B. 2 yellow, 4 green
C. 3 yellow, 2 green
D. 2 yellow, 3 green
The there is 3 yellow, 2 greens marble in the bag because there is less probability of 0 yellow, number of yellow should be higher than number of greens option (C) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
We have a graph shows the theoretical probability distribution.
As you select a marble from a bag of yellow and green marbles and put it back. You record how many yellow marbles are selected in two attempts.
Since, there is less probability of 0 yellow, number of yellow should be higher than number of greens.
Thus, the there is 3 yellow, 2 greens marble in the bag because there is less probability of 0 yellow, number of yellow should be higher than number of greens option (C) is correct.
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HELP ! Will give BRAINLEIST
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Trigonometric Ratios.
10.) Cos 40° = z/32 , Hence z = 24.51
11.) Sin 58° = 27/x , hence x = 31.83
12.) Tan 33° = w/19 , hence w = 12.33
13.) Cos 52° = k/8.7, Hence k = 5.35
What number multiplies to -50 and adds to 5?
Answer:
10 and -5
Step-by-step explanation:
10(-5) = -50
10 + (-5) = 5
Good luck!
Answer:
10 and -5
Step-by-step explanation:
The model below represents 2 x + 1 = negative x + 4. 2 green long tiles and 1 green square tile = 1 long red tile and 4 square green tiles What is the value of x when solving the equation 2 x + 1 = negative x + 4 using the algebra tiles? x = negative 3 x = negative 1 x = 1 x = 3
Answer:
The model you described is a mathematical representation using algebra tiles, and it represents the equation 2x + 1 = -x + 4.
Step-by-step explanation:
To solve this equation for x, we need to isolate x on one side of the equation by using the operations of algebra (such as addition, subtraction, multiplication, and division).
In this case, we can start by adding x to both sides:
2x + 1 + x = -x + 4 + x
This gives us:
3x + 1 = 4
The next step would be to subtract 1 from both sides:
3x = 3
then we divide both sides by 3
x = 1
So x=1 is the solution.
The algebra tiles help to visualize the manipulation of equations, but the actual solving process is algebraic manipulation of the equation.
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 2)(0,2) and (3, 686)(3,686).
Draw a model for the fraction 1/6
Answer:
Hope the picture helps you draw.
Step-by-step explanation:
A Triangle has two sides of length 16.4 and 10.2. What compound inequality describes the possible length for the 3rd side
Answer:
6.2 < x < 26.6
Step-by-step explanation:
The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.
16.4 - 10.2 = 6.2
16.4 + 10.2 = 26.6
Let x = length of third side.
6.2 < x < 26.6
A hockey team scored the following number of goals in their last 5 games:
2,3,5, 3,2
Which is the mean absolute deviation of the number of goals?
Hurry pls
The mean absolute deviation of the number of goals is 0.8 goals
What is Mean Absolute Deviation ?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
The average distance between data points and a center point is referred to as mean absolute deviation. N is the number of words in the sample, where xi is the sample's individual value and x is the sample's mean or average.
Enter the numbers in the provided input box, separated by commas.To determine the mean absolute deviation for a set of data, click the "Calculate" button.To obtain the mean absolute deviation for the various figures, click the "Reset" option to clear the fields.The mean of the goals scored is = (2+3+5+3 +2)/5 = 3
The Mean Absolute Deviation is = [tex]\frac{1}{5}\{|(2-3)| + |(3-3)| + |(5-3)| + |(3-3)| + |(2-3)|}\}\\[/tex] = 4/5 = 0.8
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A scale drawing of a rectangular playground has a length of 30 inches and a width of 20 inches as shown. The scale is 1 inch = 15 feet. What is the area of the actual playground?
10 points
Answer:
Step-by-step explanation:
L x W = A
L = 30 * 15 = 450.
L = 450.
L x W = A
450 x ? = A
W = 20 X 15
W = 300.
L x W = A
450 x 300 = A
A = 135,000
Help me ASAP! Please
Answer:
i think the answer is b
Step-by-step explanation:
Answer:
b) is correct dear!
Step-by-step explanation:
see it carefully .... you will come to know ! *b* one is exactly right.....
If x = -6, which inequality is true?
Question 1 options:
-5 - 3x > 10
-3 - 5x < -14
1 - 2x > 13
2 - x < -3
Answer:
1 - 2x > 13
Step-by-step explanation:
this is the correct answer
please answer<3 its simple but ion know how-
Answer:
y= 4/3x + 2
Step-by-step explanation:
The slope is rise/run. It would be 8/6. Once you simplify, it's 4/3. the y intercept is at 2. Put it together, and there's your answer.
hope this helps!!
what is the coefficient for x in 8+ x/2
Answer: x= 8+ x over 2 = x over 2 + 8
Step-by-step explanation:
help pls fast it is urgent
Answer:
The volume formula is pi r^2h because it is similar to the formula to the area of a circle with an extra addition of the height variable, since a cylinder is just a circle with depth. The surface area formula is 2pirh +2pi r^2 because it measures the area of both circles as well as the depth. This formula is similar to the circumference formula of a circle.
Step-by-step explanation:
Mark me brainliest pls
Help Or Else I wiLl TrOw YoU INto A ToLiet
Answer:
n o
Step-by-step explanation:
I refuse to help. punish me and put me in the toilet
jk lol
Answer:
i throw u in a toilet
Step-by-step explanation:
now u in a toilet
Is
233
in the sequence below?
2
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5
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8
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11
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14
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Answer:
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Pls can someone answer these two I will give brainliest and 30 points
Answer:
The first one is false.
3(2 ÷ x)
The second is true.
Think about all the models and strategies you have discussed today. Describe how one of them helped you better understand how to find the slope of a line.
Answer:
I could find the slope of a line by looking at the gradient of a graph that the line creates. If the line is linear, then the gradient will be a constant value, which I can use to find the value of the slope. If the line is not linear, then I can use a derivative to find the slope at a given point. However, if the line is concave or concave up, then I will need to take the second derivative of the equation to determine which point on the line is closest to the point that I'm trying to calculate.
Step-by-step explanation:
Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true? A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. C. $a-b$ is a multiple of $6$. D. $a-b$ is a multiple of $2$. List the choices in your answer separated by commas. For example, if you think they are all true, then answer "A,B,C,D".
The statements that are true, based on the multiples of 3 and 6 are:
A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. How do multiples relate ?When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.
This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.
It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.
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Water guns are on sale this week. If
this water gun is $8.50, how much
will it cost after the 30% discount
and an 8% sales tax.
Answer:
$6.43
Step-by-step explanation:
8.50 times 0.30=2.55
8.50-2.55=5.95
5.95 times 0.08=0.476
0.476+5.95=6.426 rounded would be $6.43
14)
Which statement best describes the solutions of a two-variable equation?
A)
The ordered pairs must lie near the graphed equation.
B)
The ordered pairs must have x = 0 for one coordinate.
C)
The ordered pairs must lie on the graphed equation.
D)
The ordered pairs must have y = 0 for one coordinate.
PLEASE HELP!!
Answer:
Solution of a System. In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.
Answer: A) The ordered pairs must lie near the graphed equation