The zeros of the function y = x^2 - 4x - 5 = 0 are 5 and -1.
The given function is y = x^2 - 4x - 5 = 0
We know that the general form of a quadratic equation is:
ax^2 + bx + c =0
On comparing the given equation y = x^2 - 4x - 5 = 0 with the general form of a quadratic equation ax^2 + bx + c =0 we get that:
a= 1, b = -4, c = -5
On multiplying a and c, we get -5 and the factors of it are 1 and 5.
Hence we can break the equation into:
x^2 - 5x + x - 5 = 0
We can factor it into:
x (x -5) + 1 (x - 5) = 0
(x + 1) (x - 5) = 0
Therefore, the zeros of the equation are -1 and 5.
The question is incomplete, the complete question is:
What are the zeros of the function y = x^2 - 4x - 5?
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How do you solve under root minus 16?
Answer:
4i
Step-by-step explanation:
Any negative numbers do not have any real square roots, only imaginary ones.
[tex]\sqrt{-16} = i\sqrt{16} = 4i[/tex]
hope this helps :)
What are examples of SAS congruence postulates?
The examples of SAS congruence postulates are
∆ ABC ≅ ∆DEF∆ABC ≅ ∆CEFThe SAS is stands for Side-Angle-Side congruence postulate which states that triangles are congruent if two sides and an included angle of a triangle are congruent with two sides and an included angle of a second triangle. Note that we need to include the angle between the two sides.
Example 1 : Let's say you have one triangle, ∆ABC with side lengths 5 and 10 and the angle included between those two sides is 30 degrees. If you have a second triangle, ∆DEF that also has side lengths 5 and 10 with a 30 degree angle in between, then by the SAS Postulate ∆ABC is similar to ∆DEF.
Example 2 : Point C is the midpoint of BF
so, AC = CE
Statement Reason
AC = CE C is mid point so, it
divides equal parts .
BC = CF C is mid-point
∠ACB =∠ECF Opposite angles
Thus, by the Side Angle Side postulate, the triangles are congruent i.e,∆ABC ≅ ∆CEF
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Which is the same as 98.25%10
According to question,
We know that,
To determine the percentage,
we have to divide the value by the total value and then multiply the resultant by 100,
Percentage formula
Is /of=%?100
Or
Part/whole=%/100
With the help of question,
Given data,
Put the value of percentage formula,
98.25/100×10
=9.825
98.25%×10 is the same outcome of 9.825.
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Which is an asymptote of the graph of the function y tan 3 4x?
The graph of the function y tan 3 4x has a vertical asymptote at x = π/12, which means that as x approaches π/12 from either side, the output of the function increases without bound.
The graph of the function y tan 3 4x has a vertical asymptote at x = π/12, which means that as x approaches π/12 from either side, the output of the function increases without bound. This is because when x = π/12, the denominator of the tangent function (3/4x) is 0, which creates an undefined value. As a result, the output of the function increases without bound as x approaches π/12. This is why x = π/12 is an asymptote of the graph. Asymptotes can be thought of as boundary lines, beyond which the graph of the function cannot cross. In this case, the graph of y tan 3 4x will approach the vertical asymptote of x = π/12, but will never cross it.
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What is the image of (9,-4)after a dilation by a scale factor of 5 centered at the origin?
The image of the point (9,-4) after the dilation is (45, -20).
What is the image after the dilation?If we dilate any point (x, y) by a scale factor k centered at the origin, the new coordinates of the point will be:
(k*x, k*y)
In this case we have the point (9, -4), and the scale factor is k = 5, then the image of the point after the dilation is:
(5*9, 5*-4) = (45, -20)
The image after the dilation is (45, -20).
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What is the mode of the following set of data 12 11 14 10 8 13 11 9?
The mode of the given data set is 11.
A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.
In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.
The mode is the value that occurs the most often in a given set of data.
In the data set provided here, the mode is 11, hence 11 should occur the most number of times.
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a. what is the area of the window seat when x=3
b. write a polynomial that helps represent the area of the window seats
a) The area of the window seat when x=3 is 8 ft².
b) Polynomial that represent area of the window is x² - 1
What is trapezium?
In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.Area of trapezium = 1/2 (a+b)*h
a= x ft
b = x+2 ft
c = x-1 ft
a ) When x=3;
a = 3 ft
b = 3 + 2 = 5 ft
c = 3-1 = 2 ft
Now, Area of window seat = 1/2 (3+5) 2
= 1/2 * 8 * 2
= 8 ft²
Hence, area of window seat is 8 ft².
b) Polynomial that helps represent the area of window seats
= 1/2(a+b)*h
= 1/2(x + x +2) * (x-1)
= 1/2 (2x+2)*(x-1)
= 1/2 * 2(x+1)* (x-1)
= (x+1) * (x-1)
= x² - 1
Hence, the Polynomial that represent area of the window is x² - 1.
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Where are the asymptotes for the following function located f x 7 x 2 2x 24?
As per the given function, asymptotes of the hyperbola will be at x = -4 and 6.
The term hyperbola id defined as a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant
Here we have given the following function,
f(x) = 7/x² - 2x - 24
Now, we have to calculate the asymptotes as follows,
Let us consider that f(x) = ∞ and it is not defined
=> x²- 2x - 24 = 0
Now, we have to factories the expression, then we get
=> x² - (6-4) x - 24 = 0
When we simplify the given expression, then it looks like,
=> x² -6x + 4x -24 = 0
Therefore, the value of x is calculated as
=> ( x - 6 ) ( x + 4 ) = 0
Then the rage of x is at -4 and 6.
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One plus negative two
Answer:
-1
Step-by-step explanation:
1 + (-2)
= 1 - 2
= -1
Question:
1 + (-2)
Answer:
1 + (-2)
1 - 2
-1
Step-by-step explanation:
1 + (-2)
In this step, we can see (+)(-) which is (-)
As the answer is - we should subtract it
1-2
And then put the bigger number symbol which is (-).
So, The answer is -1.which of the following situations describes a multiple regression? a.) using the brain volume to predict the iq score of an individual. b.) using the brain volume, the body height, and the body weight to predict iq score of an individual. c.) using the iq score to predict the body height and body weight of an individual. d.) using the body height and body weight to predict iq score and brain volume of an individual.
The correct answer is option b). Multiple regression is described best as "using the brain volume, the body height, and the body weight to predict the IQ score of an individual."
Multiple regression is a statistical technique that involves using two or more predictor variables to predict a single response variable. In this case, the response variable is the IQ score and the predictor variables are the brain volume, the body height, and the body weight. By using multiple predictor variables, multiple regression allows you to analyze the combined effect of these variables on the response variable, as well as to identify which variables have the greatest influence on the response variable.
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Refer to the square.
6
What is the length of the square's side?
O 12 units
O 6/√2 units
O 3 units
O 6√2 units
The length of the diagonal of the square is[tex]\text { (b) } 3 \sqrt{2} \text { units }[/tex].
What is Pythagoras theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The length of the diagonal of a square is calculated using the following Pythagoras theorem.
[tex]d^2=l^2+l^2\\[/tex]
Where:
d represents the length of the diagonal
l represents the side length of the square
So, we have:
[tex]d^2=3^2+3^2[/tex]
Evaluate the like terms
[tex]d^2=2\left(3^2\right)[/tex]
Take the square roots of both sides
[tex]d=3 \sqrt{2}[/tex]
Hence, the length of the diagonal of the square is [tex]\text { (b) } 3 \sqrt{2} \text { units }[/tex]
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I need answers for this questions
Answer:
a=7 b=2 c=0.2 d=9 e=0.064 f=8 g=16 h=0.03 i=0.714
Step-by-step explanation:
What i the conditional probability a randomly generated bit tring of length four contain at leat two conecutive zero,given that the firt bit i a 1. (aume that the probability of 0 and 1 are the ame)
The probability that a randomly generated bit string of length four contains at least two consecutive zeros, given that the first bit is a 1, is 1/8.
The probability of a randomly generated bit string of length four containing at least two consecutive zeros, given that the first bit is a 1, can be calculated by considering all of the possible combinations of four bits that meet this criteria. There are 8 possible combinations of four bits that contain two consecutive zeros and the first bit being a 1, so the probability of such a combination being chosen is 1/8. The probability of each individual bit being a 0 or a 1 is assumed to be the same, so the probability of any given combination is equal. Therefore, the probability of a randomly generated bit string of length four containing at least two consecutive zeros, given that the first bit is a 1, is 1/8.
P(2 consecutive 0s, given first bit is 1)
= (# of possible combinations with 2 consecutive 0s, given first bit is 1) / (total # of possible combinations)
P(2 consecutive 0s, given first bit is 1)
= 8 / (2^4)
P(2 consecutive 0s, given first bit is 1)
= 1/8
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At a dome-style football stadium, sports analysts noticed that as the distance of a field-goal attempt increased, the success rate of a field-goal attempt decreased. what are the explanatory variable and response variable for this relationship?
a. explanatory variable: style of stadium
response variable: distance of field-goal attempt
b. explanatory variable: style of stadium
response variable: success rate of field-goal attempt
c. explanatory variable: success rate of field-goal attempt
response variable: distance of field-goal attempt
d. explanatory variable: distance of field-goal attempt
response variable: success rate of field-goal attempt
The field goal attempt distance and success rate serve as the explanatory and response variables, respectively, for this relationship.
An example of an independent variable is an explanatory variable. However, there isn't much of a difference between the two.
A variable is considered independent if it is not at all affected by any other variables. An explanatory variable is one that cannot be determined to be independently variable.
The response variable is the result of an experiment in which the explanatory variable is changed. This variable's variation can be explained by a variety of other variables. Response variable, dependent variable, and outcome variable are all terms that are frequently used interchangeably.
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The explanatory and response variables for this relationship are the field goal attempt distance and success rate, respectively.
An explanatory variable is an illustration of an independent variable. There isn't much of a distinction between the two, though.
When a variable is completely unaffected by any other variables, it is said to be independent. Any variable that cannot be identified as an independent variable is an explanatory variable.
The outcome of an experiment in which the explanatory variable was altered is the response variable. Many different variables can be used to explain the variation of this variable. The phrases response variable, dependent variable, and outcome variable are sometimes used synonymously.
Divide: 8.56 ÷ 0.25 A) 0.0292 B) 0.292 C) 3.424 D) 34.24
Answer:
34.24
Step-by-step explanation:
when dividing by a decimal, the original number increases
To divide 8.56 by 0.25, we can perform the calculation as follows:
8.56 ÷ 0.25 = 34.24
Therefore, the correct answer is D) 34.24.
How do you solve using a graph?
Steps to graph-solve a problem:
Determine whether a graph can solve your issue. Get the graph data. Organize data to make graphing easier.Select the best graph for your data. Create the graph manually or using the software. Analyze the graph for data insights. Share your analysis. What is a graph?Generally, Identify the problem you are trying to solve and determine if a graph is an appropriate tool to help you solve it. Graphs are often used to represent relationships between different data points or to show changes in data over time.
Collect the data that you will need to create the graph. This may involve conducting research, conducting experiments, or gathering information from other sources.
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The complete Question was not found
We can solve using a graph by looking up the points on the graph.
How do you solve using a graph?We know that a graph can be regarded as a representation of facts and the graph is plotted in two axes. There is the vertical axis of the graph and there is the horizontal axis of the graph.
The vertical axis of the graph is called the y axis while the horizontal axis of the graph is called the x axis. The independent variable goes to the x axis while the dependent variable goes to the y axis.
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9 tens 9 ones 7 tenths 7 hundredths
9 ones, 9 tens 99.77 is equal to 7 tenths 7 hundredths.
Explain about the tenths and hundredths ?The place value of the digits that come after a decimal point is defined in mathematics as tenths and hundredths. When we count from right to left, the place values of the digits in a number are ones, tens, hundreds, and thousands.
The columns are labelled tenths, hundredths, thousandths, and so forth from left to right following the decimal point. The tenths column is the first digit following the decimal point. The column for hundredths is the second digit following the decimal point. The column for thousandths is the third digit following the decimal point.
The digit after the decimal point, or in the tens place, is known as the divisor. The first digit to the right of the decimal place is the tenths place digit.
9 tens = 9 x 10 = 90
9 ones =9 x 1 = 9
7 tenths = 7x 1/10 =0.7
7 hundredths = 7 x 1/100 = 0.07
= 90 + 9 +0.7 +0.07
= 99.77
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How do you find the horizontal asymptotes and vertical asymptotes of a function?
Horizontal asymptotes are found by looking at the degree of the numerator and denominator of a function. Vertical asymptotes are found by solving for all x-values where the denominator equals 0.
Horizontal asymptotes are horizontal lines that a graph of a function approaches as it goes towards positive or negative infinity. To find them, look at the degree of the numerator and denominator of a function. If the degree of the numerator is less than the degree of the denominator, the graph will approach the x-axis asymptote. If the degree of the numerator is equal to the degree of the denominator, the graph will approach the y-axis asymptote. Vertical asymptotes are vertical lines that a graph of a function approaches as it goes towards positive or negative infinity. To find them, solve for all x-values where the denominator equals 0. This will give you the x-values of the vertical asymptotes.
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What is the y-intercept of the line?
A. 1
B. 1/2
C. -2
D. 0
Answer:
A.1
Step-by-step explanation:
The line crosses when Y is one and X is 0 thus creating an intercept on the y line
INVERSE PROPORTION EXAMPLES
Answer:
Speed and Time are two examples of inverse proportion
isaiah is a high school basketball player. in a particular game, he made some free throws (worth one point each) and some two point shots. isaiah scored a total of 12 points and made 4 times as many free throws as two point shots. write a system of equations that could be used to determine the number of free throws isaiah made and the number of two point shots he made. define the variables that you use to write the system.
The system of linear equations which could be used to determine the number of free throws isaiah made and the number of two point shots he made is;
x + 2y = 12.x = 4y.Which system of.linear equations can be used to determine the number of each kind of shots he made?Let the number of free throws isaiah made be; x.
Let the number of two point shots he made be; y.
On this note, since the individual, isaiah scored a total of 12 points. The algebraic equations which represents the word phrase is;
x + 2y = 12.
Also, it follows from the task content that;
Isaiah made 4 times as many free throws as two point shots. The equation which represents the situation as described is;
x = 4y.
Consequently, the system of linear equations which correctly could be used to determine the number of free throws and two point shots isaiah made is;
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Answer:
zczczczczczcz
Step-by-step explanation:
shuffle a standard deck of 52 playing cards. turn over the top card. put the card back in the deck and shuffle again. repeat this process until you get a queen. count the number of cards you had to turn over. which conditions for a binomial setting have been met for this scenario?
The conditions for a binomial setting have been met for this scenario are;
The probability of success, denoted p, remains the same from trial to trial.The n trials are independent.How to interpret Binomial Experiment?
The conditions for a binomial experiment to be true are;
The experiment consists of n identical trials.Each trial results in one of the two outcomes, called success and failure.The probability of success, denoted p, remains the same from trial to trial.The n trials are independent.Now, in this case we keep shuffling the standard deck of 52 playing cards and picking the first in each case and replacing until we get a queen. This means that each trial is independent and does not depend on the success or failure of another event.
Secondly, the probability of success remains the same in each trial because we can't predict when we will get a queen.
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The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant's height at any time?
A) y - 21 = 7/2 (x - 3)
B) y - 21 = 7 (x - 3)
C) y - 3 = 7/2 (x - 21)
D) The relationship is nonlinear.
The equation in point slope form is y - 21 = 7(x - 3).
What is point - slope form of the line?
A line's equation in point slope form is y - y1 = m. (x – x1). As a result,
y = mx and y - 0 = m(x - 0) are the equations for a line passing through the origin with a slope of m.
To find the equation in point slope form for the given table of height of a plant first we have to find the slope.
Here
Slope = change in height / Change in time
From given table,
Change in height = 14 and Change in time = 2
⇒ Slope = 14 / 2 = 7
Now to find the point slope form.
We know that the equation in point slope form for point [tex](x_1, y_1)[/tex] and slope m is written as,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1) = (3, 21), m = 7[/tex]
So, the equation becomes
[tex]y-21 = 7(x-3)[/tex]
Hence, the equation in point slope form is y - 21 = 7(x - 3).
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Translate the answer, t2 = a3, into words: the___of the orbital period, t, of a planet is equal to the____of the average distance, a, of the planet from the sun.
a. Squareb. Square Rootc. Cube
The answer is the square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun.
Translated into words, the equation t2 = a3 can be written as:
"The square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun."
The length of time it takes an astronomical object to complete one orbit around another object is known as the orbital period (also known as the revolution period). In astronomy, it often refers to bodies like planets or asteroids revolving about the Sun, as well as moons circling other stars, exoplanets, and double stars.
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Translated into words, the equation t2 = a3 can be written as:
"The square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun."
The orbital period is the amount of time it takes an astronomical object to complete an orbit around another one (also known as the revolution period). In astronomy, it frequently refers to objects revolving about the Sun, such as planets or asteroids, as well as moons orbiting around other stars, exoplanets, and double stars.
Write the slope-intercept equation of the line through
the coordinates (4,5) and (-4,-3).
Answer:
y = 1/4x + 4
Step-by-step explanation:
Knowledge Needed
Slope: The amount the y-value changes on a constant line when the x-value increases by 1.
Slope Formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
y-intercept: When the line has a x-value of , or when it intersects the y-axis.
Slope-Intercept Form: y = mx+b
m is slope, b is y-intercept.
Leave y and x as variables so you can graph it.
Question
First, plug the points into the slope formula.
[tex]\frac{3-5}{-4-4}[/tex]
[tex]\frac{-2}{-8}[/tex]
1/4
y = 1/4x + b
Solve for b:
Use any of the 2 points to plug back in. I'll use (4,5).
We have: y = 1/4x + b
(5) = 1/4(4) + b
5 = 1 + b
5 - 1= 1 - 1 + b
b = 4
y = 1/4x + 4
Write an equation of the line with the given slope and y-intercept.
Undefined slope; (-8, 5)
A. x = -8
B. 5x - 8y = 0
C. y = 5
D. -8x + 5y = 0
Answer:
A. x = -8
Step-by-step explanation:
It can't be B because the slope of this equation is 5/8.
It can't be C because this equation slope is 0, not undefined.
It can't be D because the slope of this equation is 8/5
I say it is A because this is the only equation with an undefined slope!
LCM [a,b] = 36 HCF [a,b] = 6 find the value of a=b
All the values that are possible here are (1, 36) (4,9) (9,4), and (36,1).
The possible values of and b are (1, 36) (4,9) (9,4), and (36,1).
Given: The LCM of a and b is 36 and HCF is 1
To find: The values of a and b?
Here is the solution:
The two numbers are a and b.
LCM of a and b is 36.
HCF of a and b is 1
We know that,
product of two numbers = LCM * HCF
= A*B=36*1
i.e = a, b=36,1
in a similar way:
The all-possible values of and b are (1, 36) (4,9) (9,4), and (36,1).
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NEED HELP ASAP 100 POINTS
Using Corresponding Parts of Congruent Triangles
Recap: Once you know that triangles are congruent, you can make conclusions about corresponding sides and angles because, by definition, corresponding parts of congruent triangles are congruent. You can use congruent triangles in the proofs of many theorems.
Examples: How can you use congruent triangles to prove the statement true?
∠Q≅∠D
TV≅YW
∠Q and ∠D along with sides TV and YW are proved congruent.
What are congruent triangles?Triangles are congruent when they have exactly the same three sides and exactly the same three angles.
Given are the two triangles that are congruent.
In ΔWQE and ΔVDK -
∠W = ∠V {Given}
∠E = ∠K {Given}
WQ = VD {Given}
By AAS criteria, the triangles are congruent.
So, by corresponding parts of congruent triangles, ∠Q and ∠D are congruent.
In ΔVTY and ΔWYX -
∠Y = ∠X {Given}
∠T = ∠Y {Given}
VY = WX {Given}
By AAS criteria, the triangles are congruent.
So, by corresponding parts of congruent triangles, TV and YW are congruent.
Therefore, ∠Q and ∠D along with sides TV and YW are proved congruent.
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Is 16x2 3 =( 2x 5 )( 5x 3 a quadratic equation?
a quadratic equation is only different from a linear equation in one respect :one or more of the figures is squared. The common form of a quadratic equation is ax2+bx+c=11
What are quadratic equations?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
16x2−3=(2x+5)(5x−3)
16x^2 - 3 = 10x^2 + 19x -15
6x^2 - 19x + 12 = 9
THIS IS QUADRATIC.
a quadratic equation is only different from a linear equation in one respect:one or more of the figures is squared.The common form of a quadratic equation is ax2+bx+c=11
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How do you reverse a 2 digit number?
We are aware that to reverse a number, the TENS and ONE's positions must be reversed. As a result, its reverse "ba" usually takes the form (10 times "b" multiplied by "a")
What are 2-digit numbers?When a number has two digits, it is called a 2-digit number.
2-digit numbers have two digits and range from 10 to 99.
They are unable, to begin with, zero since it will then be regarded as a single-digit number.
Any number between 1 and 9 can be used as the digit in the tens place.
For instance, the numbers 45, 78, and 12 have two digits.
When it comes to two-digit numbers and their reversal, there are two common logics.
The two-digit number "ab" has the generic form (10 times a) Plus b.
We are aware that the TENS and ONE's positions should be switched in order to reverse a number.
As a result, the typical form of its reverse "ba" is (10 times "b" multiplied by "a")
Therefore, we are aware that to reverse a number, the TENS and ONE's positions must be reversed. As a result, its reverse "ba" usually takes the form (10 times "b" multiplied by "a")
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