As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). An identity holds true regardless of the value given to the variables.
given
Equation as given:
y = 6 (x - 1/2)(x+3)
To identify the equation's graph's y-intercept
Put x = 0 in place of it in the equation.
y = 6 (0 - 1/2)(0+3)
Apply the math operation, then find y.
y = -9
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
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Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.
The assumption is equivalent to the following two statements:
(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]
(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]
Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].
Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.
How many pairs of potential clients can be randomly chosen from pool or eight candidates
There are 34 ways by which pairs of potential clients can be randomly chosen from pool or eight candidates.
What is combination?We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.
As such we would have the use of the formula for combination as follows;
C = n!/r!( n - r)!
C = 8!/2!(8 - 2)!
C = 8 * 7 * 6!/2! 61
C = 8 * 7/ 2 * 1
C = 28
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Please help will mark Brainly
Answer:
Step-by-step explanation:
the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.
(tan A)/(sec(A) - 1) + (tan A)/(sec(A) + 1) = 2cos ecA
Answer:
Step-by-step explanation:
LHS = tanθ/secθ - 1 + tanθ/secθ + 1
Cross multiplication,
tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ
= tanθ(1 - secθ - 1 - secθ)/-tan^2θ
= -2secθ/-tanθ
= 2 x 1/cosθ / sinθ/cosθ
= 2cosecθ = RHS
Hence proved.
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide.
an image
What is the length of the fence not including the gate?
m
Use π
= 3.14
Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.
What is the length of the fence?Let the circular pool has the radius (r ) = x cm.Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.Length of fence = Circumference of the pool – width of the gate.Length of fence = 2 π r – 150Length of fence = 2 × 3.14 × x – 150Length of fence = 6.28x – 150 cm.a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius.To learn more about length of the fence refers to:
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Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. What is the ratio of the number of burgers without onions to the number of burgers with onions?
The ratio of number of burgers without onions to the number of burgers with onions is 4:1.
Ratio of numbers.The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.
Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;
ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)
= 12/ 3
= 4/ 1
The ratio of number of burgers without onions to burgers with onions = 4:1
Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.
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Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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(100 points) Need help asap!
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=\frac{1}{9} x^{12}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=-\frac{1}{10} x^{18}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The end behavior of the function f(x) = 1/9 x¹² is
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞The end behavior of the function f(x) = -1/10 x¹⁸ is
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of functionThe given function is:
f(x) = 1/9 x¹²
The positive exponents will mean that x will always yield positive values hence f(x) is always positive
f(x) = -1/10 x¹⁸
The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative
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(6 × 10a) + (6 × 10b) + (6 × 10c) = 6006.6
Write down a possible set of values of a, b and c.
The values of a , b and c from the equation is ( 3 , 0 , -1 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6 be equation (1)
Now , the number 6006.6 is written as
6000 + 6 + 0.6 = 6006.6
On simplifying the equation , we get
( 6 × 10ᵃ ) = 6000
Divide by 6 on both sides of the equation , we get
10ᵃ = 1000
So , 10ᵃ = 10³
Therefore , the value of a = 3
Now , ( 6 × 10ᵇ ) = 6
Divide by 6 on both sides of the equation , we get
10ᵇ = 1
when b = 0
10⁰ = 1
Therefore , the value of b = 0
Now , ( 6 × 10^c ) = 0.6
Divide by 6 on both sides of the equation , we get
10^c = 0.1
when c = -1
10⁻¹ = 0.1
Therefore , the value of c = -1
Hence , the value of a , b and c is 3 , 0 and -1 respectively
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Find the product. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar. 4/3*5/3
The solution to the product expression 4/3 * 5/3 is 20/9
How to evaluate the product expression?From the question, we have the following parameters that can be used in our computation:
The product 4/3*5/3
To start with, we need to represent the statement as an expression
So, we have the following representation
4/3 * 5/3
Using a calculator, we multiply the numerator
So, we have the following representation
4/3 * 5/3 = 20/3 * 1/3
Using a calculator, we multiply the denominator
So, we have the following representation
4/3 * 5/3 = 20/9
Hence, the solution is 20/9
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Given the number 254, 476, 951
What number is in the TEN THOUSAND's SPOT?
Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.
guys please help its due today!
Answer:
Step-by-step explanation:
the answer is 6
Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at (-2, -2) , and point D′ is at (4, -2) .
The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The vertices of the original polygon for this problem are given as follows:
A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).
The scale factor for the dilation in this problem is given as follows:
k = 2.
Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
(as each coordinate of each vertex was multiplied by the scale factor of 2).
Missing InformationThe problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.
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What is the slope for y=-3/4x+7
Answer:
-3/4
Step-by-step explanation:
y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.
Two straight lines are perpendicular to each other at point M. One of the lines passes through (2, 6) and the equation of the other line is 2y + 3x -5 = 0. Calculate the co-ordinates of M.
Answer: The equation of a line in the form y = mx + b can be written as y - mx - b = 0. So we can rewrite the equation of the line as 2y - 3x + 5 = 0. This means that the slope of the line is -3/2.
The slope of a line perpendicular to this line would be the negative reciprocal of -3/2, which is 2/3. Let's call the point M (x, y). We know that the line passing through (2, 6) has a slope of 2/3. So we can write the equation of this line as:
y - (2/3)x - b = 0
Substituting the point (2, 6) into this equation, we get:
6 - (2/3)(2) - b = 0
b = 4
So the equation of the line passing through (2, 6) is:
y - (2/3)x - 4 = 0
To find the coordinates of point M, we need to find the point where these two lines intersect. Setting the two equations equal to each other and solving for x and y, we get:
2y - 3x + 5 = y - (2/3)x - 4
5 - 2y = y - (5/3)x + 4
(5/3)x = 3 - y
x = (3 - y) * (3/5)
Substituting this expression for x into one of the original equations, we can solve for y:
2y - 3((3 - y) * (3/5)) + 5 = 0
2y - (9 - 3y)(3/5) + 5 = 0
(10/5)y - (9/5) + 5 = 0
y = (9/5) + (5/5)
y = 2
Substituting this value for y back into the expression for x, we get:
x = (3 - 2) * (3/5)
x = 1
So the coordinates of point M are (1, 2).
Step-by-step explanation:
I need help, and I forgot how to do this
Answer: 5. 2x+8 6. 5(x-9) 7. -3x+-21
Step-by-step explanation: Multiply the number outside the parenthesis by everything inside it
An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram. What is the area, in square units, of parallelogram ABCD? Enter your answer in the box.
In the new logo, what fraction of the parallelogram is shaded.
a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.
b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).
How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:
Area = base x height.
The base and the height for this problem are obtained counting the number of dots, hence:
Base: 4 units.Height: 6 units.Hence the area is given as follows:
Area = 4 x 6
Area = 24 units squared.
The shaded region is composed by a triangle with base 4 and height 3, hence:
Area shaded = 0.5 x 4 x 3 = 6 units squared.
(formula for the area of the triangle).
Meaning that the fraction is given as follows:
6/24 = 1/4.
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Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?
The probability that the area of the triangle is at most 20 is 5/9
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is
1/2×12×6=36
Now if the area of the triangle is at most 20 then the required probability is = 20/36
=5/9
Hence, The probability that the area of the triangle is at most 20 is 5/9
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How many Proper Fractions are there?
29) Which is a counterexample that shows the following conjecture is false: "If 21 and 22 are complementary, then one of the angles is obtuse" ? A. m/1 = 90° and m42 = 90° B. m/1 = 53° and m42 = 127° C. mz1 = 100° and m42 = 80° D. mz1 = 45° and mz2 = 45
D. mz1 = 45° and mz2 = 45 are complementary angles (mz1 + mz2 = 90°), but neither angle is obtuse (greater than 90°), so the guess is wrong. This is a counter-example to show.
What are supplementary angles?A supplementary angle is an angle where the sum of two angles is 90 degrees. That is, if angle A and angle B are complementary, angle A measurement + angle B measurement = 90 degrees. Supplementary angles may be adjacent (having a common vertex and edge) or non-adjacent (having no common vertex or edge), but they always complement each other.
There are various kinds of angles to study.
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Given it was not a strike, what is the probability it was a knuckle
ball? Enter the answer as a percent (%)to the nearest tenth.
On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 1000
obtained = 500
so, 500/1000X100 = 50%
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How can you divide polynomials? What are the different methods you can use?Which method do you prefer and why?
Pls help with my math
This is the hard question for me
Thnx
The ratio of yellow houses to white houses on a street is 18 to 26.
Simplify the ratio.
Enter your answer by filling in the boxes.
to
Answer: The ratio 18:26 simplified is 9:13.
Step-by-step explanation:
To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.
The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13
Answer:9/13
explanation: k12
X+X+X+Y+Y=
im doing algebra and cant understand the above question
Answer:
3x + 2y
Step-by-step explanation:
X+X+X+Y+Y=
you simply count equal letters and add them x+x+x is 3x and y + y = 2y.
x + x + x + y + y =
3x + 2y
not knowing the value of x or y we stop hereFind the slope of the line in which x=-24
Answer:
it is undefined
Step-by-step explanation:
Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.
Answer:
undefined slope
Step-by-step explanation:
When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.
how long would it tak to go 75 miles if you can go 45 mph
How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?
It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.
How to find the present value of bike?You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:
n = (1200 - 2550) ln / ln (1 - 0.05)
Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.
When we enter the values, we will get:
n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months
The motorcycle will take approximately 15.7 months to drop in value to less than £1200.
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Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was 1,350. Five months after he purchased the computer , his balance was 1,050. What is an equation that models the balance B after m Months
Answer: y = -150x + 1800
Step-by-step explanation:
1. Find the linear slope of the line between two points.
(Change in Y)/(Change in X)
2. Write out an equation in point slope form.
(y-y1) = m(x-x1)
y-1800 = -150(x-0)
3. Simplify the equation and turn it into slope-intercept form.
y = -150x + 1800
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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