Answer:
x = 45y + 650/2
Step-by-step explanation:
20x - 45y = 650
20x - 45y + 45y = 650 + 45y
20x = 650 + 45y
20x/20 = (650 + 45y)/2
x = 45y + 650/2
Thus, The value of x is 45y + 650/2
a polynomial function of degree n has at most real zeros and at most relative extrema. t or f
A polynomial function of degree n has at most n real zeros and at most n-1 turning points.
What is polynomial function ?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
What isa Zeros of Polynomials?
Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.
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During the holiday, students went swimming in a local rectangular pool. The pool measures 20 feet by 35 feet. It is surrounded by a patio that is uniform width. Find the width of the patio if the total area of the pool and patio is 1350 sqr feet. Write a quadratic equation to solve the problem.
Answer:
The width of the patio is 3/2 feet.
Step-by-step explanation:
following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
To find the width of the patio, we need to find the area of the pool and the area of the patio. Let's call the width of the patio "w". The area of the pool is 20 * 35 = <<20*35=700>>700 square feet. The area of the patio is (20+2w) * (35+2w) = 1350 sqr feet. We can set up the following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
This means that the width of the patio is either 3/2 or -5/2 feet. Since the width cannot be negative, the width of the patio must be 3/2 feet.
The quadratic equation we can use to solve this problem is:
w^2 + 14w - 65 = 0
The flak are in the hape of cone. The maller flak ha a bae radiu of
8
cm and a vertical height of
20
cm. The larger flak ha a bae radiu of
14
cm. The larger flak i now partly filled with liquid up to a vertical height of
15
cm. Calculate the volume of liquid in the flak. Give your anwer in term of π
The volume of the liquid in the bigger flask which is in the shape of the cone is V = 980π.
What is a cone?
A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The
Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."
The apex is the pointy end, while the base is the level area.
So, the volume of liquid in the bigger flask:
We know that the radius of the bigger flask is 14cm.
The liquid is filled to a height of 15cm.
The volume of cone formula: V = πr²h/3
Substitute values as follows:
V = πr²h/3
V = π(14)²15/3
V = π196*5
V = 980π
Therefore, the volume of the liquid in the bigger flask which is in the shape of the cone is V = 980π.
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The time,
T
(seconds), it takes for a pot of water to boil is proportional to the amount,
A
(litres), of water.
It takes 200 seconds to boil 2.7 litres of water.
Work out how much water is in the pot if it boils in 220 seconds.
The relationship between the time it takes to boil a pot of water, T (in seconds), and the amount of water, A (in litres),
T ∝ A,
setting up the equation and solving:
2.96 liters of water will boils in 220 seconds.
what is equation?An equation is a mathematical statement that shows that two expressions are equal.
what is proportionality constant?A proportionality constant is a coefficient that relates two quantities that are proportional to each other. In other words, if two quantities are proportional, their ratio is always the same, and this constant ratio is the proportionality constant.
This proportionality can be written as an equation by introducing a constant of proportionality, k:
T = k * A
We are given that it takes 200 seconds to boil 2.7 litres of water, so we can set up an equation using this information:
200 = k * 2.7
Solving for k, we find that k = 200/2.7 = 74.07407407407407.
Now that we know the value of the constant of proportionality, we can use it to find the amount of water in the pot if it boils in 220 seconds. We can set up the following equation:
220 = 74.07407407407407 * A
Solving for A, we find that the amount of water in the pot is A = 220 / 74.07407407407407 = 2.962962962962963 litres.
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8x = 2 write the value of x
Answer: x=1/4
Step-by-step explanation:
1. You want to isolate the variable, in other words get it by itself. You do that be dividing by 8 to both sides, 8x/8 is just x and 2/8 is 1/4, so therefore x=1/4
2. you can plug in 1/4 for x to check it. 8 x 1/4 is 2, and 2=2 ✅
Answer:x=1/4 or x=0.25 I hope this helpful mark me brainlist if correct
Step-by-step explanation:
8x=2
Divide both sides of the equation by 8
8x divide 8=2 divide 8
Any expression divided by itself equals 1
x=2 divide 8
then write the the division as a fraction
X=2/8
Cancel out the common factor 2 and 8
X=1/4 or x=0.25
The interest rate on your loan is lowered from 3.5% to 3%
A) What is the percentage change
B) what is the percentage point of change
I NEED HELP ASAP!! ITS URGENT
If the interest rate on your loan is lowered from 3.5% to 3%:
A) The percentage change is 14.28%
B) The percentage point of change is 0.5%
What is meant by interest rate?A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe. An interest rate is the percentage of a loan, deposit, or borrowing that must be paid in interest each period (called the principal sum). The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.
Let the capital will be 100
For interest rate 3.5% then the loan amount will be:
100×(3.5/100)=3.5
For interest rate 3% then the loan amount will be:
100×(3/100)=3
A) Percentage change=((-3.5+3)/3.5)×100
=(-0.5/3.5)×100
=14.28%
B) Percentage point of change=3.5%-3.0%
=0.5%
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Use the properties of rigid motions to explain why triangle ABC is congruent to triangle XYZ
If ∆ABC is rotated around the origin 180 degrees, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent.
Are the triangles congruent via rigid motion?
Stiff motion makes these two triangles congruent. The SAS Theorem asserts that two triangles are congruent if they have two pairs of matching congruent sides in common and if the included angle is likewise congruent.
Use rigid motions to explain why ∆ABC ≅ ∆XYZ. If ∆ABC is rotated around the origin 180 degrees, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent. If ∆ABC is translated, it will map to ∆XYZ.
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Aisha models a can of ground coffee as a right cylinder. She measures its height as 5 and 1/2 and its radius as 1/2 in. Find the volume of the can in cubic inches. Round your answer to the nearest tenth if necessary.
25^x = 5^4x+1
what is the value of x? pls help me :(
Answer:
x = -0.5
Step-by-step explanation:
[tex]factors \: of \: 25 \\ 25 = 5 {}^{2} \\ 5 {}^{(2)x} = 5 {}^{4x + 1} \\ since \: bases \: are \: equal \: \\ hence \: exponents \: are \: equal \\ 2x = 4x + 1 \\ collect \: like \: term \\ 2x - 4x = 1 \\ - 2x = 1 \\ divide \: by \: - 2 \: both \: sides \\ x = - 0.5[/tex]
How is the value of b related to the y-intercept of the graph of y = 3x + b?
Answer:
b is the y-intercept.
Step-by-step explanation:
The equation is in the y = mx + b form.
b is the y-intercept.
If a cubic millimeter of blood contains 5,800,000 red blood cells, how many red blood cells are contained in 50 cubic of blood? Express your answer in scientific notation
In linear equation, Total number of red blood cells in the body is 29 * 10¹¹ .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Red blood per cubic millimeter = 5,800,000 = 5.8 * 10⁵
Red blood in 5 litres of blood = 5.8 * 10⁵ * 5 * 10⁵
= 29.0 * 10¹⁰
= 29 * 10¹⁰ * 10
= 29 * 10¹¹
Total number of red blood cells in the body is 29 * 10¹¹.
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Given (x – 1)2 = 50, select the values of x.
Answer: x=26
Step-by-step explanation:
(x-1) = 50/2
x-1 = 25
x = 25 +1
x = 26
If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.Thanks
The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the bay can be modeled by d = 35 - 28 cos (π/6. 2 t)
where d is the depth in feet and t is the time in hours. Consider a day in which t = 0 represents 12:00 A. M. At what time is the water depth 14 feet.
(please include explanation)
The exists no solution for which the water depth 14 feet in the ocean near the shore.
Explain the term time period?A time period (T) is the length of time it takes for one complete vibration cycle to pass over a certain location. As the frequency of a wave rises, so does its period. The length of time is expressed in "seconds."We determine the function's period since that is the number of it takes hours for the ocean to return to its original depth of a specific number of feet.
The function's duration is 2π/ (π/6.2) = 12.4 hours.
When t = 0, midnight, or 12:00AM, it is low tide.
As a result, the next low tide will occur at 12:24 PM, or t = 12.4, 12.4 hours from now.
A high tide will occur halfway between those two low tides, at t=6.2 hours after midnight, or at 6:12AM.
Another high tide will occur at t=18.6 hours after midnight, or at 6:36 PM, 12.4 hours later.
If t = 0 is used in the equation, the low tide occurs at that time;
d = 35 - 28cos(pi/6.2)t
d = 35-28cos(pi/6.2)0
d = 35-28cos(0)
d = 35-28(1)
d - 35-28
d = 7
Therefore, there will never be 4 feet there because the lowest depth that may exist is 7 feet.
Thus, the exists no solution for which the water depth 14 feet in the ocean near the shore.
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22) The function y = -16t² + 56t+ 4 must have a root between
which of the following x- values?
A) 0 and 1
B) 1 and 2
C) 2 and 3
D) 3 and 4
E) 4 and 5
t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4
What is quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable (x) using the formula ax² + bx + c = 0 and a≠0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.
According to question.
y = -16t² + 56t+ 4
⇒ -16t² + 56t + 4
⇒ -4t² + 14t + 1
⇒ t = [-14 ±√((14)² - 4*(-4)*1)]/-8
⇒ t = [-14 ±√(212)]/-8
⇒ t = [-14 ± 14.560]/-8
⇒ t = [-14 ± 14.560]/-8
⇒ t = -(28.56)/-8 and t = 0.560/-8
⇒ t = 3.750 and t = 0.070
hence, t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4
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Which of these relations is a function?
The relation that is a function is the graph (d)
How to determine the function?From the question, we have the graphs to represent the given parameters that can be used in our computation
We are to find out which of them represents a function
For a graph to represent a function, the graph must pass the vertical line test
This means that a line drawn from the x-axis must touch the graph at most once
So, we draw these lines and attach the graphs (see attachment)
The graph that pass the vertical line test is graph d
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6. The coordinates of point A are given. The midpoint of AB is (3,-5). Find the coordinates of point B.
a. A(4,-8)
b. A(2.5, -6.5)
HELP PLEASEEE
Find the measure of HG
Answer:
40 m
Step-by-step explanation:
Given midline JK = (6x -4) m and baseline HG = 10x m, you want the measure of HG.
MidlineThe midline of a triangle is half the length of the parallel baseline.
JK = 1/2·HG
6x -4 = 1/2(10x)
x -4 = 0 . . . . . . . . . subtract 5x
x = 4
10x = 10·4 = 40
The measure of HG is 40 meters.
When conveiling units, summarize the steps using the direct method
Answer:
1. Identify the unit of measure to be converted.
2. Determine the conversion factor between the original and desired units.
3. Multiply the original measure by the conversion factor to obtain the new unit measure.
4. Check the new unit measure to ensure accuracy.
Step-by-step explanation:
What is pie to the second power
Answer:
9.869604...
Step-by-step explanation:
Pie to the second power, or pi squared, is the mathematical operation of multiplying pi (3.14159...) by itself. The result of this operation is equal to 9.869604...
In mathematical notation, pi squared is written as π^2, which is the same as saying "pi to the power of 2". This means that π^2 = π * π = 9.869604...
In general, raising a number to the second power means multiplying the number by itself. For example, 2^2 = 2 * 2 = 4, and 3^2 = 3 * 3 = 9. Similarly, pi squared is just the product of pi multiplied by itself.
pi is approximately 3.14159265359
pi^2 (pi to the second power) is approximately 9.86960440109
this graph shows a proportional relationship containing the point (3,6) and (4,8)
What is the constant of proportionality ?
The constant of proportionality is 2.
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
A proportional relationship is described by ...
y = kx
The value of k can be found by dividing by x:
k = y/x
For the given non-zero point (3,6), the value of k is found to be ...
k = 6/3 = 2
k = 2
The constant of proportionality is 2.
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the equation of a line is y = 7x + 8 what is the gradient of the line
Answer:
7
Step-by-step explanation:
The gradient of a line is a measure of how steep the line is. It is calculated as the change in the y-value (the "rise") divided by the change in the x-value (the "run").
In the equation y = 7x + 8, the coefficient of x (7) is the gradient of the line. This means that for every 1 unit change in the x-value, the y-value changes by 7 units.
So the gradient of the line y = 7x + 8 is 7.
the degree to which an instrument appears to measure what it is supposed to be measuring is referred to as:
When we reject the null and the null is true, we have a made a _________ __________.
When we reject the null and the null is true, we have a made a type I error
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
null hypothesis is denoted as H₀
Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. When you can reject the null hypothesis, your results are statistically significant.
when the p-value is greater than your significance level, you fail to reject the null hypothesis.
Sometimes , we reject our null hypothesis even when its true
there we made a type I error in hypothesis
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Answer for 10 points!
The computation of (9 × 20 + 60) ÷ 4 - 16 + 4 × (20 × 5) is 444.
How to simplify an expression?The expression can be simplified using PEMDAS rule.
Therefore,
P = parenthesisE = exponentialM = multiplicationD = divisionA = additionS = subtractionHence, we have to simplify the expression according to the operator that comes first in the PEMDAS rule.
Therefore,
(9 × 20 + 60) ÷ 4 - 16 + 4 × (20 × 5)
(180 + 60) ÷ 4 - 16 + 4 × 100
240 ÷ 4 - 16 + 400
60 - 16 + 400 = 444
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What is the major difference between the alternate hypothesis and the null hypothesis?.
The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
What is Hypothesis?A hypothesis is a put forth explanation for a phenomenon (plural: hypotheses).
A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.
Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.
A working hypothesis is a theory that has been tentatively accepted and is proposed for future study[1], starting with an informed guess or thinking.
Hence, The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
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J(2,-4), k(3,7), L(6,-1); x-axis
The reflection of the points J(2,-4), K(3,7), and L(6,-1) is (2, 4), (3, -7) and (6, 1) respectively.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
The given points are,
J(2,-4), K(3,7), and L(6,-1)
The reflection of a point (x, y) over the x-axis (x, -y),
So the reflection of point J(2, -4) is M(2, 4)
Reflection of point (3, 7) is (3, -7)
And reflection of point (6, -1) is (6, 1)
The reflection of the points J(2,-4), K(3,7), and L(6,-1) is (2, 4), (3, -7) and (6, 1) respectively.
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how to simplify radical expressions
The way to simplify radical expressions include:
Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.Use the product rule to rewrite the radical as the product of two radicals.Simplify the root of the perfect power.What is a radical expression?Any expression with the radical symbol is referred to as a radical expression. This symbol, which is frequently used to calculate the square root of a number, is frequently called the "square root" symbol by mistake.
But it can also refer to a cube root, a fourth root, or something higher. Radical equations are equations that contain radicals.
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What is the solution ?
4/2 = √3x-2
Answer:
x = 2
Step-by-step explanation:
[tex] \frac{4}{2}=\sqrt{3x-2} [/tex]
[tex] 2=\sqrt{3x-2} [/tex]
4 = 3x - 2
3x = 6
x = 2
Find the equation of the straight line RS. A)y = -2x + 3 B)y = -2x + 6 C)y = 2x + 3 D)y = 2x + 6
The equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.
What is the slope of the equation?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
To find the equation of the line passing through the points (0, 6) and (3, 0), we can use the two-point form:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we get:
m = (0 - 6) / (3 - 0)
= -6 / 3
= -2
Substituting this value for m and the coordinates of one of the given points into the two-point form, we get:
y - 6 = -2(x - 0)
Combining like terms and multiplying through the parentheses, we get:
y = -2x + 6
Hence, the equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.
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