Answer:
Step-by-step explanation:
12 + 3t
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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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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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
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.
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
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
hats and mittens are on sale at the store
On solving the question, we got that - one hat costs $2, while a pair of mittens costs $5.
What is equation?A mathematical equation is a statement that contains two algebraic expressions on each side of the equal sign (=). Both of the expressions—the one on the left and the one on the right—are shown as being equal. LHS = RHS is shown.
The shop has hats and mittens on sale!
For $30, one woman was able to get four pairs of mittens and five hats.
For $19, another woman bought two hats and three pairs of mittens.
x is the cost of one hat.
One pair of mittens costs y dollars.
We must locate x and y.
One woman spent $30 to purchase 4 pairs of mittens and 5 hats.
One hat costs x dollars.
The cost of a single pair of mittens is y.
- Divide four pairs of mittens by y, multiply five hats by x, and equal
30 times their total
[tex]5x + 4y = 30 ........................ (1)[/tex]
For $19, another woman bought two hats and three pairs of mittens.
- Divide three pairs of mittens by y, multiply two hats by x, and equate
multiplied by 19
[tex]2x + 3y = 19 ............................ (2)[/tex]
Now,
[tex]-10x - 8y = -60 ................(3)\\10x + 15y = 95 .......... (4)\\Add equations (3) and (4)\\ 7y = 35\\Divide both sides by 7\\ y = 5\\Substitute the value of y in equation (1) or (2) to find x\\ 2x + 3(5) = 19\\ 2x + 15 = 19\\ Subtract 15 from both sides\\ 2x = 4\\ Divide both sides by 2\\x=2\\[/tex]
One hat costs $2, while a pair of mittens costs $5.
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The correct question -
Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30. Another woman purchased 3 pairs of mittens and 2 hats for $19. Find the price of one hat (x) and one pair of mittens (y).
Need Help with geometry
Answer: 23
Step-by-step explanation: ML is in between JL. Line ML is 15 and KL is 8.
Since ML is in between we already know there is 15, and the space left is about the same size as line KL. so 15+8=23.
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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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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How much money will be in an account with an annual interest rate of 7.5% compounded annually, if $5300 was deposited 7 years ago? Be sure to write your answer as money.
Answer:
Step-by-step explanation:
To find the amount of money in the account after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount in the account, P is the initial deposit (5300), r is the annual interest rate (7.5%), n is the number of times the interest is compounded per year (1, since the interest is compounded annually), and t is the number of years the money is invested (7).
Plugging these values into the formula, we get:
A = 5300(1 + 0.075/1)^(1*7)
= 5300(1.075)^7
= $7953.33
So, the amount of money in the account after 7 years would be $7953.33.
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.
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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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:
Joey, Keith, and Eli have a combined height of 7 meters. If Joey is 1 2/5 meters tall and Eli is 2 7/10 meters tall, how tall is Keith?
Answer: 2 9/10 or 2.9 metres
Step-by-step explanation: Form an equation with the information given
1 2/5 + 2 7/10 +x =7
Let x represent the height of Keith
Change mixed fractions into improper fractions
1 2/5=7/5 as an improper fraction we say 1*5+2=7 and put it over the denominator 5
2 7/10 =27/10 as an improper fraction we say 2*10+7 =27 and put it over the denominator 10
we now have the following:
7/5+27/10+x=7
We simplify these fractions by adding them up
7/5
7/5*2/2+27/10=14/10+27/10=41/10
41/10+x=7
To solve for x
take 41/10 from both sides
7-41/10
Making the denominators the same we get the following:
x=70/10-41/10=29/10=2 9/10
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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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
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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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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which function is represented on the graph
Answer: was there supposed to be a picture attached to this question ?
Step-by-step explanation:
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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Substitute the values into the appropriate formula and solve for x.
Answer: Hi so its pretty straight forwad use the cosine formula as you have 2 sides and angle opposite of the x. Answer: 21.35
Step-by-step explanation:
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.
write an equation for the line that passes through point (0,4) and is parallel to the line with equation y = -5x + 3
The equation of a line which is parallel to line y = -5x + 3 and passes through points (0, 4) is 5x + y -4 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given line of equation is,
y = -5x + 3
The slope of the given line m = -5.
The slope of the required line which is parallel to given line will be equal to -5.
To find the line of equation that passes through the point (0, 4),
Use formula y - y₁ = m(x - x₁)
The required equation of line having slope -5 and passes through points (0, 4) is,
y - 4 = -5(x - 0)
y - 4 = -5x
5x + y -4 = 0
The required equation of line is 5x + y -4 = 0.
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Find a counterexample to how that the conjecture i fale. Conjecture: Any number that i diviible by 2 i alo diviible by 4
A number that is divisible by 2 is also divisible by 4. The counterexample of this conjecture should be a number that is divisible by 2 but not divisible by 4 .
What is Conjecture ?
A conjecture is a statement that is guessed by someone and it may or may not be true.
What is counterexample ?
A counterexample is an example that proves the conjecture to be false.
Let's go through the list of values and test the claim
Is 32 divisible by 2? Yes because 16*2 = 32. Is it also divisible by 4? Yes because 8*4 = 32. So we can cross choice A off the list
Is 12 divisible by 2? Yes because 6*2 = 12. Is it also divisible by 4? Yes because 3*4 = 12. So we can cross choice B off the list.
Is 40 divisible by 2? Yes because 2*20 = 40. Is it also divisible by 4? Yes because 4*10 = 40. Choice C is also crossed off the list.
Is 18 divisible by 2? Yes because 2*9 = 18. Is it also divisible by 4? No. We can see that by dividing 18/4 = 4.5 which is not a whole number result. Or you can list out the multiples of 4 which are 4, 8, 12, 16, 20 and we see that 18 is not on the list. This is a counter example to show that the claim "if number is divisible by 2, then it is also divisible by 4" is a false statement.
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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
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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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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I need help please. It’s for a practice test
Answer:
$13,000
Step-by-step explanation:
You want to know the class width when the class ranges are defined as ...
$35,000–$47,999$48,000–$60,999$61,000–$73,999Class widthThe class width is the difference between adjacent corresponding boundaries. These are the differences of the low boundaries.
$48,000 -$35,000 = $13,000
$61,000 -$48,000 = $13,000
The class width is $13,000.
__
Additional comment
Often, the class boundaries are defined to be values that cannot be part of the data set. If data is rounded to the nearest dollar, the boundaries might be defined as $34,999.50 and 47,999.50, for example. That way, it is clear that both of the values $35,000 and $47,999 will fall into the first class.
The way the classes are defined here, we have to assume that both $35,000 and $47,999 will fall into the first class. However you define the classes, the class for any given data value should never be ambiguous.
The problem with gaps, such as the gap between 47,999 and 48,000, is that you don't know how to assign an "in-between" value to a class. We have to assume here that the ambiguity is resolved by not allowing any data values in that gap.
For your test, you'll want to know how your curriculum defines class width, data or class range, and class boundary, and the procedure recommended for determining class boundaries.
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