The child's position after 90 seconds would be (0, -1).
How to find the child's positionThe carousel revolves 360 degrees in one minute, which means it revolves 360/60 = 6 degrees per second.
After 90 seconds, the carousel would have revolved 90 * 6 = 540 degrees.
When the carousel revolves counterclockwise, the point (0, 1) would rotate to a new position by 540 degrees.
To find the new position, we can use the transformation:
540 - 360 = 180
hence the transformation is 180 degrees which is reflection across x axis
The rule for a reflection over the x -axis is (x, y) → (x, −y)
point (0, 1) → (0, −1)
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a number increasd by 10 is 2 times the sum of the number and 3
Answer: n= 4
Step-by-step explanation:
n+10=2(n+6) where n represents the number
you solve this.
n+10=2n+6
n+10-6=2n
n+4=2n
n=4
A cookie recipe calls for 1.5 cups of sugar for two dozen cookies. How many cups of sugar are needed for one dozen cookies?? Plss help!!!
For a dozen cookies, 0.75 cups of sugar are needed in total.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
given, A cookie recipe calls for 1.5 cups of sugar for two dozen cookies.
Since,
For two dozen of cookies, there are a total of 1.5 cups of sugar required.
In 2 dozen cookies, required sugar = 1.5 cups
In 1 dozen cookies, required sugar = 1.5/2 cups
In 1 dozen cookies, required sugar = 0.75 cups
Therefore, The total number of cups of sugar required for one dozen cookies is 0.75.
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7. 23% of the class was unhappy. 19 students were unhappy. How many students were in the class? Round to the nearest student.
The total number of students in the class given the percentage of unhappy students is 263 students.
How many students were in the class?Percentage of unhappy students= 7.23%
Number of unhappy students= 19
Total number of students in class= x
Number of unhappy students = Percentage of unhappy students × Total number of students in class
19 = 7.23% × x
19 = 0.0723 × x
19 = 0.0723x
divide both sides by 0.0723
x = 19/0.0723
x = 262.7939142461964
Approximately,
x = 263 students
Therefore, there are 263 students in the class.
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Please help will mark Brainly
Answer:
1
Step-by-step explanation:
Y intercept is 1
Y intercept is the point where the line crosses the y axis (point where x=0, you see the line crosses y axis at 1). Thus even if you put 0 in equation 9^x you will get 9^0 and anything power of 0 is 1.
One of the world's heaviest hailstones weighed 2.2 pounds. Which is more appropriate to express its mass, 1 kilogram or 1 gram?
Answer:
Well, it depends, but I'd reckon kilograms.
Step-by-step explanation:
2.2 pounds is approximately 0.998 kg, which can be rounded off to 1 kg. However, you really do have to be precise, you may measure it in grams (that's, 998 grams).
So, the most appropriate way is to use 1 kilogram, as a hailstone can be considered quite heavy and we may not be keen on looking for a really precise measurements, as they're measured in hundreds of grams!
Hope this helps :)
Given m||n, find the value of x.
(7x-1)º
(9x+5)º
The value of x is 11 for the given condition that m||n.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).
Angles on a straight line sum up 180°
Let us take the line t as our straight line
(7x – 1)° + (9x + 5)° = 180°
(7x + 9x + 5 – 1) = 180
16x + 4 = 180
16x = 180 – 4
16x = 176
(16x)/16 = (176/16)
x = 11
Hence, the value of x is 11.
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Work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)
The equation of line having a slope of 2 and passing through the point (1,4) is y = 2x + 2.
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line has a gradient of 2 and passes through the point (1, 4).
x₁ = 1y₁ = 4Slope m = 2Plug the given values into the point-slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - 4 = 2( x - 1 )
y - 4 = 2x - 2
Add 4 to both sides of the equation
y - 4 + 4 = 2x - 2 + 4
y = 2x - 2 + 4
y = 2x + 2
Therefore, the equation of the line is y = 2x + 2.
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Which of the following tables represents a linear relationship that is also proportional?
x −2 0 2
y −4 −3 −2
x −1 0 1
y 0 2 4
x −1 0 1
y −4 −1 2
x −3 0 3
y −1 0 1
The only table that represents both a linear and proportional relationship is table 4
How to identify a proportional relationship?A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.
In the first table, we see that the proportion of y to x are;
-4/-2 = 2
-3/0 = undefined
-2/2 = -1
Second table shows that;
0/-1 = 0
2/0 = undefined
4/1 = 4
Third table shows that;
-4/-1 = 4
-1/0 = undefined
2/1 = 2
Fourth table shows that;
-1/-3 = 1/3
0/0 = 0
1/3 = 1/3
Looking at the tables. the only one that is a proportional relationship is table 4
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Answer:
The only table that represents both a linear and proportional relationship is table 4
How to identify a proportional relationship?
A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.
In the first table, we see that the proportion of y to x are;
-4/-2 = 2
-3/0 = undefined
-2/2 = -1
Second table shows that;
0/-1 = 0
2/0 = undefined
4/1 = 4
Third table shows that;
-4/-1 = 4
-1/0 = undefined
2/1 = 2
Fourth table shows that;
-1/-3 = 1/3
0/0 = 0
1/3 = 1/3
Looking at the tables. the only one that is a proportional relationship is table 4
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Step-by-step explanation:
This is the sketch of a graph of y=(x-1)(x-3)
Question is below
From the graph, the coordinates of the points of the equation y=(x-1)(x-3): (1,0) (4,0), P(0,3) and turning point (2.5,2)
How to find the coordinates?You should know that these are possible reading from the graph
The scale of the graph is [laced at 1 com to 1 unit on both axes
From the graph, the coordinates of A are (1, 0) This is where x=1 and y=0
The coordinates of B = (4, 0) This is where x=4 and y=0
b) The coordinates of point P are (0,3) This is where x=0 and y= 3
c) The coordinates of the turning point are (2.5, 2) This is the minimum value of the curve
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Given AABC with AB contained in the line 2x + 3y = 5. If AABC is dilated to get AA'B'C
which of the following lines could contain A'B'?
3x + 2y = 10
2x - 3y = 10
2x+3y=10
3x-2y = 10
The line could contain A'B' is 3x+2y=10, so correct option is (a).
What do you mean by equation?It usually consists of variables, coefficients, and constants, connected by operations such as addition, subtraction, multiplication, and division. Equations are used to model relationships between different quantities and to solve problems in various fields such as physics, engineering, and economics. For example, the equation y = mx + b represents a straight line in two-dimensional space, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
The line 2x + 3y = 5 contains AB, so AB lies on the line 2x + 3y = 5. To dilate triangle ABC to A'B'C, the center of dilation is a fixed point and the scale factor is a constant. Since AB lies on the line 2x + 3y = 5, the line containing A'B' after dilation must be parallel to the line 2x + 3y = 5, so the correct answer is (a) 3x + 2y = 10.
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I need a real answer with solution please need help.
The required solution of the given differentiation is given as y'(2) = 135/16. Option A is correct.
The method of determining the derivative of an implicit function is by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
here,
y = [x - 1/x]³
y' = 3[x - 1/x]² × [1 + 1/x²]
put x = 2
y'(2) = 3 [2 - 1/2]² × [1 + 1/4]
y'(2) = 3[3/2]²[5/4]
y'(2) = 27/4 × 5/4
y'(2) = 135/16
Thus, the required solution of the given differentiation is given as y'(2) = 135/16.
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Answer to the question posted below
The change will be approximately $100 million by solving through simple algebra.
The purpose of percentage calculationsThe use of percentages is widespread and diverse. For instance, percentages are used to convey discounts in stores, bank interest rates, inflation rates, and various statistics in the media. For comprehending the financial aspects of daily life, percentages are crucial.
The simple percentage method is what?Divide the whole number by 100, then multiply the result by the requested percentage to find a percentage of the given number: For instance, 12% of 250 equals (250 100) x 12 = 30.
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If you have 2 1/2 bags of grapes each bag of grapes weighs 1/2 pounds how many pounds of grapes do you have
53) Jim drove 180 miles in 5 hours. If he can keep the same pace, how long will it take him to drive 900 miles?
The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of hours for Jim to drive 900 miles be A
Now , the number of hours = 5 hours
The total distance traveled by Jim in 5 hours = 180 miles
Now , the distance traveled by Jim = 900 miles
And , the proportion will be
A / 900 = 5 / 180
Multiply both sides of the equation by 900 , we get
A = ( 5 x 900 ) / 180
On simplifying the equation , we get
A = 5 x 5
A = 25 hours
Hence , the number of hours is 25 hours
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The graph below shows an exponential function and a quadratic function.
m c012-1.j pg
How do the functions compare over the interval m c012-2.j pg?
The exponential grows at approximately half the rate of the quadratic.
The exponential grows at approximately the same rate as the quadratic.
The exponential grows at approximately twice the rate of the quadratic.
The exponential grows at approximately four times the rate of the quadratic.
The exponential grows at the same rate as the quadratic in the interval
0 ≤ x ≤ 1.
What is the Average Rate of Change function?The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.
A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by
[tex](f(a) - f(b))/(b-a)[/tex].
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by
= (2-1)/1 = 1
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by
=(1 - 0)/1 = 1
Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.
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If the answer is correct and well explained i will give the brainliest
Answer:
Option: 4
Step-by-step explanation:
It is in the form of ar^n-1.
For eg:
2nd term/1st term=3rd term/2nd term=4th term/3rd term
PLEASE HELP!!!!!!!!!!!!!!
The required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.
What is decimal value?Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,
here,
The decimal value is shown in the image,
= 31 / 100
= 0.31
From the options,
0.31 > 0.1
0.31 < 0.5
0.31 < 0.32
0.31 < 0.4
Thus, the required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.
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which is greater 4 4/10 or 32/10
Answer:
4 4/10 is greater.
Step-by-step explanation:
4 = 40/10
then:
4 4/10 = 4 + 4/10 = 40/10 + 4/10 = (40+4)/10 = 44/10
Then:
44 > 32
44 is greater.
represent the shaded area in the drawing as a mixed number and also as an improper fraction
I got 1 3/4 & 3/5 but it is incorrect
Answer:
Mixed number: 1 3/8
Improper fraction: 11/8
Step-by-step explanation:
The first circle is 1 whole 1 = 8/8
The second circle is 3/8 *
8/8 + 3/8 = 11/8
----------------------
If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.
1 3/8 Mixed number
1x8=8
8+3=11
11/8 Improper fraction
-----------------------
* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.
----------------------
I hope this helps!
find the equation of the line parallel and perpendicular to the line 3x + 7y = 8 and passes through (4,5)
(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.
Find the equation ?Therefore, we must first determine this's slope.
-3x - 7y = 10
To both sides, add three.
-7y = 3x + 10
Add -7 to both sides.
y = -3/7x - 10/7
Our slope is thus -3/7.
The slopes always remain the same when searching for a line that is parallel to something.
Remember that y = mx+b is the slope-intercept form as well.
Where b is the y-intercept and m is the slope.
Our y-intercept is -3 since the coordinates (-5,-3) are available.
The slope here is -3/7.
Put those numbers into the slope-intercept form equation, then, to solve.
y = mx + b
y = -3/7x - 3
(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.
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The equation of the line parallel to the given line is y = -3x/7 + 47/7
The equation of the perpendicular will be y = 7x/3 -13/3
What is a Equation of a line ?The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope. The slope of the original line's perpendicular line is -2, which is the original line's negative reciprocal.
The equation of the line is 3x + 7y = 8
The slope of the line is = -3/7
so the equation of the line parallel to the given line is y = -3x/7 + c
the point given as (4,5)
The line is 5 = -3*4/7 + c
or, c = 5 + 12/7 = 47/7
the equation of the line parallel to the given line is y = -3x/7 + 47/7
The slope of the line perpendicular to the given line is 7/3
So, the equation of the line is y = 7x/3 + c
The intercept is 5 = 7*4/3 + c
or, c = 5 - 28/3 = -13/3
The equation of the perpendicular will be y = 7x/3 -13/3
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A politician's support increases from 34% to 50% Determine the actual and relative change in this sitation.
The politician experience 16% of actual change and 47% relative change in his support.
Actual change refers to the simple difference between the ending and initial condition. In this case, actual change is the gap of the politician's support increase. The actual change of the politician's support is:
Actual change = Ending% - Initial %
Actual change = 50% - 34%
Actual change = 16%
Relative change is the percentage change between ending and initial condition based on the perspective of the initial condition. Relative change measures the gap between the ending and initial conditions compared to the initial condition. Relative change can be calculated by dividing the gap of 2 conditions with the initial condition.
The relative change of politician's support is:
Relative change = Ending% - Initial %
Initial %
Relative change = 50% - 34%
34%
Relative change = 47%
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$6,446 $ 6,446 is invested, part at 13% 13 % and the rest at 10% 10 % . If the interest earned from the amount invested at 13% 13 % exceeds the interest earned from the amount invested at 10% 10 % by $568.65 $ 568.65 , how much is invested at each rate? (
The amount invested at 10% by $568.65 and investment rate is -
amount invested at 13%. is $5275
amount invested at 10%. is $1171
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
here, we have,
Let x represent the amount invested at 13%.
Let y represent the amount invested at 10%.
$6,446 is invested, part at 13 % and the rest at 11%.
This means that
x + y = 6,446
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the amount invested at 13%,
P = x
R = 13%
T =1 year
I = (x × 13 × 1)/100 = 0.13x
Considering the amount invested at 10%,
P = y
R =10%
T = 1 year
I = (x × 10 × 1)/100 = 0.10y
If the interest earned from the amount invested at
13% exceeds the interest earned from the amount invested at
10% 10 % by $568.65, it means that
0.13x - 0.10y = 568.65,- - -- - - - - -1
Substituting x = 6,446 - y into equation 1, it becomes
0.13(6,446- y) - 0.10y =568.65
i.e. y= 1171
solving, we get,
x=5275
y= 1171
amount invested at 13%. is $5275
amount invested at 11%. is $1171
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 6 in. The area of the base is 15.6 in². The slant height of the pyramid is 8 in.
What is the surface area of the pyramid?
Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:
A = (s^2 * sqrt(3)) / 4
where s is the side length of the triangle. Plugging in the values, we get:
15.6 = (6^2 * sqrt(3)) / 4
Solving for the height of the base, h:
h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)
Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:
h^2 + (base/2)^2 = slant height^2
where base is the length of one side of the base of the pyramid. Plugging in the values, we get:
h^2 + (6/2)^2 = 8^2
Solving for h:
h = sqrt(64 - 9) = sqrt(55)
Finally, the surface area of the pyramid can be found using the formula:
SA = base area + (perimeter * slant height) / 2
where perimeter is the total length of the sides of the base. Plugging in the values, we get:
SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²
So, the surface area of the triangular pyramid is 51.6 in².
Step-by-step explanation:
One inequality in a system is y ≥ 2x + 3. Write another
possible inequality in the system so that (-2, 6) is a solution of the
system.
ystem of
Answer:
Step-by-step explanation
y≥ 2x + 3 is -6,2
The graph below shows an exponential function and a quadratic function.
mc012-1. Jpg
How do the functions compare over the interval mc012-2. Jpg?
The exponential grows at approximately half the rate of the quadratic.
The exponential grows at approximately the same rate as the quadratic.
The exponential grows at approximately twice the rate of the quadratic.
The exponential grows at approximately four times the rate of the quadratic.
The exponential grows at the same rate as the quadratic in the interval
0 ≤ x ≤ 1.
What is the Average Rate of Change function?The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.
A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by
[tex](f(a) - f(b))/(b-a)[/tex].
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by
= (2-1)/1 = 1
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by
=(1 - 0)/1 = 1
Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.
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Answer:
B
Step-by-step explanation:
can someone please help me answer 1, 2, and 5! Thank you so muchhhh here’s 30 points for it!!! Please do it right, thank you.
Answer: i don't know give me more info
Step-by-step explanation:
I need to know the system of equations for both graphs 3 and 4
The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.
What is two-point form?
One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.
We are given two lines on the graph
Both the lines meet on the y-axis at (0,-2)
This means (0,-2) is the common solution.
Another point of the steeper line is (1,2)
Another point of the flatter line is (3,-3)
Now, as we know the two points of the line, using the two-point form, we get
[tex]\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]
⇒ (y+2)/(x-0) = (2+2)/(1-0)
⇒ y+2 = 4x
⇒ y = 4x-2
⇒ 4x - y - 2 = 0
Similarly,
⇒ (y+3)/(x-3) = (-2+3)/(0-3)
⇒ (y+3)/(x-3) = -1/3
⇒ (y+3) = -(x-3)/3
⇒ y+3 = -x/3 + 1
⇒ y = -x/3 - 2
⇒x + 3y + 6 = 0
Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.
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Since there are multiple questions so, the question answered above is attached below
Consider the line y=7x-3.
Find the equation of the line that is parallel to this line and passes through the point (-4,-6).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, -6).
The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The slope intercept form of a line is:
y = mx + b
where m is the slope and b is the y intercept
Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.
Given the line:
y = 7x - 3
The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7
The equation of the line that is parallel to this line and passes through the point (-4,-6) is:
y - (-6) = 7(x - (-4))
y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:
y - (-6) = (-1/7)(x - (-4))
y = -(1/7)x - 46/7
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What is the solution to the equation
2x=5
Answer:
5/2 or 2.5
Step-by-step explanation:
Divide both sides by 2.
43) A tree 13 feet high grows at the rate of3feet each year. How many years will it take for the tree to grow to a height of 28 feet?