Final answer:
The rate of change for the equation y=9x+4 is 9, representing a constant slope where for every unit increase in x, y increases by 9 units.
Explanation:
The rate of change in the linear equation y=9x + 4 is the coefficient of the x term, which represents the slope of the line. In this case, the rate of change is 9. This means that for every one unit increase in x, the value of y increases by 9 units. Since this is a linear equation, the rate of change is constant, meaning it does not change regardless of the value of x.
Two mathematically similar frustums have heights of 20cm and 30cm.
The surface area of the smaller frustum is 450cm².
Calculate the surface area of the larger frustum.
The larger frustum has a surface area of 1516.875cm². This is calculated by first finding the ratio of the heights, then cubing this ratio and finally multiplying the result by the surface area of the smaller frustum.
Explanation:In Mathematics, similar frustums follow a rule in which the ratio of their dimensions is the cube root of their surface area ratio. Since the height of the larger frustum is 30cm, and the height of the smaller one is 20cm, their ratio is 30:20 or 1.5:1.
To find the ratio of the surface areas, you'll want to cube this ratio (1.5 ^ 3 = 3.375).
So, the surface area of the larger frustum is the surface area of the smaller frustum (which is 450cm² ) multiplied by this ratio. In mathematical terms, 3.375 * 450 = 1516.875cm².
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How do I find 680% as a fraction mixed number or whole number in simplest form
To convert 680% to a fraction, write it as 680/100 and simplify to 34/5. This improper fraction can also be written as the mixed number 6 [tex]\frac{4}{5}[/tex].
To convert 680% to a fraction or mixed number, follow these steps:
First, write the percent as a fraction with a denominator of 100. So, 680% becomes 680/100.
Next, simplify the fraction by finding the greatest common divisor (GCD) of 680 and 100. The GCD of 680 and 100 is 20.
Divide both the numerator and the denominator by their GCD:
680 ÷ 20 = 34
100 ÷ 20 = 5
So, 680/100 simplifies to 34/5.
Finally, convert the improper fraction to a mixed number. To do this, divide the numerator by the denominator:
34 ÷ 5 = 6 (with a remainder of 4).
This gives us the mixed number 6 [tex]\frac{4}{5}[/tex].
Therefore, 680% as a fraction is 34/5 and as a mixed number is 6 [tex]\frac{4}{5}[/tex].
Geometry
Given triangle ABC with coordinate A(-2,5),B(-2,2) and C(-4,1) and it’s image A’B’C’ with A’(2,1), B’(-1,1) and C’(-2,-1), find the line of reflection.
The line reflection is at y= __
The weekly revenue for a company is r equals negative 3 p squared plus 70 p plus 988r=−3p2+70p+988, where p is the price of the company's product. use the discriminant to find whether there is a price for which the weekly revenue would be $18001800.
Help!!!
What equation is graphed in this figure?
y − 4 = −1/3 (x + 2)
y − 3 = 1/3 (x + 1)
y + 2 = −3 (x − 1)
y − 5 = 3 (x − 1)
The equation of the line is y + 2 = −3 (x − 1). The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The points from which the line passes are ( 0,1) and (1,-2). The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2 - 1 ) / ( 1 )
Slope = -3
The equation of the line will be written as,
y - y₁ = m ( x - x₁ )
y +2 = -3 ( x - 1 )
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There is a line whose slope is 5 and whose y intercept is 7 what is its equation in slope intercept form ?
Write your answer using integers proper fractions and improper fractions in simplest form
The equation of the line with a slope of 5 and a y-intercept of 7 is y = 5x + 7.
Explanation:The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. Given that the slope (m) is 5 and the y-intercept (b) is 7, the equation of the line can be written as y = 5x + 7. This equation tells us that for every increase of 1 on the x-axis, the value of y rises by 5 units, and the line crosses the y-axis at the point (0, 7).
An arithmetic series contains 20 numbers. The first number is 102. The last number is 159. Which expression represents the sum of the series?
Answer:
It's B
Step-by-step explanation:
20(102+159/2)
Factor completely 5c5 + 60c4 + 180c3.
The Ukita family from Japan probably has a greater ecological footprint than the Wu family from China.
True
False
Answer:
True
Step-by-step explanation:
If you look at the different countries ranked based off of the size of their ecological footprint, you will see that Japan is ranked around 5 and china around 10.
This means The average ecological foot print of a person living in Japan is larger than a person living in China.
What are the coordinates of the vertices of the triangle under the translation (x, y) mc014-2.jpg (x - 1, y - 3)?
(-4, 5), (0, 0), (4, 5)
(0, -8), (-1, -1), (-5, -4)
(5, -4), (0, 0), (5, 4)
(-8, 0), (-1, -1), (-4, -5)
After applying the translation (x - 1, y - 3), the vertices of the triangle originally at (-4, 5), (0, 0), and (4, 5) will move to new locations (-5, 2), (-1, -3), and (3, 2).
Explanation:The question is about translation in mathematics, specifically in geometry. A translation is a function that moves every point a constant distance in a specific direction. If we have a point at coordinates (x, y), a translation of the form (x - a, y - b) will shift that point a units to the left and b units down:
The point (-4, 5) will shift to (-4 - 1, 5 - 3) = (-5, 2)The point (0, 0) will shift to (0 - 1, 0 -3) = (-1, -3)The point (4, 5) will shift to (4 - 1, 5 - 3) = (3, 2).So, the vertices of the triangle after the translation (x - 1, y - 3) will be (-5, 2), (-1, -3), and (3, 2).
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Elian bought 1.87 pounds of chicken and 2.46 pounds of turkey at the deli about how much meat did he buy altogether
The total meat Elian bought is 4.33 pounds.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, Elian bought 1.87 pounds of chicken and 2.46 pounds of turkey at the deli.
∴ The total meat Elian bought is the sum of pounds of chicken bought and pounds of turkey bought.
= (1.87 + 2.46) pounds.
= 4.33 pounds.
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Vincent has cut three pieces of rope to complete a science project. two pieces are of equal length. the third piece is one-quarter the length of each of the others. he cut the three pieces from a rope 54 meters long without any rope left over. find the number of meters in each piece.
Penny had $117, which is 9 times as much money as Kari had. How much money did Kari have?
Final answer:
Kari had $13. We found this by dividing Penny's amount, $117, by 9, since Penny's amount is 9 times greater than Kari's.
Explanation:
The question is asking us to determine how much money Kari had if Penny had $117, which is 9 times as much as what Kari had. To do this, we need to perform a division, because if Penny's amount is 9 times Kari's, we can find Kari's amount by dividing Penny's $117 by 9.
To solve for K, divide both sides of the equation by 9: K = $117 / 9.
Therefore, Kari had $13.
125 square yards to square meters (to the nearest tenth)
how many x-intercepts does the graph of the given equation have?
y= -4x^2+3x-2
a.none
b. one
c. two
D. Three
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
Answer:
The answer is 6 inches
Step-by-step explanation:
Since the angle is isosceles, angle A and angle B have the same measure,
The sum of the angles of any triangle is 180°.
So 2 times the measure of angle B plus 120° = 180°, then the equation:
Solving for x we get:
Now we use the law of sine on the triangle BMC like this:
Solving for BC we get :
We apply the law of sin again on the isosceles triangle ABC like this:
Solving for AB we get:
6 inches
Answer:
Answer:
The answer is 6 inches
Step-by-step explanation:
Since the angle is isosceles, angle A and angle B have the same measure,
The sum of the angles of any triangle is 180°.
So 2 times the measure of angle B plus 120° = 180°, then the equation:
Solving for x we get:
Now we use the law of sine on the triangle BMC like this:
Solving for BC we get :
We apply the law of sin again on the isosceles triangle ABC like this:
Solving for AB we get:
6 inches
Read more on Brainly.com - https://brainly.com/question/6638938#readmoreStep-by-step explanation:
A triangle has one angle that measures 15 degrees, one angle that measures 44 degrees, and one angle that measures 121 degrees. what kind of triangle is it
The given triangle can be known as a scalene triangle.
What is a triangle?A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
The measures of the different angles are given as 15°, 44° and 121° respectively.
Since, all the angles have different measures.
The given triangle is neither equilateral or isosceles.
Thus, the given triangle is scalene triangle.
Hence, the given triangle can be called as a scalene triangle.
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Heterogeneous mixtures can be physically separated into their individual components.
True
False
True because their different
Please explain
Use a matrix to find solution to the system of equations
{-8x - 8y = -16
6x - 9y = -108
(-6,8)
(6,8)
(8,-6)
(6,-8)
Answer:
Step-by-step explanation:
the right answer is a (-6,8) where x=-6 and y=8
We're going to use Cramer's rule to resolve this question.
First of all, we're going to give a number to the equations:
(1) -8x-8y=-16
(2) 6x-9y=-108
where constant 1=c1=-16 and the constant 2=c2=-108
now we need to find the next determinants:
D: system determinant,Dx and Dy.
now we're going to find "D."
for that, we're going to take the coefficients of x and y in (1) and (2)
x y
D= [tex]\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right][/tex]
this is how we need to put the matrix, using the numbers next to x and y in the (1) and (2) equation.
to solve this matrix, we need to multiplicate in X, and subtract the results; so for D we have:
(-8*-9)-(6*-8)
72-(-48)=
72+48=120
now we're doing the same process to find Dx and Dy, but in each case, we're going to replace x or y with the constants (the constants are the numbers right to the "=")
to find Dx we're going to use the values of c1 and c2 instead of x
C1&2 y
Dx= [tex]\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right][/tex]
Now we do the same as with D
(-16*-9)-(-108*-8)=
144-(864)
144-864=-720
and now for Dy=
x C1&2
Dy= [tex]\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right][/tex]
= (-8*-108)-(6*-16)=
864-(-96)=
864+96=960
now the last step is to find x and y .
x= [tex]\frac{Dx}{D}[/tex] Y= [tex]\frac{Dy}{D}[/tex]
x= -720/120=-6
y=960/120=8
x=-6 y= 8
answer = (-6,8)
PLEASE HELP
Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student. The Dino Discovery Museum simply charges $7 per student. For how many students will the Science Center charge less than the Dino Discovery Museum charges?
fewer than 40 students
78 or fewer students
78 or more students
more than 40 students
Please help, will give brainliest if you explain
Which ordered pairs are solutions to the following inequality?
(the < has a line under it)
2y - x < -6
Select EACH correct answer
a) (1,-4)
b) (2,-2)
c) (-3,0)
EXPERTS/ACE ONLY!! explain! Ill mark as brainlist!!
Classify the variable according to the set of numbers that best describes its values, the amount of money m spent is a vending machine. The answers I can chose are. A rational numbers, B Irrational numbers, C integers, D natural numbers
The variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The amount of money m spent is a vending machine.
As we know, in the vending machine we cannot insert money in negative quantity.
And integers range from (-∞, ∞)
The real number starts from 1 and continues 2, 3, 4,5 ,6 and so on
Thus, the variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.
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What is the slope ? Thanks
Graph the function by the table. Is the function linear or nonlinear?
A. Nonlinear
B. Linear
Answer:
Option A - Non-linear
Step-by-step explanation:
Given : Graph the function by the table.
x y
1 12.3
2 19.6
3 26.6
4 34.2
5 41.5
To find : Is the function linear or nonlinear?
Solution :
The function is linear when there slopes are equal.
So, we find the slope of the points.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]
[tex]m=\frac{19.6-12.3}{2-1}[/tex]
[tex]m=\frac{7.3}{1}[/tex]
[tex]m=7.3[/tex]
Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]
[tex]m=\frac{26.6-19.6}{3-2}[/tex]
[tex]m=\frac{7}{1}[/tex]
[tex]m=7[/tex]
We have seen that slope between points are not equal.
Therefore, The given points are non-linear.
So, Option A is correct.
What does an exponent in front of a square root mean?
Alinethatincludesthepoint(6, 3)hasaslopeof 2 . what isitsequationin slope -intercept form?
y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find the equation of line that includes the point (6, 3) has a slope of 2.
y minus y one equal to m time of x minus x one.
(y-y₁)=m(x-x₁)
x₁=6,y₁=3 and m is 2
y-3=2(x-3)
Apply distributive property on right hand side.
y-3=2x-6
Shift -3 to the RHS side
y=2x-6+3
y=2x-3
Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
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Jan has 3 1/3 feet of rope to use on a camping trip. Assume 1 foot = 30.48 centimeters. What is the best estimate of the centimeters of rope Jan has?
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
y = -3/4x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –3/4(x – 4)
y + 2 = 3/4 (x + 4)
Answer:
Option B and E
Step-by-step explanation:
A line is given as 3x - 4y = 7
We have to find the equation of a line parralel to the given line which passes through point (-4, -2).
Let the equation is y = mx + c
Line parallel to 3x - 4y = 7 will have same slope
3x - 4y = 7
-4y = 7 - 3x
4y = 3x - 7
y = [tex]\frac{1}{4}[/tex] (3x - 7 ) ≈ [tex]\frac{3}{4}[/tex]x - [tex]\frac{7}{4}[/tex]
So slope of the line will be m = [tex]\frac{3}{4}[/tex]
Since the given line passes through (-4, -2)
So we put the values in y = mx + c to get the value of c.
-2 = [tex]\frac{3}{4}[/tex] (-4 ) + c
-2 = -30 +c
c = 3 - 2 = 1
Therefore, equation will be
y = [tex]\frac{3}{4}[/tex]x + 1 ----------(1)
We further solve equation (1)
4y = 3x + 4
3x - 4y = -4 ---Option B
By solving the equation (1) in other way
y + 2 = [tex]\frac{3}{4}[/tex]x + 1 + 2
[tex]\frac{3}{4}[/tex]x + 3
y + 2 = [tex]\frac{3}{4}[/tex] (x+4) --Option E
Option B and E are the answers.
The most efficient first step in the process to factor the trinomial 4x3-20x2+24x
A. factor out –1
B. factor out 4
C. factor out 4x
D. factor out (x – 3)
Factor out 4x from the given trinomial. Therefore, option C is the correct answer.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given trinomial is 4x³-20x²+24x.
Here, 4x(x²-5x+6)
= 4x(x²-3x-2x+6)
= 4x[(x(x-3)-2(x-3)]
= 4x(x-3)(x-2)
Therefore, option C is the correct answer.
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