The value of k in the point (2, k) which lies on the line is -4.
How to find the value of k?
Every point lying on the curve of the line satisfies the equation of curve. Therefore, substitute the point in the given equation of line to find the value of k.
According to the given question:
The given equation is: 2y = - 3x - 2.
This is written as: 3x + 2y + 2 = 0.
Given the point (2, k) lies on the line given.
That means it should satisfy the given equation.
So, to find the value of 'k', simply substitute the point on the line.
So, it becomes: 3(2) + 2(k) + 2 = 0
⇒ 6 + 2k + 2 = 0
⇒ 2k = - 8
Dividing by 2 throughout, we get: k = - 4
Hence, (2, -4) lies on the line.
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how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
help
We can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.
What are equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, the quantity of mixed nuts we need is x pounds.
There are 0.70 pounds of peanuts in this mixture.
3 pounds of peanuts make up the 20% mix, or 0.20*15.
We got the equation:
0.70 x + 3 = 0.40(x + 15)
Now, solve this equation as follows:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, we can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.
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What is the equation, in standard form, of a parabola that models the values in the table x-3 0 2 f(x) -8 -2 -28
The equation in the standard form of a parabola is y = -3x² - 7x - 2
What is the standard form of a parabola?
Another equation that, when graphed, produces a parabola is one written in standard form. Like the letters in the vertex form equation, each letter in the standard form equation provides a nugget of knowledge about the parabola.
Here, we have
The standard equation of a parabola is
y = ax² + bx + c
Substitute the given values in this equation
When x = - 3 and y = -8
-8 = a (-3)² + b (-3) + c
-8 = 9a - 3b + c …. (1)
When x = 0 and y = - 2
-2 = a (0)² + b (0) + c
c = -2....(2)
When x = 2 and y = -28
-28 = a (2)² + b (2) + c
-28 = 4a + 2b + c …. (3)
Equations (1) and (3) can be written as
9a - 3b + c = -8 …. (4)
4a + 2b + c = -28 …. (5)
Multiply equation (4) by 2 and equation (5) by 3 to eliminate 'b'
18a - 6b + 2c = -16
12a + 6b + 3c = -84
Subtracting these equations
30a + 5c = -100
Substitute the value of 'c' here
30a + 5(-2) = -100
30a = -100 + 10
30a = -90
a = -3
Substitute the value of a and c in equation (1)
-8 = 9a - 3b + c
-8 = -27 - 3b -2
-6 = -27 - 3b
3b = -21
b = -7
Here the value of a = -3, b = -7, and c = -2.
Hence, the equation in the standard form of a parabola is y = -3x² - 7x - 2
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Subtract 81/6-45/6 Simplify the answer and write a mixed number
The value of the given fraction in mixed numbers is 6, or 36/6.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.
Here,
=81/6-45/6
=(81-45)/6
=36/6
=6
The value for given fraction in mixed number will be 6 that is 36/6.
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Yo guys I need help ASAP
Solve the equation 2x + 3y = 5 for x.
Step-by-step explanation:
[tex]2x + 3y = 5[/tex]
[tex]2x = 5 - 3y[/tex]
[tex]x = \frac{5 - 3y}{2} \\ [/tex]
Answer: Add 3y to both sides of the equation. 2x=5+3y Divide each term in 2x=5+3y by 2 and simplify.
The Grinch does not like to talk about his age, But, he does tell people that he is 400 reduced by 2 times his
age is 244. So how old is he really? 78 years old
Answer:88 i think
Step-by-step explanation:
The average cost of a gallon of gas in year one was $2.95. The average cost of a gallon of gas in year two was $2.78. What is the percent of change in the average cost of a gallon from year one to year two? (4 points)
6.2%
6.1%
5.7%
5.8%
the percent of change in the average cost of a gallon from year one to year two is 5.8%
What is average cost change?The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced.
The overall cost of production can also be divided into fixed and variable costs. Since total fixed costs often remain constant, changes in total variable costs are the main cause of changes in average costs.
SolutionThe average cost of a gallon of gas in year one was $2.95
The average cost of a gallon of gas in year two was $2.78
The change in the average cost of a gallon from year one to year two is
$2.95 - $ 2.78
⇒$0.17
So percent of change in the average cost of a gallon from year one to year two is
($0.17/$2.95) * 100%
⇒ 0.0576 * 100%
⇒ 5.76%
⇒ 5.8%
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What is the volume of this rectangular prism?
Solve 9x^2 + 5 = 18x using quadratic formula
Answer:
x= 1/3rd and 5/3rds
Step-by-step explanation:
9x^2 + 5 = 18x
9x^2-18x+5=0
a=9 b=-18 c=6
x=-b+- the Square root of b^2-4ac all over 2a
so x= 18+- the Square root of -18^2 -4x9x5 all divided by 18
x= 18+- the square root of 144 all over 18
so 18+12 over 18 and 18-12 over 18
this simplifies down to x= 5/3 and 1/3
Sonya's heart rate was 76 beats per minute.
She ran a mile on her treadmill and checked
her heart rate again. This time, her heart rate
was 133 beats per minute. What was the
percent increase in Sonya's heart rate?
HELP !!!
Answer: Sonya's heart rate increased by 75% after running a mile on the treadmill.
Step-by-step explanation:
To find the percent increase in Sonya's heart rate, we can use the following formula:
Percent increase = (New value - Old value) / Old value * 100
Substituting the given values into the formula, we get:
Percent increase = (133 beats per minute - 76 beats per minute) / 76 beats per minute * 100
Calculating the result, we get:
Percent increase = 57 beats per minute / 76 beats per minute * 100
= 0.75 * 100
= 75%
Therefore, Sonya's heart rate increased by 75% after running a mile on the treadmill.
The density of grape juice is 1.07 grams per cm³.
The density of fruit syrup is 1.6 grams per cm³.
The density of carbonated water is 0.99 grams per cm³.
35 cm³ of grape juice are mixed with 25 cm³ of fruit syrup and
310 cm³ of carbonated water to make a drink with a volume of 370 cm³.
Work out the density of the drink.
Give your answer correct to 2 decimal places.
The density of the drink is 1.04 grams per cm³
How to work out the density of the drink?
Given:
density of grape juice = 1.07 grams per cm³, density of fruit syrup = 1.6 grams per cm³ and density of carbonated water = 0.99 grams per cm³
volume of grape juice = 35 cm³, volume of fruit syrup = 25 cm³ and volume of carbonated water = 310 cm³
First, find the mass of grape juice, fruit syrup and carbonated water using their volume and density:
density = mass / volume
=> mass = density × volume
mass of grape juice = 1.07 × 35 = 37.45 grams
mass of fruit syrup = 1.6 × 25 = 40 grams
mass of carbonated water = 0.99 × 310 = 306.9 grams
Total mass = 37.45 + 40 + 306.9 = 384.35 grams
Total volume = 35 + 25 + 310 = 370 cm³
density of the drink = Total mass / Total volume
density of the drink = 384.35 / 370 = 1.04 grams per cm³
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A circle of radius 5 is centered at the origin. The line x + 2y = −5 intersects this circle at the points A and B. Determine the length of the major arc AB.
The length of the major arc AB is 15.44 units
How to determine the length of the major arc?Given: line x + 2y = −5 and circle of radius 5 centered at the origin
The equation of a circle of radius r whose center is the origin O (0, 0) is given by x²+y² = r². Thus:
x²+y² = 5²
x²+y² = 25
To find the points where the line intersects the circle, we can substitute the equation of the circle into the equation of the line.
Substituting this into the equation of the line, we have;
x + 2y = -5
x²+y² = 25
Solving for x, we have
x = (-5 ±√(33))/2
Since the circle is centered at the origin, both of these points are on the circle. Thus, the coordinates of the points A and B are
A: (-5 +√(33))/2, (-5 - √(33))/4
B: (-5 - √(33))/2, (5 - √(33))/4
To find the length of the major arc AB, we can use the formula
length = θ/360 × 2πr
where r is the radius of the circle, and θ is the central angle formed by points A and B. The central angle can be found using the formula
θ= 180 - 2cos⁻¹((AB² + r² - AC²)/(2 × AB × r))
where AB is the distance between the points A and B, and AC is the distance between point A and the center of the circle (which is the origin)
We can use the Pythagorean Theorem to find AB and AC:
AB = √(((-5 + √(33))/2 - (-5 - √(33))/2)² + ((-5 - √(33))/4 - (5 - √(33))/4)²)
= √(66)
AC = √(((-5 + √(33))/2)² + ((-5 - √(33))/4)²)
= √(25 + 33)/2
= √(58)/2
Substituting these values into the formula for θ, we have
θ = 180 - 2cos⁻¹((√(66)² + 5² - (√(58)/2)²)/(2 × √(66) ×5))
= 180 - 2cos⁻¹((66 + 25 - 29)/(20))
= 180 -2cos⁻¹(62/20)
= 180 - 2cos⁻¹(3.1)
= 180 - 2 × 1.43
= 180 - 2.86
= 177.14
Finally, substituting this value into the formula for the length of the major arc, we have
length = 2 × π × 5 × (177.14/360)
= 2 × π 5 × (0.4925)
= 2 × 3.14 × 5 × (0.4925)
= 6.28 × 5 × (0.4925)
= 31.4 × (0.4925)
= 15.44 units
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SOMEONE PLEASE HELP ME
7*2*4 = 56.
7 is the length, 2 is the height, 4 is the widght
Equation for volume is l*h*w
Can Cramer's rule be used to solve this system of equations?
-211 - 12
= 2
- 3
- 3x1 - 272
Yes
No
If Yes, write the determinants used to compute x₂.
x2
det(
det(
Compute
12
-2
-3
-2
-3
-1
-2
31₁
2
-3
The Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.
What is Cramer's Rule?For a given system of equations ax + by = c ; px + qy =r, if the determinant of the coefficient matrix [tex]A = \begin{bmatrix}a&b\\p&q\end{bmatrix}[/tex] is non-zero, then as per the Cramer rule, the solution to the system of equations is:
[tex]x=\frac{ \begin{vmatrix}c&b\\r&q\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}\quad\text{and}\quad y=\frac{ \begin{vmatrix}a&c\\p&r\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}[/tex]
The given system of equations is:
-2x₁ - x₂ = 2
-3x₁ - 2x₂ = -3
The coefficient matrix of the system of equations is:
[tex]A = \begin{bmatrix}-2&-1\\-3&-2\end{bmatrix}[/tex]
Now, find the determinant of the coefficient matrix:
[tex]A = \begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}\\A = 4-3\\A =1[/tex]
Since the determinant of the coefficient matrix is non-zero, the Cramer rule can be applied.
According to the Cramer rule, it follows:
[tex]x_2=\frac{\begin{vmatrix}-2&2\\-3&-3\end{vmatrix}}{\begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}}\\\\x_2=\frac{6-(-6)}{1}\\\\x_{2}=12[/tex]
Hence, the Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.
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Which of the following is equivalent to the expression below? √64
-6i
6i
-8i
8i
Answer:
√64 = 8
8i
Step-by-step explanation:
i = √-1
but √64 is a positive number which will produce 8i
A. Use the appropriate formula to determine the periodic deposit.
B. How much of the financial goal comes from deposits and how much comes from interest?
Periodic Deposit: $? at the end of each year
Rate: 6% compounded annually
Time: 18 years
Financial Goal: $130,000
The periodic deposit is? $
By using compound interest, it can be calculated that-
A) Deposit is $45544.69
B) Interest = $84455.31
What is compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then amount is calculated by
[tex]A = p(1 + \frac{r}{100})^n[/tex]
The difference between the amount and the principal is the compound interest
A)Here,
Let the principal be $p
Rate = 6%
Time = 18 years
Amount = $130000
[tex]130000 = p(1 + \frac{6}{100})^{18}[/tex]
[tex]130000 = p(1 + \frac{3}{50})^{18}[/tex]
[tex]130000 = p(\frac{53}{50})^{18}[/tex]
[tex]130000 = p(1.06)^{18}[/tex]
[tex]p = \frac{130000}{1.06^{18}}[/tex]
p = $45544.69
B) Interest = $(130000 - 45544.69)
= $84455.31
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Graph the function f(x) = 14(0.87). Does this function show growth or decay? What is the equation of the asymptote?
Growth; y = 0
Growth; y = 14
Decay; y = 0
Decay; y = 14
The function f(x) = 14(0.87) has is a constant function has no growth or decay.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.
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Gwen and Max had breakfast at a cafe. Muffins cost $2 each, and fruit cups cost $4 each. Gwen had 2 muffins and 1 fruit cup. Max had 2 muffins and 1 fruit cup. How much did their breakfast cost?
Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total
Answer:
their breakfast cost 16 dollars
Step-by-step explanation:
because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing
If sin (0) = -5.7, what is sin (2π - 0)?
A. -7.5
B.-5.7
C. 5.7
D. 7/5
51. A company offers cable television at $29.95 per month plus a one-time installation fee. The total cost for the first six months of service is $214.70. a. Write an equation in point-slope form that represents the total cost you pay for cable television after x months.
The equation that represents the total cost you pay for cable television after x months is y = 35 + 29.95x.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Given that a cable operator offers that buy a television at $29.95 per month plus a one-time installation fee.
The total cost that need to pay after 6 months is $214.70.
Assume that a be the cost one-time installation fee.
Then total cost that need to pay after 6 months is (6 × 29.95) + a = 179.7 + a
Therefore,
179.7 + a = $214.70
a = 35.
After x month, he needs to pay 35 + 29.95x.
Assume that y represents total cost after x months.
y = 35 + 29.95x
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Closing: What Is the Value of Each Number, and Which Is Larger? Use your teacher’s verbal clues and this number line to determine which number is larger. −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all.
What is a number line?In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.
As per the given numbers in the number line has been drawn below,
The value of a number in the number line is the absolute value without considering the sign.
For example value of -2 is the distance from zero to -2 so it will be 2.
The largest value is 8 among all numbers.
Hence "The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all".
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What is 6 3/5-2 7/10
The value of the given expression 6 3/5-2 7/10 is 39/10.
What is an expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Here, we have
Given: 6 3/5-2 7/10
We have to solve this expression and find the value of the given expression.
6 3/5-2 7/10 = 33/5 - 27/10
6 3/5-2 7/10 = (66-27)/10
6 3/5-2 7/10 = 39/10
Hence, the value of the given expression is 39/10.
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A wood state casket labeled 6/6XX would measure in length 6 feet 6 inches and in width
Answer: 28 inches
Hope this helps!!! :)
Write the equation of the line graphed in Point-Slope Form.
Answer: y-3 = -4/5(x+0)
Step-by-step explanation:
formula
y-y1=m(x-x1)
y = y coordinate of the second point
y1 = y coordinate of point one
m = slope
x = x coordinate of the second point
x1 = x coordinate of point one
slope formula
y2-y1/x2-x1
-1-3/5-0
slope = -4/5
the 2 points on the graph are (0,3) (5,-1)
substitute and solve
y-3 = -4/5(x+0)
y-3=-4/5x
A cylinder has a radius of 5 centimeters and a height of 10 centimeters. What is the volume of the cylinder to the nearest cubic
centimeter? Use 3.14 for
Answer: centimeters 3
Solve the compound inequality and graph on the number lines provided.
7) -2 x ≤ 4 AND 10>-2 x
8) 10<3 x-2 or -3 x-2>14
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
-2 x ≤ 4 and 10 > -2x
x ≤ 4/-2 and 10/2 > -x
x ≤ -2 and 5 > -x
x ≤ 2 and x > -5
This means.
-5 < x ≤ 2
The number line can be graphed as,
<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->
o---------------------------------------- o
10 < 3x - 2 or -3x - 2 > 14
10 + 2 < 3x or -3x > 14 + 2
12 < 3x or -3x > 16
x > 4 or -x > 16/3
x > 4 or x < -16/3
x > 4 or x < -5.3
x > 4 can be represented on a line graph as,
__-1__0__1__2__3__4__5__6__7--------->
o----------------------->
x < -5.3 can be represented on a number graph as,
<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->
<--------------------------o
Thus,
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
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1.) Focus (0,4) and a directrix y = -4
2.) Focus of (3,0) and a directrix of x = -3
3.) A parabola has a focus of (-2,0) and a directrix at x = 2. ( Answer the following)
- What is the vertex of the parabola?
- Is the equation in the form y= ax^2 or x = ay^2?
- What is the focal length?
- What is the equation of the parabola?
Thank you.
On solving the question, we that when focus is (0,4) and a directrix y is -4 coordinate is (0,0).
What are Directrix and Focus?Parabola is the name of the graph of the quadratic function. Another way to think of this is the collection of all points whose distance from the focal point is equal to the distance from the line.
Focus (0,4) ,
the directrix y is (-4)
The vertex (h ,k) - halfway between the,
directrix and focus.
y = [y coordinate of focus + directrix] / 2.
The x coordinate will be the same as the x coordinate of the focus.
[tex]\frac{(0, 4-4)}{2} \\(0,0)[/tex]
Focus of (3,0),
a directrix of x = -3
The vertex (h , k) is halfway
between the directrix
and focus.
x = [x coordinate of focus + directrix] / 2.
The x coordinate will be the same as the y coordinate of the focus.
[tex]\frac{3-3,0}{3} \\(0,0)[/tex]
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please help, it tells u to write the expression in simplified radical form
The given expression in simplified radical form is 2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
Define Radicals.
The term "radical" is used to represent the square root or nth roots.
Expression with a square root is referred to as a radical expression.
Radicand: The value or phrase contained within the radical symbol.
Given expression is,
[tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]
Rewrite this expression,
we know, 2⁵ = 32
[tex]\sqrt[4]{(2x^4.y^3)^4 .y^3 .2}[/tex]
You see this expression is equal to given expression i.e, [tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]
Take out the term from under the radical,
2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
Hence, the given expression in simplified radical form is 2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
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9. Why is it not possible to make a right triangle using
lengths of 4 feet, 8 feet, and 10 feet? (2 pts)
A 4+8 is greater than 10.
B
10-8 does not equal 4.
C
42+82 does not equal 10².
Answer:
C. 4² +8² ≠ 10²
Step-by-step explanation:
You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.
Pythagorean theoremThe side lengths of a right triangle must satisfy the Pythagorean relation:
a² +b² = c²
These numbers do not:
4² +8² = 16 +64 = 80 ≠ 10² = 100
A right triangle is not formed because ...
4² +8² ≠ 10²
__
Additional comment
The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.
When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.
4:8:10 reduces to 2:4:5 which has an odd sum.
What is Maria’s overtime rate per hour if her regular rate is $10.75 (remember, we use 1.5 when calculating our overtime rate and we round to two decimal places)
Answer:
16.13
Step-by-step explanation:
multiply 10.75 and 1.5 which equals 16.125 so you would round up to 16.13 so your final answer would be $16.13 per hour
How can fossils tell us about Earth's past?
A. Fossils give clues about environmental changes where the organisms lived.
B. Fossils can be used to date the time period of rocks and rock layers when the organisms lived.
C. Fossils can give clues of changes in the organism's body structure over time.
D. All of these are true.
E. None of these are true.