The equation of the parallel line is y = -3/5x + 5
How to determine the line equation?The equation is given as
3x + 5y = 6
The point is also given as
Point = (0, 5)
The equation of a line can be represented as
y = mx + c
Where
Slope = m and c represents the y-intercept
So, we have
3x + 5y = 6
This gives
5y = -3x + 6
Divide
y = -3/5x + 6/5
By comparing the equations y = mx + c and y = -3/5x + 6/5, we have the following
m = -3/5
This means that the slope of y = -3/5x + 6/5 is -3/5
So, we have
m = -3/5
The slopes of parallel lines are equal
This means that the slope of the other line is -3/5
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -3/5
(x₁, y₁) = (0, 5)
So, we have
y = -3/5(x + 0) + 5
Open the brackets and evaluate
y = -3/5x + 5
Hence, the parallel line has an equation of y = -3/5x + 5
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What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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write the vertex form equation of the parabola with, vertex: (10,9), passes through: (12,-7)
Th equation of a parabola in its vertex form is;
y = a(x-h)² + k
(h,k) are the coordinates of the vertex and a is a constant
(h, k) = (10, 9)
substitute the above into the equation
y = a(x- 10)² + 9 -------------------(1)
Next is to find the value of a
substitute x=12 and y= -7 into equation (1)
-7 = a (12 - 10)² + 9
-7 - 9 = 4a
-16 = 4a
a = -4
The equation of the parabola will be formed by substituting a = -4 in equation (1)
y = -4(x - 10)² + 9
what are the coordinates of the focus of the conic section shown below (y+2)^2/16-(x-3)^2/9=1
Given the function of the conic section:
[tex]\mleft(y+2\mright)^2/16-\mleft(x-3\mright)^2/9=1[/tex]This conic section is a hyperbola.
Use this form below to determine the values used to find vertices and asymptotes of the hyperbola:
[tex]\frac{(x-h)^2}{a^2}\text{ - }\frac{(y-k)^2}{b^2}\text{ = }1[/tex]Match the values in this hyperbola to those of the standard form.
The variable h represents the x-offset from the origin b, k represents the y-offset from origin a.
We get,
a = 4
b = 3
k = 3
h = -2
A. The first focus of a hyperbola can be found by adding the distance of the center to a focus or c to h.
But first, let's determine the value of c. We will be using the formula below:
[tex]\sqrt[]{a^2+b^2}[/tex]Let's now determine the value of c.
[tex]\sqrt[]{a^2+b^2}\text{ = }\sqrt[]{4^2+3^2}\text{ = }\sqrt[]{16\text{ + 9}}\text{ = }\sqrt[]{25}[/tex][tex]\text{ c = 5}[/tex]Let's now determine the coordinates of the first foci:
[tex]\text{Coordinates of 1st Foci: (}h\text{ + c, k) = (-2 + 5, 3) = 3,3}[/tex]B. The second focus of a hyperbola can be found by subtracting c from h.
[tex]\text{ Coordinates of 2nd Foci: (h - c, k) = (-2 - 5, 3) = -7,3}[/tex]Therefore, the conic section has two focus and their coordinates are 3,3 and -7,3.
In other forms, the foci of the hyperbola is:
[tex]\text{ }(h\text{ }\pm\text{ }\sqrt[]{a^2+b^2},\text{ k) or (-2 }\pm\text{ 5, 3)}[/tex]Therefore, the answer is letter B.
Answer :It's A lol
Step-by-step explanation:
Find equation of a parallel line and the given points. Write the equation in slope-intercept form Line y=3x+4 point (2,5)
Given the equation:
y = 3x + 4
Given the point:
(x, y ) ==> (2, 5)
Let's find the equation of a line parallel to the given equation and which passes through the point.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Hence, the slope of the given equation is:
m = 3
Parallel lines have equal slopes.
Therefore, the slope of the paralle line is = 3
To find the y-intercept of the parallel line, substitute 3 for m, then input the values of the point for x and y.
We have:
y = mx + b
5 = 3(2) + b
5 = 6 + b
Substitute 6 from both sides:
5 - 6 = 6 - 6 + b
-1 = b
b = -1
Therefore, the y-intercept of the parallel line is -1.
Hence, the equation of the parallel line in slope-intercept form is:
y = 3x - 1
ANSWER:
[tex]y=3x-1[/tex]
Joyce paid $154.00 for an item at the store that was 30 percent off the original price. What was the original price?
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there are 12 questionsI got 7 right what did I make?
there are 12 questions
I got 7 right
the easiest way to solve this is by using a rule of three
Step 1
Let
[tex]12\text{ questiones }\Rightarrow100\text{ percent}[/tex]then
[tex]7\text{ questions }\Rightarrow x\text{ percent}[/tex]Step 2
do the relation and solver for x
[tex]\begin{gathered} \frac{12}{100}=\frac{7}{x} \\ 12\cdot x=100\cdot7 \\ 12\cdot x=700 \\ x=\frac{700}{12} \\ x=58.33 \\ \end{gathered}[/tex]so, you did the 58.33 %
Select all of the expressions approval to c⁶/d⁶:
answers:
(cd-¹)⁶
c¹²d¹⁸/c²d³
c⁸d⁹/c²d³
c⁶d-⁶
c-⁶d⁶
(c‐¹d)-⁶
Answer:
is = c⁸d⁹/c²d³
hope it helps
mark me brainliest
Find two positive numbers whose difference is 14 and whose product is 1976
The positive numbers that the difference is 14 and the product is 1976 are 38 and 52.
How to find the positive numbers?The difference of the positive numbers is 14 and the products of the positive numbers is 1976.
The positive numbers are the numbers that are greater than zero.
Positive numbers includes fractions, In general, positive numbers are natural counting numbers.
Therefore,
let the numbers be x and y
Hence, the difference of the positive numbers is 14.
x - y = 14
The product of the positive numbers is 1976. Therefore,
xy = 1976
Make x the subject of the formula in equation(ii)
x = 1976 / y
Substitute the value of x in equation(i)
1976 / y - y = 14
14y = 1976 - y²
solve the quadratic equation formed.
y² + 14y - 1976 = 0
Hence,
y² - 38y + 52y - 1976
y(y - 38) + 52(y - 38)
(y - 38)(y + 52)
Therefore,
y = 38 and y = -52
The number is positive .
Therefore, we can only use 38.
y = 38
Substitute the value of y in equation(i)
x - 38 = 14
x = 14 + 38
x = 52
Therefore, the positive numbers are 38 and 52.
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Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
For the function f(x) = 6e^x, calculate the following function values:f(-3) = f(-1)=f(0)= f(1)= f(3)=
Consider the given function,
[tex]f(x)=6e^x[/tex]Solve for x=-3 as,
[tex]\begin{gathered} f(-3)=6e^{-3} \\ f(-3)=6(0.049787) \\ f(-3)=0.2987 \end{gathered}[/tex]Thus, the value of f(-3) is 0.2987 approximately.
Solve for x=-1 as,
[tex]\begin{gathered} f(-1)=6e^{-1} \\ f(-1)=6(0.367879) \\ f(-1)=2.2073 \end{gathered}[/tex]Thus, the value of f(-1) is 2.2073 approximately.
Solve for x=0 as,
[tex]\begin{gathered} f(0)=6e^0 \\ f(0)=6(1) \\ f(0)=6 \end{gathered}[/tex]Thus, the value of f(0) is 6 .
Solve for x=1 as,
[tex]\begin{gathered} f(1)=6e^1 \\ f(1)=6(2.71828) \\ f(1)=16.3097 \end{gathered}[/tex]Thus, the value of f(1) is 16.3097 approximately.
Solve for x=3 as,
[tex]\begin{gathered} f(3)=6e^3 \\ f(3)=6(20.0855) \\ f(3)=120.5132 \end{gathered}[/tex]Thus, the value of f(3) is 120.5132 approximately.
Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
Determine if the situation below are biased or unbiased and explain why. Two people from each 8th period class are askedwhat they think the theme of the next dance shouldbe.
Answer
The situation is not biased because it takes a random sample from each group.
34 Sat purchased some art supplies and cord stock in order to make greeting cards. The graphbelow shows the relationship between the number of cards Sat makes and the total cost etthe materials used te make the cardsCost of Noking Greeting CardsTotal Cost(dollars)2 4 6 8 10Number of Cards MadeBased on the graph what will be the total cost of making 25 greeting cards?*2.50G$50.00N $52.50$15.00
step 1
Find the slope
we have the points
(3,4) and (7,6)
m=(6-4)/(7-3)
m=2/4
m=$0.5 per card
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=0.50
b=?
point (3,4)
substitute
4=0.5(3)+b
b=4-1.50
b=2.50
y=0.50x+2.5
so
For x=25 cards
substitute
y=0.50(25)+2.50
y=15.00
answer is the option JIt takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make twoomelets. What is the cost per omelet if eggs cost $.99 per dozen,1 lb of cheese costs $4.29, and 1/2 lb of butter costs $1.25?a. $2.15b. $1.34c. $1.08d. $.31
Given:
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make two
omelets
Eggs cost per dozen = $0.99
So, the cost of 6 eggs = 0.99/2 = 0.495
1 lb of cheese costs $4.29
1 lb = 16 oz
So, the cost of 5 oz =
[tex]\frac{5}{16}\cdot4.29=1.34[/tex]1/2 lb of butter costs $1.25
So, the cost of 2 oz =
[tex]\frac{2}{8}\cdot1.25=0.3125[/tex]So, the cost of two omelets = 0.495+1.34+0.3125 = 2.1475
So, the cost of one omelet = 2.1475/2 ≈ 1.08
So, the answer will be option c. $1.08
Use the standard algorithm to solve the equation 36 x 25 =
Answer: 900
Step-by-step explanation:
Column method
Frank uses 27/5 tablespoons of pista extract to make 9 servings of a recipe. How many tablespoons of pista extract does each serving need?
Answer: 3/5 tablespoons.
if I may ask may you help me solve this
Explanation
In the image,
[tex]QT=18[/tex]We can see that line SQ is a perpendicular line that serves as the bisector of RT
This implies that;
[tex]RQ=QT=18[/tex]Since;
[tex]\begin{gathered} RQ+QT=RT \\ 18+18=RT \\ RT=36 \end{gathered}[/tex]Answer: 36
I have answer for the question it in the image but I don't know if it right and I don't know any other formulas to find the area of a triangle
Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.
Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.
Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:
Another formula that can be used is Heron's formula;
Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:
[tex]S=\sqrt{\rho\cdot(\rho-a)\cdot(\rho-b)\cdot(\rho-c)}[/tex]Where
[tex]\rho=\dfrac{a+b+c}{2}[/tex]is the semiperimeter of the triangle.
This is the answer we've been looking for.
The width of a rectangle measures (5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The most appropriate choice for perimeter of rectangle will be given by -
Perimeter of rectangle = (22v + 14w) cm
What is perimeter of rectangle?
At first it is important to know about rectangle.
Rectangle is a parallelogram in which every angle of the parallelogram is 90°.
Perimeter of rectangle is the length of the boundary of the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by
Perimeter of rectangle = [tex]2(l + b)[/tex]
Length of rectangle = (5v - w) cm
Breadth of rectangle = (6v + 8w) cm
Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]
= 2(11v + 7w)
= (22v + 14w) cm
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Complete Question
The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Draw the image of the figure under thegiven transformation.8. reflection across the y-axis
Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)
.
The coodinates of A(3,0) and after reflection A'(-3,0)
The coordinates B(1,4) and after reflection B'(-1,0)
The coordinates C(5,3) and after reflection C'(-5,3)
Plot the image on the graph
Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
2/4 turn into decimal
Answer:
The decimal form of 2/4 is;
[tex]0.5[/tex]Explanation:
We want to turn the fraction to decimal.
[tex]\frac{2}{4}=0.5[/tex]it can be obtained by;
Therefore, the decimal form of 2/4 is;
[tex]0.5[/tex]Consider the function f(x) = 6 - 7x ^ 2 on the interval [- 6, 7] Find the average or mean slope of the function on this interval , (7)-f(-6) 7-(-6) = boxed |
Answer:
• Mean Slope = -7
,• c=0.5
Explanation:
Given the function:
[tex]f\mleft(x\mright)=6-7x^2[/tex]Part A
We want to find the mean slope on the interval [-6, 7].
First, evaluate f(7) and f(-6):
[tex]\begin{gathered} f(7)=6-7(7^2)=6-7(49)=6-343=-337 \\ f(-6)=6-7(-6)^2=6-7(36)=6-252=-246 \end{gathered}[/tex]Next, substitute these values into the formula for the mean slope.
[tex]\begin{gathered} \text{ Mean Slope}=\frac{f(7)-f(-6)}{7-(-6)}=\frac{-337-(-246)}{7+6}=\frac{-337+246}{13} \\ =-\frac{91}{13} \\ =-7 \end{gathered}[/tex]The mean slope of the function over the interval [-6,7] is -7.
Part B
Given the function, f(x):
[tex]f\mleft(x\mright)=6-7x^2[/tex]Its derivative, f'(x) will be:
[tex]f^{\prime}(x)=-14x[/tex]Replace c for x:
[tex]f^{\prime}(c)=-14c[/tex]Equate f'(c) to the mean slope obtained in part a.
[tex]-14c=-7[/tex]Solve for c:
[tex]\begin{gathered} \frac{-14c}{-14}=\frac{-7}{-14} \\ c=0.5 \end{gathered}[/tex]The value of c that satisfies the mean value theorem is 0.5.
Compute the square root of 532 to the nearest tenth. Use the "divideand average method.
ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]We calculate by means of the divide and average method.
The first thing is to look for exact roots between those two values
Step 1 estimate
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the equation(-3, -5); y = -5x+2
The equation is y = -5x-20.
GIven:
The equation is, y = -5x + 2.
A point on the line is (-3, 5).
The objective is to write an equation that passes throught the point and parallel to the given equation.
For parallel lines the product of slope values will be equal.
From the given equation, consider the slope of the equation as, m1 = -5.
Then, the slope of the parallel line will also be, m2 = -5.
Then, the equation of parallel line can be written as,
[tex]\begin{gathered} y=m_2x+b \\ y=-5x+b \end{gathered}[/tex]Here b represents the y intercept of the parellel line.
To find the value of b, substitute the given points in the above equation.
[tex]\begin{gathered} -5=-5(-3)+b \\ -5=15+b \\ b=-5-15 \\ b=-20 \end{gathered}[/tex]Now, substitute the value of b in the equation of parellel line.
[tex]y=-5x-20[/tex]Hence, the equation of parellel line is y = -5x-20.
Graph the exponential function.f(x)=4(5/4)^xPlot five points on the graph of the function,
We are required to graph the exponential function:
[tex]f(x)=4(\frac{5}{4})^x[/tex]First, we determine the five points which we plot on the graph.
[tex]\begin{gathered} \text{When x=-1, }f(-1)=4(\frac{5}{4})^{-1}=3.2\text{ }\implies(-1,3.2) \\ \text{When x=0, }f(0)=4(\frac{5}{4})^0=4\text{ }\implies(0,4) \\ \text{When x=1, }f(1)=4(\frac{5}{4})^1=5\implies(1,5) \\ \text{When x=2, }f(2)=4(\frac{5}{4})^2=6.25\implies(2,6.25) \\ \text{When x=3, }f(3)=4(\frac{5}{4})^3=7.8125\text{ }\implies(3,7.8125) \end{gathered}[/tex]Next, we plot the points on the graph.
This is the graph of the given exponential function.
Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
The following hyperbola has a horizontal transverse axis: (x + 2) (w+7)=11617
for the given hyperbola
[tex]\frac{(x+2)^2}{16}-\frac{(y+7)^2}{17}=1[/tex]We have the following graph. Visually we can see that this hyperbola does have a transverse axis, however you can do all the calculations to check it
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ h=-2 \\ k=-7 \\ a^2=16 \\ b^2=17 \\ c^2=16+17 \\ c=\sqrt[]{33}=5.7 \\ f_1=(h-c,k) \\ f_1=(-2-5.7,-7) \\ f_2=(-7.7,-7) \\ f_2=(3.7,-7) \\ y=-7\to\text{ is the ecuation of the transversal axis} \end{gathered}[/tex]As we can see y = -7 is a line parallel to the x axis, turning the transversal axis horizontal.
That is, this hyperbola does have a horizontal transverse axis and the answer is TRUE
complete the square to writey= x2 + 4x +9 in graphing form.
In order to express y = x² + 4x +9 in graphing form and graphing it we can follow these steps:
1. complete squares to express the equation in the form y = (x - p)² + q
We have to add and subtract (b/2)² on the right, where b is the coefficient of the second term of the equation
y = x² + 4x +9 + (4/2)² - (4/2)²
y = x² + 4x +9 + (2)² - (2)²
We can gorup and factor some terms of the equation by applying the following formula:
(x + a)² = x² + 2ax + a²
then by writing 4x as 2×2x we get:
y = x² + 2×2x + (2)² - (2)² +9
y = (x + 2)² - (2)² + 9
y = (x + 2)² - 4 + 9
y = (x + 2)² + 5
For an equation of the form y = (x - p)² + q, the vertex is (q, p), then, the vertex of the parabola is (-2, 5)
2. Determine the x-intercepts by replacing 0 for y and solving for x, like this:
0 = (x + 2)² + 5
0 - 5 = (x + 2)² + 5 - 5
-5 = (x + 2)²
±√-5 = √(x + 2)²
±√-5 = x + 2
x = -2 ± √-5
As you can see, on the right side the argument of the square root is a negative number, which makes the solution of this equation a complex number, then which means that the parabola won't intercept the x-axis.
3. Find the y-intercept by replacing 0 for x:
y = (0 + 2)² + 5
y = (2)² + 5
y = 4 + 5
y = 9
Then, the y-intercept of this parabola is (0, 9)
By graphing the vertex (-2, 5) and the y-intercept (0, 9) and joining them with the parabola we get the following graph:
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
True.
Since it is strictly greater
