Answer:
B(a) = a/6 - 9
Step-by-step explanation:
The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.
What is the area of a trapezoid?
If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as
= [(a + b)h]/2
Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.
Therefore, 'b' is the parallel side of the base.
The given function that represents the area of the trapezoid is:
A(b) = [12(b + 9)]/2
Let, A(b) = a.
Therefore, a = [12(b + 9)]/2
⇒ 2a = 12(b + 9)
⇒ a = 6(b + 9)
⇒ a = 6b + 54
⇒ 6b = a - 54
⇒ b = (a - 54)/6
⇒ b = a/6 - 9
If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:
B(a) = a/6 - 9
Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
line ED =45
line DF = 27
line EF = 36
sin D =
sin E =
cos D =
cos E =
The value of each term is
sin D = 4/5sin E = 3/5cos D = 3/5cos E = 4/5The length of the line ED = 45 units
The length of the line DF = 27 units
The length of the line EF = 36 units
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
Substitute the value in the equation
sin D = Opposite side / Hypotenuse
= 36/45
= 4/5
sin E = Opposite side / Hypotenuse
= 27/45
= 3/5
cos D = Adjacent side / Hypotenuse
= 27/45
= 3/5
cos E = Adjacent side / Hypotenuse
= 36/45
= 4/5
Hence, the value of each term is
sin D = 4/5sin E = 3/5cos D = 3/5cos E = 4/5Learn more about trigonometric function here
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Ellie bought cookies and cupcakes for $102.44. If she spent $36.44 on cookies
and the cupcakes are $11 per box, how many boxes did she buy?
Answer:
Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars
66/11=6 cupcake boxes
6 cupcake boxes + 1 cookie box = 7 boxes in total
Estimate the value of 96.8×9.74
Answer: Estimate : 1000 Exact : 942.83
Step-by-step explanation:
The estimate is 1000 because 96.8 is rounded to 100 and 9.74 is rounded to 10, so 100 times 10 is 1000. If you wanted the exact, then the exact is 942.83200, If you simplify this total, then the final answer is 942.83.
what is the equation of the line in point slope form that contains the point (-2,5) and has a slope of 1/3?
Have an answer I got already, wanting to check and see if its correct :) thank you in advance
An equation of the line in point-slope form that contains the point (-2, 5) and has a slope of 1/3 is y - 5 = 1/3(x + 2).
What is the point-slope form?In Mathematics, the point-slope form can be defined as a type of equation that is typically used when the slope of a straight line and one of the points on this line is given (known).
Mathematically, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 5 = 1/3(x - (-2))
y - 5 = 1/3(x + 2)
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Write the equation of the line that is perpendicular
to the y-axis and passes through the point (3, 12).
Answer:
[tex]y=12[/tex]
Step-by-step explanation:
The [tex]y[/tex]-axis has equation [tex]x=0[/tex], so the equation of a line perpendicular to the [tex]y[/tex]-axis would be of the form [tex]y=c[/tex].
The equation of this line given the point [tex](3,12)[/tex] is [tex]y=12[/tex].
What is the next fraction in this sequence? Simplify your answer.
9
14
,
4
7
,
1
2
,
3
7
,
Answer:
5/14
Step-by-step explanation:
they subtract 1/14th each time
(You cant simplify)
(8/10)=(9/n)
Solve for n
Answer:
n=90/80
Step-by-step explanation:
you make n the subject of the formular
Solve the equation for all values of x.
2x(x + 7)(x²+49) = 0
Answer:
Step-by-step explanation:
2x(x + 7)(x²+49) = 0
(apply the zero product)
x=0 or x+7 =0 or x² + 49 = 0
x+7 =0
x=-7
x² + 49 = 0
no real solution for this i think
Answer = x=0 or x=-7
William plans on buying the new Callaway Rogue Max ST driver for at least $550 He already has $325 saved and earns $20 each time he details his parents car. Write and solve an inequality to determine the number of times he must detail his parents car to have enough money to buy the golf club.
William needs to detail his parents at least 12 times to buy the golf club.
What is Inequality:An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
The symbols we use in Inequality Expressions are
Not equal ' ≠ '
Greater than ' > '
Less than ' < '
Less than or equal ' ≤ '
Greater than or equal ' ≥'
Here we have
William plans to buy the new Callaway Rogue for at least $ 550
The amount that William saved = $ 325
The amount he earns each time he details his parents = $ 20
Here we don't know how many times he detailed his parents,
So represent it with a variable x
After detailing x times the amount he earned will equal $ 20x
The total amount that William will have = $ 325 + $ 20x
William wants at least $550
Therefore,
The inequality that will represent the above situation is
=> 325 + 20x ≥ 550 ------(1)
Now solve the above inequality to get the value of x
=> 65 + 4x ≥ 110
=> 4x ≥ 45
=> x ≥ 11.25
Here we can say 11.25 times so x = 12 times
Therefore,
William needs to detail his parents at least 12 times to buy the golf club.
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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
The equation 4y = -x is a direct variation and k = - 1 / 4.
The equation 3x = 2y - 7 is neither a direct variation nor a inverse variation.
How to solve direct and inverse equation?Direct variation describes a simple relationship between two variables . We say y varies directly to x when it is represented as follows:
y = kx
where
k = constant of proportionalityTherefore,
4y = - x
divide both sides of the equation by 4
4y / 4 = -x / 4
[tex]y =- \frac{x}{4}[/tex]
Therefore, the equation is direct variation and the value of k is - 1 / 4.
For two quantities with inverse variation, as one quantity increases, the other quantity decreases. Inverse variation is represented as follows:
y = k / x
Therefore, 3x = 2y - 7 is neither an inverse nor a direct variation.
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What are the solutions to the equation 3k² + k-3=0?
Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as
a list of numbers, separated with commas. Example: 3.25,4.16
k=
The answer will be 0.33 using quadratic equation.
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation given 3k² + k -3=0
(3k-1)(k+3)=0
k =1/3
k=0.33
Hence the value of k is 0.33.
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BD = 5, CX = 3, CD = 5
what is BC
Answer:
need more information to answer
Find the side length of x. Round your answer to nearest hundredth
For the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).
As given in the question,
Given right angled triangle,
Base of the triangle is equal to 10 units
Perpendicular side of a triangle is equal to 9 units
Side length 'x' is the hypotenuse of the right angled triangle.
Using Pythagoras theorem we get,
(Hypotenuse)² = ( Base)² + ( Perpendicular side)²
⇒ x² = (10)² + (9)²
⇒ x² = 100 + 81
⇒ x² = 181
⇒ x = √181
⇒ x = 13.4536...
⇒ x = 13.45 units ( nearest hundredth)
Therefore, for the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).
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Please answer this as soon as possible.
The equation of the transformed graph is y = -2|x| + 2
(graph attached)
What is transformation ?Transformation is a term used in mathematics to refer to the movements made by objects.
How to determine the coordinates of H after transformationinformation from the question
equation of the preimage f(x) = |x|
A graph showing the transformed image
The image show a reflection over x axis, the transformation rule for this is
Transformation rule (x, y) → (x, -y)
applying the rule to f(x) = |x| gives -f(x) = -|x|
followed by translation 2 units up, this achieved by Transformation rule
-f(x) → -f(x) + 2
Then a vertical stretch of 2 units, transformation rule for vertical stretch is
-2f(x) → -2|x| + 2
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1. Which graph best represents y = 4* - 1? (1 point)
Answer:
a little confused, but it should just be a horizontal line on -4 because of 4 times negative 1 = -4
Step-by-step explanation:
Value of x in 4,5,x,480
Step-by-step explanation:
you need to give us also some context.
because that sequence can be anything.
but I suspect you mean
4 : 5 = x : 480
0.8 = x / 480
x = 480 × 0.8 = 384
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Length = y
Width = y - 5
Area = 750
The area of a rectangle is written as,
Length x Width = Area
y x (y - 5) = 750
y² - 5y = 750
y² - 5y - 750 = 0
(y + 25)(y – 30) = 0
The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.
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Calculate: (Round your final answers to the nearest cent.) Units Unit Cost Beg. Inventory Jan. 1 20 $ 8.00 May 10 15 $ 11.00 June 30 17 $ 20.00 Dec. 10 12 $ 21.00 24 units not sold LIFO FIFO Weighted-Average Cost of Ending Inventory A C E Cost of Goods Sold B D F
1. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:
LIFO FIFO Weighted-Average
Ending inventory $425 $691 $573
Cost of goods sold $492 $226 $344
How do the inventory methods differ?FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
The weighted-average method uses the average cost of goods to compute the ending inventory and the cost of goods sold.
LIFO:
Ending inventory = $425 ($917 - $492)
Cost of goods sold = $492 (12 x $20 + 12 x $21)
FIFO:
Ending inventory = $691 (9 x $11 + 17 x $20 + 12 x $21)
Cost of goods sold = $226 ($917 - $691)
Weighted Average:
Ending inventory = $573 (40 x $14.33)
Cost of goods sold = $344 (24 x $14.33)
Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 20 $8.00 $160
May 10 Purchases 15 $11.00 $165
June 30 Purchases 17 $20.00 $340
Dec. 10 Purchases 12 $21.00 $252
Total 64 $917
Units sold 24
Ending inventory 40 (64 - 24)
Average cost = $14.33 ($917/64)
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Rapunzel's team participated in a total of 143 wrestling matches. Rapunzel participated in 67 percent of the wrestling matches. What fraction of the wrestling matches did Rapunzel participate in?
Using the percentage, Rapunzel participated in 9581/100 matches.
In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.
Rapunzel's team participated in a total of 143 wrestling matches.
Rapunzel participated in 67 percent of the wrestling matches.
Total matches = 143
Participated in = 67%
Total number of matches in which Rapunzel participated is
= 143*67%
= 143* 67/100
= 9581/100
Rapunzel participated in 9581/100 matches.
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2x+18=4x-14 pls help me - johnny
Answer: x=16
Step-by-step explanation: 18=2x-14
32=2x
x= 16
Select the values that make the inequality
Answer: -4, -1, 1, 3, 3.9, 3.99, 3.999, 4
Step-by-step explanation:
That inequality symbol means less than or equal to. So that includes 4 and any number that precedes it on the number line.
write the equation of the line perpendicular to y= 3/2x + 1/2 that passes through the point (-2,4)
The equation of the line is y = (-2/3)x + 8/3
What is a perpendicular line?
Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular line can be used to graphically depict the condition of perpendicularity. It can be defined between any pair of lines, any pair of planes, or any pair of lines and planes.
The slope-intercept form of a line is written in the form:
y = mx + b
where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept
Here, We have
y= 3/2x + 1/2 that passes through the point (-2,4)
But we do not know the value of b.
We can do this by substituting the point(-2,4), into the equation and we get
y = mx + b
4 = (-2/3)(-2) + b
b = 8/3
Now that you know all your values, rewrite the equation in slope-intercept form:
y = (-2/3)x + 8/3
Hence, the equation of the line is y = (-2/3)x + 8/3
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help please for brianlest???
Answer:
Step-by-step explanation:
domain: 1,2,3,4
Range: 8,6,4,2
D=-2
[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula
The municipal swimming pool in Charlotte, North Carolina has three different ways of paying for individual open swimming. Nick is trying to decide which way to pay.
Early Pay: Pay $110.00 before Memorial Day; swim any number of days
Deposit Plus: $30.00 deposit plus $6.00 per day
Daily Pay: $9.00 per day
Write an equation for each method of payment. Write your equations in slope-intercept form so that x is the number of days and y is the cost.
a. Early Pay:
b. Deposit Plus:
c. Daily Pay:
the answer must be a y=mx+b equation for a b and c
The equations for early pay, deposit plus and daily pay is y = 110, y = 6x + 30 and y = 9x respectively.
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Let y represent the total cost for swimming x numbers of days.
Early Pay: Pay $110.00 before Memorial Day; swim any number of days. Hence:
y = 110
Deposit Plus: $30.00 deposit plus $6.00 per day. Hence:
y = 6x + 30
Daily Pay: $9.00 per day. Hence:
y = 9x
The equation for early pay is y = 110
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What is the value of X?
Answer:
x=28
Step-by-step explanation:
angle b and angle c are the same measure because it is a iso triangle.
you know triangle sum is 180 so 3x+2(x+20)=180. simplify it to 5x=140
divide both sides by 5
x=28
Answer:
x = 28
Step-by-step explanation:
The triangle is isosceles, meaning that the two base angles (x + 20) are congruent. We can then create an equation that states: (x + 20) + (x + 20) + 3x = 180. Simplifying this, we get 5x + 40 = 180. We can then use reverse order of operations to solve it. Subtract 40 from both sides to get 5x = 140. We will then divide both sides by 5 to get x by itself, getting us the equation x = 28.
Graph the linear function w(x)=3/5x+2
The graph of the linear function w(x) = 3/5x + 2 is coordinates or points (0,2), (1,2.6) (2,3.2) (3,3.8)
What is a linear function?
A linear function is a straight line on an x-y coordinate.
Formula
w(x) = 3/5x +2 in each coordinate I have a x so for example 3.
I would rewrite this as 3/5(3) + 2
w(x) = 3/5x +2
w(3) = 3/5(3) + 2
y = 1.8 + 2
y = 3.8
Claire Russell is buying a car. Her November monthly interest was $210 % interest. What is Claire’s principal balance at the beginning of November? Use 360 days. (Use 360 days. Do not round the denominator in your calculation and round your final answer to the nearest dollar.)
The Claire's principal balance at the beginning of November is 32516.
Given that,
Vehicle purchase by Claire Russell. Her interest rate for the month of November was 210 percent at 7 3/4%. Employ 360 days. When calculating, do not round the numerator; instead, round your result to the nearest dollar.
We have to find how much was left on Claire's principal at the start of November.
We know that,
Principal= Interest / time× rate of interest
Here,
Interest is 210
Time is 30/360
Rate of interest is 0.0775
Principal = 210/(30/360)×0.0775
Principal= 210/ 0.00645833
Principal =32516
Therefore, The Claire's principal balance at the beginning of November is 32516.
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Micheal wants to buy an efficient smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Micheal picked out costs $16,100. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 70 months. The equation y= -230x+16,100 represents the amount, Y (in dollars), that Michael owes his father after X months.
A) How much does Michael owe his dad after six months?
B) determine the slope of the line and interpret its meaning in the context of this problem.
1) Micheal owes his father $[ ] after 6 months.
2) The slope is [ ]
3) The amount Michael owes his father [choose one] by $[ ] per month.
The intercept reveals that the first loan amount was $1,560.00.
Every month, Michael's debt to his father drops by 290.
What is an intercept?The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.acc to our question-
The amount Michael owes is given by :
y = - 290x +18,560
x = number of months ; y = amount owed
Amount owed after 3 months :
Put x = 3 in the equation :
y= - 290(3) +18,560
y = - 870 + 18560
y = 17690
According to the general form of a linear equation :
y = mx + c
Where, m = slope ; c = intercept
The slope = - 290 ; Intercept = 18560
Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month
The intercept shows that the original amount borrowed is 18560.
Hence,The intercept reveals that the first loan amount was $1,560.00.
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2x - 5 = 6x + 4
I got 2.25x I think? It's wrong though...
Answer:
x = -2.25
Step-by-step explanation:
To solve this we want to put the x alone on one side
Then by subtracting 6x from both sides
2x - 5 - 6x = 6x + 4 - 6x
- 4x - 5 =4
add 5 for both sides
- 4x - 5 + 5 = 4 + 5
- 4x = 9
Divide both sides by - 4
Then x = 9 / -4 = -2.25
So you only forget the negative sign
Glad to Help
Answer: x= - 9/4 or -2.25
Step-by-step explanation:
2x - 5 = 6x + 4(subtract 4 from the right side to move to the left side and subtract 2x from left side to move to right side)
-4 - 5 = 6x - 2x (now subtract these numbers as they have the same components)
-9 = 4x (divide by 4 to get X alone)
-9/4 = x
Andrea puts 100 g weight on a pan balance how many 10 g weights does she need to balance the scale?
answer:
10
step-by-step explanation:
easy: 100 ÷ 10 = 10. you need 10
explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:
100 = 10x. solve by dividing each side by 10.
10 = x. verify by doing 10 x 10 = 100
