Answer: Sales Price = ($17,000 * 20%) + $17,000 = $20,400
9
LBCA and LACD form a linear pair. LBCA is
represented by (2x - 5)° and LACD is
represented by (3x + 10)°.
What is the mLACD?
A. 35°
B. 61°
C. 65°
D. 115°
Answer:
D
Step-by-step explanation:
[tex]m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}[/tex]
How many square feet of tiles do you need to purchase to cover the floor of a 10.5 foot by 8.5 foot bathroom
You would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
To determine the number of square feet of tiles needed to cover a 10.5-foot by 8.5-foot bathroom floor, we can use the formula for the area of a rectangle, L × W
As per the question, the length of the floor is 10.5 feet and the width is 8.5 feet, so the total area of the floor is 10.5 feet × 8.5 feet = 89.25 square feet.
Therefore, you would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
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The median monthly rent in 2000 was $602 and $651 in 2003. What was the percent increase in the median monthly rent prices from 2000 to 2003? Round to the nearest tenth of a percent.
Answer:9.8
Step-by-step explanation:
An airplane was flying at an altitude of 11,200 feet above sea level. The airplane then increased its altitude by 10,150 feet. The airplane will land at an airport that is located at sea level. What change in altitude must the airplane make in order to land?
With the application of Arithmetic operators altitude must the airplane make in order to land is 21350 feets.
What is Arithmetic operators ?
By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions ADD, SUBTRACT, DIVIDE, and MULTIPLY additionally allow for the specification of arithmetic operations.
solution:
An airplane was flying at an altitude above the sea level is 11,200 feet
The airplane then increased its altitude by 10,150 feet.
By adding both the altitude 11,200 + 10,150 = 21350 feets
Therefore, altitude must the airplane make in order to land is 21350 feets
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Kim bought a new car for $28,000. She paid a 20% down payment and financed the remaining balance for 48 months with an APR of 4.3%. Assuming she made monthly payments, determine the total cost of Kim's car. Round your answer to the nearest cent, if necessary.
The total cost of kim's car is $30,021.61
What is total ?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.
20% of the car price
= (20 * 28,000 ) / 100
= $5600
She paid $5600 as down payment for new car
Financed remaining for 48 months = 4 years
APR = 4.3%
Loan amount = 28000 - 5600
= 22400
Monthly payment = [tex]\frac{P * R * (1+R)^{n} }{(1+R)^{n} - 1}[/tex]
Rate of interest = (R/12)/100
For 4.3 % R will be = 0.00358333
Monthly payment is = $508.78
So the total interest paid will be = $ 2021.61
Total cost of the car = cost price + interest
= 28000 + 2021.61
= 30021.61
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Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing. How much material remains for the blanket?
The remaining material for sewing is 5/2 material.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing.
1/6 of 3 = 3x1/6 = 1/2
The remaining material = 3-1/2
= 5/2
Hence, The remaining material for sewing is 5/2 material.
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find the length and the slope of each side of the triangle below. then, find the coordinates of the midpoint of each side. when the slope is undefined, write undefined in the response box.
The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2
how to determine the length and slope of the side of a triangle?suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).
slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)
according to trigonometric ratio, tanα = opposite side/base = x/y
tanα is the slope of hypotenuse.
the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.
the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.
When does a slope is defined?As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.
hence, the triangle is right-angled, and the biggest side has a slope only.
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U V||R T{. Find ST
ST=
Submit
Using the congruence angel theorem, the value of ST is 38.
In the given question given that, UV||RT.
We have to find the value of ST.
Given: UV||RT
Prove: Value of ST.
From the given diagram we can see that;
UT = 19
VS = 39
RS = 26
Using the Congruence Triangle Theorem;
∆USV≈∆TSR
So using the theorem;
US/VS = ST/RS………………(1)
From the given diagram we can see that
US = UT+ST
US = 19+ST
Now putting the value to the condition 1
(19+ST)/39 = ST/26
Simplifying
26(19+ST) = 39ST
494+26ST = 39ST
Subtract 26TS on both side, we get
13ST = 494
Divide by 13 on both side, we get;
ST = 38
Hence, the value of ST is 38.
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Consider the following graph:
What is the slope/rate of change between the inputs of 0 and 4? _______.
What is the slope/rate of change between the domain values of 4 and 8? ______.
Is the slope/rate of change constant (not changing/the same)? ______.
Is the function linear? _______.
The solution is
a) The slope/rate of change between the inputs in m = -1/2
b) Slope/rate of change between the domain values of 4 and 8 is m = -1/2
c) The slope/rate of change is constant
d) The function is a linear function
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be = A
Now , the value of A is
a)
when the inputs are 0 and 4 , the values of x = 0 and x = 4
So , the values of y = 5 and y = 3 respectively
Let the first point be P = P ( 0 , 5 )
Let the second point be Q = Q ( 4 , 3 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 5 ) / ( 4 - 0 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
b)
when the domain values are 4 and 8 , the values of x = 4 and x = 8
So , the values of y = 3 and y = 1 respectively
Let the first point be Q = Q ( 4 , 3 )
Let the second point be R = R ( 8 , 1 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 1 - 3 ) / ( 8 - 4 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
c)
The slope of the line m = -1/2 and it is constant
d)
The function is a linear function and the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = -1/2 ( x - 0 )
On simplifying the equation , we get
y - 5 = -1/2 ( x )
Adding 5 on both sides of the equation , we get
y = ( -1/2 )x + 5
Therefore , the equation of line is y = ( -1/2 )x + 5 and it is linear
Hence , the equation of line is y = ( -1/2 )x + 5 and it is linear where the slope of the line is m = -1/2
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what is the value of X in the figure below?
Answer:
x = 35
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
(x + 110)° is an exterior angle of the triangle , then
x + 35 + x + 40 = x + 110
2x + 75 = x + 110 ( subtract x from both sides )
x + 75 = 110 ( subtract 75 from both sides )
x = 35
Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 140 square meters.
The dimensions of the field are 17 meters and 8.5 meters.
What is dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.
Given:
Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank.
Since,
Area of rectangle = A = l x w ..(1)
where l = length and w = width
Perimeter = 2w + l
34 = 2w + l
l = 34 - 2w ..(2)
Plug this value in equation (1).
A = (34 - 2w) x w
140 = 34w - 2w^2
2w^2 - 34w + 140 = 0
The dimension w can be found as follows;
w = - b / 2a
Here a = 2, b = -34
⇒ w = -(-34)/2(2) = 34/4 = 8.5
Hence, the width is 8.5 meters.
Now to find the length.
Plug w = 8.5 in equation (2)
l = 34 - 2(8.5)
l = 34 - 17
l = 17
Hence, the dimensions of the field are 17 meters and 8.5 meters.
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Complete question:
Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 140 square meters.
List each set of possible dimensions (length and width) of the field.
5 Bob is 5 years younger than twice Mark's age. Bob is 31. How old is Mark?
Answer:
57 years old
Step-by-step explanation:
Bob=31
Mark= 31 x 2 - 5
31 x 2= 62
62- 5 = 57
Mark is 57 years old
Answer:
Mark is 18
Step-by-step explanation:
How to solve-2–(-12)
Answer:
10
Step-by-step explanation:
[tex]-2-(-12)\\=-2+12\\=12-2 \\=10[/tex]
It says to find the surface area of the figure and to round to nearest hundredth. confused..
The sphere is a geometric body generated by turning a semicircle around its diameter ?
The theory tells us that the sphere is a three-dimensional body that arises by rotating a semicircle around its diameter.
¿What is the sphere?The sphere has been a three-dimensional body. The main characteristics of this body are:
All the points that make up the surface of the sphere are at the same distance from a particular point known as the center. It is a geometric field that arises when a semicircle rotates around its own diameter.In the attached image let's see an example of a sphere.
¡Hope this helped!
100 POINTS PLEASE HELP Supply curves shift to the left when a product is more expensive to create. All of the following are examples of scenarios that would cause this EXCEPT:
A. higher materials cost
B. higher minimum wage for employees
C. higher demand from customers
Answer:
C. Higher Demand from customers
Step-by-step explanation:
Higher Materials cost leads to higher production cost
Higher minimum wage leads to higher production cost
The demand for the final product does not increase the production cost of the products
Answer: C. Higher Demand from customers
Step-by-step explanation:
Eight minus a number is less than or equal to seventeen.
Find the measure of the arc or angle indicated.
The measure of arc DA is 104°.
What is inscribed angle?
In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.
We have to find the measure of arc DA.
In the given diagram the angle DBA is the inscribed angle.
Since, the measure of arc formed by inscribed angle is twice the measure of inscribed angle.
Here, m ∠DBA = 52°
Hence,
measure of arc DA = 2 (m ∠DBA)
= 2(52°)
measure of arc DA = 104°
Hence, the measure of arc DA is 104°.
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Find the missing angles
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 3(1.09)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)
The solution is
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is given by
f ( a ) = 3 ( 1.09 )ᵃ
A)
To find the domain of the function f ( a )
The length of the fish was approximately 5.98 cm
So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,
And , f ( a ) = 5.98 cm
So , 5.98 = 3 ( 1.09 )ᵃ
Solving for a , we get
Divide by 3 on both sides of the equation , we get
1.9933 = ( 1.09 )ᵃ
a = 8
So , the value of a is 8
So , the domain of the function is [ 0 , 8 ]
B)
The y-intercept of the graph is given by substituting the value of a = 0,
So , f ( a ) = 3 ( 1.09 )ᵃ
when a = 0 , we get
f ( 0 ) = 3 ( 1.09 )⁰
f ( 0 ) = 3 cm
Therefore, the value of f ( 0 ) = 3 cm
C)
The average rate of change from m =2 to m = 8 is given by the equation ,
when m = 2 ,
f ( a ) = 3 ( 1.09 )ᵃ
f ( 2 ) = 3 ( 1.09 )²
f ( 2 ) = 3 x 1.1881²
f ( 2 ) = 3.5643
And , when a = 8
f ( a ) = 3 ( 1.09 )ᵃ
f ( 8 ) = 3 ( 1.09 )⁸
f ( 8 ) = 3 x 1.99256
f ( 8 ) = 5.97768
So , the average rate of change is the slope of the graph
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )
Slope = ( 5.97768 - 3.5643 ) / 6
Slope = 2.4133879 / 6
Slope = 0.40223 cm per month
Therefore ,
The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month
Hence ,
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
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How can you use rates to determine weather a situation is proportional relationship?
Answer: If the rate is constant, then the situation is a proportional relationship. If the rate is not constant, then the situation cannot be a proportional relationship.
3. Pozfrescims nepibricoms
a) $5 x+8 ≤2-3 x
The value of x for the given inequality is always greater than and equal to -3/4.
In the given question we have to find the value of x.
The given inequality is 5x+8 ≤2-3x.
Now solving the given inequality.
To solve the inequality we firstly subtract 2 on both side, Then we equate the coefficient and variable in one side.
5x+8 ≤2-3x
Subtract 2 on both side, we get
5x+6≤-3x
Now subtract 5x on both side, we get
6≤-8x
Now divide by -8 on bot side, we get;
x≤-6/8
x≤-3/4
We change the inequality because the sign is changed.
Hence, the value of x for the given inequality is always greater than and equal to -3/4.
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Could someone help me answer this multiple-answer question? I'm stuck
Answer:
x = 2
<1 = 28
Step-by-step explanation:
The two angles equal each other.
4x + 20 = 5x + 18 Subtract 4x from both sides
20 = x + 18 Subtract 18 from both sides
2 = x
4x + 20
4(2) + 20
8 + 20
28
3(6x-4y)-5. Help i do not know how to do this it’s very confusing I need help
Answer:
3(6x-4y) -5 18x-12y-5MAY BE IT'S HELP UHHH=^._.^
Answer:
The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.
Step-by-step explanation:
To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.
In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.
Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.
Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.
a pineapple which was bought for $1.00 was sold at $1.30. calculate the profit percent
Answer:
The profit percent is 30%.
Step-by-step explanation:
Answer: 30%
Step-by-step explanation:
Your profit is $0.30 so you have to calculate what percent 30 is of 100 (I converted both numbers to cents) and you would get 30%
SIMPLIFY 2X+3Y^2(X-Y^2)
The required simplified expression is 2x + 3xy² - 3y⁴ which is determined by using the distributive property.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:2x + 3y²(x - y²)
We have to simplify the given expression.
As per the question, we have
⇒ 2x + 3y²(x - y²)
Apply the distributive property of multiplication
⇒ 2x + 3xy² - 3y⁴
Therefore, the simplified expression is 2x + 3xy² - 3y⁴.
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Triangle KLM is formed by connecting the midpoints of the side of triangle HIJ.
The lengths of the sides of triangle KLM are shown. What is the length of HJ?
Figures not necessarily drawn to scale.
Applying the triangle midsegment theorem, the length of HJ is: 8 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that when a line connects the midpoints of two sides of a triangle, it is parallel to the third side and also has a length that is half of the length of the third side.
In the image attached below, segment LK is a midsegment of the triangle which is parallel to a third side, segment HJ.
Therefore:
LK = 1/2(HJ) [triangle midsegment theorem]
Substitute
4 = 1/2(HJ)
Multiply both sides by 2
4 × 2 = 1/2(HJ) × 2
8 = HJ
Length of HJ = 8 units.
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What is the value of X
Answer:
x = 2
Step-by-step explanation:
Let's find our third angle:
60 + 60 + A = 180
A = 60
Because all of our angles are the same, the triangle must be equilateral, meaning all of the sides are the same length as well!
(Pick any two sides):
2x + 3 = 4x - 5
(add 5 to both sides):
2x + 8 = 4x
(Subtract 2x from both sides):
2x = 4
(divide both sides by two):
x = 2!
Simplify 5i/3-5i. Show your work for full credit.
Answer:15i-25/34
Step-by-step explanation:
You have to multiply by 3+5i to get rid of the i on the bottom since you can't have it.
5i/3-5i x 3+5i/3+5i
MATHEMATICAL CONNECTIONS In Exercises 23 and 24,
use the given information to write and solve a system of
linear equations to find the values of x and y.
23. LMN = PQR, L = 40°, M = 90°,
P = (17x − y)°, R = (2x + 4y)º
The value of x and y are 3 and 11.
What is the congruent triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Given that,
△LMN = △PQR
Thus ∠L = ∠P, ∠M = ∠Q, and ∠N = ∠R.
Also, ∠L = 40°, ∠M = 90°, ∠P = (17x − y)°, ∠R = (2x + 4y)°.
The sum of interior angles of a triangle is 180°.
∠L + ∠M + ∠N = 180°
40° + 90° + ∠N = 180°
∠N = 50°.
Therefore,
17x − y = 40 .....(i)
2x + 4y = 50 .....(ii)
Multiply equation (i) with 4 and add with equation (ii)
68x - 4y = 160
2x + 4y = 50
_________
70x = 210
x = 210/70
x = 3
Putting x = 3 in equation (ii)
6 + 4y = 50
4y = 44
y = 11
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