Part A) If the original price of the model car was $40, and it was sold on the third day, with a daily discount of 5%, the sales amount is $34.30.
Part B) The percentage discount from the original price is 14%.
Calculating the percentage discount:The percentage discount is the total discount divided by the original price multiplied by 100.
In this instance, we compute the total discount as $5.70, then express this value as a numerator with $40 as the denominator. The quotient is multiplied by 100.
Original price of the model car = $40
Daily discount = 5%
The date the car sells = the third day
The sales price on the third day = $34.30 ($40 x 95% x 95% x 95%)
Total discounts = $5.70 ($40 - $34.30)
Percentage discount for three days =14.25% ($5.70/$40 x 100)
= 14%
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What is the equation of the line that passes through the points − 2 1 and 4/5 in the Cartesian coordinate plane?
The equation of the line that passes through the points (2, 1 ) and (4,5) in the Cartesian coordinate plane is y = (2/3)(x - 4) + 5.
By subtracting the y coordinates [5 - 1] = 4, we get
Subtract the x coordinates in the same order [4 - (-2)] = [4 + 2] = 6
The slope is given by y-coordinate/x-coordinate = 4/6 = 2/3.
Now, just choose one point say (4,5), and substitute the coordinates in this formula-
y - [y-coordinate of our point] - (slope)* [ x - ( the x-coordinate of our point)]
y - 5 = (2/3)(x - 4) ...........(adding 5 to both sides)
y = (2/3)(x - 4) + 5
Hence, the equation of the line in the "slope-intercept" form is y = (2/3)(x - 4) + 5.
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The complete question is -
what is the equation of the line that passes through the points (-2,1) and (4,5) in the cartesian coordinate plane?
The circumference of a circular garden is 84 feet. What is the diameter of the garden
Round your answer to the nearest hundredth.
Diameter is 25.46 feet as circumference is 2πr and 2r is d so we just simply divide the circumference with π and get the value as 25.46
Step-by-step explanation:
Answer:
26.727feet
Step-by-step explanation:
Circumference = 22 x diameter
7
7x 84= 22d
d= 588
22
= 26.727feet
What is the y-coordinate of the solution to the following system of equations?
y=2x + 1
x+y = 1
Answer : y coordinate is 1
y = 2x + 1
x + y = 1
solve for y : x + y = 1
-x -x
y = -x + 1
Graph them,
(0,1) (x,y) y value is 1
What does it mean to dilate a rectangle?
To dilate a rectangle means to either expand or contract the size of rectangle without changing it's shape .
Dilation is where the polygon grows or shrinks but keeps the same overall shape.
To dilate a rectangle means to either expanding or contracting the rectangle without changing it's shape .
For example: Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.
Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)
To dilate this rectangle by factor 3 , then every coordinate point of the original triangle will multiplied by the scale factor
Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4, -4)
Therefore, When we dilate a rectangle by scale factor 2 ,
The rectangle has enlarge it's size .
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show that -5(3m-7) and -15+35 are equivalent
Answer:
they are equivalent when m = 1
Step-by-step explanation:
-5(3m-7) = -15+35
-5(3m-7) = 20
-15m+35 = 20
-15m+35 = 20
-15m = -15
m = 1
Does dilation change the position?
Yes , Dilation do changes the position
Dilation is the process of changing the size or shape of an object. With the aid of the specified scale factor, it is a transformation that makes the objects smaller or larger.
The pre-image is the original figure before dilation, while the new figure is referred to as the image.
Dilation can be of two types:
Expansion - When the size of an object is increased.Contraction - When the size of an object is decreased.Dilation does not change the shape of the object from preimage to image only size and position are changed.
The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or shrunk but the proportion of each dimension of the shape and the angles remain the same.
Hence , It is true that dilation changes the position
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When θ = 28° , which equation can be used to find the distance from point a to point b?
The equation used to represent the distance between two points A and B is AB = x Cos 28°
The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.
As per the given question,
A and B are the points in a triangleΘ = 28Let the hypotenuse be x
The two points A and B are on the base of the triangle so,
Base - length = AB
The distance between the two points is
⇒ cos Θ = base / hypotenuse
where, base = AB
hypotenuse = x
⇒ cos Θ = AB / x
⇒ AB = x cos Θ → 1
Substitute Θ = 28 in 1,
⇒ AB = x cos 28°
Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.
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The complete question is
When θ = 28° , which equation can be used to find the distance from point a to point b?
how many small cube with side length of 6 cm are needed to completely fill a larger cube with side lengths of 30 cm
Answer:
1,728 small cubes are needed to completely fill a larger cube with side lengths of 30 cm.
Step-by-step explanation:
I need to find the measure of the arc or angle indicated and assume that the lines that appear to be tangent are tangent
By using tangent chord angle formula, the measure of angle FGH is 50°.
What is tangent chord angle?
The angle formed by the chord in the alternate segment is equal to the angle formed by the tangent through the point of contact of the tangent for any circle, according to the theorem.
Another name for the tangent-chord theorem is the alternate segment theorem.
We have to find the m ∠FGH.
Since, by tangent - chord angle theorem, the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle.
GH = 2(m ∠FGH)⇒ m ∠FGH = 1/2(GH)
Here GH = 100° ⇒ m ∠FGH = 1/2(100°) m ∠FGH = 50°
Hence, by using tangent chord angle formula, the measure of angle FGH is 50°.
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Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes three times as long as Meredith to edit a textbook. Together, it takes them 15 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
hours
How long does it take Meredith to edit a textbook if she works alone?
The number of hours taken by Meredith to edit a textbook if she works alone is 20 hours and time taken by Phil alone to edit text book is 60 hours..
Given that, Phil and Meredith work for a book publisher editing mathematics textbooks.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let the time taken by Meredith be x.
Phil has less experience and takes three times as long as Meredith to edit a textbook.
So, time taken by Phil be 3x.
Now, 1/x +1/3x =1/15
⇒ (3+1)/3x =1/15
⇒ 4/3x =1/15
⇒ 4/x =1/5
⇒ x=20 hours
So, time taken by Phil =3x =60 hours
Therefore, the number of hours are 60 hours.
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the serving size for the granola that ted likes to eat for breakfast is 3/4 cup. how many servings are there in a box that holds 13 cups? (what operation should be used here? solve the problem.)
With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.
Given that:
Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.
We need to know how many servings of 3/4 cup can be obtained from 13 cups.
now we need to divide 13 by 3/4
=13 ÷ 3/4
= 13 × 4/3
= 52/3
= 17[tex]\frac{1}{3}[/tex]
With one third of a serving remaining, there are 17 servings total.
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lesson practice what is the approximate volume of this cylinder? what is the closest to the volume of a bowling ball with a diameter of 21.8 centimeters?
volume of ball = 5421.85[tex]cm^{3}[/tex]
Volume of a Sphere
A sphere is a set of points in space that are a given distance r from the center.
The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units( in3,ft3,cm3,m3 , et cetera). Be sure that all of the measurements are in the same unit before computing the volume.
The volume V of a sphere is four-thirds times pi times the radius cubed.
V=4/3πr^3
The volume of a hemisphere is one-half the volume of the related sphere.
Given that
diameter of ball = 21.8 cm
now we need to find the volume of ball
volume of the sphere =[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
diameter = 21.8cm
radius = diameter/2
= 21.8/2
=10.9
now substitute the value of radius in the volume formula
volume of ball =[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex](10.9)^{3}[/tex]
volume of ball = 5421.85[tex]cm^{3}[/tex]
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Select all the statements that are true of the relation.
Answer: A C and D
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling pizza slices and sodas. Each pizza slice sells for $2.50 and each soda sells for $1.25. At the end of the night you made a total of $696.25. You sold a total of 384 pizza slices and sodas combined. You must report the number of pizza slices sold and the number of sodas sold. What equations did you use to solve this where P = the number of pizza slices sold and S = the number of sodas sold?
Gabriel's salary is £24500.
Next year he is due to get a 9% increase.
What will his new salary be?
Answer:
26,705
Step-by-step explanation:
First find 9% of 24500
24500 x 0.09 = 2205
Second add 2205 + 24500
2205 + 24500 = 26,705
8th grade math help plsssss
members of the fitness club hosted a benefit. They charged $4 for adults and $3 for students. if they earned a total $435 and 120 people attended, how many students were there?
Answer:
101.25
Step-by-step explanation:
To find the number of students, we need to first determine the total amount earned from the students. We can do this by multiplying the number of people by the cost per student: $3/student * 120 people = $<<3*120=360>>360.
Since the total amount earned was $435 and we know that $360 of that came from students, we can find the number of students by subtracting the total earned from students from the total amount earned: $435 total - $360 from students = $75 from adults.
Since the cost per adult was $4, we can divide the total amount earned from adults by the cost per adult to find the number of adults: $75 / $4/adult = <<75/4=18.75>>18.75 adults.
Since there were 120 people in total and 18.75 of them were adults, there must have been 120 people - 18.75 people = <<120-18.75=101.25>>101.25 students
50x=10 please help!!!
Answer:
[tex]\boxed{\boxed{\tt x=\frac{1}{5}}\: \bf Or\:\boxed{\tt x=0.2}}[/tex]
Step-by-step explanation:
[tex]\tt 50x=10[/tex]
Divide both sides by 50:-
[tex]\tt \cfrac{50x}{50}=\cfrac{10}{50}[/tex]
Simplify:-
[tex]\tt x=\cfrac{1}{5}[/tex]
_____________________
Hope this helps!
Have a great day!
Find the equation of a line that passes through the point (0,5) and has a gradient of 3. Leave your answer in the form y = m x + c.
The equation of a line with point (0,5) and gradient 3 in the form of y = mx + c is y = 3x + 5.
The point slope form of the equation to be used for finding the equation is -
y - [tex] y_{1}[/tex] = m (x - [tex] x_{1}[/tex] )
As per the mentioned information, m or slope is 3, [tex] y_{1}[/tex] is 5 and [tex] x_{1}[/tex] is 0. Keep the values in point slope form to find the equation.
y - 5 = 3 (x - 0)
Performing multiplication on Right Hand Side
y - 5 = 3x - 0
Shifting 5 to Right Hand Side
y = 3x + 5
Thus, the answer is y = 3x + 5.
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What is the end behavior of the graph of the polynomial function y 7x12 3x8 9x4?
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
Given,
The polynomial function; y = 7x12 – 3x8 – 9x4
We have to find the nd behavior of the graph of the polynomial function;
End behavior of polynomial function;
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ), the end behavior of a function represents the trend of the graph.
Here,
We examine the polynomial's degree and the sign of the coefficient of the variable with the highest exponent to determine the graph's final behavior.
The degree is even 12.The coefficient, 7, is a positive number.That is,
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
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help.
Find the area of the figure.
the area of the triangle is 7.5
which figure has rotational symmetry and line symmetry?
Answer:
Figure 1 (The Star)
Step-by-step explanation:
Line symmetry is symmetry created by a line that divides a shape. Only the "star" (Figure 1) and the "A" (Figure 2) can be split through the center into two identical halves, therefore we can rule out Figures 3 & 4. Rotational symmetry is when a shape looks the same after a partial turn. Rotational symmetry is only true for the "star" (Figure 1) which will be symmetric every 72-degree (360/5) turn. However, the "A" (Figure 2) can only be flipped 180 degrees to remain symmetric.
Therefore Figure 1 is the only figure with both rotational and line symmetry.
Kyle buys a mobile phone that weighs 310 g to 2 significant figures.
He puts the phone inside a protective case that weighs 15.6 g to 1 decimal
place.
Work out the smallest possible total weight, in grams (g), of the phone and
case combined.
Answer:
325.6g
Step-by-step explanation:
weight of phone + weight of case
= 310 + 15.6
= 325.6g
mark as brainliest pls
I need help can someone help pls?
Answer: B
Step-by-step explanation:
3times a number is 4 less than the square of that number find the negative solution
Answer: the answer is -1
create a birthday polynomial with 10-12-2247
The birthday polynomial with 10-12-2247 is given as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
How to create a birthday polynomial?A birthday polynomial is created attributing each digit of the birthday as a coefficient of the polynomial.
The birthday in this problem is given as follows:
10-12-2247.
Thus the coefficients of each term of the polynomial, in order, are given as follows:
1.0.1.2.2.2.4.7.There are eight coefficients, hence the polynomial is of the seventh degree.
The signs of each coefficient is not important, they can be chosen at random, and thus the birthday polynomial for the date of 10-12-2247 can be defined as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
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The italian mathematician fibonacci is known for introducing what mathematical concept?
Given the points (-15, 30) and (5, 50). The slope of the line between the two points would be?
Answer:
The slope of the line is 1
Step-by-step explanation:
gradient = difference of y-coordinates / difference of x-coordinates
gradient = (y2-y1) / (x2-x1)
gradient = 50-30 / 5-(-15)
gradient = 20/20
gradient = 1
what is 5 3/4 divided by 3 1/2
Step-by-step explanation:
convert, Keep Change Flip, convert back
[tex]\frac{23}{4} * \frac{2}{7}[/tex]
[tex]\frac{46}{28} \\[/tex]
[tex]1\frac{18}{28}[/tex]
please help, answers only!!
Answer:
Step-by-step explanation:
Upper right graph meets both of the requirement, the line lays on both (0,9) on the y axis and (3,0) on the x axis
the tunnel under the english channel that connects england and france is actually three separate tunnels built end to end. each is a half-cylinder that is 50,000 meters long and 4 meters high. how many cubic meters of dirt had to be removed to build the tunnel?
Answer: im not exactly sure but i think 600,000m³
Step-by-step explanation: multiply 50,000m by 4 to get 200,000m and then multiply that by 3 (because 200,000 is only one section of the tunnel)
and by doing that you get 600,000m and then add cubed onto the end because it says cubic meters