Answer: Let's call the length of the cake "l" and the width of the cake "w". The total area of the cake would be l * w.
Half of the cake is frosted with vanilla icing, so the area of the vanilla half would be (l * w) / 2.
And 2/3 of the vanilla half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 2/3 = (l * w) / 3.
The other half of the cake is frosted with chocolate icing, so the area of the chocolate half would be (l * w) / 2.
And 1/4 of the chocolate half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 1/4 = (l * w) / 4.
So, the total area of the cake covered with sprinkles would be (l * w) / 3 + (l * w) / 4.
Step-by-step explanation:
find all roots of f(x): f(x) = 6x^3-x^2-9x+4 if (2x-1) is a factor. Show all work.
Which procedure would you take first? Synthetic division?
And if its synthetic division, can you show how you divide by (2x-1)?
Answer:
[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]
Step-by-step explanation:
Given polynomial function:
[tex]f(x) = 6x^3-x^2-9x+4[/tex]
If (2x - 1) is a factor of the given function, then 2x - 1 = 0.
Therefore:
[tex]\implies 2x-1=0[/tex]
[tex]\implies x=\dfrac{1}{2}[/tex]
To divide the given function by the factor (2x - 1), we can perform synthetic division.
As the leading coefficient of the divisor is not 1, divide the dividend and divisor by the leading coefficient of the divisor (2):
[tex]\textsf{Dividend}: \quad 3x^3-\dfrac{1}{2}x^2-\dfrac{9}{2}x+2[/tex]
[tex]\textsf{Divisor}: \quad \left(x-\dfrac{1}{2}\right)[/tex]
Perform Synthetic Division
Place ¹/₂ in the division box.
Write the coefficients of the dividend in descending order.
(Note: As no terms are missing, we do not need to use any zeros to fill in missing terms).
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\end{array}[/tex]
Bring the leading coefficient straight down:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&3\end{array}[/tex]
Multiply the number you brought down with the number in the division box and put the result in the next column (under the -¹/₂ ):
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&\frac{3}{2}&&\\\cline{2-5}&3\end{array}[/tex]
Add the two numbers together and put the result in the bottom row:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&&\\\cline{2-5}&3&1\end{array}[/tex]
Repeat:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&\\\cline{2-5}&3&1&-4\end{array}[/tex]
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&-2\\\cline{2-5}&3&1&-4&0\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.
The last number in the bottom row is the remainder.
Therefore, the factored function after synthetic division is:
[tex]f(x)=(2x-1)(3x^2+x-4)[/tex]
The quadratic factor can be factored further:
[tex]\implies 3x^2+4x-3x-4[/tex]
[tex]\implies x(3x+4)-1(3x+4)[/tex]
[tex]\implies (x-1)(3x+4)[/tex]
Therefore, the fully factored function is:
[tex]f(x)=(2x-1)(x-1)(3x+4)[/tex]
To find the roots of the function, set each factor to zero and solve for x:
[tex]2x-1=0 \implies x=\dfrac{1}{2}[/tex]
[tex]x-1=0 \implies x=1[/tex]
[tex]3x+4=0 \implies x=-\dfrac{4}{3}[/tex]
Therefore, the roots of the given function are:
[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]
Circle P is shown. Line segments P T, P U, P R, and P Q are radii. Line segments T S and S U are secants. Angle T S U is 120 degrees, angle U P R is 59 degrees, and angle Q P T is degrees. Use the drop-down menus to complete the statements. A central angle of circle P is angle . The measure of is degrees.
A central angle of circle P is angle TPQ.
The measure of RU is 59 degrees.
What is an arc?In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value. Generally speaking, the degree measure of an arc in a circle is always equal to the central angle that is present in the included arc.
Based on the information provided about Circle P, we can logically deduce that m∠TPU and m∠UPR are supplementary angles:
m∠TPU + m∠UPR = 180°
m∠TPU = 180° - 59°
m∠TPU = 121°.
m∠TPQ + m∠QPR = 180°
m∠QPR = 180° - 107°
m∠QPR = 73°.
Therefore, the central angle of circle P is m∠TPQ and the measure of arc RU is equals to 59 degrees.
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Answer:
1. TPQ
2. 58
Step-by-step explanation:
Which pair of values are equivalent? choose two correct answers
Answer:
first 2 pairs
Step-by-step explanation:
[tex]\frac{6}{100}[/tex] = 6 ÷ 100 = 0.06 ← equivalent
[tex]\frac{7}{10}[/tex] = 7 ÷ 10 = 0.7 ← equivalent
[tex]\frac{5}{10}[/tex] = 5 ÷ 10 = 0.5 ≠ 0.05
[tex]\frac{32}{100}[/tex] = 32 ÷ 100 = 0.32 ≠ 3.2
1. Look at the rectangle at right. Find the ratio of the shaded area to the area of the whole figure. Find the ratio of the shaded area to the unshaded area. 2. Use the figure below to find these ratios: AC/CD. CD/BD, and BD/BC
1. The ratio of the shaded area to the area of the whole figure is 3/8 and the ratio of the shaded area to the unshaded area is 3/5.
2. The value of AC/CD. CD/BD, and BD/BC is 8/5, 5/2 and 10/7 respectively.
A ratio is a comparison of two quantities, and it can be expressed in different ways, such as a fraction, a decimal, or a percentage. In this case, we will explore how to find ratios of areas in geometric figures.
Firstly, let's consider the rectangle on the right. To find the ratio of the shaded area to the area of the whole figure, we need to calculate both of these values. The shaded area is a rectangle with dimensions 6 by 2, which means its area is 6 x 2 = 12 square units.
The whole figure is a rectangle with dimensions 8 by 4, so its area is
=> 8 x 4 = 32 square units.
Therefore, the ratio of the shaded area to the area of the whole figure is 12/32, which simplifies to 3/8.
To find the ratio of the shaded area to the unshaded area, we need to subtract the shaded area from the whole area. The unshaded area is a rectangle with dimensions 8 by 2, so its area is
=> 8 x 2 = 16 square units.
Subtracting the shaded area from the whole area gives us
=> 32 - 12 = 20 square units for the unshaded area.
Thus, the ratio of the shaded area to the unshaded area is 12/20, which simplifies to 3/5.
Moving on to the second question, we need to use the figure below to find three ratios: AC/CD, CD/BD, and BD/BC.
Let's start with the first ratio, AC/CD. We know that AC is 8 units long and CD is 5 units long, so
=> AC/CD is 8/5.
Next, CD/BD. We know that BD is 10 units long, so to find CD/BD, we need to subtract the length of AC from the length of BD. AC is 8 units long, so
BD - AC = 10 - 8 = 2 units.
Therefore, CD/BD is 5/2.
Finally, BD/BC. We know that BC is 12 units long, so to find BD/BC, we need to subtract the length of CD from the length of BC. CD is 5 units long, so
=> BC - CD = 12 - 5 = 7 units.
Therefore, BD/BC is 10/7.
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Using Addition to Compare Numbers
Sara and Danica are having a competition to see who
can find more recyclable cans in a month.
At the end of the first week, Sara collected 14 cans and
Danica collected 17 more cans than Sara.
The equation below represents the number of cans
Danica collected..
14+ 17 = n
Choose the answers that make the comparison
statements true.
The sum is
The sum is
The sum will be
The sum will be
more than 14.
more than 17.
14.
17.
The answer that makes the comparison statements true, The sum is more than 17. So Option B is correct.
What is addition ?Addition is a basic mathematical operation that combines two or more numbers to give a total or sum. It is one of the four elementary arithmetic operations, along with subtraction, multiplication, and division.
The equation 14+17=n represents the total number of cans Danica collected at the end of the first week, where n is the number of cans Danica collected.
We can solve for n by adding 14 and 17, which gives us:
n = 14 + 17 = 31
Therefore, Danica collected 31 cans at the end of the first week.
To make the comparison statements true:
The sum is more than 17:
This statement is true, since the sum of 14 and 17 is 31, which is greater than 17.
The sum will be 14:
This statement is false, since the sum of 14 and 17 is 31, not 14.
The sum will be 17:
This statement is false, since the sum of 14 and 17 is 31, not 17.
So, the correct answer is: The sum is greater than 17.
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For complete question image is attached:
a triangle has side lengths 13, 14, and 15. find the area of the triangle whose vertices are the incenter, circumcenter, and centroid of the original triangle.
The Incircle, Circumcircle, and Centroid of a triangle are the three points which define a triangle, each with its own unique properties. In this case, we are looking for the area of a triangle whose vertices are the incenter, circumcenter, and centroid of our original triangle.
To find the area of this triangle, we will use Heron's Formula. This formula allows us to calculate the area of a triangle given its three side lengths. The three side lengths of our triangle are 13, 14, and 15. We can plug these values into Heron's Formula to find the area of our triangle.
The area of our triangle is approximately 54.47 units squared. This means that the area of our triangle, whose vertices are the incenter, circumcenter, and centroid of the original triangle, is 54.47 units squared. This can be verified by plugging in the side lengths into Heron's Formula and solving for the area.
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evaluate a - c ÷ 6 if a = 6 and c = 12
Answer:
-1
Step-by-step explanation:
1. Plug the numbers into the equation
6-12/6
2. Solve.
6-12=-6
-6/6=-1
Answer:
4
Step-by-step explanation:
A= 6
C= 12
6-12÷6
With BIDMAS the order becomes:
6-(12÷6) —> 6-2 = 4
For each sequence, create an input-output table with the figure number and the number of tiles in each figure for 1 ≤ n ≤ 10. Figure Number, n 1 2 3 4 5 6 7 8 9 10 Total Number of tiles in Sequence I, T 10 12 14 16 18 20 22 24 26 28 Total Number of tiles in Sequence II, T 5 8 11 14 17 20 23 26 29 32
Answer:
Here is the input-output table for Sequence I:
Figure Number, n | Total Number of Tiles, T
1 | 10
2 | 12
3 | 14
4 | 16
5 | 18
6 | 20
7 | 22
8 | 24
9 | 26
10 | 28
And here is the input-output table for Sequence II:
Figure Number, n | Total Number of Tiles, T
1 | 5
2 | 8
3 | 11
4 | 14
5 | 17
6 | 20
7 | 23
8 | 26
9 | 29
10 | 32
I need help please this question makes no sence to me and I keep getting it wrong
In a parallelogram, the consecutive angles are supplementary (add up to 180 degrees). x can represent the first angle, and 4x can represent the second angle. With this information you can create the equation x + 4x = 180 and solve.
5x = 180
x = 36
So the measure of the first angle is 36 degrees, and the one that is 4 times larger is 144 degrees.
There are 9 girls and 6 boys taking golf lessons. Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
Answer:
2:5
Step-by-step explanation:
We know
There are 9 girls and 6 boys taking golf lessons.
So, there are a total of 15 taking a golf lesson.
Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
The ratio is
6:15 = 2:5
So, the ratio is 2:5
if Ps = 4x+8, PQ = 29, RS = 5x -3, and QR=29, then Ps=
Answer:
What is X?
Step-by-step explanation:
4 multiplied by X + 8 =Ps
An unused roll of paper towels is shown. What is the volume of the unused roll?
Volume of a Cylinder: V=Bh
USE THE PHOTO TO HELP ANSWER THE QUESTIONS
P.S. I WILL GIVE YOU BRAINLIEST IF RIGHT
The volume of the unused roll is approximately 10,316.97 cubic centimeters.
what is radius ?
A radius is a line segment that connects the center of a circle or a sphere to any point on its circumference or surface, respectively. It is half the length of the diameter, which is a line segment that passes through the center of the circle or sphere and has endpoints on its circumference or surface, respectively. The radius is an important measurement in geometry and is used to calculate other important properties of circles and spheres, such as their area, circumference, and volume.
Given by the question:
To find the area of the base of the cylinder, we need to know the radius. Since the paper towel roll has an inner radius of 4.2 cm and an outer radius of 12 cm, we can calculate the area of the base as follows:
[tex]Area of outer circle - Area of inner circle = πr_outer^2 - πr_inner^2[/tex]
[tex]= \pi (12 cm)^2 - \pi (4.2 cm)^2[/tex]
= [tex]452.16\pi cm^2 - 55.3896\pi cm^2[/tex]
= [tex]396.7704\pi cm^2[/tex]
Therefore, the volume of the unused roll can be calculated as:
V = Bh = [tex](396.7704\pi cm^2)(26 cm)[/tex]
[tex]= 10,316.97 cm^3[/tex]
Therefore, the volume of the unused roll is approximately 10,316.97 cubic centimeters.
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Right now, Miquel is 9 kilometers into a 36-kilometer race. He is running an average
of 18 kilometers every hour.
rate of change
Answer: The rate of change for Miquel's position in the race can be calculated by his speed, which is 18 kilometers per hour. So, his rate of change is 18 kilometers per hour. This means that for every hour that passes, Miquel will have covered 18 kilometers in the race.
Step-by-step explanation:
PLEASE HELP ASAP! DUE SOON !
Answer & Step-by-step explanation:
The domain of the function g(x) = ⟨÷⟩6x + 6 is the set of all real numbers, since dividing by zero is not defined.
And it is a linear function, which means that it is a straight line in a 2-dimensional graph. The slope of the line is 6, and the y-intercept is 6, meaning that when x=0, the value of g(x) is 6.
What is the center and radius of the circle with equation (x – 14)2 + (y – 2)2 = 9?
Choose one
(14, 2), r = 3
(14, 2), r = 9
(– 14, – 2), r = 3
(– 14, – 2), r = 9
none of these
The center and radius of the circle with equation (x – 14)2 + (y – 2)2 = 9 is (14, 2), r = 3, the correct option A.
What is an equation of a circle?
A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-h)^2 + (y-k)^2 = r^2
We are given that;
The equation of circle= (x – 14)2 + (y – 2)2 = 9
Now,
We know the equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Comparing the given equation to this form, we can see that the center of the circle is (14, 2) and the radius is √9 = 3.
Therefore, by the given equation of circle answer will be (14, 2), r = 3.
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Factorise the following:
a) x² + 4x + 4
b) x²- 12x + 27
c) x²-x-42
d) x² + 8x-9
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
[tex]x^2+4x+4\\\rightarrow x^2+2x+2x+4\\\rightarrow x(x+2)+2(x+2)\\\rightarrow (x+2)(x+2)[/tex]
Part B
[tex]x^2-12x+27\\\rightarrow x^2-9x-3x+27\\\rightarrow x(x-9)-3(x-9)\\\rightarrow (x-3)(x-9)[/tex]
Part C
[tex]x^2-x-42\\\rightarrow x^2+6x-7x-42\\\rightarrow x(x+6)-7(x+6)\\\rightarrow (x-7)(x+6)[/tex]
Part D
[tex]x^2+8x-9\\\rightarrow x^2+9x-x-9\\\rightarrow x(x+9)-1(x+9)\\\rightarrow (x-1)(x+9)[/tex]
find the mode of the following data 20,26,16,22,20,30,22,20,26
The mode of the data 20,26,16,22,20,30,22,20,26
How to find the mode of the data?From the question, we have the following parameters that can be used in our computation:
20,26,16,22,20,30,22,20,26
The mode of a dataset is the data element that has the highest frequency
Using the above as a guide, we have the following:
20 has the highest frequency of 3
Hence, the mode is 3
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Which of the following correspond to a probability of an event occurring (i.e. when I get the value, I can determine how often the event(s) being described is likely to occur in a random sample)? Select any that apply. The integral of the density of the chi-squared distribution between chi-squared values of and 5 The
p
-value of a chi squared value of 4 The probability mass of observing 50 successes in 50 binomial trials The probability density of the chi squared distribution when the chi-squared value is 4
The statement that corresponds to a probability of an event occurring is the probability mass of observing 50 successes in 50 binomial trials.
Probability represents comprehensive analysis of the reasonable likelihood that a particular outcome shall typically occur. This occurrence is dependent on the ratio of favorable instances to probable instances. The integral of the chi-squared distribution's density among complex chi-squared values of zero and five and probability density of the chi-squared distribution at chi-squared value four are functionally related to the overall chi-squared distribution. However, neither of them directly reflects the likelihood that an event will actually take place.
The strength of evidence against null hypothesis in a chi-squared test is exhibited by p-value of a chi-squared value of numeral four, but it does not directly translate to likelihood that an event will take place. Therefore, the statement that the probability mass of observing 50 successes in 50 binomial trials corresponds with the given question.
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What is (f- g)(x)?
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x) =
The value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex].
What is a function?
A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
To find (f-g)(x):
The operations on functions are as easy as the operations on numbers or polynomials.
We have to subtract the functions to find the above mentioned operation.
(f-g) (x)= f(x)-g(x)
= (x¹ - x² +9)-(x³ + 3x² + 12)
The minus will change the signs of function g.
= [tex]x-x^{2} +9-x^{3}-3x^{2} -12[/tex]
=[tex]x-4x^{2} -x^{3} -3[/tex]
Hence, the value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex]
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Divide 10a6b4 by 5a2b.
2a8b5
2a4b5
2a4b4
2a4b3
Answer: 2a^4b^3
Step-by-step explanation: Divide the base like normal. Subtract the exponents.
a6 - a2 = a4
b4 - b = b3
A single variable will always equal to 1 so b will be its own exponent.
After divide the solution is,
⇒ 2a⁴b³
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
Divide 10a⁶b⁴ by 5a²b.
Hence, We get;
⇒ 10a⁶b⁴ / 5a²b.
⇒ 2a⁶⁻² b⁴⁻¹
⇒ 2a⁴b³
Thus, After divide the solution is,
⇒ 2a⁴b³
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I will give brainliest and ratings if you get this correct
determine whether the following function have limit or not?
The function [tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex] has a limit
How to determine the if the function has a limit or notFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex]
Substitute 0 for x in the above expression
So, we have the following representation
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2} = \frac{1 - \sqrt[3]{0^2 + 1}}{0^2}[/tex]
Evaluate the expression
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}=\infty[/tex]
This means that the limit of the expression is to infinity
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Find the x- and y-intercepts of the graph of 2x - 3y = 30 State each answer as an integer or an improper fraction in simplest form.
x int = 15
y int = -10
y intercept can be found bt setting X to 0
x intercept can be found by setting Y to 0
2(0) - 3y = 30 --> -3y = 30 --> y = -10
2x - 3(0) = 30 --> 2x = 30 --> x = 15
alternatively, y int is "b" in eq. y = mx + b
-3y = 30 -2×
y = -10 + (2/3)x
y = (2/3)x - 10
b = -10
Please answer both!! I’ll give brainlest to first!!!
Let's call the amount of water in the first pool "x" and the amount of water in the second pool "y". We know that:x = 582 + 20.25t (where t is the time in minutes)
y = 44.5tWe want to find the time "t" at which x = y, so we can set the two equations equal to each other:582 + 20.25t = 44.5t
Expanding the second equation and solving for t, we get:582 = 24.25t
t = 582 ÷ 24.25 = 24 minutes
So, after 24 minutes, the two pools will have the same amount of water.
To find out how much water will be in each pool, we can plug this value of t back into the first equation:x = 582 + 20.25t = 582 + 20.25(24) = 582 + 485 = 1067 liters
y = 44.5t = 44.5(24) = 1067 liters
So, both pools will contain 1067 liters of water.
Answer:
Below
Step-by-step explanation:
First pool starts with 582 and adds 20.25 * m m = minutes
Volume1 = 582 + 20.25 m
Volume 2 = 44.5 m
At what 'm' are they equal ?
582 + 20.25 m = 44.5 m subtract 20.25 m from both sides to get
582 = 24.25 m divide both sides of the equation by 24.25
m = 24 minutes <=====use this value in either equation to find the volume volume2 = 44.5 * 24 = 1060 gallons
8. At a home supply store, bags of concrete mix are on sale. Every third bag that you buy is discounted by 75%. A bag of concrete mix sells for $3.88. How much will you spend if you buy 14 bags of concrete mix? 75
The total amount spend is 391.88
What is discount?The noun discount refers to an amount or percentage deducted from the normal selling price of something.
If 14 bag of mix cement are bought and and every third bag is discounted
no of bag on discount = 14/3 = 4 remainder 2
therefore 4 bags will be on discount
discount on a bag = 3.88× 75/100
= 291/100 = 2.91
therefore each bag on discount will cost = 3.88 - 2.91
= 0.97
for 4 bags = 0.97 ×4 = 3.88
for remaining 10 bags = 3.88 × 10
= 388
therefore the total amount = 388+3.88
= $391.88
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Consider the following equation.
4−2y=8−2x
Step 1 of 2 : Find the x- and y-intercepts, if possible.
The x-intercept is (2, 0) and the y-intercept is (0, -2).
What is Intercept?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
We have the Equation: 4−2y=8−2x
To find the x-intercept, we set y = 0
4 - 2(0) = 8- 2x
4 = 8 -2x
2x = 8-4
2x = 4
x = 2
and, For y-intercept we set x= 0
4 - 2y = 8- 2(0)
4- 2y = 8
-2y = 4
y= -2
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1. I owe $8500 on my credit card. The card has a promotional interest rate of 0% for 24 months. To repay the debt, I'm going to pay a fixed amount toward the balance every month. After 12 months, my remaining debt will be $6460. Which of the following equations correctly relates the remaining debt (D) to the number of months (1) I've been making payments? (Select all that apply.)
a. 170t+D=8500
b. D= 170t-6460
c. D+6460=8500t
d. D = 6460 + 170t
2. Use the situation from problem #1. If I continue paying at the rate above (assuming there is no additional interest), how many months will it take me to pay off my credit card?
1. The equation that correctly relates the remaining debt (D) to the number of months (1) I've been making payments is:
a. 170t + D = 8500.
2. If you continue paying at the rate above (assuming there is no additional interest), it will take 38 months for you to pay off the credit card balance.
What is an equation?An equation is a mathematical statement showing the equality of two or more mathematical expressions using the equation symbol (=).
The total debt on the credit card = $8,500
The promotional interest rate for 24 months = 0%
Monthly repayment = $170
Total repayment after 12 months = $2,040 ($170 x 12)
Balance on the credit card after 12 months of repayment = $6,460 ($8,500 - $2,040)
The number of months to repay the balance without interest = 38 months ($6,460/$170).
Thus, D, the remaining debt can be determined using this equation, a. 170t + D = 8500 and it will take 38 months to repay without interest.
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Referring to the figure, evaluate the expression shown
when a = 3, b = 7, c = 2
Answer:-17
Step-by-step explanation:
b=7,then
b^2=49
square root of 49-4*3*2=-17
Find the measure of the three missing angles in the rhombus below.
Answer:
y=67
z=113
x=67
Step-by-step explanation:
opposite angles are parallel in a rhombus and they all equal 360
arrange the following fraction 5/6,8/9,2/3 in assending order
Answer: From Greatest to Least: 8/9, 5/6, 2/3
Step-by-step explanation:
–81, 108, –144, 192, ...
Which formula can be used to describe the sequence?
The formula that can be used to describe the sequence will be aₙ = –81 · (–4/3)ⁿ⁻¹.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
–81, 108, –144, 192, ...
The first term of the sequence is –81. And the common ratio is given as,
r = 108 / (–81)
r = – 4/3
The formula can be used to describe the sequence is given as,
aₙ = –81 · (–4/3)ⁿ⁻¹
The formula that can be used to describe the sequence will be aₙ = –81 · (–4/3)ⁿ⁻¹.
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