Alex had (3x + 1) yards of silk. He then purchases (x2 + 5x + 4) packages each containing (2x + 1) yards of silk. If he uses (2x3 + 8x2 + 10x + 4) yards of silk to make a kite, how much silk remains?
Final answer:
To find out the amount of silk remaining, we need to subtract the amount of silk used to make the kite from the total amount of silk Alex had before purchasing the packages. After performing the calculations, we find that Alex doesn't have any silk remaining.
Explanation:
To find out how much silk remains, we need to subtract the amount of silk used to make the kite from the total amount of silk Alex had before purchasing the packages. Let's first simplify the expressions:
Total silk Alex had = 3x + 1
Total silk purchased = (x^2 + 5x + 4) × (2x + 1)
Silk used for kite = 2x^3 + 8x^2 + 10x + 4
Now, substitute the given values of x:
Total silk Alex had = 3(1500) + 1 = 4501 yards
Total silk purchased = (1500^2 + 5*1500 + 4) * (2*1500 + 1) = 22537500 yards
Silk used for kite = 2(1500^3) + 8(1500^2) + 10(1500) + 4 = 53910002004 yards
Finally, subtract the silk used for the kite from the total silk Alex had:
Silk remaining = Total silk Alex had - Silk used for kite = 4501 - 53910002004 = -53910001403 yards
Since the result is negative, it means that Alex doesn't have any silk remaining.
PLEASE HELP ME!!!! 20 PNTS!!!!!
Simplify the expression:
[tex] \frac{ \sqrt{ - 16} }{(3 - 3i) + (1 - 2i)} [/tex]
A.
[tex] \frac{ - 20 - 16i}{9} [/tex]
B.
[tex] \frac{8 + 4i}{15} [/tex]
C.
[tex] \frac{8 - 4i}{15} [/tex]
D.
[tex] \frac{ - 20 + 16i}{41} [/tex]
A rectangular box has a length of 7 ft a width of 3 ft and a height of 2ft what is the volume
what is the answer for 4x-9=k solve for x
A rectangle's length is 5 units more than the width. the perimeter is 9 times the width. what are the length and the width of the rectangle described?
This circle is centered at the point (4,5) and the length of its radius is 3. What is the equation of the circle
What is the simplest form of this?
The slope of a line is -3. Find the slope of a line that is perpendicular to this line.
A.-3
B.-1/3
C.1/3
Greg made $306 for 17 hours of work. at the same rate, how much would he make for 12 hours of work?
If you triple a number and add 11 you get 200 what is the number
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.
Which equations can be used to solve for y, the length of the room? Check all that apply.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
the correct answer is
B)y2 – 5y = 750
C)750 – y(y – 5) = 0
E)(y + 25)(y – 30) = 0
I JUST took the test
A proof uses logical reasoning that starts with accepted ideas and proceeds through logic to reach a conclusion.
Which type of reasoning does a mathematical proof use?
deductive or inductive
Landscapers plan to spread a layer of stone on a path. The number ss of bags of stone needed varies directly with the depth dd (in inches) of the layer. They need 20 bags to spread a layer of stone that is 2 inches deep. How deep will the layer of stone be when they use 15 bags of stone?
2/20 = x/15
cross multiply
20x/30
x = 30/20 = 1.5
it will be 1.5 inches deep
2/20 = x/15
cross multiply
20x/30
x = 30/20 = 1.5
it will be 1.5 inches deep
What is the answer of 6=1-2n+5
A line has slope 56 and y–intercept −3. Which answer is the equation of the line? y=−3x+5/6 y=5/6x−3 y=3x+5/6 y=5/6x+3
Answer:
The answer is the second one for sure y=5/6x−3.
Step-by-step explanation:
The equation of the line is y = (5/6)x - 3 which is the correct answer would be option (B).
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
We have been given a line that has a slope of 5/6 and a y-intercept is -3.
Let the required line of the equation would be as
y = mx + c
Where m is the slope of the line
We have given the y-intercept is -3 which means the x-coordinates will be zero.
Substitute the value of x = 0 and y = -3 in the above equation to get c.
⇒ -3 = m(0) + c
⇒ -3 = c
The slope of the line m = 5/6 which is given in the question,
Substitute the value of m = 5/6 and c = -3 in the equation y = mx + c
⇒ y = (5/6)x - 3
Therefore, the equation of the line is y = (5/6)x - 3.
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Noelle has 5/6 of a yard of purple ribbon and 9/10 of a yard of Pink ribbon. How mucho ribbon does se have altogether?
Using the approximation 3.14 for pi, what is the radius of a circle with circumference 28.3 m?
Using π ≈ 3.14, the radius of a circle with circumference 28.3 m is approximately 4.5 meters.
Step 1:
Write down the formula for the circumference of a circle.
The formula for the circumference (C) of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
Step 2:
Substitute the given value for the circumference into the formula.
Given [tex]\(C = 28.3\)[/tex] m, we use the approximation [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ 28.3 = 2 \times 3.14 \times r \][/tex]
Step 3:
Solve for the radius (r).
Divide both sides of the equation by [tex]\(2 \times 3.14\)[/tex]:
[tex]\[ r = \frac{28.3}{2 \times 3.14} \][/tex]
Step 4:
Calculate the value of (r).
[tex]\[ r = \frac{28.3}{6.28} \][/tex]
[tex]\[ r \approx 4.5 \text{ m} \][/tex]
So, the radius of the circle with a circumference of 28.3 m, using the approximation [tex]\(\pi \approx 3.14\)[/tex], is approximately 4.5 meters.
When it is 10:00 am solar time at location x, at which location is 11:00 am solar time being observed?
There are a total of 360 degrees and a total of 24 hours, therefore there are 15 degrees per hour.
Location x is located at 45 degrees, so therefore the location after 1 hour must be at 60 degrees.
Answer:
D
Answer:
it is letter D
Step-by-step explanation:
its letter D when I was doing it, in go formative
For the function f(t)=pe rt , if p=9 and r=0.09 then what is the value of f(9) to the nearest tenth
A random sample of n = 4 scores is obtained from a population with a mean of m = 80 and a standard deviation of s = 10. if the sample mean is m = 90, what is the z-score for the sample mean
Justin is constructing a line through point Q that is perpendicular to line n. He has already constructed the arcs shown. A line n and an arc with center Q is drawn. Center Q lies above the line n. The arc cuts the line on two points A and B. A is left of B. Another arc is made with a center at A. The arc cut the line segment A B near point B. The arc is symmetric to line A B. He places his compass on point B to construct an arc. What must be true about the width of the compass opening when Justin draws the arc?
I believe that this problem has the following choices:
It must be equal to BQ .
It must be wider than when he constructed the arc centered at
point A.
It must be equal to AB .
It must be the same as when he constructed the arc centered
at point A.
The correct answer is the last one:
It must be the same as when he constructed the arc centered at point A.
Answer:
The compass must be the same width as it was when he constructed the arc from point A.
Step-by-step explanation:
In order to construct a perpendicular line to a given line, we need to construct a point above and a point below the line such that the segment through them meets the line at a right angle.
When he constructed the arc from point A, it gave him one piece to creating these points. An arc from point B, intersecting the arc from point A at two points, will give him the two points he needs.
In order for the arc from point B to intersect the arc from point A, however, the width of the compass must be the same as it was when he constructed the arc from point A.
A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive ...?
The expression 6s2 represents the surface area of a cube with edges of length s. what is the cube's surface area when s = 8?
PLEASE HELP ASAP!!!
Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
The Venn diagram that illustrates the given conditional statement is:
Option: a
Step-by-step explanation:Cars are motor vehicles.
This means that all the cars are motor vehicles but converse need not be true.
i.e. all the motor vehicles cant be cars.
i.e. Cars are contained in Motor Vehicles.
Hence, the correct Venn diagram is: Option: a
( Option: b represent the statement
Some cars are Motor vehicles and some motor vehicles are cars.
Option: c represent the statement
Motor vehicles are Cars.
Option: d represent the statement:
Some motor vehicles are cars and some cars are motor vehicles.)
A certain oxyacid is derived from the oxyanion so3(-2). the formula for the oxyacid is which
To make this anion into a complete acid, then this must be added with Hydrogen ion H+. So the chemical equation looks like:
H+ + SO3(2-) --> ?
Now to balance it:
H+ + SO3(2-) --> H2SO3
Answer:
H2SO3
Answer:
H2SO3-
Step-by-step explanation:
A segment has endpoints with coordinates - 3 and 4. What is the length of the segment?
Answer: 7 units
Step-by-step explanation: In this problem, the given numbers -3 and 4 represent the coordinates of the endpoints of a segment and we are asked to find the length of the segment.
To find the length of a segment, we take the greater endpoint coordinate minus the lesser endpoint coordinate.
In this case, the greater endpoint coordinate is 4 and the lesser endpoint coordinate is -3.
So, we have 4 - (-3) which can also be thought of as 4 + 3 which equals 7.
Therefore, the length of this segment is 7 units.
Simplify. The answer should contain only positive exponents.
Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine
The rational number that equals to 2.8 (a decimal number that has repeating 8), from the options given, is twenty six over nine (26/9) because when converted to decimal it gives 2.89, which is closest to 2.8
Explanation:The question is asking which rational number is equal to 2.8 where the bar over the number indicates that it is repeating. The dot over the 8 implies that the number is actually 2.8888..., where the 8 is repeated indefinitely. So we need to find which fraction out of your given options: twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine, equals to this decimal number.
To convert these fractions to decimal form:
22/9 = 2.44,
24/9 = 2.67,
26/9 = 2.89,
28/9 = 3.11
By comparing these values, we can see that twenty six over nine (26/9) is the decimal equivalent to 2.8 as it gives us 2.89 which is closest to it.
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How many permutations of three items can be selected from a group of six? use the letters a, b, c, d, e, and f to identify the items, and list each of the permutations of items b, d, and f?
The number of permutations of 6 items that can be selected from a group of 6 is; 120 ways.
List of permutations of items b,d and f is; bdf, bfd, dbf, dfb, fdb, fbd
Permutations and selectionThe permutation required can be evaluated as follows;
6P36!/3!6× 5× 4 × 3!/3!= 6×5×4 = 120 ways.
The List of permutations of items b,d and f is;
bdfbfddbfdfbfdbfbdRead more on permutation;
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The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?