Answer:
A
Step-by-step explanation:
Use the long division method to find the result when 4x3 -2x2 – 15x + 6 is
divided by x-2
Answer:
[tex]4x^2+6x-3[/tex]
Step-by-step explanation:
"/" substitutes the normal division symbol
[tex]4x^2[/tex] [tex]+6x[/tex] [tex]-3[/tex]
______________
[tex]x-2/4x^3-2x^2-15x+6[/tex]
[tex]4x^3[/tex] [tex]-8x^2[/tex]
______________________
[tex]6x^2[/tex] [tex]-12x[/tex]
______________________
[tex]-3x+6[/tex]
x multiplied by what equals [tex]4x^3[/tex]? [tex]x(4x^2)=4x^3[/tex], so the first number that goes on top is [tex]4x^2[/tex]. Multiply x by [tex]4x^2[/tex] and put it below to the [tex]4x^3[/tex] on the first row. Multiply x-2 by [tex]4x^2[/tex] and put it below the [tex]-2x^2[/tex] . Subtract the first row from the second row.
x multiplied by what equals [tex]6x^2[/tex]? [tex]6x[/tex]. Repeat the same process as before except with [tex]6x^2[/tex]
Find the surface area and volume of a 1-inch cube and a 10-inch cube. What is the ratio of the surface areas? What is the ratio of the volumes?
[tex]\maltese \: \: \underline{\underline{\frak{Understanding~the~question :-}}} \\ \\[/tex]
For solving this question, we will take the help of the branch of mathematics that studies the sizes of different shapes may they be 2D or 3D, called mensuration.
⠀
There are two parts in the question, in the first part we have been asked to calculate the ratio of the total surface area of the two cubes, for that we will calculate their total surface areas and divide them in order to calculate the ratio. In the second part, we have been asked to calculate the ratio of the volume of the two cubes, and in order to calculate the ratio, at first we will calculate the volumes of the respective cubes and then divide them. And, thus, in this way, we will get our required answer.
⠀
[tex] \maltese \: \underline{ \underline{ \frak{Given :-}}} \\ \\ [/tex]
Two cubes in which the sides measure,
Cube 1 say A = 1 inchCube 2 say B = 10 inch⠀
[tex] \maltese \: \: \underline{ \underline{ \frak{Formula~Applied :-}}} \\ \\ [/tex]
[tex] \bigstar \begin{cases} \sf 1.~Volume_{cube} = {a} ^3\\ \\\sf 2.~T.S.A._{cube} = 6{a}^2\end{cases} \\ \\ [/tex]
[tex] \maltese \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ [/tex]
Calculating the total surface areas,
⠀
[tex] \sf \longrightarrow TSA \: of \: A = 6( {1)}^{2} \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A =6 \times 1 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A = {6 \: inch}^{2} \\ \\ [/tex]
[tex]\sf \longrightarrow TSA \: of \: B =6 {(10)}^{2} \: \: \: \: \: \: \\ \\ \\\sf \longrightarrow TSA \: of \: B =6 \times 100 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: B = {600 \: inch}^{2} \\ \\ [/tex]
Thus, now we can calculate the ratio,
⠀
[tex]\sf \longrightarrow Ratio = \dfrac{TSA~of~A} {TSA~of~B} \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{1}{100} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 100 \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the total surface area of the cubes is 1 : 100. Now, moving to the second part of the question, and calculating the volume of the cubes, we have,
⠀
[tex]\sf \longrightarrow Volume \: of \: A= {(a)}^{3 } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {(1)}^{3} \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {1 \: inch}^{3} \\ \\ [/tex]
[tex]\sf \longrightarrow Volume \: of \: B = {(a)}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {(10)}^{3} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {1000 \: inch}^{3} \\ \\ [/tex]
Now, calculating the ratio,
⠀
[tex]\sf \longrightarrow Ratio =\dfrac{Volume ~of~A} {Volume~of~B} \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{ {1 \: inch}^{3} }{1000 \: {inch}^{3} } \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel\dfrac{ {1 \: inch}^{3} }{ {1000 \: inch}^{3} } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 1000 \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the volume of the cubes is 1 : 1000.
⠀
[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]
If you borrow $1000 for 5 years at an interest rate of 10%, the amount of interest you pay is?
Answer:
p=1000
t=5 years
r=10%
i=(ptr)/100
i=(1000×5×10)/100
i=50000/100
i=500
Please help!!
Find the value of x
A. 12
B. 6
C. 10
Answer:
x = 12
Step-by-step explanation:
Let's find the measure of major arc MNB:
360 - arc MB = major arc MNB
Now, let's plug in what we know:
360 - (80 + 60) = major arc MNB
Next, combine like terms, and replace "major arc MNB" with "x."
360 - 140 = x
220 = x
Now, we know that the measure of major arc MNB equals 220 degrees.
Angle MLB is going to be double the measure of major arc MNB, so let's set up an equation for this situation:
2(Angle MLB) = major arc MNB
Now, let's plug in what we know:
2(9x + 2) = 220
Finally, let's solve for x:
18x + 4 = 220
18x = 216
x = 12
please answer it correctly
Answer:
40 degrees
Step-by-step explanation:
if the lines are perpendicular, then they are also sharing the same line so that means, its a simple equation of 180-140=40.
Answer:
The value of angle 2 = 40°
Step-by-step explanation:
Given : angle 1 = 140°
angle 1 + angle 2 = 180° { because they are linear pair }
=> 140 + angle 2 = 180°
=> angle 2 = 180 - 140
=> angle 2 = 40°
A circle has a central angle measuring startfraction 7 pi over 6 endfraction radians that intersects an arc of length 18 cm. what is the length of the radius of the circle? round your answer to the nearest tenth. use 3.14 for pi. 3.7 cm 4.9 cm 14.3 cm 15.4 cm
The length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
How to calculate the length of aan arc?The formula for calculating the legnth of an arc is expressed as:
L = rtheta
r is the radius
Theta is the subtended angle
Given the following
18 = r(7pi/6)
7pi r = 18 * 6
7pi r = 108
r = 108/7pi
r = 4.9cm
Hence the length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
Learn more on length of an arc here: https://brainly.com/question/2005046
Answer:
B or 4.9cm
Step-by-step explanation:
Sam buys a DVD player for $55. 95 and it is on sale for 40% off regular price. How much money will same save
Answer:
$ 22.38
Step-by-step explanation:
If the pre-sale price is $ 55.95
40 % of this would be .4 * 55.95 = $ 22.38
A circle with center O is inscribed in a square with a
perimeter of 40, as shown below. What is the area of the
shaded region?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Areas and Volumes.
Area of Shaded region = Area of Square - Area of inscribed Circle.
Radius if circle = 10/2 ==> 5 units
hence,
Area of circle = 25 π units
Area of square = (10)^2 ==> 100 units
hence the area of shaded region = 100 - 25π
==> Area of shaded region = 25 (4 - π)
Correct option is G.)
simplify the expression -6(3x-4)
Answer:
-18x + 36 for the -6(3x-4) and 12x - 20 for the one on the image.
Step-by-step explanation:
You have 2 questions so I'll answer both of them (One written and the image as well)
-6 (3x-4)
You need to multiply -6 by 3x and -4
-18x + 36 Is the simplified version
**Remember that when multiplying two negatives they turn into a positive.
-2x (-6 + 10)
You need to multiply -2x by -6 and 10
12x - 20
can anyone help me???
Answer:
6
Step-by-step explanation:
3 3/4 = 15 / 4 = 105 / 28
2 7/28 = 63/28
105/68 + 63/28 = (105 + 63) / 28 = 168/28 = 6
[tex]3 \frac{3}{4 } + 2 \frac{7}{28} [/tex]
to find:the simplest form.
solution:[tex] \frac{15}{4} + \frac{9}{4} [/tex]
[tex] = \frac{(15 \times 4) + (9 \times 4)}{4 \times 4} [/tex]
[tex] = \frac{60 + 36}{16} [/tex]
[tex] = \frac{96}{16} [/tex]
[tex] = 6[/tex]
therefore the correct answer is option C.
In ΔFGH, = 440 inches, = 990 inches and ∠G=164°. Find the length of , .
Answer:
1418 ( Hope this helps! )
Step-by-step explanation:
g= 440+990-2(440)(990) cos 164
g=193600+980100-2
g=193600+980100+837451.1895
g= 2011151.1895 Square root and round
An appropriate statistical tool for accounting for sampling error in an estimate is A. A scatter chart B. A frequency distribution C. A confidence interval D. A standardized score E. All of the above F. None of the above
The statistical tool for accounting for sampling error in an estimate is confidence interval.
What is sampling?The term sampling has to do with the selection of a given number of participants from the population in susch a way that reflects the population of the entire population.
Sampling is usually prone to given degree of error. The statistical tool for accounting for sampling error in an estimate is confidence interval.
Learn more about sampling: https://brainly.com/question/11045407
#SPJ1
I’ll markbrainluest A local water park has two types of season passes. Plan A costs a one-time fee of $140 for admission plus $8
for parking every trip. Plan B costs a one-time fee of $50 for parking plus $23 for admission every trip. How
many visits must a person make for plan A and plan B to be equal in value?
Answer:
6
Step-by-step explanation:
140+8X=50+23X
8X-23X=50-140
-15X=-90
X=-90/-15
X=6 TRIPS IS THE ANSWER.
PROOF:
140+8*6=50+23*6
140+48=50+138
188=188
If you can mow 90 lawns in 45 hours, how long will it take to mow 12?
Work Shown:
(90 lawns)/(45 hours) = (12 lawns)/(x hours)
90/45 = 12/x
2 = 12/x
2x = 12
x = 12/2
x = 6
It takes 6 hours to mow 12 lawns.
Please solve and show your work
SA=π(9)²+π9*19
* is how I do the multiplication symbol btw
Answer:
791.28
Step-by-step explanation:
1. 3.14*9²=254.34
2. 3.14*9*19=536.94
3. 536.94+254.34=791.28
Convert 389.1 L to mL
Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio.
4, 13/3, 14/3, 5, 16/3, …
Is the answer: Neither?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's see if the sequence is Arithmetic or Geometric :} [/tex]
[tex] \textsf{If the difference between successive terms is } [/tex] [tex] \textsf{equal then, the terms are in AP} [/tex]
[tex] \sf{ \dfrac{14}{3}- \dfrac{13}{3} = \dfrac{1}{3}} [/tex][tex] \sf{ {5}{}- \dfrac{14}{3} = \dfrac{15-14}{3} =\dfrac{1}{3}} [/tex][tex] \textsf{Since the common difference is same, } [/tex] [tex] \textsf{we can infer that it's an Arithmetic progression} [/tex] [tex] \textsf{with common difference of } \sf \dfrac{1}{3} [/tex]
Answer:
Arithmetic with common difference of [tex]\sf \frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\textsf{Given sequence}=4, \dfrac{13}{3}, \dfrac{14}{3}, 5, \dfrac{16}{3},...[/tex]
If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).
If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).
[tex]\sf 4\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad\dfrac{13}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{14}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad 5\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{16}{3}[/tex]
As the difference between consecutive terms is [tex]\sf \frac{1}{3}[/tex] then the sequence is arithmetic with common difference of [tex]\sf \frac{1}{3}[/tex]
General form of an arithmetic sequence: [tex]\sf a_n=a+(n-1)d[/tex]
where:
[tex]\sf a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
a = 4[tex]\sf d=\dfrac{1}{3}[/tex]So the formula for the nth term of this sequence is:
[tex]\implies \sf a_n=4+(n-1)\dfrac{1}{3}[/tex]
[tex]\implies \sf a_n=\dfrac{1}{3}n+\dfrac{11}{3}[/tex]
(982x5.47)-(598x78)+28=y
Answer:
4805.38
Step-by-step explanation:
982×5.47=5371.54
598×78=46,644
5371.54-46644=4805.10
4805.10+28=4805.38
Drag the numbers to order them from greatest to least, with the greatest at the top.
Answer:
the order that they are in right now is right
Step-by-step explanation:
19. The ratio of blue to green marbles is
2:3. If there are only blue and green
marbles, what percent of the
marbles are blue?
Answer: 40%
Step-by-step explanation:
Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest hundredth of an inch if necessary.
The height of the ramp rise from the ground at its highest end to the nearest hundredth is 8.79 inches.
The situation forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides can be found using trigonometric ratios.
Therefore, the hypotenuse of the right triangle formed is the length of the fiberboard.
The height of the ramp formed is the opposite side of the right triangle.
Hence,
sin 19° = opposite / hypotenuse
sin 19° = h / 27
cross multiply
h = 27 × sin 19°
h = 27 × 0.32556815445
h = 8.79034017034
h = 8.79 inches.
Therefore, the height of the ramp rise from the ground at its highest end to the nearest hundredth is 8.79 inches.
learn more on right triangle here: https://brainly.com/question/25566098
Answer:
8.79 inches
Step-by-step explanation:
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 9 boys and 9 girls are competing, how many different ways could the six medals possibly be given out?
Answer:
the six medals possibly be given out by three medals for girl and three medals for boy
Mei runs the same distance 6 days each week. In 4 weeks, she runs 151.68 miles. How many miles does Mei run each day?
Answer: 6.32
Step-by-step explanation: 6 days a week in 4weeks Is 24days
Divide the total distance by 24
A bakery sold a total of 400 cupcakes in a day, and 184 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?
Answer:
46%
Step-by-step explanation:
184/400=vanilla
184/400=46/100=46%
hope this helps
To obtain an average (arithmetic mean) of exactly 2/3, what fraction must be added to 1/6, 1/2, and 1/3?
A. 2/3
B. 1/1
C. 3/2
D. 5/3
Answer:
D. 5/3
Step-by-step explanation:
[tex]\frac{1/6+1/2+1/3+x}{4} =2/3[/tex]
[tex]1/6+1/2+1/3+x=8/3[/tex]
[tex]x=8/3-1/6-1/2-1/3[/tex]
[tex]x=8/3-1/6-3/6-2/6[/tex]
[tex]x=8/3-6/6[/tex]
[tex]x=16/6-6/6=10/6[/tex]
simplified
[tex]x=5/3[/tex]
Hope this helps
Peter set up the iron board to iron his shirt. 3 If m 3 is 65°, what is the measure of its vertical angle? OA. 155° OB. 65 OC. 25° OD. 115°
Answer:
the same 65 degrees
Step-by-step explanation:
Hillsdale Orchard's owners decide to plant 30 new Gala apple trees. Complete the ratio table to find the number of new Fuji apple trees the owner should plant if they want to maintain the same ratio of Fuji apple trees to Gala apple trees.
Ratio table
Fuji apple trees | __ __ 160
Gala apple trees | 30 __ 120
Please fill in the blank spaces in the table
Hillsdale Orchard's owners decide to plant 30 new Gala apple trees, he needs to pllat 40 new fuji trees so as to maintain the same ratio of Fuji apple trees to Gala apple trees.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the table:
Ratio of Fuji apple trees to Gala apple trees = 160 / 120 = 4/3
Hence, for 30 new galla trees, number of Fuji trees is:
Fuji trees = (4/3) * 30 = 40
Hillsdale Orchard's owners decide to plant 30 new Gala apple trees, he needs to pllat 40 new fuji trees so as to maintain the same ratio of Fuji apple trees to Gala apple trees.
Find out more on equation at: https://brainly.com/question/1214333
If sin 1/3, what are of the values of cos 0 and tan 0?
Answer:
B
Step-by-step explanation:
SohCahToa
Sin opposite/hypotenuse
Cos adjacent/hypotenuse
Tan opposite/adjacent
so if sin is 1/3 the opposite is 1 and the hypotenuse is 3
to find cos do a^2+b^2=c^2
1^2 + x^2 = 3^2
1+x^2=9
subtract 1 from both sides
x^2=8
do the square root x=2 sq root 2
that leaves u with
opposite is 1
hypotenuse is 3
adjacent is 2 sq rt 2
cos= 2 sqrt 2 / 3
tan= 1 / 2 sq rt 2 which is also eqal to sq rt 2 / 4
B
Please Help i need to know this asap
Answer:
(0, - 6)
Step-by-step explanation:
Midpoint Formula
M = (x₁ + x₂ / 2, y₁ + y₂ / 2)Solving
M = (-3 + 3 / 2, -7 - 5 / 2)M = (0, -12/2)M = (0, - 6)Answer:
The midpoint is (0, -6)
Step-by-step explanation:
Step 1: Determine the midpoint
[tex]midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex]midpoint = (\frac{-3 + 3}{2}, \frac{-7 + (-5)}{2})[/tex]
[tex]midpoint = (\frac{0}{2}, \frac{-7 -5}{2})[/tex]
[tex]midpoint = (0, \frac{-12}{2})[/tex]
[tex]midpoint = (0, -6)[/tex]
Answer: The midpoint is (0, -6)
Find the value of the trigonometric ratio. Express your answer as a fraction in lowest terms.
Answer:
12/13
Step-by-step explanation:
We know that cosine is the adjacent side divided by the hypotenuse in a right triangle.
The adjacent side to angle C is BC
The hypotenuse is AC because it is opposite to the right angle
So...
cosine is (BC)/(AC)
36/39
12/13