Answer:
The smallest composite number for [tex]n[/tex] is 24, which is the product 2 and 12.
Step-by-step explanation:
A composite number is an integer that is not a prime number, that is, a number that can be divided only by one and itself. Let be [tex]n[/tex] the smallest composite number such that there are two positive integers [tex]x[/tex], [tex]y[/tex] such that [tex]x - y = 10[/tex] and [tex]x\cdot y = n[/tex]. [tex]n[/tex] is a positive integer, since both integers are positive. Then, we can use the following formula:
[tex](y+10)\cdot y = n[/tex]
[tex]y^{2}+10\cdot y = n[/tex]
[tex]y^{2}+10\cdot y - n = 0[/tex] (1)
We obtain the roots of this second order polynomial by means of the Quadratic Formula:
[tex]y = \frac{-10\pm \sqrt{10^{2}-4\cdot (1)\cdot (-n)}}{2}[/tex]
[tex]y = -5\pm \sqrt{25+n}[/tex] (2)
Given that [tex]y > 0[/tex], we must observe the following inequation:
[tex]-5\pm \sqrt{25+n}>0[/tex] (3)
[tex]\sqrt{25+n} > 5[/tex]
[tex]25 + n > 25[/tex]
[tex]n > 0[/tex]
Let is find the values of x and y by iterative means:
x = 11, y = 1
[tex](11)\cdot (1) = 11[/tex]
11 is not a composite number, but a prime number.
x = 12, y = 2
[tex](12)\cdot (2) = 24[/tex]
24 is a composite number, which contains the following product of prime numbers:
[tex]2^{3}\cdot 3 = 24[/tex]
The smallest composite number for [tex]n[/tex] is 24, which is the product 2 and 12.
The image point of A after a translation right 4 units and down 4 units is the point B(12, – 7). Determine the coordinates of the pre-image point A.
Answer:
(8, –3)Step-by-step explanation:
Translation right or left means change of the x-coordinate.
Translation up or down means change of the y-coordinate.
Translation right or up means adding.
Translation left or down means subtracting.
[tex]A=(x_A, y_A)\quad\rightarrow\quad B=(x_A+4,\,y_A-4)\\\\x_A+4=12\qquad\qquad y_A-4=-7\\\\x_A=12-4\qquad\qquad y_A=-7+4\\\\x_A=8\qquad\qquad\qquad y_A=-3\\\\A=(8,-3)[/tex]
amanda had to pay sales tax on a new iphone case she purchased last week. The iphone case was 35.00 and she pid 2.45 in taxes, what percent of the original price did she pay in taxes?
HELP
Answer:
7%
Step-by-step explanation:
[tex]\frac{2.45}{35} = \frac{x}{100}[/tex]
[tex]2.45*100[/tex] and [tex]35x[/tex]
[tex]\frac{245}{35} = \frac{35x}{35}[/tex]
[tex]245/35=7[/tex]
What is the approximate area of the circle shown below?
A. 94 cm2
B. 11,310 cm2
C. 2827 cm2
D. 188 cm2
Please help
Answer:
Step-by-step explanation:
we have the diameter =60 cm, the radius is 60/2=30 cm
A circle is 3.14*r^2=2827 cm^2
Answer: C. 2827 cm2
Step-by-step explanation:
The area of a circle is calculated by pir^2; r = the radius
In the diagram, the diameter is provided. The radius is half of the diameter. 60/2 = 30, so the radius is 30 cm.
Plug these values into the formula
A = 3.14*30^2
A = 2827.43, which would round to 2827 cm2
HELP ASAP FOR BRAINLIEST
Answer: i am pretty sure its the first one
Step-by-step explanation:
i don't know for sure
the order of the surd 6 √2187 after simplification is
Answer:
[tex]n = 162[/tex]
Step-by-step explanation:
Given
[tex]6\sqrt{2187[/tex]
Required
Determine the order of the surd
If a surd is represented as [tex]n\sqrt{r[/tex], then the order of the surd is [tex]n[/tex]
[tex]6\sqrt{2187[/tex]
Express 2187 as [tex]3^6 * 3[/tex]
[tex]6\sqrt{2187} = 6\sqrt{3^6 * 3}[/tex]
Split the surd
[tex]6\sqrt{2187} = 6\sqrt{3^6} * \sqrt{3}[/tex]
Apply the following law of indices:
[tex]\sqrt{a} = a^{\frac{1}{2}}[/tex]
The expression becomes:
[tex]6\sqrt{2187} = 6 * 3^{\frac{6}{2}} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 3^{3} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 27 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 \sqrt{3}[/tex]
By comparing [tex]162 \sqrt{3}[/tex] to [tex]n\sqrt{r[/tex], we can say that:
[tex]n = 162[/tex]
[tex]r = 3[/tex]
Conclusively, the order of the surd is 162
whats 9 + 10? if you get it right brainliest
Answer:
19.
Step-by-step explanation:
Select the correct answer from each drop-down menu.
April and Jasmine found the volume of the rectangular prism below.
5x8x6
April packed the rectangular prism with centimeter cubes to find the volume. She packed 4 layers of centimeter cubes. Each layer had 8 rows with 6 cubes in each row.
Jasmine multiplied the side lengths to find the volume.
One of the students made a mistake, and her work will result in an incorrect volume.
The student who made the mistake was
.April or Jasmine
Her mistake was
she did not multiply the correct numbers
she did not pack enough layers of centimeter cubes
she should have added the length sides
She packed too many centimeter cubes in each layer
The correct volume of the rectangular prism is cubic centimeters. 240 or 200 or 270
Answer:
AprilShe did not pack enough layers of centimeter cubes240 cubic centimetersStep-by-step explanation:
Dimensions of the prism is 5x8x6
April made a mistake, she packed 4 layers of unit cubes instead of 5 layers
Correct volume of the prism is:
5*8*6 = 240 cm³Correct answer choices:
AprilShe did not pack enough layers of centimeter cubes240 cubic centimeters(01.02 MC)Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?
1.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 1.
2.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 5.
3.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 5.
4.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 1.
Answer:
I think the answer is 1. The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative. So the answer is A
hope this helps sorry if it wrong
pls let me now if right or wrong
The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1. Option A is correct.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
4 + (- 5)
The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1.
Thus, option A is correct.
Learn more about number line here:
brainly.com/question/17683084
#SPJ2
Write the equation of the line that is parallel to y = -6x + 10 and crosses the y-axis at -4.
Answer:
y= -6x-4
Step-by-step explanation:
As two lines are parallel, their slope is same which is -6
Now, use:y-y1=m(x-x1)
y-(-4)= -6(x-0) (y1=-4,x1=0, cause the equation of y axis is x=0)
So,y= -6x-4
It is 49,280 yards from Topeka to Tonko. How many miles
is this?
Answer:
Step-by-step explanation:
1 yard = 0.000568 miles
49280 yards = 28 miles
1 mile = 1,760 yards
Divide total feet by 1760
49,280 / 1760 = 28 miles.
(ii) Use the quadratic formula to solve 4x2 +11x-300 = 0.
Show all your working and give your answers correct to 2 decimal
places.
... or x =
[4]
mm
Solve the following equation: -3 = 1 3/5 + m.
-2 3/5
-4 3/5
-4 2/5
-1 2/5
Answer:
-4 3/5
Step-by-step explanation:
I subtracted 1 3/5 from -3 and got -4 3/5. I also added 1 3/5 + -4 3/5 to check my work and it is correct.
Solve.
−35x=18
−30
−1045
1045
30
Answer:
if you're trying to solve -35x= 18 .. then do the following
Step-by-step explanation:
x = -18 / 35
x= -0.5142857143
I'm guessing that b/c the answer is not an easy number that you probably are trying to do something else. .. ask again :)
Answer:
−30
Step-by-step explanation:
Will give crown help
Answer:
There are 5 spaces between point J and I
Point J is at (-7,-2)
Point I is at (-2,-2)
They have the same y value, but a difference of 5 in the x value. So, they are 5 units apart.
I WILL MARK BRAINLIEST!
A cylindrical well is 20 meters deep and has a diameter of 1.5 meters. Approximately how many cubic meters of soil were dug out to make the well? (Use π = 3.14.) (5 points)
11.78 cubic meters
35.33 cubic meters
121.20 cubic meters
141.30 cubic meters
Answer:
35.33
the drill use the volume formula for a cylinder then plug in the numbers
Please help! Divide. Write the quotient in lowest terms.
HELP I WILL GIVE MANY THX AND BRAINLIST (it says high school but im in middle)
what is 5⁴ in expanded form
Answer:
5 * 5 * 5 * 5
Step-by-step explanation:
=625
sarah has a rope that is 36 feet long she is cutting it into 6 foot pieces to make jump ropes how many jump ropes can sarah make ?
Answer:
she can make 6 jump ropes
This is the one that will decide my note, help once more please
Answer: x = 17
Step-by-step explanation:
180 - 94 = 86
So all the inside angles of a triangle = 180
180 - 86 - 60 = 34
34/2 = 17
Answer:
it's answer is 17
Step-by-step explanation:
we know exterior angle of a triangle is equal to the sum of two opposite interior angles. So,
2x + 60° = 94°
2x = 94° - 60°
2x = 34°
x = 34° /2
x = 17°
EXPERTS OR ACES PLEASE ANSWER THIS FAST DUE IN 2 MIN 50 POINTS
Answer:
24 blocks
Step-by-step explanation:
b = 2(9) + 6b = 18 + 6b = 24A boy wants to purchase 1,400 green marbles. If there are 70 green marbles in each bag, how many bags of marbles should the boy buy?
Answer:
20 bags
Step-by-step explanation:
1400/70
Answer:
20 bags
Step-by-step explanation:
1400 ÷ 70 = 20
I don’t know how to do this
Answer:
the following points: (6,-1),(2,-4), and (-2,3)
Step-by-step explanation:
imagine that the y axis is a mirror. Everything that happens is reflected. So (1,2) becomes (-1,2) so your three points are (-6, -1),(-2,-4), and (2,3) when you reflect them, you get the following points: (6,-1),(2,-4), and (-2,3)
Which boat was farther from the dock at the beginning and which traveled more quickly
Answer:
Nvm
Step-by-step explanation:
Johns boat was 30 miles away. It traveled 20 miles in 5 hours (50-30 = 20)
20/5 = 4
It traveled at 4 miles per hour.
The equation for Roberta’s boat multiplied 5 by x( number of hours) so this means her boat is traveling at 5 miles per hour.
Then 25 gets added at the end, this means her boat was 25 miles away at the beginning.
Johns boat was further away at the beginning and Robertas boat is traveling faster.
Yyhhjfffghjjgdrttyhhhftthvfrtgvfffgf
Answer: So the star equals 4 and the triangle equals 1
Step-by-step explanation:
Which is a solution to the equation 7g-2=47
Answer:
g=7
Step-by-step explanation:
7g-2=47
+2 +2
7g=49
÷7 ÷7
g=7
Which of the following best describes an Extraneous Solution?
Answer:
An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.
Step-by-step explanation:
At a computer store, the package of the DVDs sell for $15 each. One customer buys $120 worth of the DVDs.
Write an equation to model the number of the packages of the DVDs the customer bought, and then solve the equation. Plus, I need help with question number 9. A and B of Solve Simple Equation Word Problem will be marked as brainliest if your answer fully completed with complete step-by-step explanation! :)
Answer:
The customer bought 8 DVDs for $120.00
Step-by-step explanation:
120*15=8 DVDS or as a ratio 8:1
A type of opinion based on observation and evidence.
Answer:
hypothesis
Step-by-step explanation:
Answer:
It is a hypothesis
Step-by-step explanation:
u gather evidence and based on the info u have, u make an opinion (hypothesis)
What is the probability that Mark and Bobby will both choose mushrooms?
Answer: choose mushrooms out of what?
Evaluate x+y when x= −4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form.
Answer:
-7/15
Step-by-step explanation:
=-4/5 + 1/3
=(-12+5)/15
=-7/15
Answer:
-7/15
Explanation:
x + y
-4/5 + 1/3
-12/15 + 5/15
= -7/15