Answer:
$878.25
Step-by-step explanation:
Continuously compounded interest is:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of compoundings.
Here, P = 560, r = 0.09, and t = 5.
A = 560e^(0.09×5)
A = 878.25
Final answer:
To calculate the future value of an investment compounded continuously, use the formula A = Pert. In this case, the investment will be worth approximately $877.29 in 5 years.
Explanation:
To calculate the future value of an investment compounded continuously, we can use the formula A = Pert, where A is the future value, P is the initial principal, r is the annual interest rate, and t is the time in years. In this case, P = $560, r = 0.09, and t = 5. Plugging these values into the formula, we get:
A = 560e^(0.09⋅5)
A ≈ 560e^0.45
A ≈ 560 ⋅ 1.5662
A ≈ $877.29
Therefore, the investment will be worth approximately $877.29 in 5 years.
Petra jogs 5 miles in 40 minutes. At this rate, how long would it take her to jog 13 miles?
It would take Petra 104 minutes to jog 13 miles
because 40/5 is 8 minutes per mile
you'd multiply 13 miles by 8 minutes
How can I solve this question???
Answer:
144°
Step-by-step explanation:
step 1
Find the measure of the central angle of the regular pentagon
Divide 360 degrees by 5 (the number of sides)
[tex]360\°/5=72\°[/tex]
Let
c----> the center of the pentagon
we know that
m∠ECA=72°
m∠ACB=72°
therefore
m∠ECB=m∠ECA+m∠ACB
substitute the values
m∠ECB=72°+72°=144°
The measure of angle ECB is equal to the degrees that the pentagon rotate
Highly appreciated if someone help me with this question
Answer:
C
Step-by-step explanation:
B and D are equal. You could call their sum = 2x
a = 25 degrees (Vertically Opposite Angles)
C = 95 degrees. (Vertically Opposite Angles)
The total is 360 degrees. So let's add everything up and see what we get.
a+b+c + 25 + d + 95 = 360 degrees. Substitute for the known letters.
25 + x + 95 + 25 + x + 95 = 360 Combine like terms on the left
50 + 2x + 95 + 95 = 360 Combine numbers on the left
240 + 2x = 360 Subtract 240 on both sides
240 - 240 + 2x = 360 - 240 Combine
2x = 120 Divide by 2
x = 60
b = 60
a = 25
a + b =60 + 25 = 85
Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).
The midpoint of the line segment with endpoints (-2, 5) and (4, -9) is found using the midpoint formula and is (1, -2).
Explanation:To find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9), you use the midpoint formula, which is derived from finding the average of the x-coordinates and the y-coordinates of the endpoints respectively.
The midpoint formula is:
( (x1 + x2) / 2, (y1 + y2) / 2 )
Plugging in our given endpoints (-2, 5) and (4, -9) into the formula, it becomes:
( (-2 + 4) / 2, (5 + (-9)) / 2 )
This simplifies to:
( 2 / 2, -4 / 2 )
And finally:
( 1, -2 )
Therefore, the midpoint of the line segment is at coordinates (1, -2).
An athletic coach conducted an experiment to test whether a four week strength training program will reduce the number of muscular injuries that occur during athletic events. The coach randomly selected 30 athletes from several sports and assigned 15 athletes to a four week strength training program. The remaining 15 athletes did not participate in any type of strength training program during the four weeks of the program. After the program was completed, the coach monitored each of the 30 athletes for five athletic events. At the end of this process, he reported that the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program. What can be concluded from the coach's report? A. There is not enough information to make any conclusions regarding the coach's report. B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event. C. It can be concluded that the strength training program increases the number of muscular injuries that occur during an athletic event. D. It can be concluded that the strength training program reduces the number of muscular injuries that occur during an athletic event.
Answer: B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event.
Step-by-step explanation: In the question it states the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program.
From the coach's report, it can be concluded that the strength training program does not reduce the number of muscular injuries that occur during athletic events. This conclusion is drawn from the experiment's finding that both participants in the training program and those who did not participated had the same average number of injuries.
Explanation:The student's question concerns the effectiveness of a strength training program in reducing the number of muscular injuries during athletic events. The coach conducted an experiment with 30 athletes, where half participated in a strength training program and the other half did not. After both groups were monitored for five athletic events, it was found that the average number of muscular injuries was the same for both groups. Hence, from the given information, the correct conclusion would be:
B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event.It's important to note that this conclusion does not necessarily imply that strength training is ineffective in all contexts, just that in this specific experiment, it did not lead to a reduction in injuries. Further, the conclusion does not indicate that the strength training program increases injuries, which eliminates option C. Meanwhile, option D is also incorrect because the data indicates no reduction in injuries.
Which linear inequality is represented by the graph? PLEASE HELP ASAP!!!
Answer: I'm pretty sure it's A!
Answer:
it's A because when you find the slope you fill find 1 over 3 and it's visible in the graph that the intercept is -1.3 so when you connect the function it will give you that the function is bigger or equal than y.
how much would it be worth in 5, 10, 20 years
Answer:
$675
$850
$1200
Step-by-step explanation:
Use formula for simple interest:
A = P (1+rt)
where
A = accrued amount (principal + interest) = what we want to find
P = Principal (initial) amount = Given as $500
r = rate of interest = Given as 7% = 0.07
t = time
For 5 years, t = 5
A = 500 [ 1 + 0.07(5) ] = $675
For 10 years, t = 10
A = 500 [ 1 + 0.07(10) ] = $850
For 20 years, t = 20
A = 500 [ 1 + 0.07(20) ] = $1200
PLEASE HURRY. 55P WRONG ANSWERS GET REMOVED!!!!!!!
1172. 08 in²
Step-by-step explanation:Hi there !
A(prism) = 2(lw + lh + wh) - Ab(cylinder)
= 2(16*11 + 16*11 + 11*11) - πr²
= 2(176 + 176 + 121) - 3.14*16
= 2*473 - 50.4
= 946 - 50.24
= 895.76 in²
A(cylinder) = πr² + 2πr*h
= 3.14*16 + 2*3.14*4*9
= 50.24 + 226.08
= 276.32 in²
A(total) = 895.76in² + 276.32in² = 1172.08 in²
Good luck !
What is the slope of a line is parallel to y = (1/2)x+ 3?
Answer here
Answer:1/2
Step-by-step explanation:
the slope of a line in an equation comes before x
since we know parallel lines have the same slope it is 1/2
Factorise e2 + 4e
pls help me thanks xoxox
Answer:
e =0 or e= -4
Step-by-step explanation:
First we'll equate the given equation with zero then it'll be proper answer and after that it follows like this
By taking e has common
[tex]e(e + 4) = 0 \\ [/tex]
Now,
From this we compare both equation separately and we get
e=0 and e= -4
Note:- If you don't wanna equate the equation with 0 then your answer will be
[tex]e(e + 4)[/tex]
Hope it helps you ...☺
Step-by-step explanation:
Here,
e²+4e
If we take e common we will get,
=e. e+ 4e
= e(e+4)
Which is your final result but you cannot equate it to zero because it is not mentioned in the question. But I think the question is incomplete.
Which of the following points lies on the circle whose center is at the origin and whose radius is 13?
(-5, 12)
W13, 13)
(6.-7)
any point that is on the circle will have a distance of "radius" units, namely 13 units, since the radius is just that.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-5-0)^2+(12-0)^2}\implies d=\sqrt{(-5)^2+12^2} \\\\\\ d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13[/tex]
Final answer:
The point (-5, 12) lies on the circle with a radius of 13 and a center at the origin because it satisfies the equation [tex]x^2 +[/tex] [tex]y^2 = 13^2.[/tex]
Explanation:
The student is asking which point lies on the circle with a center at the origin and a radius of 13. To determine if a point lies on a circle defined by the equation [tex]x^2 + y^2 = r^2,[/tex] where r is the radius, we plug the point's coordinates into the equation and see if they satisfy it.
Let's examine each point:
[tex](-5, 12): (-5)^2 + (12)^2 = 25 + 144 = 169[/tex]
[tex](13, 13): (13)^2 + (13)^2 = 169 + 169 does not equal 169[/tex]
[tex](6, -7): (6)^2 + (-7)^2 = 36 + 49 = 85 does not equal 169[/tex]
Therefore, the point (-5, 12) lies on the circle because it satisfies the equation [tex](-5)^2 + (12)^2 = 13^2.[/tex]
how many cubes were used to make this figure?
Rectangular prism composed of unit cubes. Prism is 5 units by 2 units by 3 units.*
Answer:
I think its 30 I'm not 100% sure tho
Answer:
30
Step-by-step explanation:
To know how many cubes were used to create a resctangular prism you only have to calcute the volume of the rectangular prism, in order to do this you´ll need the next formula:
[tex]BxH[/tex]
Which is base area, multiplied by the height:
5x2= 10 units of base.
The base you multiply it by 3:
10x3=30
The total volume is 30 units, and those are the number of units needed to make the rectangular prism.
a triangle has two sides of lenghts 7 and 12 what value could the length of the third side be check all that apply
Answer:
Third length =
12-7 = 5
12+7 = 19
Third length can be only in this range
5Means the third length must be greater than 5 and less than 19.
Step-by-step explanation:
How many atoms are there in a 5.2-g copper
Answer:
There are [tex]4.93\times 10^{22}[/tex] copper atoms in 5.2 gram of metallic copper.
Step-by-step explanation:
Start by finding the number of moles of copper atoms in that 5.2 gram of metallic copper. Look up the relative atomic mass of copper on a modern periodic table.
Cu: 63.546.In other words, the mass of one mole of copper atoms is 63.546 gram.
[tex]M(\mathrm{Cu}) = \rm 63.546\; g\cdot mol^{-1}[/tex].
How many moles of copper atoms in that 5.2 gram sample?
[tex]\displaystyle n = \frac{m}{M} =\rm \frac{5.2\; g}{63.546\; g\cdot mol^{-1}} = 0.0818305\; mol[/tex].
Now, how many atoms is [tex]\rm 0.0818305\; mol[/tex]?
The Avogadro's Number gives the number of particles in one mole:
[tex]N_A \approx \rm 6.022\times 10^{23}\;mol^{-1}[/tex]. (Encyclopedia Britannica)
There are [tex]6.022\times 10^{23}[/tex] particles (a very large number) in one mole. [tex]\rm 0.0818305\; mol[/tex] of copper atoms will thus contain
[tex]N = n\cdot N_A \approx \rm 0.0818305\; mol\times 6.023\times 10^{23}\;mol^{-1} \approx 4.93\times 10^{22}[/tex]
copper atoms.
Match the vocabulary word with the correct definition.
1. trapezoid
A trapezoid with legs of the same length.
2. bases of a trapezoid
A quadrilateral with at least one pair of parallel sides.
3. legs of a trapezoid
The parallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
The nonparallel sides
Answer:
1. trapezoid
A quadrilateral with at least one pair of parallel sides.
2. bases of a trapezoid
The parallel sides
3. legs of a trapezoid
The nonparallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
A trapezoid with legs of the same length.
Answer:
Trapezoid:A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.
Bases of a trapezoid:The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.
Legs of a trapezoid:The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.
Median of a trapezoid:The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.
Isosceles trapezoid:As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.
Therefore, the right matches are
1. Trapezoid: A quadrilateral with at least one pair of parallel sides.
2. Bases of a trapezoid: The parallel sides.
3. Legs of a trapezoid: The nonparallel sides.
4. Median of a trapezoid: The segment connecting the midpoints of the legs.
5. Isosceles trapezoid: A trapezoid with legs of the same length.
simplify 5^12/ 5^2 x 5
give your answer in power of 5
Answer:
[tex]5^{11}[/tex]
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
Given
[tex]\frac{5^{12} }{5^{2} }[/tex] × [tex]5^{1}[/tex], then
= [tex]5^{(12-2)}[/tex] × [tex]5^{1}[/tex]
= [tex]5^{10}[/tex] × [tex]5^{1}[/tex]
= [tex]5^{(10+1)}[/tex]
= [tex]5^{11}[/tex]
Find the average of –25, –70, 15, –31, –25, and 40.
Question 12 options:
–16
–25
–96
16
Answer:
-16
Step-by-step explanation:
The average of –25, –70, 15, –31, –25, and 40 is -16
To determine the average of the numbers given, we shall find their sum then divide this sum by the number of values;
The sum of the numbers is;
-25-70+15-31-25+40 = -96
We have a total of 6 values, thus the average becomes;
(-96)/6 = -16
Answer: FIRST OPTION.
Step-by-step explanation:
To calculate the average of a set of numbers, we need to add the numbers and divide the sum by the amount of values into that set.
For example, given a set of numbers:
[tex]a,b,c,d[/tex]
The average will be:
[tex]average=\frac{a+b+c+d}{4}[/tex]
Then, the average of the given set of numbers (-25, -70, 15, -31, -25, and 40) is:
[tex]average=\frac{-25+(-70)+ 15+(-31)+(-25)+40}{6}\\\\average=\frac{-25-70+ 15-31-25+40}{6}\\\\average=-16[/tex]
which graph depicts the path of a projectile
Step-by-step explanation:
Step-by-step explanation:
When an object is thrown at an angle with horizontal under the action of gravity is called projectile motion and the object which is thrown is called a projectile. The path followed by the object is parabolic. An object when thrown in upward direction, after reaching maximum height it will come back to ground.
Graph (b) shows the path of a projectile.
Which calculator correctly shows the quotient of
6.47 x 10-15
3.36 * 10-29
Answer:
the second one
Step-by-step explanation:
Answer:
the second one
Step-by-step explanation:
the one that says +14
Find the area of a circle with diameter 18 ft.
Answer:
81 π / 254.469004941 ft²
Step-by-step explanation:
Area of circle = π × r²
Half the diameter = radius
18 ft ÷ 2 = 9 ft
9 ft = radius
Area of circle = π × 9²
Area of circle = 81π
Area of circle = 81 π / 254.469004941
Area of circle =
To find the area of a circle with a diameter of 18 feet, first find the radius (9 feet), then apply the formula A = πr². The area is approximately 254.47 square feet.
To find the area of a circle, you need to use the formula:
A = πr²
Given the circle's diameter is 18 feet, we first need to find the radius. The radius (r) is half the diameter:
r = D / 2 = 18 ft / 2 = 9 ft
Now, substitute the radius back into the area formula:
A = πr² = π(9 ft)² = π(81 ft²)
Using the approximation π ≈ 3.14159, we get:
A ≈ 3.14159 × 81 ft² ≈ 254.47 ft²
Therefore, the area of the circle is approximately 254.47 square feet.
SHORT ANSWER Use the Distributive
Property to write a numerical
expression that is equivalent to
25 + 10.
Answer:
5(5 + 2)
Step-by-step explanation:
The distributive property states that If 2 numbers have a common factor you can divide the common factor out. Similarily, if they share a common factor, you can distribute the common factor into each number in the parenthesis.
Find the factors of 25 & 10:
25: 1, 5, 25
10: 1, 2, 5, 10
Note that the largest common factor is 5. Divide 5 from both number:
(25 + 10)/5 = 5(5 + 2)
5(5 + 2) is your answer.
~
What is an equation bof the line that is perpendicular to y-4=2(x-6);and passes through the point (-3,-5)
Answer:
y+5=-1/2(x+3)
Step-by-step explanation:
as perpendicular,
compare that given eqn with y-y1=m(x-x1),
m1=2
then,
perpendicular case,
m1×m2=-1
m2=-1/2
now,
as the eqn passes through point (-3,-5),
we know,
y-y1=m(x-x1)
then putting value,
y+5=-1/2(x+3)
Answer:
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line.
y - 4 = 2(x - 6) is in this form with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Hence the equation passing through (- 3, - 5) is
y - (- 5) = - [tex]\frac{1}2}[/tex] (x - (- 3)), that is
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line
Suppose the first equation in a system of two linear equations is 12x + 7y = 25. The second equation being which of these will cause the system to have no solution?
A.
12x + 7y = 20
B.
12x + 7y = 25
C.
12x + 9y = 20
D.
12x + 9y = 25
Answer:
A. 12x + 7y = 20
Step-by-step explanation:
Obviously, 12x + 7y cannot both be equivalent to unique [different] quantities.
Option A (12x + 7y = 20) would make the system of linear equations with 12x + 7y = 25 have no solution because the lines would be parallel and never intersect.
Second equation would make a system of linear equations with 12x + 7y = 25 have no solution. A system of linear equations will have no solution if the two lines represented by the equations are parallel, which means they have the same slope but different y-intercepts. Since the first equation is 12x + 7y = 25, we need a second equation with the same coefficients for x and y but a different constant term in order to represent parallel lines.
Option A (12x + 7y = 20) meets the criteria for causing the system to have no solution because it has the same coefficients for x and y as the first equation but a different constant term. This indicates that the lines are parallel and will never intersect, hence no solution exists for this pair of equations.
What is the solution to log (9x)-log2^3= 3?
For this case we have that by definition of properties logarithm is met:
[tex]log_ {b} (x) -log_ {b} (y) = log_ {b} (\frac {x} {y})[/tex]
So, rewriting the expression we have:
[tex]log (\frac {9x} {2 ^ 3}) = 3\\log (\frac {9x} {8}) = 3[/tex]
By definition of logarithm we have to:
[tex]log_ {b} (x) = y[/tex]is equivalent to[tex]b ^ y = x[/tex]
So:
[tex]10 ^ 3 = \frac {9x} {8}\\9x = 8 * 10 ^ 3\\9x = 8 * 1000\\9x = 8000\\x = \frac {8000} {9}[/tex]
ANswer:
[tex]x = \frac {8000} {9}[/tex]
Answer:
bStep-by-step explanation: i got it right on edg
After you rewrite subtraction as addition of the
additive inverse, how can the like terms be
grouped?
[3a2 + (-3a2)] + (-5ab + 8ab) + [b2 + (-2b2)]
[3a2 + (-3a2)] + (-5ab + 8ab) + (b2 + 262)
© (3a2 + 3a2) + (-5ab + (-8ab)] + [b2 + (-262)]
(3a2 + 3a2) + (-5ab + (-262)] + [b2 + (-8ab)]
Answer:
(3a2 + 3a2) + [–5ab + (–8ab)] + [b2 + (–2b2)]
Step-by-step explanation:
Answer: c. (3a^2+3a^2)+[-5ab+(-8ab)]+[b^2+(-2b^2)]
for the second part: =a. 6a^2-13ab-b^2
Step-by-step explanation:
i did it
Identify all sets to which the number belongs. –0.249851765...
Answer:
i. Irrational numbers
ii. Real numbers
Step-by-step explanation:
The given decimal is –0.249851765...
This number does not recur and it does not also terminate.
It belongs to the set of irrational numbers because it cannot be written in the form [tex]\frac{a}{b}[/tex] where [tex]a,b\in R[/tex] and [tex]b\ne0[/tex].
This numbers also belongs to the set of real numbers.
Answer:
irrational
Step-by-step explanation:
Use the converse of the side-splitter theorem to determine
if TU || Rs. Which statement is true?
Answer:
Line segment TU is parallel to line segment RS because 32/36 = 40/45.
Step-by-step explanation:
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The converse theorem states that if TU || RS, then the ratio of the corresponding sides will be constant.
32 / 36 = 40 / 45 = 8 / 9 = constant
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
Then the correct option is A.
The graph is given below.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
A circle is centered at the point (5, -4) and passes through the point (-3, 2).
The equation of this circle is
Answer:
[tex](x-5)^{2} +(y+4)^{2} =10^{2}[/tex]
Step-by-step explanation:
To calculate the formula of a circle that is not in the center fo the graph, you need two things, the point where the cirlce is centered and any point in the circumference, and with this you can calculate the radius, to calculate the first part you just need the next formula:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
Where [tex]x^{c}y^{c}[/tex] are the x and y where the center of the circle is, so you just evaluate with the values you are given:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
[tex](x-(5))+(y-(-4))=r^{2}[/tex]
[tex](x-5)+(y+4)=r^{2}[/tex]
Now that you have the first part, we can calculate the radius, remember taht the radius of any given circumference in the graph is the hypotenuse of the X´s and Y´s that are part of those two points given, so we just calculate it like any hypotenuse:
[tex]c=\sqrt{x^{2}+ y^{2} }[/tex]
To calculate this we would rest to the point in the circumference, the center of the circumference, like this:
[tex]c=\sqrt{(x^{2}-x^{1})^{2}+ (y^{2}-y^{1})^{2} }[/tex]
[tex]c=\sqrt{(-3-5)^{2}+ (2-(-4))^{2} }[/tex]
[tex]c=\sqrt{(-8)^{2}+ (6)^{2} }[/tex]
[tex]c=\sqrt{64+ 36 }[/tex]
[tex]c=\sqrt{100 }[/tex]
[tex]c=10[/tex]
So your radius would be 10, now we just put that into our previous formula:
[tex](x-5)+(y+4)=r^{2}[/tex]
[tex](x-5)+(y+4)=10^{2}[/tex]
So the formula for the circle that is centered at (5,-4) and passes through the point (-3,2) would be:
[tex](x-5)+(y+4)=10^{2}[/tex]
what is the answer to:
-1.5x -3 < 5.5
For this case we have the following expression:
[tex]-1.5x-3 <5.5[/tex]
Adding 3.1 to both sides of the inequality:
[tex]-1.5x <5.5 + 3\\-1.5x <8.5[/tex]
Dividing between -1.5 on both sides of the inequality, keeping in mind that the sign changes direction:
[tex]x> \frac {8.5} {- 1.5}\\x> -5.66666[/tex]
Answer:
[tex]x> -5.66666[/tex]
x> -5.6 periodical number
Answer:
{x| x > -5.667}
Step-by-step explanation:
We have the following inequality[tex]-1.5x -3 < 5.5[/tex]
We must solve the incus for the variable x
[tex]-1.5x -3 < 5.5[/tex]
Add 3 on both sides of inequality
[tex]-1.5x -3 +3 < 5.5 +3\\\\-1.5x<5.5 +3\\\\-1.5x<8.5[/tex]
Multiply by -1 both sides of the inequality
[tex](-1)*(-1.5)x<8.5*(-1)\\\\1.5x>-8.5[/tex]
Divide between 1.5 both sides of the inequality
[tex]\frac{1.5}{1.5}x>-\frac{8.5}{1.5}\\\\x > -5.667[/tex]
The answer is:
[tex]x > -5.667[/tex]
{x| x > -5.667}
What is the greatest common factor of 8m, 36m3, and 12
ANSWER
GCF=4
EXPLANATION
The given monomials are:
[tex]8m = {2}^{3} m[/tex]
[tex]36 {m}^{3} = {2}^{2} \times {3}^{2} {m}^{3} [/tex]
[tex]12 = {2}^{2} \times 3[/tex]
The greatest common factor is the product of all the least powers of the common factors.
We can see that:
[tex] {2}^{2} [/tex]
is the common to all the factors.
Therefore the greatest common factor is
[tex] {2}^{2} = 4[/tex]
Answer: [tex]GCF=4[/tex]
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of 8m, 36m³, and 12, you need to descompose them into their prime factors. Then:
[tex]8m=2*2*2*m=2^3*m\\\\36m^3=2*2*3*3*m^3=2^2*3^2*m^3\\\\12=2*2*3=2^2*3[/tex]
You can observe that the common factor with the lowest exponent is the following:
[tex]2^2[/tex]
Therefore, the Greatest Common Factor (GCF) of 8m, 36m³, and 12 is:
[tex]GCF=2^2\\GCF=4[/tex]