[tex]\displaystyle\\\text{Decompose numbers into prime factors.}\\\\32=2^5\\\\48=2^4\times3\\\\64=2^6\\\\\text{greatest common divisor (gcd)~}~=2^4=\boxed{\bf16 m}\\\\\boxed{\text{\bf The maximum possible length of each wire cut is 16 m.}}[/tex]
The maximum possible length for each cut of wire that Mrs. Agustin can make from the 32m, 48m, and 64m wire coils is 16m.
Explanation:In this problem, Mrs. Agustin is aiming to cut three different lengths of wires into equal parts. Therefore, the maximum possible length of each cut of wire can be calculated by finding the greatest common divisor (GCD) of the lengths of the three wires. The lengths of the wire coils are 32 m, 48 m, and 64 m. The GCD of these numbers is 16 m.
Thus, the maximum possible length of each cut wire would be 16 m.
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How to do solve this?
4x^2(5x^4 / 2x^2)
Answer:
4x^2(5x^4 / 2x^2)= 10 x^4
Step-by-step explanation:
We want factorize the expression 4x^2(5x^4 / 2x^2)
And to do this, we need to remember key properties of exponents.
Those are:
[tex]x^{m} / x^{n} = x^{m-n}[/tex]
[tex]x^{m} * x^{n} = x^{m+n}[/tex]
So
4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4
Enter the correct answer in the box.
Cheryl is taking an online test that gives her instant results. After answering 16 questions, the test revealed that 10 were answered correctly. She
then answered I consecutive questions correctly and achieved her goal of 80% accuracy, Write an equation that can be used to determine how
many questions she answered correctly to reach her goal.
sin cos tan sin costant
na Big
λ μ ρ φ
1-
CSC seccot log log. In
L
.
0.80 =
Reset
Next
Answer:
(L + 10)/(L + 16) = 0.8
Step-by-step explanation:
She needs to answer L more questions to get a grade of 80%.
When she answers L more questions correctly, she will have answered L + 10 questions correctly.
The total number of questions will be L + 16.
L + 10 must be 80% of L + 16
(L + 10)/(L + 16) = 0.8
Cheryl must use the equation 0.80 = (10 + I) / (16 + I) to determine how many consecutive questions she needs to answer correctly to reach her goal of 80% accuracy on her test.
Cheryl has answered 16 questions on her online test with 10 correct responses. To achieve her goal of 80% accuracy, she must determine how many additional questions she must answer correctly in a row.
To find the necessary total number of correct answers (T) for 80% accuracy, we use the equation:
0.80 = (10 + I) / (16 + I)
where I represents the number of consecutive questions Cheryl answered correctly after the initial 16 questions.
A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water.
Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]
Step-by-step explanation:
First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1) by the denominator (which is 2) of the fraction:
[tex]\frac{1}{2}=0.5[/tex]
Now you must add 0.5 to the whole number part. Then:
[tex]1+0.5=1.5[/tex]
In order to find the ratio of cleaner to water, you must divide 1.5 cups of cleaner by 12 cups of water.
Therefore, the ratio is:
[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]
Write the equation of the line that passes through the points (7, –4) and (–1, 3), first in point-slope form, and then in slope-intercept form.
Final answer:
The equation of the line through (7, -4) and (-1, 3) has a slope of -7/8. It can be written in a point-slope form as y + 4 = -7/8(x - 7), and in slope-intercept form as y = -7/8x + 25/8.
Explanation:
To write the equation of the line that passes through the points (7, –4) and (–1, 3), the first step is to find the slope of the line. The slope (m) is given by the rise over run, which is the change in y divided by the change in x:
m = (3 - (-4)) / (-1 - 7) = 7 / -8 = -7/8Now that we have the slope, we can use the point-slope form which is given by the formula:
y - y1 = m(x - x1)We can choose one of the points for x1 and y1; let's use (7, -4):
y - (-4) = -7/8(x - 7)Therefore, the point-slope form of the line is:
y + 4 = -7/8(x - 7)Now, to convert this into the slope-intercept form (y = mx + b), we just solve for y:
y = -7/8x + 7/8 × 7 - 4After simplifying the constant term:
y = -7/8x + 25/8The slope-intercept form is y = -7/8x + 25/8, where -7/8 is the slope and 25/8 is the y-intercept.
If two angles are complementary and one of them is 13º, what is the measure of the other angle?
A.73
B.77
C.63
D.13
Final answer:
The measure of the other angle that is complementary to a 13º angle is 77º.
Explanation:
If two angles are complementary, it means they add up to 90 degrees. In this case, one angle is given as 13º. To find the measure of the other angle, we subtract the given angle from 90º because complementary angles sum up to 90 degrees.
So, if we let x represent the measure of the other angle, the equation becomes:
13° + x = 90°
To find x, we subtract 13 from both sides:
The calculation would be:
90º - 13º = 77º.
Therefore, the measure of the other angle is 77º.
Hence, the correct answer is:
B. 77
simplify: (8 2/3^4)
Answer:
Simplify:
[tex](8\frac{2}{3} )^4[/tex]
Step-by-step explanation:
[tex](8\frac{2}{3})^4 =(\frac{26}{3} )^4=\frac{456976}{81}[/tex]
Answer:
The answer is
650/81
Step-by-step explanation:
I think this is a better representation
Of the given expression
(8 2/3^4)
To solve the problem let us perform a step by step operation
Step one
Let's us solve the bracket terms first
=(8 2/3^4)
3⁴= 3*3*3*3=81
=(8 2/81)
=Simplifying we have
=((81*8)+2)/81
=(648+2)/81
=650/81
What is the only even prime number?
Answer:
2 is the only even prime number.
Step-by-step explanation:
Two is the only even prime number. It's the only even number that can be divided by only itself (2) and one.
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the y-intercept of the line perpendicular to the line y = -x + 1 that includes the point (4, 1)?
Answer:
-3
Step-by-step explanation:
If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3
Find the measure of the numbered angle.
Select one:
A. 115
B. 125
C. 120
D. 130
Answer:
Option B 125°
Step-by-step explanation:
In this problem we need to calculate the measure of angle ∠6
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
see the attached figure to better understand the problem
∠6=(1/2)[arc AB+arc CD]
(arc AB+arc CD)=360°-(60°+50°)=250°
substitute
∠6=(1/2)[250°]=125°
A wooden pole is 20 m high. A steel wire is tied to the top of the pole and fixed to the ground. If the angle made by the
wire with the ground is 60°, find the length of the steel wire.
Answer:
23.09 meters.
Step-by-step explanation:
Sin(60) = opposite / hypotenuse = pole / steel wire
pole = 20 m
angle = 60 degrees.
sin(60) = 20/ hypotenuse multiply both sides by the hypotenuse
hypotenuse * sin(60) = 20 divide by sin(60)
hypotenuse = 20 / 0.866 do the division
hypotenuse = 23.09
The steel wire = 23.09 meters.
Choose the correct translation for the following statement.
It is at most ten.
x < 10
x ≤ 10
x > 10
x ≥ 10
Answer:
[tex]x\leq10[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase "It is at most ten" is equal to
[tex]x\leq10[/tex]
All real numbers less than or equal to 10 (the number 10 is included)
The solution of this inequality is the interval -----> (-∞,10]
Answer:
B
Step-by-step explanation:
Find the value of 1.85+38*4.1
Answer:
157.65
Step-by-step explanation:
38*4.1=155.8
155.8+1.85=157.65
For this case we must find the value of the following expression:
[tex]1.85 + 38 * 4.1 =[/tex]
According to the PEMDAS algebraic resolution method, multiplications must be made before the addition. So, we have:
[tex]1.85 + 155.8 =[/tex]
Adding we have:
157.65
Answer:
157.65
The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original
number. Determine the original number.
Let t = the tens digit, u = the units digit, and u + t = 16. Which of the following equations would complete the system?
Answer:
10u+t=18+10t+u
(If this doesn't match one of the equations, please post your options so I can put it in the form of one of your options.)
Step-by-step explanation:
Let there be a number [tu] where t is the tens and u is ones digit.
t+u=16.
Now we reverse the number [ut] is 8 more than [tu].
[ut]=18+[tu]
So [ut]=10u+t because u is the tens and t is the ones digit
and [tu]=10t+u because t is the tens and u is the ones digit.
The equation you are looking for is
10u+t=18+10t+u.
Let's solve it just for fun:
Subtract u on both sids:
9u+t=18+10t
Subtract 10t on both sides:
9u-9t=18
Divide both sides by 9:
u-t=2
The system is:
u-t=2
u+t=16
--------------add!
2u =18
u=9
If u=9 and u+t=16, then t=7.
To the original number is 79.
The new number is 97 (is this 18 more than the other; yep).
Answer:
97.
Step-by-step explanation:
The price of a concert ticket was $85.00 two decades ago. A report says that a concert ticket is now 250% of what it was 20 years ago, how much would it cost today? Express answer rounded to the nearest cent.
Answer: $212.5
Step-by-step explanation:
250% = 2.5
So we multiply 85.00 by 2.5
85*2.5=212.5
So it is $212.5
Answer:
your answer is $212.5
Step-by-step explanation:
The problem refers to triangle ABC. Find the area of the triangle. Round to three significant digits. B = 9° 20', C = 80° 40', b = 2.92 ft
Answer:
Area of the triangle is 25.9 feet²
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°
∵ b = 2.92 feet
- b is the side opposite to angle B
∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°
- Lets find c the side opposite to angle C by sing the sine rule
∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]
∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]
- By using cross multiplication
∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]
- The area of the triangle = 1/2 (b)(c)sin∠A
∵ The sum of the interior angles of a triangle is 180°
∴ m∠ A + m∠ B + m∠ C = 180°
∵ m∠ B = (28/3)°
∵ m∠ C = (242/3)°
∴ m∠ A + 28/3 + 242/3 = 180
∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides
∴ m∠ A = 90°
∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)
∵ sin(90) = 1
∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²
* Area of the triangle is 25.9 feet²
Lola tossed a coin twice. She made a tree diagram to show the possible outcomes. Which tree diagram shows the sample
Answer:
Its C. XD sorry i just answered this.
Step-by-step explanation:
Hope this helped again! :3
Answer:
Each path in the diagram is a possible outcome with a probability of 1/4. The sum of all paths should equal 1.
The answer is C.
what can you conclude about the survey
I WILL MARK YOU BRAINLIEST
full questions and answer options above
Answer: G.
Step-by-step explanation: When reading the choices F & J will make you say : "Well F is not true because look at the amount of men compared to women. And J, the choice is unbiased doesn't refers to any kind of opinion based reponse so I'll cross 'em off immediatly". The leave you with G & H H is true but it's also opinion based reponse, and G told you that more men are surveyed than women an it's true because look at the sport section! High off top! But still more than women even if the minivans section is little of men but women also so fair and square!
- I'm sorry this is so long. Just comment if you have questions :)
The sum of one third a number and 4 is at the most the sum of twice that number and 12
Answer:
1/3x+4 ≤ 2x+12
Step-by-step explanation:
x ≤ -24/5
Answer:
4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
Step-by-step explanation:
Given : The sum of one third a number and 4 is at the most the sum of twice that number and 12.
To find : Write expression .
Solution : We have given statement
According to question :
Let the number = x
One third of a number = [tex]\frac{1x}{3}[/tex].
Sum of one third of number and 4 = 4 + [tex]\frac{1x}{3}[/tex].
Twice a number = 2x
Sum of twice that number and 12 = 2x + 12
So, sum of one third a number and 4 is at the most the sum of twice that number and 12.
4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
greater than equal to sign for at most.
Therefore, 4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
what are all the possible rectangles with whole-number side
lengths that have a perimeter of 10 units.
Answer:
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
Step-by-step explanation:
The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.
We have that P=10, so 10=2L+2W.
10=2L+2W
10=2(L+W) By factoring using the distributive property.
2(5)=2(L+W) I factored 10 as 2(5).
If 2(5)=2(L+W), then 5=L+W.
Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.
I think they want natural numbers {1,2,3,4,...}. This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.
So now looking for numbers from this set that satisfy: L+W=5.
L+W=5
1+4=5
4+1=5
2+3=5
3+2=5
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
Find the product.
(y-3)(y-4)=
Answer:
y^2+12-7y
Step-by-step explanation:
(y-3)(y-4)
I will split it up for us
y*y= y^2
-3*y= -3y. \
y*-4= -4y. / -7y
-3*-4= 12
y^2+12-7y
The product of (y-3)(y-4), is y^2 - 7y + 12.
To find the product of (y-3)(y-4), we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials.
First: Multiply the first terms of each binomial: y × y = y^2.
Outer: Multiply the outer terms: y × -4 = -4y.
Inner: Multiply the inner terms: -3 × y = -3y.
Last: Multiply the last terms of each binomial: -3 × -4 = 12.
Adding these products together, we get: y^2 - 4y - 3y + 12. Simplifying by combining like terms, the final product is: y^2 - 7y + 12.
Line CD passes through points (0, 2) and (4.6). Which equation represents line CD?
O y=2x-2
O y=28=2
O y=x+2
O y=x-2
Answer:
y = x + 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
============================================
We have the points (0, 2) → b = 2 and (4, 6).
Calculate the slope:
[tex]m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1[/tex]
Substitute the values of the slope and the y-intercept to the equation of a line:
[tex]y=1x+2[/tex]
Answer:
y=x+2
Step-by-step explanation:
find the missing factor in exponential form 33^9 = 11^9 * blank
Answer:
3^9 * 11^9
Step-by-step explanation:
33^9 =
We know that (ab)^c = a^c * b^c
(33)^9 = (3*11)^9 = 3^9 * 11^9
SOLVE y = 3x – 2 x – y = 4 BY USING SUBSTITUTION!! SHOW ALL WORK! HELPPP!
The value of x = -1
The value of y = -5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be A
The value of A is
y = 3x - 2 be equation (1)
Let the second equation be B
The value of B is
x - y = 4 be equation (2)
On simplifying equation (2) , we get
Adding y on both sides of the equation , we get
x = y + 4 be equation (3)
Substituting the value of x in equation (1) , we get
y = 3x - 2
y = 3 ( y + 4 ) - 2
y = 3y + 12 - 2
y = 3y + 10
Subtracting y on both sides of the equation , we get
2y + 10 = 0
Subtracting 10 on both sides of the equation , we get
2y = -10
Divide by 2 on both sides of the equation , we get
y = -5
Substitute the value of y in equation (3) , we get
x = y + 4
x = -5 + 4
x = -1
Therefore , the value of x is -1 and the value of y is -5
Hence , The value of x = -1
The value of y = -5
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Final answer:
To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.
Explanation:
To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.
Step 1: Isolate y in the first equation.
We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.
Step 2: Substitute y into the second equation.
Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.
Step 3: Solve for x.
Now, we simplify and solve for x:
x - 3x + 2 = 4
-2x + 2 = 4
-2x = 4 - 2
-2x = 2
x = -1
Step 4: Substitute x back into the first equation to solve for y.
Using x = -1 in the first equation y = 3x - 2, we get:
y = 3(-1) - 2
y = -3 - 2
y = -5
Therefore, the solution to the system of equations is x = -1 and y = -5.
Write as an equation: Patrick age increased by 8 years is 18 years
Let P = Patrick's age
P + 8 = 18
The equation is P + 8 = 18
Let P = Patrick's age
What's an equation example?An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.
A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.
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20 POINTS!!! Please Help
At a space exploration center, astronauts are training on a human centrifuge that has a diameter of 70 feet.
a. The centrifuge makes 72 complete revolutions in 2 minutes. What is the angular velocity of the centrifuge in radians per second? What distance does an astronaut travel around the center each second?
b. Acceleration is the rate of change of velocity with time. An object
moving at a constant velocity v in circular motion with a radius of r 2
has an acceleration a of a = _v_. What is the astronaut’s acceleration? r
(Note that the acceleration will have units of feet per second squared.)
c. One“g”istheaccelerationcausedonEarth’ssurfacebygravity.This acceleration is what gives you your weight. Some roller coasters can produce an acceleration in a tight loop of 5 or even 6 g’s. Earth’s gravity produces an acceleration of 32 ft/s2. How many g’s is the astronaut experiencing in the centrifuge?
The astronaut is experiencing approximately 6.21 g's in the centrifuge.
a. To find the angular velocity of the centrifuge in radians per second, we first need to convert the number of revolutions per minute to revolutions per second. Since there are 60 seconds in a minute, the angular velocity (ω) can be calculated as follows:
Angular velocity (ω) = (Number of revolutions per minute) / 60
Given that the centrifuge makes 72 complete revolutions in 2 minutes:
ω = 72 / 2 / 60 = 1.2 revolutions per second
Next, to find the distance an astronaut travels around the center each second, we can use the formula for the circumference of a circle:
Circumference = π × diameter
Circumference = π × 70 feet
Circumference ≈ 220 feet
Distance traveled each second = Circumference × ω
Distance traveled each second = 220 feet × 1.2 revolutions per second ≈ 264 feet
So, the angular velocity of the centrifuge is approximately 1.2 radians per second, and an astronaut travels around the center approximately 264 feet each second.
b. The acceleration (a) of an object moving in circular motion with a constant velocity (v) and a radius (r) is given by the formula:
[tex]a = v^2 / r[/tex]
Since the astronaut is moving at a constant velocity around the center of the centrifuge, we can use the same formula to find their acceleration. The velocity of the astronaut is the distance traveled each second (264 feet) and the radius of the centrifuge is half of its diameter (70 feet / 2 = 35 feet):
Acceleration (a) = (264 feet per second)^2 / 35 feet ≈ 198.86 feet per second squared
So, the astronaut's acceleration is approximately 198.86 feet per second squared.
c. To find how many g's the astronaut is experiencing in the centrifuge, we need to compare their acceleration with the acceleration due to gravity on Earth (32 feet per second squared). One g is equivalent to the acceleration due to gravity.
Number of g's = Acceleration (astronaut) / Acceleration due to gravity on Earth
Number of g's = 198.86 feet per second squared / 32 feet per second squared ≈ 6.21 g's
So, the astronaut is experiencing approximately 6.21 g's in the centrifuge.
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Use the recursive formula to answer the question.
a(1)=20 a(n)=a(n)-1-5
What is the 4th term in the sequence?
Answer:
5
Step-by-step explanation:
[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]
The circumference of a circle is 20 π.what is the radius of this circle
Answer:
The correct option is 10....
Step-by-step explanation:
The formula of circumference of the circle is:
C = 2πr
where C is the circumference of the circle
r = radius
In this question we have given the circumference and we have to find out the radius:
Thus substitute the values in the formula:
C = 2πr
20π= 2πr
Move 2π to the L.H.S.
20π/2π = r
Cancel out π by π and 20/2 by the table of 2
Therefore we have:
10=r
Thus the correct option is 10....
Answer is provided in the image attached.
Rhombus EFHS is shown. What is the measure of HGJ? Help me ASAP
Answer:
Id say 35
Sorry of im wrong :{
Sound travels along a telephone cable at 1.91 * 10^8 ms^-1 .How long does it take Tetsuo's voice to travel from his office phone in Tokyo to his wife's phone 3740m away?
Answer:
1.958 * 10^-5 seconds or 0.00001958 seconds.
Step-by-step explanation:
3740 = 3.74 * 10^3 in scientific notation.
Time = distance / speed.
= 3. 74 * 10^3 / 1.91 * 10^8
= 1.958 * 10^-5 seconds.
It takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away using the speed of sound in telephone cables.
Explanation:SolutionTo find the time it takes for sound to travel a certain distance, we can use the formula time = distance / speed. In this case, the speed of sound along the telephone cable is 1.91 * 10^8 ms⁻¹ and the distance is 3740m.
So the time = 3740 / 1.91 * 10^8 = 1.96 * 10^-5 seconds.
Therefore, it takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away.
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g(x) = 5x - 12. What is g(8)?
Answer:
28
Step-by-step explanation:
Substitute 8 for x in g(x) = 5x - 12:
g(8) = 5(8) - 12 = 28
By using PEDMAS rule, g(8) = 28
What is PEDMAS rule?PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.
Given
g(x) = 5x - 12
Substitute x = 8
g(8) = [tex]5\times 8-12[/tex]
Calculate the product
g(8) = [tex]40-12[/tex]
Calculate the sum or difference
g(8) = 28
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