In linear equation, plant b height will exceed the height of plant a after 16 days.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Plant a: 5 cm tall and rate of change = 2.5 cm per month
Plant b: 4 cm tall and rate of change = 4.5 cm per month.
Now we have to form the linear equations.
Plant a:
y = 2.5x + 5, where y is the total height and "x" be the number of months.
Plant b:
y = 4.5x + 4 , where y is the total height and "x" be the number of months.
Now we have to when the height of the plant a and plant b are the same.
To do that, we have to equivate both the equations and find x.
2.5x + 5 =4. 5x + 4
Isolate the variables terms and constants.
4.5x - 2.5x = 5 - 4
2x = 1
Dividing both sides by 2, we get
x = 1 ÷ 2
x = 0.5 months.
So after 15 days, the height of the plant a and plant b are the same.
Therefore, plant b height will exceed the height of plant a after 16 days.
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A belt connects two pulleys. Larger pulley has a radius of 60cm and the smaller pulley has a radius of 20cm. The smaller pulley runs at 48 revolutions per min
a) how many revolutions per minute does the larger pulley run at? [hint: find the circumference of each pulley]
(i got 16 rev per min i don't know if that's correct)
b) find angular speed of the smaller pulley in radians per min
c) find the angular speed of the larger pulley in radians per min
d) find the speed of the smaller pulley in cm per min
Therefore the solution to this question of 2 pulleys is )16 rpm
b)360 rad/min c)39.6 rad/min d) 7200cm/min
What is Angular speed?A pseudovector used in physics to express how quickly an object's angular position or orientation changes over time is called an angular velocity, rotational velocity, or angular frequency vector.
For the smaller pulley, it does 48 rpm (revolutions per minute) each revolution is 360 degrees. This indicates that the pulley completes one revolution every second .
radians / π = degrees / 180
radians = πx 360 / 180 = 2 π radians per second
The distance covered by both pulleys is equivalent for the larger pulley.
then d1 = d2
every second, small pulley covers a distance of 40π (small pulley circumference) = d1
d2 = 40π = 120π (large pulley circumference) x factor (f)
f = 1/3
a) the revolutions per min by larger pulley=16 rpm
b) the speed of smaller pulley = 3*2π=6π=6rad/sec=360rad/min
c) then speed of the large pulley = 1/3 * 2π = 2/3 π = 0.66 rad/sec=39.6rad/min
d)the speed of smaller pulley=7200 cm/min
Therefore the solution to this question of 2 pulleys is )16 rpm
b)360 rad/min c)39.6 rad/min d) 7200cm/min
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Fill in the gaps to factorise this expression.
p² - 36 = (p+_) (p − −)
Answer:
Step-by-step explanation:
wait
The radius of a circle is 4.5 cm. Find the circumference
to the nearest tenth
Answer: C≈28.27cm
Step-by-step explanation:
C=2πr=2·π·4.5≈28.27433cm
Answer:
28.3 cm
Step-by-step explanation:
You want the circumference of a circle with radius 4.5 cm.
CircumferenceThe circumference of a circle is given by ...
C = 2πr
For the given circle, the circumference is ...
C = 2π(4.5 cm) = 9π cm ≈ 28.3 cm
The circumference is about 28.3 cm.
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The price of the shirt was $38. It was reduced by 20% and then again by 10%.
Answer:$26.6
Step-by-step explanation:
Answer:
= 26.6
Step-by-step explanation:
38 * 20/100 = 38 *1/5 = 7.6
38 - 7.6 = 30.4
38 * 10/100 = 38 *1/10 = 3.8
30.4 - 3.8 = 26.6
Hi y’all i’m so lost, please help
Answer:
108
324
12
and 54
Step-by-step explanation:
Which statements are not true and true?
statement 1: the sum of two negative integers is positive
Statement 2: the product of two negative integers is positive
Statement 3: the difference of two negative integers is positive
Statement 4: the quotient of two negative integers is positive
For both statements that are not true at all, provide one counter example for each statement that proves the statement can be false.
Answer: Statements 1, 3, and 4 are not true. The sum, difference, and quotient of two negative integers can be positive, negative, or zero, depending on the values of the two integers. For example, the sum of -5 and -7 is -12, which is a negative number. The difference of -5 and -7 is 2, which is a positive number. The quotient of -5 and -7 is -0.7142857142857143, which is a negative number.
Only statement 2 is true. The product of two negative integers is always a positive number. For example, the product of -5 and -7 is 35, which is a positive number. This is because the two negative signs "cancel out" when multiplying two numbers, resulting in a positive product.
PLEASE HELP ILL GIVE BRAINLIEST use the similar triangles as a guild to find the slope of the line
Answer:
Slope is 1, since we use rise over run which is expressed as 1/1
What is the area of AFGH?
-10 -8 -6
H
Area =
-4 -2
square units
104
-8
6
4
2
0
2
-4
-6
-8
-10
4
6
8
00
F
X
10
G
Answer:
-2 = x 4-2 square units
Step-by-step explanation:
sum = as per as chart
Tyshawn has a quarters and y dimes, having at most 22 coins worth no less than
$3.40 combined. At most 16 of the coins are quarters and a maximum of 6 of the
coins are dimes. Solve this system of inequalities graphically and determine one
possible solution.
Answer: To solve this system of inequalities graphically, we can plot the two inequalities on the same coordinate plane and find the region where they overlap.
First, let's consider the inequality that states that Tyshawn has at most 22 coins worth no less than $3.40 combined. We can represent this inequality as follows:
Quarters * $0.25 + Dimes * $0.10 ≥ $3.40
Next, we can consider the inequality that states that at most 16 of the coins are quarters. We can represent this inequality as follows:
Quarters ≤ 16
Finally, we can consider the inequality that states that a maximum of 6 of the coins are dimes. We can represent this inequality as follows:
Dimes ≤ 6
To solve the system of inequalities graphically, we can plot the three inequalities on the same coordinate plane and find the region where they overlap. The region where the three inequalities overlap represents all of the possible values of Quarters and Dimes that satisfy all three inequalities.
One possible solution to the system of inequalities is (Quarters = 12, Dimes = 10). This solution satisfies all three inequalities and is represented by a point within the region where the three inequalities overlap on the coordinate plane.
You're given AIKJ with m/JIK = 53°, m/IKJ = (82-5x), and m/KJI = (7z+24)°. What is mZIKJ? Your final answer might not look to
scale. Do NOT round your answer.
Angle ∠IKJ is 29.5 degrees for triangle IKJ.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is IKJ.
The angles are given as follow.
∠JIK = 53°,
∠IKJ = (82-5x), and
∠KJI = (7x+24)°.
We need to find the angle ∠IKJ .
By angle sum property of triangle, the sum of three angles is 180 degrees.
∠JIK+∠IKJ+∠KJI = 180
Fifty three plus eighty two minus five times of x plus seven times of x plus twenty four equal to one hundred and eighty.
53+82-5x+7x+24=180
Add the like terms
159+2x=180
One hundred fifty nine plus two times of x equal to one hundred eighty.
subtract 159 on both sides
2x=21
Divide both sides by 2.
x=10.5
So ∠IKJ is 82-5(10.5)=29.5 degrees.
Hence, the value of angle ∠IKJ is 29.5 degrees.
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“The sum of three and a number, divided by three, is five”
I need help again due tomorrow
Answer: The number is 12
Step-by-step explanation:
Let x= the number that is unknown
The sum of three and a "number"= 3+"x"
Divided by three, means that x+3 is divided by 3
Is five, means that (x+3)/3=5
Algebra:
[tex]\frac{x+3}{3}=5[/tex]
Multiply by 3 to arrive at x+3=15
Subtract both sides by 3, then x=12
Help Pleaseee ONLY CORRECT ANSWERSS> I WILL GIVE BRAINIEST.
Answer:
16[tex]\pi[/tex]
Step-by-step explanation:
Area = [tex]\frac{\pi r^{2} }{4}[/tex] It is only 1/4 of a circle so we have to divide by 4
a = [tex]\frac{8^{2}\pi }{4}[/tex]
a = 16[tex]\pi[/tex]
Raquel wants to buy a concert ticket online. Raquel has a coupon code to discount the cost of the concert ticket. The cost of the concert ticket online has been found to be t-.25t + 15, where t the cost of the ticket in dollars.
By what percent is the ticket cos being discount ?
How much is the flat booking fee ?
Answer:
the percent being discounted is 25% and the flat booking fee is 15
Step-by-step explanation:
t is the cost of the ticket. -.25t is the 25% coupon being taken off. The 15 is the booking fee.
how do i comeplete this equation using substitution?
The solution to the equations using the substitution method is x = - 2 and y = 0
What are the solutions?The two equations given are known as system of equations. The equations have to be solved simultaneously to determine the required values.
y = 6x + 12 equation 1
y = 4x + 8 equation 2
Equate equation 1 and equation 2 together
6x + 12 = 4x + 8
6x - 4x = 8 - 12
2x = -4
x = -4 / 2
x = -2
Substitute for x in equation 1:
y = 4(-2) + 8
y = -8 + 8
Y = 0
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The sales tax rate is 4.315% for the city and 4% for the state. Find the total amount paid for 2 boxes of chocolates at $17.07 each.
PLS HELP ME
Answer: $18.49
Step-by-step explanation:
First, add both the tax rate, 4.315 + 4 = 8.315%
Then take 17.07 divided by 100%, then times 8.315% = $1.42
Then add 17.07 + 1.42 = $18.49
Henry took 42.7 minutes to complete an exam Laticia took 28.7 minutes to complete the same exam who completed their exam first
Answer:
Unless these took place in different time periods, Laticia did first.
Step-by-step explanation:
28.7 < 42.7
Reduce -15/-3 to the standard form
Answer:
5 x 10⁰
Step-by-step explanation:
-15 / -3 = 5
5 in standard form is 5 x 10⁰
Answer: 5
Step-by-step explanation:
-15/-3
negative signs cancel out each other to make positive
⇒15/3
⇒5/1
⇒5 answer.
hope that helps...
50 PTS Determine if you can use the hypotenuse-leg congruency property to prove the triangles are congruent.
A. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if a leg of one triangle is congruent to a leg of the other triangle.
B. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
C. Yes, the hypotenuse-leg congruence property can be applied.
D. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the triangles are right triangles.
8. Larissa plans to bake at
most 10 loaves of bread.
She makes x loaves of banana bread that sell for
$1.25 each and y loaves of nut bread that sell for
$1.50 each. She hopes to make at least $24 in sales.
Write and graph a system of inequalities for this
situation. What does the
graph show?
The system of inequalities is:
x + y ≤ 10
x*$1.25 + y*$1.50 ≥ $24
And the graph can be seen below, on the graph, we can see that there are no solutions.
How to write and graph a system of inequalities?So we need to start by defining the variables we will be using, these are:
x = number of loaves of banana bread.y = number of loaves of nut bread.First, we know that Larissa wants to make at most 10 loaves of bread, then we can start with the inequality:
x + y ≤ 10
We also know that each banana bread sells for $1.25 and each but bread sells for $1.50, and she wants to make at least $24, then:
x*$1.25 + y*$1.50 ≥ $24
So the system of inequalities is:
x + y ≤ 10
x*$1.25 + y*$1.50 ≥ $24
So to graph these inequalities, we need to shade the region abovce the first line:
x + y = 10
and below the second line:
1.25*x + 1.50*x = 24
The graph of that system of inequalities can be seen below. The graph shows that the system has no real solutions (only has solutions for negative values of x).
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A line passes through (−1, 5) and (1, 3).
Which answer is the equation of the line? PLEASE HELP
Find what K is in this question
Answer:
[tex]\huge\boxed{\sf k = 3}[/tex]
Step-by-step explanation:
Given that,[tex]5+6i+(-2+ki)=3+9i\\\\5 + 6i-2+ki=3+9i\\\\Combine \ like \ terms\\\\5-2+6i+ki=3+9i\\\\3+(6+k)i=3+9i\\\\Comparing \ both \ sides\\\\6 + k = 9\\\\Subtract \ 6 \ both \ sides\\\\k = 9-6\\\\k = 3\\\\\rule[225]{225}{2}[/tex]
Ivan,Bella, and Ian agreed to hare a pizza which wa cut into 10 lice. Ivan at 40% of the pizza
Using the percentage writing form, we know that Ivan ate 4 pizza slices.
What are percentages?By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.
The percentage calculation formula is (value/total value)100%.
Add all percentages as numbered values, divide by the total number of sets, and you get the average percentage.
The results by 100.
So, we know that:
Ivan ate 40% of the pizza.
And the pizza was cut into 10 slices.
Rewrite the percentage value as:
4/100 = 0.4
We can calculate how many slices Ivan consumed by multiplying the percentage value by the number of slices:
10 + 0.4 = 4
Hence, Ivan ate 4 slices of pizza.
Therefore, using the percentage writing form, we know that Ivan ate 4 pizza slices.
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Five times a number decreased by 2 is 4, find the number.
Answer: x= 6/5
Step-by-step explanation:
Let an unknown number be x
5x - 2 = 4
5x = 6
x= 6/5
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a pianist plans to play 3 pieces at a recital from her repertoire of 23 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. how many different recital programs are possible?
Answer:
10626 different recital programs possible
Step-by-step explanation:
Since there is no repetition we can tackle this problem in the following manner.
Out of the 23 pieces, the pianist can choose the first one in 23 ways
Out of the remaining 22 pieces she can choose the second one in 22 different ways
Out of the remaining 21 pieces she can choose the third one in 21 different ways
So total number of ways in which 3 pieces can be played without repetition is 23 x 22 x 21 = 10,626 ways
There is a formula for this kind of situation
If there are a total of n items and you want to choose r items from this, the number of possible ways to do this without repetition is given by the formula
[tex]_{n}P_{r} = \dfrac{n!}{(n-r)!}[/tex]
In this case, n = 23, r = 3 so we get
[tex]_{23}P_{3} = \dfrac{23!}{(23-3)!} = \dfrac{23!}{20!} = 23 \times 22 \times 21 = 10626[/tex]
Same as the above
Jessica deposits her summer babysitting earnings, $600, in a savings account. How many years will it take her to earn $150 in interest at a simple annual rate of 5%? Enter the correct number in the formula.
150 = (600) (.05) (?)
this is a middle school question not high school sorry
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 150\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 150 = (600)(0.05)(t) \implies \cfrac{150}{(600)(0.05)}=t\implies 5=t[/tex]
help pretty please :)
Answer: B
Step-by-step explanation:
A line has a slope of –20/11 and passes through the point (0, –2) What is its equation in slope intercept form?
Select the expressions that are equivalent to 8(5q). 8 + 5g 8(5 + q) 40q (q + 5)8
I don't know what is equivalent to 8(5q) ?
Answer:
the answer is 40q
Step-by-step explanation:
8x5 is 40 when using the distributive property
Not understanding this question
The unknown angle in the triangle is as follows:
∠E = 100 degrees.
How to find angles in a triangle?The sum of angles in a triangle is 180 degrees.
In the diagram, BCD is cut by transversal ACE , AB and perpendicular to BCD and CE ≅ ED.
Therefore,
∠ACB = 180 - 50 - 90 (sum of angles in a triangle)
∠ACB = 180 - 140
∠ACB = 40 degrees
Therefore,
∠ACB ≅ ∠DCE
Hence,
∠DCE = 40 degrees.
Triangle CDE is an isosceles triangle since CE ≅ DE.
Hence,
∠CDE = 40 degrees
∠E = 180 - 40 - 40
∠E = 180 - 80
∠E = 100 degrees.
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for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
As per the concept of margin of error, the standard deviation increases as the margin of error increases.
The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.
Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.
Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
And we need to find the missing term in the statement.
Here let us consider that the following values are represented the given situation,
=> σ = Standard deviation for population
=> m = Margin of error
=> Z = Empirical value of Z-score at a given confidence level
Then the minimum sample size for a given confidence level is written as
=> (Z x σ)²/m²
Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.
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