Write a system of equations using A and B as the variables
The first equation is the sum of the lengths of the plants
[tex]A+B=41[/tex]The second equation is the relation of growth that plant A grew 5cm more than plant B
[tex]A=B+5[/tex]Insert the second equation into the first one to solve for B
[tex]\begin{gathered} A+B=41 \\ (B+5)+B=41 \end{gathered}[/tex]Solve the equation for B
[tex]\begin{gathered} 2B+5=41 \\ 2B=41-5 \\ 2B=36 \\ B=\frac{36}{2} \\ B=18 \end{gathered}[/tex]Use the value of B in the second equation to find the value of A
[tex]\begin{gathered} A=B+5 \\ A=18+5 \\ A=23 \end{gathered}[/tex]Plant A is 23 cm long on Tuesday and plant B is 18 cm long on Tuesday.
∠A and \angle B∠B are vertical angles. If m\angle A=(x+12)^{\circ}∠A=(x+12)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the measure of \angle B∠B
Measure of ∠B = 16°
∠A and ∠B are Vertical angles with ∠A = x+12° and ∠B = 6x-8°.
Vertical angles are angles formed between two lines at the intersection of them and are opposite to each other.
Also measures of Vertical angles are equal.
Now to find the measure of ∠B, we need to find x.
So here, ∠A = ∠B
⇒ x+12° = 6x-8°
⇒ 6x - x = 12 + 8
⇒ 5x = 20
⇒ x = 4
Hence, ∠B = 6x-8° = 6 x 4 -8 = 16°
So measure of ∠B = 16°
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Luna brought all her savings with her to Rome, in euros. For the first week, she spent the same amount of money each day. The table shows how much Luna had left at the end of each day. What was the initial value of Luna's savings? Day Euros ? 315 1 2 280 3 245 4 210 5 175 6 140 7 105 35 euros 315 euros 80 euros 350 euros
every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350
Therefore, the initial value was $350
Ben is a coal miner and spends most of his workday in an underground mine. Which is the most likely depth he is at while doing his job?
Answer:-900 feet. I think this is correct so don't use it unless you think its right
Step-by-step explanation:
What percent of 90 is 200?
Can someone pls help me find the equation for the arithmetic sequence and help me fill out the graph
Solution
- The question gives us the following arithmetic sequence:
[tex]t(n+1)=t(n)-4[/tex]- We are asked to write out the explicit function for the sequence.
- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.
- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:
[tex]\begin{gathered} t(m)=a+(m-1)d \\ \text{where,} \\ a=\text{first term of the sequence} \\ d=\text{common difference} \\ m=\text{ number of terms} \\ \\ (\text{Note that: }m=n+1\text{, since the formula starts assumes that the sequence starts from the 1st term not zeroth term} \end{gathered}[/tex]- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.
[tex]\begin{gathered} \text{Let n=2} \\ \text{The formula becomes} \\ t(2+1)=t(2)-4 \\ t(3)=t(2)-4 \\ \\ \text{But we know that }t(2)=10 \\ \therefore t(3)=10-4 \\ t(3)=6 \\ \\ \text{Let n=3} \\ t(3+1)=t(3)-4 \\ t(4)=6-4 \\ t(4)=2 \\ \\ \text{Let n=4} \\ t(4+1)=t(4)-4 \\ t(5)=2-4 \\ t(5)=-2 \\ \\ \text{Thus, we can write out the terms of the sequence as follows:} \\ \ldots,t(2),t(3),t(4),t(5),\ldots=\ldots10,6,2,-2\ldots \\ \\ \text{ We can observe that the common difference is -4 since,} \\ 6-10=-4 \\ 2-6=-4 \\ -2-2=-4 \\ \text{And so on}\ldots \\ \\ \text{Thus, we can trace our sequence back to its first term as follows:} \\ t(2)-t(1)=-4 \\ 10-t(1)=-4 \\ \text{Subtract 10 from both sides} \\ -t(1)=-4-10 \\ \therefore t(1)=14 \\ \\ t(1)-t(0)=-4 \\ 14-t(0)=-4 \\ \text{Subtract 14 from both sides} \\ -t(0)=-4-14=-18 \\ \therefore t(0)=18. \\ \\ \text{Thus, the first term }t(0)=18 \end{gathered}[/tex]- Let us now apply the formula for the nth term of a sequence to find the explicit formula:
[tex]\begin{gathered} first\text{ term =}t(0)=a=18 \\ \text{common difference}=d=-4 \\ t(m)=a+(m-1)d \\ \\ t(m)=18+(m-1)(-4) \\ \text{Expand the bracket} \\ t(m)=18+m(-4)-1(-4) \\ t(m)=18-4m+4 \\ \\ \therefore t(m)=22-4m \\ \\ \text{Let us write the sequence in terms of n} \\ m=n+1 \\ t(n)=22-4(n+1) \\ t(n)=22-4n-4 \\ t(n)=18-4n \\ \\ \text{Thus, the explicit function is:} \\ t(n)=18-4n \end{gathered}[/tex]- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.
[tex]\begin{gathered} t(n)=18-4n \\ \\ \text{when n = 0} \\ t(0)=18-4(0) \\ t(0)=18 \\ \\ \text{when n= 1} \\ t(1)=18-4(1) \\ t(1)=14 \\ \\ \text{when n=2} \\ t(2)=18-4(2) \\ t(2)=10 \\ \\ \text{when n = 3} \\ t(3)=18-4(3) \\ t(3)=18-12=6 \\ \\ \text{when n = 4} \\ t(4)=18-4(4) \\ t(4)=2 \\ \\ \text{when n = 5} \\ t(5)=18-4(5) \\ t(5)=-2 \end{gathered}[/tex]- On the table, we have the values filled in below:
Final Answer
The explicit form of the sequence is:
[tex]t(n)=18-4n[/tex]The slant height and the base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
The most appropriate choice for cone and total surface area of cone will be given by-
Total surface area of the cone is [tex]198235.71 cm^2[/tex]
What is cone and total surface area of cone?
Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.
Cone is obtained by revolving a right angled triangle about one of its legs.
Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.
If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by
[tex]\pi r(r+l)[/tex]
Here
Ratio of the slant height and radius of base of the cone = 2:1
Radius = 145cm
Slant height = [tex]145 \times 2[/tex]
= 290 cm
Total surface area of cone = [tex]\pi r(r+l)\\[/tex]
= [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]
= [tex]\frac{22}{7} \times 145 \times 435[/tex]
= [tex]198235.71 cm^2[/tex]
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Complete Question
The slant height and the radius of base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
Solve the equation for all values of x.
|5x + 8| 8 = 3x
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The system of the equations are,
3x + y - 2z = 22 .... (i)
x + 5y + z = 4 .... (ii)
x = - 3z .... (iii)
Now,
Solve the equations as;
Substitute x = - 3z in both equations, we get;
⇒ 3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22 .... (iii)
And, x + 5y + z = 4
- 3z + 5y + z = 4
5y - 2z = 4 ... (iv)
Solve equation (iii) and (iv) we get;
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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Achromycin is to be administered 11mg per pound in 4 equal doses to a patient weighing 34kg. Oral suspension is available 125mg per 5mL. How many millilitres should you give per dose? Use 1 kg = 2.2 lbs and round your final answer to 1 decimal place.
We are told that 11 mg of Achromycin per patient pound must be administered, we are also given the weight of the patient as 34 kg, in order to properly use this weight we must convert it from kg to pounds by multiplying the weight in kg by 2.2, like this:
34×2.2 = 74.8
Then, the patient weight is 74.8 lbs, by multiplying this by the 11 mg per pound of Achromycin that have to be administered we can determine the mg of Achromycin, like this:
74.8×11 = 822.8
Then, 822.8 mg of Achromycin has to be administered, by dividing this amount by 4, we can determine the amount for each dose:
822.8/4 = 205.7
Then 205.7 mg are given per dose, since 5 mL contains 125 mg, we can take the ratio of mL to mg to get:
5/125 = 1/25
By multiplying the above ratio by 205.7 we can determine the milliliters that should be given per dose, like this:
205.7×1/25 = 8.2
Then, 8.2 mL must be given per dose
please helpppppppppppppp
Answer:
Step-by-step explanation:
Substitute a and b with 1/4 and 6
5b/ 32a^2
5(6)/ 32(1/4)^2
30/32(1.96)
30/62.72
0.5102 Answer
determine the answer to the nearest tenth of a percent.12 out of 52 cards in a deck are face cards.What percentage of cards in a deck are face cards?
Total number of cards: 52
Number of face cards: 12
To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:
[tex]\frac{12}{52}\times100[/tex]The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.
Solving the operations:
-solving the division
[tex]0.2308\times100[/tex]-solving the multiplication:
[tex]23.08[/tex]The face cards represent 23.08%.
Rounding to the nearest tenth of a percent (one decimal place):
[tex]\approx23.1[/tex]Answer: 23.1%
Use 2 methods to predict the output for an input of 200.
Given a table represents a relation between x and y
As shown, the change of (x) and (y) vary with a constant rate
So, the table represents a linear function
The general equation will be: y = m * x + b
where (m) is the slope, (b) is the value of y when (x=0)
So, from the table, when x = 0 , y = 25
The slope will be as follows:
[tex]m=\frac{30-25}{1-0}=\frac{5}{1}=5[/tex]So, the equation will be:
[tex]y=5x+25[/tex]When the input = 200, x = 200
So, substitute with (x) to find the output (y)
[tex]y=5\cdot200+25=1000+25=1025[/tex]So, the answer will be:
For an input 200, the output is 1025
===================================================
Another method to solve using the arithmetic sequence.
As shown in the table consider (x) represents the number of terms
So, (y) will be an arithmetic sequence
The first term = a = 30
The common difference = d = 35 - 30 = 5
the general rule of the arithmetic sequence is:
[tex]y_{}=a+d(x-1)[/tex]substitute with (a) and (d)
[tex]y=30+5(x-1)[/tex]When x = 200
[tex]y=30+5(200-1)=30+5\cdot199=1025[/tex]So, for an input 200, the output = 1025
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $72.How much is each allowance?
you [][][][][]
friend[][][][]
The allowance of each person is
You: $40Friend: $32How to determine the amount of each person's allowance?From the question, the tape diagram that can be used in our computation is given as
you [][][][][]
friend[][][][]
Counting the number of boxes, we have
You = 5
Friend = 4
Next, we represent the boxes as a ratio
So, we have
You : Friend = 5 : 4
This means that
You = 5/9 * Total allowance
Friend = 4/9 * Total allowance
From the question, we have
Total allowance = $72
Substitute the known values in the above equation
So, we have the following equation
You = 5/9 * 72
Friend = 4/9 * 72
Evaluate the products
You = 40
Friend = 32
Hence, the amount of each person's allowance is $40 and $32, respectively
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what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We have to determine the lcm of the rational algebraic equation
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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Write a sequence of transformations that takes A to A'.
A rotation of 270 degrees about the origin would transform the figure as follows:
Which does not maps the A to A'.
Now, one sequence of transformations that take A to A' is:
1)First, a reflection over the x-axis would transform the figure as follows:
2) We translate the figure 3 units up and 4 units to the right:
Answer: Reflection over the x-axis, translation 3 units up and 4 units to the right.
Real world compositionsShoe sizes are marked differently in many countries. In Japan, a shoe size is 16 more than the size in the United States. In Korea, a shoe size is 224 more than the size in Japan. Determine the function of the U.S. size of a shoe in terms of the shoe size in Korea. What is the U.S. shoe size of a shoe that is 250 in Korea? Solve using composite functions
To solve this exercise, we define the following variables:
• j = Japan size of shoes,
,• u = United Sates size of shoes,
,• k = Korea size of shoes.
From the statement of the problem, we know that:
0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,
,1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.
We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).
1) From point 1, we have:
[tex]\begin{gathered} j=16+u, \\ u=j-16. \end{gathered}[/tex]2) From point 2, we have:
[tex]\begin{gathered} k=224+j, \\ j=k-224. \end{gathered}[/tex]Replacing the expression of j in terms of k in the expression of u, we get:
[tex]u=j-16=(k-224)-16=k-240.[/tex]Replacing the value k = 250 in the last equation, we get:
[tex]u=250-240=10.[/tex]Answer
The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.
ASAP!!!!
PLEASE HELP!!!
When a whole number is multiplied by 10 to the power of 2, how does the placement of the decimal point change?
a) It moves two places to the right.
b) It moves ten places to the right.
c) It moves two places to the left.
d) It moves ten places to the left.
Answer: A) moves two places to the right
Example:
[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]
The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.
How do scatter plots and histograms differ from line graphs?
None of the above
All three are used synonymously
Scatter plots and histograms show trends, or how data changes over time while line
graphs show how data is distributed.
Scatter plots and histograms show how data is distributed while line graphs show
trends, or how data changes over time.
Answer: Scatter plots, to show relationships among numerical variables. Line graphs, to show change over time. Histograms, to show data distributions.
Step-by-step explanation: I looked it up
Carefully follow the steps to find the solution to the three equation system.
a. Use equations 2 and 3 and eliminate the by multiplication and addition, creating a new equation with only two variables.
b. Use equations 1 and 2 and eliminate the by multiplication and addition, creating a second equation with only two variables.
c. Use the two new equations, and eliminate the -variable by multiplication and addition, finding the value for the -variable.
d. Substitute -value in the second new equation and find the -value.
e. Substitute the and values into original equation 2 to find the -value
(-2,-5,-3)
(1,4,2)
(-4,1,-2)
(1,2,4)
(2,5,3)
Answer:
The answer is (1,4,2)
Part A: On the imagePart B: What is the answer of k?
The effect on the graph replacing f(x) by f(x)+k is a vertical shift k units.
According to the graph the resulting function is 2 units higher from the original one. This means k has a value of 2.
In the circle below, the central angle is measured in radians.When rounded to the nearest .01 of a centimeter,the length of arc Sis?? cm?
Length of the given arc
[tex]\begin{gathered} l=r\theta \\ =2\times\frac{\pi}{4} \\ =\frac{\pi}{2} \\ =\frac{22}{14} \\ =1.571 \\ =1.57 \end{gathered}[/tex]So the length of the given arc is 1.57 cm
Mrs. Smith spent $50 more at a store than mrs. Jones. Combined they spent at most $250. What is the most they each could have spent?
By working with inequalities, we will see that:
Mrs. Jones can spend between $0 and $100.Mrs. Smith can spend between $50 and $150.How much each spent?Let's define:
S = amount that Mrs. Smith spent.J = amount that Mrs. Jones spentWe know that Mrs. Smith spent $50 more at a store than Mrs. Jones, then:
S = J + 50
And together they spent at most $250, then:
S + J ≤ 250
Now, replacing the equation in the inequality, we get:
(J + 50) + J ≤ 250
2*J + 50 ≤ 250
2*J ≤ 250 - 50
2*J ≤ 200
J ≤ 200/2
J ≤ 100
So Mrs. Jones spent at most 100 dollars.
And Mrs Smith spent $50 more than that, so we can write the inequality.
50 ≤ S ≤ 150
She spends between $50 and $150.
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Using the bankers rule, find the simple interest on 18,000 pesos at 17.25% from Feb.4 to Apr 21 of the same leap year.
From the question
By the bunkers rule
[tex]I=\text{PRT}[/tex]P = 18,000
R = 17.25% = 0.1725
For the time
Since the year is a leap year then
February has 29 days
Hence
From Feb.4 to Apr 21 implies
The number of days left in Feb. = 25
Number of days in March = 31
Number of days for April = 21
Therefore, Total number of days = 25 + 31 + 21 = 77
By Bankers rule, total days for the year will be 360
Hence the interest is
[tex]\begin{gathered} I=18000\times0.1725\times\frac{77}{360} \\ I=18000\times0.1725\times0.2139 \\ I=664.16 \end{gathered}[/tex]Therefore, the interest is 664.16
A cyclist rides her bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate:km/hDistance traveled in 2 hours:km
Given:
1 mile = 1.6 km
So, 8 miles per hour in kilometers per hour is given by:
[tex]\frac{1}{8}=\frac{1.6}{x}[/tex]Where x = # of kilometers
So, solve for x:
[tex]\begin{gathered} x\cdot1=1.6\cdot8 \\ x=12.8 \end{gathered}[/tex]This is 12.8 km per hour
Next, the distance traveled in 2 hours is:
[tex]rate=\frac{distance}{time}\rightarrow distance=rate\times time[/tex]Substitute the values:
[tex]distance=12.8\times2=25.6[/tex]Answer:
Rate: 12.8 km/h
Distance traveled in 2 hours: 25.6 km
Determine the continuity at x = 2. Be sure to clearly state your reasoning. fastest answer get ranked brainliest
The answer is in my screenshot pic.
From the diagram below, what is the measure of the angle of depression from point A
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.
Thus, the angle of depression is 45°
(2 3/5) Multiply (-2 2/3)
[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]
ATTACHED IS THE SOLUTION
Answer:
(-104/15)
Step-by-step explanation:
3 2
2 ------ × -2 -------
5 3
5 × 2 = 10
10 + 3 = 13
3 × -2 = -6
-6 + -2 = -8
13 -8 104
------- × ------- = (-) -------
5 3 15
I hope this helps!
HELP ASAP Determine the values of x in the equation x2 = 81.
x = −9
x = ±9
x = ±40.5
x = 40.5
The value of x in the given quadratic equation are; +9 and -9.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. An equation of degree 2 containing a single variable is known as the quadratic equation. Its general form is ax² + bx + c = 0 , where variables are x and constants are a, b, and c.
As equation is x²= 81
Taking square root on both sides;
⇒ √x² = √81
⇒ X = ± 9
Thus the value of X is ± 9
Hence, The roots of the given quadratic equation are; +9 and -9.
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Under his cell phone plan, Deion pays a flat cost of $39 per month and $4 per gigabyte. He wants to keep his bill at $49.40 per month. How many gigabytes of data can he use while staying within his budget?
Answer:
(49.4 - 39) / 4
= 10.4 / 4
= 2.6GB
Step-by-step explanation:
It takes 4 oranges to makes 6 ounces of orange juice. What are the two unit rates?
Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.
Step-by-step explanation: