I attached a picture with a practice problem from my prep guide, it has 5 questions that are included with the problem. You will find that below. I am having trouble doing this, and need help,Please note that this is complex and lengthy. 1. What is the balance of Albert’s $2000 after 10 years?2. What is the balance of Marie’s $2000 after 10 years??3. What is the balance of Han’s $2000 after 10 years??4. What is the balance of Max’s $2000 after 10 years?? Lastly, 5. Who is $10,000 richer at the end of this competition?
Answers
This is a question on present and
We are required to find out how much the future sums of the $2000 handed to them will amount to. This will test our knowledge on simple and compound interest.
Our approach is to take each one's case and analyse the appreciation or depreciation of the sums assigned using the appropriate formulae.
The compound interest formula goes thus:
[tex]F=P(1+\frac{i}{m})nm[/tex]Where:
F = future sum
P = Present sum / Principal
i = interest rate
n = no. of years
m = number of compounding periods in a year.
The simple interest rate formula goes thus:
[tex]F=Pi\text{n}[/tex]Albert:
Firstly, he had $1000 compounded monthly by 1.2%
[tex]\begin{gathered} F=1000(1+\frac{0.012}{12})^{10\times12} \\ F=\text{ \$1,127.43} \end{gathered}[/tex]He lost 2% of $500 over the course of the 10 years.
[tex]F=500(100\text{ \% - }2\text{ \%) = 500(0.98)= \$490}[/tex]Firstly, he had $500 compounded monthly by 0.8%
[tex]F=500(1+\frac{0.008}{1})^{10}=541.47[/tex]Total sum he gained over the course of the 10 years:
[tex]1127.43+490+541.47\text{ = \$2,158.90}[/tex]Marie:
Firstly, she had $1500 compounded quarterly by 1.4%
[tex]\begin{gathered} F=1500(1+\frac{0.014}{4})^{10\times4} \\ F=\text{ \$1,724}.99 \end{gathered}[/tex]She lost $500 by 4% over the course of the 10 years.
[tex]F=500(100\text{ \% + 4 \%) = 500(1.04)= \$}520[/tex]Total sum gained by Marie over the course of the 10 years:
[tex]\text{ \$1724.99 + \$520 = \$2,244.99}[/tex]Hans
He had $2000 compounded annually by 0.9%
[tex]\begin{gathered} F=2000(1+\frac{0.009}{1})^{10} \\ F=\text{ \$}2187.47 \end{gathered}[/tex]Total sum gained by Hans over the course of the 10 years:
[tex]\text{ \$2187.47}[/tex]Max:
$1000 decreased in value exponentially at a rate of 0.5% annually.
[tex]1000(1-\frac{0.005}{1})^{10}=\text{ \$951.11}[/tex]He had $1000 compounded biannually by 1.8%
[tex]\begin{gathered} F=1000(1+\frac{0.018}{2})^{10\times2} \\ F=\text{ \$}1196.25 \end{gathered}[/tex]Total sum gained by Max over the course of the 10 years:
[tex]\text{ \$9}51.11+\text{ \$1196.25=\$2,147.36}[/tex]
Related Questions
The perimeter of a parallelogram is 120cm. If one of the sides is greater than the other by 10cm,
find the length of all the sides of the parallelogram
Answers
Answer:
Two of the sides are 25cm and the other two sides are 35cm.
Step-by-step explanation:
The perimeter is the distance all the way around the shape.
The shape is a parallelogram, so two sides across from each other are the same length. And the other two sides are also the same as each other. See image.
The shorter sides can be labelled x and the longer sides can be labelled x + 10. This is because the question said the long side is 10cm more than the short side.
see image.
Add up all the sides to make them equal to the perimeter. Set it equal to 120. See image.
Solve for x.
x + x+10 + x + x+10 = 120
4x + 20 = 120
Subtract 20.
4x = 100
Divide by 4.
x = 25
The short sides are 25cm and the long sides are 35cm.
Check:
25+35+25+35=
120 Check!
2. What is the product of m^3, 2m^5, and 1/m^2?
Answers
the expression is given as follows,
[tex]=m^3\times2m^5\times\frac{1}{m^2}[/tex][tex]\begin{gathered} =m\times2m^5 \\ =2m^6 \end{gathered}[/tex]so the answer is 2m^6
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
Answers
If an individual borrowed 84000 the Starting loan principal is $84,000; Interest rate is 3%; Number of payment per year is 12 payments per year; Loan term is 23 years; Payment amount is $422.
Principal loana. Identifying the starting loan principal, the interest rate, the number of payments per year, the loan term, and the payment amount.
Starting loan principal = $84,000
Interest rate =3%
Number of payment per year = 12 payments per year
Loan term = 23 years
Payment amount = $422
b. Total payment
There are 12 payments every year for 23 years, so
12 × 23 = 276
c. Total amount
Total amount 276× $422
Total amount = $116,472
d. Toward principal and interest
Toward Principal = $84,000
Toward Interest = $116,472 - $84,000
Toward Interest = $32,472
Therefore the starting loan principal is $84,000.
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The complete question is:
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
A. The amount borrowed is
The annual interest rate is
The number of payments per year is
The loan term is
The payment amount is
B. How many total payments does the loan require? What is the total amount paid over the full term of the loan?
C. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
The percentage paid toward the principal is
and the percentage paid for interest is:
Question 2: Attached in screenshot below: If chart from question 1 is needed just tell me.
Answers
EXPLANATION
The slope field can be obtained by applying a graph drawing as shown as follows:
f(x)=2x^3+6x^2-5x-3
Find (f-g)(x)
Answers
The solution to the function expression, (f - g)(x) is: D. 2x³ + 6x² - 8x + 1.
How to Subtract Functions?To evaluate or subtract functions that has polynomials, all we simply need to do is to pair like terms together and combine them.
Given the following:
f(x) = 2x³ + 6x² – 5x – 3 and g(x) = 3x – 4
Therefore:
(f - g)(x) = f(x) - g(x)
Substitute
(2x³ + 6x² – 5x – 3) – (3x – 4)
2x³ + 6x² - 5x - 3 - 3x + 4
Combine like terms
2x³ + 6x² - 5x - 3x - 3 + 4
2x³ + 6x² - 8x + 1
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Complete Question:
f(x) = 2x³ + 6x² – 5x – 3
g(x) = 3x – 4
Find (f - g)(x).
O A. (f - g)(x) = 2x³ + 6x² – 2x – 7
O B. (f - g)(x) = 2x³ + 6x² – 2x + 1
O c. (f - g)(x) = 2x³ + 6x² – 8x – 7
O D. (f - g)(x) = 2x³ + 6x² – 8x + 1
Decide whether it is an even function, an odd function, or neither
Answers
Given:
There are 2 graphs and 2 functions given in the question
Required:
We need to identify that which are even and which are odd
Explanation:
Even function:
f(-x) = f(x)
The graph of an even function is symmetric with respect to the y-axis.
Odd function:
f(-x) = -f(x)
The graph of an odd function is symmetric with respect to the origin
Here 1st graph is neither even nor odd function because it is not symmetric with respect to the y-axis and also not symmetric with respect to the origin
2nd graph is even because it is
1st function is neither even nor odd because
[tex]f(-x)=-6(-x)^5+7x^2=6x^5+7x^2\ne-f(x)[/tex]2nd function is
look at this diagram. if TV and WY are parallel lines and m
Answers
The measure of the angle ∠YXU is 138°.
We are given that the lines TV and WY are parallel to each other. Parallel lines in geometry are two lines in the same plane that are at an equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. We are given two angles in the diagram. The measure of the angle ∠VUS is 138°. We can see that the angles ∠VUS and ∠YXU are corresponding angles. Corresponding angles are any pair of angles that are both on the same side of a transversal. So, the angles must be equal to each other.
∠YXU = ∠VUS = 138°
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One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
Answers
We have to find the price of one loaf of bread.
With the information we have, we can construct a system of equations.
Let B be the price of one loaf of bread and R the price of a roll.
Then, if one loaf of bread and six rolls cost $1.80, we can write:
[tex]B+6R=1.80[/tex]We also know that two loaves of bread and four rolls cost $2.40, so we can write:
[tex]2B+4R=2.40[/tex]We can solve for B with the method of elimination: we can substract the first equation from 1.5 times the second equation.
This can be express in mathematica terms as:
[tex]\begin{gathered} 1.5(2B+4R)-(B+6R)=1.5\cdot2.40-1.80 \\ 3B+6R-B-6R=3.60-1.80 \\ (3-1)B+(6-6)R=1.80 \\ 2B=1.80 \\ B=\frac{1.80}{2} \\ B=0.90 \end{gathered}[/tex]Then, we have just calculated that the loaf of bread costs $0.90.
Answer: the cost of a loaf of bread is $0.90.
Rectangle A measures 20 cm by 4 cm. Rectangle B is a scaled copy of Rectangle A. Select ALL of the measurement pairs that could be the
dimensions of Rectangle B.
100 cm by 20 cm
15 cm by 5 cm
12.5 cm by 2.5 cm
20 cm by 5 cm
5 cm by 1 cm
Answers
The measurement pairs that could be the dimensions of rectangle B are 100 cm by 20 cm, 12.5 cm by 2.5 cm, and 5 cm by 1 cm.
The rectangle A measures 20 cm by 4 cm.
The ratio of the dimensions of rectangle A is 20:4 = 5.
Rectangle B is a scaled copy of rectangle A.
The dimensions of rectangle B must be in the same ratio as those of rectangle A.
The first set of dimensions is 100 cm by 20 cm.
The ratio of dimensions is 100:20 = 5.
Thus, these could be the dimensions of the rectangle B.
The second set of dimensions is 15 cm by 5 cm.
The ratio of dimensions is 15:5 = 3.
Thus, these cannot be the dimensions of the rectangle B.
The third set of dimensions is 12.5 cm by 2.5 cm.
The ratio of dimensions is 12.5:2.5 = 5.
Thus, these could be the dimensions of the rectangle B.
The fourth set of dimensions is 20 cm by 5 cm.
The ratio of dimensions is 20:5 = 4.
Thus, these cannot be the dimensions of the rectangle B.
The fifth set of dimensions is 5 cm by 1 cm.
The ratio of dimensions is 5:1 = 5.
Thus, these could be the dimensions of the rectangle B.
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in the diagram below angle E congruent angle H enter the segments in tye blanks provided that would result in a true equation
Answers
ANSWER
DF/GF or DE/GH
EXPLANATION
We know that angle H and angle E are congruent. We also know that angles HFG and EFD are congruent too because they are vertical angles. Thus, by the AA postulate, triangles HGF and EDF are similar.
If two figures are similar, the ratio between corresponding sides must be constant. Of these two triangles, the corresponding sides are
• EF and HF
,• DF and GF
,• DE and GH
So the ratio between corresponding sides is,
[tex]\frac{EF}{HF}=\frac{DF}{GF}=\frac{DE}{GH}[/tex]The answers could be DF/GF or DE/GH
24) j(h - 9) + 2; use h=9, and j = 8
Answers
Answer:
The value of the expression at h=9 and j=8 is;
[tex]2[/tex]Explanation:
Given the expression;
[tex]j(h-9)^3+2[/tex]At;
[tex]\begin{gathered} h=9 \\ j=8 \end{gathered}[/tex]substituting the given values of the variables;
[tex]\begin{gathered} j(h-9)^3+2 \\ 8(9-9)^3+2 \\ 8(0)+2 \\ =2 \end{gathered}[/tex]Therefore, the value of the expression at h=9 and j=8 is;
[tex]2[/tex]Answer:
2
Step-by-step explanation:
j(h - 9) + 2
Let h=9 and j=8
8(9 - 9) + 2
Parentheses first
8(0) + 2
Multiply
0+2
Add
2
Step 1 of 2: Red the rational expression to its lowest terms 2 - 2x^2/2x^2 - 2Step 2 of 2: Find the restricted values of X, if any, for the given rational expression.
Answers
Step1
we can factor the numerator and denominator because we have a square subtract
[tex]\begin{gathered} \frac{(\sqrt[]{2}+\sqrt[]{2}x)(\sqrt[]{2}-\sqrt[]{2}x)}{(\sqrt[]{2}x-\sqrt[]{2})(\sqrt[]{2}x+\sqrt[]{2})} \\ \\ \frac{(\sqrt[]{2}+\sqrt[]{2}x)}{\sqrt[]{2}x+\sqrt[]{2})}\cdot\frac{(\sqrt[]{2}-\sqrt[]{2}x)}{(\sqrt[]{2}x-\sqrt[]{2})} \\ \\ 1\cdot-1 \\ \\ =-1 \end{gathered}[/tex]step 2
restricted values of X are when the denominator is 0
then
[tex]2x^2-2=0[/tex]factor this
[tex](\sqrt[]{2}x-\sqrt[]{2})(\sqrt[]{2}x+\sqrt[]{2})=0[/tex]and find the value of x what make each parenthesis 0
[tex]\begin{gathered} \sqrt[]{2}x-\sqrt[]{2}=0 \\ \sqrt[]{2}x=\sqrt[]{2} \\ x=1 \end{gathered}[/tex]first restricted value is x=1
[tex]\begin{gathered} \sqrt[]{2}x+\sqrt[]{2}=0 \\ \sqrt[]{2}x=-\sqrt[]{2} \\ x=-1 \end{gathered}[/tex]
and the other restricted value is x=-1
find:For f(x) = 5x – 2 and g(2) = 4xa) (f - g)(x) =wb) (f-9)(-3) =
Answers
We have functions f and g defined as:
f(x) = 5x - 2
g(x) = 4x - 2
We can subtract both functions:
f(x) - g(x) = (5x - 2) - (4x - 2) = 5x - 2 - 4x + 2
Then:
f(x) - g(x) = x
But, by definition, we know that:
(f - g)(x) = f(x) - g(x)
Putting these together:
(f - g)(x) = x
Now, if x = -3:
(f - g)(-3) = -3
what is the average rate of change of the equation f(x)=x^2+3x-5 from x=2 to x=4
Answers
The formula to calculate the average rate of change is as follows:
[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]Where "a" represents the starting point and "b" the ending point.
So, a = 2 and b = 4 in this case, so we have:
[tex]\begin{gathered} a=2 \\ f(a)=f(2)=2^2+3\cdot2-5=4+6-5=5 \\ b=4 \\ f(b)=f(4)=4^2+3\cdot4-5=16+12-5=23 \end{gathered}[/tex]Thus:
[tex]R=\frac{23-5}{4-2}=\frac{18}{2}=9[/tex]The average rate of change is 9.
HELP PLEASEEEEEE!!!!!!!! ILL MARK AS BRAINLIEST
Answers
A horizontal line with evenly spaced numerical increments is referred to as a number line.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
What is meant by number line?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It exists assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments exists directed to as a number line. How the number on the line can be answered depends on the numbers present. The utilize of the number exists defied by the question that it corresponds to, such as when graphing a point.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
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1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
What exactly is a number line?In basic mathematics, real numbers are represented by a number line, a representation of a graduated straight line. The presumption is that each point on a number line represents a real number, and that each real number represents a point.
There is something known as a number line, which is a horizontal line with uniformly spaced numerical increments. The numbers available determine how to respond to the number on the line. The number can be used in ways that defy the question it answers, such as when graphing a point.
1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
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If cos x= √2/2 and x is a fourth quadrant angle, evaluate tan x
Answers
Given that;
[tex]\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ and\text{ x is a fourth angle quadrant.} \end{gathered}[/tex]Note that cosine is positive on the fourth angle quadrant while tangent is negative.
From;
[tex]\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ \text{adjacent}=\sqrt[]{2},\text{ hypotenuse= 2} \\ \text{opposite}=\text{ }\sqrt[]{2^2-(\sqrt[]{2})^2} \\ \text{opposite}=\sqrt[]{4-2} \\ \text{opposite}=\sqrt[]{2} \\ \end{gathered}[/tex]Thus, the tangent is;
[tex]\begin{gathered} \tan x=\frac{-\sqrt[]{2}}{\sqrt[]{2}} \\ \tan x=-1 \end{gathered}[/tex]Solve for points please
Answers
Harrison Heights Elementary School has 3 fourth grade classrooms. Each classroom has 28 students. Howmany fourth grade students attend Harrison Heights Elementary?
Answers
Harrison Heights Elementary School has 3 fourth grade classrooms. Each classroom has 28 students.
From the given statement;
Number of four grade classrooms = 3
Number of student in each classromm = 28
So,
for total number of students in 3 four grade students = 3 x (number of student in one class)
= 3 x (28)
= 84 students
Answer : 84 students
Instructions: Find the area of the sector with the red outline. Round your answer to the nearest tenth.
Answers
HeHeThe area of a sector is given as:
[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex][tex]\begin{gathered} r\rightarrow radius,\theta\rightarrow angle\text{ at the centre} \\ r=14ft \\ \theta=210^0 \end{gathered}[/tex][tex]\begin{gathered} A=\frac{210^0}{360^0}\times\pi\times14^2 \\ A=\frac{7}{12}\times196\times\pi \\ A=359.2ft^2 \end{gathered}[/tex]Hence, the area in the nearest tenth is
which has the larger 15th term when comparing the arithmetric and geometric sequences below? show evidence that support your answer Arithmetic sequence: 150, 650, 1150, 1650Geometric sequence:4,12, 36, 108
Answers
Answer
For the arithmetic sequence,
15th term = 7,500
For the geometric sequence,
15th term = 19,131,876
We can see that the geometric sequence has the larger 15th term.
Explanation
The general formula for an arithmetic progression is
f(n) = a + (n - 1)d
where
a = first term = 150
n = number of terms
d = common difference
= (Second term) - (First term)
= (Third term) - (Second term)
= Difference between consecutive terms
= 650 - 150
= 500
f(n) = 150 + (n - 1)500
f(n) = 150 + 500n - 500
f(n) = -350 + 500n
For the 15th term, n = 15
f(n) = -350 + 500n
f(15) = -350 + 500(15)
f(15) = -350 + 7500
f(15) = 7,150
For the geometric sequence,
[tex]f(n)=ar^{n-1}[/tex]where
a = first term = 4
n = number of terms
r = common ratio
= (Second term)/(First term)
= (Third term)/(Second term)
= Ratio of consecutive terms
= (12/4)
= 3
For the 15th term, n = 15
[tex]\begin{gathered} f(n)=ar^{n-1} \\ f(15)=4\times3^{15-1} \\ f(15)=4\times3^{14} \\ f(15)=19,131,876 \end{gathered}[/tex]Hope this Helps!!!
Rule: y = 2xx|y9| |101|
Answers
you have the equation:
y = 2x
in order to complete the table, proceed as follow:
for x=9
y = 2(9) = 18
for y=10, solve the equation for x and replace y:
x=y/2
x=10/2=5
for x=1
y = 2(1) = 2
Then, you have:
x | y
9 18
5 10
Write a formula for the function obtained when the graph is shifted as described.
Answers
The given function is
f(x) = x^3
Recall, if a function, f(x) is shifted c units upwards, the new function would be f(x) + c. This means that if we translate the given function 3 units upwards, the new function would be x^3 + 3
Also, if a function, f(x) is shifted d units to the left, the new function would be
f(x + d). This means that if we translate x^3 + 3 7 units to the left, the new function would be (x + 7)^3 + 3
The function is
f(x) = (x + 7)^3 + 3
At the start of a trip, a car’s gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 LaTeX: \frac{1}{8}1 8 gallons of gasoline. How much gasoline is left in the tank?
Answers
At the beginning we have 12 gallons and during the trip the car consumes 10 1/8 of the tank. Then the expression we are looking for is
[tex]12-10\text{ 1/8}[/tex]A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 2 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then us
this equation to find the total length of the road after the crew has worked 32 days.
Equation:
Total length of the road after 32 days: ___ miles
Answers
Answer: 456 Miles
Step-by-step explanation:
There are different types of proofs: two-column, paragraph and flow chart. Which of these type of proofs do you prefer? Why?
Answers
I prefer the two-column proof since it is the most common format in high school textbooks. One can easily find each of the steps of the proof, and one can correct any step so you can continue the next one step by step in a chronological list of them.
It is easy to audit this type of proof, and I am very comfortable using it.
Find the equation of the tangent line e^-4t at t=0
Answers
Given -
y = e^-4t
To Find -
The equation of the tangent =?
Step-by-Step Explanation -
y = e^-4t
So, dy/dx =
y' = -4e^-4t
also,
m = y'(0) = -4e^-4(0)
= -4
So,
when x = 0, y = e^0 = 1
So, point of tangency is (0,1)
Slope of tangent is -4
Using point-slope form:
y - 1 = -4(x - 0)
y = -4x +1
Final Answer -
The equation of the tangent =
y = -4x +1 or at x = t
y = -4t +1
An order is received for 180 mL of a 2.5% solution to be prepared from diluting a 15% solution with water. How much of the stock 15% solution is needed?
a.
20 mL
b.
25 mL
c.
30 mL
d.
35 mL
Answers
We need 30 ml of the 15 percent solution to complete the order.
Here, we are given that we need to prepare 180 mL of a 2.5% solution by diluting a 15% solution with water.
the 180 ml 2.5% solution will contain-
2.5% pf 180 ml acid
= 2.5/100 × 180
= 25/1000 × 180
= 1/40 × 180
= 18/4
= 9/2
= 4.5 ml
Water in the 180 ml solution will be = 180 - 4.5 = 175.5
Now, we have say x ml of 15% solution
It must contain 4.5 ml of acid
Thus-
15% of x = 4.5
15/100 × x = 4.5
x = 4.5 × 100/15
x = 450/15
x = 30
Thus, we need 30 ml of the 15 percent solution, hence, option C.
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(x,y) --> (x-8,y+4)
what is the image A(2,6)
Answers
Translation involves changing the position of a shape. The image of A is A' is (-6,10)
The translation rule is given as: ( x, y)--->( x-8,y+4)
The point is given as: A = (2,6)
Substitute 2 for x and 6 for y
(2,6)------>(2-8,6+4)
(2,6)------>(-6,10)
This means that: (-6,10)
Hence, the image of A is: A' = (-6,10)
What is a translated image?
Image-to-image translation is the process of transforming an image from one domain to another with the goal of learning to associate an input image with an output image.
The translation image of a form can be found using the following rule or formula. Suppose you want to translate or move point P a unit horizontally and b unit vertically. Then change the x and y values of the P coordinates. The points of the triangle are A(-3, 1), B(-, 3) and C(-2 ).
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Why are lysosomes important to the health of cells?(1 point)
Responses
They break down worn-out cell parts that are no longer needed.
They break down worn-out cell parts that are no longer needed.
They move proteins around the cell.
They move proteins around the cell.
They allow cell organelles to move freely through the cell as needed.
They allow cell organelles to move freely through the cell as needed.
They create cell boundaries and make cells rigid.
They create cell boundaries and make cells rigid.
PLEASE HELP ME!!!
Answers
Lysosomes are important to the health of cells of the following reason:
They break down worn-out cell parts that are no longer needed.What are Lysosomes?Lysosomes can be defined as protective organelles that contain enzymes that can be used to break down negative microorganisms that invade the body. The Lysosomes are very important to the health of cells because they protect the cells from being damaged by viruses and bacteria that can limit the growth of the body.
So, the option that explains why lysosomes are important to the health of cells is that they break down worn-out cell parts that are no longer needed. Option A is accurate.
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What are the missing reasons in the proof?
50 points!
Answers
The missing reasons in the proof that shows that the triangles are congruent by SSS are:
3. Definition or parallelogram
4. Alternate interior angles theorem
5. Reflexive property of congruency
6. SSS Congruence Theorem
What is the SSS Congruence Theorem?The SSS congruence theorem is applicable when two triangles have three pair of corresponding side lengths that are congruent to each other. The SSS congruence theorem states that they are congruent to each other. This theorem can be used in proof where it is established that the three sides of two triangles are equal to each other.
What is the Reflexive Property of Congruency?A side is congruent to itself according to the reflexive property of congruency. This means that if two triangles share a common side, the two angles therefore have a pair of corresponding congruent sides in a proof.
Therefore, the missing reasons for the proof are explained below:
Statements Reasons
1. AD║BC 1. Definition or parallelogram
2. ∠ADB ≅ ∠CBD 2. Alternate interior angles theorem
3. AB║CD 3. Definition or parallelogram
4. ∠ABD ≅ ∠CDB 4. Alternate interior angles theorem
5. DB ≅ DB 5. Reflexive property of congruency
6. ΔABD ≅ ΔCDB 6. SSS Congruence Theorem
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