The equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3) is f(x) = 4.366*log10(x+4)
To find the equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3), we need to determine the values of a, b, h, and k.
First, we know that the function passes through (1,0), so we can substitute x=1 and y=0 in the general equation of the transformed logarithmic function to get:
0 = a x log b(1-h) + k
Since log b(1-h) = 0 for any base b and any value of h, we can simplify the equation to:
0 = k
Therefore, k=0 and the equation becomes:
f(x) = a x log b(x-h)
Now, we have two equations with two unknowns (a and h), which we can solve by substitution or elimination. For simplicity, we can substitute b=10 (base 10 logarithm) since it is a common base and the values of a and h do not depend on the base of the logarithm. We get:
10⁶/ᵃ = 3-h
Since h is the horizontal shift of the graph, we can choose any value of h that makes the expression inside the logarithm positive. For example, we can choose h=-4, which makes x-h=-3-(-4)=1, the same as the x-coordinate of the point (1,0).
Taking the logarithm of both sides with base 10, we get:
log(4) = (6/a)*log(10)
Solving for a, we get:
a = 6/(log(4)*log(10)) ≈ 4.366
Now, we can substitute the values of a and h in the equation of the transformed logarithmic function to get:
f(x) = 4.366*log10(x+4)
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The function h(t)=-4t^2+14t+8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked. How long does it take for the football to hit the ground?
Answer:
t = 4
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function, when h(t) equals 0 that means the ball is touching the ground, giving the maximum time it took for the ball to hit the ground.
[tex]\frac{-b\frac{+}{-} \sqrt{b^2-4*a*c} }{2*a} \\\frac{-14\frac{+}{-} \sqrt{14^2-4*-4*8} }{2*-4} \\t = -0.5,4[/tex]
It takes 4 seconds, since time can not be negative
Angles in a Triangle
Answer:
a = 40°
Step-by-step explanation:
An isosceles triangle has two sides that are the same size. The angles opposite from those sides are equal (they are called base angles.) And, the three angles in a triangle add up to 180°
So,
100 + a + a = 180
combine like terms
100 + 2a = 180
subtract 100
2a = 80
divide by 2
a = 40
IF YOU CAN ANSWER THIS CORRECT WITH A Good explanation I'll give 5 stars, a thanks and brainly (also your very smart)
Rebecca is x years old.Mary is 8 years older than rebecca. Jill is three times older than mary. The sum of their ages is 67.
A) form an expression in terms of x
Answer:
A) 5x+32=67
Rebecca is 7, Mary is 15, and Jill is 45
Step-by-step explanation:
Rebecca is x years old.
If Mary is 8 years older than Rebecca, Mary's age is 8 more than x.
We can write Mary's age as:
x+8
Jill is three times older than Mary.
This means that Jill's age is equal to three times x+8.
We can write Jill's age as:
3(x+8)
Use the distributive property.
3(x+8)=
3x+24
So, Jill's age (in terms of x) is 3x+24.
The sum of their ages is 67, so if we add all of their ages, we will get 67.
x+(x+8)+(3x+24)=67=
5x+32=67
Not sure if you want this solved, but here it is:
5x+32=67=
5x=35=
x=7
Let's find Mary's age.
x+8=
7+8=
15.
Now, let's find Jill's age.
3x+24=
3(7)+24=
21+24=
45.
So, Rebecca is 7, Mary is 15, and Jill is 45.
please help me, i need it :)
Chloe can travel 4.4 miles less than Jin on one gallon of gas.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
Chloe travels 93 miles on 5 gallons of gas, hence the constant is given as follows:
k = 93/5
k = 18.6 miles per gallon.
Jin's ratio is of 23 miles per gallon, hence he can travel more and the difference is given as follows:
23 - 18.6 = 4.4 miles per gallon.
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The scale drawing car length is 3cm. If the scale is 1cm:4ft, what is the actual car length?
Answer: The actual car length is 12ft.
Step-by-step explanation:
Actual car length = 3cm x 4ft/cm = 12ft
Two different rectangles are joined together to make a compound shape. Shape A has a length of (x + 3) and a width of (x + 2). Shape B has a length of (x + 6) and a width of (x-2). All measurements are in centimetres. (x+3) Shape A Shape B (x+6) (x + 2) NOT TO SCALE (x-2) Find an expression for the area of the compound shape in cm². Give your answer in the form ax² + bx + c.
The expression for the area of the compound shape in cm² is 2x^2 + 11x - 6.
What is the expression for the area?To find the expression for the area of the compound shape, we need to first calculate the individual areas of Shape A and Shape B, and then add them together.
The area of Shape A is given by multiplying its length and width:
Area of Shape A = (x + 3) * (x + 2)
The area of Shape B is given by multiplying its length and width:
Area of Shape B = (x + 6) * (x - 2)
Now, we can add the two areas together to get the expression for the area of the compound shape:
Area of compound shape = Area of Shape A + Area of Shape B
= (x + 3) * (x + 2) + (x + 6) * (x - 2)
Expanding the above expression, we get:
= x^2 + 2x + 3x + 6 + x^2 + 6x - 12
= 2x^2 + 11x - 6
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Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
To the nearest whole dollar, the antique dresser was purchased by Danielle as follows: A. purchase price: $120, advertised price: $300.
How the purchase price is determined?The purchase price of the antique dresser can be determined by reversing the solution from the discounted price.
The discounted price is divided by the discount factor to calculate the advertised or marked price.
Let the purchase price of the antique dresser = x
Markup = 250%
Discount = 15%
Discounted price = $255
Discount factor = 0.85 (1 - 0.15)
Marked up or advertised price = $300 ($255 ÷ 0.85)
Purchase price = $120 ($300 ÷ 2.5)
Thus, the correct option is Option A.
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In circle O, chords AB and CD intersect at E, AE = 3 inches, BE = 8 inches, and CE is 2 inches longer than DE. What is the length of DE, expressed in inches?
Okay, let's break this down step-by-step:
* Circle O has chords AB and CD that intersect at E
* AE = 3 inches
* BE = 8 inches
* CE is 2 inches longer than DE
So we know:
AE = 3 inches
BE = 8 inches
CE = DE + 2 inches
To find DE, we can use the Pythagorean theorem for any right triangle:
a^2 + b^2 = c^2
In this case:
3^2 + 8^2 = c^2
9 + 64 = 73
c = 8 inches
So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.
Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).
We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):
sin(A) = DE / 8
DE = 8 * sin(A)
Without knowing the angle A, we can make an estimate:
sin(A) ≈ A (for small A)
So DE ≈ 8A inches
Now we know:
CE = DE + 2 inches
And DE ≈ 8A inches
So: 8A + 2 = DE
=> DE = 10A
And since A is small, we can say: DE ≈ 10 * A inches
To summary, if AE = 3 inches and BE = 8 inches,
then DE ≈ 10 * A inches
DE is approximately 10 times some small angle A.
Does this make sense? Let me know if you have any other questions!
Minimise : 3x+2y
Subject to: 5x+y=10
X+y=6
X+4y= 12
Find this question?
This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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=
Suppose that you decide to borrow $14,000 for a new car. You can select one of the following loans, each requiring
regular monthly payments.
Installment Loan A: three-year loan at 5.1%
Installment Loan B: five-year loan at 4.8%
PA
[1-(1-+-:)]
Use PMT=
to complete parts (a) through (c) below.
a. Find the monthly payments and the total interest for Loan A.
The monthly payment for Loan A is S
(Do not round until the final answer. Then round to the nearest cent as needed.)
mlm
*****
H
√
V
1,
(0,0)
More
Answer:
$2,602.44
Step-by-step explanation:
To find the monthly payments and the total interest for Loan A, we can use the formula for the present value of an installment loan:
PV = PMT x [1 - (1 + r/n)^(-nt)] x (n/r)
where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years of the loan.
For Loan A, we have:
PV = $14,000
r = 0.051 (5.1% as a decimal)
n = 12 (monthly payments)
t = 3
Substituting these values into the formula and solving for PMT, we get:
PMT = PV / ([1 - (1 + r/n)^(-nt)] x (n/r))
= 14000 / ([1 - (1 + 0.051/12)^(-12*3)] x (12/0.051))
= $417.79
So the monthly payment for Loan A is $417.79.
To find the total interest paid over the life of the loan, we can simply multiply the monthly payment by the total number of payments and subtract the original loan amount:
Total interest = PMT x (nt) - PV
= 417.79 x (3 x 12) - 14000
= $2,602.44
Therefore, the total interest paid for Loan A is $2,602.44.
you roll a 6 sided die; what is P(4 or less than 3)
Answer:
1/2
Step-by-step explanation:
The probablility of any number on a die is 1/6.
So the numbers 4, 2, and 1 each have a probability of 1/6 meaning that each have a total probability of: 1/2. 3 is not accounted for due to our restriction.
Select the statement that shows equivalent measurements.
4.5 meters = 0.0045 kilometers
4.5 meters = 0.045 centimeters
4.5 meters = 0.45 decimeters
4.5 meters = 45 decameters
The statement that shows equivalent measurements is "4.5 meters = 0.0045 kilometers".
How to solve the problem?
To convert meters to kilometers, we need to divide by 1000, since there are 1000 meters in a kilometer. Therefore, 4.5 meters is equal to 4.5/1000 = 0.0045 kilometers.
The other statements are incorrect:
4.5 meters is not equal to 0.045 centimeters, since there are 100 centimeters in a meter, so 4.5 meters is equal to 450 centimeters.
4.5 meters is not equal to 0.45 decimeters, since there are 10 decimeters in a meter, so 4.5 meters is equal to 45 decimeters.
4.5 meters is not equal to 45 decameters, since there are 10 meters in a decameter, so 4.5 meters is equal to 0.45 decameters.
It is important to be able to convert between different units of measurement in order to make accurate comparisons and calculations. In this case, the correct conversion factor was used to convert meters to kilometers, resulting in an equivalent measurement.
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Calculate how far the village is north of O
Step-by-step explanation:
See image
It’s probability and I need your help pls
The theoretical probabilities are: 0.15, 0.15, and 0.05 respectively
What is probability?Probability is a branch of mathematics concerned with the analysis of random phenomena
The given parameters that will help us to get the probabilities are
25% are stakeholders
20% have dark hair
The probability of being stakeholders 20%/25%
= 0.20/0.25 = 0.
b) 1-0.8 * 1.0.25
0.2 * 0.75 = 0.15
c. 0.2 * 0.75 = 0.15
d. Has light hair and is a stakeholder
0.20 * 0.25
= 0.05
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I need help with questions 2 and 3 please.
Answer:
1.x=7 or x=-7
2.x=root of 65 or x=-root of 65
Step-by-step explanation:
I have put what I mean by root 65
HELPP Billie solved the equation below by completing the square, but she got the incorrect solution. In which step did Billie first make an error?
Step 1 : x 2 + 6 x = 16
Step 2 : x 2 + 6 x + 9 = 16
Step 3 : ( x + 3 ) 2 = 16
Step 4 : x + 3 = ± 4 Step 5 : x = 1 , x = − 7
Billie made the error in the second step of the equation
How to solve the equationBillie made an error in Step 2. She added 9 to one sides of the equation, but she should have added 9 to the left side only. The correct steps are as follows:
Step 1: x^2 + 6x = 16
Step 2: x^2 + 6x + 9 = 16 + 9
Step 3: (x + 3)^2 = 25
Step 4: x + 3 = ±√25
Step 5: x = -3 + 5, x = -3 - 5
Step 6: x = 2, x = -8
So, the correct solutions are x = 2 and x = -8.
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Find the measure of 3x-46+14=90
Answer:
Step-by-step explanation:
3x = 90 + 46 - 14
3x = 122
x=[tex]\frac{122}{3}[/tex]≈40,7
Answer: 40.6 repeated
Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated
A lunch box is 24 cm long, 15 cm wide and 5 cm thick. What is
the volume of the lunch box?
Answer:
( Use this formula below to help you find the volume of all equations using volume)
Volume formal = L × W × H
Volume formal = 24 × 15 × 5
Answer = 24 × 15 × 5 = 1,800
9. Maria is twice the age of Jonas, who is
twice the age of Franklin. Franklin is 2. yr
less than half Maria's age. How old are
Maria, Jonas, and Franklin?
Answer: Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.
Step-by-step explanation: Let's start by assigning variables to represent the ages of Maria, Jonas, and Franklin.
Let's use the variable "M" to represent Maria's age.
Let's use the variable "J" to represent Jonas's age.
Let's use the variable "F" to represent Franklin's age.
From the problem statement, we know that:
Maria is twice the age of Jonas: M = 2J
Jonas is twice the age of Franklin: J = 2F
Franklin is 2 years less than half of Maria's age: F = 0.5M - 2
We can use these equations to solve for the ages of Maria, Jonas, and Franklin.
First, we can substitute J = 2F into the equation M = 2J to get M = 2(2F) = 4F.
Next, we can substitute this expression for M into the equation F = 0.5M - 2 to get F = 0.5(4F) - 2, which simplifies to 2F = 6 and therefore F = 3.
Now that we know Franklin's age, we can use the equation J = 2F to find Jonas's age: J = 2(3) = 6.
Finally, we can use the equation M = 2J to find Maria's age: M = 2(6) = 12.
Therefore, Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.
Find a rational number halfway in between the two numbers.
8/10 and 1/8
A rational number between 8/10 and 1/8 is 37/80.
We know that a rational number between two rational numbers can be given by finding the average of the two given numbers:
The numbers are 8/10 and 1/8.
Let's simplify the fractions first:
8/10 = 4/5 (dividing both numerator and denominator by 2)
1/8 = 1/8 (already in simplest form)
Average = [tex](\frac{4}{5} + \frac{1}{8})/2[/tex]
= [tex](\frac{(4*8) + (5*1)}{40} )/2[/tex]
= [tex](\frac{37}{40}) /2[/tex]
= [tex]\frac{37}{80}[/tex]
So, the rational number halfway between 8/10 and 1/8 is 37/80.
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help me in 8th grade mathhh
Answer:
C
Step-by-step explanation:
input y=x+3 into the second equation and solve for x
-2x+y=1
so -2x +x+3 =1
solve for x
x = 2
y= 5
A drawer is filled with 2 white shirts, 5 black shirts, and 3 gray shirts. One shirt is
chosen at random from the drawer. Find the probability that it is not a white shirt.
Okay, let's break this down step-by-step:
* There are 2 white shirts, 5 black shirts, and 3 gray shirts in the drawer.
* That's a total of 2 + 5 + 3 = 10 shirts.
* We want to find the probability that the chosen shirt is NOT white.
* So there are 5 + 3 = 8 shirts that are NOT white.
* Probability = (Number of favorable outcomes) / (Total possible outcomes)
* So in this case, Probability = 8/10 = 4/5
Therefore, the probability that the chosen shirt is NOT white is 4/5.
HELP ASAP (I chose 34 as random number) (please good explanation because I want to know how to do this well)
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 28 and 39. This number will represent how many points you earned. If you have a pop quiz worth a total of 40 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer. (4 points)
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40 points.
What is a percentage?A percentage is a means to represent a piece of 100 as a ratio or percentage. The sign for it is % (percent), which stands for "per hundred." If you state, for instance, that 50 out of 100 people like chocolate, then means that 50 out of 100 people, or 0.5 (50/100), like chocolate overall. In several disciplines, including finance, business, mathematics, and statistics, percentages are frequently used.
Part A:
Say we decide to set the number of points gained on the quiz at 40. The following formula is used to determine your percentage score if the quiz was worth a total of 40 points and you received 34 of them:
(Points earned / Total Points) x 100% is the percentage score.
Score in percentage: (34 / 40) x 100%
Score in percentages: 85%
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40.
Part B:
You would receive a B on the specified grading scale based on the percentage score of 85%. The percentage score gained in section A falls within the range required for a B grade on the grading scale, which is awarded for percentage scores between 80% and 89%.
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Suppose that 7 green balls and 9 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?
Answer: 0.2461
Step-by-step explanation:
There are 16 balls in total, and 9 of them are purple. If the first ball drawn is replaced before the second is drawn, then the number of purple balls and the number of total balls in the urn remain the same for the second draw.
The probability of drawing a purple ball on the first draw is 9/16. Since the ball is replaced, the probability of drawing a purple ball on the second draw is also 9/16.
The probability that the second ball drawn is a purple ball, given that the first ball drawn was replaced and was a green ball:
(7/16) * (9/16) = 63/256 ≈ 0.2461
In 1852, a person sold a house to a lady for $30. If the lady had put the $30 into a bank account paying 6% interest, how much would the investment have been worth in the year 2012 if interest were compounded in the following ways?
What is the equation of the line that represents the horizontal asymptote of the function
f(x) = 3000 (1 +0.09)^x-2 +4?
Answer: y=4
Step-by-step explanation:
The Parent function [tex]y=a^{x}[/tex] has a horizontal asymtote at y=0
because the function approaches 0 but never touches it no matter how small the number you input. See image. Asymtotes are like a boundary that is not passed
Your curve has been shifted up 4 so y=4
See image
Extra info: y-intercept = 3000
shifted right 2
to graph -5,5 start at 0,0 and then go?
Answer:
No
Step-by-step explanation:
to grap (-5,5) do not start at (0,0)
-5 is at the x axis so start it at (-0) then for 5 its juts (0) so (-0,0)
Cylinder 1 contains a 1.25 M stock solution of Cu(NO3)2. What volume of stock is needed to prepare 20.0 mL of 0.0750 M Cu(NO3)2 solution shown in Cylinder 2?
The Volume of stock solution needed = 1 mL
How to solveMolarity of stock solution (M1) = 1.50 M
The volume of stock solution needed (V1) = to be calculated
Molarity of diluted solution (M2) = 0.0750 M
The volume of diluted solution (V2) = 20 mL
M1V1 = M2V2
Volume of stock solution (V1) = M2V2 / M1 = (0.075 M x 20 mL) / (1.5 M) = 1 mL
So; the Volume of stock solution needed = 1 mL
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Adeline has a box full of notebooks. If she gives 13 notebooks to each of her children, she will have 8. notebooks left. if she gives 15 notebooks to each childish will have zero notebooks left.how many notebooks and how many children does Adeline have
Answer:
Adeline has 60 notebooks and 4 children.
Step-by-step explanation:
Let's assume that Adeline has 'x' notebooks and 'y' children.
According to the given information, if Adeline gives 13 notebooks to each child, she will have 8 notebooks left. This can be represented by the equation:
x - 13y = 8 ...(1)
Similarly, if she gives 15 notebooks to each child, they will have zero notebooks left, which can be represented by the equation:
x - 15y = 0 ...(2)
We now have two equations with two variables. To solve for 'x' and 'y', we can use the method of elimination. Multiplying equation (1) by 15 and equation (2) by 13, we get:
15x - 195y = 120 ...(3)
13x - 195y = 0 ...(4)
Subtracting equation (4) from equation (3), we get:
2x = 120
x = 60
Substituting the value of 'x' in equation (2), we get:
60 - 15y = 0
y = 4
Therefore, Adeline has 60 notebooks and 4 children.
Find the area of the shapes below. Make sure to label your answers with units.
You must show all of your work to receive credit.
Find the area for a
a) The area of the triangle is 13.3 square units.
b) The area of the rectangle is 57.4 square units.
Let's start with the triangle. The area of a triangle can be calculated by multiplying its base and height and then dividing the result by 2. In your case, the base of the triangle is 7 units and the height is 3.8 units. Therefore, the area of the triangle can be calculated as:
Area of triangle = (Base × Height) ÷ 2
= (7 × 3.8) ÷ 2
= 13.3 square units
Now, let's move on to the rectangle. The area of a rectangle can be calculated by multiplying its length and width. In your case, the width of the rectangle is 7 units and the height is 8.2 units. Therefore, the area of the rectangle can be calculated as:
Area of rectangle = Length × Width
= 8.2 × 7
= 57.4 square units
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