Answers
Angle A = arccos(5/13) = 67.4 degrees
yes the answer was the same
Related Questions
The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%
Answers
You can obtain this answer by looking at the percentage of each subgrouping. For instance, 33% of the class in juniors and 45% of them list soccer as their favorites. Thus showing that 14.85% of the entire school is made up of juniors that enjoy soccer.
If you do the totaling for all soccer lovers, you get a total of 41.95% of the school. By dividing the two numbers you get the answer above.
The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.
How to calculate the probability?The percentage of student on Junior level who like soccer will be:
= 33% × 45%
= 0.1485
The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:
= 0.1485/0.42
= 0.354
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The measure of angle x is 25 more than 4 times the measure of its complement. find the measure of x. x= degrees
Answers
x = 385 -4x . . . . . . . . . eliminate parentheses
5x = 385 . . . . . . . . . . . .add 4x
x = 77 . . . . . . . . . . . . . . divide by 5
The measue of angle x is 77°.
The table shows different geologic time periods: Period Number of Years Ago Jurassic 2.08 ⋅ 108 Silurian 4.38 ⋅ 108 Tertiary 6.64 ⋅ 107 Triassic 2.45 ⋅ 108
Order the time periods from oldest to youngest. (4 points)
1. Tertiary, Jurassic, Triassic, Silurian
2.Jurassic, Triassic, Silurian, Tertiary
3.Silurian, Triassic, Jurassic, Tertiary
4.Triassic, Silurian, Jurassic, Tertiary
Answers
A knife is 3 times the cost of the spoon 9 spoons and 12 knives costs £82.80 work out the cost of 1 knife
Answers
Hope this helped!
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon.9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations.The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12\times(3x)= 82.80[/tex]
[tex]9x + 36x = 82.80[/tex]
[tex]45x =82.80[/tex]
[tex]x = 1.84[/tex]
Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].
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Rosen 15 how many solutions are there to the equation x1 x2 x3 x4 x5
Answers
Therefore, if x⁵ is the highest exponent, then there are 5 possible answers.
However, it is important to note that not all of these have real answers for each one. In some cases, an x⁵ equation will have a number of real answers and a number of imaginary answers. Nevertheless, they will always add to 5.
if 7(t-4)-2t=4(t-3), what is the value of t?
Answers
multiply 7 and 4 by all in parentheses
(7*t) + (7*-4) - 2t= (4*t) + (4*-3)
7t -28 - 2t= 4t - 12
combine like factors
5t - 28= 4t - 12
add 28 to both sides
5t= 4t + 16
subtract 4t from both sides
t= 16
CHECK:
7(t-4)-2t=4(t-3)
7(16-4) - 2(16)= 4(16-3)
7(12) - 32= 4(13)
84 - 32= 52
52= 52
ANSWER: t= 16
Hope this helps! :)
What is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
{x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
Answers
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
The domain is formed by the values of x, the first value of the ordered pairs (x,y), in this case 3, 6, -1, 5, and -4. Ordering the values:
Domain of the function={x | x = –4, –1, 3, 5, 6}
Answer: First option {x | x = –4, –1, 3, 5, 6}
Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (2,4) and has the origin as its vertex. what is the standard form of the equation
Answers
.. f(x) = a(x -0)^2 +0
.. f(x) = ax^2
For the given point,
.. f(2) = 4 = a*2^2 = 4a
Then a=1 and your equation is
.. f(x) = x^2
What is the measure of
A. Cannot be determined
B. 74
C. 16
D. 32
Answers
Why? The triangle in the problem is an isosceles triangle. That means the two legs of the triangle are equal and the angle opposite to the equal legs are also equal.
Therefore, angle C is also 74°.
The sum of the interior angles of a triangle is equal to 180°.
Thus,
180° = ∡A + ∡B + ∡C
180° = 74° + ∡B + 74°
180° = 148° + ∡B
∡B = 180° - 148°
∡B = 32°
Simone is buying 10 bracelets for her friends. Each bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
Answers
that is $100 so I'm assuming the extra $2 is because of taxes
=98 which mean simone is right
The height of a tree was 4.8m .After one year the height of the tree was increased by 12.5%.find its new height
Answers
The new height of the tree after it has increased by 12.5% is 5.4 meters
To find the new height of the tree after it has increased by 12.5%, we start by calculating the increase in height using the following equation
Increase = 12.5% of the original height
The original height is given as 4.8m. So, the formula can be expressed as follows
Increase = 12.5% * 4.8
Increase = 0.125 * 4.8
Increase = 0.6 meters
Add the increase to the original height
New height = Original height + Increase
The above equation can then be expressed as follows
New height = 4.8 + 0.6
New height = 5.4 meters
How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Answers
Since Y and Z are on the same horizontal line, the distance between them is the difference of their x-coordinates: 6 - 1 = 5.
The segment XZ is the hypotenuse of a right triangle with sides 3 and 5, so its length is
.. XZ = √(3^2 +5^2) = √34
XY = 3
YZ = 5
XZ = √34 ≈ 5.83095
I need help ASAP. I don't understand how to solve this
3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45 day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?
4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45 day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?
Answers
3. Your emergency fund is 4 times your expenses so is
.. emergency fund = 4*(1500.45) = 6001.80
Half that amount is 3000.90.
The interest earned at 3.15% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0315*(45/365) = 11.65
The interest earned at 4.65% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0465*(45/365) = 17.20
Your total interest in 45 days is $11.65 +17.20 = $28.85
4. The calculation is the same, only the amounts are different.
The interest earned at 3.15% for 45 days on 1500.45 is
.. I = Prt = 1500.45*.0315*(45/365) = 5.83
The interest earned at 4.65% for 45 days on 4501.35 is
.. I = Prt = 4501.35*.0465*(45/365) = 25.81
The total interest earned in this scenario is $5.83 +25.81 = $31.64
This is $31.64 -28.85 = $2.79 more than the interest earned in question 3.
_____
You could work this using weighted average interest rates.
3. The rate earned is (3.15 +4.65)/2 = 3.90% for 45 days, or 0.480822% of the 6001.80 balance, about $28.86
4. The rate earned is (3.15 +3*4.65)/4 = 4.275% for 45 days, or 0.527055% of the balance. The difference is 0.046233% of the balance, or $2.77.
Note the pennies difference from the numbers above. The differences are due to the way the numbers round off when there are two accounts. The numbers above would better match what you would see at your bank.
The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.
Calculating Interest for Emergency Funds in Savings and CDs
To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.
Answer to Question 3
Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.
Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.
The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.
So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.
The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.
Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.
Answer to Question 4
If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.
The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.
So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.
The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.
Which of the following is equal to (2x/3 - 7) + 7
A. (2x - 7) + 21
B. 2x - 21/3
C. 3x/2
D. 2x/3
@texaschic101
Answers
The order of the mathematical operations is PEMDAS.
Therefor the first step you will take is to solve the operation inside the parenthesis.
(2x/3 - 7) =(2x/3 - 7)* 3/3 = 2x/3 - 21/3 = (2x - 21)/3
While adding or subtracting fractions, dont forget to check that each term have the same denominator.
Then the operation outside the parenthesis,
(2x - 21)/3 + 7 = (2x-21)/3 + 7 * 3/3 = (2x - 21)/3 + 21/3 =
(2x - 21 + 21) / 3 = 2x/3
The final answer is D. 2x/3
Y= v^2/2a solve for v
Answers
Y = (a v^2)/2
Y = (a v^2)/2 is equivalent to (a v^2)/2 = Y:
(a v^2)/2 = Y
Divide both sides by a/2:
v^2 = (2 Y)/a
Take the square root of both sides:
Answer: v = sqrt(2) sqrt(Y/a) or v = -sqrt(2) sqrt(Y/a)
Final answer:
To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).
Explanation:
The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.
Multiply both sides of the equation by 2a: 2ay = v²Take the square root of both sides to solve for v: v = √(2ay)This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.
PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
Answers
And it's obvious that it's d
What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answers
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
Select all of the potential solution(s) of the equation 2log5x=log54.
Answers
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21
Answers
Cube Root 53 = 3.76
The ratio is 10.36/3.76 = 2.76
Cube Root (21) = 2.76 to 3 places.
D <<<<<<<answer.
There is another way to do this (much better I think).
1113/53 = 21
A solid has 3 dimensions. Each dimension of the big solid will be k times bigger than the little one.
Therefore the volumes are related by a factor of cube root(large one ) to small one = cube root (21)
helppppppppppppppppppppppppppppppp
Answers
8 < 2b
2b > 8
b > 8 ÷ 2
b > 4
2b + 15 < 5
2b < 5 - 15
2b < -10
b < -10 ÷ 2
b < -5
Ans: b > 4 or b < - 5 (Answer A)
If the public debt of the United States in 2002 was $6,228,235,965,597.16 and the budget deficit in 2003 was $554,995,097,146.46, what was the public debt in 2003?
A. $11,778,186,937,061.76
B. $5,673,240,868,450.70
C. $5,549,950,971,464.60
D. $6,783,231,062,743.62
Answers
i am taking the test as well
Based on the public debt in 2002 and the budget deficit incurred in 2003, the public debt in 2003 was D. $6,783,231,062,743.62.
The budget deficit refers to the amount that the government had to borrow in order to fund the budget of the country.
To find the public debt in 2003 therefore, you need to add the debt of the previous year to the deficit of the current year.
= 2002 Public debt + Budget deficit
= 6,228,235,965,597.16 + 554,995,097,146.46
= $6,783,231,062,743.62
In conclusion, the public debt in 2003 was $6,783,231,062,743.62.
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.please help me thank you you will be given brainley
Answers
Hope this helps!
Eighty percent of the dogs have completed obedience classes. How many of the dogs have completed obedience classes? Five dogs of different breeds 4 dogs 3 dogs 2 dogs 1 dog
Answers
x--------> number of dogs that completed the obedience class
we know that
total number of dogs=5
Eighty percent of the dogs have completed obedience classes
so
x=0.80*5------> x=4
the answer is
4 dogs have completed obedience classes
4 dogs have completed the obedience classes
Explanation:
We are given that 80% of the dogs completed the obedience classes and that the total number of dogs who attended the class was 5
This means that 80% of the 5 dogs have completed the class
Therefore:
number of dogs that completed the class = 80% * 5
= 0.8 * 5
= 4 dogs
Hope this helps :)
1. A sine function has the following key features:
Frequency = 16π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
2. A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
3. A sine function has the following key features:
Period = 4π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
4. picture
5. picture
Answers
See the attached image (figure 1)
16pi seems like a typo. I'm going to assume that it's a fraction and it is 1/(6pi)
f = 1/(6pi) = frequency
T = 1/f = 1/(1/(6pi)) = 6pi
Amplitude = 2
a = 2
b = 2pi/T = 2pi/(6pi) = 1/3
Midline: y = 3
d = 3
The function is
y = a*sin(bx-c)+d
y = 2*sin(1/3*x-0)+3
y = 2*sin(x/3)+3
===============================================
Problem 2
See the attached image (figure 2)
T = 12 is the period
a = 4 is the amplitude
b = 2pi/T = 2pi/12 = pi/6
y = 1 is the midline so d = 1
The y intercept is (0,1) which is the midline, which indicates no phase shifts have occurred so c = 0
The function is
y = a*sin(bx-c)+d
y = 4*sin((pi/6)x-0)+1
y = 4*sin((pi/6)x)+1
===============================================
Problem 3
See the attached image (figure 3)
Period = 4pi
T = 4pi
b = 2pi/T = 2pi/(4pi) = 1/2 = 0.5
Amplitude = 2
a = 2
Midline: y = 3
d = 3
y-intercept: (0,3)
The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2
The function is
y = a*sin(bx-c)+d
y = -2*sin(0.5x-0)+3
y = -2*sin(0.5x)+3
===============================================
Problem 4
See the attached image (figure 4)
a = 10 which is half of the distance between the highest and lowest points
T = 8 is the period
b = 2pi/T = 2pi/8 = pi/4
c = -pi/2 is the phase shift since its really a cosine graph
d = 0 is the midline
The function is
y = a*sin(bx-c)+d
y = 10*sin((pi/4)*x+(-pi/2))+0
y = 10*sin((pi/4)*x+pi/2)
===============================================
Problem 5
See the attached image (figure 5)
a = 2 is the amplitude since it bobs up and down this distance from the midline
T = 8 seconds is the period (double that of the time it takes for it to go from the highest to the lowest point)
b = 2pi/T = 2pi/8 = pi/4
c = 0 is the phase shift as the buoy starts at normal depth of 20 meters
d = 20 is the midline
The function is
y = a*sin(bx-c)+d
y = 2*sin((pi/4)x-0)+20
y = 2*sin((pi/4)x)+20
===============================================
Answer:
1. Picture Below
2. Ordered Pair : (0,1) (3,5) (6,1) - Function: f(x)=4sin(pi/6x)+1
3. Ordered Pair : (0,3) (3.14,5) (6.27,3) - Function: f(x)= 2sin(1/2x)+3
4. I have no idea.
5. Plot the first point at (0, 20) and the second point at (2, 22)
Step-by-step explanation:
o valor da expressão a=1,67 . 10 + 3,95 . 10
Answers
First we rewrite the expression:
a = (1.67 * 10) + (3.95 * 10)
We multiply each member of the parenthesis by 10:
a = 16.7 + 39.5
We add both values:
a = 56.2
Answer:
We note that the value of the expression for a is:
a = 56.2
Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]
Answers
This brings us to our first step: filling in the x-coordinates (of the domain) in the formula.
f(0) = 3*0 - 2 = -2
f(5) = 3*5 - 2 = 15- 2 = 13
We now have found the following coordinates
(0,-2) and (5,13).
To find the avarage rate of change we need to use the following formula:
rate of change = Δy / Δx
With Δ representing the change of coordinates. Filling in this formula, gives us:
rate of change = [tex] \frac{13 - -2}{5 - 0} = \frac{15}{5} = 3 [/tex]
So our answer: the average rate of change on the interval (domain) [0,5] is 3.
The average rate of change of the function over the given interval is 3.
Explanation:To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.
Step 1: Calculate the function values for the two endpoints of the interval.
f(0) = 3(0) - 2 = -2
f(5) = 3(5) - 2 = 13
Step 2: Calculate the change in the function values.
Change in function values = f(5) - f(0) = 13 - (-2) = 15
Step 3: Calculate the change in the input values.
Change in input values = 5 - 0 = 5
Step 4: Divide the change in function values by the change in input values.
Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3
The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
Answers
a) Basically, you are adding the length of porch to the original length of the parlor.
Let's say that the newly added porch is x.
(50 + x)(32 + x)
1600 + 50x + 32x + x²
x² + 82x + 1600
b) Just make the polynomial x² + 82x + 1600 equal to 2320.
x² + 82x + 1600 = 2320
subtract 2320 on both sides to make the polynomial equal to 0.
x² + 82x - 720 = 0
factor this
(x - 8)(x + 90) = 0
(x - 8) =0 (x + 90) = 0
x = 8 x = - 90
(-90ft doesn't make sense. So don't mind about this.)
So the porch should be 8ft.
Hope this helped!
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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#SPJ2
Find the measure of “rst”
Answers
Answer: it is 110 bcs each section in 10° and there are 11 sections
Which properties of equality justify steps b and d?
1. Multiplication Property of Equality; Subtraction Property of Equality
2. Subtraction Property of Equality; Division Property of Equality
3. Subtraction Property of Equality; Multiplication Property of Equality
4. Subtraction Property of Equality; Subtraction Property of Equality
Answers
Subtracting seven from both sides is the justification for step b to get rid of the positive seven on both sides. Multiplying by 2 on both sides to get rid of the fraction on the left side of the equation is the justification for step d.
The properties that justify steps b and d, is 1. Multiplication Property of Equality; Subtraction Property of Equality.
Understanding these properties is crucial in solving equations properly.
Key Properties of Equality:
Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex], then [tex]a \times c = b \times c[/tex].
Subtraction Property of Equality: This property indicates that if you subtract the same number from both sides of an equation, the two sides will also remain equal.
Example: If [tex]a = b[/tex], then (a - c = b - c.
Division Property of Equality: Similar to multiplication, this property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex] and [tex]c \neq 0[/tex], then [tex]\frac{a}{c} = \frac{b}{c}[/tex].
Justification Steps b and d:
Given the context, let's assume step b involves subtracting a term from both sides of an equation, and step d involves multiplying both sides by a number.
For step b (subtracting x):
This step is justified by the Subtraction Property of Equality because the same amount [tex]x[/tex] is subtracted from both sides, which keeps the equality balanced.
For step d (multiplying by a number):
This step is justified by the Multiplication Property of Equality as you are multiplying both sides of the equation by the same non-zero number, thus preserving the equality.
Three brothers have ages that are consecutive even integers. the product of the first and third boys' ages is 20 more than wice the second boy's age. find the age of each of the three boys.
Answers
second brother = x + 2
third brother = x + 4
The product of the first and third boys' ages is 20 more than twice the second boy's age:
x(x+4) = 2(x+2) + 20
x² + 4x = 2x + 4 + 20
x² + 4x - 2x - 24 = 0
x² + 2x - 24 = 0
(x - 4)(x + 6) = 0
x = 4 or -6 (rejected, age cannot be negative)
First brother = 4
Second brother = 4 + 2 = 6
Third brother = 4 + 4 = 8
The three boys are 4, 6, and 8 years old.
Let x be the age of the first boy, snce they are consecutive even integers, they will be 2 way from each other.
1st boy= x
2nd boy= x+2
3rd boy = x+4
"product means the answer to a multiplication problem;
x(x+4)=20+2(x+2)
x%5E2+4x=20+2x+4
x%5E2+4x-2x=20+4
x%5E2+2x=24
x%5E2+2x-24=0
(x+6)(x-4)=0
x+6=0
x=-6
x-4=0
x=4
SInce we know they are even integers, the answerhas to be;
x=4
so the first boys age = 4
2nd boy= 4+2=6
3rd boy= 4+4=8
Hope this helps you