[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{45 = 3(4b - 1)}[/tex]
[tex]\mathsf{3(4b - 1) = 45}[/tex]
[tex]\mathsf{3(4b) + 3(-1) = 45}[/tex]
[tex]\mathsf{12b - 3 = 45}[/tex]
[tex]\large\textsf{ADD 3 to BOTH SIDES}[/tex]
[tex]\mathsf{12b - 3 + 3 = 45 + 3}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{12b = 45 + 3}[/tex]
[tex]\mathsf{12b = 48}[/tex]
[tex]\large\textsf{DIVIDE 12 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{12b}{12} = \dfrac{48}{12}}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{b = \dfrac{48}{12}}[/tex]
[tex]\mathsf{b = 4}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{b = 4}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
Determine a, b, c ∈ N*, different two by two, so that: [tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{c}[/tex] is an integer
Using a system of equations, a possible set of values for a, b and c such that it results in an integer number is given by:
a = 6, b = 3, c = 2.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this problem, the variables are the given ones of:
a, b and c.
An integer number is a number that has no decimal part, hence the easiest way to solve this is making the sum of 1.
Attributing a = 6, we have that:
[tex]\frac{1}{6} + \frac{1}{b} + \frac{1}{c} = 1[/tex]
[tex]\frac{1}{b} + \frac{1}{c} = \frac{5}{6}[/tex]
This is possible with these two fractions:
[tex]\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6}[/tex]
Hence the other possible values are given by:
b = 2, c = 3.
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whowever does my online math homework will get 200 points it yr9 maths (grade 8) maths
Answer:
I hope the deadline hasn't passed!
Your last question got deleted
mikala and joanna were each given $20 to spend on a trip mikala spent 3/4 of her money and jonna spent 3/5 of her money how much money did they spend together
Answer:
$27
Step-by-step explanation:
[tex] \frac{3}{4} (20) + \frac{3}{5} (20) = 15 + 12 = 27[/tex]
What is the image point of (0,5)(0,5) after the transformation r_{y=x}\circ R_{180^{\circ}}r y=x ∘R 180 ∘ ?
The image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The point is (0, 5)
As we know, the
The rule for the above transformation:
(x, y) → (-x, -y)
(0, 5) → (0, -5)
Thus, the image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
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Members of a softball team raised $1186.50 to go to a tournament. They rented a bus
for $842.50 and budgeted $21.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
The equation to determine the number of players the team can bring is $842.50 + $21.50y = $1,186.50
The team can bring 16 players to the tournament.
To go to a tournament, softball team members raised $1186.50 and rented a bus for $842.50, and the cost of meals of each player is $21.50.
Let y represent the number of players.
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50y = $1,186.50
Subtracting $842.50 from each side.
$21.50y = $1,186.50 - $842.50
$21.50y = $344
Divide both side of the equation by $21.50.
x = $344 / $21.50
x = 16 players
As a result, the team is allowed to enter 16 players into the competition.
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2. Ying sees this flyer. She decides to buy 12 of these boxes for her shoes. What total volume will these boxes occupy in her closet?
Step 1. Find the volume of just one box.
To find the volume V of one box, we multiply all of the dimensions of the box:
In this case, the volume of one box is:
[tex]V=29.5cm\times18cm\times9.5cm[/tex]The result is:
[tex]V=5,044.5cm^3[/tex]Step 2. We are told that Ying bought 12 boxes, so the total volume that the boxes occupy will be the volume of one box multiplied by 12:
[tex]12\times5,044.5cm^3=\boxed{60,534cm^3}[/tex]Answer:
[tex]\boxed{60,534cm^3}[/tex]What is the missing perfect square in this list?
81, 100, 121, ____, 169
A. 125
B. 160
C. 12
D. 144
Answer:
d 144
Step-by-step explanation:
Each number is the square starting with 10
10² = 100
11² = 121
12² = __?
13²=169
How to solve these three questions?
Using the normal distribution, it is found that:
a) The sampling distribution is approximately normal, with mean 45 and standard deviation 4.
b) The answer is not dependent on the sample size, as the underlying distribution is normal.
c) 0.0001 = 0.01% probability that the average is less than half an hour.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n is approximately normal, with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. If the underlying distribution is normal, there are no sample size restrictions, while if the underlying distribution is not normal, the Central Limit Theorem is only valid for sample sizes of 30 and greater.For this problem, the parameters are given as follows:
[tex]\mu = 45, \sigma = 12, n = 9[/tex]
Hence the standard error of the approximately normal sampling distribution of sample means of size 9 is:
s = 12/sqrt(9) = 12/3 = 4.
As stated in the problem, the underlying distribution is normal, hence this is not dependent on the sample size.
For item c, the probability is the p-value of Z when X = 30, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (30 - 45)/4
Z = -3.75
Z = -3.75 has a p-value of 0.0001.
Hence the probability is of 0.0001 = 0.01%.
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What is 7,984 -9,151 =
i need help with this please:-))
When two lines are perpendicular, their slopes have the following relation:
[tex]m_1=\frac{-1}{m_2}[/tex]If we rewrite this expression, we have:
[tex]m_1\cdot m_2=-1[/tex]The product of each slope is equal to -1.
Therefore the correct option is the fourth one.
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence
Answer is;
[tex]a_n=3n[/tex][tex]\begin{gathered} \text{common difference (d) =6-3=3} \\ By\text{ formula, } \\ a_n=a+(n-1)d\text{ , where a=3} \\ a_n=3+(n-1)3 \\ a_n=3+3n-3 \\ a_n=3n \end{gathered}[/tex]please help fast how do i what property do i need to solve this
h to the 3rd power g to the -7th power
Answer: the property needed to find this is negative exponents
Step-by-step explanation: find the reciprocal of g to the -7th power which would be 1 over g to the 7th power
Tiana deposited $60 in an account earning 10% interest compounded annually.
To the nearest cent, how much will she have in 3 years
PLSSS HELP MEEE
Classify quadrilateral RSTV. Support your answer by showing calculations.
The given quadrilateral RSTV is a kite.
What are quadrilaterals?The following characteristics apply to quadrilaterals, which are polygons.
It has four sides and four vertices surrounding four angles.A quadrilateral's interior angles add up to 360 degrees.To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:
[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]
In the given quadrilateral RSTV,
RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]
RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]
ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]
VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]
The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.
A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.
Therefore, the quadrilateral is a kite.
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An urn has 13 balls that are identical except that 6 are white and 7 are red. A sample of 7 is selected randomly without replacement.
What is the probability that exactly 5 are white and 2 are red?
What is the probability that at least 5 of the balls are white?
The probability that the exactly 5 are white and 2 are red is126/1716 and,
the probability that at least 5 of the balls are white is 133/1716
Given that:-
Total number of balls in the urn = 13
Number of white balls = 6
Number of red balls = 7
Number of randomly selected balls = 7
We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.
Probability that exactly 5 balls are white and 2 are red, P(x = 5) = [tex]\frac{^6C_5*^7C_2}{^{13}C_7}[/tex] = 126/1716 = 21/286
We know that,
Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)
We know that,
P(x = 6) = [tex]\frac{^6C_6*^7C_1}{^{13}C_7}[/tex] = 7/1716
Hence,
Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.
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A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length L (in miles) that is left to lay after d days is given by the following L (d)=189-7d
The number of days it will take the crew to lay all the track is; 27 days
The number of miles of track the crew has left to lay after 18 days is; 65 miles
How to solve Algebraic Equations?
We are given the equation that represents the length L (in miles) that is left to lay after d days as;
L(d) = 189 - 7d
where;
L is length in miles
d is number of days
Thus, the number of days it will take to lay all the tracks is;
Number of days = 189/7
Number of days = 27 days
The length L (in miles) that is left to lay after 18 days is;
L= 189 - 7(18)
L= 189 - 126
L= 65 miles
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Complete question is;
A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function. L(d) = 189 - 7d
(How many days will it take the crew to lay all the track?)
(How many miles of track does the crew have left to lay after 18 days?)
f(x)=4x+6 and g(x)=1/2*f(x) What is the function rule for function g?
g(x) = _________________ x+ _____________________
g(x) is a dilation of scale factor 1/2 of f(x), and the rule is:
g(x) = 2x + 3
What is the rule for function g?
Here we have the function f(x) = 4x + 6 and the function g(x) that is defined as:
g(x) = (1/2)*f(x)
So g(x) is a vertical dilation of scale factor k = 1/2 of f(x).
Replacing f(x) in there we get:
g(x) = (1/2)*(4x + 6) = (4/2)*x + 6/2 = 2x + 3
The rule for g is:
g(x) = 2x + 3
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A 7ft board is cut into 2 pieces. If one piece is x feet long, express the other length in terms of x
Answer:
7-x
Step-by-step explanation:
If one piece is x, and the whole is 7, the missing piece would be 7-x
Hope this helps :)
Write an equation of the line that passes through P(0, 0) and is parallel to the line y=4x-7. Your answer should be written in slope-intercept
Answer:
[tex]y=4x[/tex]
Step-by-step explanation:
Slope-intercept form:
[tex]y=mx+b\\[/tex]
m is the slope
b is the y-intercept
Parallel lines have the same slope, therefore we know that our new line will have the slope m = 4.
Since the point is the origin (0,0) we also know that the y-intercept will be 0.
Using this information, write the equation of the line:
[tex]y=4x+0[/tex]
Simplify:
[tex]y=4x[/tex]
What’s the correct answer answer now for brainlist better he right
Answer:
they filter the air coming into the body
Use front end rounding to round each number. Then add the rounded
numbers to get an estimated answer. Finally, find the exact answer.
35.25
197.39
+ 4.835
An estimated answer is 237.44 and the exact answer is 237.475.
The first number is 35.25.The second number is 197.39.The third number is 4.835.We need to use front end rounding to round each number and then add the rounded numbers to get an estimated answer.First, look only at the whole numbers and add the digits.35 + 197 + 4 = 236Next, look at the decimals and round them.0.25 is approximately equal to 0.2.0.39 is approximately equal to 0.4.0.835 is approximately equal to 0.84.Add the rounded decimals.0.2 + 0.4 + 0.84 = 1.44Now add the whole number part and the decimal part together.236 + 1.44 = 237.44An estimated answer is 237.44.Now we will calculate exact answer :35.25 + 197.39 + 4.835 = 237.475The exact answer is 237.475.To learn more about rounding off numbers, visit :
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Choose the graph that represents the following set.
the whole numbers greater than 3
O
1 2 3 4 5 6 7 8 9 ...
-1 0 1 2 3 4 5 6 7
1011H
0 1 2 3 4 5 6 7 8
Answer:
option 3
It has a zero a set of whole no has 0 in it and it start after the no 3 as it says GREATER then 3.
A) In a hostel , 30% of the beds are vacant. There are 210 guest beds at the hostel currently. How many beds are there at the hostel?
B) The hostel plans to increase its bed capacity by 15% over the next year. What is the planned bed capacity at the hostel?
C) The jeweler is trying to determine which box has the greatest weight. A box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. Which box is heavier?
A. The number of beds that are at the hostel will be 700 beds.
B. The planned capacity will be 105 beds.
C. The box of silver is heavier.
How to illustrate the information?A. In a hostel , 30% of the beds are vacant and T
there are 210 guest beds at the hostel currently. The number of beds will be:
= 30% of x = 210
0.3x = 210
x = 210/0.3
x = 700
The number of beds is 700.
B. The planned capacity will be:
= 15% × 700
= 0.15 × 700
= 105 beds.
C. When the jeweler is trying to determine which box has the greatest weight and a box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. It should be noted that 14/25 = 0.56. Therefore, the silver is heavier.
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The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.
The equation of the tangent line to the curve at B is 3x + 2y = 28.
Find the equation of the support arm, AB.
B(4,8)
Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”
Answer:
[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sidesSo slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Calculate your take-home pay (net pay) for the following situation. Gross Salary: $3,500 per month. You are paid once a month. Federal Income Tax Withholding = 20% of Gross Salary. State Income Tax Withholding = 12% of Gross Salary. Social Security Tax Withholding = 8.25% of Gross Salary. 401k Contribution = 4% of Gross Salary.
What is the amount of Federal Income Tax Withholding each month?
What is the amount of State Income Tax Withholding each month?
What is the amount of Social Security Tax Withholding each month?
What is the amount contributed to the 401k each month?
What is the net pay (take-home pay) each month?
What is the total take-home pay for a full-year?
Using proportions, the amounts are given as follows:
Federal Income Tax Withholding each month: $700.State Income Tax Withholding each month: $420.Social Security Tax Withholding each month: $288.75.Amount contributed to the 401k each month: $140.The take-home pay for the month is $1,951.25.The take-home pay for the year is $23,415.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
One example of application is for percentage problems, as the equivalent amount can be found multiplying the equivalent decimal by the total amount.
The amount of Federal Income Tax Withholding each month is given by:
0.2 x 3500 = $700.
The amount of State Income Tax Withholding each month is given by:
0.12 x 3500 = $420.
The amount of Social Security Tax Withholding each month is given by:
0.0825 x 3500 = $288.75.
The amount contributed to the 401k each month is:
0.04 x 3500 = $140.
The take-home pay for the month is the $3,5500 subtracted by all the with holdings, hence:
3500 - (700 + 420 + 288.75 + 140) = $1,951.25.
A year has 12 months, hence the take-home pay for the year is given by:
12 x 1951.25 = $23,415.
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Please explain step by step I do not explain this,
The value of f(1/2) for the given function f(x) = -3(4x² + 12) + 3/4(8x) - 2x is: -37. (None of the options are correct).
How to Evaluate a Function?If given a function, to evaluate the function for a given value of x, input the value of x in the equation and solve to evaluate the function.
Given the function, f(x) = -3(4x² + 12) + 3/4(8x) - 2x, to find the value of f(1/2), substitute x = 1/2 into the equation:
f(1/2) = -3(4(1/2)² + 12) + 3/4(8(1/2)) - 2(1/2)
Evaluate
f(1/2) = -3(4(1/4) + 12) + 3/4(4) - 1
f(1/2) = -3(1 + 12) + 3 - 1
f(1/2) = -3(13) + 2
f(1/2) = -39 + 2
f(1/2) = -37
The value of the function f(1/2) is: -37. (none of the given options are correct).
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Mai and Priya play on the same basketball team. During basketball practice yesterday, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did Mai make yesterday?
Next question
Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?
Answer:
Mai made 10 successful free throws yesterday.
(25%=1/4 40/4=10)
Today Priya made 18 successful free throws.
(150%=1 1/2 12/2=6 12+6=18)
Lmk if u didn't understand my explanation :')
Last year cost 24500 today worth 14300 what is the percentage change
The most appropriate choice for percentage will be given by- Percentage change in cost = 37.09 %
What is percentage?
A number or ratio which can be expressed as just a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a portion per hundred. Per 100 is what the word percent means. The letter "%" stands for it. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his final exam. This rate is computed based on Ram's overall grade point average (GPA) across all subjects.
For example 2% means [tex]\frac{2}{100}[/tex].
Here,
Cost last year = 24500
Cost today = 14300
Change in cost = 24500 - 14300
= 10200
Percentage change in cost = [tex]\frac{10200}{24500} \times 100[/tex]
= 37.09 %
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Use the drawing tool(s) to form the correct answers on the provided graph. F(x)=(x^4-16)(x^4+3x-18) Find the real zeros of the following function, and plot them on the graph.
The real zeros of the following function [tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex] are
2,-2,3,-6, and the graph is attached below
This is further explained below.
What are the Zeros?[tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex]
as we know the formula a^2-b^2=(a-b)(a+b)
[tex]\begin{aligned}x^4-16 &=\left[\left(x^2\right)^2-(4)^4\right]=\left(x^2-4\right)\left(x^2+4\right) \\&=\left((x)^2-(2)^2\right)\left(x^2+4\right) \\x^4-16 &=(x-2)(x+2)\left(x^2+4\right)\end{aligned}[/tex]
substituting it in equation (1) we get.
[tex]\begin{gathered}f(x)=(x-2)(x+2)\left(x^2+4\right)\left(x^2+3 x-18\right) \\\\\left(x^2+3 x-18\right)=x^2+6 x-3 x-18=x(x+6)-3(x+6) \\\\f(x)=(x-2)(x+2)(x-3)(x+6)\left(x^2+4\right) \\\\x^2+4=(x+2 i)(x-2 i)=\left[(x)^2-(2 i)^2\right] \\\\f(x)=(x-2)(x+2)(x-3)(x+6)(x+2 i)(x-2 i)\end{gathered}[/tex]
Real zuoes =2,-2,3,-6
imaginary zuroes =2 i,-2 i
In conclusion, In the question, we have to answer the real zeroes of the function f(x)
which is 2,-2,3,-6
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vertical
none
obtuse
complementary
adjacent
answer:
vertical
explanation:
vertical angles are angles opposite each other.