The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
According to the given question.
We have an expression 3[2(x - 3) + 2] + 5(x - 3).
To simplify the above expression we will use the distributive law and add and subtract the like terms.
Therefore,
3[2(x - 3) + 2] + 5(x - 3)
= 3[2x - 6 + 5x - 15] (distributive rule)
= 3[7x - 21] (adding the like terms)
= 21x - 63
Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
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Katelynn and Petra both commute to work. Katelynn's commute on the bus takes 15 minutes more than 1/3 as many minutes as Petra's commute by car. It takes Katelynn 45 minutes to get to work. Write an equation to determine how many minutes it takes Petra to get to work.
Help! 100 points.
Answer:
2) (1/3)x + 15 = 45
Step-by-step explanation:
Given that,
→ Katelynn's commute takes 15 minutes more than 1/3 as many min as Petra's.
→ It takes Katelynn 45 minutes.
Then the equation will be,
→ (1/3) times + 15 = 45
→ (1/3)x + 15 = 45
Hence, option (2) is correct.
HELP ASP SHOW UR WORK YOULL GET BRAINILEST I think u show work on this but if u can go ahead
Answer:
i had this question before and the correct answer was "subtract 12r from both sides of the equation" im sorry if im wrong that was my correct answer when i had this question
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Jake is thinking of two numbers. Adding 3 times the first number and 4 times the second number gives a total of 1. Also, adding 2 times the first number and 3 times the second number gives 2.
What are the two numbers? The first number is --- , and the second number is--- .
The first number (a) is - 5 and the second number (b) is 4.
let the first number be a
let the second number be b
given,
On adding 3 times the first number and 4 times the second number we get 1
=> 3 a + 4 b = 1 - eq 1
On adding 2 times the first number and 3 times the second number we get 2
=> 2 a + 3 b = 2 - eq 2
To solve the obtained equations using elimination method
Multiplying eq 1 with 3 and eq 2 with 4, we get
9 a + 12 b = 3 - eq 3
8 a + 12 b = 8 - eq 4
Subtract eq 4 from eq 3
=> a = - 5
On Substituting the value of a in either eq 1 or eq 2, we get
b = 16
Therefore, using the elimination method, we get the first number as - 5 and the second number as 4.
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The cost to download data for a certain mobile phone plan is modeled by c(x), where x represents the total number of gigabytes downloaded. The mobile phone company plans to raise the rate per gigabyte by $2. 50, and charge 20% more if the number of gigabytes downloaded is 5 or more. Identify a function for the new rates
The new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
Here, we have, the new cost function for downloading data based on the given conditions.
If 0 <= x < 2 gigabytes:
The original cost function is C(x) = 12x.
After raising the rate by $2.50, the new cost function for this range becomes C₁(x) = (12+ 2.50)x = 14.50x.
If x >= 2 gigabytes:
The original cost function is C(x) = 18x.
After raising the rate by $2.50, the new cost function for this range becomes C₂(x) = 18x + 2.50x = 20.50x.
If x >= 5 gigabytes (20% more):
The original cost function is C(x) = 18x.
After raising the rate by $2.50 and charging 20% more, the new cost function for this range becomes C₃(x) = [1.20 * (18+ 2.50)]x = 24.60x.
Now, we need to combine these functions to get a single function for the new rates:
For 0 <= x < 2 gigabytes: C(x) = C₁(x) = 14.50x
For 2 <= x < 5 gigabytes: C(x) = C₂(x) = 20.50x
For x >= 5 gigabytes: C(x) = C₃(x) = 24.60x
So, the new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
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Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.) (0, 15), (9, 0)
The required slope of the line through the points (0, 15), (9, 0)
is -5 / 3.
Given that,
To determine the slope of the line passing through the pair of points (0, 15), (9, 0).
The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
Here,
Slope of line ( m ) = [ y₂ - y₁ ] / [x₂ - x₁]
We have points (0, 15), (9, 0).
y₂ = 0 y₁ = 15 x₂ = 9 x₁ = 9
now,
m = 0 - 15 / 9 - 0
m = -15 / 9
m = -5 / 3
Thus, the required slope of the line is -5 / 3.
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On a number line, point A is at coordinate -2. Point B is at coordinate 0. Fine the coordinate that is the midpoint from A to B.
Answer:
The midpoint of the line segment AB
is at (−1, 0).
Step-by-step explanation:
Midpoint Formula:In a general sense the midpoint formula for a line segment whose endpoints are
[tex] \sf ( x_1 + x_2) (y_1 + y_2)[/tex]
would be the mean of the abscissa and the ordinate as seen in the formula below:
[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )[/tex]
When the line segment lies on one axis, then the there would be only one non-zero value in the ordered pair.
Assuming that the line segment AB
is in the x-axis, then the coordinates of the points would be:
[tex] \sf \: A(−2, 0)B(0,0)[/tex]
To get the midpoint, substitute the points above in the formula for the midpoint:
[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} ) \\ \sf \: = ( \frac{ - 2 + 0}{2} ),0 \\ \sf \: = ( \frac{ - 2}{2} ), 0 \: \: \: \: \: \: \: \: \\ \sf \: ( - 1, 0)[/tex]
The midpoint of the line segment AB
is at (−1, 0).
Each interior angle measure equals each exterior angle measure??
Answer:
No, they must sum up to give 360 degrees so it's not possible for them to be equal, if they are equal like 180 degrees each, there won't be a polygon formed!
What is the equation of the line that passes through (0,-5) and (-3,-12)?
Answer:
-20
Step-by-step explanation:
Point-slope form
Complete the point-slope equation of the line through
(-1, 6) and (1, 5).
Use exact numbers.
y-6= ?
Answer: y - 6 = -(1/2)(x+1)
Step-by-step explanation:
1. First step is to remember point slope form (a common way of expressing the equation for a line).
y - y1 = m(x - x1)
2. Next fill in the data we are given.
y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)
3. Next step is to find the value of the slope (m) using slope formula.
m = (y2 - y1) / (x2 - x1)
4. Fill in the data
m = (5 - 6) / (1 +1) = - 1 /2
5. Add the calculated slope to the point slope form.
y - 6 = -(1/2)(x+1)
Simplify the expression 13. 8+(-11. 5). Use pencil and paper. How are 13. 8 + (-11. 5) and (-13. 8) +11. 5
related? Explain without computing. Using a property of operations, what can you say about their sum?
On simplifying the expression 13.8+ (-11.5) , we get 2.3 . And additions
13.8 + (-11.5) and (-13.8) + 11.5 are numbers will same value and opposite sign.
What are rules for adding a positive and a negative number?For adding a negative and a positive number, use the sign of the larger number and subtract.
For example: (–8) + 2 = -6
Given that we have to solve 13.8 + (-11.5) = 13.8-11.5 (we subtract smaller no from larger and will use the sign of lager number that is + here)
13.8+(-11.5) = 13.8-11.5 =2.3
13.8+(-11.5) simply means that 13.8 -11.5 which is subtraction of 11.5 from 13.8
but (-13.8) + 11.5 = -13.8 +11.5 = -( 13.8 -11.5) [taking -1 common from the expression]
Therefore , -13.8 + 11.5 has same value as 13.8- 11.5 but opposite in sign.
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∠A and \angle B∠B are complementary angles. If m∠A=(3x-8)∘ and m∠B=(x+26)∘ then find the measure of ∠A
Answer:
m∠B = 26°
Step-by-step explanation:
∠A and ∠B being complementary means m∠A + m∠B = 90°
4x + 24 + 3x - 4 = 90
7x + 20 = 90
7x = 70
x = 10
m∠B = (3•10 - 4)° = 26°
Answer:
m∠A = 46°
Step-by-step explanation:
∠A and ∠B are complementary angles (Given)-> m∠A + m∠B = 90°-> (3x - 8)° + (x + 26)° = 90°-> (3x - 8 + x + 26)° = 90°-> (4x + 18)° = 90°-> 4x + 18 = 90-> 4x = 90 - 18 -> 4x = 72-> x = 72/4-> x = 18 (3x - 8)° = (3*18 - 8)° = (54 - 8)° = 46°-> m∠A = 46°A rabbit population in a forest doubles each month. The Department of Natural Resources estimates that the forest contains 525 rabbits at the start of the first month. Write an explicit formula describing the number of rabbits an, in the forest n months later.
Answer: [tex]525(2)^{n-1}[/tex]
Step-by-step explanation:
We can represent this as a geometric sequence with first term 525 and common ratio 2.
the tuition for a private college is currently 18000 for each semester. The college will raise tuition by 500 dollars per semester per year How much is tuition per year. By how much will tuition increase each year.
Based on the calculation below, we have:
The tuition per year is $36,000; and
The amount of increase in the tuition each year is $1,000.
How do we calculate tuition and an increase in tuition?The tuition per year and the amount of increase in the tuition each year can be calculated as follows:
Number of semesters in a year = 2
Tuition per semester = $18,000
Amount of increase in the tuition each semester = $500
Therefore, we have:
Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000
Amount of increase in the tuition each year = Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000
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Solve the application problem.
In one day a baker used 2/3 of a pound of flour, then 3/4 of a pound of flour, then 5/12 of a pound of flour. How much flour was used that day?
Answer:
1 5/6 or 11/6
Step-by-step explanation:
2/3+3/4+5/12 = 11/6
Answer:
22/12
Step-by-step explanation:
Add all 2/3 + 3/4 +5/12
=take LCM of 3 , 4, 12
=
12/8 +9 + 5
= 22/12
8-3(k+2)=2-3k
My teacher doesn't teach very well I need help its 10th-grade algebra
Answer:
Step-by-step explanation:
8-3k-6 = 2-3k (distribute -3 to (k+2))
-3k+2 = 2-3k (8-6 is 2)
2 = 2 (subtract 3k from both sides)
2 = 2 means all real numbers
Answer:
0
Step-by-step explanation:
Distribute
8-3(k+2)=2-3k
8-3k+2=2-3k
subtract
8-6=2
2-3k+2=3k
rearrange
-3k+2=3k
I dont feel like typing the rest, watch khan academy
(ill take your email if you want to review on the weekend)
The proper angle for a ladder is about 75° from the ground. Suppose you have a 19 foot ladder. How far from
the house should you place the base of the ladder?
1
Answer:
4.92 ft
Step-by-step explanation:
The ladder is the hypotenuse of a right triangle
adjacent leg / hypotenuse = cos 75
cos 75 = adjacent leg / 19
19 cos 75 ° = adjacent leg = 4.92 ft
For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
number of miles driven and fuel expenses
For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.
Correlation is a relationship between the values of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.
Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.
The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.
We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.
Negative correlation: y decreases as x increases.
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Write an equation of a parabola with vertex at the origin and the given focus.
focus at (2,0)
A parabola having vertex at the origin and focus at (2,0) is expressed by the following equation:
x = y²/8
What is a parabolic function?A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.
Since the vertex and the focal axis are on the same axis, we analyze that:
v = (0, 0)f = (6, 0) the focus is on the right so the parabola is of the form X = Y².(y - 0)² = 4p(x - 0)
Focus
f = (0 + p, 0)0 + p = 2
p = 0 + 2
p= 2
(y - 0)² = 4*2(x - 0)
(Y)² = 8(X)
x = y²/8
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How many solutions are there to this equation?
7x3(x - 1) = 2(2x + 3)
A. no solution
B. exactly one solution
C. at least two solutions
D. infinitely many solutions
Answer:
at least two solution so c
A rock climber descends 94 feet into a canyon, and then climbs up 52 feet. What is his final position?
4. Point A has coordinates (3, 4). After a translation 4 units left, a reflection
across the x-axis, and a translation 2 units down, what are the coordinates
of the image? (Lesson 1-6)
5. Here is triangle XYZ:
After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, the coordinates of the image are (-1, 2).
What is translation?In mathematics, a translation is the movement of a shape to the left or right, and/or up or down. The translated shapes appear to be the same size as the original shape, implying that the shapes are congruent.
They have simply been moved in one or more directions. There is no change in the shape because it is simply moving from one location to another.
According to transformation rule in graph, when moving it to the right, you add the x value And when moving to the left, you subtract the x value,
Value of x = 3
Here the reflection of x has translated 4 units left, which implies
3 - 4 = -1
And, when moving up you add to the y value and when moving down you subtract to the y value,
Value of y = 4
Here the reflection of y has translated 2 units down, which implies
4 - 2 = 2
Thus, the coordinates of the image formed by the reflection are (-1, 2)
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The current of a river flows north at a constant rate. What is the constant in the mathematical expression 3x + 5y + 3 ?
A constant is a value or number that is consistently the same regardless of how it is expressed.
In the mathematical expression 3x + 5y + 3 the constant is 3.
What is a constant in a mathematical expression?Constants are a particular kind of term that can be utilized in an equation in algebra.A constant is a value or number that is consistently the same regardless of how it is expressed.A term in an equation with a fixed value that is unaffected by variations in the variable. Constant functions can also be referred to as constants.Any input value can affect a function's output, but a constant function always produces the same result. A constant is typically represented as c to reflect a fixed value when written as a variable.Therefore, in the mathematical expression 3x + 5y + 3 the constant is 3.
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Which of the following best describes the number π?
O Positive Integer
O Negative Rational Number
O Whole Number
O Positive Irrational Number
Answer:
Positive Irrational Number
Step-by-step explanation:
The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. Integers are the numbers that can be positive, negative or zero, but cannot be a fraction. All rational numbers can be expressed as a fraction whose denominator is non-zero. Whereas, pi cannot be expressed in the fraction of two integers and has no accurate decimal value, so pi is an irrational number.
Divide 7/15 by 3/5.
A.7521
B. 21/75
c.7/9
D.7/25
Answer: C. 7/9
Step-by-step explanation:
the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am what temperature is it at 9:00pm
When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.
How to illustrate the information?From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.
Therefore, the temperature at 9:00pm will be:
=6° - 15° + 25°
= 16°
Therefore, the temperature at 9:00pm will be 16°.
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Work out the area of a circle with a radius of 6mm in terms of pi
Answer:
[tex]{ \tt{area = \pi {r}^{2} }} \\ \\ { \tt{ = 3.14 \times {6}^{2} }} \\ \\ = 113.04 \: mm {}^{2} [/tex]
Answer:
A = 113.1 mm²
Step-by-step explanation:
Area of circle = πr²
A = 22/7(6mm)²
A = 22/7(36mm²)
A = 792mm²/7
A = 113.1 mm²
Therefore the area of the circle is 113.1mm².
What is the equation of each line in slope-intercept form?
a. the line parallel to 4 x+2 y=7 through (4,-2) ,
The slope-intercept form is y = 1/2x - 4 for line perpendicular to 4 x+2 y=7 through (4,-2) ,
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that 4 x+2 y=7
can also be written as
y = -2x + 7/2
Here -2 is the slope and 7/2 is the y-intercept
To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = 1/2, x₁ = 4and y₁ = -2
y - (-2)= 1/2(x - 4)
y + 2= 1/2x - 2
y = 1/2x - 4
We have the slope-intercept form y = 1/2x - 4 of a line perpendicular to 4 x+2 y=7 through (4,-2)
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Below are the decimal expansions for some fractions with a denominator of 12. When you look at the
numbers, you might notice that the decimal expansion in the first row always ends in three; the decimal
expansion in the second row always ends in six; and the third row "comes out even". Now explore the decimal
expansions for the 9ths and describe the pattern you find. Start with finding the decimal for 1/9, then 2/9, and
so on
If we find the decimal values of 1/9,2/9 and so on then we will get 1/9=0.11,2/9=0.22,3/9=0.33,4/9=0.44,5/9=0.55,6/9=0.66,7/9=0.77,
8/9=0.88,9/9=1.
Given some values in which the denominator is 12 and we are required to find the values of numbers whose denominator is 9.
Decimal expansion is basically representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator.
1/9=0.11
2/9=0.22
3/9=0.33
4/9=0.44
5/9=0.55
6/9=0.66
7/9=0.77
8/9=0.88
9/9=1
Hence if we find the values of 1/9,2/9 and so on then we will get decimals of 1/9=0.11,2/9=0.22,3/9=0.33, 4/9=0.44,5/9=0.55,6/9=0.66, 7/9=0.77, 8/9=0.88,9/9=1.
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Solve the following X + 8 < 3 or -8x < -40
Answer:
Not 100% sure. Hope it helps you
Simon has c cousins. Anna has 5 more cousins. Write an expression that shows how many
cousins Anna has.
The expression to represent the number of cousins that Anna has is c + 5.
We are given a statement that says:
Number of cousins that Simon has is equal to = c
Now, it is also given that Anna has 5 more cousins than Simon.
So, we have to write an expression to show the number of cousins that Anna has.
An expression is a combination of constants and variables to express something or a statement.
So, the expression will be made by adding 5 to c
So, we get the expression as:
The number of cousins that Anna has = c + 5
Therefore, we get that, the expression to represent the number of cousins that Anna has is c + 5.
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