Write the following as an algebraic expression. Then simplify.
Five times the sum of some number plus 3 is
equal to 9 times the number minus 9.
Five times the sum of some number plus 3 is equal to 9 times the number minus 9.
5 (x + 3) = 9x - 9
expand left side:
5x + 15 = 9x - 9
subtract 15 from both sides:
5x + 15 - 15 = 9x - 9 - 15
5x = 9x - 24
subtract 9x from both sides:
5x - 9x = 9x - 24 - 9x
-4x = -24
divide both sides by -4:
-4x/(-4) = -24/(-4)
x = 6
For this question, use the information given in the situation, as well as your answers to the previous questions.
After looking through different hotel options, Gabriela and Luis decided to estimate a budget of $1,200 for hotel costs. They want to stay 6 nights at a hotel. In addition, they know they should plan to pay $240 in taxes and tips. Let c represent the total cost per night they should plan for the hotel.
1. How do you know that the solution you found in the previous question is correct?
2. What does the solution to the equation mean for the Morales family?
Write 2 or 3 sentences to answer the two questions. Be sure to use clear, correct math language. Number your responses (1 and 2) so that your teacher knows which question you are answering.Your response will be automatically saved. So, once you finish your response, wait a few seconds, and then move on to the next activity.
According to the information given, the equation that represents the situation is 6c - 1200 = 240.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
The total costs are:
$240 in taxes and trips.
6 nights at the hotel, each night with a cost of c, hence 6c
Then:
T = 6c + 240
The budget is of $1200, hence, since the total cost is equals to the budget:
T = 1200
6c + 240 = 1200
Rearranging:
6c - 1200 = 240
Hence, according to the information given, the equation that represents the situation is 6c - 1200 = 240.
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,200 ft Determine the flag's width and length if the length is 480 ft greater than the width.
The flag's width is ft. Its length is ft.
4
Answer:
the width of the flag is 310 ft and the length is 790 ft.
Step-by-step explanation:
Let "w" be the width of the flag and "l" be the length of the flag. We can set up the following equation to represent the problem:
2w + 2l = 2200
We know that the length of the flag is 480 ft greater than the width, so we can set up the following equation to represent this relationship:
l = w + 480
We can substitute the second equation into the first equation to solve for the width of the flag:
2w + 2(w + 480) = 2200
This simplifies to:
4w + 960 = 2200
Subtracting 960 from both sides gives us:
4w = 1240
Dividing both sides by 4 gives us:
w = 310
So the width of the flag is 310 ft.
We can use this value to find the length of the flag by substituting it into the equation l = w + 480:
l = 310 + 480
This simplifies to:
l = 790
So the length of the flag is 790 ft.
Therefore, the width of the flag is 310 ft and the length is 790 ft.
zaida took a square piece of paper and folded two of its sides to the diagonal, as shown, to obtain a quadrilateral. what is the size of the largest angle of the quadrilateral?
Answer:
112.5°
Step-by-step explanation:
The corner of the square that remains is a 90° angle.
The opposite corner started as a 90° angle that was folded in half into two 45° angles. Then each 45° angle was folded in half into two 22.5° angles. Then you put two 22.5° angles together to make a 45° angle.
So far we have two opposite angles measuring 90° and 45°.
The quadrilateral is a kite. The other two opposite angles are congruent.
The sum of the measures of the angles of a quadrilateral is 360°.
360° - 90° - 45° = 225°
225°/2 = 112.5°
Spent $650
Spent $842
Earned $522
Earned $650
Part A - Write an integer to represent the positive or negative value for each transaction. Make sure to include your signs!
Part B - Spending $650 and earning $650 are opposite transactions but they have the same absolute value.
Why? Explain what makes these values opposites AND how their absolute value is the same
-$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.
What is Number system?A number system is defined as a system of writing to express numbers.
Spent $650
Spent $842
Earned $522
Earned $650
Spent -$650, Spent -$842, Earned +$522 and Earned +$650.
Spending $650 and earning $650 are opposite transactions but they have the same absolute value because the absolute value of a number n is written as |n|.
The absolute value of 0 is 0. Two numbers are opposites if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0.
Hence, -$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.
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help me asap i need the full answer please
Answer:
dont get it
Step-by-step explanation:
You receive $8 for raking leaves for 2 hours. what is the expression?
Answer:
8x2
Step-by-step explanation:
Enter the letter for the function graphed
below.
3
√x - 3
a) y =
b) y = ³√√x - 3
c)y = 3 = ³√√x
3
d) y = ³√√x +3
e) y = √√x +3
a)
Step-by-step explanation:
we only need to look at the point, where y = 0.
that is clearly at x = 3.
which function gives y = 0 as result, when x = 3 ?
only a)
y =
[tex] \sqrt[3]{3 - 3} [/tex]
the cubic root of 0 is 0.
as 3 is not equal to the cubic root of 3, b), c) and e) are out.
and d) is
[tex]y = \sqrt[3]{3 + 3} [/tex]
the cubic root of 6 is NOT 0.
so, only a) is the only right answer.
Simplify : a) 2(x 2 + y 2 ) + 3 ( x 2 − y 2 )
Answer:
8x2−8y2+6x−6y
Step-by-step explanation:
x2 means x squared
A basketball team had a mean score of 66 points per game. The total number of points they scored is 924. How many games have they played?
Answer:
the team played a total of 14 games
Step-by-step explanation:
To find the number of games the team played, you can divide the total number of points they scored by the mean number of points they scored per game. In this case, you would divide 924 by 66 to get:
[tex]924 / 66 = < < 924/66=14 > > 14 games[/tex]
So, the team played a total of 14 games.
a least squares linear trend line is just a simple regression line with the years recoded. group of answer choices true false
a least squares linear trend line is just a simple regression line with the years recoded then it is a true statement
The simple linear regression model is;
y = mx + c
Where,
y = dependent variable
m is the slope
x is the independent variable
c is the y- intercept
The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.
The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.
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Zander has a set of toy pyramids that have a square base and measure of 6 inches tall. The set includes four equal-sized pyramids. What is the combined volume of all four pyramids?
Answer:
72 in^3
Step-by-step explanation:((3*3*6)/3 ) * 4
Identify the type of angle shown
A. Corresponding angles
B. Same side interior angles
C. Alternate exterior angles
D. Alternate interior angles
Help!!!
Answer:
A. Corresponding Angles
Step-by-step explanation:
They are both the same angle, and on the same side
Answer:
A. Corresponding angles
Step-by-step explanation:
Corresponding angles hold the same relative position as another angle somewhere else in the triangle. They have the same degree too. So answer is A
O{-4, -1, 15, 18}
O{-4, -1, 1, 4, 7, 8, 15, 18}
{-1, 4, 8, 18)
O{-4, 1, 7, 15}
-1.
4-
8-
18
-4
7
-15
using a class width of 5, make a frequency distribution table starting with score 26
The frequency distribution table starting with score 26 will be illustrated as:
Class interval Number of data.
26 - 31. 2
32 - 37. 4
38 - 43. 0
44 - 49. 1
How to illustrate the frequency?Based on the information illustrated, let's assume that the numbers that we have include 27, 26, 45, 32, 35, 37, 36.
It should be noted that frequency distribution are portrayed as frequency table me chart. It shows the actual number or observations.
In this case, the class width is 26 - 31, 32 - 37, etc. The frequency distribution is illustrated above.
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The graph shown here is the graph of which of the following rational functions?
what is the answer to 5x-4=y and -2x+2y=8
Answer:
x = 2
y = 6
Step-by-step explanation:
5x-4=y
We add 4 and subtract y from both sides
5x - y = 4
Now we have 2 equation
5x - y = 4
-2x + 2y = 8
Let's find the x first! We time the first equation by 2
10x - 2y = 8
-2x + 2y = 8
Now add both equations
8x = 16
x = 2
Now let find the y by put 2 back in the x
-2(2)+2y=8
-4 + 2y = 8
2y = 12
y = 6
Please help me raise my grade!
We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is 33.33 and the score of Viktor is 84.
What is Percentile Rank?According to the pupils in the particular norm group, a student's performance is shown by their percentile rank. Let's try to put the percentile rank in a tidy mathematical equation now that you are clearer on what it actually is. A collection of values A = x1, x2, x3,..., xn with N values will be used in our attempt to calculate the percentile rank of the data point xm. In this scenario:
PR = L / N × 100 where:
PR stands for percentile rank and has a range of 0 to 100;
L is the quantity of values in set A that are less than or equal to the value of your data, xm; and
The entire collection of values in A has a total of N values.
Calculation:Given some of the test scores. Arrange the test Scores in ascending order.
A={58,64,66,70,71,75,77,80,84,85,87,90,93,95,96}
N=15
Now find out the values in the set which are less than or equal to 71.
L=5
Apply, PR=L/N ×100
⇒PR=5/15 × 100
PR=33.33 is the Percentile Rank of score 71.
Viktor is in 60th percentile, so find out L.
⇒60=L/15 ×100
⇒L=60×15/100
L=9.
So 84 is Viktor Score.
We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is 33.33 and the score of Viktor is 84.
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prove that there are no solutions in integers x and y to the equation 2x2 + 5y2 = 14.
The quadratic equation does not have solutions where both x and y are integers.
How to prove that there are no integer solutions for the equation?Here we have the following quadratic equation:
2x^2 + 5y^2 = 14
We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:
2x^2 + 5y^2 = 14
5y^2 = 14 - 2x^2
y^2 = (14 - 2x^2)/5
y = ±√((14 - 2x^2)/5)
Now, trivially:
(14 - 2x^2)/5
Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.
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Sam went to TV City to buy
a new TV. When he got
there,
he found that the
manager was offering a 25% discount on every TV in the store. The one Sam
wanted was last year's model sO he got an additional 10% discount on his
purchase. When he got to the cash register, he found
out he would save even
more because
the store offered a 5% discount for paying cash. These
discounts were applied
successively, and he paid $371.93 for the TV. What
was the original price before any discounts were taken?
What was the total percent
discount Sam got?
Answer:
1/ Total percent of discount is 40%
2/ The original price is $520.70
Step-by-step explanation:
1/ We add a 25% discount on every TV store, a 10% discount on purchases, 5% discount for paying cash, so the total is a 40% discount.
2/ Now, let's find the original price
100% - 40% = 60%
We know that the 60% he has to pay is $371.93, so we have to find the 40% discount.
40% = 0.4
Take 371.93 times 0.4 = $148.77
Then we add both numbers together
148.77 + 371.93 = $520.70
how many one-to-one functions are there from a set containing 5 elements to a set containing 6 elements?
There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.
A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.
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Use m=−8, n=4, p=−12
4 ( 7mp + 3p ) + 4n
Answer: 2560
Step-by-step explanation:
m= -8
n=4
p= -12
4(7mp+3p)+4n= 4((7 x -8 x -12)) +4(4)= 2560
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
(Please explain, thanks!)
The system of equations presented in the graph is written as
y > -2x/3 + 2y = xHow to write the inequalitiesLinear function in the slope intercept formula is written in the form
y = mx + c
definition of variable
y = output variable
m = slope
x = input variable
c = y intercept
The dashed line represents inequality without "equal to" hence less than or greater then only. shading above the line is greater than
the line passed through points (0, 2) and (3, 0)
the slope, m is = (2 - 0) / (0 - 3) = -2/3
the y intercept = 2
y > -2x/3 + 2
The solid line means the inequality has equal to hence it either greater than or equal to OR less than or equal to. no shading means it is only equal to
the line passed through points (0, 0) and (2, 2)
the slope, m is = (0 - 2) / (0 - 2) = 1
the y intercept = 0
y = x
The equation of the graph is
y > -2x/3 + 2
y = x
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100 points!!!! Please answer ALL 3
Part A
Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).
Part B
Find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part A.
Part C
Graph the function f(x) and the line you identified in part B. How do the graphs relate to each other? What does the slope of the line represent about the function at the given point?
please answer ALL 3
Part A: Calculation of the limit at x = 3In order to find the limit of the function, we can factorize the numerator by factoring out (x-3). Limit [tex][tex](x 3)\frac{(x^3 - 27)}{ (x-3)} )[/tex]Now, factorize x³ - 27 to get the difference of cubes. The
limit equation becomes, Limit [tex](x 3) \frac{ (x-3)(x² + 3x + 9)]}{(x-3)}[/tex] Now, we can cancel out the term (x-3) from the numerator and denominator to get the limit equation as
Part B: Limit [tex](x 3) (x^2 + 3x + 9)[/tex]The limit of the function at x = 3 is the value of the function as x approaches 3. By plugging in x = 3 in the equation above, we get, Limit ([tex](x 3) (x^2 + 3x + 9) = (3)^2 + 3(3) + 9[/tex] = 27Part B: Equation of line through f(3) with slope = 27
The slope of the line is 27, and it passes through the point (3, f(3)). The equation of the line can be found using the point-slope form. [tex]y - f(3) = 27(x - 3)[/tex]
Part C: Simplifying the equation, we get,[tex]y = 27x - 78[/tex] Part C: Graphical representation of the line and the function
The graph of the function f(x) is a parabola opening upward with a vertex at (3, 0). The slope of the line is positive, which means the line will have a positive y-intercept.
The line will intersect the y-axis at (0, -78).Both the graph of the function and the line pass through the point (3, 0). The line is tangent to the graph of the function at that point.
The slope of the line represents the instantaneous rate of change of the function at the point (3, 0). It is the same as the limit we calculated in Part A.
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Libby receives pay of $734 which she deposits in her cheque account. She then writes out cheques for $558 and $453. If her account Is now $78 overdrawn what was her cheque account balance before she received her pay?
Answer: $355
Step-by-step explanation:
First, find the total of cheques she writes out by taking 558 + 453 = $1011
Then add 78 to it because she is overdrawn by $78 at the end, so we now have $ 1089.
Then we take 1089 - 734 = $355
So, her cheque account balance before she received her pay was $355
Mary deposits $260.00 into a new savings account.
The account earns 2.5% simple interest per year. No
money is added or removed from the account for
5 years. What is the total amount of money in her
savings account at the end of the 5 years?
A) $292.50
C) $65.00
D) $325.00
B) $32.50
Answer:
A
Step-by-step explanation:
To solve this problem, we need to first find out how much interest the account earns each year. If the account earns 2.5% simple interest per year, and it starts with an initial balance of $260, then the interest earned each year is 0.025 * $260 = $6.50.
Over 5 years, the account will earn a total of 5 * $6.50 = $<<5*6.5=32.50>>32.50 in interest.
To find the total amount of money in the account at the end of the 5 years, we need to add the interest earned to the initial balance of the account. The total amount of money in the account will be $260 + $32.50 = $<<260+32.5=292.50>>292.50.
Therefore, the total amount of money in the account at the end of the 5 years is $292.50.
Answer:
A) $292.50
Step-by-step explanation:
Simple Interest Formula
A = P(1 + rt)
where:
A = Final amountP = Principal amountr = Interest rate (in decimal form)t = Time (in years)Given:
P = $260.00r = 2.5% = 0.025t = 5 yearsSubstitute the given values into the formula and solve for A:
⇒ A = 260(1 + 0.025 · 5)
⇒ A = 260(1 + 0.125)
⇒ A = 260(1.125)
⇒ A = 292.50
Therefore, the total amount of money in her savings account at the end of 5 years is $292.50.
HELP PLLZZZZZZZZZZZZZZ
Answer: 2.2 | 4.2 | 4.1
Step-by-step explanation:
What are the equations of the asymptotes of the hyperbola?
(y+4)^2. (x-6)^2
——— - ———. =. 1
36. 49
Enter your answer in a point-slope form by filling in the boxes. Enter the slope as a simplified fraction.
y= ……= +…..(x…..)
The equations of the asymptotes of the hyperbola is 6y = -7x,
Define Asymptotes of the hyperbola.There are two asymptotes on each hyperbola. A hyperbola with a horizontal transverse axis and centre at (h, k) contains one asymptote with equation y = k + (x - h) and the other with equation y = k - (x - h). A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity. The two vertices, the two focus points, and the centre are all on the same horizontal line and equally spaced from one another. This is a horizontal hyperbola because of this. Our graph of the hyperbola follows the lines of the asymptotes.
Given,
Equations of hyperbola,
(y+4)². (x-6)²
——— - ———. =. 1
36. 49
a² = 36
a = 6
b² = 49
b = 7
Asymptotes of the hyperbola:
y = ±b/a × x
y = 7/6x
6y = 7x
y = -7/6 x
6y = -7x
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if the end behavior is decreasing to the left and increasing to the right, which statement must be true about the function?
The correct statement is end behavior is decreasing to the left and increasing to the right, which statement must be true about the function is The order is odd and the leading coefficient is negative.
As x approaches infinity it is detected by its limit. On the left side, it is given by:
Rim x -> - ∞ f(x)On the right-hand side, it is given byRim x -> ∞ f(x)Since x tends to infinity, this is the limit, so we only consider the highest order term and its predecessors.So the described behavior is i. H. lim→→ = ∞, lim⭑→∞ =1∞ if:The order is odd and the leading coefficient is negative.For more information about borders, visit
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How many solutions does each system of equations have? Part A: {3x−y=13y+3=9x
The system of equations have Unique solution.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation is,
⇒ 3x - y = 13
⇒ y + 3 = 9x
Now,
Since, The system of equation is,
⇒ 3x - y = 13
⇒ y + 3 = 9x
It can be written as,
⇒ 3x - y = 13
⇒ 9x - y = 3
Clearly, We have;
⇒ 3/9 = - 1 / - 1
⇒ 1/3 ≠ 1
Thus, It has Unique solution.
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