The linear equation y = x - 5 show's Evie's net loss or gain
Linear EquationLinear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
In solving this problem, we have to write the problem in a form of linear equation.
Let;
y = The number of stamps available nowx = number of stamps she originally hady = x + 4 - 9
y = x - 5
The equation to show Evie's net gain or loss is y = x - 5
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A youth group i planning a trip to a local amuement park. They are taking a van which hold 10 people. It will cot $25 for parking and ticket to enter the park are $18 per peron. Create a table to repreent the ituation, howing the poible total cot for the variou number of people who could go?
Answer:
See below
Step-by-step explanation:
Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
y = 4x + 3
4x + y = 3
Answer: neither
Step-by-step explanation:
For a graph to be parallel, it must have the same slope.
e.g., y = 2x and y = 2x + 1 are parallel because they both have the slope "2"
For a graph to be perpendicular, its slopes must be the reciprocal of each other, and the sign (positive/negative) is flipped
e.g., y = 2x and y = -1/2x + 1 are parallel because their slopes are reciprocals to each other, and the sign is flipped.
To know whether y = 4x + 3 and 4x + y = 3 are parallel, perpendicular, or neither, we have to identify the slopes and use what was mentioned previously:
Identifying the slope:
y = 4x + 3 slope = 4
4x + y = 3 --> y = -4x + 3 slope = -4
The slopes are different, so they are not parallel
As the slopes are not reciprocals, they are not perpendicular.
The graphs are neither parallel nor perpendicular.
12x + 30= 6(2x+a) in the equation above, (a) is constant. For what value of (a) does the equation have an infinite number of solutions? Explain!
The value of a for which the equation has an infinite number of solutions is 5.
The solution to the equation: The result is a distribution of weights to the variables involved, establishing a balance in the calculation.
The equation given is written below:
Both sides of the equation must have the same value for an infinite number of solutions.
12x + 30 = 6(2x + a)
Simplifying the equation:
12x + 30 = 12x + 6a
Canceling 12x both sides. We get,
the value of a = 5
The value of a for which the equation has an infinite number of solutions is 5.
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Help me please i am stuck
Answer:
106 ft^2
Step-by-step explanation:
we can make this a full rectangle and find the area of that
10 by 16 is the dimensions of the new rectangle so we multiply
16x10
160
And then we subtract by what we added by finding the are of the tiny rectangle with the dimensions of 6 and 9
6x9
54
Now we subtract 54 from 160
160-54
106
Hopes this helps please mark brainliest
(06.01)
Which of the following shows the correct evaluation for the exponential expression (6/7) exponent 2
By using the concept of exponent, the result is-
The correct option is the third option
6 over 7 times 6 over 7 equals 36 over 49
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times.... \times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m + n}[/tex]
[tex]a^m \div a^n = a^{m - n}[/tex]
[tex]a^0 = 1[/tex]
[tex](a^m)^n = a^{mn}[/tex]
[tex](\frac{a}{b})^m = \frac{a^m}{b^m}[/tex]
[tex]a^{-m} = \frac{1}{a^m}[/tex]
Here, the given exponent is [tex](\frac{6}{7})^2[/tex]
[tex](\frac{6}{7})^2 \\\\= \frac{6}{7}\times \frac{6}{7}\\\= \frac{36}{49}[/tex]
[tex]= \frac{36}{49}[/tex]
So the correct option is the third option
6 over 7 times 6 over 7 equals 36 over 49
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Complete Question
Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?
6 over 7 plus 2 equals 2 and 6 over 7
6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7
6 over 7 times 6 over 7 equals 36 over 49
6 over 7 divided by 2 equals 6 over 14
A set of points is shown on the graph.
Scatter plot with a point at negative 3 comma 9, a point at 0 comma 5, a point at 1 comma 8, a point at 6 comma 7, and a point at 8 comma 3.
Which of the following equations is the best model for a line of fit for the data?
y equals 2 thirds times x plus 7
y equals negative 2 thirds times x plus 7
y equals 1 third times x plus 7
y equals negative 1 third times x plus 7
Answer:
[tex]\textsf{D)} \quad y =-\dfrac{1}{3}x+7[/tex]
Step-by-step explanation:
The line of best fit of a scatter plot is a straight line that represents the general trend or pattern. It should pass as close as possible to the majority of the data points, minimizing the overall distance between the line and the points.
From observation of the given scatter plot, the line shows a negative association. Therefore, the slope of the line is negative. This means we can immediately discount the equations with positive slopes.
If we plot the line with the slope -2/3 (attachment 1 - blue line), we can see that the line passes through the first point, then has 3 points above the line but only 1 point below it. The distance between point (6, 7) and the line is much greater than the distance between the line and the other points.
If we plot the line with the slope -1/3 (attachment 2 - red line), we can see that the line passes as close as possible to the majority of the data points, and minimizes the overall distance between the line and the points.
Therefore, the equation that is the best model for the line of best fit for the data is:
[tex]y =-\dfrac{1}{3}x+7[/tex]
Mr. Seals wants to make a scale drawing of the rectangular floor in his classroom. In the scale drawing, the width of the classroom is 5 inches. The width of the actual classroom is 20 feet.
What scale did Mr. Seals use to create the scale drawing of his classroom?
A.1 inch represents 4 feet
B.4 inches represents 1 foot
C.1 inch represents
foot
D.4 inches represents
foot
The scale which Mr. Seals used to create the scale of the drawing as required is; Choice A; 1 inch represents 4 feet.
What scale did Mr. Seals use to create the scale drawing of his classroom?It follows from the task content that the scale used by Mr. Seals is to be determined.
According to the task content; the width of the classroom is 5 inches and the width of the actual classroom is 20 feet.
On this note, it follows by proportion that we have;
5 inches / 20 feet.
= 1 inch / 4 feet.
Consequently, it can be inferred that the required scale is; 1 inch represents 4 feet.
Hence, Choice A is correct.
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How did islamic scholars contribute to the growth of scientific and mathematic knowledge?.
A viable method of numeration that contained zero and allowed for the solution of equations was developed by Muslim academics, who also used logic to establish mathematical ideas and relationships.
The current arithmetic decimal system and the basic operations associated with it—addition, subtraction, multiplication, division, raising to a power, and extracting the square root and cubic root—were created by Muslim mathematicians.
The Indian numeral system, which is now known as Arabic numerals, was swiftly adopted by Islamic mathematicians. The development of algebra, the use of decimals, mathematical induction, and trigonometry were among the further contributions.
The Arabic translation of mathematical, medicinal, and astronomical writings from their original languages is one of the Islamic world's greatest contributions to contemporary science.
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I will give Brainlest!
Answer:
15 miles per hour
Step-by-step explanation:
unit rate is when you how much it is for 1 like 3 dollars for 1 pound or 15 miles per hour
Hopes this helps please mark brainliest
Answer:
15 miles per hour
Step-by-step explanation:
Let's remember what exactly unit rate is:
Unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate. Or, it takes one second to run the 7 yards.
For this question, I first notice that we have 2 answers that pertain to the same thing:
15 miles per hour and 30 miles in two hours
We have 1 cake / 3 hours, but the 1 is not in the denominator so it is not a unit rate.
And we have $5.50 per 1.5 pounds. Again, the one is not in the denominator so it is not a unit rate.
Going back to the other two (15 miles per hour and 30 miles in two hours)
We can write these in fraction form
[tex]\frac{15 miles}{1hour}[/tex] and [tex]\frac{30miles}{2hours}[/tex]
The 15 miles per hour has the one in it's denominator, so it is the unit rate.
Which table represents a direct variation function?
Input x 3 4 5
Output y 6 10 14
Input x 1 2 3
Output y 2 4 8
Input x 4 6 8
Output y 6 9 12
Input x 1 2 3
Output y 3 9 15
Option 3 is the solution. The direct variation in this question is gotten from the option where we have the input x: 4 6 8, output y: 6 9 12
What is direct variation?In mathematics, the direct variation in the form that is
y = kx
To define the term k, k is the constant of proportionality.
The equation is written and interpreted as y is directly to x. At option 3,
y = kx
when y = 6 and x = 4, we would have 6 = 4k.
then k = 6/4
= 1.5
To confirm, we have to put the input values to see if they correspond with their y values.
1.5 x 6 = 9
1.5 x 8 = 12
Hence option 3.
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Build a model to show 9/8 i-Ready
A model to show [tex]\frac{9}{8}[/tex] is given below.
What is an improper fraction?
When the numerator of a fraction is more than or equal to the denominator, the fraction is said to be improper. The number at the top is the numerator, and the number at the bottom is the denominator.
Given, improper fraction = [tex]\frac{9}{8}[/tex]
Now, convert the given improper fraction into a mixed fraction
i.e. [tex]\frac{9}{8} = 1\frac{1}{8}[/tex] ( mixed fraction)
That we can write [tex]1\frac{1}{8} = 1 + \frac{1}{8}[/tex]
The model to show [tex]\frac{9}{8}[/tex] is given below:
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Represent the following expressions as a power of the number a where a ‡0.
((a−²)-¹)-¹ ÷ (a÷a¯¹)²
Properties we are going to use :
1. (a^m)^n = a^mn
2. a^m : a^n = a^(m-n)
((a^-2)^-1)^-1 = (a^(-2 x -1))^-1 = (a^2)^-1 = a^-2
(a : a^-1)^2 = (a^1 - (-1))^2 = (a^2)^2 = a^4
Therefore, the expression is simplified down to a^-2 : a^4
a^-2 : a^4 = a^(-2 - 4) = a^-6.
I don’t understand these three algebra 1 problems. They are in the topic of solving multi-step inequalities and I also don’t get the adding like terms portion.
Thank you for answering this!
The solutions to the inequalities are given as follows:
6. x < 4.
7. x ≤ 1.8.
8. x ≥ -7.
How to solve an inequality?An inequality is solved similarly to an equality, isolating the variable and then finding a range of values.
For item 6, the inequality is:
x < 0.25(3x + 4)
x < 0.75x + 1
x - 0.75x < 1
0.25x < 1
x < 1/0.25
x < 4.
For item 7, the inequality is:
1.5 + 0.25(x/0.2) ≤ 3.75.
The composition is explained as follows:
1.5: cost for the first 0.2 miles.0.25(x/0.2) : cost for each additional 0.2 = 1/5 mile.Hence the solution is obtained as follows:
1.5 + 0.25(x/0.2) ≤ 3.75.
1.25x ≤ 2.25
x ≤ 2.25/1.25
x ≤ 1.8.
For item 8, the inequality is:
2(x + 4) ≤ 3(x + 7) - 4
No more = less or equal than
Hence
2x + 8 ≤ 3x + 21 - 4
2x + 8 ≤ 3x + 15
x ≥ 8 - 15
x ≥ -7.
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A class is made up of 6 boys and 14 girls. half of the boys wear glasses. a student is selected at random from the class. what is the probability that the student is a boy with glasses? write your answer as a fraction in simplest form.
A class is made up of 6 boys and 14 girls. half of the boys wear glasses. a student is selected at random from the class.
0.2% probability that the student is a boy with glasses.
In order to calculate a probability we first need to know the total possible outcomes, so the total is boys plus the girls, 6+14=20, we have a total of 20 students, and we need the total number of successful outcomes, which is half of the girls, 4 girls use glasses.
So the probability is:
[tex]Probability = \frac{Successful Outcomes}{Total Possible outcomes}[/tex]
[tex]Probability = \frac{4}{20} \\\\Probability = \frac{1}{5} \\\\Probability = 0.2[/tex]
So the probability is 0.2% that if you pick a student at random you will pick a girl with glasses.
Hence the answer is 0.2% probability that the student is a boy with glasses.
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What is the answer to 68 plus 899
Find the measure of x.
40
45°
X
x = [?]
X
Round to the nearest tenth.
Answer:
x ≈ 28.3
Step-by-step explanation:
using the cosine ratio in the right triangle
cos45°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )
40 × cos45° = x , then
x ≈ 28.3 ( to the nearest tenth )
Given the equation \(5^(-2x -10) = 25^(x + 1)\), solve for the value of x that will make the equation true.
Answer:
x is -3
Once the expression has equal bases, it is a bit easier
when students are tested and the test results are used to place them in a certain category of classes (remedial, advanced, college prep, etc.), this process is called:
Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
What is tracking?Tracking in mathematics has become a hot topic in many school systems. By definition, tracking means that students are separated into different levels of courses due to their. mathematical ability and prior performance.The term "tracking" refers to a strategy many secondary schools employ to classify students based on their perceived aptitude, IQ, or levels of achievement. In an effort to match the curriculum and instruction to the students' needs, they are divided into high, middle, and low tracks.Tracking is the most commonly used term for ability grouping, the practice of lumping children together according to their talents in the classroom. On the elementary level, the divisions sound harmless enough: Kids are divided into the Bluebirds and Redbirds.hence,Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
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at what rate (in ft/s) is his distance from second base decreasing when he is halfway to first base? (round your answer to one decimal place.)
When he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.
The length of the side of the base is 90 ft. Its speed is 24 ft/s.
Let x = distance he has run at time t and
D = distance from second base at time t, then speed dx/dt = 24 and we calculate dD/dt where x = 45.
From Pythagorean Theorem,
[tex]D^{2} =(90-x)^{2} +90^{2}[/tex] ,
differentiating with respect to t
2D*dD/dt = 2 (90 − x) (−1) dx/dt + 0
D*dD/dt = − (90 − x)dx/dt
Now, when x = 45,
D =[tex]\sqrt{(90-45)^{2}+90^{2} }[/tex]
[tex]=\sqrt{45^{2}+90^{2} }[/tex]
by substituting D we get,
[tex]\sqrt{45^{2}+90^{2} }[/tex]dD/dt = − (90 − 45) · 24
dD/dt = −45 · 24/[tex]\sqrt{45^{2}+90^{2} }[/tex]
= −10.73 ft/s
Hence, when he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.
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Simplify the following expression 6x^2+2x-8-7x^2
Answer:
-x^2+2x-8
Step-by-step explanation:
6x^2+2x-8-7x^2 Different features used to show like terms
Simplify =
-x^2+2x-8
which of the following statements is true of random assignment and random sampling?
A. Random assignment is the same as random sampling
B. Random assignment, if effective, allows us to make sure the only difference between the various treatment groups is what we are studying
C. Random assignment allows us to obtain a sample representative of the population
D. All of the above
Answer:
Random assignment is necessary for internal validity, whereas random assignment is necessary for external validity
Step-by-step explanation:
The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by
h(t) = -16t² +48t, where t is the time (in seconds).
What is the average rate of change of the height as a function of time from t = 1 to t = 3?
mui
Step-by-step explanation:
Red Valley Cabs charges $4.50 to initiate a cab ride, plus an additional $3.20 per mile driven. Write an equation showing how the cost of a cab ride, y, depends on the number of miles driven, x.
Answer: y=$4.50+$3.20x
Step-by-step explanation: You already have to pay $4.50 plus $3.20 every mile driven (x) equals your final cost (y)
Cliff borrows $10 from his brother. The next day, he borrows another $15 from his brother. What integer represents the balance that he owes his brother?
Answer: $25
Step-by-step explanation:
Add 10 and 15 to get 25
Given: 8x-3y = -21,3x+y=-10: Prove: ×=
-3
what reasons is it
The required value of x for the given equation of line is 3.
Explain equation of line?The equation of straight line is defined as the y = mx +c or ax + by = c, where y is point on y-axis and x is the point n x-axis, m is slope of the line.
According to given data in the question:
we have,
8x-3y=21-----(1)
And 3x+y=10
multiply 3 both sides
9x+3y=30------(2)
To find the value of x,
Add equation 1 and 2, we get
x = 3
Thus required value of x is 3.
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Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π.
The volume of the sphere whose radius is 3 as represented in the task content above is; 113.04 units³.
What is the Volume of the sphere?It follows from the task content that the volume of the sphere which is as represented in the task content is to be determined.
Recall from geometry of solid shapes (3 - dimensional shapes), the volume of a sphere is given by the formula;
V = (4/3) π r³
where r = radius = 3.
Therefore, Volume, V of the sphere is;
V = (4/3) × 3.14 × 3³
V = 113.04 units³.
On this note, the volume of the sphere as described is; 113.04 units³.
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In order to solve for the variable in the equation 1 minus (x 2) 2 x = 5 (2 x minus 5) minus x, mikel first applies the distributive property. which equation is a result of this step? 1 minus x 2 2 x = 10 x minus 5 minus x 1 minus x minus 2 2 x = 10 x minus 25 minus x 1 minus x minus 1 2 x = 10 x minus 25 minus x 1 minus x minus 1 2 x = 10 x minus 5 minus x
In order to solve for the variable in the equation
We want to apply the distributive property to the given expression.
1 - x - 2 + 2x = 10x - 25 - x is the result of this step.
Let's see how to solve this:
Remember that the distributive property says that:
A*(B + C) = A*B + A*C.
Here we have the expression:
1 - (x + 2) + 2x = 5*(2x - 5) - x
We can apply the distributive property to the first term in the right side, we will get:
1 - (x + 2) + 2x = 5*(2x - 5) - x
1 - (x + 2) + 2x = 5*2x - 5*5 - x
1 - (x + 2) + 2x = 10x - 25 - x
Now we can also apply the distribute property to the second term in the left side:
1 - (x + 2) + 2x = 10x - 25 - x
1 - x - 2 + 2x = 10x - 25 - x
Hence the answer is, 1 - x - 2 + 2x = 10x - 25 - x is the result of this step.
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Complete this synthetic division table.
According to the given synthetic table, the quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
Synthetic table:
Basically, the shortcut for polynomial division when the divisor is of the form x – a. And only numeric coefficients of the dividend are used when dividing with synthetic division.
Given,
Here we have the synthetic table.
Now, we have to solve this one.
In order to find the quotient and remainder, we have to do the following steps:
Step-1 : Write down the first coefficient 5
Step-2 : Multiply our root -3 by our last result 5 to get -15 [ (-3) × 5=-15 ]
Step-3 : Add new result -15 to the next coefficient of the dividend 10, and write down the sum -5, [ 10 + (-15)=-5 ]
Step-4 : Multiply our root -3 by our last result -5 to get 15 [ (-3) × (-5)=15 ]
Step-5 : Add new result 15 to the next coefficient of the dividend -12, and write down the sum 3, [ (-12) + 15=3 ]
Step-6 : Multiply our root -3 by our last result 3 to get -9 [ (-3) × 3=-9 ]
Step-7 : Add new result -9 to the next coefficient of the dividend 11, and write down the sum 2, [ 11 + (-9)=2 ]
Step-8 : Multiply our root -3 by our last result 2 to get -6 [ (-3) × 2=-6 ]
Step-9 : Add new result -6 to the next coefficient of the dividend 7, and write down the sum 1, [ 7 + (-6)=1 ]
We have completed the table and have obtained the following coefficients 5,-5,3,2,1
Thus quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
And all these process are illustrated below.
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What is the value for x when solving the equation −x (−3) = x 3 using algebra tiles? x =
The value of x found after solving the equation using algebra tiles is -3.
What is algebra tiles?
Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have demonstrated to offer solid examples.
Solving the equation for value of x
−x + (−3) = x + 3
-x -3 = x + 3
subtracting x from both sides
(-x -3) -x = (x + 3) -x
-2x -3 = 3
Adding 3 to both sides
-2x -3 + 3 = 3 + 3
-2x = 6
Dividing by 2 both side.
x = -3
Therefore the value of x = -3
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Answer:
-3
Step-by-step explanation:
a least squares regression line . a.may be used to predict a value of y if the corresponding x value is given b.implies a cause-effect relationship between x and y c.can only be determined if a good linear relationship exists between x and y d.is only used for positively correlated data
The least square regression line implies a mathematical equation that models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given. The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope-intercept form.The predicted value of y or x if the corresponding value of either variable is given.
what is regression?
A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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