The equation of the line that passes through (-2, 5) and (−2,−8) is: x = -2.
What of the Equation of a Line?The equation of a line that passes two given points on the line, can be expressed in slope-intercept form as y = mx + b. In this form, the variable "m" represents the slope of the line, while the "b" represents the y-intercept.
Find the slope using the two points (-2, 5) and (−2,−8):
Slope (m) = change in y / change in x = (-8 - 5)/(-2 -(-2))
Slope (m) = -13/0 [cannot divide]
The slope of the line is undefined. This means the line is a vertical line that intercepts the x-axis at -2.
The equation of the vertical line would therefore be: x = -2.
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find the value of the variable
Answer:
Step-by-step explanation:
Set 3y+53 equal to 7y-55
3y+53=7y-55 //subtract 3y
53=4y-55 //add 55
108=4y //divide by 4
y=27
A population numbers 17,000 organisms initially and decreases by 4% each year.
Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.
An exponential model to represent this situation [tex]P =17000 (0.96)^{t}[/tex]
What is exponential growth of population?Exponential growth occurs when a population's per capita growth rate remains constant regardless of population size, causing the population to grow faster and faster as it grows larger.
In exponential growth, the per capita (per individual) growth rate of a population remains constant regardless of population size, causing the population to grow faster and faster as it grows larger. In nature, populations may grow exponentially for a time, but they are eventually constrained by resource availability.
Given that,
P represents population, and
t the number of years of growth.
As we know,
P = [tex]a(b)^{t}[/tex]
[here 'a' is the initial amount of population and 'b' is the amount of growth or shrink]
To get 'b,' start at 1 and either add or remove the decimal growth rate depending on whether it is rising or decreasing.
In this case a = 17,000, it is the value of population at the time zero.
As the population decreases 4% each year, then b = 1-0.04 = 0.96
So, the equation becomes, P = [tex]17000 (0.96)^{t}[/tex]
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Jake got a part-time job to make some extra money. His goal was to make $150 per week. He was within $25 of his goal. If x represents Jake’s earnings, write an equation that represents the minimum and maximum that he could have earned.
Answer:
minimum: 125
Maximum: 175
Step-by-step explanation:
To do this, you know that Jake had a goal of getting $150 in the week. He was within $25 of reaching his goals. This means that he could have $25 less than or more than $150.
You can subtract 25 from 150 to get his minimum:
$150 - $25 = $125
And you can add 25 to get his maximum:
$150 + $25 = $175
y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in your O A. The solution(s) is/are (Type an ordered pair. Use a comma to separate answe B. There is no solution.
To determine whether or not this system has a solution, we proceed as follows:
[tex]-x+3=x^2+5x+8\Rightarrow x^2+6x+5=0[/tex]Now, we use the quadratic function to solve, that is:
[tex]x=\frac{-(6)\pm\sqrt[]{6^2-4(1)(5)}}{2(1)}\Rightarrow\begin{cases}x=-1 \\ x=-5\end{cases}[/tex]From this, we have that the system has two solutions, we determine which replacing x in one of the functions, that is:
[tex]y_1=-(-1)+3\Rightarrow y_1=4[/tex]One solution is the point (-1, 4).
[tex]y_2=-(-5)+3\Rightarrow y_2=8[/tex]And, another solution is the point (-5, 8).
We can see each solution in the following graph:
How much greater is the average temperature on Earth than the average temperature on Jupiter?
The average temperature on Earth is greater than the average temperature on Jupiter by 225°F.
By how many degrees Fahrenheit is the average temperature on Earth than the average temperature on Jupiter?The average temperature on earth is greater than the average temperature in Jupiter by 225°F. This can be obtained by getting the average temperatures as follows:
The average temperature on Earth is = 59°F
The average temperature on Jupiter is = -166°F.
Now we represent this in an equation as follows:
-166°F + x = 59°F
x = 59 - (-166)
x = 59 + 166
x = 225°F.
So, the figure with which the average temperature of the earth surpasses the average temperature of Jupiter is 225°F.
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Dilate a square with vertices $\left(0,\ 0\right)$(0, 0) , $\left(0,\ 4\right)$(0, 4) , $\left(4,\ 4\right)$(4, 4) , and $\left(4,\ 0\right)$(4, 0) using the scale factor $k=0.5$k=0.5 . What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio (new to original) of the perimeters is equal to 1/2 or 0.5. Also, the ratio (new to original) of the areas is equal to 1/4 or 0.25.
How to determine the value of the ratio (new to original)?In Mathematics, the ratio of the perimeters of two (2) geometric figures would be equal to the scale factor when the two (2) geometric figures are similar;
Let z represent the scale factor.Let y represent the perimeter of the original square.Let x represent the perimeter of the new square.Mathematically, the scale factor of a geometric figure can be calculated by using this formula:
Scale factor, z = Dimension of image/Dimension of original figure = y/x
Scale factor, z = 1/2 or 0.5.
In Geometry, the ratio of the areas of two (2) geometric figures would be equal to the square of scale factor when the two (2) geometric figures are similar.
Scale factor, z = (y/x)²
Scale factor, z = (1/2)²
Scale factor, z = 1/4 or 0.25.
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Complete Question:
Dilate a square with vertices (0, 0). (0, 4). (4, 4), and (4, 0) using the scale factor k = 0.5. What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio of the perimeters is
The ratio of the areas is
Lily solved the equation 3x − 10 = -3x + 8. The explanation of her process is shown. Select the text that shows an error in her process or justification of steps, if one exists. 1. I used the addition property of equality to achieve 6x − 10 = 8. 2. I used the addition property of equality to achieve 6x = 18. 3. I used the subtraction property of equality to achieve the solution of x = 3. There is no error in Lily’s process or justification of steps.
Answer: 3x - 10 = -3x + 8 Add 3x to both sides 6x - 10 = 8 Add 10 to both sides 6x = 18 Divide both sides by 6x = 3
Step-by-step explanation:
Solve: 2(7-4k) > 12 or 5 < 0.2(15k + 10)
The solution the inequality expression given as 2(7-4k) > 12 or 5 < 0.2(15k + 10) is 0.25 > k > -0.4
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
2(7-4k) > 12 or 5 < 0.2(15k + 10)
Open the brackets
So, we have
14 - 8k > 12 or 5 < 7.5k + 2
Collect the like terms
So, we have
- 8k > 12 - 14 or 5 - 2 < 7.5k
Evaluate the like terms
So, we have
- 8k > -2 or -3 < 7.5k
Divide both sides by the coefficient of k
So, we have
k < 0.25 or -0.4 < k
Rewrite as
0.25 > k or k > -0.4
Combine
0.25 > k > -0.4
Hence, the solution is 0.25 > k > -0.4
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Which of the following are possible
side lengths for a triangle?
A. 18, 12, 6
B. 9, 15,4
C. 5, 18, 14
Answer:
C
Step-by-step explanation:
when u take the 2 shortest sides and add them up, they must be greater than the longest length.
Using the slope formula, find the slope of the line through the given points.
(1,1) and (8,8)
Work Shown:
[tex](x_1,y_1) = (1,1) \text{ and } (x_2,y_2) = (8,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - 1}{8 - 1}\\\\m = \frac{7}{7}\\\\m = 1\\\\[/tex]
highest common factor of 350 and 150
Answer: 50
Step-by-step explanation: Common factor of 150 and 350 = 1, 2, 5, 5. Highest common factor of 150 and 350 = 2 × 5 × 5 = 50.
Evaluate the expression if g=2, r=3, and t=11
The result of the expression 3g × [tex](g+r)^2[/tex] - 1, when g = 2 , r = 3 , and t = 11 is 149
The given expression is
3g × [tex](g+r)^2[/tex] - 1
The expression is the mathematical a sentence with a minimum of two variables and at least one math operation, the math operation might be addition, subtraction, division, multiplication etc..
The value of g = 2
The value of r = 3
The value of t = 11
Substitute the values in the expression
= 3×2× [tex](2+3)^2[/tex] - 1
Do the arithmetic operation in bracket first
= 6×[tex]5^2[/tex] - 1
= 150 - 1
= 149
Hence, the result of the expression 3g × [tex](g+r)^2[/tex] - 1, when g = 2 , r = 3 , and t = 11 is 149
The complete question is :
Evaluate the expression 3g × [tex](g+r)^2[/tex] - 1, if g=2, r=3, and t=11
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The theatre can seat 10,950 people.There are 90 rows of seats in the theater. If each row has the same number of seats, how many seats are in each row?
122
Step-by-step explanation:
u just say 10 950 dividied by 90 which is 121 recurring and then u say 121 plus 1 because it has a remainder
8. Stavros has 22 coins in his piggy bank, all dimes and quarters. Altogether, the
coins are worth more than $3.40. At least how many coins are quarters? At most,
how many of the coins are dimes?
Stavros has 9 at least quarters and 13 at most coins.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given Data
Stavros has 22 coins in his piggy bank, all dimes and quarters. Altogether, the coins are worth more than $3.40.
He only has quarters and dimes in his possession. For quarters and dimes, assign variables.
Let x = the quantity of dime
Let y = the quantity of quarters.
Create an inequality and equation to depict the scenario.
We can use an equation because he has exactly 22 coins.
x + y = 22
He has more than $3.40 in his total, thus we can apply an inequality.
0.10x + 0.25y > 3.40
To figure out how many of each coin he possesses, we apply the substitution approach. In order to express the inequality in terms of x, substitute the equation into the inequality.
0.10x + 0.25(22 - x) > 3.40
The inequality can now be resolved.
0.10x + 5.5 - 0.25x > 3.40
-0.15x + 5.5 > 3.40
-0.15x > -2.1
x > 14
In an equation where we divide by a negative coefficient, We reverse the sign in inequality.
x < 14
Stavros has a maximum of 13 dimes.
The value of x can then be substituted into the equation since an equation provides you the most precise and minimal value you can have.
y = 22 - 13
y = 9
Stavros has 9 quarters and 13 dimes.
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Write the equation of the ellipse that has its center at the origin with focus at (0,4) and vertex (0,7).
1) Notice that, in this case, the center is at (0,0) the focus at (0,4) and the Vertex is at (0,7)
2) Since the focus is at the y-axis, and the center is at the origin we can start from the following formula:
[tex]undefined[/tex]Pleaseeee help me with this
The solution of scalar multiplication 2A is Option(D).
[tex]2A = \left[\begin{array}{ccc}10&2&6\\12&8&4\\\end{array}\right][/tex]
What is scalar multiplication in matrices?A matrix is a rectangular array of numbers divided into rows and columns. A matrix element or entry is each number in the matrix. If A = [tex][aij]_{m*n}[/tex] is a matrix and k is a scalar, then kA is a matrix formed by multiplying each element of A by the scalar k. Real numbers are considered as scalars while working with matrices. The product of a real number with a matrix is referred to as scalar multiplication. Each entry in the matrix is multiplied by the given scalar in scalar multiplication. It is a straightforward multiplication.The given matrix is:
[tex]A = \left[\begin{array}{ccc}5&1&3\\6&4&2\\\end{array}\right][/tex]
To do the scalar multiplication to determine 2A, just multiply a 2 on every entry in the matrix:
[tex]2A = \left[\begin{array}{ccc}2*5&2*1&2*3\\2*6&2*4&2*2\\\end{array}\right][/tex]
[tex]2A = \left[\begin{array}{ccc}10&2&6\\12&8&4\\\end{array}\right][/tex]
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a process capability index has been calculated for a stable, non-automated process, then the operator is told to check samples at random and make centering adjustments to the process based on the sample readings. based on this information one would expect to find:
The process capability index gauges how much variance a process encounters in comparison to its specification parameters.
We might compare various procedures in terms of the ideal circumstance or whether they live up to our expectations. In the event that the process is not centered, the capability ratio formula is employed.
Process capability uses capability indices to compare an in-control process output to the specification's upper and lower bounds.
Calculated for steady, non-automated processes is the process capability index. The operator is then instructed to check samples at random and center the process.
The processing capability declined.
One would expect to find that the process capability has gotten worse.
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Graph the line that passes through the point (1,-1) and is parallel to another line whose slope is 1 .
Answer:
The image is inserted below.
Step-by-step explanation:
The blue line is the line that passes through the point (1,-1) which is marked as A on the graph.
The green line is the new line you need to graph that is parallel to the original line and has a slope of 1.
need asap pleaseeee
Which is the best definition of an equation?
A statement that can only be simplified.
A number, variable, or combination of numbers and variables with an addition sign.
A number, variable, or combination of numbers and variables that also includes a multiplication sign.
A statement where two expressions are joined with an equal sign.
Answer:
I think the answer is (A statement where two expressions are joined with an equal sign.)
Step-by-step explanation:
The equation $f\left(x\right)=2x-9$ translated 6 units up is $g\left(x\right)=$ .
The equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
The equation is
f(x) = 2x - 9
Then it is translated 6 units up
The translation is the process of moving the shape to left/right of up or down. During the translation process the shape and size of the graph will not change. In translation we are only changing the coordinates of the points of the shape.
Here it is translated 6 units up.
During the upward motion it will be positive
g(x) = f(x) + 6
Substitute the value of f(x)
g(x) = 2x-9 + 6
g(x) = 2x-3
Hence, the equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
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The cost of the entrance tickets to the zoo for 2 adults and 3 children is $78.80. the cost of the entrance tickets for 1 adult and 1 child is $33.10 . what is the cost of the entrance ticket for a child
The cost of the entrance ticket for a child is $12.80.
Using algebraic expression and equation, we can express each statement and determine the cost of the entrance ticket for a child
Let x = cost of the entrance ticket for a child
y = cost of the entrance ticket for an adult
If the cost of the entrance tickets to the zoo for 2 adults and 3 children is $78.80, then we can express this as:
3x + 2y = $78.80 (equation 1)
If the cost of the entrance tickets for 1 adult and 1 child is $33.10, then we can express this as:
x + y = $33.10 ⇒ x = $33.10 - y (equation 2)
Substitute equation 2 to equation 1 and solve for y.
3x + 2y = $78.80 (equation 1)
3($33.10 - y) + 2y = $78.80
$99.30 - 3y + 2y = $78.80
3y - 2y = $99.10 - $78.80
y = $20.30
Substitute the value of y to equation 2 and solve for x.
x = $33.10 - y (equation 2)
x = $33.10 - $20.30
x = $12.80
cost of the entrance ticket for a child = $12.80
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The time it takes to read 20 pages of a book can be represented with the equation y = 12.4 over 20 x near the line. Where y represents the total time in minutes and x represents the number of pages read. Determine how long it will take to read a book that has 424 pages.
Answer choses
262.88 min
683.87 min
424.38 min
2,012.4 min
Please help me
Using the equation y = 12.4/20, the amount of time it would take to read a book that has 424 pages is: A. 262.88 min.
What is a Proportional Relationship Equation?The equation, y = kx, represents a proportional relationship where the value of k is the unit rate of the relationship between the two variables, x and y.
In the scenario given:
x = number of pagesy = total time in minutesThe equation given that models how long (y) in minutes it would take to read x amount of pages is, y = 12.4/20x.To find how long it will take to read a book with 424 pages, substitute x = 424 into the equation y = 12.4/20x:
y = 12.4/20(424)
y = 262.88 minutes.
To read 424 pages, it will take: A. 262.88 min.
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please help tomorrow is my exam please help
Answer:
30.2 meters
Step-by-step explanation:
The key is to realize that a 30 60 90 triangle can be constructed and the height of the house can be found from there. It may be helpful to draw a diagram.
I will use the diagram attached for reference to this solution.
Remember that the answer is asking for y, or the length of DE.
The angle CAB is 30 degrees, and the angle ACB is 90 degrees
The length of CB is 25 * sqrt3
Since ACB is a 30 60 90 triangle, and we know the length of one of the sides, the length of the other sides can be calculated.
CB is the shortest length, and so the middle length, AC, is sqrt(3) times longer than the length of the shortest length, CB
CB's length * sqrt 3 = AC's length = 25 * sqrt3 * sqrt3
AC = 75
length of A to F (I can't combine the letters a and f because then brainly thinks i'm swearing ) = 75 + x = 107
x = 32
Since length of BE = length of CF,
32 = BD + DE = 1.8 + y
y = 30.2 meters
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How long would it take to drive 1km at a speed of 1.71km/h (with working)
It would take 0.58 hours to cover a distance of 1 kilometer.
The speed of a body is defined as the total distance covered by the body per unit time by taken by the body.
S = D/t
where,
S is the speed of the body,
D is the distance covered by the body and
t is the time taken by the body.
Here, in the provided situation,
The distance D to be covered is 1 kilometer.
The speed S at which the body moving is 1.7 km/h.
using formula,
S = D/t
1.7 = 1/t
t = 1/1.7
t = 0.58 hours.
Time taken by the body is 0.58 hours.
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Which equation represents a line that passes through the point (6,−3) and is parallel to the graph of y=3x+1? A y=3x−21 B y=3x+15 C y=−13x−1 D y=−13x+5
Answer:
Choice A
Step-by-step explanation:
The line we need to find has the same slope as the slope of the given line which is 3.
And why there two possible solutions to the equation, X over 2 = 100?
There are two possible solutions because a power is involved. This can be shown in the graph. When we graph to the power of 2, we get a parabola. This gives us two x-intercepts, giving us two answers.
And why is this? When you square a negative number, you get a positive number since a negative times a negative is a positive.
Example: 2 * 2 equals 4, and -2 * -2 also equals 4. This means both 2² and (-2)² are equal to 4.
This means that we will get a positive and negative number value that both equal the same thing when being squared, which is why you get two possible solutions to this equation.
Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
y =
The equation that is parallel to y = -3x + 7 and passes through the point (2, -1) is y=-3x+5.
What is slope Intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
y=mx+b
where m is the slope of the line and b is the y intercept.
The slope of the given equation,
y=-3x+7 is -3.
So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of -3
y-y₁=m(x-x₁)
where (2,-1) are x₁, y₁
y-(-1)=-3(x-2)
y+1=-3(x-2)
Multiply with 3 on RHS side
y+1=-3x+6
We have to write in slope intercept form, so shift 1 to RHS.
y=-3x+6-1
y=-3x+5
As you can see, the slope of this line is -3
, which means that the two equations are parallel to each other.
Hence y=-3x+5 is the equation that is parallel to y = -3x + 7 and passes through the point (2, -1).
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identify the mapping diagram that represents the relation and determine whether the relation is a function {(-3,-6),(-1,-6),(5,-6),(8,-6)}
Answer:
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Skylar bought 23 chicken wings for $32.20. How much would it cost for 13 wings?
If Skylar bought 23 chicken wings for $32.20 then the cost of 13 wings would be using the concept of estimation.
As per the question statement, Skylar bought 23 chicken wings for $32.20. We are supposed to calculate the cost of 13 wings. We will use the concept of estimation.
Cost of 23 wings = $32.20
Cost of 1 wing = $32.20/23 = $1.40
Therefore cost of 13 wings = $1.40 * 13 = $18.20
So, if Skylar bought 23 chicken wings for $32.20 then the cost of 13 wings would be using the concept of estimation.
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As a part of a lesson on earthquakes a science class is researching the movement if a nearby fault line. the line moved 3/5 of an inch during the past year and 7/8 of an inch the year before. how far did the fault line move in all?