Answers
Answer: slope = [tex]\frac{1}{4} x[/tex]
point on the line= (0,-4.25)
Step-by-step explanation:
[tex]y+3\\[/tex] = [tex]\frac{1}{4} (x-5)[/tex]
[tex]y=\frac{1}{4} x-\frac{5}{4} -3\\\\y= \frac{1}{4}x -3\frac{5}{4} \\\\y=\frac{1}{4}x -\frac{17}{4}[/tex]
therefore the value with the x is the gradient so the gradient (slope) is [tex]\frac{1}{4} x[/tex]
since the y-intercept is [tex]-\frac{17}{4}\\[/tex] get the simplified version in decimals which is -4.25... so the point will be (0,-4.25)
Related Questions
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
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Harold brought two loaves of raisin bread to share with his friends. If there are 12 people total, including Harold, how much of the bread does each person receive?
A. 0.06
B. The decimal is 0.16 with 6 repeating.
C. 0.25
D. The term states the decimal 0.3 repeating.
Answers
Hope this helped
Determine the solution to the inequality. one half times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 6 x ≤ −13 or x ≥ 13 x ≤ −13 or x ≥ 11 x ≤ −4 or x ≥ 11 x ≥ 2 or x ≤ −4
Answers
The solution to the inequality:
(1/2)*|x + 1| ≤ 6
is:
x ≤ 11 or x ≥ -13
How to solve the absolute value inequality?Here we want to solve the inequality below:
(1/2)*|x + 1| ≤ 6
To solve it we need to isolate x, so let's start by multiplying both sides by 2:
2*(1/2)*|x + 1| ≤ 2*6
|x + 1| ≤ 12
Now we can break the absolute value part into two inequalities:
(x + 1) ≤ 12
(x + 1) ≥ -12
Solving these two we will get:
x ≤ 12 - 1 = 11
x ≥ -12 -1 = -13
That is the solution.
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to raise money, a physics club sells tickets to a physics demo extravaganza. the tickets cost $6 for adults over 18 and $4 for younglings. after the show, they have raked in a total of $438 from the 82 people who came. how many adults and how many younglings attended?
Answers
There are 55 adults and 27 younglings attended the club.
let the number of adults attended the club be x
let the number of younglings attended the club be y
total people attended the club = 82
so,
x + y = 82.....[1]
cost for the adult = $6
cost for the younglings = $4
so total amount collected = $438
so, equation formed is ,
6x + 4y = 438.......[2]
from equation [1]
x + y = 82
x = 82 - y
put this in equation [2]
6(82 - y) + 4y = 438
492 - 6y + 4y = 438
492 - 2y = 438
492 - 438 = 2y
2y = 54
y = 27
put this value in equation [1]
x + y = 82
x + 27 = 82
x = 82 - 27
x = 55
so, there are 55 adults and 27 younglings attended the club.
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five quare cake of ide 30cm i arranged to from a rectangle, Find the perimeter of the cake
Answers
The perimeter of five square and perimeter of rectangular cake is equal,
So, the perimeter of cakes is 600 cm.
The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.
We have five square cakes of side 30cm.
the perimeter of one cake is =4a
=4×30
=120 cm
So, the perimeter of five cake = 5(120)
=600 cm
The perimeter of five square and perimeter of rectangular cake is equal,
So, the perimeter of cakes is 600 cm.
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Zeke is buying a rare car for 120,000. The dealership told Zeke that this car will gain interest at an annual rate of 1. 4% per year and he plans to sell the car after 10 years. How much will the car be worth after 10 years?
Part A: Write an Exponential Function to model the situation.
A(t)=
(
) ^ t
Part B: Round your answer to the nearest dollar.
After 10 years the car will be worth $
Answers
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &120000\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A = 120000(1 + 0.014)^{10} \implies A \approx 137898.90 ~\hfill \boxed{A=120000(1.014)^t}[/tex]
hi help pls n thanks
Answers
The function represents the domain of a function is x ≥ -2.
What is a graph of a quadratic function?
A graph of a quadratic function is a type of parabola, which is a symmetric, U-shaped curve that opens either upward or downward. The equation of a quadratic function is y = ax² + bx + c, where x and y are variables, and a, b, and c are constants.
The graph of a quadratic function is determined by the value of the coefficient a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The vertex of the parabola is the highest or lowest point on the graph and it is the point of symmetry of the parabola. The x-coordinate of the vertex is given by -b/(2a) and the y-coordinate of the vertex is given by the value of the function at that point.
In the given figure, we can see that it is a parabola, and if we look towards the options, then the third option is a domain of the given function
x ≥ -2
So we can say this is the perfect match for the given figure.
Hence, the function represents the domain of a function is x ≥ -2.
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A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?
|x – 42.80| = 12
|x + 42.80| = 12
|x – 12| = 42.80
|x + 12| = 42.80
Answers
The solution is Option A.
The value of the modulus function is | x - 42.80 | = 12
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the modulus function be represented as A
Now , the equation will be
The amount James borrowed from Rita or Rita borrowed from James = $ 12
And , Let x be the amount of money James will have after he sees Rita
The amount of money with James in his wallet = $ 48
So ,
when James pays Rita , the equation will be
x = 42.80 - 12
On subtracting 42.80 on both sides of the equation , we get
x - 42.80 = -12 be equation (1)
And , when James receives the amount from Rita , the equation is
x = 42.80 + 12
On subtracting 42.80 on both sides of the equation , we get
x - 42.80 = 12 be equation (2)
Now , the modulus function will be
| x - 42.80 | = 12
Hence , the function is | x - 42.80 | = 12
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Several classes in your school are going on a field trip. To transport the students, the teachers rent buses and vans. A total of 120 students are going on this field trip. Each bus can seat 24 students, and each van can seat 8 students. (a) Write a linear equation that describes the relationship of the number of buses and the number of vans needed, assuming exactly 120 students need transportation. (b) If the teachers rent 4 buses, how many vans will they need to transport all the students? (c) If the teachers rent 6 vans, how many buses will they need to transport all the students? (d) Suppose the teachers rented only vans. How many vans would they need? Show your work, and explain your answer. (e) Suppose the teachers rented only buses. How many buses would they need? Show your work, and explain your answer.
Answers
a) A linear equation that describes the relationship between the number of buses and the number of vans needed for 120 students is 24x + 8y = 120.
b) If the teachers rent 4 buses, the number of vans they will need to transport all the students is 3.
c) If the teachers rent 6 vans, the number of buses they will need to transport all the students is 3.
d) If the teachers rent only vans, the number of vans needed will be 15.
e) Suppose the teachers rented only buses, the number of buses needed will be 5.
What is a linear equation?A linear equation is an algebraic equation of the form y = mx+b.
A linear equation involves a constant and a first-order (linear) term, with m as the slope and b as the y-intercept.
The total number of students on the field trip = 120
The number of students a bus can seat = 24
The number of students a van can seat = 8
Linear equation:Let the number of buses = x and the number of vans = y
24x + 8y = 120
b) Renting 4 buses, the number of vans needed:
24(4) + 8y = 120
96 + 8y = 120
8y = 24
y = 3
c) Renting 6 vans, the number of buses will be:
24x + 8(6) = 120
24x = 48 = 120
24x = 72
x = 3
d) Renting only vans, the number needed will be:
24(0) + 8y = 120
8y = 120
y = 15
e) Renting only buses, the number needed will be:
24x + 8(0) = 120
24x = 120
x = 5
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The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.
b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles
Answers
The amount of gas used for 140 miles is 3.5 gallons and the inverse equation is g = m/40
How to determine the amount of gas usedFrom the question, we have the following parameters that can be used in our computation:
m = 40g
The number of miles is given as
m = 140
substitute the known values in the above equation, so, we have the following representation
40g = 140
Divide by 40
g = 3.5
Hence, the amount of gas is 3.5 gallons
How to determine the inverse functionRecall that, we have
m = 40g
Divide by 40
g = m/40
Hence, the inverse is g = m/40
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What is the equation to Eric works 13 hours the first week and earns 119.60. the second week, he earns 184
Answers
The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation to Eric works 13 hours the first week and earns 119.60. the second week, he earns 184.
Let 'x' be the number of hours. Then the equation is given as,
x / 184 = 13 / 119.60
Simplify the equation, then we have
x / 184 = 13 / 119.60
x = 184 x 13 / 119.60
x = 2392 / 119.60
x = 20 hours
The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.
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through a combination of fertility rate and decreased poverty levels, a population’s energy use is growing exponentially 1% per year. how many years until the energy use doubles?
Answers
For the energy use to double it will take approximately 69.66 years.
To find out how many years it will take for the energy use to double, we can use the formula for exponential growth:
P = P₀ * (1 + r)^t
where P is the final amount of energy use, P₀ is the initial amount of energy use, r is the growth rate (1% per year in this case), and t is the number of years.
Setting P = 2 * P₀ and solving for t, we get:
2 * P₀ = P₀ * (1 + r)^t
Dividing both sides by P₀:
2 = (1 + r)^t
Taking the natural logarithm of both sides:
ln(2) = t * ln(1 + r)
Dividing both sides by ln(1 + r):
t = ln(2) / ln(1 + r)
Plugging in the values for r = 0.01 and using the natural logarithm function, we get:
t = ln(2) / ln(1 + 0.01) = 69.66 years
So it will take approximately 69.66 years for the energy use to double.
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Round 849 to the nearest ten
Answers
Answer:
850
Step-by-step explanation:
Everything above 5 goes to the next tenth. Example:
17 = 20
Everything below 5 goes to the next below tenth. Example:
13 = 10
You get it or more expantion?
Simplify: 2 3/20 + 1/10
Answers
Answer: 2 1/4
Step-by-step explanation: Exact Form:
9/4
Decimal Form:
2.25
Mixed Number Form: 2 1/4
You work in a hospital and are in charge of a patient with rheumatic fever. At the beginning of your shift you record the patient’s temperature at 99.9°. In ten minutes you return and record his temperature to be 100.7°. After 2 hours his temperature has now risen to 102.4°.
a. Calculate the slope and
y
-intercept of the equation modeling this situation. Explain the meaning of the slope in context of this situation. What does the
y
-intercept represent?
b. On graph paper, graph the line. Using the graph and your equation determine the patient’s temperature 30 minutes, 1 hour, and 90 minutes after the beginning of your shift. You do not need to submit your graph.
c. You need to predict what his temperature will be 4 hours later. Explain your result. Is it reasonable?
d. What does the domain represent in this situation?
e. What does the range represent in this situation?
f. Should the domain have any restrictions or can it go to infinity?
g. Should the range have any restrictions or can it go to infinity?
Answers
The slope of the line is 0.93 and the y intercept is 100.54
Value of tempareture at time 30 mins = 1/2 hr = 101.01°
Value of tempareture at 1 hr is = 101.47°
Value of temperature at 90 mins =1.5 hr = 101.935°
What is a Equation ?An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.
A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A - > B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.
As per the problem
at starting that is x =0 hrs The temperature y = 99.9°
at x = 10/60 = 1/6 , y = 100.7° and at x = 2 , y = 102.4°
The equation of the line is
y-y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)
(y - 100.7) = (102.4 - 100.7)/(2 - 1/6) * (x - 1/6)
y = 0.93x + 100.54
The slope of the line is 0.93 and the y intercept is 100.54
Value of tempareture at time 30 mins = 1/2 hr = 101.01°
Value of tempareture at 1 hr is = 101.47°
Value of temperature at 90 mins =1.5 hr = 101.935°
Temperature at 4 hrs past current time = 104.26°
The domain of the function will be the time which can go upto infinite.
The range will be the temperature and have a fixed value between the range of a human body temperature as the body temperature can not exceed that temperature.
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What operation does the expression x + 5 involve?
Answers
Answer:
addition
Step-by-step explanation:
there's only one sign + so it means addition
Answer: addition
Step-by-step explanation:
Number 14
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Answers
Answer: 14
Step-by-step explanation: your correct
*
The equation p(n) = 12/5n²-17 represents the overall profit
from production for a company where p is the total profit
in dollars and n is the number of hours per day that
the production line operates. Determine the profit when
n = 101/2 hours.
Answers
The profit when n = 101/2 hours is $1,842.50.
Determine the profit when n = 101/2 hours.When the production line operates for 101/2 hours, the total profit can be determined using the equation p(n) = 12/5n²-17.When n = 101/2, the equation becomes p(101/2) = 12/5(101/2)²-17.By simplifying this equation, we can find that the total profit for 101/2 hours of production time is p(101/2) = $723.Therefore, when the production line operates for 101/2 hours, the total profit for the company will be $723.The equation p(101/2) = 12/5(101/2)^2 - 17 can be used to determine the total profit when the production line operates for 101/2 hours. To solve this equation, the expression 12/5(101/2)^2 can be simplified to 12(101)^2/25 which evaluates to 12,405. Subtracting 17 from this result yields a total profit of 12,388 dollars when the production line operates for 101/2 hours. The profit when n = 101/2 hours can be calculated by substituting the value of n into the equation p(n) = 12/5n²-17. This yields a total profit of $323.36 when the production line operates for 101/2 hours.To learn more about the overall profit from production refer to:
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Write a function rule for “the output is the square of the input”
Answers
Answer:
y=x^2
Step-by-step explanation:
Please help with this question
Answers
The area of the given figure would be = 508yd
What is an area of an object?The area of an object is defined as the total space that is being occupied by that object.
The are of the given shape above= area of a rectangle - area of square.
Area of the rectangle = length × width
= 36 × 18 = 648yd
Are of a square = length × width
= 10×14 = 140
Therefore, area of the figure, 648 - 140 = 508yd
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Could someone help please!! i really need these done
Answers
The specified equations in the question are in logarithmic form. The exponential form of the equations are as follows;
x³ = y10² = 1003³ = 2710⁰ = 1a¹ = a[tex]10^y[/tex] = x[tex]5^q[/tex] = py²⁰ = x2⁴ = 165² = 25What is the logarithmic form of an exponential equation?The logarithmic form of an exponential equation is the form logₐ(c) = b
The exponential form from which the logarithmic form is obtained, is the form aᵇ = c
The form of the equations in the question are in the logarithmic form, the exponential form of the equation are found as follows;
(1) 3 = logₓy
Therefore, x³ = y
(2) log₁₀100 = 2
Therefore, 10² = 100
(3) log₃27 = 3
Therefore, 3³ = 27
(4) log₁₀1 = 0
Therefore, 10⁰ = 1
(5) logₐa = 1
Therefore, a¹ = a
(6) log₁₀x = y
Therefore, [tex]10^y[/tex] = x
(7) log₅p = q
Therefore, [tex]5^q[/tex] = p
(8) [tex]log_yx=20[/tex]
Therefore, y²⁰ = x
(9) log₂16 = 4
Therefore, 2⁴ = 16
(10) log₅25 = 2
Therefore, 5² = 25
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what is the vertex of this quadratic function?
y=(x+4)^2-9
( , )
Answers
Step-by-step explanation:
the vertex form of a quadratic function is
y = (x - h)² + k
with (h, k) being the vertex.
luckily for us the function is already defined in that form.
so, when we compare
y = (x + 4)² - 9
with the general form about (h, k) above we see
h = -4
k = -9
so, the vertex is (-4, -9).
gradient of 1 and passing through (0,4)
Answers
The equation of line with a gradient of 1 which runs through the point (0,4) is y = x + 4.
What is the equation of line with a slope of 1 and passing through (0,4)?The slope-intercept form is expresses as;
y = mx + b
Where m is slope and b is y-intercept.
The point-slope form is expressed as;
y - y₁ = m( x - x₁ )
Given that, the slope of the line m = 1 and it passes through (0,4)
Plug the slope m = 1 and point ( 0,4 ) into the point-slope form above and simplify.
y - y₁ = m( x - x₁ )
y - 4 = 1( x - 0 )
y - 4 = x - 0
y - 4 = x
Add 4 to both sides
y = x + 4
Therefore, the equation of the line is y = x + 4.
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The top four winners in a golf tournament share the prize money in the ratio 9:5:2:1. If the top prize winner receives $45,00, then how much prize money is awarded in total?
(explanation would be appreciated I have to write it down)
Answers
$85000 is the prize money is awarded in total.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that top four winners in a golf tournament share the prize money in the ratio 9:5:2:1.
The top prize winner receives $45,000
We need to find the prize money is awarded in total.
9+5+2+1=17
9/17 x = 45000
Divide both sides by 9/17
x=$85000
Hence, $85000 is the prize money is awarded in total.
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What is in mathematics 24divided4x2-2=
Answers
Answer:
10
Step-by-step explanation:
PEMDAS
a characteristic of interest for the elements is called a a. sample. b. data set. c. variable. d. quality.
Answers
A characteristic of interest for the elements is called C) Variable.
A dataset is a grouping or set of data. This set is typically displayed in a tabular format. Each column provides information about a distinct variable. In accordance with the stated question, each row represents a certain component of the data set. The management of data includes datasets.
A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.
A qualitative variable, often known as a categorical variable, is one in which the variable categories are expressed verbally rather than as sets of numbers. Nominal and ordinal are the two subtypes of categorical data. Nominal variables don't have numerical values; they have "names."
Therefore, A characteristic of interest for the elements is called C) Variable.
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I just need to know the value of s
Answers
Answer:
S = 25
Step-by-step explanation:
Since it's stated as a square, that means all sides equal each other
In other words;
s+50 = 3s
To get S alone, we will first subtract 50 on both sides
s = 3s-50
Let's now subtract 3s from both sides
s-3s = -50, aka -2s = -50
Changing those to positive, 2s = 50
Last step is to divide both sides by 2
s = 25
A line passes through the points (-1,-9) and (1,7) write it’s equation in slope intercept form 
Answers
The equation of the line in slope intercept form is y = 8x -1.
What is slope intercept form?
The graph of the equation y = mx + b is a line with slope m and y-intercepts b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.
The slope, m, of a line indicates how steep it is. The gradient of a line is another name for the slope of a line. The y-intercept of a line is the y-coordinate of the location where the line's graph crosses the y-axis.
We are given two points which are (-1,-9) and (1,7).
First, we need to find the slope(m)
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]m=\frac{7 +9 }{1+1 }[/tex]
m = 16/2
m = 8
We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)
So,
⇒b = (-9) + 1(7 + 9)/(1+1)
⇒b = -9 + 8
⇒b = -1
The equation comes out to be
⇒y = mx + b
⇒y = 8x -1
Hence, the equation of the line in slope intercept form is y = 8x -1.
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GIVING 35 POINTS!!
The solids are similar. Find the volume V of the smaller solid.
Volume =
Answers
Answer:
Step-by-step explanation:
Answer:
Volume =936.3 ft³
Step-by-step explanation:
Solution Given:
The mathematics tells us that the cube of the ratio of the lengths is equal to the ratio of the volumes.
[tex]{(\frac{Side\: of\: bigger \: solid}{Side \: of \: smaller \: solid} )}^3 = \frac{volume\: of \: bigger \: solid}{volume \: of \: smaller \: solid} [/tex]
let volume of smaller solid be x.
by equation
[tex] {(\frac{12}{8} )}^3 = \frac{3160}{x} [/tex]
doing criss cross multiplication
12³*x=3160*8³
we get
[tex]x = \frac{3160 \times 8^3}{12^3} [/tex]
x= 936.296296296 ft³
(2, -3) is a solution of the equation 3x - y = 3.