Answer:
A straight line is represented by a linear equation.
The possible equations are:
\mathbf{3y = 2x + 4}3y=2x+4 .
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
.
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2 .
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
The points are given as:
\mathbf{(x,y) = \{(1,2),(4,4)\}}(x,y)={(1,2),(4,4)}
Start by calculating the slope (m)
\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}m=
x
2
−x
1
y
2
−y
1
So, we have:
\mathbf{m = \frac{4-2}{4-1}}m=
4−1
4−2
\mathbf{m = \frac{2}{3}}m=
3
2
The equation in slope intercept form is then calculated as:
\mathbf{y = m(x - x_1) + y_1}y=m(x−x
1
)+y
1
So, we have:
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2
or
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
Expand \mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2
\mathbf{y = \frac 23x - \frac 23 + 2}y=
3
2
x−
3
2
+2
Take LCM
\mathbf{y = \frac 23x + \frac{-2 + 6}{3}}y=
3
2
x+
3
−2+6
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
Multiply through by 3
\mathbf{3y = 2x + 4}3y=2x+4
So, the possible equations are:
\mathbf{3y = 2x + 4}3y=2x+4 .
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
.
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2 .
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.
The point is on the graph. Explain what this means in terms of the car.
Is the point on this graph? Explain how you know.\
The point (1, 60). on the graph how's the speed that the car travels.
How to illustrate the value?It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.
Therefore, it should be noted that the point (3.5, 120) shows the distance.
The slope of the like which is the speed will be:
= Distance / Time
= 210 / 3.5
= 60 mph
Therefore, it should be noted that the point B(1, 60) lies on the graph.
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A line is drawn through (-7, 11) and (8,-9). The equation
y-11 = -4/3(x + 7) is written to represent the line. Which
equations also represent the line? Check all that apply.
Answer:
[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\textsf{Standard form}: \quad 4x+3y=5[/tex]
Step-by-step explanation:
Given linear equation:
[tex]y-11=-\dfrac{4}{3}(x+7)[/tex]
The given linear equation is point-slope form.
[tex]\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
To write the equation in slope-intercept form, isolate y:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies y-11=-\dfrac{4}{3}x-\dfrac{28}{3}[/tex]
[tex]\implies y-11+11=-\dfrac{4}{3}x-\dfrac{28}{3}+11[/tex]
[tex]\implies y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}[/tex]
To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies (y-11) \cdot 3=-\dfrac{4}{3}(x+7) \cdot 3[/tex]
[tex]\implies 3y-33=-4(x+7)[/tex]
[tex]\implies 3y-33=-4x-28[/tex]
[tex]\implies 3y-33+4x=-4x-28+4x[/tex]
[tex]\implies 3y-33+4x=-28[/tex]
[tex]\implies 3y-33+4x+33=-28+33[/tex]
[tex]\implies 4x+3y=5[/tex]
Avani and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75. Avani has a total of $15 to spend
on peaches and mangos. Write an inequality that would represent the possible values
for the number of peaches purchased, p, and the number of mangos purchased, m.
The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Avni and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75.
And, Avni has a total of $15 to spend on peaches and mangos.
Now,
Let number of peaches purchased = p
And, Number of Mangos purchased = m
Since, Each peach costs $0.75.
Hence, Total cost of peaches purchased = $0.75p
And, Each mango costs $1.75.
Hence, Total cost of mangos purchased = $1.75m
Since, Avani has a total of $15 to spend on peaches and mangos.
So, An inequality that would represent the possible values of peaches and mangos will be;
⇒ $0.75p + $1.75m = $15
Thus, The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
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Which graph represents the solution to the inequality 2(b + 2) ≥ 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
The graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .
In the question ,
the inequality is given as
2(b + 2) ≥ 24
Solving the inequality further , we get
2b + 2*2 ≥ 24
2b + 4 ≥ 24
Simplifying further we get
2b ≥ 24-4
2b ≥ 20
b ≥ 10 .
Since the inequality has equal to sign, hence number line representing the inequality will have a closed point 10 ,
And on number line as the number increases the value move towards right ,
hence the arrow will point Right .
Therefore , the graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .
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Answer: C number line with closed point at 10 with arrow pointing right
Step-by-step explanation:
I took the test and I got it right. :)
hope this helps
What is the equation of a line that contains the points (5, 0) and (5,-2)?
Ox=5
Ox=0
Oy=0
Oy=5
Answer:
x=5
you're welcome
DO,K = (9, 6) (3, 2) The scale factor is___ 1/3 6 3
Based on the dilation, the scale factor of dilation of the point is 1/3
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the scale factor of dilation?From the question, we have the following parameters
Dilation rule: Do,k
Point = (9, 6)
Image = (3, 2)
As a general rule of dilation, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe side lengths may or may not be whole numbersUsing the above as a guide, the scaled factor is calculated as
Scaled factor = Image/Poins
This gives
Scaled factor, k = (3, 2)/(9, 6)
This gives
Scaled factor, k = 1/3
Hence, the scale factor is 1/3
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Suppose the domain of f is ( -1, 1).
Define the fucnction g by g(x)=f([tex]\frac{x+1}{x-1}[/tex]).
What is the domain of g?
If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)
What is the domain of the function?The domain of a function refers to the set of all possible intput values that make the function possible.
Now, we are given the function;
g(x) = f((x + 1)/(x - 1))
The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.
Since the domain of f(x) is -1 < x < 1 ,
Then the domain of f(x + 1) is -1 < x + 1 < 1 .
domain of -1 < x + 1 < 1 will simplify to -2 < x < 0
Thus, we can say that the domain of f(x + 1) is (-2, 0).
Thus;
g(x) = f(x + 1) and as such, the domain of g(x) is (-2, 0) .
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Write each number as a polynomial and then simplify the sum or difference
Answer:
[tex]90a+10b[/tex]
Step-by-step explanation:
[tex](100a+10b+c)-(10a+c) \\ \\ =100a+10b+c-10a-c \\ \\ =90a+10b[/tex]
Find the value of the exterior or interior angle!!
Answer:
137°
Step-by-step explanation:
By the exterior angle theorem, [tex]m\angle JKX=93^{\circ}+44^{\circ}=137^{\circ}[/tex].
A number, c, rounded to 1 d.p. is 47.3
Another number, d, rounded to 1 d.p. is 4.6
What are the lower and upper bounds of c- d?
The lower and upper bounds of c- d are 42.0 and 43.0 respectively.
What is termed as the rounding off?Rounding off merely refers to an estimate. Rounding off is the process of estimating this same actual number to a nearby number.Examine this same unit place digit:If indeed the unit place digit is a little less than 5, keep a tens place digit unchanged and replace it with 0.Whereas if unit place is 5 or greater, replace the tens digit with its successor and place 0 just at unit place.For the given question;
A number, c, rounded to 1 decimal place is 47.3
Another number, d, rounded to 1 decimal place is 4.6
c- d = 47.3 - 4.6
c- d = 42.7
Lower bound = 42.0
Upper bound = 43.0.
Thus, the lower and upper bounds of c- d are 42.0 and 43.0 respectively.
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What is the amplitude of the function y = sin 5лx?
The amplitude of the function y = sin 5лx is found as 1.
What is defined as the amplitude of function? The maximum deviation of a variable out of its mean value is referred to as its amplitude. The amplitude formula aids in the calculation of the cosine and sine functions. A is the symbol for amplitude. The amplitude formula can also be conveyed as the average of the sine or cosine function's maximum and minimum values.The sine (or cosine) function can be written as,
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ)
x = displacement of wave (meter)A = amplitudeω = angular frequency (rad/s)t = time periodϕ = phase angleTo find the variables used to calculate the amplitude, use the formula;
y = asin(bx - c) + d.
Where a is the amplitude.
The given equation of function is y = sin 5лx.
Comparing the function with the standard form
a = 1
Thus, the amplitude of the function y = sin 5лx is found as 1.
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Given the function, [tex]f(x)=-2x-1[/tex] express the value of [tex]\frac{f(x+h)-f(x)}{h}[/tex] in simplest form.
Value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
As given,
Given function:
f(x) = -2x -1
Express value of in simplest form:
f( x + h ) = -2 (x + h ) - 1
= -2x -2h -1 ___(1)
Simplify the function by substituting value of f(x +h and f(x),
[f(x + h) - f(x) ] /h
= [ (-2x -2h -1 )- ( -2x -1 ) ] /h
= ( -2x -2h -1 +2x +1 ) /h
= -2h /h
= -2
Therefore, value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
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What is the slope of a line that goes through the points (1,-5) and (-3, 2)?
O
O
O
7
4
3
3
Answer:
[tex]\sf -\dfrac{7}{4}[/tex]
Step-by-step explanation:
Finding the slope of a line:(1, -5) ⇒ x₁ = 1 ; y₁ = -5
(-3, 2) ⇒ x₂ = -3 ; y₂ = 2
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]
Solve the problem
A = (50+50)
B=(85*85+A)
C = (15*0.9+B)
D = (10*15+4+C)
Answer:
7,492.5
Step-by-step explanation:
Solve the problem
A = (50+50)
B=(85*85+A)
C = (15*0.9+B)
D = (10*15+4+C)
10*15+4+15*0.9+85*85+50+50=
150+4+13.5+7,225+100=
7,492.5
Answer:
A= 100
B= 7,325
C= 7,338.5
D= 7,492.5
brainlyist Write a paragraph proof. Given: ∠1≅∠4; Prove: 2≅∠3
From the figure given the required prove is achieved using transitive property of equality to show that 2 ≅ ∠3
What is transitive property of equality
The term transitive property of equality is used in situation where say three values: x, y, and z are related as follows
if x = y and y = z then x = zHow to Prove that 2 ≅ ∠3
given data
Given: ∠1 ≅ ∠4
Information deduced from the figure
∠1 ≅ ∠2 vertical opposite angle∠4 ≅ ∠3 vertical opposite angleHence we can say that ∠2 ≅ ∠3 using the transitive property of equality
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Do the ordered pairs represent a function?
Answer: A.
Step-by-step explanation:
Something is a function if the x value is not repeated. The y value can be repeated however.
What is the radius of a circle with a circumference of 26 69 centimeters
In the rectangle below
Simplify 9 3 × 9 2 × 9 4 leaving your answer in index form.
Answer:
804,264
Step-by-step explanation:
Evaluate 93×92×94
We have 1 of the number 93
We have 1 of the number 92
We have 1 of the number 94
Group numbers by powers:
93×92×94 = 93[1]92[1]94[1]
93[1]92[1]94[1] = 804,264
Select the correct answer. which situation is best met through long-term saving? a. a broken refrigerator b. retirement c. an unexpected car repair d. an unexpected medical bill
The situation best met through long term saving is retirement (Option B).
In many cases, the retirement fund is taken out of the paychecks at your job and is accumulated over years of your service and job till retirement, it is a long-term saving.
The purpose of long-term saving is the type of saving for long term financial goals. The other options are not long-term financial goals rather unexpected expenses. Hence, a situation best fulfilled through long term saving is retirement.
There are several long-term saving accounts use to save for long term financial goals such as retirement, buying a house, children’s education, or similar one-time, long-term expenses.
Hence, the correct answer is retirement – Option B
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If GI and JL are parallel lines and mZJKH = 70°, what is m<LKM
WILL GIVE BRAINLIEST
Answer:
70°
Step-by-step explanation:
Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.
the 5ft tall person casts a shadow that is 4 ft long. how tall is the flagpole if it 28 foot shadow?
The flagpole is 35ft tall.
How to find the shadow's height?Given,
A 5ft tall person casts a shadow that is 4 ft long.
Flagpole has a 28-foot shadow.
Solution:
Let x be the height of the flagpole.
5/x = 4/28
x = 35ft
The flagpole is 35ft tall.
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please helpp i am very confused on finding the answer
Answer:
C. Lines l and m appear to be skew--they are not parallel, and they are not intersecting each other.
is 2y-3>11 a expression equation or inequality
Answer:
Inequality
Step-by-step explanation:
An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.
Write an equation of the line that passes through each pair of points
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}[/tex]
find the lcm of the numbers 3,6,16 using lists of multiples
Answer:
48
Step-by-step explanation:
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
6 12 18 24 30 36 40 48
16 32 48
The school that Brenda goes to is selling tickets to a choral performance. On the first day of
ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school
took in $190 on the second day by selling 10 adult tickets and 10 student tickets. What is the
price each of one adult ticket and one student ticket?
The price of one adult ticket is $5 and one student ticket is $14
What is algebra ?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.
Given that : first day of ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school took in $190 on the second day by selling 10 adult tickets and 10 student tickets.
Let the price for adult ticket x and for student ticket y
we have ,
14x + 5y =140.....(i)
10x + 10y = 190....(ii)
10 x + 10y = 190
x + y = 19
y = 19-x .....(iii)
put the value of y in equation i
14x + 5(19-x) = 140
14x + 95 - 5x = 140
9x = 45
x = 5
Now put value of x in equation iii
y = 19 - 5
y = 14
The price of one adult ticket is $5 and one student ticket is $14
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The equation y=0.52x+186 gives the cost y of renting a car if the care is driven x miles. Based on this equation, for every mile the car is driven the cost of increases by how much?
For every mile the car is driven, the cost increases by 0.52 units.
Consider a line that passes through the origin at a distance 'a' from the Y-axis and has a slope of m. In this situation, the distance an is the definition of the line's y-intercept. At this moment, the line will cross the y-axis (0, a). The equation for the line will then be y = mx + a. The same goes for a line that crosses the X-axis at a position b from the origin and has a slope of m. (b,0). The distance b is the line's x-intercept. The equation for the line will be y = m* (x-b)
Given, the equation that relates cost of renting and miles driven is
y = 0.52 x + 186
Therefore, for a car travelling one mile, cost is y₁ = 0.52*1 + 186 = 186.52
For a car travelling two miles, cost is y₂ = (0.52*2) + 186 = 187.04
Thus, for every next mile the cost increases by = y₂ - y₁ = 187.04 - 186.52 = 0.52 units
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Find three consecutive odd integers such that the sum of three times the smaller and twice the largest is equal to one less than four times the middle. find the integers.
Answer:
-1, 1, 3
Step-by-step explanation:
Let x equal the first odd integer.
The three consecutive odd integers would be represented by x, then x+2, then x+4.
So 3x + 2(x + 4) = 4(x + 2) - 1
Solve for x
3x + 2x + 8 = 4x + 8 -1
5x + 8 = 4x + 7
x = -1
Ram, a self-employed salesperson, purchased two to a september 2021 concert for himself and a prospective client. he also took the client out to dinner prior to the show. the tickets cost $200 each and the meal cost $110. how much may ram deduct as a business expense?
Answer:
$620 Ram deduct as a business expense.
Step-by-step explanation:
GIVEN-
Ram, a self-employed salesperson, purchased two for a September 2021 concert for himself and a prospective client. he also took the client out to dinner before the show;
The tickets cost $200.
The meal cost $110.
to answer-how, much may ram deduct as a business expense?
total expense for two persons =$200*2+$110*2
=$620
$620 ram deduct as a business expense
Answer:
no 110 tax cuts and job act took away tickets and entertainments
Step-by-step explanation: