The point-slope form of a line with slope that contains the point
(-3, 6) is y-6=2(x+3)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The point-slope form of a line is given by y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is a point on the line.
We are given that the line has a slope, but we are not given what the slope is.
The given point is (-3, 6)
y - 6 = m(x - (-3))
y - 6 = m(x+3)
As per the given options which matches the point slope form is y-6=-2(x+3)
Hence, the point-slope form of a line with slope that contains the point
(-3, 6) is y-6=2(x+3)
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1. The scale on a map reads 3 inches = 25 miles.
If two cities are 7.5 inches apart on the map,
find their actual distance.
A. 54.5 miles
B. 57.5 miles
C. 59.5 miles
D. 62.5 miles
Answer:
D. 62.5
Step-by-step explanation:
2 ways
1.
7.5 ÷ 3 = 2.5
25 times 2.5 = 62.5
2.
3/7.5 = 25/x
3x = 187.5
187.5 ÷ 3 = 62.5
The actual distance for a length on a map is 62.5. so correct option is D.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Given The scale on a map reads 3 inches = 25 miles.
If two cities are 7.5 inches apart on the map,
Find the actual distance for a length on a map.
Let x be the actual distance
7.5 ÷ 3 = 2.5
25 times 2.5 = 62.5
Thus,
3/7.5 = 25/x
3x = 187.5
187.5 ÷ 3 = 62.5
Therefore, the actual distance for a length on a map is 62.5.
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anybody can help me im stuck U_U
Graph (b) represents the data provided that option (b) would be the correct choice.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have the data shown in the table.
The equation of the line M = 3n represents the data provided,
After plotting all the points on the coordinate plane.
We will get a graph that represents the data.
Thus, graph (b) represents the data provided the option (b) would be the correct choice.
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What is the approximate circumference of the circle shown below?
A.20cm
B.31.4cm
C.62.8cm
D.40cm
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formula for finding the circumference:}[/tex]
[tex]\mathbf{2\times\pi\times radius = circumference}[/tex]
[tex]\huge\textbf{So, your equation should look like this:}[/tex]
[tex]\mathbf{\boxed{\textbf{circumference}} \approx 2\times3.14\times10}[/tex]
[tex]\huge\textbf{Now, that we have that information}\\\\\huge\textbf{out of the way, we can answer the}\\\\\huge\textbf{question, shall we begin?}[/tex]
[tex]\mathbf{\boxed{\textbf{circumference}} \approx 2\times3.14\times10}[/tex]
[tex]\mathbf{\boxed{\text{\bf circumference}}\approx 6.28 \times 10}[/tex]
[tex]\mathbf{\boxed{\bf circumference} \approx 62.8}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\textsf{Option C. 62.8 cm}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
Answer is C 62.8cm
Step-by-step explanation:
I just took the quiz!
question on the image
Answer:
475.2
Step-by-step explanation:
682 is 1.55 of the original amount so 1.55x=682
682/1.55=440
440*1.08=475.2
△JKL∼△PQR
Two similar triangles. JKL and PQR. The length of JL is 28. The length of LK is unknown. The length of JK is labeled x. Angle J is labeled 35 degrees. The length of PQ is 38. The length of PR is 42. Angle P is labeled 35 degrees.
What is the value of x?
Enter your answer in the box. Round to the nearest hundredth.
x =
Answer: 25.33
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{x}{28}=\frac{38}{42}\\\\x={28} \left(\frac{38}{42} \right) \approx \boxed{25.33}[/tex]
An engineering student is studying the effects of cryogenic treatments on a particular material. The treatment involves cooling the material with specific applications of liquid nitrogen.
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the treatment began.
The true statement about the graph from the attached image below is: The material's temperature reaches a minimum at 15 hours.
What is the parabolic graph of the quadratic equation?The parabolic graph is a curved U-shaped graph that is established from a quadratic equation.
The parabola of the graph can be downward creating a maximum or upward (minimum).
From the given image, the correct interpretation shows that as a result of cryogenic treatment, the material's temperature reaches a minimum at 15 hours.
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Lewis is planning a cycling holiday.
a) He decides to cycle for 6 hours each day.
He thinks he can cycle at an average speed of 12 miles per hour.
How far would Lewis cycle each day?
miles
Answer:
72 miles/day
Step-by-step explanation:
12 m/hr * 6 hr / day = 72 mi/day
write the numerical expression for each statement
An expression is defined as a set of numbers, variables, and mathematical operations. The sum of three and the square root of a number is expressed as 3 + √x.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the unknown number be represented by x.
1.) The sum of three and the square root of a number.
3 + √x
2.) Nine less than a number cubed.
x³ - 9
3.) The quotient of a number and 7.
x ÷ 7
4.) Four times a quantity plus five.
4x + 5
Hence, The sum of three and the square root of a number is expressed as 3 + √x.
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write the linear inequality shown in the graph the gray represents the shaded region
The fit line equation is Y = -2.61x +152.51, where x is variable 1 and Y is variable 2. According to the equation, what is the expected value of Y when x-value is 45?
The expected value of y when x is equals to 45 in the equation is 35.06
How to find variable from an equation?The equation is given as follows;
y = -2.61x + 152.51
where
x = variable 1y = variable 2Therefore,
when
x = 45
y = -2.61x + 152.51
y = -2.61(45) + 152.51
y = - 117.45 + 152.51
y = 35.06
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A(n) _______ appears behind selected text. dotted line double-arrow point blue line shaded background
A (n) Shaded background Appears behind selected text so option. 4) Is correct.
What is shading background?
Shading background is process, When selecting a particular text there behind the text a shad will form which shows the number of texts selected
Thus, shaded background appears behind selected text
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help me please i dont understand
Answer:
22
Step-by-step explanation:
The line where it says 2cm, extend that line to the top. You know have 2 triangles, call the one on the left A and the one on the right B
area of recntangle = bh
Rect A:
b = 5
h = 4 - 2
h = 2
bh = 5 x 2
bh = 10
Rect B:
b = 3
h = 4
bh = 4 X 3
bh = 12
Total = 10 + 12
Total = 22
Please help me thank youuu
Answer:
(c) -3.8, 3
Step-by-step explanation:
The solutions to the equation f(x) = g(x) are the values of x where the function values are equal. These are the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect each other.
Points of intersectionThe points where the graphs cross can be estimated to be ...
(-3.8, 6.5) and (3, -6)
The x-coordinates of these points are the solutions to the equation:
x = -3.8, 3
Veronica needs blinds for the window in her bedroom. the window is 2 meters tall and 4 meters wide. what is the area of the window?
The area of the window is 8[tex]m^{2}[/tex].
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space. The length and width of a form are used to compute its area.
Any shape's area can be calculated by counting how many unit squares will fit inside of it.
According to the question,
Length of window=2m
Width of window=4m
Area of window=Length*Width
=2*4
=8[tex]m^{2}[/tex]
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Evaluate.
5a for a = 15
Answer: 75
Step-by-step explanation:
5a = 5(15) = 75
Construct the graph of the equation given. Categorize this graph a horizontal or vertical line. Label the intercept as well as the axis on the graph.
x = -2.5
The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A linear equation is in the form:
y = mx + b
Where m is the slope and b is the y intercept.
The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)
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Translate The Following Into An Expression:
s% of 1/r
(1r is a fraction)
The equation s% of 1/r translates to the expression s/100r
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
s% of 1/r
= (s/100) * (1/r)
= s/100r
The equation s% of 1/r translates to the expression s/100r
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the volume of a cylinder is 539 cm cube and the circumference of the base is 22 cm. find the height of the cylinder.
Answer:
13.994[tex]cm (5.sf)[/tex]
Step-by-step explanation:
We know that the base of the cylinder is a circular base.
So circumference of base = [tex]2\pi r[/tex]
Given [tex]2\pi r=22cm\\\\r=\frac{22}{2\pi } \\r=\frac{11}{\pi } cm\\[/tex]
Volume of a cylinder = [tex]\pi r^{2} h[/tex] = 539[tex]cm^{3}[/tex]
Substitute r into the formula for volume of cylinder.
[tex]\pi (\frac{11}{\pi } )^{2} h=539\\\pi (\frac{121}{\pi ^{2} } )h=539[/tex]
Now, we will cancel [tex]\pi[/tex] from the numerator and denominator.
[tex](\frac{121}{\pi } )h=539\\h = \frac{539}{\frac{121}{\pi } } \\h = 539 * \frac{\pi }{121} \\h = 13.994cm(5s.f)[/tex]
Answer:
Aproximated height is:
14 cm
Step-by-step explanation:
volume of a cylinder = л r² h
л = 3.1416 (aprox)
r = radius
h = height
r = circunference/2л
r = 22/(2*3.1416)
r = 3.5 (aprox)
then volume is:
539 = 3.1416 * 3.5² * h
539 = 3.1416 * 12.25 * h
539 = 38.5 * h
h = 539/38.5
h = 14 cm (aprox)
Question 1
1 pts
You borrow money to purchase a car. You secure a 5 year loan for $15,000 with an annual percentage
rate of 5%. How much will your monthly payments be?
Answer:
$283.07
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = monthly interest rate (in decimal form)n = term of the loan (in months)Given:
P = 15000i = 5% / 12 = 0.05 / 12n = 5 years = 60 monthsSubstitute the given values into the formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{15000\left(\frac{0.05}{12}\right)\left(1+\frac{0.05}{12}\right)^{60}}{\left(1+\frac{0.05}{12}\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=283.0685047...[/tex]
Therefore, the monthly payments will be $283.07.
Please Help fast!!!!! I'll give 30 pts.!
Use the information in this table(in the attachment) to help you answer the questions. Remember, you have a budget of $20,000 for the car.
1. What add-on options do you want in your car?
Sun-roof, and Keyless entry
2. Write an inequality to model purchasing a car from Dealership A with the desired add-on options and staying within your budget. Use x to represent the base price of the car. (Assume that only the base price of the car is taxed to simplify the problem.)
3. Solve for x. Explain in words what the solution to the inequality means.
4. Graph the possible base price values that are included in the solution. Please upload an image of your graph.
5. Complete 2–4 for Dealership B using the same add-on options.
Will you buy from Dealership A or from Dealership B? Why?
The best buy is from dealership B because dealership B has a lesser base price
The add-on optionsFor the purpose of this exercise, the add-on options to select are:
SunroofKeyless entryDealership AThe total amount of the add-on options is:
Total = $500 + $1500
Total = $2000
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 17248.44
Divide both sides by (1 + 6.75%)
x ≤ 16157.79
The solution means that the base price of the car cannot exceed $16157.78 for dealership A
The graph of the possible base price
See attachment
Dealership BThe total amount of the add-on options is:
Total = $750 + $1000
Total = $1750
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 16725.28
Divide both sides by (1 + 6.75%)
x ≤ 15667.71
The solution means that the base price of the car cannot exceed $15667.71 for dealership B
The graph of the possible base price
See attachment
Where to buy fromBuy from dealership B because dealership B has a lesser base price
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Find the tangent of angle Θ in the triangle below.
A. 7/7
B. 0
C. sqroot2
D. 1
E. 7/sqroot98
Answer:
The tangent of the angle is 1
Step-by-step explanation:
The solution is in the image
Solve 7x = 54.
Pls help
Answer:
x= 54/7
Step-by-step explanation:
x= 54/7
Answer:
x = 54/7
Step-by-step explanation:
7x = 54
Divide both sides by seven (7)
7x/7 = 54/7
7 cancel out 7
x = 54/7
Construct a perpendicular to t through A
A
The perpendicular line to line t is drawn below.
The two-line in which the angle between these two lines is 90° i.e. both are right angle to each other then two lines are perpendicular to each other.
Here the given point is point A.
and the line given is line t
we have to draw a line that should be perpendicular to line t.
Let that perpendicular line cut the line t at the point O.
OA ⊥ t
∠AOt= 90°
From above we can draw the line OA which is perpendicular to line t.
The picture is drawn below.
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Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary
Answer:
9.4 in
Step-by-step explanation:
sin A = O/H
sin 19° = x/29
x = 29sin19°
x = 9.441 in
x = 9.4 in
If (x2 – 4) ÷ (x 2) = x – 2, which polynomial should fill in the blank below? (x 2) ´ ______ = x2 – 4
The polynomial which shoud be filled in the blank is (x+2).
Given expression ([tex]x^{2} -4)/x^{2} =x-2[/tex] and the expression (x+2)____=[tex](x^{2} -4)[/tex]
We have to find a polynomial which fills the blank in the given expression.
Polynomial is expression of more than two algebraic terms mainly the sum of several terms that contain different powers of the same variable.
We have been given [tex](x^{2} -4)/x+2=x-2[/tex]
first multiply both sides by (x+2)
([tex]x^{2}[/tex]-4)/(x+2) *(x+2)=(x-2)(x+2)
cancelling (x+2) from numerator and denominator we get
([tex]x^{2}[/tex]-4)=(x-2)(x+2)
If we carefully observes the expression we found that both the given expression in which blank takes place are same just on the place of blank there is (x+2).
Hence the polynomial which fills the blank is (x+2).
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Question is wrong as in this the expressions would be :
([tex]x^{2} -4)/x+2=x-2[/tex] and (x+2)____=[tex]x^{2} -4[/tex]
Polygon LMNOP was transformed to create polygon L'M'N'O'P'.2 pentagons have identical side lengths and angle measures. The points are labeled with the same letters.
Which angle corresponds to AngleN?
Angle
Angle
Angle
Angle
The Angle that would correspond to Angle N after the transformation is; Angle N'
How to Interpret Transformations?
A polygon is defined as a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
In the transformation of LMNOP to create polygon L'M'N'O'P', we have that;
L corresponds to L'
M corresponds to M'
N corresponds to N'
O corresponds to O'
P corresponds to P'
Thus, we can conclude that Angle N would correspond to Angle N'
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which coordinates represent a translation of B (1,2) 3 units to the left and 2 units up
Answer:
(-2,4)
Step-by-step explanation:
By going 3 back you go 0,-1,-2 then you are already up 2 so if you go up 2 more you are at (-2,4). Hope this helps!
A marble is selected from a bag containing eight marbles numbered 1 to 8. The number on the marble selected will be recorded as the outcome. Consider the following events. Event A : The marble selected has an even number. Event B : The marble selected has a number greater than 3. Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
Answer:
Event A: 1/2
Event B: 5/8
I don't know how to solve this at all, i just need some help on how to figure it out. Thanks!
Answer:
[tex]\sf \dfrac{3}{{z-3} }[/tex]
Explanation:
[tex]\Longrightarrow \sf \dfrac{1}{z} \div \dfrac{z-3}{3z}[/tex]
apply the theorem when [tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex] then [tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
[tex]\Longrightarrow \sf \dfrac{1}{z} \times \dfrac{3z}{z-3}[/tex]
Join the fractions
[tex]\Longrightarrow \sf \dfrac{3z}{z({z-3)} }[/tex]
Cancel out common factor z
[tex]\Longrightarrow \sf \dfrac{3}{{z-3} }[/tex]
The answer is : [tex]\boxed {\frac{3}{z-3}}[/tex]
Remember that dividing fractions is the same as multiplying the 1st fraction by the reciprocal of the other.
[tex]\mathsf {\frac{1}{z} \div \frac{z-3}{3z}}[/tex]
[tex]\mathsf {\frac{1}{z} \times \frac{3z}{z - 3}}[/tex]
[tex]\mathsf {\frac{3}{z-3}}[/tex]
Is -(3x + 5)^2 a perfect trinomial? Why or why not?
The given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial.
What is a perfect trinomial?A perfect square trinomial is takes the algebraic expression form ax^2 +bx + c, where the square root of the first term and the third term is the equation to the second term.
Given that:
-(3x + 5)^2
Open brackets
= - (9x +30x + 55)
Multiply through by (-)
= -9x^2 - 30x - 55
Therefore, we can conclude that the given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial. i.e. the multiplication of the square root of the first and the third term did not result in the 2nd term.
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