Using the distance formula, the area of the rectangle is: 16 units².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the vertices:
A(−3, −1)B(1, 3)C(3, 1)D(−1, −3)Area = (AB)(BC)
Apply the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB and BC:
AB = √[(1−(−3))² + (3−(−1))²]
AB = √[(4)² + (4)²]
AB = √32
BC = √[(1−3)² + (3−1)²]
BC = √[(−2)² + (2)²]
BC = √8
Area = (√32)(√8) = √256
Area = 16 units²
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Match the following items.
1.(4, 2)
2.(-4, -2)
3.(-5, 0)
4.(-1, 1)
5.(2, 5)
6.(2, -4)
7.(4, -2)
8.(0, -5)
A
C
E
F
H
B
D
G
Based on the points on the graph, the correct matches are:
A - (-4, -2).B - .(2, -4)C - (4, -2).D - (2, 5)E - (-1, 1)F - (-5, 0)G - (4, 2)H - (0, -5)How are points located on a graph?To find a point, you need to look at the x-axis first and then the y-axis.
Find where the point is located on the x-axis, and then look for where the point intersects with the y-axis point.
For instance, the point A is located at (-4, -2) so look at the -4 point on the x axis, then go down to the -2 point on the y-axis. You'll find point A.
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The question is in the photo
Answer:
Answer is in the photo
Step-by-step explanation:
The formula for multiplying two numbers with same base but different exponents is
a^m×a^n= a^(m+n)
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]
△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]
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]
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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The line AB is shown on the grid.
a) Find the gradient of a line
perpendicular to AB.
b) Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.
X
a) The gradient of a line perpendicular to AB is -2.
b) equation of line is y=-2x+6
What is gradient?The gradient is the measure of the steepness of a straight line.
a)The gradient of line is
=(-2-2)/(7+1)
=-4/8
=-1/2
So, gradient of a line perpendicular to AB is -2
b)The coordinates of mid point (3, 0)
m = -2
So,
0= -6+ b
b= 6
So, equation of line is y=-2x+6
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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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4x^2-3x+4 What is the value of the expression below when x = 5?
NEED ANSWER PLEASE!
Answer:
89
Step-by-step explanation:
To find the value of the
Quadratic expressionwhen x = 5 we substitute x = 5 into the expression.
4x^2 - 3x + 4
putting x = 5
4(5)^2 - 3(5) + 4
4(25) - 15 + 4
100 - 11 = 89
Find the perimeter and area of the following composite figure. GEOMETRY!! HELPPP PLS
Answer:
perimeter=80 area=252
Step-by-step explanation:
The perimeter is the total length of the boundary of the shape added together: 12+20+12+8+20+8=80
The area is the value of the space inside the shape: the rectangle would be 20*9=180 plus the two triangles: (8*9)/2 = 36 180+72=252
Answer:
p=80 a=252
Step-by-step explanation:
Add all side lengths to get the perimeter.
20+12+12+8+20+8=80
Perimeter is 80
Area of a trapezoid is average of parallel lines*height
((20+36)/2)*9=252
Area=252
Evaluate.
5a for a = 15
Answer: 75
Step-by-step explanation:
5a = 5(15) = 75
Using the angle addition postulate, m BAD+m DAC=?
0 BCA
0 BAE
0 90*
0 BAC
Answer:
0 BAC
Step-by-step explanation:
m BAD+m DAC=m BAC(180°)
The value of m(BAD) + m(DAC) is equal to the measure of angle BAC.
Let's use the angle addition postulate to find the value of m(BAD) + m(DAC):
The angle addition postulate states that if you have an angle formed by two rays, say ∠BAD, and another angle formed by two rays, say ∠DAC, then the sum of their measures is equal to the measure of the angle formed by the original rays extended to meet the rays of the second angle. In other words:
m(BAD) + m(DAC) = m(BAC)
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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)
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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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
I need help asappp please, I attached a image
Answer:
Just look at the other answer
Step-by-step explanation:
write the linear inequality shown in the graph the gray represents the shaded region
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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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
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
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!
The length of a rectangle is 5 inches more than the width. the perimeter is 30 inches. find the length and the width
Answer:
Length = 10 inches
Width = 5 inches
Step-by-step explanation:
p = 2w + 2l
l = w + 5
30 = (2w + 2(w + 5))
30 = 4w + 10
20 = 4w
w = 5
l = w + 5
= 5 + 5
= 10
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?
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 A because the fees of dealership B is more expensive
The add-on optionsFor the purpose of this exercise, the add-on options to select are:
Air-conditioningSunroofGPSBluetoothPower door and windowDealership AThe total amount of the add-on options is:
Total = $1000 + $500 + $3500 + $500 + $750
Total = $6250
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 12998.44
Divide both sides by (1 + 6.75%)
x ≤ 12176.52
The solution means that the base price of the car cannot exceed $12176.52 for dealership A
The graph of the possible base price
See attachment
Dealership BThe total amount of the add-on options is:
Total = $500 + $750 + $2750 + $750 + $500
Total = $5250
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 13225.28
Divide both sides by (1 + 6.75%)
x ≤ 12389.02
The solution means that the base price of the car cannot exceed $12389.02 for dealership B
The graph of the possible base price
See attachment
Where to buy fromBuy from dealership A because the fees of dealership B is more expensive
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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
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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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
Ken has a total of 74 notes. They are either $2 or $5 notes. He has 16 more pieces of $5 notes than $2 notes. Find the total value of all his notes.
Answer:
$283
Step-by-step explanation:
Let,
x - for $2 notes
x + 16 - for $5 notes
EQUATION:
(x) + (x + 16) = 74
2x = 74 - 16
2x = 58
x = 29
SUBSTITUTE
x = 29 pieces of $2 notes
x + 16 = 29 + 16 = 45 pieces of $5 notes
TOTAL VALUE IS:
(29 x $2) + (45 x $5) = $283
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 line passes through (5,-2) with a slope of 1/4. Write the equation in slope-intercept
form.
Answer: y = [tex]\frac{1}{4}[/tex]x - 3 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Slope-intercept form is in the form of y=mx + b where m is the slope and b is the y-intercept.
We are given the slope, so we will plug this in.
y = mx + b
y = ([tex]\frac{1}{4}[/tex])x + b
Now, we will solve for the y-intercept by plugging in the point they give us.
y = ([tex]\frac{1}{4}[/tex])x + b
(-2) = ([tex]\frac{1}{4}[/tex])(5) + b
-2 = 1.25 + b
-3 [tex]\frac{1}{4}[/tex] = b
Lastly, we will plug this variable into the equation we wrote above for our final answer.
y = [tex]\frac{1}{4}[/tex]x - 3 [tex]\frac{1}{4}[/tex]
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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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