Find the exact lengths of the sides of quadrilateral ABCD with vertice
A(4, 5), B(-3, 3), C(-6, -13) and D(6, - 2).
Answer:
[tex]AB=\sqrt{53}[/tex]
[tex]BC=\sqrt{265}[/tex]
[tex]CD=\sqrt{265}[/tex]
[tex]DA=\sqrt{53}[/tex]
ABCD is a kite.
Step-by-step explanation:
Given vertices of quadrilateral ABCD:
A = (4, 5)B = (-3, 3)C = (-6, -13)D = (6, -2)To find the exact lengths of the sides of the quadrilateral, use the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-4)^2+(3-5)^2}\\&=\sqrt{(-7)^2+(-2)^2}\\&=\sqrt{49+4}\\&=\sqrt{53}\\\end{aligned}[/tex]
[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-6-(-3))^2+(-13-3)^2}\\&=\sqrt{(-3)^2+(-16)^2}\\&=\sqrt{9+256}\\&=\sqrt{265}\\\end{aligned}[/tex]
[tex]\begin{aligned}CD&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(6-(-6))^2+(-2-(-13))^2}\\&=\sqrt{(12)^2+(11)^2}\\&=\sqrt{144+121}\\&=\sqrt{265}\\\end{aligned}[/tex]
[tex]\begin{aligned}DA&=\sqrt{(x_A-x_D)^2+(y_A-y_D)^2}\\&=\sqrt{(4-6)^2+(5-(-2))^2}\\&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\\\end{aligned}[/tex]
A kite has two pairs of adjacent equal sides.
Therefore, quadrilateral ABCD is a kite as:
AB is adjacent to DA and AB = DA.BC is adjacent to CD and BC = CD.Ginger borrowed $850 to purchase software and a camera. The simple interest rate is 8% per year. How much will she save if she pays off the loan in two and a half years instead of three years?
The amount of money she will save if she pays off the loan in two and a half years instead of three years would be = $34
What is interest rate?Interest rate is the amount of money an individual receives in addition to the main amount of money that was invested or borrowed out after certain period of time.
The amount of money Ginger borrowed(p) = $850
The simple interest rate (r)= 8%
The time to pay off the loan(t) = 2.5 year
simple interest generated
= p×t×r/100
= 850×2.5×8 /100
= 17000/100
= $170
If she paid off in 3 years the simple interest would be
= 850×3×8/100
=20400/100
= $204
Therefore she would have save a total of = 204-170 = $34
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A submarine starts at 0 units and has groups of 3 floats and groups of 4 anchors attached. Which expression would make the submarine sink the lowest?
A : -(5)(3)+(2)(-4)
B :(5)(3)-(2)(-4)
C: -(5)(3)-(2)(-4)
D: (2)(3)+(5)(-4)
E: -(2)(3)-(5)(-4)
(Select all that apply)
The expression that would make the submarine sink the lowest will be A. -(5)(3)+(2)(-4)
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, the expression that would make the submarine sink the lowest will be:
: -(5)(3)+(2)(-4)
= -15 - 8
= -23
This is the value with the lowest point.
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DUE SOON! PLEASE HELP EXPLAIN THIS!! QUESTION DOWN BELOW!!!!!
Answer:
D) 4.45 m by 6.82 m
Step-by-step explanation:
The given dimensions of the floor plan are 4.9 cm by 7.5 cm.
Given scale factor = 0.011
⇒ 0.011 m = (0.011 × 100) cm = 1.1 cm
Therefore, every 1.1 cm on the plan equals 1 m in the actual room.
To find the dimensions of the actual room in meters, divide the floor plan dimensions by 1.1:
⇒ 4.9 ÷ 1.1 = 4.45 m (2 d.p.)
⇒ 7.5 ÷ 1.1 = 6.82 m (2 d.p.)
Complete the statements below about the area of the red rectangle.
Each red block has area of [tex]\frac{7}{12}[/tex] square unit.
The area of the red rectangle is = [tex]\frac{7}{8}[/tex]× [tex]\frac{2}{3}[/tex] = [tex]\frac{7\times 2}{8\times 3}[/tex] = [tex]\frac{7}{12}[/tex] square unit.
What is area of rectangle?
The area of a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Here the given rectangle measures are,
Length of the rectangle = [tex]\frac{7}{8}[/tex]
Breadth of the rectangle = [tex]\frac{2}{3}[/tex]
Now area of the rectangle = length × breadth
=> A = lb
=> A= [tex]\frac{7}{8}[/tex]× [tex]\frac{2}{3}[/tex] = [tex]\frac{7\times 2}{8\times 3}[/tex] = [tex]\frac{7}{12}[/tex] square unit.
Hence each red block has area of [tex]\frac{7}{12}[/tex] square unit.
The area of the red rectangle is = [tex]\frac{7}{8}[/tex]× [tex]\frac{2}{3}[/tex] = [tex]\frac{7\times 2}{8\times 3}[/tex] = [tex]\frac{7}{12}[/tex] square unit.
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Determine whether the graph represents a proportional relationship. (4 points)
Number of Wheels
15
14
13
12
11
10
2987654321
→
1-
1 2 3 4 5 6 7 8 9 X
Number of Cars
Yes, it is a proportional relationship because the graph is a straight line
No, it is not a proportional relationship because the graph does not go through the origin
OYes, it is a proportional relationship because the graph goes through the origin
No, it is not a proportional relationship because the graph is not a straight line
Set A 9, 10, 12
Set B 1, 9, 12
What is the union of sets A and B?
Union of set A and B is {1, 9, 10, 12}
What is Set ?A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
The components from both sets A and B, or both sets together, make up the union of the two sets A and B. It is represented by the letter "U." For instance, if set A = 1, 2, 3, and set B = 4, 5, then A U B = 1, 2, 3, and 4, respectively. A U B is pronounced "A union B."
The set that contains every element of the supplied sets is the union of two or more sets. The symbol "U" can be used to represent a union of sets. Assume that X U Y may be used to represent the union of two sets, X and Y.
Set A = {9, 10, 12}
Set B = {1, 9, 12}
Union of set A and B is {1, 9, 10, 12}
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The GDP of Florida¹ is 1059 billion dollars with a growth rate² of 2.9%. Write an equation that can be used to
estimate the size of Florida's economy in a future year, assuming the same relative yearly growth rate. Let g
be the state's GDP in billions of dollars in t years from now.
a. The equation is:
b. The equation is in the Select an answer
family
c. Use the equation to determine Florida's GDP in 8 years from now? Round to the nearest billion dollars.
billions
The value added produced through the production of products and services in a nation over a specific time period is typically measured by its gross domestic product (GDP).
What GDP means?The value added produced through the production of products and services in a nation over a specific time period is typically measured by its gross domestic product (GDP). As a result, it also accounts for the money made from that manufacturing, or the total amount spent on finished goods and services (less imports).
GDP is calculated as private consumption plus gross domestic product (GDP), government investment, and government spending (exports – imports). Usually, GDP is estimated using the international standard by the nation's national statistical agency.
The average annual growth rate (AAGR) is the average rise or fall in the value of an investment asset, portfolio, or cash flow over a given time frame. By averaging out the provided year-over-year growth rates, the AAGR is calculated.
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Find the area and perimeter of rectangle IJKL.
(GIVE EXPLANATION)
Given rectangle IJKL
From the diagram we can write the length os sides
IJ=4
JL=[tex]\sqrt{20}[/tex]
From the fundamental properties of rectangle
We can say each interior angle is 90°
Consider the above property we can say IJL is an right angle triangle
From the Pythagoras
The square of hypotenous side is equal to the sum of squares of the other two sides.
A²=B²+C²
JL²=LI² + JI²
[tex]( \sqrt{20} )^{2}=4^{2}+LI^{2}[/tex]
LI²=20-16
LI²=4
LI=√4
LI=2
Therefore ,we have two sides JI(length) =4 and LI(breadth) =2
Formula for Perimeter of the rectangle=2(length + breadth)
Perimeter of the rectangle =2(4+2)
Perimeter of the rectangle=2(6)
Therefore,Perimeter of the rectangle = 12 units
Formula for area of rectangle=length*breadth
Area of rectangle=4*2
Therefore,Area of rectangle=8 square units.
Select the graph of the solution. Click until the correct graph appears. |x| + 1 < 3
The solution to the given inequality is x<2. Therefore, option C is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is |x|+1<3.
Here, subtract 1 on both the sides of an inequality, we get
x<2
Therefore, option C is the correct answer.
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Find the slope of the line that passes through (2, 11) and (4, 6).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Between the points (9, 5) and (5, 4), the supplied line must have a 1/4 slope.
Which direction does the line slope in?A line's tangent angle to the horizontal creates the slope of the line. Specifically, m = tanx, with x in degrees.
The line that intersects (9, 5) and (5, 4).
Given as m = (y2 - y1) / (x2 - x1), the slope of the line.
Replacing the tenth (9,5) and (5, 4).
As seen in the equation above, m = 1 / 4 m = 4 - 5 / 5 - 9
The needed slope of the provided line, which goes through the points (9, 5) and (5, 4), is therefore 1/4.
Between the points (9, 5) and (5, 4), the supplied line must have a 1/4 slope.
The complete question is,
Calculate the slope of the line that goes through (9, 5) and (5, 4).
Write your response as an integer, a correct fraction, or both to make it as simple as possible.
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Sketch, on a single diagram showing values of x from-180° to +180°, the graphs of
y = tan x and y = 4 cos x.
The equation
tan x = 4 cos x
has two roots in the interval-180° ≤x≤ 180°. These are denoted by a and ß, where a
Show a and ß on your sketch, and express ß in terms of a.
Show that the equation tan x = 4 cos x may be written as
Hence find the value of ß-a, correct to the nearest degree.
4 sin’x+ sinx−4=0,
The equation tan x = 4 cos x may be written as the nearest degree 4sinx^2 + sinx -4 = 0
What is Quadratic equation ?
Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .
Given ,
values of x from-180° to +180°, the graphs of
y = tan x and y = 4 cos x.
from this we get ,
y = tanx
y = 4cosx
tanx = 4cosx
cos^2 x = sinx
The equation
tan x = 4 cos x
has two roots in the interval -180° ≤x≤ 180°
And the given equation ,
4sinx^2 + sinx -4 = 0
Hence, The equation tanx = 4cosx .
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center at origin, circle passes through (-2, -3)
The equation of a circle passing through the point (- 2, - 3) is -
(x)² + (y)² = 13.
What is the general equation of a circle?The general equation of a circle is -
(x - h)² + (y - k)² = r²
where (h, k) is the center and (r) is the radius.
Given is a that circle passes through (-2, -3).
For the center at origin, we can write -
(x)² + (y)² = r²
(x)² + (y)² = (- 3 - 0)² + (- 2 - 0)²
(x)² + (y)² = 9 + 4
(x)² + (y)² = 13
Therefore, the equation of a circle passing through the point (- 2, - 3) is -
(x)² + (y)² = 13.
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Find the rate of change from the table
6x + 7y = 4x + 4y
Complete the missing value in the solution to the equation
(6, -4) is the missing value in the solution to the equation.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that the value of y = -4 and find the value of x
6x+7y=4x+4y
6x - 4x = 4y -7y
2x = -3y
Putting the value of y in the above equation.
2x = -3y
2x = -3(-4)
2x = 12
x = 6
Therefore, the Missing value in the solution to the equation is (6,-4).
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Complete question:
6x + 7y = 4x + 4y
Complete the missing value in the solution to the equation.
(__,-4)
Which ordered pair is on the inverse of f(x)?
(–4, –2)
(–2, –2)
(–1, –2)
The range of the inverse of f(x) is
.
Answer:
(-1,-2)
because the inverse of (-4,-2) is (-2,-4) so when we simplify both number or when we divide by both numbers by 2 we get (-1,-2)
so the inverse of f(x) _ (-4,-2) is (-1,-2)
QUESTION DOWN BELOW!
ITS DUE SOON PLEASE HELP EXPLAIN THIS!!
A machinist made a gear 101 inches in diameter with 54 teeth using this same ratio how many teeth will be on a gear with a 7 inch diameter
Therefore , the solution of the given problem of ratio comes out to be
x= 3.74 teeth in another gear.
A ratio is defined.The simple formula "a / b" can be used to define an equality pair of integers "a" and "b," where "b" cannot be greater than zero. Two ratios are combined to form a ratio. If there were only one man with three women, the ratio might be represented as 1:3. The group is made up of 3/4 girls and 1/4 guys. A split between two or more objects, a statistic, or a piece of a part's volume are all examples of parts.
Here,
Given :
A 101-inch-diameter gear with 54 teeth was created by a machinist.
Therefore, another gear's diameter is 7 inches.
To find the teeth of other gear let it be x :
=> 101/54 = 7/x
=> x = 7*54 /101
=> x= 3.74
Therefore , the solution of the given problem of ratio comes out to be
x= 3.74 teeth in another gear.
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Sal cuts a piece of yarn into 3 equal lengths. He cuts 5 inches off one piece leaving 4 inches. What was the length of the yarn
Find a positive angle that is coterminal to 1,028 that is between 0 and 360
The value of the co-terminal angle in the range [ 0 , 360° ] is 308° , located in the fourth quadrant
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
In the first quadrant, sin, cos and tan are all positive.
In the second quadrant going anti-clockwise, only sin is positive.
In the third quadrant going anti-clockwise, only tan is positive.
In the fourth quadrant going anti-clockwise, only cos is positive
Given data ,
Let the co-terminal angle be represented as A
Now , it is the angle that share the terminal side of an angle occupying the standard position
Positive co-terminal angles: 308°, 668°, 1028°, 1388°, 1748°
Negative co-terminal angles: -52°, -412°, -772°, -1132°
Now , the trigonometric relations in the fourth quadrant going anti-clockwise, only cos is positive
Hence , the positive angle in the co-terminal angle is 308°
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Find the exact lengths of the sides of quadrilateral ABCD with vertices A(4, 5), B( − 3, 3), C( – 6,- 13) and
D(6,-2).
Answer:
AB = 7.28
AD = 7.28
BC = 16.28
DC = 16.28
Hope this helps!
Step-by-step explanation:
how do you slove this
in the pic
The approximate values for the given expressions, will be 240, 250, 220 and 270
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Given are some expressions, we need to solve them by adding or subtracting, and then approximate the results,
1) 349.6 - 112.8 = 236.8 ≈ 240
2) 173.3 + 78.4 = 251.7 ≈ 250
3) 817.2 - 597.1 = 220.1 ≈ 220
4) 108.8 + 159.3 = 268.1 ≈ 270
Hence, the correct values will be 240, 250, 220 and 270
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PLSS HELPEPAngel is using a spool of ribbon to make gift wrap bows. The spool contains 8 1/6 yards of ribbon. If Angel uses the entire spool to make 7 identical bows, how much ribbon, in yards, would be used for each bow? Write your answer in simplest form.
Answer:
5/6 yards
Step-by-step explanation:
7/6 yards of ribbon would be used to make the 7 identical bows.
To find out how much ribbon is used for each bow, we need to divide the total amount of ribbon on the spool by the number of bows.
To divide 8 1/6 by 7, we can convert the mixed number to an improper fraction first:
8 1/6 = (8 x 6 + 1) / 6 = 49/6
Now we can divide:
49/6 ÷ 7 = 7/6
So each bow would use 7/6 of a yard of ribbon. To write this in simplest form, we divide both the numerator and denominator by their greatest common factor. In this case, it is 1.
Therefore, 7/6 is the simplest form.
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I really need help on this one pleaseee:)
Answer:482
Step-by-step explanation:
Select the correct statement in the table. Brittany is knitting a rectangular blanket. She plans on having a border made from an expensive type of yarn so she needs the perimeter of the blanket to be no more than 200 inches. Brittany also needs the length of the blanket to be at least 12 inches more than the width. Construct a system, where x is the blanket's width and y is the blanket's length, that models the situation. Use the system to test the following situations and determine which is true. (31,43) is not a viable solution because it does not meet the length constraint. (29,71) is not a viable solution because it does not meet the perimeter constraint. (44,56) is not a viable solution because it does not meet either constraint. (56,78) is not a viable solution because it does not meet the length constraint. (35,70) is not a viable solution because it does not meet the perimeter constraint. (60,40) is not a viable solution because it does not meet either constraint.
The length and breadth for the rectangular yarn will be length(y)=56 inch and breadth(x)=44 inch.
What is a rectangle?
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.
Perimeter of a Rectangle:-
The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of perimeter is given by:
Perimeter, P = 2 (Length + Width)
Now,
As Perimeter {2(x + y)} = 200inch
and y-x=12inch
Hence,
x + y =100
y-x=12
adding both equations we get
y=56 inch and x=44inch
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HELLLPPPPPPPP!!!!!! 20 POINTSSSSSS!!! AND BRAINLIEST!!!!!!!!!
Write one multiplication equation and one division equation that are equivalent to 24/6 = 4 .
Answer:
4 x 6 = 24 six times four is twenty four
division one is 24 divided by 4 is 6
HELPPPPP
Question: The table and the graph each show equivalent ratios.Use the drop-down menus to explain how the ratio shown in the table compares to the ratio shown on the graph.
x
8
10
12
y
12
15
18
Ratio in graph is 1.5, So constant ratios are shown in both.
How may equivalent ratios be displayed in a table?Making a Table of Equivalent Ratios: Steps
Find the ratio given in the issue in step one.
Step 2: Add or subtract the same amount from both sides of the ratio to get equal ratios.
Repeat Step 2 to add equivalent ratios to the table in Step 3.
In table we have the ratios.
In table we have (8, 12),(10,15), (12,18)
in graph have (3,2), (6,4)
Ratio in table & 5/12 = 10 /15 =12 / 18 = 0.667
Ratio in graph = 3/2 = 6/4=1.5
So constant ratios are shown in both.
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Mick's zoo offers a promotional deal: get a free $3 cotton candy and a free
$2 soda with the purchase of five $12 admission tickets. A group of 20
students will each purchase a ticket. If half of them want cotton candy and
1/4 of them want soda, how many dollars would they save by using the
promotional deal?
(pleaseeee explain, last time I only got the answer) ✋
Answer:
A group of 20 students will purchase 205 = 100 admission tickets
Half of them want cotton candy, so 20/2 = 10 students want cotton candy
1/4 of them want soda, so 20/4 = 5 students want soda
So in total, they would save 103 = $30 on cotton candy
And they would save 5*2 = $10 on soda
Therefore, they would save a total of $30 + $10 = $40 by using the promotional deal.
Find the product of polynomials (First Screenshot)
Problem 1.5 (Second Screenshot)
Polynomials have the following product: 3x5 + 2x4 + 5x3 + 2x2 - 32x + 14. An algebraic formula with variables is called a polynomial.
what is polynomials ?A polynomial is a mathematical expression consisting exclusively of additions, subtractions, multiplications, and positive integer powers of variables. It is an expression of coefficients and uncertainty. x2 4x + 7 represents a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic formula that includes variables and coefficients. Addition, subtraction, multiplication, and non-negative integer exponents are the only operations that can be included in an expression. This type of statement is known as a polynomial.
given
Multiply each combination of terms:
Combine like terms.
3x^5 + 2x^4 + (-7x^3 + 12x^3) + (8x^2 - 6x^2 ) + (-28x - 4x) +14=
3x^5 + 2x^4 + 5x^3 + 2x^2 - 32x + 14.
Polynomials have the following product: 3x5 + 2x4 + 5x3 + 2x2 - 32x + 14. An algebraic formula with variables is called a polynomial.
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Mateo made a cylindrical plant stand out of a block of wood. The plant stand has the measurements shown.
Mateo wants to paint all sides of the plant stand with a waterproof sealer. What is the approximate surface area, using 3.14 for m? Use the formula for surface area of a cylinder, А = 2πr² + 2πrh. PLLEASER HELP ME
r= radius. 5in. h= height. 12 in
The surface area of the plant stand will be 533.8 square inches.
The formula for the surface area of a cylinder is A = 2πr² + 2πrh,
where r is the radius and h is the height of the cylinder.
To find the surface area of the plant stand, we can plug in the given values for r and h:
A = 2π(5²) + 2π(5)(12)
A = 2π(25) + 2π(60)
A = 50π + 120π
A = 170π
We can approximate π as 3.14
A ≈ 170 × 3.14 = 533.8 square inches
Thus, the surface area is 533.8 square inches.
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