Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope. A(3, 5), B(7, 6), C(6, 2), D(2, 1)
Answers
In the imaged attached, the most precise name for ABCD is known to be rhombus.
What is the shape about?Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.
Using the Diagonal midpoints of AC and BD, the equation will be:
(A+C)/2
(B+D)/2
To find if the midpoints are similar, then:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.
In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
So the lengths will be (3√2 vs 5√2).
Note also that the dot-product of these values need to be zero if they are perpendicular and as such:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.
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Related Questions
3.
The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.
Answers
Answer:
x = 5.00 cm
Step-by-step explanation:
• area of the rectangle = [tex]x[/tex] x [tex](x + 1)[/tex]
= [tex]x^2 + x[/tex]
• area of the circle = π r²
= [tex]\frac{22}{7}[/tex] x [tex](x + 2)^2[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4)[/tex]
∴ [tex]x^2 + x[/tex] + [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4) = 184[/tex]
⇒ [tex]x^2 + x[/tex] + [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]
⇒ [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]
• Using quadratic formula, where
a = [tex]\frac{29}{7}[/tex]
b = [tex]\frac{95}{7}[/tex]
c = [tex]\frac{-1200}{7}[/tex] ,
[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]
[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]
[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]
As length (x) cannot be a negative number,
x = 5.00 cm
I will give brainiest to the first person who responds BUT only if the answer is correct
Answers
Answer:
70 cm2??
Step-by-step explanation:
The area of the rectangle: 50 cm2
The area of the triangle: About 20 cm2
50 cm2 + 20 cm2 +
help pls i’ll do anything D:
Answers
Answer:
search it up ok that's all you can do
What are “like terms”? Why can we only add like terms?
13.)What is the closure property? What does it have to do with adding, subtracting, and multiplying polynomials?
Answers
Answer:
Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.
Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.
Step-by-step explanation:
Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".
Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.
What is closure property? That’s a good question. Closure property is a method and idea used in math that often emphasizes the explanation that the sum of two whole numbers will always result in a whole number (that is what it has to do with addition). In subtraction, closure property states that the difference between two rational numbers (pi excluded) will always result in a rational number. When multiplying polynomials, the rule is that, like subtraction, the multiplication of two rational numbers always will end in a rational number.
a fence is 2m high by 33m long, if a gallon of paint is enough to paint 2.5m^2, how many gallons will be used to paint the entire fence?
Answers
The number of gallons of paint needed to paint the entire fence is 26.4 gallons.
Area of rectangleLength = 33 mWidth = 2 mArea = length × width
= 33 m × 2 m
= 66 square meter.
A gallon of paint = 2.5 m²Number of gallons of paint needed = 66 square meter / 2.5 m²
= 26.4 gallons
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evaluate this equation
Answers
The correct answer is option B which is Sn = -111974.
What is geometric expansion?When there is a constant between the two successive numbers in the series then it is called a geometric series.
Here we have the following data:-
[tex]\sum_{n=1}^7-2.6^{n-1}[/tex]
[tex]a_n = a_1r^{n-1}\ \ \ \ \ S_n = a_1(\dfrac{1-r^n}{1-r})[/tex]
Here we need to calculate the first term second term and common ratio to calculate the sum of the series.
a₁ = -2.(6¹⁻¹) = -2
a₂ = -2.( 6²⁻¹) = -2 (6) =-12
Common ratio:-
[tex]a_n = a_1r^{n-1}[/tex]
[tex]-12 = -2r^{2-1}[/tex]
r = 6
Put all the values in the sum formula:-
[tex]S_n = -2(\dfrac{1-6^7}{1-6})[/tex]
[tex]S_n = -2(\dfrac{279935}{5})=-2\times 55987[/tex]
[tex]S_n[/tex] = -111974
Therefore the correct answer is option B which is Sn = -111974.
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consider an investment of $6000 that earns 4.5% interest.
How long would it take for the investment
to reach $15,000 if the interest is
compounded monthly? Round your
answer to the nearest tenth.
Answers
Answer:
20.4 years (nearest tenth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $15,000P = $6,000r = 4.5% = 0.045n = 12 (monthly)Substitute the given values into the formula and solve for t:
[tex]\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}[/tex]
[tex]\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf 2.5=\left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)[/tex]
[tex]\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}[/tex]
[tex]\implies \sf t=20.40017123[/tex]
Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.
How do i graph those
Answers
The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Plotting the graph using geogebra online graphing tool.
The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).
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Solve for x.
Enter your answer in the box.
x = ...°
(Please refer to attached image.)
Answers
Answer:
132
Step-by-step explanation:
6 angles plug in for n
(n-2)*180
4*180
720 degrees in all
subtract all other angles
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answers
Answer:
f(x) = -2x+1
Step-by-step explanation:
See attached image
The equation of line will be;
⇒ f (x) = - 1/2x + x
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 3) and (4, -1).
Now,
Since, The equation of line passes through the points (- 4, 3) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (3)) / (4 + 4)
m = - 4 / 8
m = - 1/2
Thus, The equation of line with slope - 1/2 is,
⇒ y - (3) = - 1/2 (x + 4)
⇒ y - 3 = - 1/2x - 2
⇒ y = - 1/2x + x
Therefore, The equation of line will be;
⇒ f (x) = - 1/2x + x
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A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length. Find the dimensions of the pen.
Answers
The length of the rectangle is 60 feet and the width of the rectangle is 45 feet.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L×W square units
A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length.
L = W + 15
Then we have
2700 = W(W + 15)
W² + 15W - 2700 = 0
W² + 60W - 45W - 2700 = 0
(W + 60)(W - 45) = 0
W = 45, -60
Then the dimension of the rectangle will be
W = 45 feet
L = W + 15
L = 45 + 15
L = 60 feet
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Jacob and his sister, jenny, share the job of cutting the grass in their yard. jacob cuts 2 of the yard, and jenny cuts the rest can cut 3/4 of an an entire tard of an hour
Answers
Answer:
okay
Step-by-step
no of yards they cut in an hour
Jacob = 2 yard
jenny 3/4 of a yard
no of yards it will take jenny to cut 3 yards = 4 hours
A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.
Two dot plots are shown one below the other. The title for the top dot plot is Online Customers and the title for the bottom plot is Walk In Customers. Below the line for each dot plot is written Number of Packs. There are markings from 1 to 5 on each line at intervals of one. For the top line there are 0, 0, 1, 4, 5 dots respectively for marks from 1 to 5. For the bottom line there are 3, 6, 1, 0, 0 dots respectively for marks from 1 to 5. On the right side, towards the middle of the two plots is shown a dot symbol equal to 10 customers.
Which inference can be drawn about the buying pattern of the online customers versus that of the walk-in customers?
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 1 pack.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 1 pack.
Answers
Answer:
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Step-by-step explanation:
Create the dot plots (see attached diagrams)
Online customers: blue dots
Walk-in customers: red dots
To calculate the average packs both groups of customers buy, sum all data values and divide by the total number of data values.
[tex]\textsf{Average of Online customers}=\dfrac{ 1 \times 3+ 4 \times 4+ 5\times 5}{10}=4.4[/tex]
[tex]\textsf{Average of Walk-in customers}=\dfrac{ 3 \times 1+ 6\times 2+ 1\times 3}{10}=1.8[/tex]
Online: 4.4 rounds down to 4
Walk-in: 1.8 rounds up to 2
Therefore, online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Find average of both customers
Online :-
3+4(4)+5(5)/103+16+25/1044/104.44Offline
3+6(2)+3/106+12/1018/101.82option C
If x is 300 percent of 25 and y is 25 percent more than
40, the x is what percent of y?
al 50%
c) 66.5%
b) 75%
d) 150%
Anyone here to help me!!!
Answers
Answer:
d) 150%
Step-by-step explanation:
[tex]x=25*300\%=25*3=75\\[/tex]
[tex]y=25\%*40+40=50[/tex]
[tex]x/y*100\%=75\div50*100\%=150\%[/tex]
Answer:d
150%
Step-by-step explanation:
does anyone know how to simplify this problem
Answers
Answer:
[tex]x^{-\frac{2}{7} }[/tex]
Step-by-step explanation:
→ Add the powers together
[tex]x^{\frac{3}{7} {-\frac{5}{7} }[/tex]
→ Simplify
[tex]x^{-\frac{2}{7} }[/tex]
Wilma is 5 times as old as yvonne. in ten years, yvonne's age will be a third of wilma's age. how old are they now?
Answers
Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Wilma's age.Variable y: Yvonne's age.Wilma is 5 times as old as yvonne, hence:
x = 5y.
In ten years, yvonne's age will be a third of wilma's age, hence:
[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]
Since x = 5y:
[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]
[tex]y + 10 = \frac{1}{3}(5y + 10)[/tex]
3y + 30 = 5y + 10
2y = 20.
y = 10.
Then:
x = 5y = 5 x 10 = 50.
Wilma is 50 years old and Yvonne is 10 years old.
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Sketch the graph of y = x^2+2x-15 using your graphing calculator. What are the x-intercepts of this graph?
Answers
The intercept is 3 and 5
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
To find x- intercept, y=0
x² + 2x -15=0
x² -5x + 3x -15=0
x(x-5) - 3(x-5) = 0
(x-5)(x-3)=0
Hence, the x- intercept is 3 and 5.
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In a 19 sided polygon what is the sum of the exterior angles ??
Answers
Answer:
the sum of all exterior angle is 360 degree
(a^3b^4/a^2b)^6=a^xb^y
Answers
Answer:x = 6 , y = 18
Step-by-step explanation:
What is the measure of angle AFR?
O 124 degrees
O 91 degrees
O 13 degrees
O 117 degrees
Answers
Answer:
13°Step-by-step explanation:
AFR = VFN (opposite angle rule)
7x + 33 = 9x + 7
33 - 7 = 9x - 7x
26 = 2x
x = 26 : 2
x = 13°
-----------------
check
7 * 13 + 33 = 9 * 13 + 7 (remember PEMDAS)
91 + 33 = 117 + 7
124 = 124
the answer is good
the tabel shows the time merrida spent driving and the number of miles she drove she drove the same number of miles each other
Answers
Answer:
35 miles/hour
Step-by-step explanation:
See attached image.
What is the sum of the polynomials?
(6x+7+x²)+(2x²-3)
1. -x² +6x+4
2. 3x²+6x+4
3. 9x + 4
4. gx²+4
Answers
Answer:
6x+4+3x²Step-by-step explanation:
Given polynomials:
(6x+7+x²)+(2x²-3)
Solution:
(6x+7+x²)+(2x²-3)Removing brackets,
6x+7+x²+2x²-3Collecting like terms,
6x+7-3+x²+2x²Simplifying ,
6x+4+3x²Done!
Hence option 3 is correct.
What is quadratic equation?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form: ax² + bx + c = 0.
The given expression is;
(6x+7+x²)+(2x²-3)
Now add the like term in the given expression,
⇒ x² + 2x² + 6x + 7 - 3
⇒ 3x² + 6x + 4
Hence,
The sum of polynomial is 3x² + 6x + 4.
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A TV's regular price is $349. It is on
clearance for 30% off, and a customer uses
a 15% off coupon after that. What is the
final cost of the TV before sales tax?
Answers
Answer:
rounded is $207.66
Step-by-step explanation:
you start by doing 349(0.30) which would be 104.7
349-104.7=244.3
next you do 244.3(.15)=36.645
244.3-36.645= $207.655
2. On the snow day, 8 kids from the neighbor-
hood gathered to build snowmen. The kids
used two buttons as the eyes on each snowman.
7 more kids joined to make snowmen and used
buttons for the eyes, too. How many buttons
were used to make the snowmen?
Answers
Answer: 30 buttons
Step-by-step explanation:
If there were 8 kids, and 7 more joined, then there were 15 kids making snowmen (8+7 = 15). Each child used 2 buttons for the eyes, so 30 buttons were used (15 x2 = 30). This is assuming no other buttons were used on the snowmen for anything else
Get a similar question You can retry this question below
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 35 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Find the Largest angle:
Answers
Sum of triangle angles = 180
smallest angle = x
second angle = 3x
third angle = x +35
180 = x + 3x + x + 35
145 = 5x
x = 29 is the smallest
the second is 87
the third is 64
Fully simplify.
15x(4)y(4)(-5x³y(5))
Answers
Step-by-step explanation:
please mark me as brainlest
An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support. How many villages does the organization support worldwide?
Answers
If organisation supports 125 villages financially and it is 11% of world wide then the total villages in world wide that needs help is 1136.36 villages.
Given An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support.
If 125 villages are 11% of worldwide villages who need help financially then we have to find 100% value according to organisation figure which can be calculated as under:
if 125 is 11% then 1% will be 125/11
then 100% will be 125/11*100
=12500/11
=1136.36
=1136 Approx
Hence 1136 villages are totally present worldwide which need help financially.
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What is the solution to x^3+ 4x^2>X+4?
04
O4
O4 < x < -1 or x> 1
Ox<-4 or-1
Thank yoooou!
Answers
The solution of the inequality x³ + 4x² > x + 4 will be -4 < x < -1 or x > 1. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
x³ + 4x² > x + 4
Then the inequality can be written as
x³ + 4x² – x – 4 > 0
Then the factor will be
x²(x + 4) – 1(x + 4) > 0
(x² – 1)(x + 4) > 0
(x – 1)(x + 1)(x + 4) > 0
Then the solution will be
x – 1 > 0
x > 1
x + 1 < 0
x < -1
x + 4 > 0
x > -4
Then the correct option is C.
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simplify algebraic equation x^2-4/x^2+2x
Answers
Answer:
Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
Step-by-step explanation:
Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.
The given algebraic equation is [tex]x^{2} -\frac{4}{x^{2} } +2x[/tex]
now for simplifying it
First of all take L.C.M of [tex]x^{2}[/tex]
= [tex]\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }[/tex]
We get [tex]\frac{x^{2} -4+2x^{3}}{x^{2} }[/tex]
Further we can write it as [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
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Simplify the exponential expression 48 ^1/2
O 2 (24^1/2)
O 3 (16^1/2)
O 4 (3^1/2)
O 16 (3^1/2)
Answers
Step-by-step explanation:
Hi There! Let me help you :)
To answer this question, we have to know about the way to simplify it. First, you find the factor of 48.
[tex] = {48}^{ \frac{1}{2} } [/tex]
[tex] = {(16 \times 3)}^{ \frac{1}{2} } [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] \: [/tex]
—Use the general formula of the exponential, where a^m/n = ^n√a^m.
[tex] \: [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] = \sqrt[2]{16} \times {3}^{ \frac{1}{2} } [/tex]
[tex] = 4 \times {3}^{ \frac{1}{2} } [/tex]
The answer is C.
