Answer:
The given quadrilateral is a rectangle.
Step-by-step explanation:
We are given the vertices of a quadrilateral,
We can use the slopes and modulus of all sides to determine whether it is a rectangle or not. The four sides of the quadrilateral are Ab, BC, CD and AD. So finding slopes of all sides using the formula
[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where x_1 and y_1 are the coordinates of firsst vertex and x_2 and y_2 are coordinates of second vertex.
So.
Slopes are:
Slope of AB = 2 and Length=2.23
Slope of BC = -1/2 and length = 4.47
Slope of CD = 2 and length = 2.23
Slope of AD = -1/2 and length = 4.47
As we can see that the slope of AB and CD is equal which means that they are parallel and their lengths are also same.
Similarly BC and AD have same slope which means that they are also parallel and their lengths are also equal.
More over the product of slopes of AB and CD, BC and CD, CD and AD and AD and AB is equal to -1 which indicated that these sides are parallel to each other so it can be concluded that as the opposite sides of the quadrilateral are equal and the interior angles are 90 degrees so the quadrilateral is a rectangle ..
Answer:
I am given that the vertices of quadrilateral ABCD are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). The slope formula applied to each pair of adjacent vertices gives the slopes (m) of the sides:
slope of AB (m AB) = 4 - 6 / -2 - -1) = -2 / -1 =2
slope of BC (m BC) = 2 - 4 / 2 - (-2) = -2 / 4 = - 1 / 2
slope of CD (m CD) = 4 - 2 / 3 -2 = 2 / 1 = 2
slope of DA (m DA) = 6 - 4 / - 1 -3 = 2 / - 4 = - 1 / 2
Because line segments with equal slopes are parallel, segment AB is parallel to segment CD and segment BC is parallel to segment DA.
Multiplying the slopes of one pair of adjacent sides, I find that.
mAB * mBC = 2 * - 1/2 = - 1
If the product of the slopes of two segments is -1, then they are perpendicular. Since both pairs of opposite sides have been proven parallel, proving one pair of adjacent sides perpendicular implies that the other pair of adjacent sides are also perpendicular. Therefore, by definition, quadrilateral ABCD is a rectangle.
Step-by-step explanation:
When given a function and the point at which it is discontinuous, how do you classify the discontinuity as jump, removable, or asymptotic?
Answer:
Jump discontinuities - No defined limit; the left-handed and right-handed limits will be different, converging at two different finite values
Removable - The limit at this point is defined; the left and right-hand limits both converge on the same value
Asymptotic - The left-and-right-handed limits at this point will either tend to ∞ or -∞
Please Help Me With This Problem
Answer:
[tex]Area=1,325\ yd^2\\Perimeter=204\ yd[/tex]
Step-by-step explanation:
You can use the following formula to calculate the area of the triangle:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
You can observe in the figure that:
[tex]b=53\ yd\\h=50\ yd[/tex]
Then, the area is:
[tex]A=\frac{(53\ yd)(50\ yd)}{2}=1,325\ yd^2[/tex]
To find the perimeter you must add the lenght of each side of the triangle. Then, this is:
[tex]P=97\ yd+53\ yd+54\ yd\\\\P=204\ yd[/tex]
Sheila bought a new computer for $2000 and has agreed to finance it at 12% interest, with $100 payments each month. When she makes her first payment next month, how much will she pay for interest alone?
Answer:
rate per month = .01 agreed = r
Luckily they only ask for the first month so it is 0.01 * 20 .
Later months get more complicated and it is like paying off a mortgage with the term unknown but the rate and payment known.
Payment = principal value [ r / {1-(1+r)^-n } ]
100 = 2000 [ .01 / {1 - (1.01)^-n } ]
5 = 1/ {1 - (1.01)^-n }
.2 = 1 - (1.01)^-n
.8 = 1.01^-n
log .8 = -n log 1.01
n = 22.4 months :)
so over the almost two years pay 2240 total :)
* Hopefully this helps:) Mark me the brainliest:)!!!
Final answer:
For Sheila's first payment on her new computer financed at 12% annual interest with $100 monthly payments, she will pay $20 towards interest and the remaining $80 will go towards the principal.
Explanation:
Sheila bought a new computer for $2000 and agreed to finance it at 12% annual interest, with $100 monthly payments. To calculate the interest she will pay with the first payment, we need to find 1% of $2000 (since 12% per year is equivalent to 1% per month).
(1% of $2000) = 0.01 * $2000 = $20
Therefore, when Sheila makes her first monthly payment of $100, $20 will go towards interest, and the remaining $80 will reduce the principal on her loan.
What is the value of X in the equation 2x+3y=36, when y=6?
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Find the radius of a sphere with a surface area of 64(pie) sq.m. Round your answer to the nearest whole number.
a.
8 m
c.
16 m
b.
2 m
d.
4 m
[tex]\bf \textit{area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=64\pi \end{cases}\implies 64\pi =4\pi r^2 \\\\\\ \cfrac{64\pi }{4\pi }=r^2\implies 16=r^2\implies \sqrt{16}=r\implies 4=r[/tex]
The radius of the sphere will be 4 meters. Thus, the correct option is D.
What is the surface area of the sphere?Let r be the radius of the sphere. Then the surface area of the sphere will be given as,
SA = 4πr² square units
The surface area of the sphere is 64π square meters. Then the radius of the sphere is calculated as,
64π = 4 x π x r²
r² = 16
r = 4 meters
Thus, the correct option is D.
More about the surface area of the sphere link is given below.
https://brainly.com/question/29251585
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If the dot product of two nonzero vectors v1 and v2 is nonzero, what does this tell us?
A) v1 is not perpendicular to v2
B) v1 is a scalar
C) v1 is parallel to v2
D) v1 is perpendicular to v2
ANSWER
A) v1 is not perpendicular to v2
EXPLANATION
Two non-zero vectors are orthogonal or perpendicular if their dot product is zero.
In other words,if two non-zero vectors are not orthogonal or perpendicular then their dot product is not equal to zero.
From the question v1 and v2 are non-zero vectors and their dot product is not equal to zero.
This tells us that, the two vectors are not perpendicular.
The correct choice is A.
Answer:
A) v1 is not perpendicular to v2
Step-by-step explanation:
This proves that the test for orthogonality fails (doesn’t equal zero) meaning that V1 is not perpendicular to V2.
leon is installing a fence around a rectangular vegetable garden with a perimeter of 60 feet. the garden is 12 feet wide. how long is the garden?
The wide side of the garden is 12 feet, so the other side would be 12 feet aswell.
12+12=24
To find the length of each long side, you subtract 60-12, then divide by 2.
60-12=48/2=24
what is 30% of 70. show your work
Answer: 21
Step-by-step explanation:
we have two simple equations:
1) 70=100%
2) x=30%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
70/x=100%/30%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 30% of 70
70/x=100/30
(70/x)*x=(100/30)*x - we multiply both sides of the equation by
70=3.33333333333*x - we divide both sides of the equation by (3.33333333333) to get x
70/3.33333333333=x
The fore, the answer is 21
Answer:
21
Step-by-step explanation:
30% of some quantity is equivalent to 0.30 times that quantity.
In this case, 30% of 70 is 0.30(70) = 21.
A group of men and women were given a maze puzzle
Sooo whats the question
Solve for x. show your work
6/9 = x+2/24
Simplify 6/9 to 2/3
2/3 = x + 2/24
Simplify 2/24 to 1/12
2/3 = x + 1/12
Subtract 1/12 from both sides
2/3 - 1/12 = x
Simplify 2/3 - 1/12 to 7/12
7/12 = x
Switch sides
x = 7/12
Find the value of x in the solution to the system of equations shown.
Answer:
x=3
Step-by-step explanation:
i just did it on ttm
the y=14x-6
y=-4x=48
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
(HELP ASAP PLEASE)
Zoe often orders party trays from her favorite Mexican food restaurant for company events. For a recent company party, she spent $239 on 4 burrito platters and 5 taco platters. For a company meeting, she spent $208 on 3 burrito platters and 5 taco platters. How much does each type of platter cost?
Each burrito platter costs $___ and each taco platter costs $___ .
Answer:
Each burrito platter costs $_31__ and each taco platter costs $_23__ .
Step-by-step explanation:
Let the cost of a burrito platter be x and the cost of a taco platter be y;
4 burrito platters and 5 taco platters would cost;
4x + 5y = 239
3 burrito platters and 5 taco platters would cost;
3x + 5y = 208
We can solve the two equations simultaneously via elimination method. We subtract the two equations in order to eliminate y and solve for x;
4x - 3x = 239 - 208
x = 31
Using the first equation, substitute x = 31 and solve for y;
4(31) + 5y = 239
124 + 5y = 239
5y = 115
y = 23
Someone help PLEASE
Answer:
Q4. (-7)Q5. (-8)Step-by-step explanation:
The perfect square:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Q4
We have
[tex]y^2+14y+49=0\\\\y^2+2(y)(7)+7^2=0\\\\(y+7)^2=0\iff y+7=0\qquad\text{subtract 7 from both sides}\\\\\boxed{y=-7}[/tex]
Q5
We have
[tex]y^2+16y+64=0\\\\y^2+2(y)(8)+8^2=0\\\\(y+8)^2=0\iff y+8=0\qquad\text{subtract 8 from both sides}\\\\\boxed{y=-8}[/tex]
If f(x)= x^2-2x and g(x)= 6x+4 for which value of x does (f+g)(x)=0
Answer:
x = - 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4 ← equating to 0
x² + 4x + 4 = 0 ← in standard form
(x + 2)² = 0 ← in factored form, thus
x + 2 = 0 ⇒ x = - 2
Rhombus LMNO is shown with its diagonals.
Angle MNO measures 112°. What is the measure of angle LMN?
34°
45°
56°
68°
Answer:
The measure of angle LMN is 68° ⇒ the last answer
Step-by-step explanation:
* Lets revise the properties of the rhombus
- The rhombus has 4 equal sides in length
- Every two opposite angles are equal in measure
- Every two adjacent angles are supplementary (their sum = 180°)
- The two diagonals bisect each other
- The two diagonals perpendicular to each other
- The two diagonals bisect the vertices angles
* Lets solve the problem
∵ LMNO is a rhombus
∴ ∠LMN and ∠MNO are adjacent angles
∴ ∠LMN and ∠MNO are supplementary
∴ m∠LMN + ∠MNO = 180°
∵ m∠MNO = 112°
∴ m∠LMN + 112° = 180° ⇒ subtract 112 from both sides
∴ m∠LMN = 68°
* The measure of angle LMN is 68°
Answer:
68
Step-by-step explanation:
HELP!!!! Which of the following is a counterexample that proves the conditional statement false?
If a number is divisible by four, then it is divisible by eight.
12
16
24
48
Answer:
12 I think........?....
Answer:
The answer is 12
Step-by-step explanation:
In this case, we just have to try with all of them:
12/4=312/8=1,5Then it is not divisible (it is not integer). This proves the statement false.
Let's try with the others as well, just to check:
16/4=416/8=224/4=624/8=348/4=1248/8=6All the others don't prove false that statement.
need help asap choose all answers that apply
Hello There!
None of them would be the correct answer
Have a great day!
If f(x) = x+7 and g(x) = x=13, what is the domain of (fºg)(x)?
Answer:
The domain is {x I x ≠ 13} ⇒ the last answer
Step-by-step explanation:
* Lets talk about the composite function
- It is a function is found from two given functions by applying one
function into the second function.
- The applying function is the domain of the second function
- (f °g)(x) means g(x) is applying into f(x)
* Lets solve the problem
∵ f(x) = x + 7
∵ g(x) = 1/(x -13)
- To apply g(x) into f(x) replace x in f(x) by g(x)
∴ f(g(x)) = f(1/(x - 13)) = 1/(x - 13) + 7
- The domain of the function is all values of x which make the function
defined
- The domain is all real numbers except the value which makes
the denominator = 0
- To find this value put the denominator = 0
∵ The nominator of (f ° g)(x) is x - 13
∴ Put x - 13 = 0
∴ x - 13 = 0 ⇒ add 13 to both sides
∴ x = 13
∴ The domain of (f ° g)(x) is all real numbers except x = 13
* The domain is {x I x ≠ 13}
show me how to do this
Answer:
x = 7 cmStep-by-step explanation:
The perimeter of the given triangle:
P = (2x + 1) + (x + 2) + (3x - 9) and P = 36 cm.
Therefore we have the equation:
2x + 1 + x + 2 + 3x - 9 = 36 combine like terms
(2x + x + 3x) + (1 + 2 - 9) = 36
6x - 6 = 36 add 6 to both sides
6x = 42 divide both sides by 6
x = 7
If a function f(x) is defined as (4x)/(1-x), what is the expression for f(x + h)
ANSWER
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h}[/tex]
EXPLANATION
The given expression is
[tex]f(x) = \frac{4x}{1 - x} [/tex]
To find an expression for f(x+h), we substitute x+h, wherever we see x in the given expression.
This implies that,
[tex]f(x + h) = \frac{4(x + h)}{1 - (x + h)} [/tex]
We simplify to obtain;
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h} [/tex]
Answer:
A
Step-by-step explanation:
(4x+4h)/(1-x-h)
Which of the following digits could replace the □ in the thousands place to make this statement true?39□,077 rounds to 394,000 if we round to the nearest thousand.
Choose all answers that apply:
:3
:4
:5
Answer:
the answer would be 4
Step-by-step explanation:
The number 39□,077 to the nearest thousand and get 394,000, the thousands place digit must be 5 since that's the digit which would lead to rounding up. Hence, the correct digit to replace the □ would be 5.
Digits in the thousands place of the number 39□,077 would make it round to 394,000 when rounded to the nearest thousand. When rounding to the nearest thousand, we look at the hundreds place to decide whether to round up or down. The rules for rounding are if the hundreds place digit is 5 or higher, we round up, and if it is 4 or lower, we do not round up.
Therefore, to round up to 394,000, the digit in the hundreds place should be 5 or higher. This means that the options provided as possible answers:
3
4
5
Can be evaluated based on this rule. The digit 3 or 4 in the thousands place would not cause the number to round up, but the digit 5 would result in the number being rounded up to 394,000. Thus, the correct answer is 5.
Find the volume of the prism shown
Answer:
The answer is 450
Step-by-step explanation:
V = l*w*h
V = 15*10*3
V= 450
ANSWER
[tex]450 {cm}^{3} [/tex]
EXPLANATION
The prism shown is a rectangular prism or cuboid.
The volume of a cuboid is given by:
[tex]Volume=l \times b \times h[/tex]
From the diagram, the length is l=15cm ,the breadth is b=10cm and the height is h=3cm.
We substitute the values into the formula to obtain,
[tex]Volume=15 \times 10 \times 3[/tex]
We simplify to get,
[tex]Volume=450 {cm}^{3} [/tex]
What’s the perpendicular slope of 4/3
Answer:
-3/4
Step-by-step explanation:
Perpendicular slopes are reciprocal opposites of the original slope. This means that the reciprocal of 4/3 is 3/4, and the opposite of 3/4 is -3/4.
To find the perpendicular slope you must take the given slope take the opposite reciprocal (aka switch the sign and flip the fraction)
so...
[tex]\frac{-3}{4}[/tex]
^^^slope perpendicular to 4/3
Hope this helped!
~Just a girl in love with Shawn Mendes
Simplify the following expression (3i+4-i+4(6+2i)
Answer:28 + 10i
Step-by-step explanation: You first distribute.
(3i+4-i+4(6+2i)
3i +4-i+24+8i (Distribute)
3i - i = 2i + 8i= 10i and 4 + 24= 28 (Combine like terms)
10i + 28 or 28 + 10i
Answer:
Answer: 28 + 10i
Step-by-step explanation:
A P E X
Here are two steps from the derivation of the quadratic formula.
What took place between the first step and the second step?
*Apex
ANSWER
C. Factoring a perfect square trinomial.
EXPLANATION
The first step shown is:
[tex] {x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
Observe that the left hand side is a perfect square trinomial.
In other words, the left hand side is of the form,
[tex] {m}^{2} + 2mn + {n}^{2} [/tex]
which can be factored as:
[tex] {m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2} [/tex]
When we factor the perfect square trinomial on the left hand side, we obtain:
[tex]( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
The correct answer is C
Answer:
FACTORING A PERFECT SQUARE TRINOMIAL!
Step-by-step explanation:
GOT IT CORRECT ON 3.8.3 AP-EX...
it's not sq root because that comes afterwards.
it's not completing the square because that's
x^2+ bx/a +(b/2a)^2=-c/a+(b/2a)^2
Then from there it's
x^2 + bx/a + b^2/4a^2 = -c/a + b^2/4a^2
(x + b/2a)^2 = b^2/4a^2 -c/a
Then that step ends. If you don't believe me look at study 3.3.1 page 13.
This will help!
A cylinder has a circular base with a radius that measures 9 inches. Determine the diameter of the base of the cylinder.
3 inches
4.5 inches
18 inches
81 inches
The answer is 18 inches.
Let r=radius and d=diameter
2r=d
2(9)=d
18=d
Hope this helps!
Answer:
18 inches
Step-by-step explanation:
state the degree 5r^2s^3t^4
Answer:
Degree 9.
Step-by-step explanation:
The degree is the sum of all the exponents.
So it is 2 + 3 + 4 = 9.
The degree is the sum of all the exponents 5r^2s^3t^4, So it is 2 + 3 + 4 = 9.
What is the degree of the sum?The degree sum formula says that if you add up the degree of all the vertices in a (finite) graph, the result is twice the number of the edges in the graph. There's a neat way of proving this result, which involves double counting: you count the same quantity in two different ways that give you two different formulae.
The degree is the sum of all the exponents 5r^2s^3t^4
So it is 2 + 3 + 4 = 9.
What is the sum of the exponents called?Degree of the Term is the sum of the exponents of the variables. Example. 2x 4y 3 4 + 3 = 7 7 is the degree of the term. 5x-2y 5 NOT A TERM because it has a negative exponent.
To learn more about the degree sum formula, refer
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Solve for :
(x+3)/2=6
Answer:
x=9
Step-by-step explanation:
(x+3)/2=6
Multiply each side by 2
2*(x+3)/2=6*2
x+3 = 12
Subtract 3 from each side
x+3-3 = 12-3
x = 9
The Venn diagram represents the results of a survey that asked participants whether they would want a fish or turtle as a pet. Complete the table.
have a don't have Total
fish. a fish.
have turtle __. __. ___
don't have turtle__. __. ___
Total__. __. ___
Answer:
[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]
Step-by-step explanation:
From the Venn diagram:
have both turtle and fish - 6 participants;have only fish - 11 participants;have only turtle - 15 participants;don't have pets - 12 participants;So, in total,
6+11+15+12=44 participants took part in survey.
The two-way table looks like
[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]
what is 10 radical 12 times 6 radical 6
Answer:
360 radical 2 or 509.11688
Step-by-step explanation:
simplify the radicals
12 =2 radical 3
calculate the products
10* 2 radical 3 * 6 radical 6
= 120 radical 18
again simplify
360 radical 2
Answer:
360 radical 2
Step-by-step explanation: