Stephen made the following claim:
"If a quadrilateral has congruent diagonals, then it is a rectangle."
Which figure below can be used to prove that Stephen is wrong?
O Rhombus
O Square
O Isosceles Trapezoid
O Rectangle
Answers
The figure below that can be used to prove that Stephen is wrong is Isosceles Trapezoid. Option C is correct. This is further explained below.
What is Isosceles Trapezoid?Generally, Isosceles Trapezoid is simply defined as a trapezoid with base angles that are the same and non-parallel sides that are the same is called an isosceles trapezoid. If a quadrilateral has just one parallel side, we call it a trapezoid.
In conclusion, If you want to show Stephen he's incorrect, you may use the Isosceles Trapezoid in the diagram below as evidence.
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Related Questions
Let Q be the quantity Q = 110(1.137)' which is changing over timet. a. What is the quantity at time t=0? b. Is the quantity increasing or decreasing over time? c. What is the percent per unit time growth or decay rate? % growth per unit time d. Is the growth rate continuous?
Answers
a)The quantity at time t=0 is 110.
b)The quantity is increasing over time .
c) The percent per unit time growth or decay rate is 11.1% .
d)Yes, the growth rate continuous.
a. At time t=0, the quantity Q can be found using the given formula Q = 110(1.137\()^{2}\).
Plugging in t=0, we get.
Q = 110(1.137\()^{0}\)
= 110(1) = 110.
b. The quantity is increasing over time because the base (1.137) in the formula is greater than 1, which means that Q grows as time (t) increases.
c. The percent per unit time growth rate can be found by taking the derivative of the function and dividing by the initial quantity:
dQ/dt = 110(1.137\()^{t}\)* ln(1.137)
dQ/dt at t=0 = 110(1.137\()^{0}\) * ln(1.137) = 12.2
% growth per unit time = (dQ/dt)/Q * 100% = 12.2/110 * 100% = 11.1%
d. The growth rate is continuous, as it follows an exponential growth pattern described by the formula Q = 110(1.137)^t, where the base is constant and the time variable is continuous.
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Solve the following system of equations using addiction
Answers
Answer:
3x+y=13
+2x-y=12
SOlve it like what you would normally do
3x+2x=5x
y+(-y)=0
13+12=25
Basically
5x+0=25
Bring down all appropiate signs
Now solve that
5x=25
x=5
Now to find “y”
Plug in The “x”
3*5=15
15+y=13 now solve that and you’d get -2
If you plug it into the other one, it would be the same thing
2*5=10
10-y=12
-y=2
y= -2
x=5
y= -2
Write the expression in terms of a single trigonometric function. \[ \sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} \]
Answers
Let's start solving the expression using the product to sum formulae.
Here's the given expression,
\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]
Using the product-to-sum formula,
\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]
Applying the above formula in the first term,
\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]
Using the product-to-sum formula,
\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]
Applying the above formula in the second term,
\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]
Substituting these expressions back into the original expression,
we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]
Therefore, the given expression can be written in terms of a single trigonometric function as:
\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}
Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.
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if you spun the spinner 100 times would you expect it to land on red
Answers
How many colors are there in total?
which of the following basic functions is equivalent to the piecewise-defined function f(x)= x if x≥0 −x if x<0 ? question content area bottom part 1 a. f(x)= 1 x b. f(x)=x c. f(x)=x2 d.
Answers
The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.
Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.
The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.
In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
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What is the value of the expression 16 + 4 − (5 x 2) + 2? (2 points) group of answer choices 10 12 14 18
Answers
The value of the expression 16 + 4 - (5 x 2) + 2 is 12.
To evaluate the expression 16 + 4 - (5 x 2) + 2, we follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
Let's simplify the expression step by step:
First, we perform the multiplication: 5 x 2 = 10.
Next, we evaluate the expression within parentheses: 16 + 4 - 10 + 2.
Now we perform the addition and subtraction from left to right: 16 + 4 = 20, 20 - 10 = 10, 10 + 2 = 12.
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Ricardo Appliance is having a 35% off sale on all items in the store. what's the sale price on a $549.00 refrigerator
Answers
Ricardo Appliance is having a 35% off sale on all items in the store.
Sale discount = 35% of the price of the items
The price of Refrigerator is $549.00
Sale price is = Price of refrigeratoor - 35% of sale price
\(\begin{gathered} \text{ 35\% of sale price = 35\% of 549} \\ \text{ 35\% of sale price =}\frac{35\times549}{100} \\ \text{ 35\% of sale price =192.15} \end{gathered}\)Sale price = Price of refrigeratoor - 35% of sale price
Sale price = 549.00 - 192.15
Sal
Find the Valué of X when lines W and V are parallel.
A. 15.5
B. 17
C. 23.25
D. 29.5
Answers
I dont understand this problem can someone hlp me understand
Answers
The town will have a population of 20683 after 5 years
Explanations:Let the initial population be P₀
P₀ = 17000
Growth rate, R = 4% = 4/100 = 0.04
Time, T = 5
The population after 5 years will be given by the formula:
\(\begin{gathered} P=P_0(1+R)^T \\ P\text{ = 17000(1 + 0.04})^5 \\ P=17000(1.04)^5 \\ P\text{ = }20683.09 \\ P\text{ = 20683 (to the nearest whole number)} \end{gathered}\)The town will have a population of 20683 after 5 years
3. Given a nonempty polyhedron P={(x,y)∈Rn×Rk:Ax+By≥b}, let Q denote its projection onto x-space, i.e., Q={x∈Rn:∃y∈Rk,Ax+By≥b}. Prove or disprove the following statements by counterexamples: 1) Suppose that (x^,y^) is an extreme point of P. Is x^ an extreme point of Q ? 2) Suppose that x^ is an extreme point of Q. Does there exist a y^ such that (x^,y^) is an extreme point of P ? 3) Suppose that x^ is an extreme point of Q and P does not contain a line. Does there exist a y^ such that (x^,y^) is an extreme point of P ?
Answers
P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.
1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.
Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.
2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.
3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.
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a rectangular garden 450 square feet in area is to be fenced off against hyenas. find the dimensions that will require the least amount of fencing if one side of the garden is already protected by a barn. a) 30 by 15 feet b) 32 by 14 feet c) 120 by 154 feet d) 29 by 14 feet e) 90 by 5 feet
Answers
The Correct option is option (A) . Using the minimization , the dimensions of rectangular garden are 30 feet and 15 feet .
We have given that ,
Area of rectangular garden (A) = 450 sq. feet
we trying to minimize L, the length of fencing. Since , one side of the fenced area is covered by the barn, we have got to make two sides perpendicular to the barn plus one side parallel to the barn.
Suppose the length of the perpendicular side be x and the length of the parallel side be y.
Thus, A = x × y = 450 sq. feet --(1)
x + x + y = L --(2)
from (1) , y = 450/x
putting this value in equation (2) we get,
2x + 450/x = L
Now , minimize the L by taking its first derivative with respect to t and then put dL / dt = 0
dL /dx = 2 - 450/x^2
2- 450/x^2 = 0 => 450/x^2 = 2
=> x^2 = 450/2 = 225
taking square root both sides,
=> x = +-√225 = 15 or -15
but sides of any geometry never be negative
so, x = 15 put this x in equation (2)
=> y = 450/15 = 30
Hence , the dimensions of rectangular garden are (15, 30).
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Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
Answers
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
what is the median of 1,2,3,4,6
Answers
Answer:
Step-by-step explanation:
3
Please please please help *URGENT*
Answers
Answer:
1 = Communative property of addition
2 = distribution property
3 = Associative property of multiplacation
4 = Communative property of multiplacation
5 = Associative property of addition
Hope this helps! :) Please Ignore my bad spelling
Also, if you think this explanation is good, please mark it brainliest! It would help a lot! Thanks!
The cylindrical canister of a fire extinguisher
has a diameter of 4 inches and is 12 inches
high. About how many square inches of
metal (total surface area) would be needed
to manufacture one fire extinguisher?
Answers
Step-by-step explanation:
2*22/7*48=301.714 .This the answer
Answer:
Yeah, what they said above.
Step-by-step explanation:
Use the distributive property
–4(a + 3)
Answers
Answer:
-4a - 12
Step-by-step explanation:
-4(a+3)
-4(a) + -4(3)
-4a + -12
-4a - 12
Chong is grouping 705 nickels into rolls of 20 nickels. How many rolls will she have? How many extra nickels will there be?
This is not for me. I am asking it for my sister and I am to lazy to do the math myself lol!!!!
Answers
Answer:
Just divide:
705/20 = 35.25
There will be 35 roles.
Now to find how many left over, just multiply 35 times 20:
35 * 20 = 700
705 - 700 = 5
5 nickles left over!
Step-by-step explanation:
Hope it helps! =D
Answer:
35 Rolls, 5 nickels extra
Step-by-step explanation:
Think of it like so:
You have $705 in your bank account
Now many $20 Bills will you get from the ATM/Bank if you withdraw it all? The answer is: You will have 35 $20 bills.
What do you have left over? Take 20x35, than subtract that from 705
(705 - (20x35) = 5 nickels left over
9-2*x=35
A. -13
B. -22
C. 48
Answers
Answer:
x= -13 (a)
Step-by-step explanation:
-2x=35-9
-2x=26
x=-13
hope this helps x.
Answer:
-13
Step-by-step explanation:
9-2/x=35
9-2/x=35
-2/x=35-9
-2/x=26
-2=26x
26x=-2
x=-1/13
Jack is making a mixed bean salad. He is using green beans, white beans and black beans in the ratio 4:3:5. How many ounces of black beans did he use? How many total ounces is the salad?
Answers
Let G represent Green beans , W → White beans , and B →Black Beans .
• G : W : B
4 : 3 : 5
• (we can see that the green beans are in multiplicity of 8 ( 4*8 =32 ounces, therefore the ration of other beans is to be multiplied by 8 as well. )
4*8=32 : 3*8= 24 : 5*8= 40
0. This means that Jack used ,40 ounces of black beans .
,1. Total ounce of the salad will then be : 32 +24 +40 = 96 ounce.
4 of 204 of 20 Questions
Question 4
What is the equation of the line that is parallel to y−5=−13(x+2) and passes through the point (6,−1)?
Answers
Answer:
y= -13x+77
Step-by-step explanation:
Parallel lines do not share any points but have the same slope.
First, put the equation y-5=-13(x+2) into slope-intercept form.
y= -13x-21
Slope= -13x
Y-Intercept= (0,-21)
Now that we know the slope...
y-(-1)=-13(x-6)
becomes
y+1=-13x+78
y-1=-13x+78-1
y=-13x+77
shares of a technology stock and shares of a mutual fund for . Her sister, Erin, bought shares of the technology stock and shares of the same mutual fund for . Find the cost per share of the technology stock, and the cost per share of the mutual fund.
Answers
Answer:
qyerloyelopiye te eeffgghelp
Solve the following inequality algebraically. \[ 5|9-3 x|+4>19 \] Answer:
Answers
To solve the inequality algebraically, we need to isolate the absolute value expression and divide the inequality into two cases. The solution is x < 6 and x > 12.
Let's first isolate the absolute value expression.
Subtracting 4 from both sides of the inequality, we have 5|9-3x| > 15.
Dividing both sides by 5, we get |9-3x| > 3.
This leads to two cases:
9-3x > 3 and 9-3x < -3.
For the first case, 9-3x > 3, we subtract 9 from both sides to get -3x > -6. Dividing both sides by -3, we obtain x < 2.
For the second case, 9-3x < -3, we subtract 9 from both sides to get -3x < -12.
Dividing both sides by -3 and reversing the inequality, we get x > 4.
Combining the solutions from both cases, we find that x < 2 or x > 4.
Thus, the solution to the inequality is x < 2 or x > 4.
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A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75%
per year. What will the value of the car be, to the nearest cent, after 11 years?
Answers
Answer:
The value of the car will be
4450.15
Step-by-step explanation:
we know that
11.75%=11.75/100=0.1175
so Let
x-----> the value of the car after 11 years
X=17600(1-0.1175)11=4450.15
Step-by-step explanation:
consider a 3x3 matrix a this matrix has -2 as an eigen value compute a basis of eigen space corresponding to eigen value -2
Answers
To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.
The null space will give us the basis vectors of the eigen space
To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.
By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.
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I just need the answer tbh idrc how to do it.
Answers
Answer:
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Step-by-step explanation:
sec(pi/2 -x) =csc x true or false
Answers
Answer:
true
Step-by-step explanation:
if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:
\(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\frac{1}{\sin \left(x\right)}\)
\(\frac{1}{\sin \left(x\right)}\) \(=\csc \left(x\right)\)
so, yes, \(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\csc \left(x\right)\)
hope this helps!!
which could be the function graphed below?
f(x) = √x - 5+1
f(x) = √x-2
f(x) = √x
f(x) = √x+4
Answers
Answer:
Option (4)
Step-by-step explanation:
Parent function of the graph attached,
f(x) = \(\sqrt{x}\)
If the given function is shifted by 'a' units to the left,
Rule for the transformation is,
g(x) = f(x + a)
So the transformed function will be in the form of g(x) = \(\sqrt{x+a}\)
Therefore, from the given options, f(x) = \(\sqrt{x+4}\) will match our requirements.
Option (4) will be the answer.
Answer:
D
Step-by-step explanation:
Which recursive sequence would produce the sequence 8, 20, 44, ...?
Answers
Answer: Next number will be 92
Step-by-step explanation:
2×4=8
8×2+4=20
20×2+4=44
44×2+4=92
Hun Lee is skateboarding and using energy at a rate of 400 kilocalories per hour. At what rate is Hun Lee using energy in minutes per calorie?
Answers
Answer:6.66666 kilocalories per hour
Step-by-step explanation:
A game includes spinning a spinner with numbers 1 –5 and rolling a number cube with numbers 1 –6 . What is the probability of spinning an even number and rolling a 5 ?
Answers
The values of the probability from spinning the spinner and rolling the cube are;
Probability that the spinner lands on an even number = 2/5
Probability of rolling a 5 on the number cube = 1/6
the joint probability of the spinner landing on an even number and rolling a 5 = 1/15
What is the probability of an event?Probability is a measure of the likelihood that an event will occur. The probability of an event = Number of times the event occurs ÷ Sum of the frequencies of all possible events.
Probability has many uses in both analysis and games. Probability is used in sectors of real life and business where making predictions is important. The utilization of probability principles is necessary for forecasting market prices and cricket team performance. Additionally, the branch of modern technology known as artificial intelligence heavily relies on probability.
Numbers on the spinner are; 1, 2, 3, 4, and 5
Numbers in the number cube = 1, 2, 3, 4, 5, and 6
The probability of an event = The number of required outcomes ÷ The number of possible outcomes
The possible even numbers on the spinner = 2 and 4
The number of even numbers in the spinner = 2
The number of possible numbers on the spinner = 5
The ratio of the number of even numbers to the number of possible numbers, which is the probability of spinning an even number, therefore is; P(E) = 2/5
The number of 5s on the cube = 1
The number of possible numbers on the cube = 6
The probability of rolling a 5 on the number cube is therefore, p(5) = 1/6
The probability of landing on an even number and rolling a 5, P(E) × P(5) is therefore;
∴ P(E) × P(5) = (2/5) × (1/6) = 2/30 = 1/15
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