The graph that could be used to find the distance between the points
(-3, -13) and (11, 9) is given as follows:
B. graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9.
What is distance between two points?
The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation
d=√((x2 - x1)^2 + (y2 - y1)^2) is used to calculate the distance between two points.
Suppose we have a pair of points, with the coordinates given as follows:
\((x_1, y_1)\) and \((x_2, y_2)\).
The two points form a right triangle, in which the sides are given as follows:
\(y_2-y_1\\x_2-x_1\)
The distance between these two points is given by the hypotenuse of the right triangle.
Hence, applying the Pythagorean Theorem, the distance is obtained as follows:
\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
In this problem, the coordinates of the points are given as follows:
(−3, −13) and (11, 9).
Hence the correct option is given by option B.
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pls give simple working out
x is 146 degrees
This is because angle y and angle x are supplementary, which means their measures add up to 180 degrees
180 - 34 = 146
Answer: x = 146°
Step-by-step explanation:
Given that y = 35°, Using linear pair
x+y = 180
x+35=180(Substitute value of y)
x=180-35(Transposition Method)
x=145°
a) A group of 50 people are going to run a race. The top three runners earn gold, silver, and bronze medals. b) Creating a nine player batting order from the 14 players on the baseball team. c) There are 30 applicants for four Software Tester positions.
a) n (No. of peoples) = 50
r (No. of prizes) = 3
p(n,r) = p (50,3)
\(\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(50,3)=\frac{50!}{(50-3)!} \\ =117600 \end{gathered}\)b) n(No. of players)=14
r (No. of players for Batting)=9
\(\begin{gathered} P(14,9)=\frac{14!}{(14-9)!} \\ =726485760 \end{gathered}\)c)n(Total applicants)=30
r(tester positions)=4
\(\begin{gathered} P(30,4)=\frac{30!}{(30-4)!} \\ \text{ =}\frac{30!}{26!} \\ \text{ =657720} \end{gathered}\)In the figure below, points X, Z, Q, R, and S lie in plane P. Points T and Y do not lie in plane P.
For each part below, fill in the blanks to write a true statement.
The blank spaces in the statements area. S, R, and Q are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.
What are Colinear Points?Points that lie on the same straight line are collinear points.
If two lines are lie on the same plane, they are referred to as coplanar lines.
(a.) S, R, and Q are on a straight line. Therefore S, R, and Q are distinct points that are collinear.
b. TX and QS are distinct lines that intersect.
c. Point Y and line QS are on the same plane. Therefore:
Point Y and line QS are coplanar.
d. Another name for plane P is: plane QSY.
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What is the range of the exponential function shown below?
f(x)=11•(1/3)^x
A. y<0
B. y>0
C. All real numbers except 11
D. All real numbers
The range of the exponential function is B. y > 0.
The range of the exponential function f(x) = 11 × (1/3)ˣ can be determined by analyzing the behavior of the function as x approaches positive and negative infinity.
As x approaches positive infinity, (1/3) becomes smaller and smaller, tending towards zero.
f(x) approaches 11 × 0, which is equal to 0.
As a result, the function approaches 0 as x goes to infinity.
On the other hand, as x approaches negative infinity, (1/3)ˣ becomes larger and larger.
Since 1/3 is between 0 and 1, raising it to a negative power causes it to grow exponentially.
f(x) approaches infinity as x goes to negative infinity.
Combining these two behaviors, we can conclude that the range of the function f(x) = 11 × (1/3)ˣ is all positive real numbers, excluding zero.
In other words, the range is y > 0.
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What is the area of the square that measures 3.1 m on each side
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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a) (10 pts) Re-express the given differential equation as a first order differential equation by utilizing matrix
and vector notation and in accordance with ()
= () form.
b) (10 pts) Is the system obtained in (a) stable, neutrally stable of unstable? Determine this using matrix.
c) (10 pts) Compute the eigenvalues and eigenvectors of matrix.
d) (10 pts) Using the results computed in (c) find and matrices and show that =
−
relationship
(i.e., the diagonalization relationship) is a valid relationship.
a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:
\(x' = Ax\)
where x is a vector and A is a square matrix.
b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.
If all eigenvalues have negative real parts, the system is stable.
If at least one eigenvalue has a zero real part, the system is neutrally stable.
If at least one eigenvalue has a positive real part, the system is unstable.
c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation
\(det(A - \lambda I) = 0\),
where λ is the eigenvalue and I is the identity matrix.
By solving this equation, we obtain the eigenvalues.
Substituting each eigenvalue into the equation
\((A - \lambda I)v = 0\),
where v is the eigenvector, we can solve for the eigenvectors.
d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:
\(A = PDP^{(-1)}\)
where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.
To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.
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Help please and show ya work
Answer:
D: 14.5
Step-by-step explanation:
4.1 = d - 10.4 add 10.4 to each side
14.5 = d
Answer:
14.5
Step-by-step explanation:
10.4 - 4.1 = 14.5
Cómo dividir los números 24/-8
Answer:
-3
Step-by-step explanation:
Cómo dividir los números 24/-8:
24/-8 = -3
8 cabe en 24, 3 veces. Como el 8 es negativo, la respuesta es -3.
determine the diameter of
8.4x10^-6 in standard notation
As I understand, you want to write a diameter, that currently is in scientific notation, in standard notation.
The standard notation is 0.0000084
First, scientific notation is a way to write really long numbers (particularly those that have a lot of zeros) in a shorter way.
The general form is:
Ax10^n
If n is positive, we add n zeros at the right of our number.
If n is negative, we add n zeros to the left.
Here we have:
8.4x10^-6
So n is negative, meaning that we need to add the zeros at the left (also remember to correctly change the position of the decimal point) we will get:
8.4x10^-6 = 0.0000084
This is the measure in standard notation.
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CAN ANYONE HELP NE WITH THIS ONE TOO??
Answer:
326.56 in².
Step-by-step explanation:
Mathematics: Define/explain.
SURFACE AREA: The measure of the total area that an object occupies.
The formula for finding the surface area for a cylinder is:
\(SA=2\pi r^2+2\pi rh\)
\(r-radius\)
\(h-height\)
Mathematics: Solve.
According to the image, the cylinder has a height of 9 inches and a base radius of 4 inches.
Now, we can plug the numbers into the formula.
\(SA=2\pi 4^2+2\pi4*9- (2*3.14*4*4)+(2*3.14*4*9)=326.56.\)
Mathematics: Conclude.
Therefore, the surface area of this cylinder is 356.56 in².
Ringani worked overtime to raise a total amount R30 000.00 to settle his student debt. If he has deposited R8 500.00 yearly into an account earning 7,04% interest per year compounded annually. How long, rounded to one decimal place did it took her to accumulate the total amount? A. 3.0 years B. 2.4 years C. 2.8 years D. 2.0 years
It took Ringani 2.8 years to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.
To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the time in years
In this case, we have:
P = R8,500.00
A = R30,000.00
r = 7.04% = 0.0704 (in decimal form)
n = 1 (compounded annually)
We want to find the value of t.
Using the formula, we can rearrange it to solve for t:
t = (log(A/P)) / (n * log(1 + r/n))
Substituting the given values, we have:
t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))
Calculating this using a calculator, we find that t is approximately 2.8 years.
Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.
The correct answer choice is C. 2.8 years.
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Determine the slope of the line given the 2 points. Point 1(8, 2) Point 2 (-7, -1)
Answer:
1/5
Step-by-step explanation:
2 - (-1) / 8 - (-7) = 3/15 = 1/5
can someone help ASAP plzz
Answer:
c. 84 ft²
Step-by-step explanation:
lateral area = 1/2 * base perimeter * height
where
base sides = 6 ft.
height (L) = 7
lateral area = 1/2 x (4*6) * 7
lateral area = 84 ft²
LA = 1/2pl
p = base perimeter
l = length
p = (6 * 4)
p = 24
l = 7
Use the formula and solve.
LA = 1/2(24)(7)
LA = 1/2(168)
LA = 84
Therefore, the answer is C
Best of Luck!
Cot^2x+1 please simplify
HELP QUICKLY!!!
A net of a rectangular prism is shown. A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters. What is the surface area of the prism? five hundred fifty and one-fourth cm2 four hundred twelve and three-fourths cm2 two hundred seventy-five and one-eighth cm2 one hundred thirty-seven and nine-sixteenths cm2
PLEASE show a explanation
The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]
Surface area of rectangular prism = 2[23 + 1081/16 + 47]
Surface area of rectangular prism = 275 1/8 cm².
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Solve for x:
A: 3x - 7 = -19; x =
B: 2x + 3 = -11; x =
C: -3 + 1 = -26; x =
D: 6x + 3 = -15; x =
E: -9 + 7x = 33; x =
F: -2x + 8 = 4; x =
( URGENT PLEASE SOLVE !!! )
c) ¿Hay números que pueden ser múltiplos de 2.3 y 5 a la veza
ayuda pliss
Answer:
los números son 5,10,15,20,25,30,35,40,45,50,55,60
Step-by-step explanation:
Espero que esto ayude a marcar el MÁS CEREBRAL !!!
Which of the following expressions are equivalent to -8- (-1) – 5
Answer:
-(8-1+5), -8+1-5,
Only two of the list are a match for the answer of -8- (-1) – 5.
-8- (-1) – 5 = -12
-(8-1+5 = -12
-8+1-5 = -12
Have a beautiful day!
The expression into an equivalent form -8- (-1) – 5 would be; -(8-1+5), -8+1-5,
Since expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it more complex or simple.
We need to find the expression into an equivalent form -8- (-1) – 5
This expression could also be given by;
-8- (-1) – 5
Now, we know that the list is a match for the answer of -8- (-1) – 5.
-8- (-1) – 5 = -12
-(8-1+5) = -12
-8+1-5 = -12
Hence, -(8-1+5), -8+1-5, are the correct expression.
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Which of the following are solutions to the equation below? Check all that apply. x2 + 10x + 25 = 2
Answer:
-5+√2 and -5-√2
Step-by-step explanation:
With the quadratic formula:
\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)
We can also complete the square (which is faster):
\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)
solve x^3-7x^2+7x+15
Step-by-step explanation:
\underline{\textsf{Given:}}
Given:
\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx
3
+7x
2
+7x−15
\underline{\textsf{To find:}}
To find:
\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx
3
+7x
2
+7x−15
\underline{\textsf{Solution:}}
Solution:
\textsf{Factor theorem:}Factor theorem:
\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}
(x−a)isafactorP(x)⟺P(a)=0
\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x
3
+7x
2
+7x−15
\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0
\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)
\mathsf{When\;x=-3}Whenx=−3
\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)
3
+7(−3)
2
+7(−3)−15
\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15
\mathsf{P(-3)=63-63}P(−3)=63−63
\mathsf{P(-3)=0}P(−3)=0
\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor
\mathsf{When\;x=-5}Whenx=−5
\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)
3
+7(−5)
2
+7(−5)−15
\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15
\mathsf{P(-5)=175-175}P(−5)=175−175
\mathsf{P(-5)=0}P(−5)=0
\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor
\underline{\textsf{Answer:}}
Answer:
\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x
3
+7x
2
+7x−15=(x−1)(x+3)(x+5)
\underline{\textsf{Find more:}}
Find more:
How many terms are in this expression?
6w + 7x
Answer:
2
Step-by-step explanation:
6w is a term
7x is a term
Compare the corresponding vertices in problem 2 and identify the transformation that produced LMN FROM ABC
Answer:
“The Beginnings of the Maasai.”
These cattle are sacred, bec
Step-by-step explanation:
Credit card applicants have a mean credit rating score of 667. Assuming that the distribution of credit rating scores, X, is Normal with standard deviation 65, calculate the probability that a single applicant for a credit card will have a credit rating score above 700.
Calculate the z-score. Round to two decimal places. Include any leading zeros.
Calculate the probability. Round to four decimal places. Include any leading zeros.
0.306 is the z-score. Round to two decimal places. Include any leading zeros.
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Let X the random variable that represent the rating score of a population, and for this case we know the distribution for X is given by
X `N(667,65 )
Where μ = 667 and σ = 65
We are interested on this probability
P(X > 700 )
And the best way to solve this problem is using the normal standard distribution and the z score given by
Z= X - μ/σ
If we apply this formula to our probability we got this
P(X > 700 )
= P(X - μ/σ > 700 -μ/σ)
= P(Z > 700 - 667/65 )
= P(Z > 0.508 )
And we can find this probability using the complement rule and excel or a calculator and we got
P( z > 0.508 ) = 1 - P(Z - 0.508 ) = 1 - 0.694 = 0.306
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Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue, how much shaving cream does she need?
The ounces of shaving cream will be 230 ounces.
How to illustrate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:
= 56 ÷ 7/15
= 56 × 15/7
= 120
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Anna had three times as many as joe bead.they had 480 beads together. Mr taylor have an equal to each of them. Zoe then had half the number of beads that Anna had. How many beads did mr taylor give them.
Mr. Taylor gave them 1500 beads each.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators that are written in a specific order and can be evaluated to produce a value. Expressions can be simple or complex, and they can involve basic arithmetic operations like addition, subtraction, multiplication, and division, as well as more complex operations like exponents, logarithms, and trigonometric functions.
Let's start by setting up equations to represent the information given in the problem:
Let's assume that Joe has x beads.
Then, Anna has 3x beads.
Together, Joe and Anna have x + 3x = 4x beads.
We know that the total number of beads they have is 480, so:
4x = 480
Solving for x, we get
x = 120
So, Joe has 120 beads, and Anna has 3x = 3(120) = 360 beads.
Mr. Taylor gave each of them an equal number of beads, which means he gave them each (480 + Mr. Taylor's beads) / 3 beads.
Zoe had half as many beads as Anna, so she had 360 / 2 = 180 beads.
We can now set up an equation to find how many beads Mr. Taylor gave them
(480 + Mr. Taylor's beads) / 3 = 120 + 360 + 180
Simplifying and solving for Mr. Taylor's beads, we get:
480 + Mr. Taylor's beads = 3(660)
480 + Mr. Taylor's beads = 198
Mr. Taylor's beads = 1980 - 480
Mr. Taylor's beads = 1500
Therefore, Mr. Taylor gave them 1500 beads each.
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Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Step 4 of 10: Find the expected value for the number of respondents who are optimistic. Round your answer to two decimal places.
Answer:
Yes. the Psychologist can confirm his theory that the attitudes have changed over time, based on the first and second surveys.
The expected value for the number of respondents who are optimistic is:
= 16.25
Step-by-step explanation:
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Expected value of optimistic respondents:
Attitude
Optimistic Expected Value
1st Survey 8.75 (250 * 7% * 50%)
2nd Survey 7.50 (250 * 6% * 50%)
Total EV 16.25
Subtract the fractions and reduc terms. (Enter your answer as a simplified mixed number) 12 1/5 - 4 1/5
Answer:
8
Step-by-step explanation:
\(\displaystyle\bf\\12\frac{1}{5}-4\frac{1}{5}=\\\\=\frac{12\times5+1}{5}-\frac{4\times5+1}{5}=\\\\=\frac{60+1}{5}-\frac{20+1}{5}=\\\\=\frac{61}{5}-\frac{21}{5}=\\\\=\frac{61-21}{5}=\frac{40}{5}=\boxed{\bf8}\)
please help quick giving 25 points
Answer:
Step-by-step explanation: 5.) Circular shape.
6.) Feet.
7.) Circle.
8.) The circumference is 9 and the radius is 18.
9.) By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.
A single serving of hot chocolate requires 0.75 cups of milk. Nina used 7 cups of milk to make hot chocolate for her 9 friends. Did she make enough for each friend to get a serving of hot chocolate?
Answer:
nik
Step-by-step explanation: