The Exact values for the sine and cosine of the given angles are : sin(120°) = √3/2, cos(120°) = -1/2
Given that the terminal ray of an angle with measure of 120 degrees intersects a unit circle at the point (-1/2, √3/2), we can use the definition of sine and cosine to find the exact values of these trigonometric functions for the given angle.
The sine of an angle is defined as the y-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the sine is:
sin(120°) = √3/2
The cosine of an angle is defined as the x-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the cosine is:
cos(120°) = -1/2
So, the exact values for the sine and cosine of the angle with measure of 120 degrees are:
sin(120°) = √3/2
cos(120°) = -1/2
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3x^2-18x=-15 by complete the square
The solutions to the equation 3x²-18x=-15 by completing the square are x = 1 and x = 5.
How to solve quadratic equation by completing the square?In order to make an equation a perfect square, something must be added. This is known as "completing the square." This makes a number of equations simple to solve. In fact, by solving the square, all quadratic problems can be resolved.
According to question:To complete the square for the equation 3x²-18x=-15, we can follow these steps:
Move the constant term to the right side of the equation:
3x² - 18x + 15 = 0
Divide both sides by the coefficient of x^2 to make the coefficient 1:
x² - 6x + 5 = 0
To complete the square, we need to add and subtract the square of half of the coefficient of x:
x² - 6x + 9 - 4 = 0
(x - 3)² = 4
Take the square root of both sides to solve for x:
x - 3 = ±2
x = 3 ± 2
x = 1 or x = 5
Therefore, the solutions to the equation 3x²-18x=-15 by completing the square are x = 1 and x = 5.
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which one of the following are parametric equations for the tangent line to the curve at the point ( )?
The parametric equations for the tangent line to the curve
x = 26+27, t = 10+6t, z = 27+27t
In the given question points are given and we have to find the parametric equations for the tangent line to the curve.
given r(t) = <t³-1 , t²+1 , t³>
taking differentiation
r'(t) = <3t² , 2t , 3t² >
parameters corresponding to point at the point (26, 10, 27)
t²+1 = 10
=> t² = 9
=> t = √9
=>t=3
r'(t) at t = 3 is
r'(t) = <27, 6, 27 >
So the parametric equations for the tangent line to the curve
x = 26+27
t = 10+6t
z = 27+27t
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The complete question is :
Find the parametric equations for the tangent line to the curve
x = t³ - 1,
y = t² + 1,
z = t³
at the point (26, 10, 27). Use the variable t for your parameter.
T/F If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.
Answer:
Step-by-step explanation:
The answer is TRUE, If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.
i have $8$ pieces of strawberry candy (all identical) and $7$ pieces of rhubarb candy (all identical). find the number of ways i can distribute this candy to $5$ children, if it's ok to not give a child any candy.
Answer:
2 pieces of sc and 1 piece of rc
Step-by-step explanation:
In Quadrilateral ABCD , AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=27°. What is m∠5? Enter your answer in the box. ° Trapezoid A B C D with segment B D. Angle A D B is angle 1. Angle B D C is angle 2. Angle C is angle 3. Angle A is angle 4. Angle A B D is angle 5. Angle C B D is angle 6.
The measure of m∠5 of the quadrilateral is m∠5 = 27° because of alternate interior angles
The solution is Option C. Angle A B D is angle 5
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the quadrilateral be represented as ABCD
Now , the diagonal DB is the transversal line passing through the 2 parallel lines of the quadrilateral
And , the measure of m∠2 = 27°
The measure of m∠2 = measure of m∠5 ( alternate interior angles are equal )
So , the angles m∠2 and m∠5 are alternate interior angles
And , the measure of m∠5 = 27°
Hence , the measure of m∠5 = 27° ( interior angles )
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National Hurricane Center estimates that the Gulf of Mexico averages 3 major Hurricanes (Category 3 or higher) in a season.
a) What is the Mean number of major hurricanes gulf can expect in a season?
b) What is the probability that the Gulf will have no major hurricanes in 2022?
c) What is the probability that the Gulf will have at least one major hurricane in 2022?
d) What is the probability that the Gulf will have three major hurricanes in 2022?
The Mean number of major hurricanes gulf can expect in a season is 3.
What is probability?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
What is mean?
The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.”
Given:
Gulf of Mexico averages 3 major Hurricanes
Since, It is stated that the Gulf experiences 3 major hurricanes on an average in a season. Since the average is the expected no. of observations the mean no. of major hurricanes Gulf expect is 3.
Hence, the Mean number of major hurricanes gulf can expect in a season is 3.
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what is equivalent to 2/100
Answer:
1/50
Step-by-step explanation:
Divide 2/100 by 2 to get the simplest form.
show that if a and b are square, upper triangular matrices. then so is ab. (hint: the ith column of ab is a suitable linear combination of the columns of a)
Hence, if i > j, then (AB)ij is a sum of products of zeros, and is therefore zero. This means that all the entries below the main diagonal in the matrix AB are zero. Therefore, AB is also an upper triangular matrix.
To show that if a and b are square, upper triangular matrices, then so is ab, we need to prove that all the entries below the main diagonal in the matrix ab are zero.
Let A and B be square, upper triangular matrices of size n x n.
Then the (i,j)th entry of AB is given by:
(AB)ij = Σk=1n AikBkj
For i > j, we have:
(AB)ij = Σk=1n AikBkj = Σk=1j AikBkj + Σk=j+1n AikBkj
Since A is upper triangular, we have Aik = 0 for k > i.
Therefore, the first sum above is non-zero only for k ≤ i. Since B is also upper triangular, we have Bkj = 0 for k > j.
Therefore, the second sum above is non-zero only for k > j.
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Please help I can’t figure it out
Answer:
20
Step-by-step explanation:
592--------16hours
740---------x hours
x=740 ×16÷592 =20
Answer:
20 hours
Step-by-step explanation:
Find speed from distace and time taken to reach uncle's house
s = d/t = 592/16
s = 37 miles/hr
then find time from distance to chicago and time taken to reach there:
t = d/s = 740/37
t = 20 hours
Hope this helps!
CAN SOMEONE HELP WITH THIS QUESTION?
The rate at which the water level is rising when the water level is 3 cm,
⇒ 0.65 cm / sec
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Let us assume it is a regular pyramid. The (altitude) height "h" of apex from base square, slanting height and the side "a" of the base square rise uniformly and proportionally when we move from the apex point to the base.
Now, If height (altitude) h becomes x times, then side "a" of the base square becomes x times, the slanting height also becomes x times. Thus, the area b of the base square rises x² times.
Δh / h = Δa / a
Δb / b = 2 Δa / a = 2 Δh / h
Or, h₁/h₂ = a₁/a₂
Since, We know that;
⇒ V = 1/3 b h = 1/3 a² h
⇒ d V / dt = 1/3 a² dh/dt + 1/3 h a da/dt
= 1/3 a² dh /dt + 2/3 h a (a/h) (dh/dt)
= 1/3 a² dh / dt + 2/3 a² dh/dt
Hence, We get;
dV/dt = a² dh/dt
dh/dt = (1/a²) dV/dt
We have;
h₀ = 5 cm and a₀ = 3 cm
At the base;
When h = 5cm,
Hence, h / h₀ = a/a₀ ;
⇒ a = a₀ h / h₀ = 5×5/3 = 8.3 cm
And, dh/dt = 1/8.3² × 45 = 45/68.89 cm/sec = 0.65 cm / sec
Thus, The rate at which the water level is rising when the water level is 3 cm,
⇒ 0.65 cm / sec
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Un estudiante diseñó una investigación para probar el efecto del color de la luz en el crecimiento de las plantas. 1. ¿Cuál fue la variable independiente en la investigación? A. Color de la bombilla B. Altura de la planta C. Horas de luz D. Tamaño de la olla Plant Growth Investigation Blue Light Yellow Light Red Light State to
La intensidad de la luz afecta la tasa de fotosíntesis, cuanto mayor es la intensidad de la luz, mayor es la tasa de fotosíntesis y viceversa. ver explicacion.
What is plant growth?Important structures in plant development are buds, shoots, roots, leaves, and flowers; plants produce these tissues and structures throughout their life from meristems located at the tips of organs, or between mature tissues. Thus, a living plant always has embryonic tissues.
La fotosíntesis es el proceso mediante el cual las plantas verdes fabrican su propio alimento en presencia de luz solar, clorofila, dióxido de carbono y agua.
La intensidad de la luz afecta la tasa de fotosíntesis, cuanto mayor es la intensidad de la luz, mayor es la tasa de fotosíntesis y viceversa. Cuando hay una mayor intensidad de luz, hay más luz disponible para impulsar las reacciones de la fotosíntesis.
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Determine whether the functions are inverses.
f(x)=3+6
g(x)x+5/3
No, the function aren't inverse of each other.
What's Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it's defined is known as the sphere. The entire set of values that the function's affair can produce is appertained to as the range. The set of values that could be a function's labors is known as the co-domain.
Given
f( x) = 3x 6
g( x) = x5/3
So, the find the that both function are inverse of each other we've to prove
f( g( x)) = g( f( x))
So, f( g( x))
f( x+ 5/3)
= 3 (x+ 5/3) + 6
= 3x + 15 + 6
= 3x + 21
and, g( f( x))
= g(3x+ 6)
= 3x + 6 + 5/3
= 3x + 23/3
So, f( g( x)) ≠ g( f( x))
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determine if the specified linear transformation is (a) one-to-one and (b) onto. justify each answer
To determine if a linear transformation is onto, we need to check if every vector in the range has at least one pre-image in the domain.
Let T be a linear transformation from R^3 to R^2 given by:
T (x, y, z) = (2x - y, x + 3y - 4z)
(a) To check if T is one-to-one, we need to check if for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3, we have T (x1, y1, z1) ≠ T (x2, y2, z2). Equivalently, we can check if T (x1, y1, z1) - T (x2, y2, z2) ≠ 0 for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3.
So, let (x1, y1, z1) and (x2, y2, z2) be two distinct vectors in R^3. Then:
T (x1, y1, z1) - T (x2, y2, z2) = (2x1 - y1, x1 + 3y1 - 4z1) - (2x2 - y2, x2 + 3y2 - 4z2)
= (2x1 - y1 - 2x2 + y2, x1 + 3y1 - 4z1 - x2 - 3y2 + 4z2)
= (2(x1 - x2) - (y1 - y2), x1 - x2 + 3(y1 - y2) - 4(z1 - z2))
For T to be one-to-one, the only solution to T (x1, y1, z1) - T (x2, y2, z2) = 0 must be (x1, y1, z1) = (x2, y2, z2). So, we need to solve the equation above and check if the only solution is (x1, y1, z1) = (x2, y2, z2).
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determine which side would be greater given 2 triangles with 2 congruent lengths and the measure of the angle inbetween
The SAS congruence criteria, option (c), is the appropriate response. The acronym SAS stands for "side-angle-side," and it denotes that two sides and the included angle of one triangle must be congruent to two sides and the incorporated angle of another triangle for the triangles to be considered congruent.
"Right-angle-hypotenuse-side" (or option a) refers to a particular instance of the SAS criteria that only applies to right triangles.
The acronym ASA (option b) stands for "angle-side-angle," and it denotes that two angles and the included side of one triangle must be congruent with two angles and the included side of some other triangle for the triangles to be considered congruent.
Side-side-side, or SSS (option d), refers to the situation in which all three sides of one triangle are congruent with all three sides of another triangle.
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The question is -
Two triangles are congruent if two angles and the side included between them in one triangle are equal to the two angles and the side included between them in the other triangle. This is known as:
a. RHS congruence criterion
b. ASA congruence criterion
c. SAS congruence criterion
d. SSS congruence criterion
How many ways can you make change for 70 cents using only nickels, dimes, and quarters?
The number ways can make change for 70 cents using only nickels, dimes, and quarters is,
7 dimes, 0 nickels
6 dimes, 2 nickels
5 dimes, 4 nickels
4 dimes, 6 nickels
3 dimes, 8 nickels
2 dimes, 10 nickels
1 dime, 12 nickels
0 dimes, 14 nickels
What is the combination?In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.
Formula for selection of a objects from the n objects,
N = ⁿCₐ
To find the number of ways to make change for 70 cents using only nickels, dimes, and quarters, we can use a combination of systematic listing and counting.
One approach is to consider the number of quarters used to make the change, which can be 0, 1, or 2, since using more than 2 quarters would exceed the total value of 70 cents.
Here are the possible combinations of coins to make change for 70 cents:
Using 0 quarters:
7 dimes, 0 nickels
6 dimes, 2 nickels
5 dimes, 4 nickels
4 dimes, 6 nickels
3 dimes, 8 nickels
2 dimes, 10 nickels
1 dime, 12 nickels
0 dimes, 14 nickels
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Determine for what value of a is the expression x2+2x-a divisible by x+4
The expression x^2 + 2x - a is divisible by x + 4 when a = 6x.
What is polynomial long division?
A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.
By using the long division method:
x + 4 | x^2 + 2x - a
-x^2 - 2x + 4x
-------------------
-a + 6x
-x^2 - a + 6x
-------------------
2x - a
-x^2 - 2x + 4x
-------------------
0
The remainder is 0 a = 6x.
Hence, the expression x^2 + 2x - a is divisible by x + 4 when a = 6x.
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To rent a certain meeting room, a college charges a reservation fee of 37 and an additional fee of 7.90 per hour. The chemistry club wants to spend at most 92.30 on renting the meeting room.
Answer:
t ≤ 8
Step-by-step explanation:
Equation Total
1 hour 32 + 9.4 41.4
2 hours 32 + 2(9.4) 50.8
3 hours 32 + 3(9.4.) 60.2
4 hours 32 + 4(9.4.) 69.6
5 hours 32 + 5(9.4.) 79.0
6 hours 32 + 6(9.4.) 88.4
7 hours 32 + 7(9.4.) 97.8
8 hours 32 + 8(9.4.) 107.2
So we know the maximum amount of time is 8 hours. So now let's express this as an inequality:
32 + 9.4t ≤ 107.2 Now let's solve for t
9.4t ≤ 75.2
t ≤ 8
An element with a mass of 820 grams decays by 24% per minute. To the nearest
minute, how long will it be until there are 120 grams of the element remaining?
7 minutes will it be until there are 120 grams of the element remaining.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
We have,
An element with a mass of 820 grams decays by 24% per minute. To the nearest minute.
Now, 100 - 24 = 76% of the element remains after each minute.
So, 820 x (0.76[tex])^t[/tex] = 120 where t is number of minutes.
(0.76[tex])^t[/tex] = 0.146
Taking log both side we get
t log 0.76 = log 0.146
t = 7.00724
t = 7 minutes
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Mrs.Nunes has 7 yards of string and needs to split it into 4 equal sections to make bows. How long will each section of string be?
Answer: 1.75 yards
Step-by-step explanation:
You need to divide 7 by 4 to get 4 equal sections.
7/4 = 1.75
Therefore, 1.75 is your answer
abcdefgh is a regular octagon of side 12cm. find the area in square centimeters of trapezoid bcde. express your answer in simplest radical form.
Question 2(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x1 1 011
y-2-1012
x0 123 4
y-320-23
x-2-10 12
y 2 0
-102
x-2-10 1 2
y 3 1
-1-3-5
Table one and table four represent a linear function.
Which of the table represents a linear function?A linear function is simply a function that represents a straight line on the coordinate plane.
For a function to be linear, the differences of the y-values must be constant.
For table 1.
Let get the differences of the y-values
-1 - (-2) = 1
0 - (-1) = 1
1 - 0 = 1
2 - 1 = 1
Since the differences of the y-values are all 1 ( constant ), table one is a linear function.
For table 2.
2 - (-3) = 5
0 - 2 = -2
-2 - 0 = -2
3 - (-2) = 5
Since the differences of the y-values are not the same ( constant ), table two is not a linear function.
For table 3.
0 - 2 = -2
-1 - 0 = -1
0 - (-1) = 1
2 - 0 = 2
Since the differences of the y-values are not the same ( constant ), table three is not a linear function.
For table 4.
1 - 3 = -2
-1 - 1 = -2
-3 - (-1) = -2
-5 - (-3) = -2
Since the differences of the y-values are all -2 ( constant ), table four is a linear function.
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suppose that a and b are diagonalizable matrices of the same size, i.e.\ there exist invertible matrices u and v such that uau^{-1} and vbv^{-1} are diagonal. show that ab =
ab is diagonalizable and can be written as a product of invertible matrices.
Since a and b are both diagonalizable, there exist invertible matrices u and v such that [tex]uau^{-1} and vbv^{-1}[/tex] are both diagonal matrices. Thus, we can rewrite ab as [tex]uau^{-1}vbv^{-1}[/tex]. Since matrix multiplication is associative, the order of multiplication does not matter and thus [tex]ab = u(au^{-1}vb)v^{-1}[/tex]. Since the [tex]au^{-1}vb[/tex] is also diagonalizable, it can be written as c, where c is a diagonal matrix. Thus, [tex]ab = ucv^{-1}[/tex], which is also a diagonal matrix. Therefore, ab is diagonalizable and can be written as a product of invertible matrices.
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Complete questiom:
Suppose that A and B are diagonalizable matrices of the same size, i.e.\ there exist invertible matrices U and V such that [tex]UAU^{-1} and VBV^{-1}[/tex]are diagonal. Show that AB = UDEV, where UDEV is also a diagonal matrix.
27.
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 120 milligrams per deciliter (mg/dL) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 105 mg/dL and = 15 mg/dL. (Round your answers to four decimal places.)
(a) If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes?
(b) If measurements are made on three separate days and the mean result is compared with the criterion 120 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?
(a) The probability that Shelia is diagnosed as having gestational diabetes is 0.1586.
(b) The probability that Shelia is diagnosed as needing further testing for gestational diabetes is 0.0416.
What is z-score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.
Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
Given:
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy).
There is variation both in the actual glucose level and in the blood test that measures the level.
In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 120 milligrams per deciliter (mg/dL) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 105 mg/dL and = 15 mg/dL.
(a) The sample mean [tex]\bar{X}[/tex] = 120
The mean = 105
And standard deviation = 15
t = 1 - P(X ≤ 120 - 105/15)
t = 1 - P(X ≤ 15/15)
The P-Value is 0.158655.
(b) The sample mean [tex]\bar{X}[/tex] = 120
The mean = 105
And standard error = 15/√3 =
t = 1 - P(X ≤ 120 - 105/8.66025403784)
t = 1 - P(X ≤ 15/8.66025403784)
The P-Value is 0.041637.
Therefore, the P-Value is 0.041637.
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please help quick!
photo attatched!
The missing values in the ratio table on pages and minutes is :
Pages 1 / 4 3 / 4 1 ¹ / ₂ 5
Minutes 1 / 2 1 ¹ / ₂ 3 10
How to fill the ratio table ?To fill the ratio table, find the relationship between Minutes and Pages :
= 1 / 2 ÷ 1 / 4
= 2 mins per page
This means that every page is read in 2 minutes.
3 / 4 pages would be read in :
= 3 / 4 x 2
= 1 ¹ / ₂ minutes
3 minutes would allow for the reading of :
= 3 / 2
= 1 ¹ / ₂ pages
5 pages would be read in:
= 5 x 2
= 10 mins
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I will give brainliest and ratings if you get this correct
determine whether the following function have limit or not?
the sampling distribution used when making inferences about a single population's variance is a(n) _____ distribution.
The Sampling Distribution used when making inferences about a single population's variance is a(n) Chi Square distribution.
The Chi Square distribution is defined as a continuous probability distribution that takes only non-negative values. It is used to analyze the variability of a set of data and is frequently used in hypothesis testing and confidence interval estimation.
In this test, the test statistic follows a chi-square distribution with (n - 1) degrees of freedom, where n = sample size. The larger the size of the sample , the closer the sampling distribution of test statistic will approach to a Normal Distribution .
Therefore , the chi-square distribution is a statistical tool which the researchers use to draw conclusions about the variability of a population based on a sample.
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The well ordering property can be used to show that there is a unique greatest common divisor of two positive integers. Let a and b be positive integers, and let S be the set of positive integers of the form as + bt, where s and t are integers.
a) Show that S is nonempty
b) Use the well ordering property to show that S has a smallest element c.
c) Show that if d is a common divisor of a and b, then d is a divisor of c.
d) Show that c | a and c | b [Hint: First, assume that c does not divide a. Then a = qc + r, where 0 < r < c. Show that r E S, contradicting the choice of c.]
e) Conclude from (c ) and (d) that the greatest common divisor of a and b exists. Finish the proof by showing that this greatest common divisor is unique.
The well ordering property states that every non-empty set of positive integers contains a least element. This property can be used to show the existence and uniqueness of the greatest common divisor (GCD) of two positive integers.
a) To show that S is non-empty, we note that the element 0 is a member of S, since 0 = 0 + 0*b.
b) The well ordering property guarantees that S has a least element, which we denote as c.
c) Suppose d is a common divisor of a and b. We know that a = dq and b = dr for some integers q and r. Then c = a + bt = dq + drt = d(q + rt). Thus, d must be a divisor of c since it divides the terms on the right side of the equation.
d) Assume that c does not divide a. Then a = qc + r where 0 < r < c. This means r is also a member of S, contradicting the choice of c as the least element of S.
e) From (c) and (d) we can conclude that the GCD of a and b exists. To show that it is unique, we note that if a and b have two GCDs, d and e, then d and e must both divide c. Since c is the least possible value, this implies that d and e must actually be the same number, thus showing the GCD of a and b is unique.
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HURRY 100 PTS AND BRAINLIEST!!! Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 8 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Answer:
Part A: PR ≈ 16.06
Part B: QR≈ 9.60
Step-by-step explanation:
Part A)
The length of rod PR can be found using the Pythagorean theorem.
In this case, rod PQ is one leg, rod QR is the other leg, and rod PR is the hypotenuse. So, we have: PQ^2 + QR^2 = PR^2
Substituting the given lengths, we have:
14^2 + 8^2 = PR^2
Solving for PR, we get:
PR^2 = 14^2 + 8^2 = 196 + 64 = 260
Taking the square root of both sides, we have:
PR = √260
PR ≈ 16.06
Part B)
If the length of rod PR is adjusted to 17 feet, we can use the Pythagorean theorem to find the new height QR.
PQ^2 + QR^2 = 17^2
Substituting the given length of PQ, we have:
14^2 + QR^2 = 17^2
Expanding both sides, we have:
196 + QR^2 = 289
Subtracting 196 from both sides, we have:
QR^2 = 289 - 196 = 93
Taking the square root of both sides, we have:
QR = √93
QR ≈ 9.60
Suppose that 3y - 5 = 45 and y = 3x - 2.
Which of the following equations is equivalent to 3y - 5=45, but written
only in terms of x?
a) 15x-10=40
b) 9x-6=50
c) 9x-6=40
d) 15x-10= 50
An equation that is equivalent to 3y - 5=45, but written only in terms of x include the following: B. 9x - 6 = 50.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
3y - 5 = 45 .......equation 1.
y = 3x - 2 .......equation 2.
By using the substitution method to substitute equation 2 into equation 1, we have the following:
3(3x - 2) - 5 = 45
9x - 6 - 5 = 45
9x - 6 = 45 + 5
9x - 6 = 50.
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Which point on the number line is approximately 13/17
Answer:
C
Step-by-step explanation:
Cause 13/17 is 0.76 so c is nearer to 1 about 0.76
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{13}{17}}\\\\\mathsf{\rightarrow 13\div17}\\\\\mathsf{\rightarrow 0.764705882352941}}\\\\\mathsf{\approx 0.764\approx 0.75\ (in\ this\ case)}}[/tex]
[tex]\huge\text{Therefore your answer should be:} \\\\\huge\boxed{\mathsf{Point\ C.}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]