PLEASE HURRY!!
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 9 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 18 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)
Answers
Approximate new height QR of the scaffold would be 11.31 Fee
What is Pythagoras theorem?
The pythagorean theorem or Pythagoras' theorem may be a elementary relation in geometry between the 3 sides of a triangle.
Main Body:
A) Here, We'll use "Pythagoras Theorem" which tells:
a² + b² = c²
So, PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
In short, approximate length of rod PR would be 16.64 Feet.
B) Again, Use the Pythagoras Theorem,
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
Hence , approximate new height QR of the scaffold would be 11.31 Feet
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Related Questions
If f(x) = 2x² + 3x - 19, find f(-4)
Answers
32+(-12)-19= 1
Answer:
f(-4)=1
Step-by-step explanation:
f(x) = 2x² + 3x - 19
f(-4)=2(-4)² + 3(-4)-19
f(-4)=2(-16)+3(-4)-19
f(-4)=-32+3(-4)-19
f(-4)=32-12-19
f(-4)=20-19
f(-4)=1
Use the quadratic formula to solve. Express your answer in simplest form.
22d²- 35d + 12 = -3d²
Answers
Answer:
x= -22d/44 x = -48d/44 is your answer
where d =2x
Step-by-step explanation:
22d²- 35d + 12 = -3d²
22d²- 35d + 12 +3d²
25d²- 35d + 12 = a b c formula= - b-/+ / b^2 - 4 ac / 2a
= -35d -+/ 35^2 - 4 *22d *12 / 2*22d
= -35d -+/1225d-4 (22) (12) /44d
= -35d -+/1225d- (88) (12) /44d
= -35d -+/1225d- (1056) /44d
= -35d -+/169d- /44d
=-35d -/+ 13d /44 x= -22d/44 x = -48d/44
The discriminant b2−4ac>0
so, there are two real roots.
What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4
Answers
Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]
Step-by-step explanation:
The equation of the given line can be rearranged as [tex]y=2x-4[/tex].
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.
Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].
Ayuda, me gustaría su ayuda con mi tarea
Answers
Answer:
1.) x = 1, 2/3
2.) x = -3±[tex]\sqrt{6}[/tex]
3.) x = [tex]\frac{4+/-\sqrt{37} }{3}[/tex] or x = −3.36092084, 0.69425417
Step-by-step explanation:
These are quadratic equations so we use the quadratic formula method.
Use the quadratic formula by taking:
[tex]ax^{2}+bx^{2} +c=0[/tex]
1.) a = 3, b = -5, c = 2
2.) a = 1, b = 6, c = 3
3.) a = -3, b = -8, c = 7
Then, substitute into the quadratic formula:
(Check the picture provided for the quadratic formula)
Which expression is equivalent to x +11?
A. 11x
B. 11+x
C. 11-x
D. -x+11
Answers
Answer:
11x
Step-by-step explanation:
A builder need 2,964 nail to finih a project. If the nail come in package of 52, how many package hould the builder purchae?
Answers
Number of nails to finish the project by buying are required = 2964 units
1 package of nails contains per unit = 52 units
To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.
So,
Number of package required to the builder
= Total number of nails required to buy by the builder / no. of nails provided per package
=2964/52
=57 packages
Therefore, No. of packages required by the builder to buy to complete the project
=57 packages needed.
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Answer: 57
Step-by-step explanation:
Just plug it into a calculator.
2964/52 = 57
He needs to buy 57 packages
a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
Answers
Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .
What exactly is probability?Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.
Here,
Given:
Mean, μ =7.37 days
Standard Deviation, σ = 2.75 days
Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.
Formula:
Z = [tex]\frac{x-u}{\alpha }[/tex]
a) P( 5 to 6 days are spent in the hospital.)
P(5≤x≤6)
=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])
=>P(-0.861≤x≤-0.498)
=>P(Z≤-0.498) - P(Z<-0.861)
=>0.034 - 0.001 = 0.03310
=> P(5≤x≤6) =3.3%
Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.
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Need help with this, Plot the points that represent the profit you can expect to earn each month, for each business, on a single xy-plane. You can create your plot by hand or you can use Desmos to help you. HINT: Use a different, single color for each business to help you keep track of your points
Answers
A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
Based on the plot the profits of each month can be found out using a qudratic function?
The lawn care business shows diminishing returns after month 3 . So it is not a viable business to conitnue for the long term. Based on the projections around month 8 profit becomes -$14.44. This is loss.
The other two businesses are profitable. The show upward growing trend as the months progress. Following table shows projected earnings for 1 year based on the equations showed in the graph.
3. A quadratic funtion can be used to represent the profits. The equation is given in the plots
4. A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
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surveys, if not done correctly, can lead to seriously biased samples. which is not a bias due to the sampling plan?
Answers
Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
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what does x equal????
Answers
Answer:
x=15.56
Step-by-step explanation:
You need to use pythagoras for this question.
Formula for pythagoras: a^2 + b^ =c^2
a= 11
b=11
c=?
11^2+11^2=c^2
121+121=c^2
242=c^2
[tex] \sqrt{242} [/tex]
=c
c=15.56
(1 point) a true-false test contains 7 questions. in how many different ways can the 7-question test be answered? (give an exact answer.) your answer is :
Answers
The possible number of ways the 7-question test can be answered: 128
In this question, we have been given a true-false test contains 7 questions.
We need to find the possible number of combinations (ways) the 7-question test can be answered.
As, it is a true-false test, there are 2 choices per problem.
The number of problems = 7
so, the possible number of ways the 7-question test can be answered: 2*2*2*2*2*2*2
= 2^7
= 128
Therefore, in 128 different ways the 7-question test can be answered.
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Help with ixl please
Answers
The most horizontal line is straight so it equal 180°. You know that one side (lower left section) is 67° meaning the other side is 180° - 67° = 113° (lower right side).
The most vertical line is straight so it equal 180°. You know that one side (lower right side) is 113°. The entire right side you have: 113°, 42°, and f.
f = 180° - (113° + 42°)
f = 25°
Answer:25 deegrees
Step-by-step explanation:
the number of cells in a specimen of bacteria doubles every hour. what type of function best represents the growth of the bacteria?
Answers
An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.
Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.
Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.
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A rectangular fish tank has width w inches, length w + 8 inches, and height 18 - w inches. All dimensions are greater than 6 inches. The volume of the tank is 1440 cubic inches. Find the length, width, and height of the fish a. width: 12 in., length: 20 in., height: 6 in. b. width: 10 in., length: 18 in., height: 8 in. C width: 10 in., length: 8 in., height: 18 in. d. width: 12 in., length: 18 in., height: 8 in.
Answers
Answer:
To find the dimensions of the fish tank, we can set up the equation:
(width) * (length) * (height) = 1440 cubic inches
Substituting the given expressions for the dimensions of the tank, we get:
(w) * (w + 8) * (18 - w) = 1440
This is a quadratic equation in w, and we can solve it using the quadratic formula:
w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)
This simplifies to:
w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2
= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2
We can further simplify this equation by factoring:
w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2
We can then solve for w by setting each factor equal to zero:
w - 40 = 0 => w = 40
w - 144 = 0 => w = 144
Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).
Therefore, the dimensions of the fish tank are:
width: 40 inches
length: 48 inches
height: 12 inches
The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.
Step-by-step explanation:
true or false? about 60% of u.s. women older than 16 years are either currently employed or looking for work.
Answers
Answer: True
Step-by-step explanation:
Simple.
How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
Answers
Answer:
Step-by-step explanation:
To find the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
compound interest = principal * (1 + rate/n)^(n*t) - principal
where "principal" is the initial amount of money, "rate" is the annual interest rate, "n" is the number of times the interest is compounded per year, and "t" is the number of years.
Plugging in the given values, we get:
compound interest = $50,000 * (1 + 0.064/4)^(4*10) - $50,000
= $50,000 * (1.016)^40 - $50,000
= $50,000 * 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly is $28,167.50.
If DG=FG=7, m∠DEG=u+21°, and m∠FEG=2u, what is the value of u?
Answers
The value of u is 21.
What is Congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given:
DG=FG=7, m ∠DEG=u+21°, and m ∠FEG=2u,
As, from the Diagram
DE = FE (Given)
DG= FG ( Given)
GE= GE (Common)
So, ΔDEG ≅ ΔFEG by SSS Rule.
<DEG = <FEG (CPCT)
u + 21 = 2u
2u - u= 21
u=21
Hence, the value of u is 21.
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A small technology company started offering shares of stock to investors in 1987. At that time, the price of one share of stock was $0.39. Since then, the company has experienced rapid growth. Twenty-two years later, the price of a single share of stock has risen to over $110. One scatterplot shown summarizes the number of years since the initial stock offering in 1987 and the price of the stock, while the other compares years since 1987 to the log of stock price.
Based on these scatterplots, what type of model is most appropriate for summarizing the relationship between year and stock price?
A linear model is appropriate because the scatterplot of the transformed data is roughly linear.
An exponential model is appropriate because the scatterplot of time and log price is increasing.
An exponential model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
A power model is appropriate because the scatterplot of time and price shows a curved relationship.
PLS HURRY
Answers
These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
What is linear model ?These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).
Otherwise, we can simulate the relationship using an exponential model.
An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.
By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.
As a result, even though the time and price scatterplot is curved, a linear model is adequate.
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Which function has the least slope?
OA.
B.
y =
x +15
y = x - 12
C. y = 5x + 23
D. y =
=
7x6
Answers
What value of w makes the equation 3(−4w−5)=−7(5+w) true?
Answers
4 is the value of w which makes the equation true.
What is an equation?
There are many different ways to define an equation. A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.There are three main types of equations depending on the degree. More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A quadratic equation must have at least one variable with an exponent of 2.A third-order equation is a cubic equation. Cubic equations need the exponentiation of at least one variable.It is given that,
3(−4w−5)=−7(5+w)
by solving the equation,
-12w-15=-35-7w
12w-7w=35-15
5w=20
w=20/5
∴w=4
Hence, 4 is the value of w which makes the equation true.
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4/5 divided by 1/3 equals?
Answers
Answer:
4/15
Step-by-step explanation:
reciprocal of 1/3 then cross multiply
14% out of 100% equals how many people out of 10?
Answers
Answer:
1.4 people out of 10
Step-by-step explanation:
Just divide it by 10
Answer:
only 4 people
Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
Answers
The value of inserting area of an array is 0.02
What is meant by area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
Find:
Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
Therefore the value of inserting area of an array is 0.02
The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02
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Find the sum of the terms.
The numerator of the simplified sum is
Answers
Answer:
numerator = 4x + 6
Step-by-step explanation:
x²+3x + 2
(x+2)(x+1)
x/(x+2)(x+1) + 3(x+2)/(x+2)(x+1)
(x+3x+6)/(x+2)(x+1)
(4x+6)/(x+2)(x+1)
The perimeter of a rectangle i 104m the length i 7m more than twice the width. What are the dimenion of the rectangle
Answers
Size will be 37 L x 15 W.
What is perimeter?Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.
Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the breadth.
Let L be the length and W be the width
L = 7 + 2*W
P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;
104 = 14 + 6W
6*W = 90 ;
W = 15 L = 37
Hence the dimension is 37*15
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question is in the image, i need the method answer for part b.
the question says: "the diagram shows the position of two ships, A and B, and the coastguard station, C."
Answers
Step-by-step explanation:
it seems like you understood the law of cosine (extended Pythagoras for non-right-angled triangles) and applied it mostly correctly for a).
but you made a little typo : suddenly, in the second half of the formula you changed the side length BC from 83.1 to 81.3. but it is 83.1.
so, the correct calculation is
a² = 83.1² + 95.5² - 2×95.5×83.1×cos(101) =
= 16,025.86 - 15,872.1×cos(101) =
= 16,025.86 - -3,028.539456... =
= 19,054.39946...
a = sqrt(19,054.39946) = 138.037674...
the rounded result is the same (138 km), but just for your information, and also, I want to use the correct numbers for b)
for b) we need to know :
bearings are angles, measured clockwise from north (north would be 0°).
when ship A looks to station C, the bearing is 146°.
when ship A looks to ship B, the corresponding bearing is 146 - the triangle angle at A (because that is how far we have to turn from looking at C to looking at B).
so, now, we need to apply the law of cosine again. this time to get angle A, as we have now side a.
c² = a² + b² - 2ab×cos(C)
and we want to get C, means now (since you called the baseline "a" in the first part)
83.1² = 95.5² + a² - 2×a×95.5×cos(angle A)
6,905.61 = 9,120.25 + 19,054.39946... - 2×138.037674...×95.5×cos(angle A)
6,905.61 = 28,174.64946... - 26,365.19574...×cos(angle A)
-21,269.03946... = -26,365.19574...×cos(angle A)
cos(angle A) = -21,269.03946.../-26,365.19574...
= 0.806708953...
angle A = 36.22437773...°
therefore, the bearing from A to B is
146 - 36.22437773... = 109.7756223...°
Find the miing number
A number increaed by 25%. It i decreaed by __? But after decreaing it, it i the ame tarting number
Answers
When a number is first increased by 25% then if it is decreased by 25% , we will get the same starting number. hence the net increased or decreased value is zero.
What is net decrease?A decline in net income is a change from one period to the next in the amount of money you have after deducting your expenses from your revenues.
How do you calculate the net?There are two possible outcomes for net income. Your business has a positive net income when revenues exceed expenses. You have a negative net income, commonly referred to as a net loss, if all of your expenses exceed all of your revenues.
let the number is x
first it is increased by 25%
so,
x+(25/100)x=(125/100)x
now according to second condition,
we have to find a value by which it is decreased so we get the same number.
so, let that decreased value is y;
(125/100)x-y=x
-y=x-(125/100)x
-y=-(25/100)x
cancelation of sign;
y=25%
so this is our required value.
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What will happen to the graph of the line y = -54x + 3 if you change -54 to 54?
Imagine Math
Answers
fraction find the missing number 1/2 of 30= 1/4=
Answers
The missing number in the equation 1/2 of 30 = 1/4 is 60
How to determine the missing number?From the question, we have the following parameters that can be used in our computation:
1/2 of 30 = 1/4
This equation can be properly expressed as
1/2 of 30 = 1/4 of __
Represent the blank with a variable x
So, we have the following representation
1/2 of 30 = 1/4 of x
Express as products
1/2 * 30 = 1/4 * x
Multiply both sides by 4
This gives
x = 4 * 1/2 * 30
Evaluate
x = 60
Hence, the missing number is 60
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9
Are the following equations the same line? *
y - 3 = 4(x - 2)
2)
and
and y + 2 = 4(x + 7)
no, because they are not the same in slope - intercept form
it would be impossible to tell
yes, because both equations are the same in slope - intercept form
(5 Points)
Answers
Answer: No, because they are not the same in slope - intercept form
Step-by-step explanation:
First, we will distribute and simplify into slope-intercept form.
Equation 1:
y - 3 = 4(x - 2)
y = 4(x - 2) + 3
y = 4x - 8 + 3
y = 4x - 5
Equation 2:
y + 2 = 4(x + 7)
y = 4(x + 7) - 2
y = 4x + 28 - 2
y = 4x + 26
We see that the answer to this question is "No, because they are not the same in slope - intercept form" as they have different y-intercepts, one being -5 and one being 26.