how far is the end of his shadow from the bottom of the lamppost after 8 seconds. use similar triangles to solve the problem
Answers
The Distance from bottom of lamppost is 57.142 ft.
What are similar triangles?Triangles with the same shape but different sizes are called similar triangles. Examples of similar objects include squares with any side length and all equilateral triangles. To put it another way, if two triangles are similar, their angles are the same and their sides are the same size. The "~" symbol indicates the triangular resemblance here.
Given the height of lamp post is 20 ft
height of man is 6 ft
man walking away with speed of 5 ft per sec
distance covered 8 sec is 8 x 5 = 40 ft
let us consider a triangle ΔABC and consider the triangle with man ΔDEC
which is inside ΔABC as shown in figure,
AB = 20 ft, DE = 5 ft and AD = 40 ft
consider ΔABC and ΔDEC
∠BAC = ∠EDC = 90⁰
∠BCA = ∠ECD = common angle
so ΔABC ~ ΔDEC by (AA property)
according to similar triangles
AB/DE = AC/DC
let DC be x and AC is 40 + x
substitute the values
20/6 = (40 + x)/x
20x = (40 + x)6
20x = 240 + 6x
14x = 240
x = 17.142ft
AC = AD + DC = 40 + 17.142 = 57.142 ft
Hence the Distance from bottom of lamp post to the end of shadow is 57.142 ft.
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Related Questions
-2x + 15y + z = 44
4x + 3y + 3z = 18
-3x+6y-z = 8
Answers
The system of equation is inconsistent as these three equations does not give any solution.
How to solve three variable equations?
In comparison to equations with two variables, a three-variable linear equation requires a little more work to solve. The extra variable is the cause of this complexity.
Even if there are various ways to solve this kind of equation, the elimination technique is still the simplest.
To solve three variable linear equations using the elimination approach, follow these steps:
1. Avoid using fractions and decimals and write all the equations in standard form.
2. Pick an appropriate variable to remove.
3. Remove the chosen variable from any two of the three equations.
4. Choose another set of the two equations, and then take the same chosen variable out.
5. For the two variables they each include, solve the two equations from stages three and four.
6. Replace the answer in fifth step.
7. Reverify by putting them again in the equation.
So according to these given Equations we have to find the value of x, y and z respectively,
-2x + 15y + z = 44
4x + 3y + 3z = 18
-3x+6y-z = 8
After solving these three equations we do not get any solutions.
Hence the system of equations is inconsistent.
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a particular bank has two loan modification programs for distressed borrowers: home affordable modification program (hamp) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-hamp modifications, where the bank does not receive a bonus from the federal government. in order to qualify for a hamp modification, borrowers must meet a set of financial suitability criteria. what type of hypothesis test should we use to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications?
Answers
Hypothesis test for µ1 – µ2 can be used to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications.
The Independent Samples t Test analyses the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. Independent Samples t Test is known as parametric test.
The population means are deemed to be different if the two-sample means are sufficiently dissimilar from one another.
The null and alternative hypothesis for the programs is
H0: μ1 - μ2=0
H1: μ1 - μ2 ≠0
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HELP NOW A dugout needs to reach at least 54 feet below ground level. This means it needs to be more than 2 1/4 times its current depth. This depth is represented by the inequality 2 1/4d<−54, where d is the current depth of the dugout.
Select from the drop-down to correctly interpret the solution of this inequality.
The current depth of the dugout is *Choose..* feet below ground level.
a. at most 24
b. deeper than 24
c. less than 24
Answers
The depth of the dugout is less than 24.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
[tex]2\frac{1}{4}d < -54[/tex]
Where d is the depth of the dugout.
We have to find the depth of the dugout.
Now to simplify the inequality.
[tex]2\frac{1}{4}d < -54[/tex]
convert improper fraction into a fraction.
[tex]2\frac{1}{4} = \frac{9}{4}[/tex]
⇒ 9/4d < -54
Multiply both sides by 4/9
⇒ d < -54 x 4/9
d < -6 x 4
d < -24
Hence, the depth of the dugout is less than 24.
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3. Students are taking three busses to go on a field trip. On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12 To calculate the total students, their chaperone, Ms. Flores decides to add 18 and 12 to get 30 and then adds 14 to get 44. What property is Ms. Flores using to add these numbers in this order?
Answers
Ms. Flores using to add these numbers in this order is follow Commutative Property of Addition.
What is Commutative Property of Addition?
No matter what sequence the addends are in when we add two or more integers, the result is always the same. This characteristic may be expressed as A + B Equals B + A. In this case, 2+4=4 + 2 = 6. Due to the fact that the total of both phrases is 6, 2+4 is equivalent to 4+2. The Commutative Property of Addition refers to this.
On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12=44.
Ms. Flores decides to add 18 and 12 to get 30
18+12= 30
And then adds 14
30+14=44
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I need so much help please save me
Answers
Answer:
Step-by-step explanation:
One of the Answers is C
function rule to find f(3)
Answers
Answer:
30
Step-by-step explanation:
Substitute and multiply :))
f(3)=10(3)
f(3)=30
The legs of a right triangle are 3 units and 6 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points)
Question 4 options:
1)
5.20 units
2)
6.71 units
3)
9.00 units
4)
18.00 units
Answers
The length of the hypotenuse is 6.71
How to calculate the length of the hypotenuse ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
[tex]{\displaystyle a^{2}+b^{2}=c^{2},}[/tex]
Given ,
Pythagorean therum
a^2 + b^2 = c^2....a and b are ur legs and c is the hypotenuse
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2...take the sqrt of both sides....this eliminates the ^2
sqrt 45 = c
6.708 rounded = 6.71 = c
Therefore the length of the hypotenuse is 6.71
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How do I find the sum of the measures of the marked angles?
Answers
Answer: Total angles on the 4
Step-by-step explanation:
The sum of the marked angles = Total angles on the 4 straight lines – Sum of the interior angles of the quadrilateral. Sum of interior angles of polygon of 4 sides = (4 – 2) *1800 =3600
Hence, sum of the marked angles = 4 * 180° – 360° = 720° – 360° = 360°
Kayla is working two summer jobs, making $10 per hour lifeguarding and $21 per
hour tutoring. Last week Kayla worked 4 times as many hours tutoring as she worked
lifeguarding and earned a total of $188. Write a system of equations that could be
used to determine the number of hours Kayla worked lifeguarding last week and the
number of hours she worked tutoring last week. Define the variables that you use to
write the system.
Answers
Answer:
10L + 21t = 188
t = 4L
Step-by-step explanation:
Let L be the number of hours spent lifeguarding and t be the number of hours spent tutoring. Kayla earned $188 total, so 10L+ 21t = 188(the number of hours spent lifeguarding/tutoring times how much she gets paid every hour). We also know that she spent 4 times longer tutoring than lifeguarding, so t = 4L. These are our systems of equations.
a right triangle's height is 3 times the length of its base. if the area of the triangle is 150, what is its height?
Answers
The height of the right triangle if the area of the triangle is 150 square units = 30 units
In this question, we have been given a right triangle's height is 3 times the length of its base.
We need to find the height of the right triangle if the area of the triangle is 150 square units.
Let h be the height and b is the base of the right triangle.
A right triangle's height is 3 times the length of its base.
So we get an equation,
h = 3b ............(1)
Using the formula of area of right triangle,
A = 1/2 * b * h
150 = 1/2 * b * 3b .........(from equation (1))
300 = 3b^2
b^2 = 100
b = 10
Subatitute above value of b in equation (1),
h = 3 * 10
h = 30 units
Therefore, the height of right triangle is 30 units
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Write an equation of a line in slope-intercept form for the table
Answers
The equation of the line in slope-intercept form is y = -2x+8
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope and b is the y-intercept
Given the table, pick any two points in order to find the slope:
point 1: x₁ = 0, y₁ = 8
point 1: x₂ = -2, y₂ = 12
slope (m) = (y₂-y₁) / (x₂-x₁)
slope (m) = (12-8)/(-2-0) = 4/(-2) = -2
Using y = mx+b and x₁ = 0, y₁ = 8:
8 = -2(0) + b
b = 8
y = -2x+8
Thus, the equation of the line is y = -2x+8
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if you are sexually active, what are the odds of you contracting an sti by the time you are 25 years old?
Answers
The odds of you contracting an sti by the time you are 25 years old is 50%.
Even if a person has only had one physical relationship, that partner could be infected. Of course, the risks of contracting STDs (also known as sexually transmitted illnesses, or STIs) increase if a person has unprotected intercourse with a variety of partners.
Many persons with STDs have no evident indications or symptoms. As a result, individuals may assume they are "clean" and inform partners they don't need to use a protection.
But that's not a good idea. For example, almost six out of ten young people infected with HIV are unaware of their status. As a result, they risk infecting others with the AIDS virus.
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Use synthetic division to find the result when 3x^{4}-7x^{3}-14x^{2}+15x+273x
4
−7x
3
−14x
2
+15x+27 is divided by x-3x−3.
Answers
3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.
what is polynomial?Algebraic expressions called polynomials include constants and indeterminates.
Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers.
Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
According to our question-
-3x3 + 2x2 + 11x - 20 + (10/(-x-7)) = 3x4 + 19x3 - 25x2 - 57x + 150
In order to perform synthetic division, we must first remove the minus sign from the divisor and write out
-7 | -3 -19 25 57 -150
| 21 -14 -77 140
-3 2 11 -20 -10
obtain that
3x4 + 19x3 - 25x2 - 57x + 150 / (-x-7) is equivalent to 3x4 - 19x3 - 25x2 - 57x + 150 / (x+7) is equivalent to 3x3 + 2x2 + 11x - 20 + (10/(-x-7)).
Hence, 3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.
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how many license plates can be made using either 3 digits followed by 3 letters, or 3 letters followed by 3 digits?
Answers
Answer:
infinite
Step-by-step explanation:
the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite
-hope this helps-
15[tex]\frac{15}{3} =\\[/tex]
Answers
The quotient that represents the fraction 15/3 is given as follows:
5.
How to obtain the quotient from the fraction?A fraction has the standard notation given as follows:
Fraction = x/y.
In which the terms have the technical names given as follows:
The top term of the fraction x is called the numerator of the fraction.The bottom term of the fraction x is called the denominator of the fraction.Then the quotient is obtained as the division of the numerator by the denominator.
In this problem, the fraction is given as follows:
15/3.
Then the numerator and the denominator are given as follows:
Numerator: 15.Denominator: 3.Then the quotient is given as follows:
15/3 = 5.
As the division of 15 by 3 has a result of 5.
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The table and scatter plot show the number of ice cream stand customers along with the high temperature for a given day. The line of fit represents the predicted number of customers y, on a day with a high temperature of x°F. Which statement correctly analyzes the residuals?
High Temperature (°F) Customers
82 805
76 612
91 1218
87 1074
85 894
79 675
A)
The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.
B)
The smallest residual is 14, and the largest residual is 51. The largest residual does not correspond to an outlier in the data.
C)
The smallest residual is 18, and the largest residual is 45. The largest residual corresponds to an outlier in the data.
D)
The smallest residual is 18, and the largest residual is 45. The largest residual does not correspond to an outlier in the data.
Answers
Based on the information provided, the correct statement is: The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.
A residual is the difference between the actual value of the dependent variable (in this case, the number of customers) and the predicted value of the dependent variable based on the model (in this case, the line of fit). In other words, it is the error or deviation between the observed data and the model.
In this case, the smallest residual is 14, and the largest residual is 51. This means that the model is most accurate when predicting the number of customers on days with temperatures close to 82°F and least accurate when predicting the number of customers on days with temperatures close to 91°F. The large residual of 51 corresponds to an outlier in the data, which means that the model is not a good fit for this data point and may not accurately predict the number of customers on days with temperatures close to 91°F.
Option A is correct because it correctly describes the range and magnitude of the residuals and identifies the largest residual as corresponding to an outlier in the data. Options B, C, and D are all incorrect because they either do not correctly describe the range or magnitude of the residuals or do not correctly identify the largest residual as corresponding to an outlier in the data.
What do you mean by statistical?
statistics is defined as: the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
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PLEASE HELP AND FAST! ILL GIVE BRAINLIEST AND 50 POINTS BUT MAKE SURE YOU INCLUDE WORK!!!
Answers
if you want to find 15% off, you can do the total price, (24.95)(2), -(0.15)(24.95)(2)
part b.
49.9-7.485≈42.42
sale price=49.9
discounted price=42.42
part c.
100-53.46=46.54(change)
46.54/42.42=1.0971%(tax rate)
46.54-42.42=4.12(sales tax)
Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet. The enclosed area of the Alamo Mission was 480 feet long and 160 wide.
What should the length of the enclosed area of the scale model be in inches?
Responses
Answers
Representative fraction is a form of scale that can be used to change the size of an object to form an image. The required length is 32 inches.
A scale is a fraction of numbers that can be used to either increase or decrease the size of a given object. It is majorly referred to as representative fraction in scale drawing.
Representative fraction = [tex]\frac{length on drawing}{original length}[/tex]
In the given question, we have;
12 inches = 1 feet
x inches = 30 feet
So that:
x = 30 x 12 inches
= 360 inches
representative fraction = [tex]\frac{2 inches}{360 inches}[/tex]
= 5.56 x [tex]10^{-3}[/tex]
Thus, given that the length of the Alamo Mission is 480 feet long. Then:
480 feet = 480 x 12 inches
= 5760 inches
So that,
the required length in inches = 5760 x 5.56 x [tex]10^{-3}[/tex]
= 32 inches
Therefore the expected length of the Alamo Mission is 32 inches.
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Evaluate one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.
1
1.7
2.89
3.4
Answers
The given exponents simplified as 2.89. Therefore, option C is the correct answer.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
Given that, one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.
Now, ((1.7)⁶÷(1.7)⁵)²
= (1.7)²
= 2.89
The given exponents simplified as 2.89. Therefore, option C is the correct answer.
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function rule to find f(10)
Answers
Answer:
19
Step-by-step explanation:
replace x with 10
f(10)=9+10
f(10)=19
hopes this helps please mark brainliest
Ally got a haircut for $45. She wants to leave a 20% tip. How much money should she give the hair dresser altogether?
Answers
Answer:
$9
Step-by-step explanation:
20*45/100=9
So Ally should tip $9
Answer
$9.00
Reason
(45 * 0.20) = 9.
A zookeeper ha a 28 gallon of water. He divide the water equally amoung 13 animal. How many gallon of water doe each animal get?
Answers
If zookeeper have to divide the 28 gallon of water equally among 13 animal then each animal will get 2.15 gallon of water.
How much means 1 gallon?8 pints, 4 quarts, or 16 cups make up a gallon. Depending on whether you use Imperial or Metric measurements, there are 128 fluid ounces in a gallon.
Is 3 liters the same as 1 gallon?The volume of a gallon is about equal to 3.78541 liters. Consequently, a gallon is larger than three liters.
According to given to given condition
total amount of water:
=28 gallon
no. of animals:
=13 animal
then each animal get water:
=28/13
=2.15 gallon of water
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a solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. the total volume of the solid is 12 cubic centimeters. find the radius of the cylinder that produces the minimum surface area of the solid.
Answers
11.4 centimeters is the radius of the cylinder .
What does volume mean in plain terms?
The capacity of a solid shape is determined using volume, a three-dimensional quantity.
It implies that a closed figure's volume determines how much three-dimensional space it can fill.
The volume of a cylinder is given by
v = πr²h
The total volume of the two hemispheres is given by
v' = 2× 2/3 πr³
v' = 4/3 πr³
Now, the total volume of the solid is given by:
[tex]V_{T}[/tex] = πr²h + 4/3 πr³
Now, substitute the value of the total volume in the above expression and then solve for h.
12 = πr²h + 4/3 πr³
h = 12/πr² - 4r/3
Now, the surface area of the curved surface is given by:
A = πrh
Now, the surface area of the two hemispheres is given by
A' = 2 × (2πr² )
A' = 4πr²
Now, the total area is given by
[tex]A_{T}[/tex] = 2πr ( 12/πr² - 4r/3) + 4πr²
Simplify the above expression.
[tex]A_{T} =[/tex] 24/r + 4πr²/3
Now, differentiate the total area with respect to 'r'.
[tex]\frac{dA_{T} }{dr}[/tex] = -24/r² + 8πr/3
Now, equate the above expression to zero.
0 = -24/r² + 8πr/3
Simplify the above expression in order to determine the value of 'r'.
8πr³ = 60
r = 11.4
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4. Express the following in exponential form: 4x 4x4 x5x5x5
Answers
Answer: 4^3 * 5^3
Step-by-step explanation: 4 repeats itself 3 times and 5 repeats itself 3 times
4^3 * 5^3
Put the numbers in numerical order
4 comes before 5
Answer:
[tex] { 4}^{3} \times {5}^{3} [/tex]
Step-by-step explanation:
I'd assume your x's stand for multiplication, so using that logic there are three fours and three fives. Each being multiplied by itself, so the simplified/exponential version of the equation is:
[tex] {4}^{3} \times {5}^{3} [/tex]
Make sure you put in numerical order (4 goes before 5).
If X is less than 0Y is greater than zero and X plus Y equals V which statement about Z is true
Answers
four friends do yardwork for their neighbors over the weekend, earning $15,$20,$25, and $40, respectively. they decide to split their earnings equally among themselves. in total how much will the friend who earned $40 give to the others?
Answers
D would give A $10 and B $5 in total amount will the friend who earned $40 give to the others .
what is amount ?The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by. I still provide some services to them. Definitions of quantity, lot, measure, and size Additional words for "quantity".
calculation
Let A, B, C, and D each stand in for one of the four buddies.
A made $15 in earnings.
B made $20 in revenue.
C made a profit of $25.
D made $40 in revenue.
Total earnings equal 15 plus 20 plus 25 plus 40.
$100 was earned overall.
Each friend ought to receive an equal share;
Each income is calculated as follows: total income /friends
Adding a substitute to the equation, we have;
Each income equals 100/4
$25 equals each earnings.
D would therefore become; given $40.
D = $40 - $25
D = $15
As a result, D would give A $10 and B $5.
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if l lll m, solve for x (9x+25)° (13x-19)° (17y+5)°
Answers
The angles, x = 11 and y = 3,if l ll m,
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
A transversal intersects the parallel lines marked by the letters "l" and "m.
The two suplementary angles have the radii (13x - 19°) and (17y + 5)°, respectively.
Thus, (13x - 19)° plus (17y + 5)° equals 180°.
13x + 17y = 180 + 14
13x + 17y = 194 ————(1) (1)
The comparable angles are (9x + 25) and (13x - 19).
Consequently, (9x + 25) = (13x - 19)
9x - 13x = -19 - 25
-4x = -44
x = 11
By changing equation's value for 'x' (1),
13x + 17y = 194
13(11) + 17y = 194
17y = 194 - 143
17y = 51
y = 3
As a result, the solution will be x = 11 and y = 3.
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For what value of k are the graphs of 12y = 9x + 8 and 4y = k(x + 4) parallel?
perpendicular? I HAVE THE ANSWER, just need step to step explanation on how to solve it (pls be clear, answers in pic)
Answers
Answer:
parallel: k = 3perpendicular: k = -16/3Step-by-step explanation:
You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.
ParallelThe slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...
y = k/4x +1y = 3/4x +2/3For parallel lines, we want to choose the value of k so that the slopes are equal:
k/4 = 3/4
k = 3 . . . . . . . . multiply by 4
PerpendicularThe slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...
(k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1
k = -16/3 . . . . . . . . . multiply by 16/3
__
Additional comment
The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.
8th grade math help pls
Carrie Mae is designing a brace for a large rectangular painting. The painting measures 60 inches by 35 inches. What is the measure of the diagonal brace? Round you answer to the nearest tenth of an inch.
Answers
The measure of the diagonal brace of the rectangular painting is 69.5 inches.
What is a diagonal?A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.
The diagonal of the brace and the length of one side and width of one side form a right-angled triangle and by Pythagoras we have
diagonal^2 = length(L)^2 + width(W)^2
diagonal^2 = 60^2 + 35^2
diagonal^2 = 3600 + 1225
diagonal^2 = 4825
diagonal = [tex]\sqrt{4825}[/tex]
diagonal = 69.5 inches
In conclusion the diagonal of the brace is 69.5 inches
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Find the roots of the factored polynomial.
(x–3)2
Write your answer as a list of values separated by commas.
Answers
Answer:
×=3
......................