An architect wants to draw a rectangle with a diagonal of 13 centimeters. The length of the rectangle is to be 3 centimeters more than triple the width. What dimensions should she make the rectangle?
Answers
Answer:
The rectangle is 3.2 cm by 12.6 cm
Step-by-step explanation:
See attached image for a diagram.
Choose w to represent the width because the length is described by referring to the width: it's 3 more than (add 3) triple (multiplied by 3) the width.
Length = 3w + 3
The diagonal forms two right triangles, each with leg = w, other leg = 3w + 3, hypotenuse = 13.
The Pythagorean Theorem says [tex](\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2[/tex] so
[tex]w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\[/tex]
Now solve using the Quadratic Formula with [tex]a=5,\,b=9,\,c=-80[/tex].
[tex]w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2[/tex]
The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.
Related Questions
An equation always, sometimes, never has one solution?
Answers
Answer: An equation may have more than one solution, or the solution(s) may be complex, rather than real, but it will always have one solution - and sometimes more than one.
Step-by-step explanation:
57:12
Which statement is true for the net and the solid it will form when it is folded?
7cm
8 cm
32 cm
a
b
front
с
8 cm
d
The lath of sidohune the lonth of cidae
Answers
Answer:
d
Step-by-step explanation:
What are the intercepts of y = 4x − 2?
A. (2, 0) and (0, 0.5) B. (2, 0) and (0, 5) C. (2, 0) and (0, -2) D. (0.5, 0) and (0, -2)
Answers
Answer:
D. (0.5, 0) and (0, -2)
Step-by-step explanation:
We have the following equation:
[tex]y = 4x - 2[/tex]
x-intercept:
The x-intercept of an equation is the value of x when [tex]y = 0[/tex]. So
[tex]y = 0[/tex]
[tex]4x - 2 = 0[/tex]
[tex]4x = 2[/tex]
[tex]x = \frac{2}{4}[/tex]
[tex]x = 0.5[/tex]
So (0.5,0) is one of the intercepts
y-intercept:
The y-intercept of an equation is the value of y when [tex]x = 0[/tex]. So
[tex]y(0) = 4(0) - 2 = 0 - 2 = -2[/tex]
So (0, -2) is the other intercept.
The correct answer is given by option D.
the value of y is directly proportional to the value of x. if y =35 when x=140, what is the value y when x=70
Answers
Answer:
17.5
Step-by-step explanation:
35÷y = 140 ÷ 70
or, 35 = 2y
or, y= 17.5
Which point is located at the origin?
Answers
Answer:
A
Step-by-step explanation:
A is the answer because the origin is located at point (0,0)
Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences.
Answers
Answer:
Tessa is correct. They have enough money.
Please read Comfort Zone on Wattpad!!!!!!
if cos theta = 3/5 and theta is in quadrant 4, tan 2 theta =
Answers
Answer:
16/9.
Step-by-step explanation:
I am assuming you mean tan^2 theta.
The adjacent side of the triangle drawn in Q 4 = 3 (as cos theta = 3/5.
The opposite side of the triangle drawn in Q 4 = sqrt(5^2-3^2) = 4.
The tangent is negative in Q 4
So tan theta = -4/3.
tan^2 theta = 16/9.
Find the inverse for each relation:
1. [(4,2),(5,1),(6,0),(7,-1)}
Answers
Answer:
the inverse for each relation:
1. [(4,2),(5,1),(6,0),(7,-1)} is
{(2,4),(1,5),(0,6),(-1,7)}
- 2 1/3 - (-5) =
gimme please, its the i ready thingie
Answers
Answer:
8/3
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form:
8 /3
Decimal Form:
2. 6
Mixed Number Form:
2 2 /3
find the are of the triangle
Answers
It’s a, 49
Step-by-step explanation:
Area is length x width so you would count how long the triangle is and how wide it is so
7 x 7 is 49
What is the result when you combine only the constants in the following expression?
3 a minus 6 b + 3 minus 7 a + 10
Answers
Answer:
6b-4a+13
Step-by-step explanation:
3a-6b+3-7a+10
3+10=13
3a-7a=-4a
6b-4a+13
Answer:
13
Step-by-step explanation:
Determine the value of angle ABC?
Answers
Answer:it is about 90-93 degrees and also it is a obtuse
Step-by-step explanation:
it is simple because it the other side to the right says 98 if you put it in it position it is alittle bigger so thats how i got my answer
Answer:
∠ ABC = 62°
Step-by-step explanation:
The inscribed angle ABC is half the measure of its intercepted arc AC
AC = 360° - (138 + 98)° = 360° - 236° = 124° , then
∠ ABC = [tex]\frac{1}{2}[/tex] × 124° = 62°
Find the area of composite figure
Answers
Answer:
c
Step-by-step explanation:
Please help me with this assignment!
Answers
Answer:
Since potential vice presidents are chosen before the election occurs, they are often selected partially due to their potential effect on the election. Presidential candidates often choose running mates who can capture key demographics or who have a high level of experience in an area that voters regard as important.
Step-by-step explanation:
What is the solution to the system of equations below?
y = 2/5 x -3 and x = -10
-
A= (-10, -7)
B= (-10, -1)
C= (-7, -10)
D= (-1, -10)
WILL MARK FIRST CORRECT ANSWER BRAINLIEST
Answers
Answer:
here u go gurly
Step-by-step explanation:
PLEASE HELP In 2010 the population of India was 1,231,000,000. By 2016, the population had increased by 7.5%.The land area of India is 1, 269,000 miles. What was the population density of India in 2016?
Complete the density statement below, round your answer to the nearest whole number
The population density of India in 2016 was
per
Answers
Answer:
The population density of India in 2016 was of 1042.8 habitants per miles squared.
Step-by-step explanation:
Population density:
Number of habitants divided by land area.
In 2010 the population of India was 1,231,000,000. By 2016, the population had increased by 7.5%.
This means that India's population in 2016 was given by:
1,231,000,000*1.075 = 1,323,325,000
The land area of India is 1, 269,000 miles squared:
1,323,325,000/1,269,000 = 1042.8 habitants per miles squared.
The population density of India in 2016 was of 1042.8 habitants per miles squared.
20 PTS! WILL MARK BRAINLIEST
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 157 square units, and the area of the cross-section of the cylinder is 50π square units. Based on this information, which argument can be made?
The volume of the square prism is one third the volume of the cylinder.
The volume of the square prism is half the volume of the cylinder.
The volume of the square prism is equal to the volume of the cylinder.
The volume of the square prism is twice the volume of the cylinder.
Answers
Answer:
The volume of the square prism is equal to the volume of the cylinder.
Step-by-step explanation:
As per the information depicted the volume of the square prism is equal all to the volume of the cylinder. Hence option C is correct.
What is the square prism?A square prism is thee dimensional cuboid with a base and the top has an equal square while the remaining four faces have a rectangle and the opposite side angles of the square prism are congruent and parallel to each other.
As a square prism have the least two lengths that are equal to each other. Hence the volume of the square prism is equal to the volume of the cylinder as they have the same height and area of cross-section.
Find out more information about the square prism.
brainly.com/question/4315703
4. A prism has a base area of 35 cm2 and a height of 5 cm. What is the volume of the prism?
Answers
Answer:
175cm^3
Step-by-step explanation:
Volume= Length x Width x Height
Length and width =35cm^2
H=5cm
V=175cm^3
Hope this helps!
Solve the system of equations using substitution.
4x – y = 7
3y – 12x = –21
(3, 5)
(6, 17)
no solution
infinite solutions
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
solve by substitution:
solve equation 1 for y: - y = 7 - 4x; divide by -1 to simplify into y = -7 + 4x
Substitute - 7 + 4x into the second equation to obtain:
3(-7 + 4x) - 12x = -21, which yields:
-21 + 12x - 12x = -21, which simplifies 0 = 0
a result of 0 = 0 means infinite solutions such as:
(2,1), (3, 5), (4, 9), (5, 13), (6, 17)....
Answer:
infinite soulutions
Step-by-step explanation:
i just did it and it was right on ed2021...
Find the argument of the complex number z=1+iv3
Answers
Given:
The complex number is:
[tex]z=1+i\sqrt{3}[/tex]
To find:
The argument of the given complex number.
Solution:
If a complex number is [tex]z=x+iy[/tex], then the argument of the complex number is:
[tex]\theta=\tan^{-1}\dfrac{y}{x}[/tex]
We have,
[tex]z=1+i\sqrt{3}[/tex]
Here, [tex]x=1[/tex] and [tex]y=\sqrt{3}[/tex]. So, the argument of the given complex number is:
[tex]\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}[/tex]
[tex]\theta =\tan^{-1}\sqrt{3}[/tex]
[tex]\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)[/tex]
[tex]\theta =\dfrac{\pi}{3}[/tex]
Therefore, the argument of the given complex number is [tex]\theta =\dfrac{\pi}{3}[/tex].
The Sine Function
The average number of customers per day at a home improvement store is given in the following table. The sine regression equation was found to be y = 29.882sin (0.887 x 1.271) + 85.635, where x represents the day where 1 = Sun of the week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use this model to predict the average number of customers on Tuesday. Round to the nearest customer.
a. 70
b. 67
c. 71
d. 64
Please select the best answer from choices provided
Answers
Answer:
D. 64
Step-by-step explanation:
I calculated it logically
2. Sally charges $8.50 an hour to babysit for the first hour and $7.50 an hour each additional hour. Write an expression to
represent the cost Sally charges if x is the number of hours after the first hour.
Answers
Answer:
c = 8.50 + 7.50x
Step-by-step explanation:
c = 8.5 + 7.50x
akin has some money in a box.if 3/8 of the money Is N4.80, how much money does he have in the box
Answers
Answer:
N12.8
Assume the money in the box Is M.
therefore, 3/4 of M=N4.80.
Recall N1=100k..... where k 'kobo'
N4.80=X
X=4.80x100. this gives us 480k.
this implies that 3/4 X M= 480k
therefore by cross multiplication, and dividing by 3; 3M=480 X 4
M = (480 X 4) ÷3
M=1280k
converting from kobo' to Naira. the rate of conversion is;
100k = N1
1280k=?
M in naira= 1280/100
M is N12.8
What’s it the correct answer? I will mark as brainlest
Answers
Answer:
Step-by-step explanation:
(216/4)-20+3(5)
(54)-20+15
34+15 = 49
option 1
Answer:
49
Step-by-step explanation:
(6³ / 4) - 4 * 5 + 3(7 - 2)
= (216 / 4) - 20 + 3 * 5
= (216 / 4) - 20 + 15
= 54 - 20 + 15
= 34 + 15
= 49
Hope it helps
Find the volume of the cone. Round your answer to the nearest hundredth.
A) 129.72m^3
B) 134.04m^3
C) 137.71m^3
D) 143.04
Answers
Answer:
can we get the figure plz
Katie's baby took 3 naps. Each nap was
of an hour long
How long did the baby nap in all? Move numbers to the blanks to answer the question.
Answers
Answer:
the answer is 3 hours
Step-by-step explanation:
it just makes sense
1) Find the missing measures of this
isosceles triangle below .
48°
B.
C
MAC
Answers
Answer:
B measures 66°
C measures 66° .Sum of all angels is 180° .
What is the probability of spinning a yellow?
What is the probability of spinning an odd number?
What is the probability of spinning a number less than 5?
Answers
Answer:
Answer given below
Step-by-step explanation:
P (spinning yellow) = 2 / 8 = 1 / 4
P (Spinning an odd number) = 4 / 8 = 1 / 2
P ( spinning a number less than 5) = 4 / 8 = 1 / 2
Hope it helps
The probability of spinning a yellow is 1/4.
The probability of spinning an odd number is 1/2.
The probability of spinning a number less than 5 is 1/2.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
From the spinner
Blue region = 3
Red region= 1
Yellow region = 2
Purple region = 2
So, the probability of getting Yellow
P (spinning yellow) = 2 / 8
= 1 / 4
and, the probability of getting odd number
P (Spinning an odd number) = 4 / 8
= 1 / 2
and, the probability of getting less than 5
P ( spinning a number less than 5) = 4 / 8
= 1 / 2
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ7
Evaluate: 5 - 3x when X = -2
Answers
Answer:
Rewrite the equation as 5-3-2. -2 is x, as it says in the problem. All you have to do is solve, so you're answer will result in 0. :)
Answer:
Replace the variable x
with -2 in the expression.
5 − 3 x
Step-by-step explanation:
Can somebody help me