A rectangular rug divided by its diagonal becomes a right angle triangle
The length and width of the rug is 14.1 feet by 11.1 feet
A right angle triangle has the longest side as the hypotenus which is also the diagonal.Diagonal = 18 feet
width = x
length = x + 3
diagonal ² = length ² + width ²
18² = x² + (x + 3)²
18² = x² + x² + 6x + 9
324 = 2x² + 6x + 9
2x² + 6x + 9 - 324 = 0
2x² + 6x - 315 = 0
solve using quadratic formula
x = - b ± √b² - 4ac / 2a
= - 6 ± √6² - 4×2×-315 / 2×2
= -6 ± √36 - (-2520) / 4
= -6 ± √36 + 2520/4
= -6 ± √2556 / 4
= - 6 ± 6√71 / 4
= -6/4 ± 6√71 / 4
= -3/2 ± 3√71/2
x = 11.1392 or -14.1392
The value of x can't be negative
So,
x = 11.1 to the nearest tenth
Therefore, the value of width and length is
width = x
= 11.1 feet
length = x + 3
= 11.1 + 3
= 14.1 feet
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help me with this guys
Let y = cos⁻¹(x), so that cos(y) = x.
For some angle y between 0 and π, cos(y) takes on some value between -1 and 1.
For the y in this range, we have cos(y) = -1/2 exactly when y = 2π/3.
Then
tan(cos⁻¹(-1/2)) = tan(2π/3) = sin(2π/3)/cos(2π/3) = (√3/2)/(-1/2) = -√3
i) Factorise x^2 - x - 20
[tex](x + 4)(x - 5)[/tex]
hope it helps#carryonlearning
see the attachment for the explanation
A biologist observed a population of bacteria that grew at a rate expressed by the exponential equation
f(t)=256e(0.0611t)
where t is in minutes. How long will it take the population to reach 5 times its initial value?
Answer: 26.34
Step-by-step explanation:
The bacteria will take 26.3409 minutes.
What is Exponential Equations?Exponents are used in exponential equations, as the name suggests. We are aware that a number's exponent (or base) tells us how many times the original number has been multiplied. But what occurs if a number's power is a variable? An exponential equation is one in which the power is a variable and a part of the equation.
Given f(t) = 256[tex]e^{0.0611t}[/tex]
initial condition when t = 0
f(0) = 256
to find the time when population reach 5 times its initial value
= 256 x 5 = 1280
f(t) = 1280,
to calculate t
1280 = 256[tex]e^{0.0611t}[/tex]
[tex]e^{0.0611t}[/tex] = 5
0.0611t = ln(5)
0.0611t = 1.60943
t = 1.60943/0.0611
t = 26.3409 minutes.
Hence Bacteria will take 26.3409 minutes to reach 5 times.
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can someone please assist me in these equations!?!?! pls
Answer:
1. -9 because -9x6= -54, -10 because 5 x -10= -50, and x=1 because -2 x 1= -2
Step-by-step explanation:
Answer:
1. = −9
2. = −10
3. = 1
Step-by-step explanation:
What is the solution to this system of equations?
x − 2y = 15
2x + 4y = -18
A. x = 1, y = -6
B. x = 1, y = -7
C. x = 3, y = -6
D. x = 3, y = -7
Answer:
C. x = 3, y = -6
Step-by-step explanation:
You can divide the second equation by 2. Then you have ...
x +2y = -9
This gives you a couple of choices for solution. The x-coefficients match, so subtracting one equation from the other eliminates x:
(x +2y) -(x -2y) = (-9) -(15)
4y = -24 ⇒ y = -6
Adding the two equations eliminates y:
(x -2y) +(x +2y) = (15) +(-9)
2x = 6 ⇒ x = 3
The solution is (x, y) = (3, -6).
_____
Additional comment
I find it quick and easy to use a graphing calculator to find the solution. Many graphing calculators also make it simple to solve systems of equations in matrix form. Either way, you can obtain a solution in little more than the time it takes to enter the equations (or their coefficients).
What is the m 2x-3=5x-12
Answer:
15 is the answer
Step-by-step explanation:
If it was designed as an alternate angle, then it would 63 degrees
Write the equation of the line that passes through the points (9, 3) and (-7, -7).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
a
line.
Answer:
y-3=5/8(x-9)
Step-by-step explanation:
First, we can find the slope using the slope formula : -7-3/-7-9 = -10/-16 = 5/8
Now we can just plug in a point into point slope form
y-3=5/8(x-9)
A restaurant bill is $25.80. How
much is a 20% tip for this bill (NOT
the total)?
Answer:
25 pesos 80 pw
pesos I'm not sure
Step-by-step explanation:
25. 80
how do you solve something like this?
Answer:
-24
Step-by-step explanation:
First, use the equation find the value of x. Then, substitutes the value of x into 9x+12.
A circle has a diameter of 62 meters. What is the circumference of the circle
Answer:
the circumstance is 194.78
Which is the better deal? $39.55 for 7 pairs of jeans OR $22.48 for 4 pairs of jeans
Answer:
$22.48 for 4 pairs of jeans is a better deal.
Step-by-step explanation:
To find the price of one pair of jeans, you divide.
39.55 ÷ 7 = price of 1 pair of jeans
39.55 ÷ 7 = $5.65
22.48 ÷ 4 = price of 1 pair of jeans
22.48 ÷ 4 = $5.62
The price difference between the two prices is 3 cents. So, $22.48 for 4 pairs is a better deal that $39.55 for 7 pairs of jeans.
Hope this helps!
Students in Mrs. Marquez's class are watching a film on the uses of geometry
In architecture. The film projector casts the image on a flat screen as shown in
the figure. The dotted line is the bisector of
each congruence theorem to prove that
need to know.
The given information on the diagram of the projector and the image can
be used to prove the congruency of the triangles.
∠ABD, ∠BDA, and side [tex]\overline {AD}[/tex] on ΔABD are congruent to ∠CBD, ∠BDC, and
segment [tex]\overline {CD}[/tex] on ΔCBD, therefore, ΔABD ≅ ΔCBD, by AAS Theorem
Reasons:
The figure of the projector that casts an image on the screen is attached.
The bisector of the line [tex]\overline {AC}[/tex] = [tex]\overline {BD}[/tex]
From the drawing, we have;
∠ABD ≅ ∠CBD by equal number arc mark.
The two column proof is therefore, presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {BD}[/tex] is perpendicular bisector of [tex]{}[/tex][tex]\overline {AC}[/tex] Given
[tex]\overline {AD}[/tex] = [tex]\overline {CD}[/tex] [tex]{}[/tex] Definition of bisected line [tex]\overline {AC}[/tex]
∠BDC = 90° [tex]{}[/tex] [tex]\overline {BD}[/tex] is perpendicular [tex]\overline {AC}[/tex]
∠BDA = 90° [tex]{}[/tex] [tex]\overline {BD}[/tex] is perpendicular [tex]\overline {AC}[/tex]
∠ABD ≅ ∠CBD [tex]{}[/tex] Given on the diagram
ΔABD ≅ ΔCBD [tex]{}[/tex] by Angle-Angle-Side AAS Congruency rule
The Angle-Angle-Side, AAS, Congruency postulate states that two
triangles are congruent where two adjacent angles and a non included side
on one triangle are congruent to the corresponding two adjacent angles
and a non included side on the other triangle.
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Suppose a binomial trial has a probability of success of 0.7, and 75 trials are performed. What is the standard deviation of the possible outcomes. Round your answer to two decimal places
Answer: 8.22
Step-by-step explanation:
help only answer if you know!!!!
Subtract.
18 7/12−9 4/12
8
8 1/3
9
9 1/4
Answer:
9 1/4
Step-by-step explanation:
I hope this helps! it should be correct
The sports stores price went up in 2013 a bat that cost $45 in 2012 now cost $55 what is the percent of change
Answer:
10/45 = 22.2% change in price
Step-by-step explanation:
new-old/old
A bicycle store costs $1500 per month to operate. The store pays an average of $35 per bike. The average selling price of each bicycle is $85. How many bicycles must the store sell each month to break even?
Answer:
30 bikes
Step-by-step explanation:
the profit from each bike is 50 so then you divide 1500 by 50 and you get 30
Is this the right answer?
Answer:
yes great job!
Step-by-step explanation:
Is this relation a function? Justify your answer.
10
9
8
7
6
.
5
4
3
2
1 2
3
5 6 7
8 9 10
O A. Yes, because every x- and y-value is positive.
B. No, because two points with the same x-value have different y
values.
C. Yes, because the number of x-values is the same as the number of
y-values.
Answer:
C. Yes, because the number of x - values is the same as the number of y-values
Can someone pls help me
Solve for x
Please show your work
Answer:
Hence, the value of x is 9°
Step-by-step explanation:
7x + 14 = 9x - 4. [(Corres. ∠s]
⇛ 7x - 9x = -4 - 14
⇛-2x = -18
⇛x = -18÷-2
⇛x = 18/2
∴ x = 9
NOW,
7X + 14 = 7(9) + 14 = 63 + 14 = 77°.9X-4 = 9(9) - 4 = 81 - 4 = 78°.Read more:
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find the measure of angle 1, given that AB || CD...
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Jordan will hike a trail with the distance of 25 miles at a rate of 5 miles per hour. Write a linear equation to represent the distance Jordan still has to walk after x hours. What does the y-intercept of the equation represent?
Answer:
y = - 4 x + 20
Step-by-step explanation:
The trail is 20 miles
Each hour you go 4 miles, so you subtract that each hour
Jayla made 36 sugar cookies for the class party. Before you got to class the teachers ate 9 cookies, and then your classmates ate 1/3 of the remaining cookies. How many cookies are left for you to eat?
Answer:
9 cookies are left
Step-by-step explanation:
36 - 9 = 27
27 · 1/3 = 9
please help me!!!!!!
Answer:
S.I = P x R x T / 100
Step-by-step explanation:
therefore 8000 x 7 x 5 / 100 = 280000/ 100
= 2800
What is the midpoint of the segment shown below?
10
O A. (6.3)
(2,3)
(10,3)
B. (6,3)
- 10
10
C. (5,3)
-10
D. (533)
SUE
Answer:
b. (6,3)
Step-by-step explanation:
10+2=12
12/2=6
The line is always on 3, so that will be the y coordinate!
The midpoint of the line segment are (6, 3). Therefore, option B is the correct answer.
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2]
From the graph, the coordinate points of ends of line segment are (2, 3) and (10,3).
Here, midpoint = [(2+10)/2, (3+3)/2]
= (6, 3)
Therefore, option B is the correct answer.
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56 - 8 (1/4+2 / 1-3/5)
Simplify the complex fraction in the given expression.
Simplify the complete expression.
[tex]56-8(\frac{\frac{1}{4}+2 }{1-\frac{3}{5} })= 56-8(\frac{2,25}{0,4 })= 56-8.(5,625)=56-45= 11[/tex]
ok done. Thank to me :>
For an art project you are using a piece of cloth out in the shape of an right triangle What’s the area of the cloth?
Answer:
18
Step-by-step explanation:
6*6/2 = 18
GEOMETRY Find the the area of the polygon with the given vertices.
C(1,1) D(1,4)E(4,4)F(4,1)
pls give answer
worth 100
Pls help i will give brainliest!
What multiplication tables should every student memorize.
Answer:
1-15
Step-by-step explanation:
You should at least teach students 1-15 or 1-20
40 cans of food. 30% of cans damaged. how many cans were damaged?
Answer:
12 cans were damaged
EXPLANATION:
Cause When You Divide 4 To Divide 40, It Gives You 100% Calculation, And Subtract 30% from 100% it gives you 70%, which is 28 cans of food
Please tell me what the Point Slope Slope Intercept Standard is for these graphs
Answer:
1st graph:
Slope-intercept is y = -7/2x + 3
Point Slope is y + 4 = -7/2(x - 2)
Standard is 7x + 2y = 6
2nd graph:
Slope-intercept is y = 1/2x - 4
Point Slope is y + 2 = 1/2(x - 4)
Standard is x - 2y = 8
3rd graph:
Slope-intercept is y = 3x - 3
Point Slope is y - 3 = 3(x - 2)
Standard is 3x - y = 3
4th graph:
Slope-intercept is y = -2/7x - 4
Point Slope is y + 2 = -2/7(x + 7)
Standard is 2x + 7y = - 28
Step-by-step explanation:
Point Slope formula⤵⤵⤵:
[tex]y - y _{1} = m(x - x _{1})[/tex]
Slope-intercept formula⤵⤵⤵:
[tex]y = mx + b[/tex]
Standard formula⤵⤵⤵:
[tex]Ax + By = C[/tex]
Sorry this took a while, I was doing other stuff for school. I also had to relearn point slope for this, so it took me some time to figure it out. Hope this helps though :)
What’s the answer to this plssss??
Answer:
2c²
Step-by-step explanation:
8c³d² / 4cd²
= 2 * c²
= 2c²