Answers
Answer:
Below in bold.
Step-by-step explanation:
(a) Using the Pythagoras theorem:
30^2 = 21^2 + p^2
p^2 = 30^2 - 21^2 = 459
p = √459
= 21.4 cm to nearest tenth.
(b) cos P = 21/30 = 0.70
m < P = 45.57 degrees to nearest hundredth.
Answer:
a) p = 21.4 cm (nearest tenth)
B) P = 45.6° (nearest tenth)
Step-by-step explanation:
As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleFrom inspection of the triangle:
a = PQ = 21b = QR = pc = PR = 30Substitute the given values into the formula and solve for p:
[tex]\implies 21^2+p^2=30^2[/tex]
[tex]\implies 441+p^2=900[/tex]
[tex]\implies 441+p^2-441=900-441[/tex]
[tex]\implies p^2=459[/tex]
[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]
[tex]\implies p=\pm 3\sqrt{51}[/tex]
As p is the length, p can be positive only.
Therefore, p = 21.4 cm (nearest tenth)
To find the angle P, use the cosine trigonometric ratio.
Cosine trigonometric ratio
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = PA = PQ = 21H = PR = 30Substitute the given values into the formula and solve for P:
[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]
[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]
[tex]\implies \sf P=45.572996^{\circ}[/tex]
Therefore, the measure of angle P is 45.6° (nearest tenth).
Learn more about Pythagoras Theorem here:
https://brainly.com/question/27648540
Learn more about trigonometric ratios here:
https://brainly.com/question/26861422
Related Questions
Graph the image of rectangle EFGH after a reflection over the line x= –1
Answers
Answer:
G (1,7)
H (2,7)
F (1,-1)
E (2,-1)
Step-by-step explanation:
The image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
What is a translation?The process of changing the location of the image on the coordinate system will be known as the translation. A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that graph the image of rectangle EFGH after a reflection over the line x= –1. Translated image of the points is attached with the answer below. The translated points are G (1,7), H (2,7), F (1,-1), and E (2,-1).
Therefore, the image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
To know more about translation follow
https://brainly.com/question/12861087
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Two learners are planning to make baskets to raise money for the honors society at their school. Marcia will make baskets out of palms. Norma plans to make baskets out of pine straw. Together, they have $100 to spend on supplies.
The palm baskets cost $4 to make and will sell for $20.
The pine straw baskets cost $3 to make and will sell for $17.
The learners agree that they will each make at least 14 items. Let x represent the number of palm baskets and let y represent the number of pine straw baskets.
Answers
Answer:
3
Step-by-step explanation:
Pretty sure it is the third but sorry if im incorrect
A water tank holds 1,088 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds
1,360 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of
water in the two tanks be the same?
The amount of water in the two tanks will be the same in
weeks.
Answers
The first tank hold 1088 - 5t gallons of water after t weeks, while the seocnd tank holds 1360 - 9t gallons after t weeks.
Both tanks hold the same amount of water when
1088 - 5t = 1360 - 9t
Solve for t :
4t = 272
t = 68
So the tanks will hold the same amount of water after 68 weeks.
The shadows of two vertical poles were measured at the same time to be 6m and 15m long. If the first pole is 8cm long, find the height of the second pole
Answers
Answer:
20 cm
Step-by-step explanation:
Shadow of vertical poles : 6m ; 15m
Length of poles : 8cm ; h
8cm long pole = shadow length, 6m
h cm long pole = shadow length, 15 m
Using cross multiplication :
8cm * 15 m = h cm * 6m
120 = 6h
h = 120 / 6
h = 20 cm
Height of second pole = 20cm
A delivery truck has 40,000 miles on its odometer and travels an average of 22,000 miles per year.
Which function best models the linear relationship?
y = 22,000x − 40,000
y = –22,000x + 40,000
y = 22,000x + 40,000
y = 40,000x − 22,000
Answers
Answer:
Since the truck adds 22,000 PER YEAR, this would be the number we multiply by the variable depending on how many years they are calculating for. So we have y = 22,000x
The truck already has 40,000 miles on it so it s STARTING at 40,000, this is our y-intercept, or b.
Now we have y = 22,000x + 40,000
What is the answer to 10x2x5%20
Answers
Answer:
ITS 0
Step-by-step explanation:
6 Work out the sizes of the angles labelled rº, sº and tº.
Plzzzz help I suck at geometry
Answers
Answer:
t = 30
s = 25
r = 55
Step-by-step explanation:
Let's begin by r
r is angle in quadlitral shape, so the sum of the interior angles = 360
r = 360 - (95 +100+110) = 55
Then Now it's time for ( t )
Look at the triangle whose angles are r, 95 and t. The sum of the measures of the interior angles of triangle is 180
so t = 180 - ( 95 + r) = 180 - (95 + 55) = 30
Similarly, look at the triangle whose angles are r, s and 100
s = 180 - (100 + r) = 180 - (100 + 55) = 25
I hope you find this helpful! If you have any questions, please feel free to ask them in the comments
Please help me with this
Answers
Answer:
1) equation is set up to determine when the cost of printing at home is the same as the cost of printing at the office
2) p = 500 means that, at printing 500 pages, the costs of home versus office printing are the same
Step-by-step explanation:
Answer:
1) No, it does not represent the story.
2) It represents the number of pages.
Step-By-Step Explanation:
1) It has nothing to do with the story.
2) It says: Let p represent the number of pages
Answer the photo below thanks
Answers
Answer:
C. 36 degrees
Step-by-step explanation:
90 + 54 = 144
180 - 144 = 36
you were correct
180 - 90 - 54 = 36.
You selected the right answer.
Please answer please.
Answers
Answer:
Triangles are not similar.
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles are equal in measure.
2). Corresponding sides of the similar triangles are proportional.
From the given triangles,
- Corresponding angles of the given triangles are not equal in measure.
- Ratios of the corresponding sides,
[tex]\frac{KM}{XY}=\frac{CM}{RY}= \frac{KC}{XR}[/tex]
[tex]\frac{53}{53}= \frac{54}{53}= \frac{64}{53}[/tex]
But these ratios are not equal.
Therefore, both the triangles are not similar.
What is the area of an isosceles triangle with side lengths of 22 and 66
Answers
Answer:
726
Step-by-step explanation:
66*22/2=726
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Answers
Answer:
proportional
:)
Whos your favorite character from Miraculous Ladybug?! mines Alya and of course cat noir he kinda cute
Answers
Answer:
CAT NOIR
He's cool and my cousin's fav characters LOL
Step-by-step explanation:
um, he's cool i guess?
Answer:
I like Mari and Luca bc he is rlly cute for me
Answers
Answer:
Step-by-step explanation:
A,B and D
The value of an antique car is modeled by the function V\left(t\right)=10700\ \left(1.125\right)^t , where t is the number of years since 2005.
By what percent rate is the value of the car increasing per year?
a
125%
b
12.5%
c
1.125%
d
0.125%
Answers
Answer:
its c i think
Step-by-step explanation:
I need help with math here is the problem 3(2x+6)
Answers
Answer:
6x+18
Step-by-step explanation:
Step-by-step explanation:
Distribute the 3 to the 2X and 6:
3 x 2X + 6 x 3 = (3 x 2)X + 18 = 6X +18
3. Use distributive property to simplify
a. (-6) * [(-12) + (25)]
C. (+6) * [(-17) + (+28)]
e. (+7) * [(-12) – (+6)]
Solve this answer with solution please
Answers
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:PEMDAStips and formulas:orders of PEMDAS:
parenthesesexponentmultiplication ordivisionaddition orsubstractionleft to rightlet's solve:a)
remove first parentheses and add: -6×[-12+26] =-6×[14]remove third parentheses and multiply:-6×14=-84c)
remove first parentheses and add:(6)×[-17+28]=6×[11]remove third parentheses and multiply: 6×11=66e)
remove first parentheses and substract:7×[-12-(6)]=7×[-12+(-6)]=7×[-18] multiply:7×[-18]=-126car covers x plus 2 kilometre in 1 litre how much distance it will covers in Y litres
Answers
Answer:
y km = (x+2)y km
Step-by-step explanation:
Given that,
A car covers (x+2) kilometre in 1 litre.
We need to find the distance it will cover in y litres.
1 litre = (x+2) km
y km = (x+2)y km
Hence, it will cover (x+2)y km in y litres.
please simplify √16bx⁴
Answers
Answer: 4bx^2
Step-by-step explanation:
Answer:
Hey there!
I got the answer
4bx^4
Step-by-step explanation:
All you have to do is simplify the radicand up into a product of known factors , assuming positive real numbers.
HELP ME PLEASE! i'll give u brainliest
Answers
Answer:
D. Hope that helps!
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
It is D because all fractions are rational numbers, and numbers with decimals can also be fractions, so its like multiplying a fraction with a fraction, It would still be a rational number.
PLEASE HELP
How much pressure is exerted on a science lab floor if the lab
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Answers
Answer:
use pressure =Force /area
Step-by-step explanation:
12000N/1.08
Solve for a.
6a−15=72
A.12
B.27
C.14 1/2
D.9 1/2
Answers
6a-15=72
add 15 to both sides
6a = 87
Divide 6
a = 14.5
Answer:C
Step-by-step explanation:
PLEASE HELP ASAP! What is the slope of the line graphed below?
Answers
Answer:
6/3 simply so 2 your slope is 2
Step-by-step explanation:
Four students are reading books with different numbers of pages. The table shows the number of pages each student has read. Drag each name to order the students from the lowest percentage of their book read to the highest percentage of their book read. Pages Read Total Number of Pages Elliot 105 175 = Elliot Frankie 165 300 Hayden 88 220 = Frankie Ruth 117 260 = Hayden = Ruth
Answers
Answer:
i think is 434.54
Step-by-step explanation:
Answer:
434.54
Step-by-step explanation:
The sale price of an item is Rs 176. If a discount of 20% is allowed on its Marked price, what is the marked price of the item
Answers
Answer: $140.80
Step-by-step explanation:
Original price = Rs. 176.
Marked price has discount that is 20% lower than the above.
= 20% * 176
= $35.20
Marked price = Sales price - discount
= 176 - 35.20
= $140.80
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Answers
Answer:
the top one would be -40x+24, bottom one is x=12
Step-by-step explanation:
uwu
Answer:
a. -40x + 24
b. x = 4
Step-by-step explanation:
-8 * 5x = 40x, -8 * -3 = 24
-5 * -x = 5x
-5 * 4 = -20
40 - 20 = 20
20/5 = 4
Divide 600 kg into 2 boxes so that one box has twice as much in it as the other box. How
much is in the heavier box?
Help please
Answers
Answer:
200 box 1 / 400 box 2
box 2 Step-by-step explanation:
200 + 400 = 600
Answer:
Hello asuna here
600 would be your answer
Step-by-step explanation:
Hope this helps
need help to find X
thank you
Answers
Answer:
121
Step-by-step explanation:
Answer:
63.33 or 190/3
Step-by-step explanation:
1. vertical opposite angles are equal
2. corresponding angles some up to 180°
=> 3x - 20 + 10 = 180
=> 3x = 180+10
=> 3x = 190
=> x = 190/3
=> x = 63.333333333333333
Solve for x . Round to the nearest 100th if needed.
11/ x + 18 = 34
Answers
Answer:
x = 0.69
Step-by-step explanation:
11/x + 18 = 34
11/x = 16
11 = 16x
x = 0.6875 = 0.69
Need help ASAP giving 55 points and a branlist
Answers
Answer:
There are 54 squares on a rubix cube
Step-by-step explanation:
each side has 9 squares, and there are 6 sides, so you multiply 9x6 wich equals 54, so your answer would be
54 squares
Hope this helps! :)