Practice 4b
In the diagram, PQRS is a rectangular sloping surface, PQTU is a rectangle on horizontal ground and RI and
SU are vertical lines. PQ = SR=UT = 45 cm, QR = PS = 32 cm and angle RQT= 38º.

Calculate
PR,
(b) RT, and
(c) angle RPT

Practice 4bIn The Diagram, PQRS Is A Rectangular Sloping Surface, PQTU Is A Rectangle On Horizontal Ground

Answers

Answer 1

Answer:

(a) PR = 55.2 cm

(b) RT = 19.7 cm

(c) <RPT = [tex]20.8^{o}[/tex]

Step-by-step explanation:

(a) to determine the value of PR, apply the Pythagoras theorem to PQR.

PQ = 45, and SP = QR = 32. So that;

[tex]/hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]/PR/^{2}[/tex] = [tex]45^{2}[/tex] + [tex]32^{2}[/tex]

          = 2025 + 1024

          = 3049

PR = [tex]\sqrt{3049}[/tex]

     = 55.218

PR = 55.2 cm

(b) To determine RT, apply the appropriate trigonometric function to QRT.

Let RT be represented by x, so that;

Sin [tex]38^{o}[/tex] = [tex]\frac{x}{32}[/tex]

x = 32 * Sin [tex]38^{o}[/tex]

  = 32 * 0.6157

x = 19.7024

RT = 19.7 cm

(c) To determine <RPT, let the angle be represented by θ.

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

        = [tex]\frac{RT}{PR}[/tex]

Sin θ = [tex]\frac{19.7024}{55.218}[/tex]

         = 0.3568

θ = [tex]Sin^{-1}[/tex] 0.35568

  = [tex]20.84^{o}[/tex]

Thus, <RPT = [tex]20.8^{o}[/tex]


Related Questions

2x - 6 = 10 PLS HELP I NED THE ANSWERS RIGHT AWAY

Answers

Answer:

Step-by-step explanation:

-12

Answer:

x = 8

Why?

Step-by-step explanation:

2(8) - 6 = 10

16 - 6 = 10

there you go :-)

HOPE IT HELPS

(FROM CROSS)

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

i would help but i can’t see it

Mariah borrowed $1200 to buy a new computer system. She paid the simple interest loan off in 24 monthly payments of $56 each. What was the interest rate of this loan? a.2%
b.6%
c.4.4%
d.7%

Answers

Answer:

B. 6%

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

Her 24 monthly payments total 24 x $56 = $1344

That means that $1344 - $1200 = $144 is just interest.  What percent is this of her loan amount?  Divide to find out:

144 / 2400 = 0.06 = 6%

a car uses 32 L of gas to travel 450 KM. how many liters would be required to drive 800 km (to the nearest tenth)?

Answers

Answer: 56.88 L

Explanation:

Let L represents number of liters

A Car uses 32 L of gas to travel 450 km.

Write a proportion for the problem using rates.

450/32 = 800/L

Cross product is 450*L = 800*32

450L = 25600

Divide each side by 450.

450L/450 = 25600/450

L = 56.88

Quadrilateral JKLM has side lengths of JK = 2y + 3, KL = 8x – 10, LM = 5y – 6, and JM = 3x + 20. Find the values of x and y that make quadrilateral JKLM a parallelogram. A. X = 6, y = 6 B. X = 6, y = 3 C. X = 13, y = 3 D. X = 2, y = 1

Answers

Answer:

(6, 3)

Step-by-step explanation:

Note that the opposite side of parallelogram are congruent, hence;

Jk = LM

2y + 3 = 5y - 6

2y - 5y  =-6 - 3

-3y = -9

y = 9/3

y = 3

Similarly;

KL = JM

8x – 10 = 3x+20

8x - 3x =  20 + 10

5x = 30

x = 30/5

x = 6

Hence (x,y) is (6, 3)

Answer:

B.

Step-by-step explanation:

Solve for x.
..................................

Answers

Answer: For 7x-11 is There are no like terms.

I don’t know if you want me to solve because I did “Answer: There are no like terms.” or how you want it because the picture you show it confusing

For 4x-2 is Factor 4x−2

4x−2

=2(2x−1)

Answer:2(2x−1)

Step-by-step explanation: Hope this help :D

What is the volume of a cone with a diameter of 12 inches and a height of 4
inches? *

Answers

Answer:

48 cubic inches

Step-by-step explanation:

Answer:

192π

and or [tex]603in^{3}[/tex]

Step-by-step explanation:

Sally plays a game for 1 and 5-sixths hours. Judy plays a game 1-half hour longer than Sally. Question How many hours does Judy play her game? Move numbers to the boxes to show the answer. If there is no whole number, put a 0 in the first box.

Answers

Answer:

2 1/3 hours or 2 hrs, 20 min

Step-by-step explanation:

1 5/6 + 1/2

make mixed number into improper fraction and change 1/2 to 3/6

11/6 + 3/6 = 25/6

14/6 equals 2 2/6 which simplifies to be 2 1/3 or 2 hrs, 20 min

AREA OF A CIRCLE HELP PLS​

Answers

Answer:

201.06

Step-by-step explanation:

pi × 8²

determine if the pair of triangles are similar im begging plz help

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because the lines go in the order of the side than the angle and than the other side- and the lines also determine if the two sides are equal- i dont know if that makes sense

A rectangular logo is made up of 3 squares and 8 small squares the length of the rectangle is 36 cm

Find the area of the logo ​

Answers

Answer:

The total area is 594cm.²

Step-by-step explanation:

The top and bottom each have a length of 36 cm.

Blue side:

36/3= 12cm. (36/3 for the length of one side of a blue square)

12*12= 144cm.² (area of one blue square)

144*3= 432cm.² (area of all the blue squares)

Orange side:

36/8= 4.5cm. (the length of one side of an orange square)

4.5*4.5= 20.25cm.² (the area of one orange square)

20.25*8= 162cm.² (the area of all the orange squares)

Total area:

432+162= 594 cm.²

I hope this makes more sense, have a great day :D

After jumping rope for 15 minutes, Jan took a break. If Jan took a break at 3:05 p.M., at what time did she start jumping rope?

Answers

Answer: 2 : 50 pm

Step-by-step explanation:

If Jan took a break at 3:05 pm and she had been jumping rope for 15 minutes before that, to find the time she started jumping rope, subtract 15 from the current time:

= 3:05 - 15

= 2:50 pm

Jan started jumping rope at 2 : 50 pm

Find the slope of the line that passes through the points (-6,6)and(4,-2).

Answers

Answer:

=-4/5

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -2 -6)/(4 - -6)

   = (-2-6)/( 4+6)

   = -8/10

  =-4/5


In a class-test, the ratio of students passing in English only and Maths only is
2:3. Out of 314 students 15 were absent, 75 failed in both the subjects and
24 passed in both the subjects.
(i)How many students passed in English?
(ii) How many students passed in Mathematics?

Answers

Answer:

(¡)...2 + 24

= 26

¡¡)..3+24

27

An isosceles triangle has base length 18 cm and height 4cm what is the approximate length of the two other sides

Answers

Answer:

The approximate length of the two other sides is 10cm

Step-by-step explanation:

Given

[tex]Base\ Length = 18[/tex]

[tex]Height = 4[/tex]

Required

The length of the two other sides

Divide the triangle to 2 (See attachment)

Considering one of the triangles, we have:

[tex]l^2 = 4^2 + 9^2[/tex]

[tex]l^2 = 16 + 81[/tex]

[tex]l^2 = 97[/tex]

Take square roots

[tex]l = \sqrt{97[/tex]

[tex]l = 9.8488[/tex]

[tex]l = 10[/tex] --- approximated

Does the location of the first aid station actually fall in the middle of the park? Provide mathematical calculations to support your answer.

Answers

Answer:

The first aid station is at the middle of the park.

Step-by-step explanation:

Given

[tex](0,0) \to[/tex] Origin of Fun

[tex](-7, 6) \to[/tex] Quadratics in Motion

[tex](-2, 14) \to[/tex]Towers of Trigonometry

[tex](5,8) \to[/tex] The Food Equation

[tex](-1,7)\to[/tex] First aid station

Solving (a): Plot the above points

See attachment for plot

Solving (b): Determine if the first aid station is at the center of the park

From the plot, we have the opposite points to be:

(1) [tex](0,0)[/tex] and  [tex](-2, 14)[/tex]

(2) [tex](5,8)[/tex]  and [tex](-7, 6)[/tex]

Calculate midpoint using:

[tex]M = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]

For (1):

[tex]M = \frac{1}{2}(0 -2, 0 + 14)[/tex]

[tex]M = \frac{1}{2}(-2,14)[/tex]

[tex]M = (-1,7)[/tex]

For (2):

[tex]M = \frac{1}{2}(5 -7, 8 + 6)[/tex]

[tex]M = \frac{1}{2}(-2,14)[/tex]

[tex]M = (-1,7)[/tex]

From the above computation, we have midpoint to be:

[tex]M = (-1,7)[/tex]

Given that:

[tex](-1,7)\to[/tex] First aid station

We can conclude that the first aid station is at the middle of the park.

Solve the inequality and describe the solution set.
y–6≥12

Answers

Answer:

y ≥ 18

All numbers greater than or equal to 18

Step-by-step explanation:

y  – 6≥ 12

Add 6 to both sides

y ≥ 18

All numbers greater than or equal to 18

What is the volume of the Cube?

132 cubic inches
726 cubic inches
1331 cubic inches
33 cubic inches

Answers

Answer:

1331 cubic inches

Step-by-step explanation:

volume = 11×11×11 = 1,331 in³

How to make a data set with only 5 numbers. And so the mean is 7, the median is 7, and the mode is 5?

Answers

Answer:

5,5,7,8,10

Step-by-step explanation:

mode=5    so that would appear the most so start with 5,5

median=7  that would be the middle number so 7 would be next

when you add 5+5+7=17  now just choose any number to add to 17 and I choose 10 which makes 17+10=27.  

mean=7  so that means the total has to be divided by how many numbers you have, which is 5.  So the total divided by 5 should equal 7.  Since have 27, the number divided by 5 to get 7 is 35.  So, add to 27 to get 35 which would be 8.

27+8=35  that is your total.  Now divide by 5 to get the mean of 7.

Amy bakes x cakes.
Barry bakes four times as many cakes as Amy.
Ceri bakes 12 more cakes than Amy.

They bake a total of T cakes.

Find a formula, in terms of x, for the total number of cakes.
Give your formula in its simplest form​

Answers

Answer:

6x+12=T

Step-by-step explanation:

Amy bakes x cakes.

Barry bakes 4x.

Ceri bakes x+12

So the total is 6x+12=T

A Cylinder with
a volume of 27π
in 3 and a height
of 3 in. What is
the radius?

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Surface Areas and Volume.

==> Volume of Cylinder = πr^2h

==> 27π = πr^2(3)

==> 27 = r^2 (3)

==> r^2 = 9

==> r = 3 inch

hence the radius is 3 inches.

If a fish is swimming 20 feet below the surface of the ocean and a bird flying directly overhead of the fish is 12 feet above the surface, how far apart are they?

Answers

Answer:

32 feet

Step-by-step explanation:

The equation would be 12 - (-20)

                                       12 + 20 = 32

Which points reflected of each other across both exes PLEASE HELP ASAP

Answers

Answer:

I am pretty sure it is (-2,8) and (2,-8)

Step-by-step explanation:

I think my answer is correct because it goes from Quadrant 1 into 4. Other answers are just I quadrant away.

Which of the following expressions is equivalent to -6?
A: -9 + 15
B: 9 - (-15)
C:-9 - 15
D: 9 + (-15)

Answers

Answer: D This is because when you add 9 to -15, -15 is bigger so it turns negative and then it equals up to -6.

Of the marbles in a bag, 2 are blue, 4 are yellow, and 5 are green. Sandra will randomly choose
one marble from the bag. Fill in the blanks in parts a and b.
Thomh

Answers

Answer:

2 blue marbles;

4 yellow marbles;

5 green marbles;

11 marbles in total;

The chance of choosing a blue marble is 2 out of 11 or 2/11

It is unlikely that Sandra will choose a blue marble from the bag.

EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-

(if you put links or don't answer accordingly im reporting your account)

Answers

Answer:

A B D

Step-by-step explanation:

those are the answers

But a closer look shows that B will be the best answer.

Answer:

Since all the rhombus is parallelogram

some are trapezoid and quadrilateral.

So

B.parallelogram is a answer:

it opposite side are equal.

diagonal bisect angle equally.

.

Please help! Math is my worst subject

Answers

Answer:

it's answer is 73°

Step-by-step explanation:

< DCB = 50°

< ACB = x

< CAB = 57°

< ABC = < DCB = 50° {Being alternate angles }

Now

x + 50° + 57° = 180° { being sum of angles of triangle }

x + 107° = 180°

x = 180° - 107°

Therefore x = 73°

Hope it will help :)❤

if the amount of money you have matched ur phone number, how much do you have?

Answers

Answer: lma0

Step-by-step explanation:

Answer:

45 even tho my mine broke xD

have a good day :)

Step-by-step explanation:

plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help

Answers

Answer:

38°

Step-by-step explanation:

The measure of angle NPM is 38°.

To find :Measure of ∠NPM

Solution :

➠ ∠MPJ + ∠LPM = 180°

➠ ∠MPJ + 90° = 180°

➠ ∠MPJ = 180° – 90°

➠ ∠MPJ = 90°

∠NPM = ∠MPJ – ∠JPN

➠ ∠NPM = 90° – 52°

➠ ∠NPM = 38°

∴ Required answer :

∠NPM = 38°

USE CALCULATOR PI I NEED HELP ASAP

Answers

Answer:

62 ft is the answer

Step-by-step explanation:

I did the test

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