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
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]
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?
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
PLEASE HELP ME AND BE QUICK
Chantal has an outstanding balance of $256.84 on a credit card. The minimum monthly payment is 13% or $20.00, whichever is more.What is the minimum monthly payment?
Answer:
minimum is $20
Step-by-step explanation:
.13 x 256.84 = 33.39
$33.39 is less than $20.00
USE CALCULATOR PI I NEED HELP ASAP
Answer:
62 ft is the answer
Step-by-step explanation:
I did the test
A . 4
B . 16
C . 8
D . 2
Answer:
c
Step-by-step explanation:
Pls hurry, will mark brainliest
Answer:
B is correct
Step-by-step explanation:
A company is making two types of covered aluminum containers. One is a cylinder with a height of 114feet and a diameter of 1 foot. The other is a rectangular prism with a length of 34foot, a width of 34foot, and a height of 1 foot. How much greater is a cylinder's capacity?
Answer:
[tex]V_d=976.9ft[/tex]
Step-by-step explanation:
From the question we are told that:
Height of cylinder h_1=114 feet
Diameter d=1
Length of triangular prism [tex]l_2=34ft[/tex]
Width of triangular prism [tex]w_2=34ft[/tex]
Height of triangular prism [tex]h_2=1 ft[/tex]
Generally the equation for Volume of the cylinder is mathematically given by
[tex]V_c=\pir^2h[/tex]
Where
[tex]r=d/2\\r=0.5[/tex]
Therefore
[tex]V_c-=\pi*0.5*114[/tex]
[tex]V_c=57\pi[/tex]
[tex]V_c=179.1ft[/tex]
Generally the equation for Volume of a Rectangular prism is mathematically given by
[tex]V_r=whl[/tex]
[tex]V_r=34*34*1[/tex]
[tex]V_r=1156feet[/tex]
Generally the equation for Volume difference is mathematically given by
[tex]V_d=V_r-V_c[/tex]
[tex]V_d=1156-179.1[/tex]
[tex]V_d=976.9ft[/tex]
Which gives the line of best fit?
f(x)=45x
f(x)=x
f(x)=2x
f(x)=45x+45
Answer:
f(x) = x
Step-by-step explanation:
example of points on line: (40,40), (45,45), (50,50)
x-values are the same as y-values which means the line is y=x
If x = -3 evaluate the following expression
(x-2)(x+9)
________
x(x+5)
Answer:
Step-by-step explanation:
you have to substitute x with -3, so where you see x in the equation you write a -3 and calculate
[tex]\frac{(x-2)(x+9)}{x(x+5)} = \frac{(-3-2)(-3+9)}{-3(-3+5)} = \frac{-5*6}{-3*2} =\frac{-5}{-1} =5[/tex]
2x - 6 = 10 PLS HELP I NED THE ANSWERS RIGHT AWAY
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)
-6x + 2y = 10 is written in Standard form.
Rewrite it in y=form.
Answer:
y = 3x + 5
Step-by-step explanation:
add 6x to each side to get:
2y = 6x + 10
finally, divide each side by 2 to get:
y = 3x + 5
Answer: Y = 3x +5
Step-by-step explanation:
What is the solution of 1/2 x + 3x = 14?
A jogger is running around a 3/4 mile track and he has ran 2/3 around the track how far has the jogger traveled? THANKS!
Answer:
.5
Step-by-step explanation:
3/4 of a mi is equal to 0.75 mi
2/3 of .75 is .5
83/10y-(38/11-11/4y)
Answer:
I think 83 ÷ 10 and it said that it incorrect
Step-by-step explanation:
PLEASE ANSWER!!!!!!!!!!
Answer:
The answer would be C, or 3
Step-by-step explanation:
2x with a power of 2 to the power of 3 is 6x, with a power of five, plus y to the fower of 3.
Using the given equation find the missing coordinates o the points and then find the slope of the line for each equation y-2x=3; A(...;6), B(15; ...)
Answer:
(1.5,6)(15,33) slope=2
Step-by-step explanation:
Answer:
y-2x=3; A(1.5, 6) B(15,33) Slope = 2
Step-by-step explanation:
First thing, you add 2x on both sides and get y=2x+3. Since the equation y=mx+b states that m is the slope, the slope is 2.
2nd step is finding the missing coordinate for a. You plug in 6 as the y in the equation y=2x+3, and then get 2x+3=6. Now it is a simple algrebraic equation and you get x=3/2 or 1.5.
The final step is to solve for B. Using the equation y=2x+3, and substituting in x as 15, you get y=30+3 which equals 33.
I hope this gave you an in depth explanation on solving these problems!
The floor of a room is 6 m by 4 m, and its height is 3 m. Find the distance from
a corner point on the floor to the opposite corner point on the ceiling.
Answer:
6 x 4 x 3 = 72
Step-by-step explanation:
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
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.
A community college employs 88 full-time faculty number. To gain the faculty opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty number. He numbers the faculty form 1 to 88.
Answer: Hi your questions some required details attached below is the required random number table and missing question
Answer : 83, 58, 64, 26, 47, 68, 29, 4, 78
Step-by-step explanation:
The number of 9 faculty members that will be included in the sample will be written considering the fact that the 9 numbers ( first 9 ) are lesser than 88, and also considering the fact that 58 is repeated twice ( in the random number table ). Hence The number of 9 faculty members = 83, 58, 64, 26, 47, 68, 29, 4, 78
Which angles are vertical angles?
Answer:
vertical angle are angles opposite each other where two lines cross .
HELPPPP PLEASEE
How much is Vince paid for one hour of work?
A.
$3.60
B.
$9.00
C.
$9.50
D
$12.00
Answer:
B
Step-by-step explanation:
Using the graph, we pick a convenient point: (20, 180)
This point means that for 20 hours of work, Vincent is paid 180 dollars. In fraction form, we can write 20hrs/180 dollars. If we simplify the fraction by dividing both the numerator and denominator by 20 we get 1/9 AKA 1hr/9 dollars. So in 1 hour, Vinnie is paid $9.00
Have a good rest of your day
Please help! Math is my worst subject
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 :)❤
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?
Answer:
(¡)...2 + 24
= 26
¡¡)..3+24
27
determine if the pair of triangles are similar im begging plz help
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
2) 2(8r + 5) = 24 + 9r
Answer:
r = 2
Step-by-step explanation:
2(8r + 5) = 24 + 9r
16r + 10 = 24 + 9r
16r - 9r = 24 - 10
7r = 14
r = 2
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
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
please help i cannot get it
If a Tv screen is 20in wide and 15in high, what is the length?
Use the function below to find F(3). F(x)=(1/6)x A. 1/18 B. 1/216 C. 1/2 D. 1/72
Answer:
C
Step-by-step explanation:
To evaluate f(3) substitute x = 3 into f(x), that is
f(3) = [tex]\frac{1}{6}[/tex] × 3 = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex] → C
The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below:
Answer:
It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.