The sides OP and RO of triangle POR are produced to points S and T respectively. If ∠SPR = 145° and ∠POT = 115° , find ∠PRO
Answer:
[tex]\angle PRQ = 80[/tex]
Step-by-step explanation:
Given
[tex]\angle SPR = 145^o[/tex]
[tex]\angle POT = 115^o[/tex]
See attachment
Required
Find [tex]\angle PRO[/tex]
First, calculate [tex]\angle RPO[/tex]
[tex]\angle RPO + \angle SPR = 180[/tex] --- angle on a straight line
So, we have:
[tex]\angle RPO + 145 = 180[/tex]
Collect like terms
[tex]\angle RPO = 180 - 145[/tex]
[tex]\angle RPO = 35[/tex]
Next, calculate PQR
[tex]\angle POR + \angle POT = 180[/tex]
So, we have:
[tex]\angle POR + 115 = 180[/tex]
Collect like terms
[tex]\angle POR = 180-115[/tex]
[tex]\angle POR = 65[/tex]
So, PRO is calculated as:
[tex]\angle PRO + \angle POR + \angle RPO = 180[/tex] --- angles in a triangle
So, we have:
[tex]\angle PRO + 65 + 35= 180[/tex]
[tex]\angle PRO + 100= 180[/tex]
Collect like terms
[tex]\angle PRO = 180-100[/tex]
[tex]\angle PRO = 80[/tex]
The ages of several trees in a park are shown below:
2 years, 28 years, 2 years, 20 years, 22 years
What is the mean age of these trees?
56 years
12 years
14.8 years
26 years
Answer:
C or 14.8
Step-by-step explanation:
You just find the mean.
Arrange the numbers, add them then divide by the amount of numbers.
Hope it helps c:
Please help. Somebody give an answer to this question please. I need a step by step explanation as well.
Answer:
15d² + 7d - 4
Step-by-step explanation:
Distribute
(5d + 4)(3d -1)
5d (3d - 1) + 4(3d - 1)
Distribute
15d² - 5d + 4(3d- 1)
Distribute
15d² - 5d + 12d- 4
Simplify
15d² + 7d - 4
question on image
....
Answer:
1/5
Step-by-step explanation:
8/40->4/20->2-10->1/5
Hope this helps!
Answer:
1\5
Step-by-step explanation:
8/40 = 4/20 = 2/10 = 1/5
Suppose you invest $1800 at an annual interest rate of 3.3% compounded
continuously. How much will you have in the account after 1.5 years?
Answer:
$1,890
Step-by-step explanation:
To find the amount, we use the compound interest formula here
we have this as;
A = P(1 + r/n)^nt
Where ;
P is the amount invested which is $1,800
r is the interest rate which is 3.3% annually (3.3/100 = 0.033)
n is the number of times yearly interest is compounded which is 1 time yearly
t is the number of years which is 1.5 years
substituting these values, we have
A = 1800( 1 + 0.033)^(1 * 1.5)
A = 1,890
Find the volume of the prism
Answer:
A prism is a polyhedron with two parallel, congruent faces called bases that are polygons
Find an equation of a line with a slope of -4 and having
the point (2,0) on the line. Then graph the line.
Answer:
y = -4x + 2
Step-by-step explanation:
The formula for slope is: y = mx + b
Where m is slope and b is when the line intersects the y-axis.
Plug in:
y = -4x + 2
The two is the point in the line, and -4 is the slope.
Hope this helps.
en una carrera de 5 vueltas de la F1 online el jugador 1 consigue un tiempo de 2,32 minutos y el jugador 2 consigue 18 segundos mas que el jugador 1 en la segunda vuelta el jugador 1 obtiene un tiempo de 2,52 minutos y el jugador 2 20 segundos menos que el jugador 1, en la tercera vuelta ambos jugadores consiguen un tiempo de 2,18 minutos ¿Cual es la diferencia en el tiempo total de la carrera entre los jugadores 1 y 2?
Answer:
La diferencia del tiempo total de carrera entre el jugador 1 y 2 es 0.0[tex]\overline 3[/tex] minutos
Step-by-step explanation:
Primera vuelta;
El tiempo de vuelta del jugador 1 = 2,32 minutos
El tiempo de vuelta del jugador 2 = 18 segundos más que el del jugador 1
Por lo tanto, el tiempo de vuelta del jugador 2 = (2,32 + 18/60) minutos = 2,62 minutos
Segunda vuelta
El tiempo de vuelta del jugador 1 = 2,52 minutos
El tiempo de vuelta del jugador 2 = 20 segundos menos que el del jugador 1
Por lo tanto, el tiempo de vuelta del jugador 2 = (2.52 - 20/60) minutos = 2.18[tex]\overline 6[/tex] minutos
Tercera vuelta
El tiempo de vuelta del jugador 1 = 2,18 minutos
El tiempo de vuelta del jugador 2 = 2,18 minutos
El tiempo de vuelta total del jugador 1 = (2,32 + 2,52 + 2,18) minutos = 7,02 minutos
El tiempo de vuelta total del jugador 2 = (2,62 + 164/75 + 2,18) minutos = 524/75 minutos = 6.98[tex]\overline 6[/tex] minutos
La diferencia del tiempo total de carrera = (7.02 - 524/75) minutos = (1/30) minutos = 0.0[tex]\overline 3[/tex] minutos
what is the equation of linear regression that fits the data
Answer:
Option D
Step-by-step explanation:
From the table attached,
Ordered pairs to be plotted → (1, 472.08), (2, 454.26), (3, 444.95), (4, 439.49), (5, 436.55)
By using linear regression calculator,
Equation of the regression line → y = -8.583x + 475.215
Option D will be the answer.
Find the missing variables
Answer:
90
Step-by-step explanation:
Answer:
[tex] \cos(60) = \frac{9}{a} \\ \frac{1}{2} = \frac{9}{a} \\ a = 18 \\ \\ \\ \tan(60) = \frac{b}{9} \\ \sqrt{3} = \frac{b}{9} \\ b = 9 \sqrt{3} [/tex]
I hope I helped you ^_^
Venn diagram of b union b
Answer:
let b union b be
B={2,4,6,8} and B= {1,2,3,4,5}
then B union B = {1,2,3,4,5,6,8}
Step-by-step explanation:
Venn diagram of b union b is in the attachment
Hope it is helpful to you
Find the equation of the line.
Use exact numbers.
y= x+
Which are the
solutions of x2 = -7x - 8?
Answer: I think the answer is D
Step-by-step explanation:
Answer:
D is the answer (The last option)
Step-by-step explanation:
how do I solve this pls help khan academy is no smart
Answer:
3. If that doesn't work, try 1/3
Step-by-step explanation:
Figure A has a length of 9 and figure B has a length of 3. 9 divided by 3 is 3.
ahla
S : Assignment
乡,一石
Answer
what's the question?
Step-by-step explanation:
looks like your question is missing information
If the number of degrees in a certain angle added to the number of grades in the angle is 76, find the angle in degrees.
Sarah used 3/4 pound of blueberries to make 2/3 cup of jam. How many pounds of blueberries are needed per cup of jam?
3/4÷ 2/3= 3/4*3/2= 9/8= mixed fraction 1 1/8 pounds.
Can some help? Plz :)
Answer:
C. 1.05 x 10^7
Step-by-step explanation:
1.75x10^4 x 600
=1050 x 10^4
=1.05 x 10^7
QUICK HELP PLEASE! THANK YOU SO MUCH
When the shown net containing the letters SPROUT is
folded into a cube, which letter is on the side opposite the side labeled R?
Answer:
T
fold it up =t
Step-by-step explanation:
solve the linear equation
x/2-3x/4+5x/8=9
I need the full solution X by 2 minus 3x by 4 + 5x by 8 equal to 9
Answer:
24
Step-by-step explanation:
x/2-3x/4+5x/8=9
Or,(4*x-2*3x+5x)/8=9. (taking LCM)
Or, (4x-6x+5x)/8=9
Or, 3x=9*8
Or, x = 72/3
so, x=24.
You are designing a rectangular fenced outdoor space for your pet rabbit. Fencing
material costs $15.25 per metre. You have $200. What dimensions give the greatest
area, to the nearest tenth of a metre? Include a sketch of the fenced area.
Answer:
2.6 x 5
Step-by-step explanation:
2.6 x 5 is 13 x 15.25 is 198.25 and you can't go any higher than that or it will go over 200 so the dimensions that give the greatest area would be 2.6 and 5, good luck
pls pls help help help
Answer:
the diameter form for your help today with the app
Step-by-step explanation:
pa brain less
Please help thank you!
Answer:
A≈376.99yd²
d= 10yd
h = 7yd
hope it helps
the sum of legs for a right triangle be 21 and their product is 40. Find the perimeter of this triangle.
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
The sum of legs for a right triangle is 12:
[tex] a + b = 21 [/tex]
[tex] a = 21 - b [/tex] (1)
And their product is:
[tex] a*b = 40 [/tex] (2)
By entering eq (1) into (2) we have:
[tex] (21 - b)b = 40 [/tex]
[tex] 21b - b^{2} - 40 = 0 [/tex]
We can find the value of "b" by solving the above quadratic equation.
[tex] b_{1} = 2.1 [/tex]
[tex] b_{2} = 18.9 [/tex]
Since the two values satisfy the equation, we can use either of them to find "a". We will use b₁.
[tex] a = 21 - 2.1 = 18.9 [/tex]
Now, the hypotenuse of the right triangle is given by:
[tex] h = \sqrt{a^{2} + b^{2}} = \sqrt{(18.9)^{2} + (2.1)^{2}} = 19 [/tex]
Hence, the perimeter is:
[tex] P = a + b + h = 18.9 + 2.1 + 19 = 40 [/tex]
Therefore, the perimeter of the triangle is 40.
I hope it helps you!
3x+2y=4
4x+5y=10
solve the simultaneous equations (find x & y)
Answer: (0;2)
3x + 2y = 4 | * (-5)
4x + 5y = 10 | * 2
-15x - 10y = -20
8x + 10y = 20
-15x - 10y + 8x + 10y = 20 - 20
x = 0
0 + 2y = 4
2y = 4
y = 2
(0; 2)
this 2 pls i need help with explanation sum
9514 1404 393
Explanation:
8.An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.
The above relation tells us ...
∠PRS = ∠PQR +∠QPR = 2q +2p
Then ...
∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p
and
∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior
q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR
p = ∠QTR = 1/2(∠QPR) . . . . . subtract q
__
9.For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...
∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°
Substituting the congruent angles, this gives ...
∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation
Which is f(5) for the function -2x^2+2x-3
Answer:
-43
Step-by-step explanation:
f(x) = -2x^2+2x-3
Let x = 5
f(5) =-2(5)^2+2(5)-3
= -2(25)+10-3
=-50+10-3
= -43
Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day
Answer:
3 / 16
Step-by-step explanation:
Let The total amount = x
Fraction eaten on first day = 1/4x
Fraction left = x - 1/4x = 3/4x
Fraction of amount left eaten on second day = 3/4 of 3/4x
3/4 * 3/4x = 9/16x
Fraction left :
3/4x - 9/16x = (12x - 9x) /16 = 3/16x
Hence, fraction left = 3/16
HELPP IS VERY MUCH NEEDED!!!!!
Since this is a right triangle, we can use the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
7^2 + b^2 = 14^2
49 + b^2 = 196
b^2 = 147
b = sqrt(147) = 7 sqrt(3) miles
Hope this helps!
Which of the graphs below would result if you made the leading term of the
following function negative?
F{x} = x + 3x2
Answer:
Step-by-step explanation:
A positive cubic function graphed in the coordinate plane tends from lower left to upper right while a negative cubic function tends from the upper left to lower right. That graph is D (graph A is the positive cubic. Note the difference between "lower left to upper right" and "upper left to lower right")
