In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.
Given:
PQRS is a circle, PQT and SRT are straight lines.
To find:
The value of x.
Solution:
Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.
We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.
[tex]m\angle SPQ+m\angle QRS=180^\circ[/tex]
[tex]81^\circ+m\angle QRS=180^\circ[/tex]
[tex]m\angle QRS=180^\circ-81^\circ[/tex]
[tex]m\angle QRS=99^\circ[/tex]
Now, SRT is a straight line.
[tex]m\angle QRT+m\angle QRS=180^\circ[/tex] (Linear pair)
[tex]m\angle QRT+99^\circ=180^\circ[/tex]
[tex]m\angle QRT=180^\circ-99^\circ[/tex]
[tex]m\angle QRT=81^\circ[/tex] ...(i)
According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.
Using exterior angle theorem in triangle QRT, we get
[tex]m\angle PQR=m\angle QRT+m\angle QTR[/tex]
[tex]x=81^\circ+22^\circ[/tex]
[tex]x=103^\circ[/tex]
Therefore, the value of x is 103 degrees.
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
A. -1/3
B. 3
C. 5
D. 6
E. -9
Answer:
C. 5
Step-by-step explanation:
plato
Answer:
C. 5
Hope this helps!
Step-by-step explanation:
Simplify The Following: -4h + 22 + 6h -7
Answer:
2h + 15
Step-by-step explanation:
-4h + 22 + 6h -7
2h + 22 - 7
2h + 15
Find the length of the third side.if necessary, round to the nearest tenth 24 18
Answer:
30
Step-by-step explanation:
\text{Legs: 18, 24}\hspace{20px}\text{Hypotenuse: ?}
Legs: 18, 24Hypotenuse: ?
a^{2}+b^{2}=
a
2
+b
2
=
\,\,c^{2}
c
2
The Pythagorean Theorem
18^{2}+24^{2}=
18
2
+24
2
=
\,\,c^{2}
c
2
Plug in. c is the hypotenuse.
324+576=
324+576=
\,\,c^{2}
c
2
Square the numbers.
900=
900=
\,\,c^{2}
c
2
Add.
\sqrt{900}=
900
=
\,\,\sqrt{c^{2}}
c
2
Square root both sides.
30=
30=
\,\,c
c
The hypotenuse.
If A = 56° then find C.
Answer:
124
Step-by-step explanation:
If you are talking about angles, then the answer is 124 degrees. Question is a little open, though.
I hope this helps!
If 3x−y=12, what is the value of
8x
2y
Answer:
[tex]8x=32\\2y=-24[/tex]
Step-by-step explanation:
When solving for 1 variable, set the other to 0 and solve.
[tex]3x-y(0)=12\\3x=12\\x=4\\4*8=32\\8x=32\\\\3(0)-y=12\\-y=12\\y=-12\\-12*2=-24\\2y=-24[/tex]
What is 4x^2+14x+6=9x^2-6x+1 answer
Answer:
20x+5=5x^2
Step-by-step explanation:
For this type of albreic question you want to simplify
4x^2+14x+6=9x^2-6x+1
first you take the common integers(That might not be the right word)
4x^2+14x+6=9x^2-6x+1
+6x -1 -4x^2
20x+5=5x^2
You cannot simplify any further
umm pls help me ik how to do it but not sure on this specific one
9514 1404 393
Answer:
-8, +9
Step-by-step explanation:
You need factors of (6)(-12) = -72 that have a sum of +1.
From your knowledge of multiplication tables, you know that 72 = 8·9. Then -72 = (-8)(9), and those two factors have a sum of +1.
6x^2 +x -12
= 6x^2 +9x -8x -12
= 3x(2x +3) -4(2x +3)
= (3x -4)(2x +3)
A sphere has a radius of 1 inch. What is the volume of the sphere, in cubic inches?
Answer:
V≈ 4.19in³
Step-by-step explanation:
V=4/3 π r³= 4/3 ·π· 1³ ≈4.18879in³
Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007?
Answer:
370 stores
Step-by-step explanation:
Given data
initial number of stores P= 200
r= 8%
t= 1999-2007= 8 years
Let us apply the compound interest expression to find the final amount of stores
A= P(1+r)^t
A= 200(1+0.08)^8
A= 200(1.08)^8
A= 200*1.85
A=370
Hence the number of stores in 2007 is 370 stores
8/9i+12=2/9i+34 (solve for a)
Answer: I=33, O and when you said solve for a I don’t see a, I see i and that all...if you know what I mean
Step-by-step explanation: hope this help
Just want answers pls/brainliest if correct !
Answer:
If AB is 16, then AD is 8.
If AB = 12 and CB = 10, then the height of the triangle is 8.
Step-by-step explanation:
AD = [tex]\frac{AB}{2}[/tex], so AD is equal to 8.
Use the Pythagorean Theorem, [tex]\sqrt{10^{2} - 6^{2}}[/tex] equals 8, so the height of the triangle is equal to 8.
What are all t possible names for these?? Help plz
Answer:
13.....square
14....parallelogram
15....rhombus
16....trapezium
17...kite
18....rectangle
Answer:
#13 is a square, #14 is a rectangle, #15 is a rhombus, #16 is a trapezoid, #17 is a qaudrilateral, and #18 is a rectangle also.
Hope this helps :)
9.
The equation a = 640s gives the relationship between s square miles and a acres. Pam owns 7.5 square miles of farmland. How many acres does she own?
4,800 acres
11.72 acres
1.17 acres
480 acres
[tex]a = 640s[/tex]
[tex]a = 640(7.5)[/tex]
[tex]a = 4800 \: [/tex]
She owns 4800 acres.
Answer:
4,800 acres
Step-by-step explanation:
Solve for G
6G = -72
(show your work)
Answer:
-12
Step-by-step explanation:
6G = -72
G = -72 / 6
G = -12
please help me please do them all its just thrree
Step-by-step explanation:
hope this helps. I worked out then posted.
Which scenario could be represented by the value −8 ? Select each correct answer. A puppy gains 8 pounds. The temperature is 8 degrees below 0. The elevation of a hot air balloon is 8 meters. A student's class average decreases by 8 points.
plzz help ill give brainliest
Answer:
- The temperature is 8 degrees below 0
- A student's class average decreases by 8 points.
Answer:
The temp is 8 degrees below 0, a student's class average decreases by 8 points
Step-by-step explanation:
a puppy gaining 8 pounds is positive
the temp is 8 degrees below 0 which is negative
the elevation of a hot air balloon is 8 meters above the ground
A student's class average decreases by 8 points = negative
The value -8 is negative and it doesn't say you have to only select one answer
find the inequality of 3x-2÷4+3≥12
Answer:
x + 5 = ,3
Step-by-step explanation:
x+5-5= +3-5
x= -2
(3x +7x² + 2x + 3) + (x + 1)
Answer:
=7x2+6x+4
Step-by-step explanation:
3x+7x2+2x+3+x+1
Combine Like Terms:
=3x+7x2+2x+3+x+1
=(7x2)+(3x+2x+x)+(3+1)
=7x2+6x+4
Answer:
=7x2+6x+4
What is the value of so that −10and 10are both solutions of 2−=70
Answer:I think 7
Step-by-step explanation:
The sum of five consecutive integers is 0. Find the integers. Show your solution.
Does anyone know the answer?
Answer:
-2, -1, 0, 1, 2.
Solution
Let x be the middle term of this sequence of 5 terms.
Then the sequence is x-2, x-1, x, x+1, x+2.
The sum of the terms is (x-2) + (x-1) + x + (x+1) + (x+2) = 5x.
Thus 5x = 0.
It gives x = 0.
So the sequence is -2, -1, 0, 1, 2.
Johnny works after school and earns $8 per hour. He needs at least $2000 to purchase a car so he does not need to take the bus. How many hours does he need to work to reach his goal?
2hours
Step-by-step explanation:
2 hours
HELP! WILL GIVE BRAINLY!!! Find the volume of a cylinder with height = 10ft and the diameter of the base circle is 12ft.
Answer:
About 1,130.4 Cubic Feet
(My previous answer was a mistake. It has now been corrected)
Step-by-step explanation:
The Volume of a cylinder = Height * Pi * Radius^2
The radius is half the diameter, so 12 ÷ 2 = 6
Pi rounded to the hundredth place is 3.14.
Volume = 10 * 3.14 * 6^2 = 1,130.4
Therefore the Volume is about 1,130.4 cubic feet.
Answer:
Exact Volume = 360pi cubic feet
Approximate Volume = 1130.4 cubic feet
The approximate volume is found when you use pi = 3.14; use more decimal digits of pi to get a more accurate value.
===========================================================
Explanation:
The volume of a cylinder is found by the formula
V = pi*r^2*h
where,
pi = 3.14 approximatelyr = radius = 6 ft, since the radius is half the diameter.h = height = 10 ftSo,
V = pi*r^2*h
V = pi*6^2*10
V = pi*36*10
V = pi*360
V = 360pi ........... exact volume in terms of pi
V = 360*3.14
V = 1130.4 ......... approximate volume if you use pi = 3.14
The units of the volume are in "cubic feet" which we can abbreviate to "ft^3". Think of a 1 ft by 1 ft by 1 ft cube. The volume would be 1*1*1 = 1 cubic foot. So basically having a volume of roughly 1130 cubic feet means we need this many cubic blocks to form the cylinder (some of the blocks will be cut up to be able to fit).
Gabriella made 5 waffles for breakfast. She has 25 strawberries and 15 blueberries to put on top of the waffles. She will put a equal number of berries on each waffle.How many berries will gabrielle put on each waffle?
Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?
The spinner below is spun. Find the probability,
P(D greater than 1)
What is the numerator for the probability?
What is the denominator for the probability?
Answer:
5 - numerator
6 - denominator
The equation  is written in point-slope form. What is the equation written in slope-intercept form?    
Answer:y+6 = 1/3 (x, -9)
Step-by-step explanation:The equation y+6 = 1/3 (x, -9) is written in point-slope form. What is the equation written in slope-intercept form? The point-slope form of a line that has a slope of -2 and passes through point (5, -2) is shown below. ... The equation y - 2/3 = -2 (x - 1/4) is written in point-slope form.
Point s and point t are located at -6, 13 and 8, 13 on the coordinate plane what is the distance between the two points
Answer:
[tex]14[/tex] units
Step-by-step explanation:
Since both points have the same y-coordinate, we can calculate the distance between them by taking the absolute difference of their x-coordinates. Therefore, the distance between them is [tex]|-6-8|=|-14|=14[/tex] units. Hope this helps!
Susanna's family traveled 5 7 of the distance to her grandmother's house on Saturday. They traveled 1 2 of the remaining distance on Sunday. What fraction of the total distance to her grandmother's house was traveled on Sunday?
Answer:
1/7
Step-by-step explanation:
Please write these fractions as 5/7 and 1/2. 5 7 and 1 2 are incomplete and confusing.
On Saturday the distance traveled was 5/7 of the total distance.
2/7 of that total was left for Sunday. Half of 2/7 is 1/7.
1/7 of the total distance was traveled on Sunday.
Mrs. Safar purchases a bedroom set for $1600. Five percent sales tax is added to the purchase price and she must also pay a $60 delivery fee. If Mrs. Safar pays for the total cost of the bedroom set in 12 equal payments, how much is each payment? MAFS.7.EE.2.3
