Solution given:
1:
<5=<6
<5+<4=180°[co interior angle]
Substituting value of<5
<6+<4=180°[it shows a property of co interior angle]
So
l || m
2:
<1=90°[ l is perpendicular to t]
<2=90°[m is perpendicular to t]
since
<1=<2[shows property of corresponding angle]
:.
l || m.
3:
<1=<2
<1=<3
substituting value of<1 in second one
<2=<3[which shows property of alternate Angel]
So
Segment ST || segment UV.
4:
<RSP=<PQR......[I]
<QRS+<PQR=180°.....[ii]
from equation I and ii we get
<RSP+<QRS=180°[which shows property of co interior angle ]
So
Segment PS || segment QR
These pictures are the questions given in the pdf, let's get the solutions.
1) Solution
It is given that,
→ <5 = <6
Then the co interior angles,
→ <5 + <4 = 180°
Now substituting value of <5,
→ <6 + <4 = 180°
This shows property of co interior angle.
Therefore, L ll m
2) Solution
Take it as,
→ <1 = 90°
In above eq. L is perpendicular to t.
→ <2 = 90
In above eq. m is perpendicular to t.
Then it will be,
→ <1 = <2
It shows property of corresponding angle.
Therefore, L ll m.
3) Solution
It is given that,
→ <1 = <2 and <1 = <3
Now substitute,
The value of <1 in second one,
→ <2 = <3
This shows property of alternate angle.
Therefore, ST || UV.
4) Solution
It is given that,
→ <RSP = <PQR --- (1)
→ <QRS + <PQR = 180° --- (2)
Now from the equation (1) and (2),
→ <RSP + <QRS = 180
It shows property of co interior angle.
Therefore, PS || QR.
ASAPpppppppppppppppppppppp
Answer:
-4/5
Step-by-step explanation:
2/5 ÷ -1/2
Copy dot flip
2/5 * -2/1
-4/5
denise is 6 years older than her sister. 8 years ago she was 4 times as old as her sister how old is each girl now
Answer:
Denise = 16
Sister = 10
Step-by-step explanation:
D=denise
S=sister
Eq 1) D=S+6
Eq 2) D-8 =4S-8
replace D with S+6 in Eq 2
(S+6)-8 = 4S -8
S-2 = 4S -8
add 8 to both sides
S+6 =4S
subtract S from both sides
6 = 3S
divide both sides by 3
2 = S ( this is the sister age 8 years ago )
2+8 = 10 current age
plug that into Eq 1)
D = 10 +6
D=16 (Denise's current age)
so
Denise = 16
Sister = 10
if you subtract 8 from each , then there ages 8 years ago would be
Denise =8
Sister = 2
and 2*4 = 8
this checks
Find the volume of the composite solid.
10 cm
12 cm
32 cm
10 cm
Answer:
Your is answer would be choice C which is : 32 cm
Step-by-step explanation:
Can someone help pleaseeee
Answer:
tan A = 5/12
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = 5/12
x+5=7 .Find the value of x.
Answer:
x=2
Step-by-step explanation:
x+5=7
Subtract 5 from each side
x+5-5=7-5
x =2
Answer:
2
Step-by-step explanation:
x + 5 = 7
=> x = 7 - 5
=> x = 2
Relating a difficult text to a personal experience can help readers
their reading.
Answer:
connect to
Step-by-step explanation:
dont know why people whole summery just put the answer
Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.
What is difficult text?Difficult text can refer to any type of written material that presents a challenge for the reader in terms of comprehension, vocabulary, or structure.
We have,
Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.
When we connect new information to our existing knowledge and experiences, we are more likely to remember and comprehend the new information.
Additionally, making personal connections to the text can help readers to relate to the topic on a deeper, more emotional level, which can increase their interest and motivation to learn more.
For example,
If a reader is struggling to understand a complex scientific concept, they might try to relate it to an experience they had in their own life that involved similar principles.
This could involve recalling a time when they observed or experienced the concept in action or thinking about how the concept might be relevant to their own interests or goals. By making these connections, the reader may be able to better understand and remember the concept, as well as feel more invested in learning about it.
Overall, connecting difficult texts to personal experiences can be a useful strategy for improving reading comprehension and engagement, as well as making learning more enjoyable and meaningful.
Thus,
Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.
Learn more about difficult texts here:
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Two adjacent angles of a parallelogram have equal measure. Find the
measure of each of the angles of the parallelogram.
Step-by-step explanation:
Let ABCD be the parallelogram with ∠A = ∠B.
We know: Sum of adjacent angles = 180°
∠A + ∠B = 180º
2∠A = 180º (∠A = ∠B)
∠A = 90º
∠B = ∠A = 90º
∠C = ∠A = 90º (Opposite angles)
∠D = ∠B = 90º (Opposite angles)
Thus, each angle of the parallelogram measures 90º
Answer:
All 4 angles are 90 degrees.
Step-by-step explanation:
The measure of 2 adjacent angles in a parallelogram add up to 180 degrees.
If they have equal measure then they are both 90 degrees.
As it is a parallelogram:-
the measure of each angle is 90 degrees.
Help me asap
Show your work too so i don’t get grounded
Answer:
1. 496 ft, 2. 126 mm, 3. 880 in, 4 168 cm, 5. 960m, 6. 42
Step-by-step explanation:
SA= Surface area, and surface area is A=2(w×l+h×l+h×w) and volume is V=w×h×l
W=width
H=height
L=length
Answer:
1. SA=58
2. SA=48
3. SA=78
4. V=168
5. V=960
6 V=420
Step-by-step explanation:
on 1-3 you are looking for the surface area and in order to look for the surface area of a rectangle prism it is 2(height)x2(lenght)x2(width). so you just plug in the number height is how tall the shape is, length is how long the shape is and width is hpw far the shape goes back. then you multiply the H, L, W by 2 and the you add all of the numbers and boom you get your answer.
Now for the Volume you just multiply the heigh x length x width and boom you answer
Solve : Sin 2theta-cos3theta=0
Answer:
theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n
Step-by-step explanation:
sin^2 theta - cos^3 theta = 1
cos^3 theta = 1 - sin^2 theta
sin^2 theta - cos^3 theta = 0
Substitute
sin^2 theta - ( 1 - sin^2 theta ) = 0
Distribute negative
sin^2 theta - 1 + sin^2 theta = 0
Combine same values
2sin^2 theta - 1 = 0
2sin^2 theta = 1
sin^2 theta = [tex]\frac{1}{2}[/tex]
sin theta = +- [tex]\frac{1}{\sqrt{2}}[/tex]
Right Triangle: 1 - 1 - [tex]\sqrt{2}[/tex]
theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n
period of Sin function is 2[tex]\pi[/tex]
height increase (m)
Temperature drop (°C)=
200
If the temperature at a height of 500 m is 23°C, what will it be when you climb to 1300 m
How far would you need to climb to experience a temperature drop of 5°C?
Complete question is;
In mountaineering, in general, the higher you go, the colder it gets. This formula shows how the heights and temperatures are related.
Temperature drop (°C) = height increase(m)/200
A) If the temperature at a height of 500 m is 23°C, what will it be when you climb to 1300 m
B) How far would you need to climb to experience a temperature drop of 5°C
Answer:
A) 19°C
B) 1500 m
Step-by-step explanation:
A) We are told that the temperature is at a height of 500 m is 23°C, now we want to find the temperature when height increases to 1300 m.
Thus, it means;
Height increase = 1300 - 500 = 800 m
Thus, from the formula;
Temperature drop (°C) = height increase(m)/200, we have;
Temperature drop (°C) = 800/200 = 4°C
Now,since Initial temperature was 23°C, thus temperature at this increased height ; 23°C - 4°C = 19°C
B) for a temperature drop of 5°C, we have;
5°C = height increase(m)/200
Height increase = 200 × 5
Height increase = 1000 m
Thus, you will need to climb; 500 + 1000 = 1500 m
What is the value of x in the equation 3
3x+9 - ģx-37
?
Answer:
x = 6
Step-by-step explanation:
we can multiply the entire equation by 3 to simplify the numbers
-2x + 27 = 4x - 9
27 = 6x - 9
36 = 6x
x = 6
Find the maximum value for the function 2x^3 + 3x^2 - 72x + 1
Identify at least two other periodic phenomena that occur in real life. Consider your body and things closest to you to help you come up with other ideas. Explain why you chose each example as a periodic phenomenon. After identifying them, state the period of each phenomenon.
Nature tends to repeat itself, and that means periodic phenomenon is found in many places. One example would be a heart beating. It repeats itself over and over to pump blood throughout the body. The period of the heartbeat varies, so it's not going to be one specific number.
One online source I found states "It beats or contracts about 70 times per minute". So that would make the period 60/70 = 0.86 seconds approximately. Every 0.86 seconds or so, the heart completes a full cycle. This is when the person is at rest and not doing any strenuous physical activity (in which case, the period would be much shorter).
Another biological example would be the act of breathing. This is also dependent on if the person is at rest or if they're doing some physical activity such as jogging.
As for an example that's outside the personal element, you could go for something like the motion of the tides. These periodic events are due to the position of the moon, which is also a periodic phenomenon. More broadly, the motion of the planets overall is periodic. However, there may be slight changes here and there as time goes on due to imperfections.
Periodic phenomena has to do with an event that repeats itself.
What is a periodic phenomena?The term periodic phenomena has to do with an event that repeats itself. This repetition must follow a well defined pattern and the time in between the occurrence of the phenomena is called the period.
Two common examples of periodic periodic phenomenon are;
1) Day and light
2) The dropping of water from a closing tap.
The former is quite popular and the period of the phenomenon is 24 hours. In the later case, the period may range a little above five seconds or below.
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solve on the interval [0,2pi] 3(sec x)^2 -4=0
Answer:
pi/6, 5pi/6, 7pi/6, 11pi/6
Step-by-step explanation:
3(sec x)^2 -4=0
Add 4 on both sides:
3(sec x)^2=4
Divide 3 on both sides:
(sec x)^2=4/3
Take square root of both sides:
sec x=plus/minus sqrt(4/3)
Reciprocal identity:
cos x=plus/minus sqrt(3/4)
Simplify the radical:
cos x=plus/minus sqrt(3)/2
So we are looking on the unit circle where the first coordinate of the order pair is either sqrt(3)/2 or -sqrt(3)/2.
This happens at pi/6, 5pi/6, 7pi/6, 11pi/6
Answer:
[tex]\sf \boxed{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}[/tex]
Step-by-step explanation:
A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]
The given equation is ,
[tex]\sf\longrightarrow 3(sec x)^2-4=0 [/tex]
This can be written as ,
[tex]\sf\longrightarrow 3sec^2x - 4 = 0 [/tex]
Add 4 to both sides of the equation ,
[tex]\sf\longrightarrow 3sec^2x = 4 [/tex]
Divide both sides by 3 ,
[tex]\sf\longrightarrow sec^2x =\dfrac{4}{3} [/tex]
Put squareroot on both sides ,
[tex]\sf\longrightarrow sec \ x =\sqrt{\dfrac{4}{3} }[/tex]
Simplify ,
[tex]\sf\longrightarrow sec\ x =\pm \dfrac{2}{\sqrt3} [/tex]
Multiply numerator and denominator by √3 ,
[tex]\sf\longrightarrow \bf sec(x) = \dfrac{ 2\sqrt3}{3},-\dfrac{2\sqrt3}{3} [/tex]
Solve for x ,
[tex]\sf\longrightarrow x = \dfrac{\pi}{6} +2\pi n , \dfrac{11\pi}{6}+2\pi n , \textsf{ for any integer n } . [/tex]
Therefore all the possible solutions are ,
[tex]\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}} [/tex]
If a =7 , find the area of it .
Please give me the answer I have a exam at 12.00
Answer:
60cm²
Step-by-step explanation:
Area of a rectangle = length x breath
Let,
length (L) = (a-1) cm
breadth (B) = (a+3) cm
Putting the value of a = 7;
we get,
length= 7-1 = 6 cm
breadth= 7+3 = 10 cm
Therefore, area of the rectangle = L x B
= 6 x 10
= 60 cm²
Answer:
Step-by-step explanation:
Hello!
a= 7
L = 7+3 = 10
l= 7-1 = 6
area:
10*6 => 60cm²
What is the equivalent expression to 7/5y What is the equivalent expression to 0.68y What is the equivalent expression to 3/5y What is the equivalent expression to 1.32y
Given:
The expressions are:
[tex]\dfrac{7}{5}y[/tex]
[tex]0.68y[/tex]
[tex]\dfrac{3}{5}y[/tex]
[tex]1.32y[/tex]
To find:
The equivalent expression to the given expressions.
Solution:
There can be more than one equivalent expressions to the given expression.
[tex]\dfrac{7}{5}y=1.4y[/tex]
Therefore, [tex]1.4y[/tex] is equivalent to [tex]\dfrac{7}{5}y[/tex].
[tex]0.68y=\dfrac{68}{100}y[/tex]
[tex]0.68y=\dfrac{17}{25}y[/tex]
Therefore, [tex]\dfrac{17}{25}y[/tex] is equivalent to [tex]0.68y[/tex].
[tex]\dfrac{3}{5}y=0.6y[/tex]
Therefore, [tex]0.6y[/tex] is equivalent to [tex]\dfrac{3}{5}y[/tex].
[tex]1.32y=\dfrac{132}{100}y[/tex]
[tex]1.32y=\dfrac{33}{25}y[/tex]
Therefore, [tex]\dfrac{33}{25}y[/tex] is equivalent to [tex]1.32y[/tex].
In the figure given alongside, angle a=angle x and angle b= angle y, show that angle x + angle y + angle z= 180°
From the diagram shown, the sum of the angle on the straight line is 180degrees.
This means that:
m<a + m<z + m<b = 180 ............. 1
Given the following
m<a = m<x ...... 2
m<b = m<y ...... 3
Substitute equations 2 and 3 into equation1 to have:
m<x + m<y + m<y = 180
Rearrange
m<x + m<y + m<z = 180
This shows the required proof.
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Let t
4 and u = 6 + 2i. Find t * u
Answer:
24 + 8i
Step-by-step explanation:
t = 4
u = 6 + 2i
t x u
= 4 ( 6 + 2i )
= 24 + 8i
Answer:
24+8i
Step-by-step explanation:
i took the test
Please help ASAP!!!!
What is the sum of this series?
a group of 5 friends is out to dinner Each of the friends will order the dinner special and they have a coupon for $10 off the entire bill which equation can be used to find the total cost of all the dinners after the coupon is applied.
Answer:
TC = 5x -10
Step-by-step explanation:
Answer:
5d-10=C
Step-by-step explanation:
Because 5 friends are out to dinner so the cost of one meal is multiplied by five. Then you subtract 10 off the total for your answer, which is represented by the variable c
Which pair of angles are vertical angles?
ZWRU and ZSRT
ZWRS and VRT
w
ZVRU and ZTRS
R
AVRT and ZSRT
O
Given:
A figure.
To find:
The pair of vertical angles.
Solution:
If two lines intersect each other, then they form 4 disjoint angles at the intersection point. From these 4 angles the alternative angles are known as vertical angles or vertically opposite angles.
In the given figure, the line TW and line SV intersect each other at R. So, the pair of vertical angles is [tex]\angle WRS[/tex] and [tex]\angle VRT[/tex].
Therefore, the correct option is B.
∠WRS and ∠VRT are vertically opposite angles
Vertical angles:Vertical angles are a pair of opposite angles formed by intersecting lines. They are formed when two lines meet. This angles are vertically opposite each other.
Vertically opposite angles are equal or congruent.
Therefore,
∠WRS and ∠VRT are vertically opposite angles
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which statement is true regarding the functions on the graph
Answer:
f(3)=g(3)
Step-by-step explanation:
In this graph, the x (horizontal axis) represents the input and the y (vertical axis) represents the output. We know this because a function of x (f(x) and g(x) are two examples here) takes in x as the input, and y is the only variable left to be the output.
The question is asking when the two functions are equal based on the possible answers. First, we have to locate the point where the two lines meet, as depicted by the black dot in the picture. To find the x value of this, we can draw a vertical line (the light blue one I drew in the picture) and find where it meets the x axis (the horizontal one). This lines up with x=3. Similarly, for the y value, we can draw a horizontal line (the light green one) and find where it meets the y axis (the vertical one). This is when y=6.
Therefore, our functions are equal when x=3 and y=6. This means that f(3) = 6 and g(3)=6, and f(3)=6=g(3)
can someone please help ? i know one of the answers is c but couldn’t b and d also work ? when you figure them out you get x is less than 10 as well.
Answer:
b,c,d
Step-by-step explanation:
a ≤ 10 would have a closed circle at 10
b x+10 <15 x < 10 correct open circle line going to left
c x < 10 correct open circle line going to left
d 0 > x-10 10 > x x < 10 correct open circle line going to left
e 2 > x-11 13 > x would have open circle at 13
The open circle tells us that the sign is only less than/greater than, not less than/greater than or equal to. That immediately rules out A.
Now, we can see that this is a less than inequality, because the arrow is pointing to the left, toward the negative numbers. And, the inequality covers every number that is less than 10.
A - Incorrect, less than or equal to
B - Correct, when solved = x < 10
C - Correct
D - Correct, when solved = x < 10
E - Incorrect, when solved = x < 13
Hope this helps!
18
20 men, 10 women and 10 children are in a competition.
The mean score for the women is 15.6.
The mean score for the children is 9.2.
Kevin says that the mean score for all 40 people is 11.2.
Work out the mean score for the men.
Answer:
20
Step-by-step explanation:
The mean score for the women = 15.6
Sum of score for the women = 15.6*10 = 156
The mean score for the children = 9.2
Sum of score for the children = 9.2 * 10 = 92
The mean score for all 40 people = 11.2
Sum of the score of 40 people = 11.2 *40 = 448
Sum of the score for 20 men = 448 - 92 - 156 = 200
Mean of the score for the men = 200÷ 20 =20
pls answer correct
for class 9 only
Answer:
hope it helps
Step-by-step explanation::
a) Consider a body having initial velocity 'u'. Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes 'v'. Now, from the definition of acceleration we know that:
Acceleration = Time taken Change in velocity or Acceleration = time taken
Final velocity- Initial velocity
So, a= t v−u
at=v−u and, v=u + at
where v= final velocity of the body
u= initial velocity of the body
a= acceleration
and t= time taken
(b) Initial velocity, u=54km/h=15m/s
Final velocity, v=0m/s
Time, t=8s
Acceleration, a=?
a= t v−u
= 8 0−15
= 8 −15 m/s 2
=−1.875m/s 2
Nigel is making holiday cookies. His recipe calls for 1/2 pound of raisins. The recipe also calls for 1/4 pound of dates and 1/8 pound of dried apricots. How much dried fruit will be put into the cookies in all?
A: 1/8 pound
B: 3/8 pound
C: 5/8 pound
D: 7/8 pound
Answer:
D. 7/8 pound
Step-by-step explanation:
1/2+1/4+1/8=7/8
7/8 pound of dried fruit will be put into the cookies in all.
If f(x) = x2, and
g(x) = x – 1, then
f(g(x)) = [? ]x2+[?]+ [?]
Answer:
f(g(x)) = x² - 2x + 1
Step-by-step explanation:
To find f(g(x)), substitute x = g(x) into f(x) , that is
f(g(x))
= f(x - 1)
= (x - 1)² ← expand using FOIL
= x² - 2x + 1
use the zeros and the labeled point to write the quadratic function represented by the graph
Answer:
[tex]\sf \boxed{\sf y = -x^2-x +2 }[/tex]
Step-by-step explanation:
A graph of the quadratic function is given to us and by using the Zeroes , we need to write the function . From the graph , we can sew that , it cuts the x axis on (-2,0) and (1,0) .
Hence , x = -2 and 1 are the zeroes of the function .
In general if we have [tex]\alpha[/tex] and [tex]\beta[/tex] as the zeroes of the function , then the quadratic function is given by ,
[tex]\sf\longrightarrow\gray{ f(x) = (x -\alpha )(x-\beta) }[/tex]
Here the zeroes are -2 and 1 , on substituting the respective values in the formula , we have ,
[tex]\sf\longrightarrow f(x) = \{ x -(-2)\} ( x -1) [/tex]
Simplify inside the curly brackets ,
[tex]\sf\longrightarrow f(x) = ( x +2)(x-1) [/tex]
Multiply the two terms ,
[tex]\sf\longrightarrow f(x) = x ( x -1)+2(x-1) [/tex]
Simplify the brackets ,
[tex]\sf\longrightarrow f(x) = x^2-x +2x -2 [/tex]
Add the constants and the variables ,
[tex]\sf\longrightarrow f(x) = x^2+x -2 [/tex]
When the constant of the function is (-1),
[tex]\sf\longrightarrow\boxed{\blue{\sf y = -x^2-x+2}} [/tex]
Hence the equation of the function is y = -x² -x + 2 .
Answer:
the answer is " y=-3x^2-3x+6"
Step-by-step explanation:
i just took the test
which number best represents the slope of the graphed line
Answer: 1/2 it cant be an integer bc the graph is positive it can't be 2 bc 2/1 wouldn't match the line.
The required answer is 1/2
Step-by-step explanation:
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{rise}{run}[/tex] = slope
Pick point on the line where it crosses the y axis.
Notice it crosses at a corner of a square on the grid.
Find how many squares you must rise, and must run until it crosses another corner of a square on the grid.
You rise up 1 square, and run 2 squares to the right.
The number of measles cases increased 5.2% to 33 cases this year, what was the number of cases prior to the increase?
Answer:
x(1.052)= 33
x = 33/1.052 =31.36
Step-by-step explanation:
Answer:
31.284 or if you rounded to the nearest whole number it would be 31
Step-by-step explanation:
5.2% -> 0.052
33x0.052=1.716
33-1.716= 31.284
(I'm not 100% sure if this is right, but let me know if you get this right or wrong on your test.)
