For problems 1 - 4, write a two-column proof.

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!

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

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.)

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]

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

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

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

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.

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We have,

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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.

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Thus,

Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.

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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)

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

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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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

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.

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

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

Answer:

-4/5

Step-by-step explanation:

2/5 ÷ -1/2

Copy dot flip

2/5 * -2/1

-4/5

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

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]

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

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.

Answer:

Your is answer would be choice C which is : 32 cm

Step-by-step explanation:

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 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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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].

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.

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

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.

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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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

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