The sum of first three terms of an arithmetic series is 21. If the sum of the first two terms is subtracted from the third term then it would be 9. find the three terms of the series​

Answer:

m<PQT= 94°

Step-by-step explanation:

If line QS bisect <PQR

m<PQS = m < SQR

7x-6= 4x+15

7x-4x= 15+6

3x= 21

X= 21/3

X= 7

m<PQS= 7x-6

m<PQS= 7(7)-6

m<PQS= 49-6

m<PQS= 43°

m<PQS= m<SQR

<mSQR=43°

m<PQR= m<PQS + m < SQR

m<PQR=43+43

m<PQR= 86°

BUT

m<PQR= m<TQW

m<PQT= m<RQW

m<PQR+m<TQW +m<PQT+ m<RQW

= 360°

Let m<TQW= x

86+86+x+x= 360

2x+172= 360

2x= 188

X= 94°

m<PQT= 94°

Answer:

16 hrs of Sleep

6 hrs of Raking Leaves

4 hrs reading

3 hrs science project

2 hrs riding car

1 hr watching tv

Step-by-step explanation:

Its division on all of them, 9:00 PM on Friday to 9:00 PM on Sunday, would be 2 days, there being 24 hrs on one day, and since its 2 days, its 48, then you divide 48 by the denominator, and there you should get your timed answer.

For example, for the 1/3, you'll divide the denominator (the bottom number, in this case 3) by 48, since that's the whole amount, and the 3 is the amount of time they spent out of that whole. The division is written 48 ÷ 3 = 16

Hope this helped a bit :)

Answer:

Step-by-step explanation:

Our interval is 180 to 270 so that's quadrant III. In quadrant 3, both x and y are negative. If we set up our right triangle in this quadrant and label it accordingly with the values given for tangent theta, we find that the missing length is the hypotenuse. Solve for that using Pythagorean's Theorem. Doing that gives us that the hypotenuse is [tex]\sqrt{61}[/tex].  Now we can solve for your other identities. First,

[tex]cos(2\theta)=2cos^2\theta-1[/tex] (There are 3 identities for cos(2θ) and regardless of which one you pick, the answer will be the same every time...promise!)

Filling in now:

[tex]cos(2\theta)=2(\frac{-5}{\sqrt{61} })^2-1[/tex] and simplified a bit:

[tex]cos(2\theta)=2(\frac{25}{61})-1[/tex] and a bit more:

[tex]cos(2\theta)=\frac{50}{61}-\frac{61}{61}[/tex] giving us, finally:

[tex]cos(2\theta)=-\frac{11}{61}[/tex]

Now for b. We have an identity for the half angle of sin:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-cos\theta}{2} }[/tex]  and filling in:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-(-\frac{5}{\sqrt{61} } )}{2} }[/tex] which simplifies a bit to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1+\frac{5}{\sqrt{61} } }{2} }[/tex] and a bit more to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}+5 }{2\sqrt{61} } }[/tex]  I'm not sure if this is the form you need it in, but this is the answer, as convoluted and crazy as it may look.

As for the cosine half-angle, the identity is the same, except there's a + sign in the numerator of the identity instead of a -, giving us the solution:

[tex]cos(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}-5 }{2\sqrt{61} } }[/tex]

Well, in this case we can take a as the protagonist.

We can, for example, take the a in the first member of the disequation, the 2 in the second one, changing the signs

so

+ 2 > - a

a > - 2

In fact,

"If 2 > - a, then a > -2."

Answer:

y= 0.35

Step-by-step explanation:

y 1/4

when x=5,

find y=? when x=7.

given that y varies directly with x.

y = kx

Where k is the constant of proportionality

k= y/x

k= (1/4)÷ 5

k= 0.05

y= kx

y= (0.05)(7)

y= 0.35

I Hope this will helpful...

Answer:

625

Step-by-step explanation:

5⁴ = 5x5x5x5 = 625

Answer:

  all reals

Step-by-step explanation:

Simplified, you have ...

  20 -3n = 20 -3n

The equation is a tautology, true for all values of n.

The solution set is "all reals."

Answer:

3 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 60 = x/3

3 tan 60 = x

3 sqrt(3) = x

Answer:

x = 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{x}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

x = 3[tex]\sqrt{3}[/tex]

Answer: False. This expression is a monomial!

Answer:

false

Step-by-step explanation:

it is molonomial

Answer:

a + b = 90°

Step-by-step explanation:

If sum of two angles are 90°, then the two angles are complementary

Angles that are complements form corners. I've bolded the "co" letters to help remember that complementary angles form a 90 degree corner. Whereas supplementary angles form a straight line (both "supplementary" and "straight" start with "S"). So that's one way to remember the two terms.

Anyways, if a and b are complements of each other, then a+b = 90.

Convert to a simplified fraction.

(-3,-2)

3/2

(1,-6)

-1/6

Together they just equal -9, so hopefully, your teacher wants those fractions instead.

Answer:

D

Step-by-step explanation:

The midpoint is the average of the 2 endpoints, that is

midpoint = [tex]\frac{-7+12}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 → D

Step-by-step explanation:

Using distance formula:

√(- 7 - (-5))² + (3 - 2)²

√(- 7 + 5)³ + 1²

√(-2)² + 1

√4+1

√5

Answer:

base and altitude both are 6 cmand 6cm

Answer:

18.33333333%. Please mark as brainliest if I’m Correct. :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]5*\dfrac{1}{4}=\dfrac{5}{4}\\[/tex]

Using addition,

Add (1/4) , five times

[tex]\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1+1+1+1+1}{4}\\\\=\dfrac{5}{4}[/tex]

Answer:

5/4

Step-by-step explanation:

Add 1/4 together 5 times:

1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4

Answer:

A. It’s decreasing

Step-by-step explanation:

Hey there!

Well on the graph at points -1 and 1 we can tell the line is going down,

meaning the line is decreasing.

Hope this helps :)

Answer:it is increasing

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.

[tex]y=a(x-1)^2-4[/tex]

And the point (0,-1) is on the graph so we can write.

[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]

So the equation is.

[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]y=3x^{2} -6x-1[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Draw a line through the data points with about half of the points on one side of the line and the other half on the other side.  You'll see that there is a slight positive rise in the graph as we move from left to right, but the correlation is weak.  Thus, 0.4 is the correct correlation coefficient in this case.

The correlation coefficient that would best describe the data give in the table is 0.4 which is a weak positive correlation.

The statistical concept of correlation describes how closely two variables move in tandem with one another.

As the graph is scattered in such a way that,if we draw a line from the centre, we can observe that as 'x' increases 'y' also increases so the relation is positive correlation.

But it is seen in the graph that these points are scattered, so this relation is weak. For positive weak correlation the value should be less than 0.5.

Therefore, the given graph shows positive weak correlation with value 0.4.

To know more about statistics, here

https://brainly.com/question/23724696

#SPJ2

Answer:

the value of angle A is 82.819°

Answer:

x = 0

Step-by-step explanation:

Since the points are collinear , then

AB + BC = AC , that is

11 + 2x + 10 = x + 21

2x + 21 = x + 21 ( subtract x from both sides )

x + 21 = 21 ( subtract 21 from both sides )

x = 0

Answer:

"2.93BAR

LET X=2.93BAR

10X=29.393BAR

100X=293.93BAR

NOW WE WILL SUBTRACT THE FIRST EQUATION FROM THIRD EQUATION

​100X=293.93BAR

X= 2.93BAR

99X=291.00BAR

IT CAN ALSO BE WRITTEN LIKE

X=291/99"

This was an answer from the same question someone else asked.

This answer was given by grvbundela008p3f6id

Step-by-step explanation:

Answer:

C.2

Step-by-step explanation:

Faktor perdana adalah faktor numbor² bagi sesuatu nombor yang juga merupakan nombor perdana.

Faktor nombor 28 adalah 1 ,2, 4 , 7 ,14 dan 28.

Dalam list nombor perdana ini hanya 2 dan 7 merupakan nombor perdana. Maka , jawapan soalan ini adalah 2.

Answer:

1) 11[tex]\sqrt{3}[/tex]

2) 2[tex]\sqrt{2}[/tex]

3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

4) [tex]53 + 12\sqrt{10}[/tex]

5) -2

6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Step-by-step explanation:

1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]

=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]

= 11[tex]\sqrt{3}[/tex]

2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]

= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]

= 2[tex]\sqrt{2}[/tex]

3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]

= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]

= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]

= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]

= [tex]8 + 12\sqrt{10} + 45[/tex]

= [tex]53 + 12\sqrt{10}[/tex]

5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]

= [tex]1 - 3[/tex]

= -2

6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]

= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]

= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]

= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]

= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Hope the working out is clear and will help you. :)

Step-by-step explanation:

please I solved the question in the diagram above

Answer:

v = (base x height x length)/2

(7 x 10 x 13)/2 = 455 x 3.15 = 1433.25$

hope that answers your question

Answer:

16% drop

Step-by-step explanation:

4/25 drop

Multiply by 4/4

16/100

16% drop

Answer:

16%

Step-by-step explanation:

SInce 4 students left the class, and there are 25 students, let's make it a fraction.

4/25.

As it is asking for a percentage though we could simply convert our fraction to a percentage.

Simply divide the numerator (4) by the denominator (25).

This gives us 0.16.

Which is 16%.

Answer:

Below

Step-by-step explanation:

Notice that x is between 10 and -10 but takes only the values that are integers.

The inequalities:

● we can write an inequality that includes all these values.

● -10 《 x 《 10

This is a possible inequality

Multiply both sides by 2 and you will get a new one:

● -20 《 2x 《 20

You can multiply it by any number to generate a new inequality.

Or you can add or substract any number.

Answer:

√30 =

5.4772255751

It can be simplified as this only, not more

Answer:

y=-4x+16

Step-by-step explanation:

Okay, so a perpendicular line has an opposite reciprocal slope.

The slope for the first line is x/4, but I like to write it as 1/4x, since it's easier to look at.

The opposite reciprocal for 1/4x is -4x

So far, we have y=-4x+ [  ]

To find the remaining b value, we can use the given point intersection.

plug in the x and y values given (4, -1) and solve for b.

The equation for the perpendicular line is y=-4x+16