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algol [13]
2 years ago
14

B

Mathematics
1 answer:
monitta2 years ago
5 0

Answer:

x = -2 or -12

Step-by-step explanation:

That is the solution above

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The sum of the first 150 negative integers is represented using the expression
Leona [35]

Answer:

\large\boxed{-11,325}

Step-by-step explanation:

First simplify:

-1-(n-1)=-1-n-(-1)=-1-n+1=-n

Therefore we have:

\sum\limits_{n=1}^{150}[-1-(n-1)]=\sum\limits_{n=1}^{150}(-n)=(-1)+(-2)+(-3)+...+(-150)\\\\-1,\ -2,\ -3,\ -4,\ ...,\ -150-\text{it's the arithmetic sequence}\\\text{with the common difference d = -1.}\\\\\text{The formula of a sum of terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute}\ n=150,\ a_1=-1,\ a_n=-150:\\\\S_{150}=\dfrac{-1+(-150)}{2}\cdot150=(-151)(75)=-11,325

8 0
3 years ago
Four CDs and 4 DVDs cost $164. The cost of the 4 CDs is half the cost of the
Andrej [43]

Answer:

$13.67

Step-by-step explanation:

Let's say that CD= c and DVDs= d. Four CDs and 4 DVDs cost $164, so the equation will be:

i.  4c + 4d= 164

The cost of the 4 CDs is half the cost of the  4 DVDs, to put into an equation it will be:

ii.   4c= 0.5(4d)

     4c= 2d

     d= 2c

Then we can substitute the second equation (ii) into the first equation (i). The calculation will be:

4c + 4d= 164

4c + 4(2c)= 164

4c+ 8c= 164

12c= 164

c=13.67

The cost for each CD is $13.67

5 0
3 years ago
I need help and ill give brainliest
elena-s [515]

Answer:

(-2,7) reflects to (-2,-7)

(3,9) reflects to (3, -9)

(7,2) reflects to (7,-2)

(-3,9) reflects to (-3,-9)

Step-by-step explanation:

in  reflection across the x-axis the x value of the coordinate stays the same and the y value is negated to show it been reflected

7 0
3 years ago
-5x-3y=22 help plz ​
Lerok [7]

Answer:

<h2>(-2, -4)</h2>

Step-by-step explanation:

Put the coordinates of the points to the equation, and check it:

(-4, -1) → x= -4, y = -1

L = -5(-4) - 3(-1) =20 + 3 = 23

R = 22

L ≠ R

(-1, -4) → x= -1, y = -4

L = -5(-1) - 3(-4) = 5 + 12 = 17

R = 22

L ≠ R

(-2, -4) → x= -2, y = -4

L = -5(-2) - 3(-4) = 10 + 12 = 22

R = 22

L = R    CORRECT :)

(-4, -2) → x = -4, y = -2

L = -5(-4) - 3(-2) = 20 + 6 = 26

R = 22

L ≠ R

3 0
3 years ago
An artist wishes to make a sign in the shape of an isosceles triangle as shown. find the area
Katarina [22]

Answer:

Step-by-step explanation:

Drop an angle bisector from angle C until it intersects AB. Because of the symmetry of the triangles created, you will form two small right angle congruent triangles. Call the point of intersection with AB = D. In other words the bisector of <C is CD.

CB = AC                          Isosceles triangle

CD / CB = Sin(38.5)        

  CD=?

  CB = 35

CD / 35 = Sin(38.5)      Multiply both sides by 35

CD = 35 * sin(38.5)

CD = 21.79

BD/CB  =  Cos(38.5)

BD = CB* Cos(38.5)

BD = 35 * Cos (38.5)

BD = 27.39

Area = CD * BA/2

BA/2 = DB

Area = CD * BD

Area = 21.79 * 27.39

Area = 596.9

3 0
3 years ago
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