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3 years ago

4a + (–6b) – 3a + 2b factor the expression

Mathematics

1 answer:

Gemiola [76]3 years ago

5 0

Answer:

a−4b

Step-by-step explanation:

Combine Like Terms:

=4a+−6b+−3a+2b

=(4a+−3a)+(−6b+2b)

=a+−4b

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WXYZ is a parallelogram find the angle measures

Ivahew [28]

Answer:

W and Y = 91. X and Z = 89

Step-by-step explanation:

Those two angles will add to 180.

5a - 21 + 3a + 25 = 8a + 4

8a + 4 = 180

8a = 176

176 / 8 = 22 = a

Plug in a for an angle.

3(22) + 25 = 91

180 - 91 = 89

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3 years ago

Jocelyn desires to increase both her protein consumption and caloric intake. She desires to have at least 35 more grams of prote

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3 years ago

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What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10

emmasim [6.3K]

Answer:

The value of x is in the solution set of 3(x – 4) ≥ 5x + 2 is -10

Solution:

Need to determine which value of x from given option is solution set of 3(x – 4) ≥ 5x + 2

Lets first solve 3(x – 4) ≥ 5x + 2

3(x – 4) ≥ 5x + 2

=> 3x – 12 ≥ 5x + 2

=> 3x – 5x ≥ 12 + 2

=> -2x ≥ 14

=> -x ≥ 7

=> x ≤ -7

All the values of x which are less than or equal to -7 is solution set of 3(x – 4) ≥ 5x + 2. From given option there is only one value that is -10 which is less than -7

Hence from given option -10 is solution set of 3(x – 4) ≥ 5x + 2.

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3 years ago

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Maggie's brother is 10 years younger than twice her age. The sum of their ages is 32.

mixas84 [53]

Answer:22

Step-by-step explanation:

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2 years ago

Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

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3 years ago