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deff fn [24]
2 years ago
12

Show that 4(m + 7) + (m + 3)^2 = (m + 3)(m + 7) + 16

Mathematics
1 answer:
anygoal [31]2 years ago
4 0

Step-by-step explanation:

4(m+7)+(m+3)^2=(m+3)(m+7)+16\\\\L_S=4(m+7)+(m+3)^2\\\\\text{use the distributive property}:a(b+c)=ab+ac\\\text{and formula}:\ (a+b)^2=a^2+2ab+b^2\\\\L_S=(4)(m)+(4)(7)+m^2+2(m)(3)+3^2\\\\L_S=4m+28+m^2+6m+9\qquad\text{combine like terms}\\\\L_S=m^2+(4m+6m)+(28+9)\\\\L_S=m^2+10m+37

R_S=(m+3)(m+7)+16\\\\\text{use FOIL}:(a+b)(c+d)=ac+ad+bc+bd\\\\R_S=(m)(m)+(m)(7)+(3)(m)+(3)(7)+16\\\\R_S=m^2+7m+3m+21+16\qquad\text{combine like terms}\\\\R_S=m^2+(7m+3m)+(21+16)\\\\R_S=m^2+10m+37\\\\\boxed{L_S=R_S}

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Lisa is earning 7.50 dollars per hour she worked for 33 hours last week. how much money did she earn?
never [62]

Answer:

Lisa earned $247.50 for working 33 hours.

Step-by-step explanation:

WAY 1: proportional reasoning

7.50 x

------ = ----

1 h 33h

33 / 1 = 33

7.50 x 33 = 247.5

WAY 2: unit rate reasoning

7.50 per hour so x value of money for 33 h

7.50 x 33 = 247.5

7 0
2 years ago
Read 2 more answers
A carpenter is making a shelf in the shape of a parallelogram. She begins by drawing parallelogram RSTU on a coordinate plane wi
olchik [2.2K]
The coordinates would be (3, 3).

The slope from R to S is given by

m = (0 - 0)/(-4-1) = 0/-5 = 0

The distance from R to S is 5 units straight across.

This means the slope from T to U will be 0, and it will be a horizontal segment.  This means the y-coordinate of U will be 3, since the y-coordinate of T is 3.

The distance from T to U will be 5 as well; -2+5 = 3 for the x-coordinate.

This makes the point (3, 3).
3 0
3 years ago
I need help with this V-4=v+2+7v-42 ??
zubka84 [21]

Answer:

\boxed{\bold{v \ = \ \frac{36}{7}}}

Step-by-step explanation:

Subtract v from both sides

\bold{v-4-v=v+2+7v-42-v}

Simplify

\bold{-4=2+7v-42}

Switch sides

\bold{2+7v-42=-4}

Group like terms

\bold{7v+2-42=-4}

Subtract the numbers: 2 - 42 = -40

\bold{7v-40=-4}

Add 40 to both sides

\bold{7v-40+40=-4+40}

Simplify

\bold{7v=36}

Divide both sides by 7

\bold{\frac{7v}{7}=\frac{36}{7}}

Simplify

➤ \bold{v=\frac{36}{7}}

5 0
3 years ago
The square of a positive number is equal to its triple added to 28. What is this number?​
sashaice [31]

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

\huge{ \rm{Answer:}}

The roots of the equation are 7 and -4, because 7 - 4 = 3 and 7. - 4 = -28

Step-by-step explanation:

The positive number is equal to 7.

Assuming that the number is equal to "x" we have:

\begin{gathered}x^2 = 3x + 28\\\\x^2 - 3x - 28 = 0\\\\a = 1\\\\b = -3\\\\c = -28\\\end{gathered}

By the sum and product method, we have:

\begin{gathered}S = -b / a\\\\S = -(-3) / 1\\\\S = 3\\\\\end{gathered}

\begin{gathered}P= c / a\\\\P = 28 / 1\\\\P = 28\\\\\end{gathered}

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2 years ago
Cuál es el denominador común de las fracciones?​
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Answer:

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Step-by-step explanation:

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3 years ago
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