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nexus9112 [7]
3 years ago
9

If y = 2x - 1 and (3,5) and (4,7) are part of the pattern then what is the y coordinate of (5._)?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

Step-by-step explanation:

y = 2x - 1

(5,?).....so we know that x = 5....so sub in 5 for x in ur original equation and find y

y = 2x - 1

y = 2(5) - 1

y = 10 - 1

y = 9.....so ur point is (5,9).....with y being 9

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Two times the sum of a number and 7
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Step-by-step explanation:

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If (ax+2)(bx+7)=15x2+cx+14 for all values of x, and a+b=8, what are the 2 possible values fo c
dolphi86 [110]

Given:

(ax+2)(bx+7)=15x^2+cx+14

And

a+b=8

Required:

To find the two possible values of c.

Explanation:

Consider

\begin{gathered} (ax+2)(bx+7)=15x^2+cx+14 \\ abx^2+7ax+2bx+14=15x^2+cx+14 \end{gathered}

So

\begin{gathered} ab=15-----(1) \\ 7a+2b=c \end{gathered}

And also given

a+b=8---(2)

Now from (1) and (2), we get

\begin{gathered} a+\frac{15}{a}=8 \\  \\ a^2+15=8a \\  \\ a^2-8a+15=0 \end{gathered}a=3,5

Now put a in (1) we get

\begin{gathered} (3)b=15 \\ b=\frac{15}{3} \\ b=5 \\ OR \\ b=\frac{15}{5} \\ b=3 \end{gathered}

We can interpret that either of a or b are equal to 3 or 5.

When a=3 and b=5, we have

\begin{gathered} c=7(3)+2(5) \\ =21+10 \\ =31 \end{gathered}

When a=5 and b=3, we have

\begin{gathered} c=7(5)+2(3) \\ =35+6 \\ =41 \end{gathered}

Final Answer:

The option D is correct.

31 and 41

8 0
1 year ago
Solve the following inequality. 21<_-3(x - 4) < 30 A. 28<_x < 37 B. -3 <_ x < 6 C. -6 < x <_ -3 D. -10 &
Aloiza [94]

Answer:

Option C -6

Step-by-step explanation:

we have

21\leq -3(x-4)

The compound inequality can be divided into two inequality

21\leq -3(x-4) -----> inequality A

-3(x-4) ----> inequality B

Solve inequality A

21\leq -3x+12

9\leq -3x

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

-3\geq x

Rewrite

x\leq -3

The solution of the inequality A is the interval (-∞,-3]

Solve the inequality B

-3x+12

-3x

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

x>-6

The solution of the inequality B is the interval [-6,∞)

The solution of the compound inequality is

[-6,∞) ∩ (-∞,-3]=(-6,-3]

-6

3 0
3 years ago
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