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2 years ago

What is the shaded region

Mathematics

1 answer:

salantis [7]2 years ago

3 0

The difference between the area of the entire polygon and the area of the unshaded part inside the polygon

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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

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

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

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

For the dataset: 6, 3, 8, 3, 7, 12, 3 Find the mean.

adelina 88 [10]

The mean of this dataset is: 6

5 0

3 years ago

Read 2 more answers

Which answer does NOT correctly describe the graph of y = 5x + 12?

Dafna11 [192]

Answer:

The graph contains the point (5, 12) does NOT correctly describe the graph of y = 5x + 12

Solution:

Given, linear equation in two variable is y = 5x + 12.

We have to select the option that incorrectly describes about given equation.

Now, we have to check one by one option.

a) The line has a constant rate of change.

As the given line is an linear equation it will have constant slope. So this option states correctly

b) The line crosses the y-axis 12 units above the origin

When a line crosses y – axis it x value becomes 0 → y = 5(0) + 12 → y = 12

So, the line crosses the y – axis 12 units above the origin, so this option states correctly.

c) The graph contains the point (5, 12)

To contain (5, 12) in that line → 12 - 5(5) + 12 = 0 but -1 ≠ 0

So, this option is incorrect.

Hence, option c incorrectly describes about the graph.

7 0

3 years ago

Solve 2x>7 please thanks

Montano1993 [528]

Answer:

x > $\frac{7}{2}$

Step-by-step explanation:

given

2x > 7 ( isolate x by dividing both sides by 2 )

x > $\frac{7}{2}$

8 0

3 years ago

Read 2 more answers

One pound of swordfish costs as much as 1.5 pounds of salmon. Mrs. O pays $39 for 2 pounds of salmon and 3 pounds of swordfish.

Dimas [21]

Answer:

The ratio of the amount for swordfish to the amount of salmon is 6:4

Step-by-step explanation:

Given as :

The price for 1 pound of swordfish = The price of 1.5 pound of salmon

So, On this relation

The price for ( 1 × 2 ) pound of swordfish = The price of ( 1.5× 2 ) pound of salmon

i.e The price for 2 pound of swordfish = The price of 3 pound of salmon

Now According to question

Mrs. O pay the total money for 2 pounds of swordfish and 3 pound of salmon = $ 39

Let the money she pay for swordfish = 2 sw

And The money she pay for salmon = 3 sa

∵, The total money she pay for both = $ 39

I.e 2 sw + 3 sa = 39

As 2 sw = 3 sa

So, 3 sa + 3 sa = 39

Or, 6 sa = 39

or, sa = $\frac{39}{6}$ = $\frac{13}{2}$

∴ sw = $\frac{13}{2}$ × $\frac{3}{2}$

or, sw = $\frac{39}{4}$

Now, the ratio of the amount for swordfish to the amount of salmon = $\frac{\frac{39}{4}}{\frac{13}{2}}$

I.e The ratio = $\frac{6}{4}$

Hence The ratio of the amount for swordfish to the amount of salmon is 6:4

Answer

3 0

3 years ago