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katen-ka-za [31]
3 years ago
9

The longest diagonal

Mathematics
1 answer:
Ratling [72]3 years ago
8 0
The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y  ⇒x=3y/2

(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6

x=3y/2=3*6/2=9

we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34

Answer: The longest diagonal is 36 units. 
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Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks
Dennis_Churaev [7]

Answer:

y = \frac{3}{4}x - 2

Step-by-step explanation:

Equation of a line is given as y = mx + b

Where,

m = slope of the line = \frac{y_2 - y_1}{x_2 - x_1}

b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.

Let's find m and b to derive the equation for the line.

m = \frac{y_2 - y_1}{x_2 - x_1}

Use the coordinate pair of any two points on the line. Let's use the following,

(0, -2) = (x_1, y_1) => on the line, when x = 0, y = -2

(4, 1) = (x_2, y_2) => on the line, when x = 4, y = 1

Plug in the values and solve for m

m = \frac{1 - (-2)}{4 - 0}

m = \frac{1 + 2}{4}

m = \frac{3}{4}

b = -2 (the line intercepts the y-axis at this point)

Our equation would be =>

y = mx + b

y = \frac{3}{4}x + (-2)

y = \frac{3}{4}x - 2

5 0
3 years ago
Sofia learned 10 recipes to create party dishes. she learned these recipes in 2 weeks. how many recipes can Sofia learn in 5 wee
insens350 [35]
Its 25 because she learned the 10 recipes in 2 weeks so 4 weeks is 20 and 5 weeks is 25 if its wrong some how than I'm tired so don't blame me
3 0
3 years ago
Read 2 more answers
What is the missing value in the equation shown □ x1/10=0.034
grin007 [14]

Answer:

0.34

Step-by-step explanation:

Do the inverse operation so;

0.034 / 1/10 = 0.34

Now go back and subsitute,

0.34 * 1/10 = 0.034

4 0
3 years ago
If 8 people want to share a 50 pound sack of rice equally by weight about how many pounds of rice will each person get
Archy [21]

Answer:

6.25 or 6 1/4

Step-by-step explanation:

because 50 divided by 8 is 6.25

3 0
2 years ago
Place the numbers 0 to 8, inclusive, in the magic square so that the sum of the numbers in each row, column, and diagonal is the
ehidna [41]

Answer: See attached table

Step-by-step explanation:

\begin{table}[]\begin{tabular}{lllll} &  &  &  &  \\ &  &  &  &  \\ &  &  &  &  \\ &  &  &  & \end{tabular}\end{table}+---+---+---+

| 1 | 8 | 2 |

+---+---+---+

| 6 | 4 | 2 |

+---+---+---+

| 5 | 0 | 7 |

+---+---+---+

<u>Proofs:</u>
First row: 1+6+5 = 12

Second row: 8+4+0 = 12

Third row: 2+2+7 = 12

First column: 1+8+2 = 12

Second column: 6+4+2 = 12

Third column: 5+0+7 = 12

Diagonal starting from top left to bottom right: 1+4+7 = 12

Diagonal staring from top right to bottom left: 2+4+5 = 12

6 0
2 years ago
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