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antoniya [11.8K]
2 years ago
5

Someone pleeeeease help me

Mathematics
1 answer:
lukranit [14]2 years ago
7 0

Answer:

22.4cm

Step-by-step explanation:

The formula for the diagonal is:

d =  \sqrt{l^{2} + b^{2} +h {}^{2}   }

Where:

l is the length (AB, CD)

b is the width (BC, AD)

h is the height (AE, BF, CG, DH)

We know d, l, b and we can calculate h

25  =  \sqrt{10^{2} + 8^{2}  + h^{2}  }

We evaluate both sides to ² to remove the square root:

25^{2} = 100 + 64 + h {}^{2}

625 = 164 + h {}^{2}

To find the value of h we have to do the square root, as it is to the ²:

\sqrt{625 - 124}  = h

\sqrt{501}  = h = 22.4cm

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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
e-lub [12.9K]

Answer:

DC=\frac{8}{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

BM^2=AB^2-AM^2

we have

AB=5\ units\\AM=x\ units

substitute

BM^2=5^2-x^2

BM^2=25-x^2 -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

BM^2=BC^2-MC^2

we have

BC=7\ units\\MC=AC-AM=(9-x)\ units

substitute

BM^2=7^2-(9-x)^2

BM^2=49-(81-18x+x^2)  

BM^2=49-81+18x-x^2

BM^2=-x^2+18x-32 ----> equation B

equate equation A and equation B

-x^2+18x-32=25-x^2

solve for x

18x=25+32\\18x=57\\\\x=\frac{57}{18}

Simplify

x=\frac{19}{6}

<em>Find the length of DC</em>

DC=AC-2x

substitute the given values

DC=9-2(\frac{19}{6})

DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units

8 0
3 years ago
The length of an equilateral triangle is increased by 5 cm. The perimeter of the new triangle is 72 cm. What is the side length
Igoryamba

Answer:

19cm

Step-by-step explanation:

An equilateral triangle is a triangle where the length of the 3 sides are the same.

the perimeter is the sum of the 3 sides

for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15

let x = unknown length of side

length after increase = x + 5

(x + 5) x 3 = 72

divide both sides of the equation by 3

x + 5 = 24

subtract 5 from both sides of the equation

x = 24 - 5 = 19cm

6 0
3 years ago
Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef fo
olasank [31]
You can solve this by using the system of equations.
Jan - 4.95 = 2H + 3C
Wayne - 5.45 = 3H + 2C

Use elimination.
-3(2H + 3C = 4.95)
2(3H + 2C = 5.45)

Solve. And you'll get:
-6H + (-9C) = -14.85
6H + 4C = 10.9

Cross out -6H and 6H because they cancel out. And you're left with:
-9C = -14.85
4C = 10.9

Add -9C with 4C, and -14.85 with 10.9.
-5C = -3.95

Divide each side with -5.
C = $0.79

Now to figure out what H is, just substitute the C in one of the equations with 0.79.
5.45 = 3H + 2(0.79)
5.45 = 3H + 1.58
-1.58            -1.58
3.87 = 3H
3.87/3 = 3/3(H)
1.29 = H

Finished!
7 0
3 years ago
Read 2 more answers
A recipe calls for 1 3/4 cups of sugar. How many cups of sugar are needed if only 3/8 of the recipe is being made?
Katen [24]

Answer: 9/16

Step-by-step explanation:

7 0
3 years ago
If a biking tour group traveled at a constant rate of 34 miles per day for 5 days, how many miles did they cycle?
AveGali [126]

Answer:170

Step-by-step explanation:

34 miles times 5 days is 170 miles

4 0
3 years ago
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