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faltersainse [42]

3 years ago

10

Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.

1 answer:

kodGreya [7K]3 years ago

4 0

Volume of the pyramid = (1/3) x Area of the base x Height ---------- (1)

As the base length = 5 feet

So Area of the base = 5 x 5 = 25 square feet

While volume of the pyramid = 75 cubic feet

Putting values in equation (1);

75 = (1/3) x 25 x Height

Height = (75 x 3) / 25

Height = 9feet

<span>So 2nd option is correct.</span>

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A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb

Kobotan [32]

Answer:

2,500 German chocolate cake boxes.

1,500 Swiss chocolate cake boxes.

Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

$0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700$

Solving the linear system above:

$(0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500$

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

6 0

3 years ago

Factorize 2a^2+7a-15

loris [4]

$\huge\bf \pink {\underline{Solution :-}}$

$2 {a}^{2} + 7a - 15$

$= 2 {a}^{2} + 10a - 3a - 15$

$= 2a(a + 5) - 3(a + 5)$

$= (a + 5)(2a - 3)$

$\sf \red{Hence, Answer \: is \: (a + 5)(2a - 3).}$

$\\$

$\bf \purple{ \underline{ Important \: Formulas \: for \: Factorization :-}}$

$• \: {a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}$

$• \: (a + b)(a - b) = {a}^{2} - {b}^{2}$

$• \: {a}^{2} - 2 ab + {b}^{2} = {(a - b)}^{2}$

$• \: {a}^{3} + 3 {a}^{2} b + 3a {b}^{2} + {b}^{3} = {(a + b)}^{3}$

$• \: {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{3}$

$• \: {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )$

$• \: {(a + b)}^{2} - {(a - b)}^{2} = 4ab$

$• \: (a + b)( {a}^{2} -ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

$• \: (a - b)( {a}^{2} + ab + {b}^{2} ) = {a}^{3} - {b}^{3}$

$• \: {( \frac{a + b}{2} )}^{2} - ( {\frac{a - b}{2} } )^{2} = ab$

5 0

3 years ago

Read 2 more answers

Is a triangle with angle measures 34 62 and 83 possible

zysi [14]

angles must add up to 180

so 34+62+83

but 34+62+83=179

and that is less than 180

so no it is not possible

3 0

3 years ago

The length of one side of a triangular lot is 6 m less than 3 times the length of the second side. The third side is 8 m longer

Tanya [424]

second side = x

first side = 3x - 6

third side = (3x - 6) + 8

The perimeter = 80m and is equal x + (3x - 6) + [(3x - 6) + 8]

x + 3x - 6 + 3x - 6 + 8 = 80

7x - 4 = 80 |+4

7x = 84 |:7

x = 12 m

3x - 6 = 3(12) - 6 = 30 m

(3x - 6) + 8 = 3x + 2 = 3(12) + 2 = 38 m

Answer: 12m, 30m, 38m

8 0

3 years ago

If /_\CAT ~= /_\LUV then /_\c ~=/_\L. True or False?

marshall27 [118]

Answer:

True

Step-by-step explanation:

They will eat u tho

5 0

2 years ago