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2 years ago

Which of the following are solutions to the equation below?

Mathematics

1 answer:

nalin [4]2 years ago

3 0

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's solve the given equation ~

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x + 25 = 49$

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x + 25 - 49 = 0$

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x - 24 = 0$

$\qquad \tt \dashrightarrow \:4( {x}^{2} + 5x - 6) = 0$

$\qquad \tt \dashrightarrow \: {x}^{2} + 5x - 6 = 0$

$\qquad \tt \dashrightarrow \: {x}^{2} + 6x - x - 6 = 0$

$\qquad \tt \dashrightarrow \:x(x + 6) - 1(x + 6) = 0$

$\qquad \tt \dashrightarrow \:(x + 6)(x - 1) = 0$

Hence, we get -6 and 1 as our roots ~

So, the correct choices are : B and D

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A rectangular prism has a base area 56 ft.² and a volume of 840 ft.³ the length of the base is longer than the width if the sum

suter [353]

Answer:

The length of the base in feet is 8 ft.

Step-by-step explanation:

The volume V of the rectangular prism is given by

V = l × w × h

But Area, A = l × w

∴ V = A × h

Where A is the base area and h is the height

From the question

A = 56 ft.² and V = 840 ft.³

∴ 840 ft.³ = 56 ft.² × h

840 ft.³ / 56 ft.² = h

15 ft. = h

∴ h = 15 ft.

Hence, the height of the rectangular prism is 15 ft.

Also, from the question

the sum of the length and the width of the base is equal to the height

i.e l + w = h

where l is the length of the base and w is the width of the base

Then, l + w = 15 ------ (1)

Also, A = l × w

Then, 56 = l × w ------- (2)

From equation (1)

l + w = 15

Then, w = 15 - l ------- (3)

Substitute this into equation (2)

56 = l × w

56 = l × (15-l)

56 = 15l - l²

Then,

l²- 15l + 56 = 0

l² -8l -7l + 56 = 0

l(l - 8) -7(l - 8) = 0

(l - 7)(l - 8) = 0

l - 7 = 0 OR l - 8 = 0

∴ l = 7 OR l = 8

Substitute the values of l into equation (3)

w = 15 - l

when l = 7

w = 15 - 7

w = 8

and when l = 8

w = 15 - 8

w = 7

From the question, the length of the base is longer than the width

∴ l = 8 and w = 7

Hence, the length of the base in feet is 8 ft.

6 0

2 years ago

Please anyone solve this for me..No spam.

Tamiku [17]

Answer:

3096

Step-by-step explanation:

Given:

$3x-\frac{1}{4y}=24$

Rewrite it as:

$3x=\frac{1}{4y}+24$
$x=\frac{1}{12y}+8$

Simplify the expression:

$8x(6x - \frac{1}{y} ) + \frac{1}{12y^2} (4 - 3y + 36xy^2) =$
$8(\frac{1}{12y}+8)(6(\frac{1}{12y}+8) - \frac{1}{y} ) + \frac{1}{3y^2} - \frac{1}{4y} + 3x =$
$8(\frac{1}{12y}+8)(48- \frac{1}{2y} ) + \frac{1}{3y^2} - \frac{1}{4y} + 24 + \frac{1}{4y} =$
$8(\frac{4}{y}+8*48- \frac{1}{24y^2} -\frac{4}{y} ) + \frac{1}{3y^2} + 24 =$
$8(384-\frac{1}{24y^2}) + \frac{1}{3y^2} + 24 =$
$8*384-\frac{1}{3y^2} + \frac{1}{3y^2} + 24 =$
$3072+24=$
$3096$

3 0

2 years ago

Write as a product 27a^3−(a−b)^3

jarptica [38.1K]

Answer:

(2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

(p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

p = 3a
q = (a-b)

so the factorization is ...

(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

6 0

3 years ago

while visiting a mountain, John approximated the angle of elevation to the top of a hill to be 25 degrees. Alfter walking 350 fe

strojnjashka [21]

There are several ways of going about this problem, but just know that it all boils down to triangles and the rules/laws of triangles.
So we start by making a large right triangle, because the hill is vertical with the horizontal ground, with 25° as the left angle (where John looks up to top), 90° is the right angle (where ground meets hill base). So we see that the top side of the triangle is the hypotenuse, and equals the line of sight from John to hilltop.
Now we've got additional information that if John walks 350ft towards the hill, his angle of elevation increases by 14. So that = 25+14 = 39. How does that possibly help us?? Well now we can make 2 triangles inside of the one we've already made. So that now we have the triangle base split between the left angle of 25° and where he stopped 350ft to the right of that.
Now the supplement of 39 is 141, and the remaining piece of that too left triangle = 180-25-141 = 14. What does that mean? Well now we have a triangle, where we know all 3 angles and 1 side --> we can find another side by the law of sines:
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
a÷sinA = b÷sinB = c÷sinC
We really need the hypotenuse to then find our hill height, so we'll make hypotenuse = side b in attached image. That being so, then its opposite angle (B) = 141. And the top right angle (C) = 14 with its opposite side (c) = 350ft.
Now we only need b÷sinB = c÷sinC
So b/sin141 = 350/sin14 --> b = 350sin141/sin14 = 350×.63/
b = 220.3/.24 = 910.47 ft
Now that's our hypotenuse, so using our original large right triangle, we can use right triangular trig. to solve. Let's make the right side, our hill height, equal to x.
Sin ¥ = opp. side / hypotenuse -->
Sin ¥ = x / hypotenuse
Sin25 = x / 910.5
x = 910.5×sin25 = 910.5×.423
x = 384.8 ft

3 0

3 years ago

The graph of f(x)=x2 was transformed to create the graph of g(x)=(x+5)2.

alexandr1967 [171]

Answer:

a horizontal shift left

Step-by-step explanation:

my teacher always tells me whatever you think it is in the parenthisis do the opposite. Sorry not a good explanation

5 0

2 years ago