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matrenka [14]
3 years ago
7

The triangles are similar. What is the value of x?

Mathematics
2 answers:
jok3333 [9.3K]3 years ago
8 0
Given that the two triangles are similar:
\frac{7}{28} =  \frac{25}{6x + 28}
\frac{1}{4} = \frac{25}{6x + 28}
6x + 28 = 4 x 25
6x + 28 = 100
6x = 100 - 28
6x = 72
x = 12

Degger [83]3 years ago
7 0
X=12 and the number that makes the triangle larger is 4
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The straight line 2x + 3y = 7 meets the curve
NISA [10]

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.

5 0
3 years ago
How do I turn 25/8 into a mixed number
vovikov84 [41]
You can turn 25/8 into a mixed number by dividing it. It would = 3 
3 0
3 years ago
Y=-3x^2-6x+24
Lera25 [3.4K]
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




3 0
3 years ago
Plz help
Molodets [167]
The irrational numbers are √10,√27,√99.
3 0
3 years ago
The Hudson Bay tides vary between 3 feet and 9 feet. The tide is at its lowest point when time (t) is 0 and completes a full cyc
BaLLatris [955]

Answer:

y(t)= 6-3cos(\dfrac{2\pi}{14}t )

Step-by-step explanation:

The function that could model this periodic phenomenon will be of the form

y(t) = y_0+Acos(wt)

The tide varies between 3ft and 9ft, which means its amplitude A is

A =\dfrac{(9-3)ft}{2} \\\\\boxed{A = 3ft}

and its midline y_0 is

y_o=3+3 \\\\\boxed{y_o= 6ft}.

Furthermore, since at t=0 the tide is at its lowest ( 3 feet ), we know that the trigonometric function we must use is -cos(\omega t).

The period of the full cycle is 14 hours, which means

\omega t =2\pi

\omega (t+14)= 4\pi

giving us

\boxed{\omega = \dfrac{2\pi}{14}.}

With all of the values of the variables in place, the function modeling the situation now becomes

\boxed{y(t)= 6-3cos(\dfrac{2\pi}{14}t ).}

8 0
3 years ago
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