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3 years ago

Translate the verbal phrase into an algebraic expression

Mathematics

1 answer:

jekas [21]3 years ago

6 0

Answer:

Twice the sum of 13 and x is not greater than 15 Translate each verbal phrase into an algebraic expression.

Step-by-step explanation:

13 is not greater than x

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Circle B has a center at point (0, 2) and a point W on the circle at (3, 3). Which equation represents a line that is tangent to

Solnce55 [7]

According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:

y = -x + 6.

<h3>What is the equation of the circle?</h3>

The equation of a circle of center $(x_0,y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In this problem, we have that the center is at point (0,2), hence:

$x^2 + (y - 2)^2 = r^2$

It goes through point (3,3), hence:

$3^2 + (3 - 2)^2 = r^2$

$r^2 = 10$

Hence, the equation is:

$x^2 + (y - 2)^2 = 10$

<h3>What is the equation of the tangent line at point W?</h3>

It is given by:

$y - y(0) = \frac{dy}{dx}|_{W}(x - x(0))$

Applying implicit differentiation, we have that:

$2x + 2y\frac{dy}{dy} = 0$

$\frac{dy}{dx} = -\frac{x}{y}$

Point W(3,3), hence:

$(x_0, y_0) = (3,3)$

$\frac{dy}{dx} = -\frac{3}{3} = -1$

Hence the equation is:

y - 3 = -(x - 3).

y = -x + 6.

More can be learned about the equation of a tangent line at brainly.com/question/8174665

5 0

2 years ago

True or False? The graph of sine can be used to construct the graph of the secant function.

amid [387]

True

Note that:

$secant \theta = \frac{1}{cos\theta}$

The graph of sine and cosine functions are very similar. They only have a shift in the x -axis.

That is, sin x = cos (90 - x)

Since there is a great similarity between the sine and cosine graphs, and the secant graph is an inverse of the cosine graph, the graph of sine can be used to construct the graph of the secant function

Mathematically:

since sec x = 1 / cos x

and, cos x = sin (90 - x)

therefore, sec x = 1 / sin (90 - x)

The graphs of the sine and secant functions are attached to this solution

Learn more here: brainly.com/question/9554579

5 0

3 years ago

The scissor lift is a device that can lower and raise a platform. the scissor lift can raise the platform at a rate of 2.0 inche

Svetradugi [14.3K]

Answer:

i thank it is 25 seconds.

Step-by-step explanation:

3 0

3 years ago

I need help pls

andre [41]

$\large\bf{\underline{Given \: equations:}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large \: x + 71 = 180$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large \: x + 149 = 180$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large \: x + 40 = 180$

__________________________________________

$\large\bf{\underline{On \: solving :}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x + 71 = 180$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 180 - 71$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 109$

__________________________________________

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x + 149 = 180$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 180 - 149$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 31$

__________________________________________

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x + 40 = 180$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 180 - 40$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $⟹x = 140$

__________________________________________

4 0

2 years ago

99 POINTS

yan [13]

Answer:

the function given $f(x)=x^3$

for 4 units up, just add 4 as a constant

4 units up means, every old value will now be 4 more than previous value. at x=0, y=0 in the transformed curse it should x=0 and y=4, so just add it.

$f(x)=x^3+4$

for 6 units left,

each old value of y should now occur 6 units before the old value of x i.e. X=x+6

for example, the point (0,0) should occur at (-6,0) in the transformed graph,

hence, $f(x)=(x+6)^3$

so the final curve is

$f(x)=(x+6)^3+4$

3 0

3 years ago