A rectangle prism has length 12 centimeters and width 4 centimeters. If its surface area is 467 square centimeters, what is the height of the prism

Answer:

Step-by-step explanation:

te da x<3/2 y x<2, pero la segunda solucion abarca la primera. Por lo tanto creo q seria x<2

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:

Number of trees infected after t years:

The number of trees infected after t years is given by:

[tex]f(t) = e^{0.4t}[/tex]

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

[tex]f(t) = 21[/tex]

Thus:

[tex]e^{0.4t} = 21[/tex]

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

[tex]\ln{e^{0.4t}} = \ln{21}[/tex]

[tex]0.4t = \ln{21}[/tex]

[tex]t = \frac{\ln{21}}{0.4}[/tex]

[tex]t = 7.6[/tex]

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

[tex]f(x) = y = e^{0.4x}[/tex]

[tex]e^{0.4y} = x[/tex]

Again, we apply the natural logarithm to both sides of the equation, so:

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761

Answer: [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Use trigonometry (shown in image below) to find the 3 side-lengths:

According to right triangle trigonometry:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Substitute in the values:

cos θ = [tex]\frac{11}{12}[/tex]

Answer:

Yes

Step-by-step explanation:

Answer:

First choice

Step-by-step explanation:

It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Answer:

b20

Step-by-step explanation:

Answer:

θ ≈ 35.7°

Step-by-step explanation:

His mistake was in using the wrong trig. ratio

Instead of using cosine he should have used the sine ratio

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then

θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )

Answer:

The y-intercept of the parent function, f(x), is 0

The y-intercept of the child function, g(x), is  7

Step-by-step explanation:

Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.

The solution is :

Vertex is (-2, 0)

y-intercept is 4.

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

here, we have,

to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':

f(x) = (x+2)^2 = x2 + 4x + 4

Then, to find the vertex, we can use the formula:

x_v = -b / 2a

x_v = -4 / 2 = -2

Now, finding the y_vertex, we have:

f(x_v) = (-2)^2 + 4*(-2) + 4 = 0

So the vertex is (-2, 0)

To find the y-intercept, we make x = 0 and then find f(x):

f(0) = 0 + 0 + 4 = 4

So the y-intercept is 4.

To learn more on vertex click:

brainly.com/question/12563262

#SPJ2

complete question:

Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².

vertex: ( ? , ? )

y-intercept: ?

Answer:

k=10

Step-by-step explanation:

Brainliest please~

Answer:

K=10

Step-by-step explanation:

Correct on Plato

Answer:

216 cm^2

Step-by-step explanation:

15^2 -3^2 = 225 -9

= 216

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

s² + s² = 2²

2s² = 4 ( divide both sides by 2 )

s² = 2 ( take the square root of both sides )

s = [tex]\sqrt{2}[/tex]

Answer:

E.

Step-by-step explanation:

we know the diagonal of the square : 2

as you can see in the picture, there is a right-angled triangle with the baseline of Hypotenuse being the diagonal, and 2 times s being the 2 sides.

that means we can use Pythagoras to calculate s :

2² = s² + s²

4 = 2s²

2 = s²

s = sqrt(2)

Answer: Third Choice. 9

Step-by-step explanation:

Concept:

Here, we need to understand the idea of evaluation.    

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given

4x + 2y -1

x = 3, y = -1

Substitute the value of x and y

4(3) + 2(-1) - 1

Simplify by multiplication

12 - 2 - 1

Simplify by subtraction

9

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Hello!

4x= 4*3 = 12

2y = 2*-1 = -2

12-2  -1= 9

Do it by your self  ok ???

4x - 7 = 3x + 9

x = 16

they're equal because they are opposites by the vertex.

hope it helps :)

Answer:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Step-by-step explanation:

This question is asking for the function's end behavior. An even degree power function with a negative leading coefficient forms a parabola concave down. This means, its vertex represents the maximum and the parabola opens downward (towards negative infinity).

Thus,

[tex]\lim_{x\rightarrow \infty}f(x)=-\infty,\\\lim_{x\rightarrow-\infty}f(x)=-\infty[/tex]

This corresponds with the first answer choice listed:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Please look at the scanned picture.

Answer:

-3

Step-by-step explanation:

because as you vo more to the negative side the less.it gets and more to the positive side it gets moe

Answer:

FG = 7

Step-by-step explanation:

We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:

EF = 7

EH = 3

HF =?

EF² = EH² + HF²

7² = 3² + HF²

49 = 9 + HF²

Collect like terms

49 – 9 = HF²

40 = HF²

Take the square root of both side

HF = √40

Finally, we shall determine FG. This can be obtained as follow:

GH = 3

HF = √40

FG =.?

FG² = GH² + HF²

FG² = 3² + (√40)²

FG² = 9 + 40

FG² = 49

Take the square root of both side

FG = √49

FG = 7

Answer:

See explanation

Step-by-step explanation:

It should be 9x² not x²

p = (3x + 1) and q = (3x - 1)

pq + 1 = (3x + 1)(3x - 1) + 1

= (9x² - 3x + 3x - 1) + 1

= (9x² - 1) + 1

= 9x² - 1 + 1

= 9x²

Therefore,

pq + 1 = 9x²

Answer:

[tex]8[/tex]

Step-by-step explanation:

Hope it helps you:D

*copied*

Answer:

"8"

4,6,8

Step-by-step explanation:

θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means

cos²(θ) + sin²(θ) = 1   ==>   sin(θ) = -√[1 - cos²(θ)] = -3/5

Now recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ)

==>   sin(2θ) = 2 (-3/5) (4/5) = -24/25

B. x = 5

tip : if in a rush just plug in the number and see if its true

8x - 4 = 36

x = 5

Given:

your speed = 70 mph

Your friend's speed = 75 mph

You want to drive at least 500 miles per day.

You also plan to spend no more than 10 hours driving each day.

To find:

The system of linear inequalities that represents this situation.

Solution:

Let x be the number of hours you drive and let y represents the number of hours your friend will drive.

You also plan to spend no more than 10 hours driving each day.

[tex]x+y\leq 10[/tex]

Your speed is 70 mph and your friend's speed is 75 mph. So, the distance covered in x and y hours are 70x miles and 75y miles respectively.

You want to drive at least 500 miles per day. So, the total distance must be greater than or equal to 500.

[tex]70x+75y\geq 500[/tex]

[tex]5(14x+15y)\geq 500[/tex]

Divide both sides by 5.

[tex]14x+15y\geq 100[/tex]

Therefore, the required system of inequalities has two inequalities [tex]x+y\leq 10[/tex] and [tex]14x+15y\geq 100[/tex].

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\hookrightarrow\sf{ 25\% =\dfrac{25}{100}=\boxed{\bf \dfrac{1}{4} }} \\\hookrightarrow\sf{ 40\% =\dfrac{40}{100}=\boxed{\bf \dfrac{2}{5} }} \\\hookrightarrow \sf{16\%=\dfrac{16}{100}=\boxed{\bf\dfrac{4}{25}} } \\ \hookrightarrow\sf{150\%=\dfrac{150}{100}=\boxed{\bf\dfrac{3}{2} }} \\ \hookrightarrow\sf{120\%=\dfrac{120}{100}=\boxed{\bf\dfrac{6}{5} }} \\\hookrightarrow \sf{58\%=\dfrac{58}{100}=\boxed{\bf\dfrac{29}{50}} } \\\hookrightarrow \sf{32\%=\dfrac{32}{100}=\boxed{\bf\dfrac{8}{25} }} \\ \hookrightarrow\sf{175\%=\dfrac{175}{100}=\boxed{\bf\dfrac{7}{4}} } \\ [/tex]

Answer:

Step-by-step explanation:

Arrange the data set in ascending order. then find the median.

Data in ascending order:

2,  5 , 6 , 7 , 8 , 11 , 15

Median = 7

Lower quartile:

Then  again find the median of the numbers from the first to the number before the median. This is the lower quartile.

2 , 5, 6

Median = 5  ----> this  is the lower quartile.

Upper quartile:

Then  again find the median of the numbers that comes after the median to the end of the data set. This is the upper quartile.

8 , 11 , 15

Median = 11 ------> is the upper quatile

Answer:

-6

Step-by-step explanation:

The number line is created by skip counting of 2.

So, -2 ,  then -4 and then -6.

So,  blue dotted point is (-6)

Answer:

A.2x+6

B.60x-20

C.8x+4

D.6x-24y

Answer:

c) x= 15

d) x= 5

Step-by-step explanation:

c)4x + 5+ 7x +10=180

solve it like usually

for d) 3x + 15+12x=90

Answer:

15 and 3

Step-by-step explanation:

the first figure total sum of angles is 180 since it is a straight line

the second figure is a right ane(90) so sum of angles is 90

Answer:

20 miles

Step-by-step explanation:

10miles × 2 = 20miles