Hermina cut a ft by ft piece of plywood down the diagonal.

A rectangle is 4 feet wide and 8 feet long. A diagonal cut is shown with a line labeled c. The cut divides the rectangle in half and creates two right triangles. The hypotenuse of each right triangle is the line labeled c.

What is the length c of the cut, in feet?

Answer:

The slope of the graph at x=-1 is 2

Step-by-step explanation:

Instant rate of change

Given a real function f(x), the instant rate of change with respect to x is defined as the derivative of f which coincides with the instant value of the slope of the tangent line in the point (x,y).

We have the function:

[tex]\displaystyle f(x) = x^5+\frac{1}{x^3}+7[/tex]

Prepare the function to apply the power rule of the derivative:

[tex]\displaystyle f(x) = x^5+x^{-3}+7[/tex]

Recall the power rule:

[tex](x^n)' = nx^{n-1}[/tex]

Also, the derivative of a constant is zero.

Taking the derivative:

[tex]\displaystyle f'(x) = 5x^4-3x^{-4}[/tex]

Evaluating for x=-1:

[tex]\displaystyle f'(-1) = 5(-1)^4-3(-1)^{-4}[/tex]

[tex]\displaystyle f'(-1) = 5*1-3*1=2[/tex]

The slope of the graph at x=-1 is 2

Answer:

e

Step-by-step explanation:

Answer: D

Step-by-step explanation:

No, the addition symbol was dropped in the second expression is not correct.

An expression is combination of variables, numbers and operators.

No, Vance did not apply the associative property correctly.

The associative property states that the grouping of terms in an expression can be changed without affecting the value of the expression.

However, in this case, Vance changed the order of the terms, but did not actually group them in a different way.

Additionally, Vance dropped the subtraction symbol in the second expression, which is incorrect.

The correct equivalent expression using the associative property would be:

(4.5 m + 7/8) - 9 = 4.5 m + (7/8 - 9)

From there, we could simplify the expression further, if needed.

Hence, No, the addition symbol was dropped in the second expression.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ3

Answer:

Step-by-step explanation:

jjkk[

Answer:

616

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The number of necessary tutors when you divide 27 into 72, is 2.6; therefore the necessary number of tutors is 3 because you can’t have .6 of a tutor. Hope this helps!

it is a. Yes it can, because −2.5 lies to the left of −0.5. plz mark me as brainiest and tell me if I am wrong

Answer:

45 R53

Step-by-step explanation:

Hope This Helps

I'll do the first problem to get you started.

Part (a)

We have a separable equation. Get the y term to the left side and then integrate to get

[tex]\frac{dy}{dt} = ky^{1+c}\\\\\frac{dy}{y^{1+c}} = kdt\\\\\displaystyle \int\frac{dy}{y^{1+c}} = \int kdt\\\\\displaystyle \int y^{-(1+c)}dy = \int kdt\\\\\displaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\[/tex]

I'm using D as the integration constant rather than C since lowercase letter c was already taken.

Let's use initial condition that [tex]y(0) = y_0[/tex]. This means we'll plug in t = 0 and [tex]y = y_0[/tex]. After doing so, solve for D

[tex]\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\\displaystyle -\frac{1}{c*(y_0)^{c}} = k*0+D\\\\\displaystyle D = -\frac{1}{c*(y_0)^{c}}\\\\[/tex]

Let's plug that in and isolate y

[tex]\diplaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\\\diplaystyle -\frac{1}{c}y^{-c} = kt-\frac{1}{c*(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = -ckt+\frac{1}{(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle \frac{1}{y^{c}} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle y^{c} = \frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\\\\\\\diplaystyle y = \left(\frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\right)^{1/c}\\\\\\\diplaystyle y = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\[/tex]

-------------------------

We end up with [tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\[/tex] as our final solution. There are likely other forms to express this equation.

========================================================

Part (b)

We want y(t) to approach positive infinity.

Based on the solution in part (a), this will happen when the denominator approaches 0 from the left.

So [tex]y(t) \to \infty[/tex] as [tex]1-c*(y_0)^{c}kt \to 0[/tex] in which we can effectively "solve" for t showing that [tex]t \to \frac{1}{c*(y_0)^{c}k}[/tex]

If we define [tex]T = \frac{1}{c*(y_0)^{c}k}[/tex] , then approaching T from the left side will have y(t) approach positive infinity.

This uppercase T value is doomsday. This the time value lowercase t approaches from the left when the population y(t) explodes to positive infinity.

Effectively t = T is the vertical asymptote.

========================================================

Part (c)

We're told that the initial condition is y(0) = 5 since at time 0, we have 5 rabbits. This means [tex]y_0 = 5[/tex]

Another fact we know is that y(3) = 35 because after three months, there are 35 rabbits.

Lastly, we know that c = 0.01 since the exponent of dy/dt = ky^(1.01) is 1.01; so we solve 1+c = 1.01 to get c = 0.01

We'll use y(3) = 35, c = 0.01 and [tex]y_0 = 5[/tex] to solve for k

Doing so leads to the following:

[tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\\displaystyle y(3) = \frac{5}{\left(1-0.01*(5)^{0.01}k*3\right)^{1/0.01}}\\\\\\\displaystyle 35 \approx \frac{5}{\left(1-0.0304867k\right)^{100}}\\\\\\\displaystyle 35\left(1-0.0304867k\right)^{100} \approx 5\\\\\\\displaystyle \left(1-0.0304867k\right)^{100} \approx \frac{1}{7}\\\\\\[/tex]

[tex]\displaystyle \left(1-0.0304867k\right)^{100} \approx 7^{-1}\\\\\\\displaystyle 1-0.0304867k \approx \left(7^{-1}\right)^{1/100}\\\\\\\displaystyle 1-0.0304867k \approx 7^{-0.01}\\\\\\\displaystyle k \approx \frac{7^{-0.01}-1}{-0.0304867}\\\\\\\displaystyle k \approx 0.63211155281122\\\\\\\displaystyle k \approx 0.632112\\\\\\[/tex]

We can now compute the doomsday time value

[tex]T = \frac{1}{c*(y_0)^c*k}\\\\\\T \approx \frac{1}{0.01*(5)^{0.01}*0.632112}\\\\\\T \approx \frac{1}{0.00642367758836}\\\\\\T \approx 155.674064621806\\\\\\T \approx 155.67\\\\\\[/tex]

The answer is approximately 155.67 months

Answer:

yes

Step-by-step explanation:

Answer:

Hmm graph 3, i think.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Let the coordinates be:

Reflection:

Lets compare distances:

and

As we see the results are same

Answer:

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Step-by-step explanation:

Answer:

D. Raul spent the same amount of time shopping for shoes as he spent shopping for pants

Step-by-step explanation:

just trust me :)

Answer:

yes they are congruent

Step-by-step explanation:

they both the same shape and size

Answer:

I think it is 5.

Step-by-step explanation:

5/8 in decimal form is 0.625. 0.625 x 8 = 5. I hope this helps/ sorry if it didn't.

Answer:

36

Step-by-step explanation:

4 benches in 1 hour

? benches in 9 hours

36 benches

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

36 is the answer :)

Step-by-step explanation:

Answer:

Brittany needs another $3.7405.              

Step-by-step explanation:

Per pound Cost of turkey = $5.96 per pound

The amount Brittany buys the turkey = 2.55 pounds

Brittany's cost for turkey = 2.55 × $5.96 = $15.198

Per pound cost for cheese = $3.35 per pound

The amount Brittany buys the cheese = 3.7 pounds

Brittany's cost for cheese = 2.55 × $3.35 = $8.5425

So,

Brittany's total cost = Turkey cost + Cheese cost

                                = $15.198 + $8.5425

                                = $23.7405

As brittany gave the clerk 20 dollars.

So, the amount she further needs will be:

$23.7405 - $20 =  $3.7405

Therefore, Brittany needs another $3.7405.                                                                      

Answer:

The minimum sample required = 1296.65

Step-by-step explanation:

Given that:

Variance [tex]\sigma^2 = 2.89[/tex]

Standard deviation [tex]\sigma = \sqrt{2.89}[/tex]

Standard deviation [tex]\sigma = 1.7[/tex]

Margin of error = 0.11

Confidence Interval = 98%

Level of significance =  1 - 0.98 = 0.02

The critical value = [tex]Z _{\alpha//2} = Z_{0.02/2} = Z_{0.01}[/tex]

= 2.33  

Thus, the minimum sample size is given by the formula:

[tex]n = \bigg ( \dfrac{Z_{\alpha/2} \times \sigma }{E} \bigg)^2[/tex]

[tex]n = \bigg (\dfrac{2.33 \times 1.7 }{0.11} \bigg)^2[/tex]

n = 1296.65

Answer:

-3 < x ≤ 6

Step-by-step explanation:

Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.

Answer:

[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

In order to find the slope of a line you must find where the points intersect, use the formula for slope, substitute values, and simplify if needed.

In this case we were already given the points for slope:

[tex]P1=(-4,-4) = (x1,y1)[/tex]

[tex]P2=(-2,3)=(x2,y2)[/tex]

Slope formula:

[tex]slope = \frac{y2-y1}{x2-x1}[/tex]

Now substitute:

[tex]\frac{-2--4}{3--4}[/tex]

Solve using KCC: (Keep, Change, Change)

[tex]-2+4=2[/tex]

[tex]3+4=7[/tex]

=[tex]\frac{2}{7}[/tex]

Because the slope isn't a negative you do not need to simplify the answer.

Hope this helps.

Answer:

155

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I took the quiz

Answer:

171.6 minutes

Step-by-step explanation:

28.6*6

Answer:

20%

Step-by-step explanation:

Step 1:

7/35         Divide

Step 2:

1/5         Simplify

Step 3:

20/100        Multiply

Answer:

20%

Hope This Helps :)

Answer:

Joey's Cafe sold 20% regular coffee and 80% decaffeinated coffee.

Step-by-step explanation:

We are given that the cafe served 35 coffees. We are also told that of those 35 coffees, 7 coffees were regular.

Therefore, we can divide the number of regular coffees by the total number of coffees sold to get the percentage of regular coffees.

Our ratio will be set up as 7 regular coffees : 35 total coffees. We can also represent this as a fraction.

[tex]\displaystyle\frac{7}{35}=\frac{1}{5}\\\\\frac{1}{5}=0.2\\\\0.2 \times 100 = 20\%[/tex]

Therefore, of the coffees sold at the cafe, 20% of those coffees were regular.

Additionally, we can subtract this percentage from 100 to find out how much of the sales were decaffeinated coffee.

[tex]100\% - 20\% = 80\%[/tex]

Joey's Cafe sold 80% decaffeinated coffee.

Answer:

Option A (5, 0)

Step-by-step explanation:

Step 1:  Determine what is a solution

To find a solution of two lines, it has to be in the area where both of the colors intersect.  As you can see the red line goes up and the blue line goes down, but there is a shaded region where there is just white, just blue, just red, and the red and blue.  The shaded region where both red and blue is, that is where the solutions are.  

(5, 0) -> This means that the x-value is 5 and the y-value is 0 meaning that it is in the area where there is both red and blue.

(1, -3) -> This means that the x-value is 1 and the y-value is -3 meaning that it is in the area where there is only red.

(3, 3) -> This means that the x-value is 3 and the y-value is 3 meaning that it is in the area where there is only blue.

(2, 1) -> This means that the x-value is 2 and the y-value is 1 meaning that it is in the area where there is only blue.

Answer:  Option A (5, 0)

Answer:

y=1/4x-9

Step-by-step explanation:

Slope-intercept form is y=mx+b.

8y-2x=-72

Add 2x to both sides

8y=2x-72

Divide both sides by 8.

y=1/4x-9

HTH :)

Answer:

A = 50 square units

Step-by-step explanation:

Right Triangles

A right triangle is identified because it has one internal angle of 90°.

The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:

[tex]c^2=a^2+b^2[/tex]

If the triangle is also isosceles, then both legs have the same measure or a=b:

[tex]c^2=a^2+a^2=2a^2[/tex]

Since we know the hypotenuse has a measure of 10\sqrt{2}:

[tex](10\sqrt{2})^2=2a^2[/tex]

Operating:

[tex]100*2=2a^2[/tex]

Dividing by 2:

[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]

a = 10 units

The area of the triangle is:

[tex]\displaystyle A=\frac{a.b}{2}[/tex]

[tex]\displaystyle A=\frac{10*10}{2}[/tex]

A = 50 square units

Answer:

Both are proportional, because as the value of x change (increases or decreases), the value of y changes (increases or decreases).

The first equation (y = 25x) could represent that amount of teachers per students. If x = teachers (let's say there is 1 teacher), then y = students (1 teacher would teach a class of 25 students).

The second equation (y = 5x + 25) could represent the amount of money you could earn babysitting. The starting/base amount would be $25, and you would earn $5 more for every hour you babysat.

Step-by-step explanation:

Answer:

x=8 and y=21

Step-by-step explanation:

12x-28=7x+12 (the 2 angles are equivalent)

12x-7x=12+28

5x=40

x=8

9y-77 + 12x-28 =180 (the sum of those 2 angles is a flat angle (180°))

9y-77+12*8-28=180

9y=180+28+77-96

9y=189

y=21