find two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm.

Answer:

Second question in Assignment = A) 14

Step-by-step explanation:

x^2 = 14x +49

Answer: 14

Step-by-step explanation:

The first one is 25/4 then 14

Answer:

-6x + 17

Step-by-step explanation:

-(6x - 17)

= -6x + 17

=》Negative × negative = positive

=》 Positive × negative = negative

Hope it helps ⚜

Hi!

I can help you with joy!

Answer:

-6x+17

Hope it helps.

Do ask if you have any queries regarding my answer.

\(\rm{PeacefulNature\)

The given expression, log₃(6c) + log₃₁(12), can be simplified as log₃(72c) with a coefficient of 1.

To express the given expression as a single logarithm with a coefficient of 1, we can use the product rule of logarithms. The product rule states that the sum of logarithms of two numbers multiplied together is equal to the logarithm of their product.

Apply the product rule to combine the two logarithms:

log₃(6c) + log₃₁(12) = log₃(6c * 12)

Simplify the expression inside the logarithm:

6c * 12 = 72c

Rewrite the expression using a single logarithm:

log₃(72c)

Therefore, the given expression, log₃(6c) + log₃₁(12), can be simplified as log₃(72c) with a coefficient of 1.

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Answer:

B log3 c/2

Next C log7 2 + log 7 49

Next log7 49 = 2

Next log 7 98 = 2.356

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Yes, it is necessarily  true that W(orthogonal complement) = span(v k+1,......,vn)

Since {v1,....,vn} is an othogonal basis for R^n, each vector in the basis is orthogonal to every other vector in the basis. Therefore, the vectors v1,....,vk are orthogonal to the vectors vk+1,....,vn, and vice versa. This means that any vector in W is orthogonal to any vector in span(vk+1,...,vn). Hence, W and span(vk+1,...,vn) are orthogonal complements of each other.

To show that W(orthogonal complement) = span(vk+1,...,vn), we need to show that any vector in W(orthogonal complement) is also in span(vk+1,...,vn) and vice versa.

et x be a vector in W(orthogonal complement). Then, x is orthogonal to every vector in W, which means x is orthogonal to v1,....,vk. Since {v1,....,vn} is a basis for R^n, any vector in R^n can be written as a linear combination of the basis vectors.

Therefore, we can write x as a linear combination of v k+1,......,vn. This shows that x is in span(vk+1,...,vn).

Conversely, let y be a vector in span(vk+1,...,vn). Then, we can write y as a linear combination of v k+1,......,vn. Since v1,....,vk are orthogonal to v k+1,......,vn, we have y is orthogonal to v1,....,vk. Therefore, y is in W(orthogonal complement).

Hence, W(orthogonal complement) = span(vk+1,...,vn).

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Answer:

13.8cm

Step-by-step explanation:

formula

b x h / 2

6.9 x 4 / 2

= 13.8

The probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.

To find the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up, we can use conditional probability.

First, let's consider the possible outcomes when rolling a pair of fair dice.

There are a total of 36 possible outcomes, since each die has 6 possible outcomes (numbers 1 to 6)

and there are 6 possibilities for the second die for each outcome of the first die.

Next, let's consider the outcomes where one of the dice has the number 3 or less facing up and the other has at least the number 3 facing up.

If the first die has the number 3 or less, there are 3 possible outcomes:

(1,3), (2,3), (3,3). If the second die has at least the number 3 facing up, there are 16 possible outcomes:

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,3), (6,3), (4,4), (4,5), (4,6), (5,4), (5,5), (5,6), (6,4), (6,5), (6,6).

Out of these 16 outcomes, 3 outcomes also satisfy the condition that the first die has the number 3 or less facing up: (3,3), (4,3), (5,3).

Therefore, the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.


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The solution is, 76,000 mg chlorine is in the pool.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The pool has 2.5 milligrams of chlorine per liter of water.

There are 8000 gallons of water in the swimming pool.

we know,

1 gallon = 3.785 liters

Water in pool = 8000 x 3.785

Water in pool = 30,280 liters

so, we get,

Chlorine dosage = 2.5 mg / liter

Chlorine = 2.5 x 30,280

Chlorine = 75,700 mg

To the nearest thousand milligram:

Chlorine = 76,000 mg

Hence, The solution is, 76,000 mg chlorine is in the pool.

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Answer:

25% are red

Step-by-step explanation:

The fraction of the pencils that are red is

3/12 = 1/4

Changing to decimal form

.25

Multiply by 100 to get a percent

.25 * 100

25%

Answer:

8.324

Step-by-step explanation:

The 8 serves as the first digit and the "and " represents a decimal point  the remaining numbers go behind that decimal point therefore 8.324.

The rate of change of z with respect to t is 0.

To use the chain rule to find dz/dt, we need to first find the partial derivatives of z with respect to x and y, and then multiply them by the derivatives of x and y with respect to t, respectively.

Let's start by finding the partial derivatives of z:

∂z/∂x = -6y sin(x 6y)
∂z/∂y = -6x sin(x 6y)

Next, we can find the derivatives of x and y with respect to t:

dx/dt = 25t^4
dy/dt = -9/t^2

Finally, we can use the chain rule formula:

dz/dt = (∂z/∂x) (dx/dt) + (∂z/∂y) (dy/dt)

Substituting in the values we found:

dz/dt = (-6y sin(x 6y)) (25t^4) + (-6x sin(x 6y)) (-9/t^2)

Now, we just need to substitute in the given values of x and y:

x = 5t^5
y = 9/t

So:

dz/dt = (-6(9/t) sin(5t^5 6(9/t))) (25t^4) + (-6(5t^5) sin(5t^5 6(9/t))) (-9/t^2)

Simplifying:

dz/dt = -270t^3 sin(30t^4) + 270t^3 sin(30t^4)

The second term cancels out with the first term, so:

dz/dt = 0

The rate of change of z with respect to t is 0.

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From use the chain rule to determine the partial derivative of composite function. The value of \(\frac{ ∂z}{∂t}\) is equal to \( -sin( x+ 6y) 25t⁴+ sin( x+ 6y) \frac{-54}{t²}\).

The chain rule states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner. To determine the partial derivative of z, \(\frac{ ∂z}{∂t}\) use the fact that x= x(t,s) and y = y(t,s) are functions in terms of t and s, then apply the identity \(\frac{∂z}{∂t} = \frac{∂z}{∂x}\frac{∂x}{∂t} + \frac {∂z}{∂y} \frac{∂y}{∂t}\)

To compute a partial derivative ∂z/∂x kept y constant and taking the derivative with respect to x. We have z = cos(x + 6y)

x = 5t⁵ , y = 9/t

\(\frac{∂x}{∂t} = 25t⁴\)

\(\frac{∂y}{∂t} = \frac{-9}{t²}\)

\(\frac{∂z}{∂x} = -sin( x+ 6y)\)

\(\frac{∂z}{∂y} = -sin( x+ 6y)×6\)

Using Chain rule,

\(\frac{∂z}{∂t} = \frac{∂z}{∂x}\frac{∂x}{∂t} + \frac {∂z}{∂y} \frac{∂y}{∂t}\)

Substitute all known values in above formula, \(\frac{∂z}{∂t} = -sin( x+ 6y) 25t⁴ + (-6 sin( x+ 6y) )\frac{-9}{t²}\)

\(= -sin( x+ 6y) 25t⁴ + sin( x+ 6y) \frac{-54}{t²}\)

Hence, required value is \(- 25 t² sin( x+ 6y) + sin( x+ 6y) \frac{-54}{t²}\).

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Answer:

5) 9/6

6) -5/4

Step-by-step explanation:

The formula to find slope is \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\). A line rising left to right has a positive slope.     A line rising right to left has a negative slope.

Hope it helps!

Answer:

help on what like whats ur question

Step-by-step explanation:

Answer:

I hope this helps

Step-by-step explanation:

need more letters

We have that are two types of translation:

- horizontal

- vertical

Given a function f(x) and a number c, we have that

- it is translated horizontally

if f(x + c)

- it is translated vertically

if f(x) + c

For example,

the function f(x) = |x| is translated

- 2 units horizontally if we write

|x +2|

- 2 units vertically if we write

|x| + 2

In the choices we have, the choices that show horizontal translations are:

C. f(x)=-|-x+1|+4.

D. f(x)=5|x-4|-1

Answer:

2[3+4/-2(3-4)]+3

Step-by-step explanation:

2[3+-2(-1)] +3

2[3+2] +3

2(5) +3

10+3

13

It is given that the longer leg is 4 cm longer than the shorter leg.

It is also given that the hypotenuse is 8 cm longer than the shorter leg.

Let the shorter leg be x.

The longer leg be y.

Then the relation formed is

It is also given that the hypotenuse is 8 cm longer than the shorter leg.

Let the hypotenuse is z.

Then the perimeter of the right triangle is the sum of all the sides.

But to find the value of x , use the Pythagoras theorem.

Substitute the values.

Solve the quadratic equation to find the value of x.

As x cannot be negative , then the value of x is 12.

The length of shorter leg is 12.

The length of longer leg is 12+4=16.

The hypotenuse is 12+8=20.

Now , the perimeter of right triangle is

The perimeter of the triangle is 48 cm.

If your p-value is 0.11 and the significance level is 0.05, you would conclude that there is insufficient evidence to reject the null hypothesis. In other words, you cannot establish a statistically significant relationship between the variables you are studying.

To explain this further, the p-value (0.11) represents the probability of observing the data, assuming that the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis. The significance level (0.05) serves as a threshold to determine whether the p-value is small enough to reject the null hypothesis.

If the p-value is less than or equal to the significance level, you would reject the null hypothesis and conclude that there is a statistically significant relationship between the variables. However, in this case, the p-value (0.11) is greater than the significance level (0.05), which means that the probability of observing the data is not low enough to reject the null hypothesis.

Therefore, you cannot establish a statistically significant relationship between the variables, and the observed results could be due to chance or random variation.

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Justin"s heart rate decreased 3 beats per minute for each of next 4 minutes

Let his heart rate be be 1

For the first minutes

1 minute his heart rate was 1 - 3 = -2

This is because the heart rate is decreasing 3 beats per minutes

2minutes later, his heart beat will be -2 -3

-2 - 3 = -5

3 minutes later, his heart beat will be -5 - 3

-5 - 3 = -8

4 minutes later, -8 - 3

-8 - 3 = -11

Change = Final heart beat - initial heart beat / initial heart beat

Change = -11 -2 / -2

Change = -13/-2

Change = 13/2

= 6.5

Answer:

1600

Step-by-step explanation:

By rounding 1588 to the nearest hundredth we get 1600.

Answer:

all answers are true I think

Answer:

\(\frac{4080n+1585d-188}{240}\)

Step-by-step explanation:

I simplified it to the best possible state

Answer:

x = 21

Step-by-step explanation:

given : angle a = 75

we need to find the value of x.

To find the value of x.

we know that it is a straight angle so the sum of angles on a line will be 180

3x + 2x + a = 180

5x + 75 = 180

5x = 180 - 75

5x = 105

x = 105/5

x = 21

Answer: x equal 21 I think

Answer:

A. The area is \(78.54m^2\)

B. She needs to cover 1661.9 square feet of tiles for the base of the swimming pool

Step-by-step explanation:

Question A:

Let us assume that the leash is pegged to the ground using a stake. as a result, the dog can move around the stake. The path that the motion of the dog would trace is a circle, and the radius of the circle will be the length of the leash.

Since we know this, we can easily find the area of the circle using \(\pi r^2\)

Area of the circle = \(\pi \times 5 \times 5 = 78.54m^2\)

Question B

Dulce wants to cover the whole surface area of the floor of the circular swimming pool with tiles.

We already know that the swimming pool is circular, hence, the surface area of the base of the swimming pool will be the same as the area of a circle, with the same radius.

The area of the circle can be calculated using \(\pi r^2\)

Area of circle = \(\pi \times 23 \times 23 = 1661.9ft^2\)

Consequently, the interval's leftmost extreme is f(-4) = 17e^{-4}, where the absolute maximum is located.

The function f is f(x) = \((x^2 + 1)e^{-x}\)

First, solve the equation f'(x) = 0 to identify the critical locations. It will be calculated using the formula \(\frac{d}{dx}(xy) = x\frac{d}{dx}(y) + y\frac{d}{dx}(x)\).

f'(x) = \((x^2 +1)\frac{d}{dx}e^{-x}+e^{-x} \frac{d}{dx}(x^2+1)\)

f'(x) = \(-(x^2 + 1)e^{-x}+2xe^{-x}\)

Simplifying

Taking e^{-x} common

f'(x) = \([2x-(x^2+1)]e^{-x}\)

Solving the bracket

f'(x) = \(e^{-x}(-x^2+2x-1)\)

Now equating f'(x) = 0, then

\(e^{-x}(-x^2+2x-1)\) = 0

The only essential point is at x = 1 since e^{-x} is zero only at x = ∞.

f(1) = 2e^{-1}.

Then determine the value that defines the interval's extremes:

f(-4) = 17e^{-4}

The maximal candidate is f(-4) since it is the largest of all the candidates.

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Answer:

What is the question? It is incomplete

Step-by-step explanation:

Please mark as brainliest !!!!!

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Answer:

heres ur answer x=2

heres what i used to solve it PEMDAS

Let:

M = Total money = $20.56

Ca= Cost of the apple = 79 cents = $0.79

Cg = Cost of the granola bar = $1.76

Ms = Total money spent

Mr = Remaining money

So, the total money spent will be:

Ms = Ca + Cg = $0.79 + $1.76 = $2.55

And the remaining money will be:

Mr = M - Ms = $20.56 - $2.55 =$18.01

Answer:

Ken would see 40 cars pass each minute.

Step-by-step explanation:

40 x 3 = 120

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Answer:  40 cars pass per minute.

Step-by-step explanation:

\(\frac{120cars}{3minutes\\}\)  = \(\frac{?cars}{1minutes}\)

        3? = 120  [cross multiply]

          ? = 40    [divided 3 from both side]

Therefore, 40 cars passes per minute.

Answer:

the answer is 36

Step-by-step explanation:

because the bottom is going up by 9 and the top is going up by ones

Answer:

36

Step-by-step explanation:

Just do your 9's time tables

Option A

your just multiplying the 2 to what's in parentheses