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Answer:  [tex]\textsf{y = -2/5x}[/tex]

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Given:  [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]

Find:  [tex]\textsf{The equation that follows the details provided}[/tex]

Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.

Plug in the values

Distribute and simplify

Subtract 2 from both sides

Therefore, the final equation that follows the information that was provided is y = -2/5x.

When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

The equation for a quadratic function is given by

y = a(x-h)² +k²

where (h,k) is the extreme value(vertex).

Here the equation given is

y = x²-4x +8

y = x²-4x+4+4

y = (x-2)² +4

Here the value of a = 1 , h = 2 and k = 4

The extreme value is at (2,4)

Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

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Answer:

5.32⋅10−6

Step-by-step explanation:

Answer:

5320000

Step-by-step explanation:

standard notation form : 5320000

Given the egg has hatched, the egg was kept warmer than room temperature.

                      Cool      Room temperature        Warm             Total

Hatched           5              16                                21                  42

Unhatched        18           10                                 4                   32

Total                 23            26                                25                    74

To fill the blank we need to analyse the temperature carefully if see the table then cool hatched eggs are 5 , unhatched cool eggs are 18, eggs on room temperature and hatched are 16, eggs on room temperature and unhatched are 10, warm hatched eggs are 21 and warm unhatched eggs

So we can notice that hatched eggs are more in room temperature.

Hence hatched eggs are more in room temperature.

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Answer:

Given the egg has hatched the egg was kept warmer than room temperature.

Hope this helped!

Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:

p = 9/15 = 0.6 = 60%.

0.6 = 60% probability that the flower is NOT A ROSE.

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The estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college is $250

12,000 = 2900 + 36x

12,000 - 2900 = 36x

9,100 = 36x

x = 9100 / 36

x = 252.777777777777

Approximately,

$250

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Answer:

The answer is B. $250

Step-by-step explanation:

Answer:

0.93

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two possible patters of sitting:

⇒ [tex]I) M W M W M W[/tex]

⇒ [tex]II) W M W M W M[/tex]

⇒ Three ways can be used to seat each set of three people, for a total of six.

⇒ There are two groups

2 × 3 = 6 (ways in six groups.)

*The two options can be distributed in two groups.

⇒ Total methods are equal to 6 * 6 * 2 = 72 ways.

The domain of the given graph is the set of all real numbers from 0 to 8.

The graph showing the water depth on the y-axis in inches against the time in minutes on the x-axis has been attached.

Now, domain is the set of all possible input values and from the graph we see that the set of all possible input values are between 0 and 8.

Thus, we can conclude that the domain of the given graph is the set of all real numbers from 0 to 8.

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Answer:

2 1/4

Step-by-step explanation:

Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4

Answer:

College dropout is the greatest album of all-time

They are congruent because the word congruent means the same shape and size and if you look at the picture angle RAM and angle ZMA have the same shape and the same size.

Answer:

(4, 4)

Step-by-step explanation:

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]

Match the values in this hyperbola to those of the standard form. The variable h represents the x-offset from the origin, k represents the y-offset from origin, a.

a = 1

b = 3

k = 4

h = 4

Thus,

[tex](x-4)^2 - \frac{(y-4)^2}{9} = 1[/tex]

The center of a hyperbola follows the form of (h, k). Substitute in the values of h and k.

= (4, 4)

Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1  ║ 2 | 4 | -2 | -8

   ║    | -2| -2 |  4

   ║ 2 | 2|  -4 |  -4

[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

PS: if anyone knows a better way to do a synthetic division chart please let me know.

Answer:

2.15%

Step-by-step explanation:

If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.

Z-score:

550-400/2=3

500-400/2=2

Probability:

3 (from the Z-table) is .9987

2 (from the Z-table) is .9772

.9987-.9772= .0215

.0215 as a percentage is 2.15%

Mean: 400

Standard deviation: 50

Check to see if 500 and 550 fall within the standard deviations:

400+2(50) =500

400+3(50) =550

These values lie between the 2nd and 3rd deviations, so

the value is 0.0235

Percentage: 2.35%

Hope it helps!

Answer:

x = 8

Step-by-step explanation:

An undefined slope indicates that the line is vertical and parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (8, 4 ) with x- coordinate 8 , then

x = 8 ← equation of line

4

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Answer:

orange: 0.2$, apple: 0.4$

Step-by-step explanation:

we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:

10 oranges and 5 apples for 4$ means:

[tex]10x + 5y = 4[/tex]

9 oranges and 3 apples for 3$ means:

[tex]9x + 3y = 3[/tex]

we use the second equation to isolate y:

[tex]3y = 3 - 9x \\ y = 1 - 3x[/tex]

and plug it in the first equation:

[tex]10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2[/tex]

and then we find y:

[tex]y = 1 - 3 \times 0.2 \\ y = 0.4[/tex]

The number of people who can go to the amusement park is 8.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given: the group of friends had $280.

For parking=  $19.50

Remaining will be,

=$(280-19.50)

= $ 260.5

Cost of ticket per person = $33.75

Thus, number of tickets they can buy

=260.5 / 33.75

=7.718 = 8 peoples

Hence, number of people who can go to the amusement park is 8.

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Answer:

c ×=4, only

Step-by-step explanation:

4*-8×+16=0

16-32=-16

-16=-16

Answer:

D. x=4 only

Step-by-step explanation:

You can solve using the quadratic equation which is [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

where in this case a=1, b=-8, and c=16. But there is any easier way to solve the equation. You can solve by completing the square which consists of moving the constant to the right side and then adding [tex](\frac{b}{2})^2[/tex]. To both sides that way you can rewrite the left side as a perfect square binomial. This is because [tex](x+b)^2[/tex] will expand to [tex]x^2 + 2xb + b^2[/tex]. So when you add [tex](\frac{b}{2})^2[/tex] to both equations. You're able to rewrite the left side as [tex](x+(\frac{b}{2}))^2[/tex]. Because once you expand it out, it becomes [tex]x^2 + 2(\frac{b}{2})x + (\frac{b}{2})^2[/tex]. Which simplifies to [tex]x^2 + bx + (\frac{b}{2})^2[/tex] which is the original equation. In this case there is no need to move the constant, which in this case is 16, to the other side. Since if you calculate the value of (-8/2)^2 it's equal to 16! So this can already be written as a perfect square binomial.

So the equation becomes

[tex]0 = (x+\frac{b}{2})^2[/tex]

Plug values in

[tex]0 = (x+(-\frac{8}{2}))^2[/tex]

Simplify

[tex]0 = (x-4)^2[/tex]

Take the square root of both sides

[tex]0 = x-4[/tex]

Add 4 to both sides

[tex]4 = x[/tex]

Answer: six ways

Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.

The range:
[tex]{x|70\leq x\leq 82[/tex]

Answer:

[tex]x=\dfrac{11}{4}[/tex]

Step-by-step explanation:

Given:

[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

Rewrite 9 as 3² and 27 as 3³:

[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]

Multiply both sides by [tex]3^{(x-1)}[/tex] :

[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\implies 3^{(x-2)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x-2=\dfrac{3}{4}[/tex]

[tex]\implies 4(x-2)=3[/tex]

[tex]\implies 4x-8=3[/tex]

[tex]\implies 4x=11[/tex]

[tex]\implies x=\dfrac{11}{4}[/tex]

Answer:

B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Answer:

Ans : 3578.83 feet from the ground

Step-by-step explanation:

You can use sine theory so

sine 32 = height/6400

6400 x sine 32 = height

Easy

Answer:

B

Step-by-step explanation:

pythagorus theorem

a² + b² = c²

c² - b² = a²

26² - 24² = a²

676 - 576 = a²

a² = 100

a = 10

1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)

2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)

3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)

4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)

5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)

Answer

D

Step-by-step explanation:

The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:

[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]

In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:

[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]

Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):

[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]

Simplifying the combination:

[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]

Calculating the factorial terms:

[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]

[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]

P(5) ≈ 0.082

Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

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Answer:

check image below

Step-by-step explanation: