Consider the functions F(x)= x^2+9x and g(x)=1/x.

F(g(-1))is ? , and G(f(1/2))is ? .​

The given function is f(x) = x/(x^2 + 25).

Intercepts:

To find the intercepts, we set f(x) = 0 and solve for x. However, in this case, the function does not have any x-intercepts because the numerator x cannot be zero.

The y-intercept occurs when x = 0. Substituting x = 0 into the function, we have f(0) = 0/(0^2 + 25) = 0.

Relative Extrema:

To find the relative extrema, we take the derivative of the function and find the critical points where the derivative is zero or undefined. However, in this case, the function does not have any relative extrema because its derivative is always nonzero and defined for all x.

Points of Inflection:

To find the points of inflection, we need to analyze the second derivative of the function. However, in this case, the second derivative is always zero, indicating that there are no points of inflection.

Asymptotes:

The function has two asymptotes: a vertical asymptote and a horizontal asymptote.

The vertical asymptote occurs when the denominator of the function is equal to zero. Solving x^2 + 25 = 0, we find that there are no real solutions. Therefore, there is no vertical asymptote.

The horizontal asymptote can be found by examining the behavior of the function as x approaches positive or negative infinity. As x approaches positive or negative infinity, the function approaches zero. Hence, the horizontal asymptote is y = 0.

To verify these results, a graphing utility can be used to plot the function and visualize its behavior.

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Answer:

y=2x+3

Step-by-step explanation:

Lets verify

[tex]\\ \sf\longmapsto -1=2(-2)+3=-4+3=-1[/tex]

[tex]\\ \sf\longmapsto 1=2(-1)+3=-2+4=1[/tex]

Hence verified

Answer:

C): y = 2x + 3

Step-by-step explanation:

• when x is -2:

[tex]{ \tt{y = 2(- 2) + 3}} \\ { \tt{y = - 1}}[/tex]

• when x is -1:

[tex]{ \tt{y = 2( - 1) + 3}} \\ { \tt{y = 1}}[/tex]

• since y holds for -2 and -1, it'll hold for other positive integers.

Answer:

61

Step-by-step explanation:

all angles that are in a triangle add up to 180

x+80+39=180

x+119=180

x=61

Hope that helps :)

The correct answer is option B. 232.6 mg/mL which is the concentration of the vial after reconstitution.

To determine that 232.6 mg/mL is the concentration of the antibiotic vial after reconstitution, we need to calculate the amount of antibiotic in grams divided by the final volume in milliliters.

The vial states that it needs to be reconstituted with 8.6 mL of sterile water for a final volume of 10 mL. This means that the antibiotic will be dissolved in 8.6 mL of sterile water.

Since the vial contains 2 grams of antibiotic, the concentration can be calculated as follows:

Concentration = Amount of antibiotic (g) / Final volume (mL)

Concentration = 2 g / 8.6 mL

Simplifying the expression, we get:

Concentration ≈ 0.2326 g/mL

Therefore, the correct option is B) 232.6 mg/mL, the concentration of the vial after reconstitution.

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The scenario that can be solved using a two-way data table out of the options provided is to display how the profit of a lemonade stand will change when the price per cup and the count per cup change.

A two-way data table is a useful tool for conducting sensitivity analysis and exploring how changing two input variables affects the output or result of a formula or calculation. In this case, the profit of a lemonade stand is the output variable, while the price per cup and the count per cup are the two input variables. By creating a two-way data table with different values for the price per cup and the count per cup, we can systematically analyze how these two factors impact the profit of the lemonade stand. Each combination of the price per cup and the count per cup will be evaluated, and the corresponding profit will be calculated. This analysis allows us to observe the relationship between the input variables (price per cup and count per cup) and the output variable (profit). We can identify the optimal price per cup and count per cup that maximize the profit or explore different scenarios to understand how changes in these variables affect the overall profitability of the lemonade stand. Therefore, the option "b. to display how the profit of a lemonade stand will change when the price per cup and the count per cup change" can be solved using a two-way data table.

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The present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly is $131,488

To calculate the present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly, we can use the formula for compound interest:

Present Value = Future Value / (1 + r/n)^(n*t)

Where:

Future Value = $150,000

Interest Rate (r) = 2% = 0.02 (converted to decimal)

Number of Compounding Periods per Year (n) = 4 (quarterly compounding)

Number of Years (t) = 6

Substituting these values into the formula, we have:

Present Value = $150,000 / (1 + 0.02/4)^(4*6)

Calculating inside the parentheses first:

Present Value = $150,000 / (1 + 0.005)^(24)

Next, calculate the exponent:

Present Value = $150,000 / (1.005)^(24)

Using a calculator or spreadsheet, we can evaluate the expression inside the parentheses and then divide $150,000 by that result to find the present value. Rounding to the nearest dollar, the present value needed is $131,488.

Therefore, the amount to be invested now or the present value needed is $131,488.

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Answer:

1.8

Step-by-step explanation:

- hope this helps!!

Answer:

The slope is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{Y_{2} -Y_{1} }{X_{2}-X_{1} }[/tex]

-7-(-3)= -7+3= 4

4/?

7-(-9)= 7+9 = 16

4/16=1/4

I hope this helps :-)

Answer:

-43 yards is the answer...

Answer: 4

Step-by-step explanation: 13.6 divided by 3.4 = 136 then divide by 34 you get 34 from 3.4 but divide by 34. Once you divide 136 and 34 you get your answer 4.

Answer:5.7

Step-by-step explanation:

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the point Q and the ground is h-[L cos(80°)].

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The Base is the adjacent smaller side of the angle θ.

Let the height of the support be h and the height between the point q and the ground is x. Also, the distance between point Q and the support of the seesaw is L.

Now if we look at the ΔQAR, the measure of the ∠QRA is 80°, therefore, the sine of ∠QRA can be written as,

[tex]\rm Cos(\theta)=\dfrac{Base}{Perpendicular}\\\\Cos(\angle QRA) = \dfrac{AR}{QR}\\\\Cos(\angle QRA) = \dfrac{h-x}{L}\\\\L \times Cos(80^o)=h-x\\\\x=h-[L\ Cos(80^o)][/tex]

Hence, the distance between the point Q and the ground is h-[L cos(80°)].

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Answer:

[tex]5\sqrt[3]{5}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{625}[/tex] factor [tex]625^{1/3}[/tex]=[tex]5(5^{1/3} )[/tex]=5\sqrt[3]{5}

Hope that helps :)

Answer: 32, 27, 20

Step-by-step explanation: This is a quadratic table.

A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.16. The probability of success on trial 9 is 0.16.

In a binomial experiment, there are two outcomes that are possible in each trial: a success and a failure.

A binomial experiment consists of a fixed number of trials.

The term "probability" refers to the measure of how likely an event is to happen.

The probability of success on trial 5 is 0.16.

We are required to calculate the probability of success on trial 9.

Since the experiment consists of a fixed number of trials, we can say that probability of success in each trial is the same.

Let us assume the probability of success is p.

Therefore, the probability of failure in each trial is (1-p).

The probability of success on trial 5 is 0.16.

Therefore, p = 0.16.

The probability of failure on trial 5 is

1-p = 1-0.16

1-p = 0.84

The probability of success on trial 9 is given by:

P(success on trial 9) = p

P(success on trial 9) = 0.16.

Therefore, the probability of success on trial 9 is 0.16, which is option E.

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Hence, option D is the correct answer to the given question.

The correct answer to the given question is the option D. i.e r=0.818 represents a stronger correlation because 0.818 > -0.926. Explanation: The strength of the correlation can be determined by the magnitude of the correlation coefficient. The correlation coefficient values vary between -1 to 1. If the value of correlation coefficient is close to -1 or 1, it indicates strong correlation. On the other hand, if the value of correlation coefficient is close to 0, it indicates a weak correlation.A correlation coefficient value of -0.926 indicates a strong negative correlation. A correlation coefficient value of 0.818 indicates a strong positive correlation. Hence, option D is the correct answer to the given question.

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Answer:

Part A

750, 2250, 6750, 20250, 60750

Part B

1640250

Answer:

when a = 6, substitute 6 in the equation for a:

7(a + 2) = 7(6)+ 14

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

When a = 6

7(a+2)

7(6+2)

7(8)

56

Answer:

The Degree of the polynomial is 3

Answer:

Answer is (a)

Step-by-step explanation:

Well I didn’t really do any work but you can tell right away theres a ton of slope options so you can’t eliminate from there, BUT when you look at the y-intercept, 3 is the only y-intercept option here and the only choice with the y-intercept of 3 is (a).

The solution to the inequality y < 43.5 can be graphed on a number line. The graph will show all the values of y that are less than 43.5.

To graph the solution to the inequality y < 43.5 on a number line, we start by marking the point 43.5 on the number line. Since the inequality is y < 43.5, we represent it with an open circle at 43.5 to indicate that 43.5 itself is not included in the solution.

Next, we shade the region to the left of the open circle. This shaded region represents all the values of y that are less than 43.5, including any negative values and values approaching negative infinity.

The resulting graph on the number line will show a shaded region to the left of the open circle at 43.5, indicating that all values of y in that region satisfy the inequality y < 43.5.

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a) To solve the recurrence relation an = an-1 + 3(n-1), a0 = 1, we can expand the recurrence relation iteratively.

a1 = a0 + 3(1-1) = 1 + 0 = 1

a2 = a1 + 3(2-1) = 1 + 3 = 4

a3 = a2 + 3(3-1) = 4 + 6 = 10

a4 = a3 + 3(4-1) = 10 + 9 = 19

...

We can observe a pattern from the values:

a0 = 1

a1 = 1

a2 = 4

a3 = 10

a4 = 19

We can notice that an = [tex]n^2 + 1.[/tex] We can prove this by induction, but in this case, we can also recognize that the given recurrence relation generates the triangular numbers (1, 3, 6, 10, 15, ...), which are defined by the formula Tn = n(n+1)/2.

Thus, the solution to the recurrence relation is an = [tex]n^2 + 1.[/tex]

b) For the recurrence relation an = an-1 + n(n-1), a0 = 3, we can again expand it iteratively:

a1 = a0 + 1(1-1) = 3 + 0 = 3

a2 = a1 + 2(2-1) = 3 + 2 = 5

a3 = a2 + 3(3-1) = 5 + 6 = 11

a4 = a3 + 4(4-1) = 11 + 12 = 23

...

Observing the values, we can notice that an =[tex]n(n^2 + 1).[/tex]

Thus, the solution to the recurrence relation is an = [tex]n(n^2 + 1).[/tex]

c) For the recurrence relation an = an-1 +[tex]3n^2[/tex], a0 = 10, we expand it iteratively:

a1 = a0 + [tex]3(1^2)[/tex] = 10 + 3 = 13

a2 = a1 + [tex]3(2^2) =[/tex] 13 + 12 = 25

a3 = a2 + [tex]3(3^2)[/tex]= 25 + 27 = 52

a4 = a3 + [tex]3(4^2)[/tex]= 52 + 48 = 100

...

We can notice that an = [tex]n^3 + 10.[/tex]

Thus, the solution to the recurrence relation is an = [tex]n^3 + 10.[/tex]

These are the solutions to the given recurrence relations.

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Using telescoping or iteration, the closed form for the recurrence relation c₂ = 2cn-1 - 1 with co = 2 is `cₙ = 2ⁿ+1 - 1` for `n ≥ 0`.

As the recurrence relation is `c₂ = 2cn-1 - 1` with `c₀ = 2`. In the closed form, first, we write out the first few terms of the sequence: `c₀ = 2, c₁ = 3, c₂ = 5, c₃ = 9, c₄ = 17, c₅ = 33, c₆ = 65, ...`

Let's try a pattern in the sequence. Observe that `c₁ = 2c₀ + 1 = 2(2) + 1 = 5`. Similarly, `c₂ = 2c₁ + 1 = 2(5) + 1 = 11`. Continuing this process, we can see that `cₙ = 2cₙ₋₁ + 1` for `n ≥ 1`.

Let's apply telescoping to this formula:```
c₁ = 2c₀ + 1c₂ = 2c₁ + 1= 2(2c₀ + 1) + 1

= 2²c₀ + 2 + 1c₃ = 2c₂ + 1

= 2(2²c₀ + 2 + 1) + 1

= 2³c₀ + 2² + 2 + 1c₄

= 2c₃ + 1= 2(2³c₀ + 2² + 2 + 1) + 1

= 2⁴c₀ + 2³ + 2² + 2 + 1

```Note that each term in this sum telescopes. In general, we can write `cₙ = 2ⁿc₀ + 2ⁿ-1 + ... + 2² + 2 + 1`. Simplifying this expression gives:```
cₙ = 2ⁿc₀ + (2ⁿ - 1)
= 2ⁿ(2) + (2ⁿ - 1)
= 2ⁿ+1 - 1 ```

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Answer:

1. y=2x^2-8X-1

2. y=-6x^2+36x-63

3. y=-3x^2+18x-34

4. y=9x^2+54x+76

5. y=-x^2+8x-22

6. y=6x^2-48x+90

7. y=8x^2+16x+5

8. y=2x^2-8x+1

Have a great day :)

Answer:

the answer is  10

Step-by-step explanation:

Answer: 10

Why? Because 10x5=50 and then 10x2=20 ten can be used for both of them! Hope this helps^^ please give me brainlist if you could but you don’t have too!^^

Answer:

Step-by-step explanation:

x = 9

Bill should eat 4 cups of rice, 4 cups of tofu, and 4 cups of peanuts to meet his specific nutritional goals.

To determine how many cups of rice, tofu, and peanuts Bill should eat, we need to set up a system of equations based on the given nutritional information. Let's denote the number of cups of rice, tofu, and peanuts as x, y, and z respectively.

Based on the given information, we can establish the following equations

Carbohydrate equation: 46x + 6y + 26z = 312

Fat equation: 0x + 12y + 70z = 328

Protein equation: 2x + 15y + 28z = 180

We now have a system of three equations that we can solve to find the values of x, y, and z.

Using any appropriate method to solve the system of equations, we find

12y + 70z = 328

y = 328 - 70z/12

y = 27.33 - 5.833z

putting the value of y in both equation

2x + 15(27.33 - 5.833z ) + 28z = 180

2x + 28z + 409.95 - 87.45z = 180

(2x - 59.45z = -391.95)23

46x  - 1367.35z = - 9014.85

46x + 6(27.33 - 5.833z) + 26z = 312

46x + 163.98 - 34.998z + 26z = 312

46x - 8.998z = 148.02

equation both equation

- 8.998z + 1367.35z = 9014.85 + 148.02

z = 9162.87/1358.352

z ≈ 4

Solving equation we get

x = 4 cups of rice

y = 4 cups of tofu

z = 4 cups of peanuts

Therefore, Bill should eat 4 cups of rice, 4 cups of tofu, and 4 cups of peanuts to meet his nutritional goals.

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Yes, it is possible to fill all twenty mugs.

Answer:

5 :12 ; what is the ratio of the number of gumamela to the total number of flowers

5 : 7 ; what is the ratio of the number of gumamela to the number of orchids

7:5 ; what is the ratio of the number of orchids to the number of gumamela

12 : 5 ; what is the ratio of the total number of flowers to the number of gumamela

12 : 7 ; what is the ratio of the total number of flowers to the number of orchid

Step-by-step explanation:

Ratios of a to b ;is written as a : b

Ratio of b to a is written as b : a

The ratio of a to the sum of a and b equals ;

a : (a + b)

Number of orchids = 7

Number of gumamela = 5

Total number of flowers = 7 + 5 = 12

Ratio two quantities are compared. A number of times a number contains another. It makes value comparisons. When two components of the same unit are compared, it is possible to determine how much of one number is represented in the other. The quotient of two mathematical equations is shown.

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