For the function f(x)=x² + 2x-35 solve the following. f(x) ≤0

Answer:

8)  $3,284.73

9)  $202.40

Step-by-step explanation:

To solve both these problems, we can use the formula for compound interest:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]A=1600\left(1+\dfrac{0.024}{12}\right)^{12 \cdot 30}[/tex]

[tex]A=1600\left(1+0.002\right)^{360}[/tex]

[tex]A=1600\left(1.002\right)^{360}[/tex]

[tex]A=3284.730430...[/tex]

[tex]A=3284.73[/tex]

Therefore, the balance of Scott's account after 30 years will be $3,284.73.

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]A=500\left(1+\dfrac{0.034}{52}\right)^{52 \cdot 10}[/tex]

[tex]A=500\left(1.000653846...\right)^{520}[/tex]

[tex]A=702.3957509...[/tex]

[tex]A=702.40[/tex]

Therefore, the balance of the account after 10 years will be $702.40, which includes both the principal and the interest.

To find the amount of interest earned, subtract the principal:

Interest earned = $702.40 - $500 = $202.40

Therefore, Kaylee will have earned $202.40 in interest after 10 years.

Answer:

2 forms

Step-by-step explanation:

hope this helps <3

[tex] \sf \longrightarrow \: \frac{8}{5} \div 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5}{8} \times 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5 \times 6}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{30}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{8}{30} \\ [/tex]

[tex] \sf \longrightarrow \: 0.26 \\ [/tex]

_____________________________

a) The first mistake that Fatima made was in the first step.

b) She incorrectly changed the place value of 0.02 in the subtraction operation.

c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.

The place value shows the position of a digit in a number.

The right place values are essential for correct mathematical operations.

The quantity of rose petals that Fatima bought initially = 0.454 kilograms

The quantity of rose petals used for making rose water = 0.02 kilograms

The remaining quantity of rose petals = 0.434 (0.454 - 0.02)

The additional quantity of rose petals Fatima bought = 0.056

The quantity of rose petals used for making the second rose water = 0.095

The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)

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Answer: Centre: (-2,5)

Radius = 3

so

Diameter = 6

Domain: (-5,1)

Range: (2,8)

Answer:

center (-2,5)

radius =3

domain = -5< x <1

range 2 <y<8

Step-by-step explanation:

siiuu

In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A

In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.

Given that AB is a diameter = 180°.

AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.

Substituting m∠AC =54°, we get m∠BD + 54°  = 90°.

Solving for m∠BD, we get 90° - 54° = 36°.

There BD is 36°.

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Answer: yes

Step-by-step explanation:

Answer:

  y = |2x +9|

Step-by-step explanation:

You want the equation that will translate the graph of y = |2x +7| one unit to the left.

To translate the graph of f(x) by h units to the right, you want to replace x with x-h:

  f(x-h) . . . . translates f(x) by h units to the right

Here, we want a translation by 1 unit to the left, which is -1 unit to the right. This means we want to replace x in the function by (x -(-1)) = (x +1). Doing that gives ...

  y = |2(x +1) +7)| = |2x +2 +7|

  y = |2x +9|

The attachment shows the graphs.

#95141404393

The experimental probability did not match the theoretical probability.

The experimental probability is the chance that is determined from the real results of an experiment or event. It is based on practical observations or information, rather than a mathematical expression.

The theoretical probability is the chance that is worked out using a mathematical equation founded on the assumptions and situations of the event or experiment.

The experimental probability of landing on heads :

= 40 / 100

= 40 %

The theoretical probability is 50 % which means the experimental and theoretical did not match.

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Answer:

2 miles = 3,520 yards

Step-by-step explanation:

You multiply the length value by 1,760.

3520 yards is equivalent to 2 miles.

There are no intersecting points.

The given equations are

y = (2x)² - 6x+5   ....(i)

2y + x =4 ....(ii)

Since we know that,

Degree of equation (i)  = 2

Therefore,

equation (i) is a quadratic equation.,

And equation (ii) has degree 1,

So it is a equation of line,

To find the intersection,

First of we have to plot both graphs,

Then find the coordinate of the intersection of the given line and curve.

After plotting graph,

We can see that,

The given curve and line are not intersecting,

Therefore,

There are no intersecting points.

Hence we can not find the required equation of line.

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After completing the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we find that the possible result is [tex]\((x + 6)^2 = 49\)[/tex].

To complete the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we follow these steps:

1. Take half of the coefficient of the [tex]x[/tex] term, which is [tex]\(12/2 = 6\)[/tex].

2. Square this result, [tex]\(6^2 = 36\)[/tex].

3. Add this value, 36, to both sides of the equation to maintain balance:

[tex]\[x^2 + 12x + 36 - 85 = 36 - 85.\][/tex]

4. Simplify both sides of the equation by combining like terms:

  [tex]\[(x + 6)^2 - 49 = 0.\][/tex]

5. Rearrange the equation to isolate the perfect square term:

 [tex]\[(x + 6)^2 = 49.\][/tex]

From this process, we can conclude that the equation [tex]\((x + 6)^2 = 49\)[/tex] could be the result of completing the square for the given equation [tex]\(x^2 + 12x - 85\)[/tex]. This equation represents a perfect square trinomial with a perfect square term, and it allows us to solve for the value of [tex]x[/tex] by taking the square root of both sides.

It's important to note that completing the square allows us to rewrite quadratic equations in a form that reveals key properties and facilitates solving for unknowns.

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Answer:

Step-by-step explanation:

6 = a / 4 + 2

=> 6 - 2 = a / 4 + 2 - 2
=> 4  =  a / 4
=> a = 16

Answer:

a = 16

Step-by-step explanation:

[tex]6=a/4+2[/tex]

[tex]6(-2)=a/4+2(-2)[/tex]

[tex]4=a/4[/tex]

[tex]4(4)=(a/4)(4)[/tex]

[tex]16=a[/tex]

[tex]a=16[/tex]

Based on the information given, it should be noted that the length of other leg 12.

Based on the information, the owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle.

Based on the information, 1/2ab = 54

1/2 × 4/3b² = 54

b² = 81

b = ✓81

b = 9

a will be

= 4/3 × 9

= 12 feet.

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Answer:

301.59289cm²

Step-by-step explanation:

In the graph, the closing price per share of stock for a company is represented each day for 28 days. After analyzing the graph, the variable which is represented on the horizontal axis is days and the stock price generally increasing in the first week. The closing price of the stock decrease for at least 3 days in a row during day 7 to day 10.

The graph represents the closing price per share of stock for a company each day for 28 days. That's the number of days in the first week. So days is the variable represented in the horizontal axis.

In the first seven days, the graph is basically going up, and then it gets slower and then it's going up. So it's increasing the entire time. Not at the same rate, but it's increasing.

From day 7 to day 10, the closing price of the stock was decreasing three days in a row.

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The value of function for x = 6 is f(6) = 2.1

Given that f(x) = [tex]18 / [ 6 + 5^{e-0.1x ][/tex]

We have to find the value of this function at x = 6.

f(6) =

  [tex]18 / [ 6 + 5^{e-0.1 * 6} ] \\ \\ = 18 / [ 6 + 5^{e-0.6} ][/tex]

≈  2.1

Therefore, f(6) = 2.1

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Answer:

2.1

Step-by-step explanation:

Answer:

x=0, y=6

x=4, y=0

x=8, y=-6

Step-by-step explanation:

6x + 4y = 24

6(0) + 4y = 24

y = 6

So x=0, y=6

y=0

6x+4y=24

6x+4(0)=24

6x=24

x=4

When x=4, y=0

x=8

6x+4y=24

6(8) + 4y = 24

48 + 4y = 24

4y = 24-48

4y = -24

y = -24/4

y = -6

When x = 8, y = -6

volume: 2,160cm

please let me know if this was what you needed or if it was something else.

The break-even point would be when the cost is equal to 44 dollars.

Option B is the correct answer.

We have,

The break-even point represents the point at which the cost equals the revenue or the point where there is no profit or loss.

Now,

In this case, if the graph represents the cost (dollars) on the y-axis and units on the x-axis, the break-even point occurs when the cost is equal to the revenue or total sales.

Given that two lines intersect at (11, 44),

The break-even point would be when the cost is equal to 44 dollars.

Thus,

The break-even point would be when the cost is equal to 44 dollars.

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The shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

From the question, we have the following parameters that can be used in our computation:

The record of shoe sizes

From the data values, we have the following shoe sizes that appear once

5 1/2, 7, 8 and 10 1/2

These are the data values that will have only one dot  if the data is recorded on a line plot

Hence, the shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

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Answer:

710

Step-by-step explanation:

The first term of the geometric progression has the value a1 = 2.

Let r = 1.5 be the common ratio of the GP given the data.

Now, the first seven terms added together equal 64.34375.

where Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

64.34375 = a ( 1.5⁷ - 1 ) / ( 1.5 - 1 )

On simplifying , we get

64.34375 = 2a ( 1.5⁷ - 1 )

2a = 64.34375 / 16.0859375

2a = 4

Divide by 2 on both sides:

a = 2

Consequently, a = 2 is the first term of the GP.

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Answer:

78°

Step-by-step explanation:

angle on a straight line : 180° - 126° = 54°

Therefore, 48° + 54° = 102°

total angle in a triangle = 180°

So, 180° - 102° = 78°

Measure of one exterior angle = 30 degree

Measure of one interior angle = 150 degree

In the given regular pentagon

Number of terms = 12

We know that,

Sum of all exterior angles = 360 degree

To find one exterior angle,

Divide the complete angle by number of terms

Therefore,

One exterior angle = 360/12  =  30 degree

Since,

Sum of all interior angles = 180 degree

And To find one interior angle,

subtract the interior  angle by one exterior angle

Therefore,

One exterior angle = 180 - 30  =  150 degree

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The number of different sodas that can be made is given by "n!" or factorial form.

If the soda tastes different depending on the order in which the flavors are chosen, we can calculate the number of different sodas that can be made without repetition using the concept of permutations.

Let's assume we have "n" different flavors of soda available. To calculate the number of different sodas we can make, we need to find the number of permutations of "n" flavors taken "r" at a time, where "r" is the number of flavors we want to choose for each soda.

The formula to calculate permutations is given by:

P(n, r) = n! / (n - r)!

Here, "n!" represents the factorial of "n," which is the product of all positive integers less than or equal to "n."

In this case, if repetition is not allowed, each soda can have only one flavor. Therefore, we have "r = 1" for each soda.

Applying the formula, we have:

P(n, 1) = n! / (n - 1)!

= n! / (n - 1)

= n

Hence, the number of different sodas that can be made without repetition is "n."

Therefore, the number of different sodas that can be made is given by "n!" or factorial form.

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Answer: attached in image, look at both

Step-by-step explanation: