Solve for x. Round to the nearest tenth.​

Answer:

x1 =-3+3[tex]\sqrt{2}[/tex] and x2=-3-3[tex]\sqrt{2\\}[/tex]

Step-by-step explanation:

x² + 6x-9 = 0

-6±[tex]\sqrt{6^{2}-4(1)(-9) }[/tex] / 2

-6±[tex]\sqrt{72}[/tex] /2

so

x1 = -6+[tex]\sqrt{72[/tex] /2

x1 =-3+3[tex]\sqrt{2}[/tex]

and

x2 = -6-[tex]\sqrt{72[/tex] /2

x2=-3-3    [tex]\sqrt{2\\}[/tex]

Like terms are those terms that are having the same variables, also the variables are of the same order as well. The first step to solving an equation is to rearrange the like terms.

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

To solve an equation the first step is to rearrange the equation such that like terms are together.

Hence, the first step to solving an equation is to rearrange the like terms.

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The two formats used in an observation checklist are: D. Performance profiles and SMART Targets.

Observation checklist can be defined as the process of observing and evaluating  a person or group of  people performance.

When carrying out an observation checklist  endeavors to make sure that  the checklists are dated.

Observation checklist includes Performance profiles and SMART Targets. Where SMART stands for:

S=Specific

M=Measurable

A=Achievable

R=Relevant

T= Time-Bound

Therefore the correct option is D.

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Answer:

V≈25.13in³

Step-by-step explanation:

Answer:

5 1/4 gallons

Step-by-step explanation:

Hope this helps and have a nice day

Answer:

[tex](x + 2.3)^{2} + y^{2} = \frac{36}{49}[/tex]

Step-by-step explanation:

To get the equation of a circle, plug your information into this equation:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Therefore, the equation of this circle is:

[tex](x + 2.3)^{2} + y^{2} = \frac{36}{49}[/tex]

The solution -1 is an extraneous solution

Neither -1 nor -6 is a true solution to the equation.

Option D is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation x + 4 = √(x + 10), we need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical.

Here are the steps:

x + 4 = √(x + 10)

Subtract 4 from both sides:

x = √(x + 10) - 4

Square both sides:

x² = (√(x + 10) - 4)²

Expand the right side using the formula (a - b)^2 = a^2 - 2ab + b^2:

x² = x + 6 - 8√(x + 10)

Move all terms to the left side:

x² - x - 6 + 8√(x + 10) = 0

To solve this equation, we can use a substitution u = √(x + 10):

u = √(x + 10)

Square both sides:

u² = x + 10

Substitute into the original equation:

(u² - 10) + 4 = u

Simplify:

u² - u - 6 = 0

Factor:

(u - 3)(u + 2) = 0

So u = 3 or u = -2.

But u = -2 leads to a negative value under the square root in the substitution u = √(x + 10), which is not allowed.

Therefore, we only consider u = 3, which gives:

√(x + 10) = 3

Square both sides:

x + 10 = 9

Subtract 10 from both sides:

x = -1

So the solution to the original equation is x = -1.

To check if it is extraneous, we need to substitute it back into the original equation:

x + 4 = √(x + 10)

-1 + 4 = √(-1 + 10)

3 = √9

3 = 3

The equation is true, so x = -1 is a valid solution and not extraneous.

Therefore,

Neither -1 nor -6 is a true solution to the equation.

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Answer:

110.5 yd²

Formula's:

Area of triangle:

1/2 × base × height

Area of rectangle:

length × width

Area of the figure:

= area of triangle + area of rectangle's

= 1/2 × 11 × 7 + 3 × 4 + 5 × 3 + 5 × 2 + 7 × 5

= 110.5 yd²

Answer:

110.5 yd²

Step-by-step explanation:

Separate the figure into 1 triangle and 3 rectangles.

(see attached image)

Area 1

Area of a triangle = 1/2 × base × height

                             = 1/2 × (7 + 2 + 2) × 7

                             = 1/2 × 11 × 7

                             = 38.5 yd²

Area 2

Area of a rectangle = width × length

                                 = 3 × (5 + 2 + 2)

                                 = 3 × 9

                                 = 27  yd²

Area 3

Area of a rectangle = width × length

                                 = 5 × (5 + 2)

                                 = 5 × 7

                                 = 35  yd²

Area 4

Area of a rectangle = width × length

                                 = 2 × 5

                                 = 10  yd²

Total Area

Area 1 + Area 2 + Area 3 + Area 2 = 38.5 + 27 + 35 + 10

                                                        = 110.5 yd²

Using the Central Limit Theorem, it is found that the correct option is given by:

Yes. All conditions are met.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have no information about the distribution, but the sample size is greater than 30, hence all the conditions have been met.

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Answer:

height = 21 cm

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substituting given values into the formula and solving for r:

[tex]\implies \sf 343 \pi=\dfrac{1}{3} \pi r^2(3r)[/tex]

[tex]\implies \sf 343=\dfrac{1}{3}\cdot3r^3[/tex]

[tex]\implies \sf 343=r^3[/tex]

[tex]\implies \sf r=\sqrt[3]{343}[/tex]

[tex]\implies \sf r=7\:cm[/tex]

As h = 3r, substitute found value of r into the equation and solve for h:

[tex]\implies \sf h = 3r[/tex]

[tex]\implies \sf h=3(7)[/tex]

[tex]\implies \sf h=21\:cm[/tex]

Answer:

Step-by-step explanation:

Answer:

7[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Take 9 out of [tex]\sqrt{63}[/tex]

You get 3[tex]\sqrt{7}[/tex]

Take 4 out of [tex]\sqrt{28}[/tex]

You get 2[tex]\sqrt{7}[/tex]

So, 3(3[tex]\sqrt{7}[/tex]) - 2[tex]\sqrt{7}[/tex]

= 9  [tex]\sqrt{7}[/tex] - 2[tex]\sqrt{7}[/tex]

=7[tex]\sqrt{7}[/tex]

Using the given information, the value of the f(3) is 155

From the question, we are to determine the value of f(3)

From the given information,

f(n) = 5f(n-1) + 5

∴ f(2) = 5f(2-1) +5

f(2) = 5f(1) + 5

From the given information,

f(1) = 5

Then,

f(2) = 5(5) + 5

f(2) = 25 + 5

f(2) = 30

Also,

f(3) = 5f(3-1) + 5

f(3) = 5f(2) + 5

∴ f(3) = 5(30) + 5

f(3) = 150 + 5

f(3) = 155

Hence, the value of the f(3) is 155.

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The full workings for the house purchase you made on a mortgage are as follows:

1. Price of House = $499,000 (given)

2. Down Payment = $99,800 ($499,000 x 20%)

3. Amount Financed (Mortgage principal) = $399,200 ($499,000 - $99,800).

4. Monthly Payment = $2,522.94 (given)

5. Number of monthly payments = 360 months (30 x 12)

6. Total Payback = $908,258.40 ($2,522.94 x 360)

7. Total Interest = $509,058.40 ($908,258.40 - $399,200)

8. Assessed Valuation = $199,600 ($499,000 x 40%)

9. Real Estate Taxes (annual) = $6,047.88 ($199,600 x $3.03/$100)

10. Escrow Payment Per month (taxes & insurance) = $628.99 ($6,047.88 + $1,500)/12

11. Monthly Payment to lender (escrow + mortgage) = $3,151.93 ($628.99 + $2,522.94)

A mortgage is a loan arrangement that allows a borrower to buy some property, usually a house, without paying for the full cost immediately.

The borrower then makes a monthly payment, which includes the principal and its interest.

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Answer:

B

Step-by-step explanation:

answer is based on results from the Cartesian plane

Answer:

A≈9248.85

Step-by-step explanation:

A=2πrh+2πr2=2·π·32·14+2·π·322≈9248.84877

Answer:

62.8 meters

Step-by-step explanation:

Use the formula for circumference.

[tex]C = d\pi \\C = 20(3.14)\\C = 62.8[/tex]

The mean and standard deviation for the GPA of the students will be 3 and 0.8165.

The mean simply means the average of a given set of numbers. The mean will be:

= 12/4

= 3

The standard deviation will be:

= ✓2/3

= 0.8165

The 95% confidence interval for the populations mean GPA will be 1.70 < U < 4.30. The interval lower limit is:

= 3.00 - 1.299.l

= 1.70

The interval upper limit will be;

= 3.00 + 1.299

= 4.30

Also, the regression line is Y = -1.2857 + 0.3571x.

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Answer:

1/4

Step-by-step explanation:

y = a^x

1/16 = a^2

so the answer is 1/4

Answer:

Area = 1250cm²

Step-by-step explanation:

Area of a kite = pq/2

where p and q are diagonals

p = 25+25 = 50

q = 30+ 20 = 50

Area of a kite = pq/2

Area = (50*50 ) / 2

Area = 1250cm²

Step-by-step explanation:

it does not say what the card deck consists of, and how many cards of what type there are.

so, I assume a standard playing card set of 52 cards (no jokers) with 4 suits of

Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K

in that ranking of value.

so there are 4 cards of each of the 13 different types.

a card with a number greater than 9 means a 10, a J, a Q, or a K.

so, in total there are 4×4 = 16 such cards in the deck.

a card with a number less than 4 means an Ace, a 2, or a 3.

so, in total there are 4×3 = 12 such cards in the deck.

to get a number greater than 9 and a number less than 4 is a combination of the first card being greater than 9 and the 2 card being less than 4 OR the first card being less than 4 and the second card being greater than 9.

an "and" operation (without overlap) we represent by a multiplication, and an "or" operation (without overlap) by an addition.

remember, a probability is always

"desired cases / total possible cases".

so, the probability to draw a first card greater than 9 is

16/52 = 4/13

the probability to draw a second card greater than 9 (after a first card less than 4) is

16/51

because we still have all the large cards, but one of the smaller ones is now gone.

the probability to draw a first card less than 4 is

12/52 = 3/13

the probability to draw a second card less than 4 (after a first card greater than 9) is

12/51.

so, the complete probability of the scenario is

4/13 × 12/51 + 3/13 × 16/51 = 48/663 + 48/663 = 96/663 =

= 32/221 = 0.14479638...

if my assumptions about the cards are wrong, please adapt the numbers accordingly. but the basic structure of the calculation is the same.

Answer:

7(7x²-9x +1)

Step-by-step explanation:

49x²-63x+7

7(7x²-9x +1)

Answer:

A.  (96 - 72) ÷ 12

D.  24 ÷ 12

Step-by-step explanation:

Difference between 96 and 72 means subtract 72 from 96:   96 - 72

Divide by 12 means:  ÷ 12

Therefore, "Divide the difference between 96 and 72 by 12" is:  

⇒ (96 - 72) ÷ 12

As the difference between 96 and 72 is 24, we can also represent the calculation by:

⇒ 24 ÷ 12