Solve by completing the square (Show all work)
x2 – 10x + 10 = 35

Please help!

Answer:

Your answer is x=3

Step-by-step explanation:

So  you have the equation 2x+5=11

First, subtract 5 from 5 and from 11.

Then you will cancel out the 5's.

After that, you should have "2x=6"

Now divide 2 from 2x and from 6.

Your answer is x=3

Answer:

-3/7

Step-by-step explanation:

Hi,

First of all, we know that the slope is not undefine because both the x-coordinates are not the same.

To find the slope, do change in y/change in x. Here, it would be ((2/7)-(5/7))/(2-1) or (-3/7)/1. Hence, the slope is -3/7.

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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Answer:

see explanation

Step-by-step explanation:

A quadratic function in standard form is

y = ax² + bx + c (a ≠ 0 )

Given

y = - 3x² + 6x + 17 ← compare coefficients with standard form, then

a = - 3, b = 6, c = 17

Given the quadratic in standard form the the equation of the axis of symmetry is

x = - \(\frac{b}{2a}\) = - \(\frac{6}{-6}\) = 1

Equation of axis of symmetry is x = 1

The equation of the axis of symmetry is x = 1.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

A quadratic function in standard form is

y = ax² + bx + c (a ≠ 0 )

Given that, y = - 3x² + 6x + 17 ← compare coefficients with standard form, then.

a = - 3, b = 6, c = 17

The quadratic in standard form the equation of the axis of symmetry is

x = -b / 2a  = -6 / - 6 = 1

The equation of the axis of symmetry is x = 1.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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Answer:

50

Step-by-step explanation:

The upper left hand arc is also 130

The lower right hand arc is also x

A circle all the way around from some starting point is 360 degrees.

x + x + 130 + 130 = 360            Equation. Combine like terms.

2x + 260 = 360                         Subtract 260 from both sides

2x = 360 - 260                    

2x = 100                                    Divide by 2

x = 100/2

x = 50

Answer:15

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

hope this helps

If Francine adds 8.0 ml of 3.0 m KOH to 4.0 ml of 6.0 m HBr, then the resulting mixture will be neutral in nature.

To determine whether the mixture is acidic, basic or neutral, litmus test is done or some other tests can also be performed. However, the mathematical calculations help in understanding the reason behind the result of litmus test.

In the given problem, the volume and molarity of the solutions are given, so number of moles can be easily calculated.

Number of moles of KOH = (8.0 mL) x (3.0 mol/L) / 1000 mL/L = 0.024 mol

Number of moles of HBr = (4.0 mL) x (6.0 mol/L) / 1000 mL/L = 0.024 mol

Considering the chemical reaction between KOH (which is a strong base) and HBr ( which is a strong acid), the resulting product will be a salt along with water (in the form of vapors).

KOH + HBr → KBr + H2O

Since, the number of moles of KOH and HBr is same, therefore the resultant solution will have salt with neutral pH.

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Answer:

If he taped the edges of the photograph, then the width is 5 inches.

Step-by-step explanation:

The perimeter of a rectangular photo is composed of 2 lengths and 2 widths

2l + 2w = 24in

l = 7in

2*7in + 2w = 24in

14in + 2w = 24in

2w = 10in

w = 5in

Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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The error in the given equation is that the expression "cot(-x)" is incorrect. The correct expression should be "cot(x)" instead. With this correction, the equation would simplify to "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

In the given equation, the error lies in the term "cot(-x)". The cotangent function is an even function, meaning that cot(-x) is equal to cot(x). Therefore, the original equation simplifies to "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

The cotangent function, cot(x), is defined as the ratio of the adjacent side to the opposite side in a right triangle, where the angle is x. Since the cotangent function is the reciprocal of the tangent function, cot(x) is equivalent to 1/tan(x).

By substituting this equivalence into the equation, we can rewrite it as "1/tan(x) + 1/tan(x) = 2cot(x)". Simplifying further, we get "2/tan(x) = 2cot(x)". Canceling out the common factor of 2 on both sides of the equation, we arrive at "1/tan(x) = cot(x)". Therefore, the correct equation should be "1/tan(x) + cot(x) = cot(x) + cot(x) = 2cot(x)".

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Answer:

\( v =\frac{x}{t}\)

Where x represent the distance and t the time if we replace the info given we got:

\( v = \frac{200m}{54 s} =3.704 \frac{m}{s}\)

Then the average speed for this case in m/s is 3.704 for the 200 meter race

Step-by-step explanation:

The problem provides for this case the amount of distance travelled by Jessica in a given time. And we know that travels 200m in 54 seconds.

We want to find the average speed and we can use the following formula:

\( v =\frac{x}{t}\)

Where x represent the distance and t the time if we replace the info given we got:

\( v = \frac{200m}{54 s} =3.704 \frac{m}{s}\)

Then the average speed for this case in m/s is 3.704 for the 200 meter race

Answer:

i think 69

Step-by-step explanation:

The correct answer is option c. 35.3%. The annual percentage yield (apy) for money invested at the given annual rate of 3.5% compounded continuously is  35.3%.

The annual percentage yield (APY) is a measure of the total interest earned on an investment over a year, taking into account the effects of compounding.

To calculate the APY for an investment with continuous compounding, we use the formula:

\(APY = 100(e^r - 1)\),

where r is the annual interest rate expressed as a decimal.

In this case, the annual interest rate is 3.5%, which, when expressed as a decimal, is 0.035. Plugging this value into the APY formula, we get:

\(APY = 100(e^{0.035} - 1).\)

Using a calculator, we find that \(e^{0.035\) is approximately 1.03571. Substituting this value back into the APY formula, we get:

APY ≈ 100(1.03571 - 1) ≈ 3.571%.

Rounding this value to the nearest hundredth of a percent, we get 3.57%.

Among the given answer choices, option c. 35.3% is the closest to the calculated value.

Options a, b, and d are significantly different from the correct answer.

Therefore, option c. 35.3% is the most accurate representation of the APY for an investment with a 3.5% annual interest rate compounded continuously.

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Stephanie walked 6 more blocks to the coffee shop from her sister's work place.

Finding the difference between two numbers is done using the subtraction technique. If you have an object group and remove a couple of them, the object group gets smaller. For example, suppose you purchased 9 cupcakes for your birthday party and your guests consumed 7 cupcakes. You're now down to two cupcakes. This can be expressed as a reduction formula:  9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.

How to solve?

total number of blocks from the store to the coffee shop = 8

number of blocks between store and Stephanie's sister's work = 2

Number of blocks Stephanie has to walk to get coffee from her sister's work = 8 - 2 = 6

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Answer:

3, 1, -1, -3

-15

Step-by-step explanation:

The nth term is 5 - 2n.

Put n as 1, 2, 3, 4, and 10.

5 - 2(1)

5 - 2 = 3

5 - 2(2)

5 - 4 = 1

5 - 2(3)

5 - 6 = -1

5 - 2(4)

5 - 8 = -3

5 - 2(10)

5 - 20 = -15

The first four terms are 3, 1, -1, -3.

The 10th term is -15.

Answer:

The first four terms using the formula

5 - 2n is

First term

5 - 2(1) = 5 - 2 = 3

Second term

5 - 2(2) = 5 - 4 = 1

Third term

5 - 2(3) = 5 - 6 = - 1

Fourth term

5 - 2(4) = 5 - 8 = - 3

The first four terms are 3, 1 , - 1 , -3

The 10th term is

5 - 2(10) = 5 - 20 = - 15

Hope this helps you

Answer:

B: g(x) = RootIndex 3 StartRoot x minus 3 EndRoot + 4

Step-by-step explanation:

Got it right on Edge. Hope it helps!

Answer:

it is b on ed 2021

Step-by-step explanation:

Answer:

6a + 2

Step-by-step explanation:

2 ×3a = 6a 2×2 = 4

it gives 6a + 4

(If this is wrong, it would be better to attach an image)

The hypothesis test aims to determine whether there is a significant linear correlation between the average shipping time of 93 sellers and their overall satisfaction rating. The study produced a sample correlation coefficient of r=-0.216. The significance level is set at 2%.

To test the claim, the first step is to set up the null and alternative hypotheses. The null hypothesis (H0) is that there is no linear correlation between the average shipping time and the overall satisfaction rating. The alternative hypothesis (Ha) is that there is a significant linear correlation between the two variables.

H0: r = 0

Ha: r ≠ 0

Next, the test statistic (t) can be calculated using the formula:

t = r * sqrt(n - 2) / sqrt(1 - r^2)

Where n is the sample size, which is 93 in this case. Plugging in the values, we get:

t = -2.128

To determine the critical value(s), we need to look up the t-distribution table for 91 degrees of freedom (df = n - 2) and a two-tailed test at the 2% level of significance. The critical value is ±2.364.

Since the calculated t-value (-2.128) is within the acceptance region, we fail to reject the null hypothesis. Therefore, we conclude that there is no significant linear correlation between the seller's average shipping time and their overall satisfaction rating at the 2% level of significance. However, it is important to note that the study only provides evidence of the absence of linear correlation and does not necessarily imply that there is no relationship between the two variables. Other types of relationships (e.g., non-linear) may exist between the variables.

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Answer:

C. 17

Step-by-step explanation:

2 + 3n

= 2 + 3*5 ( Plug n = 5)

= 2 + 15

= 17

Answer:

10 the answer is 10 good luck!

Answer:

B

Step-by-step explanation:

The slope is -1, which equals m= -1.

The answer is B.

High-def television sets would probably be distributed using an intensive strategy. Therefore, option B. is correct.

Intensive distribution refers to a strategy where a product is made widely available through as many outlets as possible. This strategy is typically employed for products that have high demand, are low-cost, and require extensive market coverage. In the case of high-definition television sets, they are popular consumer electronics with a significant market demand.

To determine whether intensive distribution is suitable for high-def television sets, we consider the characteristics of the product. High-definition television sets are relatively low-cost compared to other options in the market, and they are in demand by a broad range of consumers. These factors suggest that an intensive distribution strategy would be appropriate for this product.

Based on the analysis, high-def television sets would most likely be distributed using an intensive strategy. This approach would ensure broad availability and accessibility for consumers, leveraging the product's popularity and fulfilling market demand. By making these television sets widely accessible through multiple outlets, manufacturers can reach a larger customer base, maximize sales potential, and effectively compete in the consumer electronics market.

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Based on the base case and the inductive step, we can conclude that every string in the set S, generated by the recursive rules, begins with the character 'a'.

To prove that every string in the set S begins with the character 'a', we can use mathematical induction to demonstrate the property for all strings generated by the recursive rules.

**Base Case:**

The base case states that the string 'a' is in the set S. This string clearly begins with the character 'a', so the property holds for the base case.

**Inductive Step:**

Now, we assume that the property holds for a string x, which means that x begins with the character 'a'. We need to show that the property also holds for the strings generated by the recursive rules using x.

**Rule 1:**

According to Rule 1, if x ∈ S, then xb ∈ S. Let's assume that x begins with 'a' since we are assuming that the property holds for x. We need to show that xb also begins with 'a'.

If x begins with 'a', then we can represent it as x = 'a' + y, where y is a string that can be empty or contain characters other than 'a'. Now, applying Rule 1, we have xb = ('a' + y) + 'b' = 'a' + (y + 'b'). Since 'a' + (y + 'b') is of the form 'a' + z, where z = y + 'b', we can conclude that xb begins with 'a'. Hence, the property holds for xb.

**Rule 2:**

According to Rule 2, if x ∈ S, then xa ∈ S. Again, assuming that x begins with 'a', we need to show that xa also begins with 'a'.

Using the same representation for x as above (x = 'a' + y), we have xa = ('a' + y) + 'a' = 'a' + (y + 'a'). Since 'a' + (y + 'a') is of the form 'a' + z, where z = y + 'a', we can conclude that xa begins with 'a'. Therefore, the property holds for xa.

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Answer:

3x km

Step-by-step explanation:

The number of customers when there are 576 towers will be 12.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Based on the information, it should be noted that the number of phone is proportional to the number of customers

The constant of proportionality will be:

= 252 / 5.25

= 48

Therefore, the customers when there are 576 towers will be:

= 576 / 48

= 12

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The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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