fractorise this\( {a}^{2} - 17a + 42\)

Answer:192$

Step-by-step explanation:

Answer:

$32

Step-by-step explanation:

$160 x 20% = $32

Answer:

22 is the correct answer of your question hope it helps you

The two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

Given that, Angle = 60°, v = 8, 6

Consider unit vector a = (x, y)

x² + y² = 1 …. (1)

Now apply the dot product of unit vector with v

a.v = |a||v|cos Ø

a.v = √ (x² + y²) √ (8² + 6²) cos 60º

8x + 6y = 1 × 10 × ½

So we get,

8x + 6y = 5 …. (2)

y = (5 - 8x) / 6

Substituting the value of y in equation (1)

x² + y² = 1

x² + [(5 - 8x)/6]² = 1

x² + 25/36 + 16x²/9 - 20x/9 = 1

25x²/9 - 20x/9 = 11/36

So we get,

4 × (25x² - 20x) = 11

100x² - 80x = 11

100x² - 80x - 11 = 0

Now solve the quadratic equation,

x = { 2/5 ± √5/10}

Substituting the value of x in equation (2)

y = 3/10 ± 2√5/15

Therefore, the two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

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Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

Answer: See below.

Step-by-step explanation:

1) x=49

2) x=-16

3) x=6/11

4) x=3

Please give Brainliest if this helped you. Have a great day!

Answer:

1)  x = 49

2)  x = -16

3)  x = ⁶/₁₁

4)  x = 3

Step-by-step explanation:

72 = x - (-23)

Apply rule -(-a) = a :

⇒ 72 = x + 23

Subtract 23 from both sides:

⇒ 72 - 23 = x + 23 - 23

⇒ 49 = x

⇒ x = 49

-5x - (7 - 4x) = 9

Apply rule -(a - b) = -a + b :

⇒ -5x - 7 + 4x = 9

Collect and combine like terms:

⇒ -5x + 4x - 7 = 9

⇒ -x - 7 = 9

Add 7 to both sides:

⇒ -x - 7 + 7 = 9 + 7

⇒ -x = 16

Divide both sides by -1:

⇒ -x ÷ -1 = 16 ÷ -1

⇒ x = -16

8x + 6 = 3(4 - x)

Distribute:

⇒ 8x + 6 = 12 - 3x

Add 3x to both sides:

⇒ 8x + 6 + 3x = 12 - 3x + 3x

⇒ 11x + 6 = 12

Subtract 6 from both sides:

⇒ 11x + 6 - 6 = 12 - 6

⇒ 11x = 6

Divide both sides by 11:

⇒ 11x ÷ 11 = 6 ÷ 11

⇒ x = ⁶/₁₁

¹/₂(4x - 16) = -2

Distribute:

⇒ 2x - 8 = -2

Add 8 to both sides:

⇒ 2x - 8 + 8 = -2 + 8

⇒ 2x = 6

Divide both sides by 2:

⇒ 2x ÷ 2 = 6 ÷ 2

⇒ x = 3

Answer:

x = -61

Step-by-step explanation:

-  2x - 35 = 87.    

         +35. +35.   Add 35 to both sides

-2x = 122.  

-2/-2 = 122/-2.     Divide by -2 on both sides

     x = -61

Therefore, the sample variance is approximately 65 using 95% confidence interval.

To find the sample variance, we need to use the formula for the confidence interval of the mean:

X ± tα/2 (s/√n)

Where:

X is the sample mean

tα/2 is the critical value for the t-distribution at the desired confidence level (with n-1 degrees of freedom)

s is the sample standard deviation

n is the sample size

From the given information, we know that the sample size n = 13, and the confidence interval is (3.5990, 19.0736) with a 95% confidence level. This means that the critical value for the t-distribution at α/2 = 0.025 and 11 degrees of freedom is approximately 2.201.

Using the formula for the confidence interval and the upper and lower bounds of the interval, we can solve for s:

19.0736 = X + 2.201(s/√13)

3.5990 = X - 2.201(s/√13)

Adding the two equations gives:

22.6726 = 2X

Therefore, X = 11.3363

Substituting this value of X into one of the original equations gives:

19.0736 = 11.3363 + 2.201(s/√13)

Solving for s, we get:

s ≈ 8.0587

Rounding to the nearest integer, the sample variance is:

s^2 ≈ 65

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A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal.

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make.

To determine which box holds more cereal, we need to calculate the volume of each box.

The volume of a rectangular box is given by the formula:

Volume = Length × Width × Height

Let's calculate the volumes for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Volume = 8 cm × 3 cm × 11 cm = 264 cm³

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Volume = 10 cm × 10 cm × 3 cm = 300 cm³

A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal because it has a larger volume of 300 cm³ compared to the original box with a volume of 264 cm³.

To determine which box requires more material to make, we need to calculate the surface area of each box.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 × (Length × Width + Length × Height + Width × Height)

Let's calculate the surface areas for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Surface Area = 2 × (8 cm × 3 cm + 8 cm × 11 cm + 3 cm × 11 cm) = 374 cm²

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Surface Area = 2 × (10 cm × 10 cm + 10 cm × 3 cm + 10 cm × 3 cm) = 380 cm²

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make because it has a larger surface area of 380 cm² compared to the original box with a surface area of 374 cm².

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The answer is \(\boxed {\frac{3b - 8}{4b}}\).

Answer:

26-9=17           26 is the answer

Step-by-step explanation:

Answer:

The number n is 26

Step-by-step explanation:

Decreased means subtract

n-9 = 17

Add 9 to each side

n-9+9 = 17+9

n = 26

The number n is 26

The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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The simplified difference quotient for the function f(x) = kx² + dx + g is 2kx + d.

The difference quotient measures the rate of change of a function at a specific point. It is defined as the limit of the average rate of change as the change in x approaches zero. In this case, we need to find the difference quotient for the given function f(x) = kx² + dx + g.

To find the difference quotient, we evaluate the function at two points: x and x+h, where h represents a small change in x. The difference quotient is then calculated as (f(x+h) - f(x))/h.

Substituting the given function into the difference quotient formula, we have:

[f(x+h) - f(x)]/h = [(k(x+h)² + d(x+h) + g) - (kx² + dx + g)]/h

Expanding the terms and simplifying, we get:

= [kx² + 2kxh + kh² + dx + dh + g - kx² - dx - g]/h

Canceling out the like terms, we have:

= (2kxh + kh² + dh)/h

Dividing each term by h, we get:

= 2kx + kh + d

As h approaches zero, the term kh approaches zero as well. Thus, the simplified difference quotient is:

2kx + d.

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Answer:

it would be A

Step-by-step explanation:

Answer:

The x-intercept represents if DeVion only baught chicken sandwitches. The y-intercept represents if DeVion only baught sodas.

Step-by-step explanation:

Answer:

The x - intercept is how much a chicken sandwich costs, and the y- intercept is how much a soda costs

Step-by-step explanation:

Answer:

Step-by-step explanation:

solution -4x+6

Answer:

50 children can go to the park before they run out of balloons.

Step-by-step explanation:

If each child gets 3 balloons each, there will be 50 kids who can go in the park before they run out of balloons. 150 (balloons given out in total) / 3 (number of balloons each child receives) = 50 (number of children who can go into the park before balloons run out.)

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A number cube has six numbers, from 1 to 6, with one number on each face.

Since the number cube is fair, the probability of each number being rolled is the same.

So, to find the probability of one specific number being rolled, we just need to divide 1 by the total amount of numbers:

The probability of rolling a 2 is the same as rolling any other number, therefore the probability is 1/6.

This forest can support approximately 5 people based on its oxygen production.

To find out how many people the forest can support based on the amount of oxygen produced, we will use the given information:

1. The forest produces 970 kg of oxygen per metric ton of wood.
2. The average person breathes 165 kg of oxygen per year.

We'll first calculate the total amount of oxygen the forest produces, and then divide that by the oxygen consumption of one person to find out how many people the forest can support.

Your answer: A forest produces approximately 970 kg of oxygen for every metric ton of wood produced. If the average person breathes about 165 kg of oxygen per year, the number of people this forest can support can be calculated using the following steps:

Step 1: Determine the total amount of oxygen produced by the forest.
Let's assume the forest produces 1 metric ton of wood.
Total oxygen produced = 970 kg of oxygen per metric ton of wood x 1 metric ton of wood = 970 kg of oxygen.

Step 2: Calculate the number of people the forest can support.
\(Number of people =  \frac{Total oxygen produced}{Oxygen consumption per person}\)
\(Number of people =  \frac{ 970 kg of oxygen}{165 kg of oxygen per person}\)
Number of people = 5.88

Since we cannot have a fraction of a person, we round down to the nearest whole number. Therefore, this forest can support approximately 5 people based on its oxygen production.

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Answer:

7.3333, so if you round down, 7.

Step-by-step explanation:

5 1/2 divided by 3/4 is 7.3333

Answer:

The correct ans is...

3 x square + 5 x - 5

Step-by-step explanation:

U can only subtract or add if u hv the same variable..

here -2x and 7x have the same variable...

so -2x + 7x = 5x

Therefore the ans is....

3 x square + 5 x - 5

Hope this helps....

Have a GOOD DAY !!!!

Pls mark my ans as brainliest

If u mark my ans as brainliest u will get 3 extra points

Sry to say....

U really need to read ur Math TBK

Answer:

3x²+5x-5

Step-by-step explanation:

collect like terms.

3x²+(-2x+7x)-5

3x²+ 5x-5

The quadratic equation in the simplest Standard form, ²+bx+c, with solutions 2 = 2 + 6√7 and 2 = 2 - 6√7, is x² - 4x - 248.

A quadratic equation with the given solutions, we can start by using the fact that if a quadratic equation has solutions x = p and x = q, then it can be written in the factored form as (x - p)(x - q) = 0.

the solutions are 2 + 6√7 and 2 - 6√7. Therefore, the factored form of the quadratic equation is:

(x - (2 + 6√7))(x - (2 - 6√7)) = 0

To simplify this, we can expand the equation:

(x - 2 - 6√7)(x - 2 + 6√7) = 0

Now, let's apply the difference of squares formula:

(x - 2)² - (6√7)² = 0

Simplifying further:

(x - 2)² - 36 * 7 = 0

(x - 2)² - 252 = 0

Finally, we can rewrite the equation in the standard quadratic form, ax² + bx + c:

x² - 4x + 4 - 252 = 0

x² - 4x - 248 = 0

Therefore, the quadratic equation in the simplest standard form, ²+bx+c, with solutions 2 = 2 + 6√7 and 2 = 2 - 6√7, is x² - 4x - 248.

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The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .

The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.

The surface area of the otter's back is A = 0.55 m2.

The fluid pressure at the depth of the otter is P = 11500 Pa.

Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .

The complete question is

An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.

Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.

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It is an equation, telling you that left side of = is same as right side and asking you to solve it (figure out the x).

\(x^2=\frac{9}{256}\)

Apply square root on both sides of the equation to get rid of power on x.

\(x=\pm\sqrt{\frac{9}{256}}\)

Now simplity the square root.

\(x=\pm\frac{\sqrt{9}}{\sqrt{256}}=\boxed{\pm\frac{9}{16}}\)

Hope this helps.

By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.

To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.

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a. The Red Sea trough refers to a dip in the upper-level height originating over the eastern Mediterranean moving southeastward, and deepening over the Red Sea.

b. This weather phenomenon manifests itself as it causes a sudden drop in temperatures, thunderstorms, and dust storms.

c. The Red Sea trough presents a challenge to weather forecasting as it is hard to predict when the trough will develop.

d. The Red Sea trough presents several hazards as causes heavy rainfall, strong winds, and a sudden drop in temperatures.

The Red Sea trough is one of the familiar weather patterns in Jordan. It is seen both in spring and fall.

a. The Red Sea trough is a dip in the upper-level height that originates over the eastern Mediterranean, advances southeastward, and deepens over the Red Sea. During the fall and spring seasons, this trough becomes more profound and generates a shallow low-pressure system over the Levant region, resulting in a northwesterly to northeasterly wind.

b. This weather phenomenon manifests itself in terms of weather in several ways. They are as follows:

c. The Red Sea trough presents a significant challenge to weather forecasting. It is difficult to predict when the trough will develop and the magnitude of its impacts on weather. The weather forecasters struggle to estimate the movement of the trough, its depth, and intensity, and the amount of rain and wind it will produce. As a result, the meteorological department often issues warnings and alerts, but the severity and impact of the weather are not always accurately forecasted.

d. The Red Sea trough presents several hazards. They are as follows:

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Answer:

9/24 and 21/56

Step-by-step explanation:

9/24 = 0.375 or 3/8

21/56 = 0.375 or 3/8