A rectangle has an area of

5x^2+ 7x-6 what are expressions

For the length and width

Alternatively, we could also restrict the domain of f(x) to a range that excludes the values of x that produce non-unique values of y, such as x = -3, which produces a value of y = 2 for f(x).

what is domain ?

In mathematics, the domain of a function is the set of all possible input values (also called independent variables) for which the function is defined and produces a valid output. It is the set of values that we are allowed to input into the function.

In the given question,

For the inverse of f(x) = x² + 6x + 5 to be a function, we need to ensure that it passes the vertical line test. In other words, for every value of x, the inverse function should produce only one unique value of y.

To ensure that the inverse of f(x) is a function, we need to restrict the domain of f(x) to a range that produces only one value of y for each value of x. This means that we need to make sure that f(x) is one-to-one, or injective, meaning that no two distinct values of x can produce the same value of y.

To check if f(x) is injective, we can use the discriminant of the quadratic equation x² + 6x + 5 = y, which is b² - 4ac, where a = 1, b = 6, and c = 5. The discriminant is:

b² - 4ac = 6² - 4(1)(5) = 16

Since the discriminant is positive, there are two distinct real roots of the quadratic equation, which means that f(x) is not injective and therefore does not have an inverse that is a function.

To ensure that the inverse of f(x) is a function, we need to restrict the domain of f(x) to a range that produces only one value of y for each value of x. One way to do this is to restrict the domain of f(x) to only include the values of x for which the discriminant is non-negative, meaning that the quadratic equation x² + 6x + 5 = y has real roots. This can be expressed as:

b² - 4ac >= 0

6² - 4(1)(5) >= 0

16 >= 0

This inequality is true for all values of x, which means that we can restrict the domain of f(x) to the entire real line to ensure that the inverse of f(x) is a function. Alternatively, we could also restrict the domain of f(x) to a range that excludes the values of x that produce non-unique values of y, such as x = -3, which produces a value of y = 2 for f(x).

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To get at least JPY 1,324 in exchange for $1,000 U.S. dollars, you would need a conversion rate of at least 1.324 JPY per USD.

The conversion rate represents the value of one currency in terms of another. In this case, we want to determine the conversion rate needed to get at least JPY 1,324 for $1,000 USD. To find the conversion rate, we divide the amount in the foreign currency (JPY) by the amount in the base currency (USD). Therefore, the conversion rate is JPY 1,324 divided by $1,000, which simplifies to 1.324 JPY per USD.

This means that for every U.S. dollar, you would receive at least 1.324 Japanese yen. In practical terms, you would need to find an exchange service or financial institution that offers a conversion rate of 1.324 JPY per USD or better in order to obtain at least JPY 1,324 for $1,000 USD. It's worth noting that exchange rates can fluctuate and may vary between different providers, so it's advisable to check with the specific exchange service for the most accurate and up-to-date conversion rate.

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The public health official can estimate the vaccination rate in the community with a 95% confidence interval.

A public health official responding to an outbreak of measles needs to estimate the vaccination rate in the community. The official will use a confidence interval of 95%.
To estimate the vaccination rate with a 95% confidence interval, the official will need to collect a sample of individuals from the community and determine the proportion of vaccinated individuals in that sample. The confidence interval will then provide a range within which the true vaccination rate in the community is likely to fall.
Here are the steps to calculate the confidence interval:
1. Determine the sample size: The official needs to decide on the desired level of precision for the estimate. A larger sample size will provide a narrower confidence interval. The official may consult statistical tables or use a formula to determine the appropriate sample size.
2. Collect the sample: The official will need to randomly select individuals from the community to participate in the study. It is important to ensure that the sample is representative of the population.
3. Calculate the sample proportion: The official will calculate the proportion of vaccinated individuals in the sample. This is done by dividing the number of vaccinated individuals by the total sample size.
4. Determine the standard error: The standard error measures the uncertainty in the estimate of the sample proportion. It is calculated using the formula: sqrt((p * (1-p)) / n), where p is the sample proportion and n is the sample size.
5. Calculate the confidence interval: Using the sample proportion and the standard error, the official can calculate the confidence interval. The formula for the confidence interval is: sample proportion +/- (critical value * standard error). The critical value depends on the desired level of confidence. For a 95% confidence interval, the critical value is typically 1.96.
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The maximum amount of fish the polar bear can transport. is 1000 pounds

The initial number of fish = 3000

Total distance to travel = 1000 miles

The bear can pull up to 1000 pounds of fish, so this is the initial pounds of fish at the beginning of the 1000-mile trip.

After every mile, the number of fish decreases by 1, so the number of fish after every successive mile is

a₀ = 1000,  to begin

a₁ = 999 = 1000 - 1   (after 1 mile)

a₂ = 998 = 1000 - 2   (after 2 miles)

Inductively, after n miles,

= 1000 - n

After 1000 miles,

a₁₀₀₀ = 1000 - 1000 = 0

This means that the bear starts pulling 1000 pounds of fish but eats them all up by the time it travels 1000 miles.

The maximum amount of fish the polar bear can transport. is 1000 pounds

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A polar bear rests by a stack of 3000 pounds of fish he has caught. He plans to travel 1000 miles across the Arctic to bring as many fish as possible to his family. He can pull a sled that holds up to 1000 pounds of fish, but he must eat 1 pound of fish at every mile to keep his energy up. What is the maximum amount of fish (in pounds) the polar bear can transport across the Arctic?

Answer:

Expanded, the answer would be 10b + 40

Step-by-step explanation:

Just multiply 8 to 2b and 8

Answer:

29

Step-by-step explanation:

-3 1/3 • -8 7/10

-10/3 • -87/10

870/30

29

The line drawing tool is used to draw the equations Y=1+1.50X and Y= 18-1.25X and the intersection point is labeled.

To draw the lines and indicate the point of intersection, you can follow these steps:

1. Draw a coordinate system on a piece of paper or using a drawing software.

2. For line A, plot two points on the coordinate system using the equation Y = 1 + 1.50X. Choose any two X values and calculate the corresponding Y values using the equation.

3. Connect the two points with a straight line and label it as line A.

4. For line B, plot two points on the coordinate system using the equation Y = 18 - 1.25X. Choose any two X values and calculate the corresponding Y values using the equation.

5. Connect the two points with a straight line and label it as line B.

6. Find the point of intersection between line A and line B. This is the point where both equations are equal. You can calculate this point by solving the system of equations Y = 1 + 1.50X and Y = 18 - 1.25X simultaneously.

7. Once you find the X and Y values of the point of intersection, mark it on the coordinate system and label it as 'Equilibrium'.

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Answer:

-5/3 or -1.7

Step-by-step explanation:

Answer:

n=  \(-1\frac{2}{3}\) or \(-\frac{5}{3}\)

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer:

657

Step-by-step explanation:

Step-by-step explanation:

similarities ratio of circumference = 2πr/2πR = r/R= 77/147= 11/21

plz mark my answer as brainlist plzzzz.hope this will be helpful to you.

Answer:

Step-by-step explanation:

what percentage is greater than 3/4 and less than 4/5

3/4 = 0.75

4/5 = 0.8

the answers between 0.75 and 0.8 are all good, take 0.78, transform into a fraction and you have 39/50

The triangles JKL and XYZ are similar by the SSS similarity statement

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

The triangles in this figure are

JKL and XYZ

These triangles are similar because:

"If three sides in one triangle are proportional to three sides in another triangle, then the two triangles are similar"

This means that they are similar by the SSS similarity statement

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Answer:

m equals 4

Step-by-step explanation:

m represents the slope of the line.

The line equation is y = mx + b, which means that m = 4 and b = 0

Answer:

Question 3 is- B. 8 ounces

Step-by-step explanation:

To determine the number of yards Ben will walk in one hour, we need to convert his speed from feet per second to yards per hour.

First, let's convert Ben's speed from feet per second to feet per hour: Speed in feet per hour = Speed in feet per second * 60 seconds * 60 minutes. Speed in feet per hour = 6 ft/s * 60 s * 60 min = 21,600 ft/hour. Next, we need to convert the speed from feet per hour to yards per hour. Since there are 3 feet in a yard: Speed in yards per hour = Speed in feet per hour / 3. Speed in yards per hour = 21,600 ft/hour / 3 = 7,200 yards/hour.

Therefore, Ben will walk 7,200 yards in one hour if he maintains a steady pace of 6 ft per second.

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sin 45° = 25/y

(√2)/2 = 25/y

y√2 = 2 × 25

y√2 = 50

y = 50/√2

y = 25√2

so the correct answer is 25sqrt2

The computation shows that the final integer is -44.

Fron the information, it was stated that Start at -3, facing right Take 4 steps forward Take 22 steps backward Turn to face left Take 25 steps backward

The appropriate integer will be:

= -3 + 4 - 22 - 25

= -46

The final integer is -44.

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Answer:

This is really hard, but what you marked is CORRECT, it is the second option :D

Mark brainliest please ;P

Answer:

1

Step-by-step explanation:

Using the sum to product formulae and the exact values

sin x + sin y = 2sin(\(\frac{x+y}{2}\) )cos(\(\frac{x-y}{2}\) )

cos x + cos y = 2cos(\(\frac{x+y}{2}\) )cos(\(\frac{x-y}{2}\) )

sin45° = cos45° = \(\frac{1}{\sqrt{2} }\) , cos30° = \(\frac{\sqrt{3} }{2}\)

Given

\(\frac{sin75+sin15}{cos75+cos15}\)

= \(\frac{2sin(\frac{75+15}{2})cos(\frac{75-15}{2}) }{2cos(\frac{75+15}{2})cos(\frac{75-15}{2}) }\)

= \(\frac{2si45cos30}{2cos45cos30}\)

= (2 × \(\frac{1}{\sqrt{2} }\) × \(\frac{\sqrt{3} }{2}\) ) ÷ (2 × \(\frac{1}{\sqrt{2} }\) × \(\frac{\sqrt{3} }{2}\) )

= 1

Answer:  1

Step-by-step explanation:

sin 75 = sin(30 + 45) = sin30 · cos45  + cos30 · sin45

                                 \(=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}\)

sin 15 = sin(45 - 30) = sin45 · cos30  - cos45 · sin30

                                  \(=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}\)

cos 75 = cos(30 + 45) = cos30 · cos45  - sin30 · sin45

                                   \(=\dfrac{\sqrt3}{2}\cdot \dfrac{\sqrt2}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}\)

cos 15 = cos(45 - 30) = cos45 · cos30  + sin45 · sin30

                                   \(=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}\)

       \(\dfrac{\sin 75+\sin 15}{\cos 75+\cos 15}\)

   \(=\dfrac{\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6-\sqrt2}{4}+\frac{\sqrt6+\sqrt2}{4}}\\\\\\=\dfrac{\frac{\sqrt6}{2}}{\frac{\sqrt6}{2}}\\\\\\=1\)

Answer:

2 : 5

Step-by-step explanation:

700 g : 1.75 kg

Since ratio should be between same units, so we'll convert either g into kg or kg into g. For convenience, kg will be converted to g

700 g : 1.75 kg × 1000

700 g : 1750 g

÷ 50 ÷50

14 : 35

÷7 ÷7

2 : 5

Step-by-step explanation:

Lets translate this word problem into math.

"Latoya's annual salary is $26,000" = We start with the number 26,000

"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24

"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12

"How much will she get paid with each paycheck?" = "Find answer pls thx"

To put it all together...

\(\frac{26,000-7,352.24}{12}\)

Now all we have to do is solve!

\(\frac{26,000-7,352.24}{12}\)

\(\frac{18,647.76}{12}\)

\(1,553.98\)

Answer:

Latoya will get paid $1,553.98 with each paycheck.

Answer: The sales tax rate is 3%.

Step-by-step explanation: $12.90 is 3% of $430.

The sales tax rate is approximately 3%.

To find the sales tax rate, we can divide the amount of sales tax by the cost of the item before tax, and then multiply by 100 to express it as a percentage.

Given that the item costs $430 before tax and the sales tax is $12.90, we can calculate the sales tax rate as follows:

Sales tax rate = (Sales tax / Cost before tax) * 100

Sales tax rate = ($12.90 / $430) * 100

Sales tax rate ≈ 0.03 * 100

Sales tax rate ≈ 3%

Therefore, the sales tax rate is approximately 3%.

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The value of x is 3. The order in which you perform operations in arithmetic and algebra is governed by a number of laws.

Given,

\($9^{-1 / 2}=27^{1 / 4} \div 3^{x+1}$\)

\(${\left[3^2\right]^{-1 / 2}=\left[(3)^4\right]^{1 / 4} \div 3^{x+1} }$\)

\($3^{-1}=3 \div 3^{x+1}$\)

\($3^{-1}=\frac{3}{3^{x+1}}$\)

\($3^{-1}=3^{1-x+1}$\)

\($3^{-1}=3^{2-x}$\)

On comparing we get,

-1=2-x

x= 3

Hence, the value of x is 3.

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Answer:

21

Step-by-step explanation:

3 (7) = 21

Answer:

The answer is 21

Step-by-step explanation:

3(3+4)

3(7)

21

Hope this helps!

Answer:

D

Step-by-step explanation:

25x+75=750

25x=675

x=27

we can't go over this amount, but we can have 27 employees, so it will be equal as well.

x<27 and x=27

The given rational function is \(\frac{x^2-x-6}{x^2-2x-8}\). We need to find the points of discontinuity, vertical asymptotes, horizontal asymptotes, holes, x-intercepts, y-intercepts, and end behavior of the function.

Firstly, let's find the points of discontinuity. The function has a discontinuity where the denominator is equal to zero. Therefore, we need to solve the equation x^2-2x-8=0. Factoring the quadratic equation, we get (x-4)(x+2)=0. Hence, the points of discontinuity are x=4 and x=-2.

Next, we need to find the vertical asymptotes. The vertical asymptotes occur at the points of discontinuity. Therefore, the vertical asymptotes of the function are x=4 and x=-2.

To find the horizontal asymptote, we need to divide the leading coefficient of the numerator by the leading coefficient of the denominator. The degree of the numerator and denominator is the same, which is 2. Therefore, the horizontal asymptote of the function is y=1.

To find the holes in the graph, we need to simplify the function and check if there are any common factors in the numerator and denominator. Factoring the numerator and denominator, we get \(\frac{(x-3)(x+2)}{(x-4)(x+2)}\). We can cancel the common factor of x+2, which gives us \(\frac{x-3}{x-4}\). Hence, there is a hole at x=-2.

To find the x-intercepts, we need to set the numerator equal to zero. Therefore, x^2-x-6=0. Factoring the quadratic equation, we get (x-3)(x+2)=0. Hence, the x-intercepts are x=3 and x=-2.

To find the y-intercept, we need to set x=0 in the function. Therefore, the y-intercept is \(\frac{-6}{-8}\), which simplifies to \(\frac{3}{4}\).

Lastly, to determine the end behavior, we need to examine the behavior of the function as x approaches infinity and negative infinity. As x approaches infinity, the function approaches 1, which is the horizontal asymptote. As x approaches negative infinity, the function also approaches 1.

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Answer:

9x+27

Step-by-step explanation:

7x+21+2x+6

9x+27

Answer:

\( \sf9x + 27\)

Step-by-step explanation:

Given expression,

→ 7(x + 3) + 2(x + 3)

Let's simplify the expression,

→ 7(x + 3) + 2(x + 3)

→ 7x + 21 + 2x + 6

→ (7x + 2x) + (21 + 6)

→ 9x + 27

→ 9(x + 3)

Hence, answer is 9x + 27.

Answer:

It is a reduction as the shape is getting smaller

Step-by-step explanation:

If the fraction is less than 1 it decreases in size

If its larger than one it inceases in size

if one then it stays the same

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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