What are the domain and range of g(x)=−14(x−21)2+47?

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

Rounded to the nearest whole number, your answer is 70 feet.

Step-by-step explanation:

I found it pretty funny that the person was "The individual". Guess they ran out of names! :P

Anyways:

All you need to do for this problem is multiply the feet of fabric by the number of blankets.

7.75 x 9 = 69.75

Rounded to the nearest whole number, your answer is 70 feet.

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The equation of the line that goes through the point (-2, -2) with a slope of -4 is y = -4x - 10.

To find the equation of a line, we need to use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point on the line, and m is the slope.

Given that the point is (-2, -2) and the slope is -4, we can substitute these values into the equation:

y - (-2) = -4(x - (-2))

Simplifying:

y + 2 = -4(x + 2)

Expanding the brackets:

y + 2 = -4x - 8

Now, let's rearrange the equation to get it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

y = -4x - 8 - 2

y = -4x - 10

Therefore, the equation of the line that goes through the point (-2, -2) with a slope of -4 is y = -4x - 10.

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The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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the fencing cost $2.5 per foot

Jones family need 393 ft of fencing

how much will they have to pay?

the Jones family have to pay $982.5 for their garden

Answer:

20 tapes will cost $5.

Step-by-step explanation:

2/8=x/20

cross product

8*x=2*20

8x=40

x=40/8

x=5

Answer:

x equals 9

Step-by-step explanation:

90 - 41 =49

49 - 22 = 27

27 ÷ 3 = 9

Answer:

77

Step-by-step explanation:

area of trapezoid =1/2 h (b1+b2)

=.5(7)(22)

=7 × 11 =77

The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Why might you use a different power of 10 instead of leaving both

numbers in scientific notation?

Because scintific notation is a simplification for large or small numbers, so a big number with a lot of zeros can be writen by a power of 10 multiplied by a number. But we cannot make substractions using this, because the powers ten represents very different values, for instance

But if they have the same power, we can use the distibutive law to make the substraction

which is the same thing. No matter the power of 10, if the power is the same you can use the same argument I've made before.

Answer: 18

Step-by-step explanation:

when there is a in front of an expression in parentheses change the sign of each term in the expression. 9+9=18 so ANSWER 18

The volume of each shape (A right triangular prism and the trapezoidal prism are):

A right triangular prism is a three-dimensional shape that has a triangular base and three rectangular faces. It is a prism because its two bases are identical and parallel. The formula for finding the volume of a right triangular prism is V = (1/2) * base * height * length.

A trapezoidal prism is a three-dimensional shape with trapezoidal bases and four rectangular faces. It is also a prism because its two bases are identical and parallel. The formula for finding the volume of a trapezoidal prism is V = ((b1 + b2) / 2) * height * length, where b1 and b2 are the lengths of the two parallel sides of the trapezoidal base.

Recall that the formula for the volume of a trapezoidal prism is:

V = (1/2)h(b1+b2)L

where:

Hence, substituting the given values, we have:

V = (1/2)(20 + 19)(7) 4

V = (1/2)(39)(7) 4

V = (273/2) 4

V = 546ft³

Therefore, the volume of the trapezoidal prism is 546ft³

2) Recall that the formula for the volume of a right triangular prism is:

V = (1/2) * b * h * L

Where:

b is the length of the base of the triangle

h is the height of the triangle

L is the length of the prism (the distance between the triangular faces)

The factor of (1/2) is included since the base of the prism is a triangle.

Given the forumla above:

b = 9ft

h = 7ft

L = 4ft


Plugging in the values given:

V = (1/2) * 9ft * 7ft * 4ft

V = 126ft³

Therefore, the volume of the right triangular prism is 126ft³

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The strategy that will help to eliminate the variable and solve the equation easily is (D) multiply the second equation by 3 and add it to the first equation.

So, to cancel the variable that will make the equation easy to solve:
Let,

So, calculate as follows:

This addition of the (2) equation to the (1) equation will give the answer:

Hence, variable x has been canceled.

Therefore, the strategy that will help to eliminate the variable and solve the equation easily is (D) multiply the second equation by 3 and add it to the first equation.

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Answer:

c

Step-by-step explanation:

Answer:

y=9x

Step-by-step explanation:

Answer:

\( \boxed{Perimeter \: of \: semicircle = 61.68 \: feet} \)

Given:

\( \sf Area \: of \: semicircle = 226.08 \: square \: feet\)

To find:

Perimeter of semicircle

Step-by-step explanation:

Let 'r' be the radius of circle

\( \sf \implies Area \: of \: semicircle = \frac{ \pi {r}^{2} }{2} \\ \\ \sf \implies 226 .08 = \frac{\pi {r}^{2} }{2} \\ \\ \sf \implies \frac{\pi {r}^{2} }{2} = 226.08 \\ \\ \sf \implies \pi {r}^{2} = 2 \times 226.08 \\ \\ \sf \implies \pi {r}^{2} = 452.16 \\ \\ \sf \implies 3.14 \times {r}^{2} = 452.16 \\ \\ \sf \implies {r}^{2} = \frac{452.16}{3.14} \\ \\ \sf \implies {r}^{2} = 144 \\ \\ \sf \implies {r}^{2} = {12}^{2} \\ \\ \sf \implies \sqrt{ {r}^{2} } = \sqrt{ {12}^{2} } \\ \\ \sf \implies r = 2 \: feet\)

So,

\( \sf Perimeter \: of \: semicircle = \pi r + 2r \\ \\ \sf =( 3.14 \times 12) +( 2 \times 12)\\ \\ \sf = 37.68 + 24 \\ \\ \sf = 61.68 \:ft\)

Answer:

A and d

Step-by-step explanation:

because x has a 1 in front of them so add the 3'x and get 3x+2

According to the information given in the exercise, the following expression represents the area of the rectangular garden:

And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:

You can identify that the word "combined" indicates that that expression was obtained by adding both areas.

Knowing the above, you can set up the following equation:

Where "A" is the area of the walkway around the rectangular garden.

Solving for "A", you get the following expression:

The answer is:

Answer:

20200

Step-by-step explanation:

As you're in a hurry, I can give it later? xx

Answer:

Step-by-step explanation:

noo its b i know for sure i just did it

Answer:

its B

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

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Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Volume of Triangular Prism = 1/2(bhl)

Base = 8

Height = 6

Length = 11

Volume = 1/2(8×6×11)

= 264yd³

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Answer:

1) μ = 8000

2)  H0:  μ ≥8000

3)   Ha: μ  < 8000

4)  α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

6) t= x`- μ/ s.d/ √n  = -0.816

7) The P- value = 0.214083.

8) The critical region is [-∞, -1.345]

9) Fail to Reject the Null Hypothesis

Step-by-step explanation:

1) The population characteristic is the population mean =μ = 8000

2) The claim is that the  addition of nitrates results in a decrease in the mean rate of uptake i.e μ < 8000

The null hypothesis is that  μ ≥ 8000

2) Null hypothesis: H0:  μ ≥8000

3) Alternative hypothesis:  Ha: μ  < 8000

4) The significance level alpha = α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

Calculating mean and standard deviation using a calculator

Sample Size, n: 15

Mean= ∑ x/n = x`=: 7788.8

∑ x/n= 116832/15

St Dev, s.d(n-1) : 1002.4307

6) Test Statistic: student's t Test with d.f = n-1 = 14

t= x`- μ/ s.d/ √n  

t= 7788.8-8000/1002.4307/√15

t= -0.816

7) The P- value for the observed t value  is 0.214083.

The result is not significant at p < 0.10. H0 is accepted.

8) The Critical value for one sided t test at α =0.1 with 14 d.f is  less than t=  -1.3406

Hence the critical region is [-∞, -1.345]

Since the calculated t -0.816  value does not fall in the critical region  [-∞, -1.345] there is not sufficient evidence to reject H0

9) Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to support the null hypothesis and conclude that  the data suggest that the addition of nitrates do not  result in a decrease in the mean rate of uptake. The claim is rejected.