calculus help, from this graph, please indicate the intervals where the function is positive and the intervals where the derivative is negative?

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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Answer:I’m guessing the second one

Step-by-step explanation:

I thinking that because if u add it all up also this is just a thought

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³

Answer:s

Step-by-step explanation:

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

5 cups of walnuts are needed.

Step-by-step explanation:

This question can be solved using a rule of three.

One batch of walnut muffins uses 1 1/3 cups of walnuts.

So one batch of walnut muffins uses \(1 + \frac{1}{3} = \frac{4}{3}\) cups of walnuts.

How many cups of walnuts are needed to make 3 3/4 batches of muffins?

How many cups are required for \(3 + \frac{3}{4} = \frac{15}{4}\) batches.

1 batch - (4/3) cups

(15/4) batches - x cups

\(x = \frac{4}{3} \times \frac{15}{4} = \frac{60}{12} = 5\)

5 cups of walnuts are needed.

Answer: I think it is 5 cups

Step-by-step explanation:

Answer:

=77x2−332x+135

Step-by-step explanation:

Answer:

  13.192 seconds

Step-by-step explanation:

You want to know the time to travel 4.500 km at a speed of 341.11 m/s.

The relation between time, speed, and distance is ...

  time = distance/speed

  time = (4500 m)/(341.11 m/s) ≈ 13.192 s

It would take Andy about 13.192 seconds to travel 4.500 km.

__

Additional comment

The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.

One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.

Answer:

1:3

1:2

Step-by-step explanation:

hope this helps

Answer:

3.3

Step-by-step explanation:

7lb 3oz

3oz/16oz=.1875lb

7lb+.1875lb=7.1875lb

7.1875lb/2.2kg=3.27kg

The final answer is 3.3 kg (round to the nearest tenth).

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

1 lb = 16 ounces

1 kg = 2.2 lb

To solve this type of questions, use ratio property,

Since,

16 ounces = 1 lb

⇒1 ounce = 1/16 lb

⇒3 ounces = 3/16 lb

Add 7 lb to 3/16,

= 3/16+7 = 7.1875 lb

Since,

2.2 lb = 1 kg

⇒1 lb = 1/2.2 kg

⇒7.1875 lb = 7.1875/2.2 kg = 3.267 kg

In round of the answer is 3.3 kg

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Hence, the piece-wise function to  represent the number of  buses required to  transport 380, 9th graders is :

f(x) = { 1, if 0 < 380 ≤60x

          2, if 60x < 380≤120x

          3, if 120x < 380≤180x

          4, if 180x < 380 ≤ 240x

          5, if 240x < 380≤300x

          6, if 300x < 380 ≤ 360x

          7, if 360x < 380 }

In mathematics, a piece-wise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different  interval in the domain. Piece-wise definition is actually a way of expressing  the function, rather than a characteristic of the function itself.

Let 'x' be the  number of buses required to transport all the 9th graders. We can write the function in two parts, for 1st part  when the number of  students is less than or equal to 60 ( that is the capacity of one bus)  and for 2nd part  when it is greater than 60.

For x buses, each with a capacity of 60, we have:

Therefore,  the piece-wise function to  represent the number of  buses required to  transport 380, 9th graders is :

f(x) = { 1, if 0 < 380 ≤60x

          2, if 60x < 380≤120x

          3, if 120x < 380≤180x

          4, if 180x < 380 ≤ 240x

          5, if 240x < 380≤300x

          6, if 300x < 380 ≤ 360x

          7, if 360x < 380 }

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We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

Answer: A C E prob idk

Answer:

Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion.

Step-by-step explanation:

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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The graph of the inequality -4 ≤ x - 5 < -1 is given by the image presented at the end of the answer.

The inequality for this problem is defined as follows:

-4 ≤ x - 5 < -1

It is a compound inequality, hence the lower bound of the solution is obtained as follows:

x - 5 ≥ -4

x ≥ 1.

(closed border).

The upper bound of the solution is obtained as follows:

x - 5 < -1

x < 4.

(open border).

Then the solution is given as follows:

1 ≤ x < 4.

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Step-by-step explanation:

i

Answer:

answer =-1.

Step-by-step explanation:

(i)write the question nicely again.

(ii) substitute the ltter with the value that is given.

(iii)u gonna use BEDMAS RULE TO SOLVE.

ANSWER:

1320 feet per minute

STEP-BY-STEP EXPLANATION:

We can calculate equivalence knowing the conversion factor between yards and feet.

We know that one yard is equal to 3 feet, so:

Therefore, the equivalence is 1320 feet per minute

Answer:

coefficent=21,9,7

constant=x,y,z

Using the z-distribution, it is found that the margin of error for a 95% confidence interval is of $0.04.

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In this problem, the values of the parameters are:

\(z = 1.96, \sigma = 0.48, n = 576\).

Hence, the margin of error, in dollars, is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(M = 1.96\frac{0.48}{\sqrt{576}}\)

M = 0.04.

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Answer:

8+√34

Step-by-step explanation:

use distance formula d =√(x2-x1)² +(y2-y1)² to find the sides

√ (1 -1)²+( -6+3)² = √9 = 3

√ (1+4)²+( -6+6)² = √25 =5

√ (1+4)² + (-3+6)² = √25+9 =√34

Perimeter is P = 3+5+√34 = 8+√34