If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=

The solution to the equation x + 2(7 - x) = 12 is x = 2.

Given the equation in the question:

x + 2(7 - x ) = 12

To solve the  equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.

x + 2(7 - x) = 12

Apply distributive property

x + 2×7 + 2×-x = 12

x + 14 - 2x = 12

Combine like terms by subtracting 14 from both sides:

x - 2x = 12 - 14

-x = -2

Solve for x by dividing both sides by -1:

-x/-1 = -2/-1

x = 2

Therefore, the value of x is 2.

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The correct statements are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

We have,

Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.

The right statements for the dot plots are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

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[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.

To show that the graphs of the functions   [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex]  intersect at the abscissa point x = 2, we need to show that both functions have the same value at  [tex]x = 2.[/tex]

First, we evaluate f(2):

[tex]f(2) = 2^2 = 4[/tex]

Next, we evaluate g(2):

[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]

Therefore,  [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .

To visualize this, we can plot the two functions on the same set of axes:

As we can see from the graph, the two curves intersect at the point (2, 4).

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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?

Answer:

the answer is C

Step-by-step explanation:

the answer is C it converges

Answer:

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.

The age of the 7th volunteer has to be 602 years so that the range of the all volunteer ages will be 557.

Given ages of 6 volunteers = (56, 81, 54, 47, 45, 94)

The range = maximum value - minimum value.

So, range of the given list = 94 - 45 = 49.

To increase, the range to 557, we have to add an age that is greater than 94, To obtain that age we have to solve 557 - 45 = 508. [here 557 is the maximum value]

Now, by adding the obtained range to the 94 we can get the required age of 7th volunteer. So 508 + 94 = 602.

From the above explanation, we can conclude that the age of the 7th volunteer has to be 602 years which is unrealistic so that the range becomes 557.

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Answer:380.1 square inches

Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.

[tex]n = \frac{2}{ \sqrt{3} } = \frac{2 \sqrt{3} }{3} [/tex]

[tex]m = \frac{4 \sqrt{3} }{3} [/tex]

Answer:

The answer is **D. 30x+15y**.

```

5(6x + 3y) = 5*6x + 5*3y = 30x + 15y

```

Step-by-step explanation:

1. Distribute the 5:

```

5(6x + 3y) = (5 * 6x) + (5 * 3y)

```

2. Simplify:

```

5(6x + 3y) = 30x + 15y

```

Therefore, 5(6x + 3y) is equivalent to 30x + 15y.

If x + 5 is a factor of the given polynomial, then (x + 5) must divide the polynomial evenly, meaning that the remainder is 0 when the polynomial is divided by x + 5.

We can use polynomial long division or synthetic division to find the quotient and remainder, but it's easier to use the fact that if x + 5 is a factor, then (-5) must be a root of the polynomial.

So, we can substitute x = -5 into the polynomial and set it equal to 0 to find m:

-3(-5)^4 - 10(-5)^3 + 20(-5)^2 - 22(-5) + m = 0

Simplifying and solving for m:

-3(625) + 10(125) + 20(25) + 110 + m = 0

-1875 + 1250 + 500 + 110 + m = 0

m = 1015

Therefore, m = 1015 so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.

The probability of drawing a second marble that is blue is 3/5

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

A red marble is drawn from a bag containing 3 red and 3 blue marbles.

If the marbles were not replaced, then we have

P(Red) = 3/6

Now there are

3 blue marbles and 2 red marbles left

So, we have

The probability of choosing a blue marble, after a red marble is

P(Blue) = 3/5

Evaluate

P(Blue) = 3/5

Hence, the probability of choosing a blue marble, after a red marble is 3/5

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Answer:

Step-by-step explanation:

If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.

To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.

Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:

Cost of carpet = area × price per square foot

= 500 × $4.30

= $2,150

Cost of installation = $75

Total cost = cost of carpet + cost of installation

= $2,150 + $75

= $2,225

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The remainder that is found when dividing 2x^2+7x-4 by x-3 is 35

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

Dividing 2x^2+7x-4 by x-3

This means that

Dividend = 2x^2 + 7x - 4

Divisor = x - 3

Set the divisor to 0

So, we have

x - 3 = 0

Evaluate

x = 3

Substitute 3 for x in the dividend equation, so, we have the following representation

Remainder = 2(3)^2 + 7(3) - 4

Evaluate

Remainder = 35

Hence, teh remainder is 35

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Answer:

24

Step-by-step explanation:

14 + 17 + 21 + 28 +40 / 5

120 / 5

24

Answer:

x = 3.5

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]

Next, isolate the variable, x. First, subtract 7 from both sides of the equation:

[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]

Finally, divide 2 from both sides of the equation:

[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]

x = 3.5 is your answer.

~

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Answer:

[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]

Step-by-step explanation:

To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.

We can do this by first combining the constants on the right-hand side of the equation:

[tex]2x+15-8=14[/tex]

[tex]2x+7=14[/tex]

Next, we can isolate x by subtracting 7 from both sides of the equation:

[tex]2x=7[/tex]

Finally, we can solve for x by dividing both sides of the equation by 2:

[tex]x=\frac{7}{2}[/tex]

Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].

There was no error in the procedure as we can see below.

In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.

We have the formula as;

[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]

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Answer:

Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.

In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%

A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.

Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.

Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.

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Answer:

D.The way you group numbers in a series of

multiplication problems doesn't change the final

product.

The probability that a respondent has both portable earbuds and a smart speaker is 0.16

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

This means that

P(earbuds) = 54.5%

P(smart speaker) = 30%

Using the above as a guide, we have the following:

P = P(earbuds) * P(smart speaker)

Substitute the known values in the above equation, so, we have the following representation

P = 54.5% * 30%

Evaluate

P = 0.16

Hence, the probability is 0.16

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Answer:

[tex]sec(-\theta)=-3.1[/tex]

[tex]sin(-\theta)=-0.62[/tex]

Step-by-step explanation:

Part a.

[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].

Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.

For any input in the domain, even functions produce the same output if the opposite of the input is used.  In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].

Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.

[tex]sec(-\theta)=-3.1[/tex]

Part b.

The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.

However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph.  Visually, this is an "odd" function.

For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output.  In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].

Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.

[tex]sin(-\theta)=-0.62[/tex]

The exact values are;

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

We are given that

tan⁡θ=-5/2 and sin⁡θ>0

First quadrant: I, 0°<θ<90°

We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

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Answer:

1, -9

Step-by-step explanation:

xy = -9

x + y = -8    solve this for x and substitute into the 1st equation

x = -8 - y

(-8 - y)y = -9

-y² - 8y + 9 = 0

y² + 8y -9 = 0

Solve for y by factoring:

(y - 1)(y + 9) = 0

y = 1, -9

x(1) = -9

x = -9

x(-9) = -9

x = -9/-9 = 1

Answer:

the function f(x) is f(x) = 5x + 4.

Step-by-step explanation:

To find f(x), we need to use the formula:

(gof)(x) = g(f(x)) = 3f(x) - 2

We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:

3f(x) - 2 = 15x + 10

Simplifying this equation, we get:

3f(x) = 15x + 12

Dividing both sides by 3, we get:

f(x) = 5x + 4

Therefore, the function f(x) is f(x) = 5x + 4.

Step-by-step explanation:

[tex] \frac{ {x}^{2} + 3x - 10 }{x + 5} \\ = \frac{(x + 5)(x - 2)}{(x + 5)} \\ = (x - 2)[/tex]

By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)

[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)

[tex]\vec a + \vec b[/tex] = (3, 1).

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Answer:

m∠R=x=37°; m∠QOR=53°

Step-by-step explanation:

Any line that is tangent to a circle (such as QR) is perpendicular to the circle's radius (QO). Therefore, ΔOQR is a right triangle, with the right angle at Q.

1. You can use  90 + (x+16) + x = 180   or    (x+16) + x = 90 to solve for x.

2. If needed, you can then use the solution from step 1 to find the measure of ∠QOR.