3. Find the value of r so the line that passes through (7,r) & (1, -1), has a slope ofm=į (9 pts)Hi can Someone please help !

Answer:

x= 0, −2, 2+i√3, 2−i√3

Step-by-step explanation:

Answer:

82 yd²

area of rectangle:

Length * Width

area of 2nd rectangle

area of triangle

total:

If the only solution is the trivial solution \(($c_1 = c_2 = c_3 = 0$)\), then the set is linearly independent. Otherwise, it is linearly dependent.

a) To determine the linear dependence or independence of the set \($\{e^t, e^{-t}\}$\) on the interval \($(-\infty, \infty)$\), we need to check whether there exist constants \($c_1$\) and \($c_2$\), not both zero, such that \($c_1e^t + c_2e^{-t} = 0$\) for all t.

Let's assume that \($c_1$\) and \($c_2$\) are such constants:

\($c_1e^t + c_2e^{-t} = 0$\)

Now, let's multiply both sides of the equation by \($e^t$\) to eliminate the negative exponent:

\($c_1e^{2t} + c_2 = 0$\)

This is a quadratic equation in terms of \($e^t$\). For this equation to hold for all t, the coefficients of \($e^{2t}$\) and the constant term must be zero.\($c_2$\)

From the coefficient of \($e^{2t}$\), we have \($c_1 = 0$\).

Substituting \($c_1 = 0$\) into the equation, we get:

\($0 + c_2 = 0$\)

This implies \($c_2 = 0$\).

Since both \($c_1$\) and \($c_2$\) are zero, the only solution to the equation is the trivial solution.

Therefore, the set \($\{e^t, e^{-t}\}$\) on the interval \($(-\infty, \infty)$\) is linearly independent.

b) To determine the linear dependence or independence of the set

\($\{1 - x, 1 + x, 1 - 3x\}$\)

on the interval \($(-\infty, \infty)$\), we need to check whether there exist constants \($c_1$\), \($c_2$\) and \($c_3$\), not all zero, such that \($c_1(1 - x) + c_2(1 + x) + c_3(1 - 3x) = 0$\) for all x.

Expanding the equation, we have:

\($c_1 - c_1x + c_2 + c_2x + c_3 - 3c_3x = 0$\)

Rearranging the terms, we get:

\($(c_1 + c_2 + c_3) + (-c_1 + c_2 - 3c_3)x = 0$\)

For this equation to hold for all x, both the constant term and the coefficient of x must be zero.

From the constant term, we have \($c_1 + c_2 + c_3 = 0$\). (Equation 1)

From the coefficient of x, we have \($-c_1 + c_2 - 3c_3 = 0$\). (Equation 2)

Now, let's consider the system of equations formed by

Equations 1 and 2:

\($c_1 + c_2 + c_3 = 0$\)

\($-c_1 + c_2 - 3c_3 = 0$\)

We can solve this system of equations to determine the values of

\($c_1$\), \($c_2$\), and \($c_3$\).

If the only solution is the trivial solution \(($c_1 = c_2 = c_3 = 0$)\), then the set is linearly independent. Otherwise, it is linearly dependent.

To know more about linearly independent, visit:

https://brainly.com/question/30884648

#SPJ11

The value of x is 4.

Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.

The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.

In the given figure ABCD is a rectangle.

OA=2x+1 and OD=x+5             [Given]

AC and BD are diagonals of a rectangle.

As we know that the diagonals of a rectangle are always equal.

So, AC = BD

We can also write it as,

2×OA=2×OD

2×(2x+1) =2×(x+5)

Apply the distributive property a(b+c)=ab+ac, we get

4x+2=2x+10

Subtract 2x from both sides, we get

4x+2-2x=2x+10-2x

2x+2=10

Subtract 2 from both sides, we get

2x+2-2=10-2

2x=8

Divide both sides by 2, we get

2x/x=8/2

x=4

Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.

Learn more about rectangles from here brainly.com/question/1549055.

#SPJ4

To rewrite Newton's formula for solving f(x) = 0 using the given function f(x) = x^2 - 8, first, let's recall the general Newton's formula:
x_{n+1} = x_n - f(x_n) / f'(x_n)

In this case, f(x) = x^2 - 8. To apply the formula, we need the derivative of f(x), f'(x):
f'(x) = 2x

Now, plug f(x) and f'(x) into the Newton's formula:
x_{n+1} = x_n - (x_n^2 - 8) / (2x_n)
This equation represents Newton's method for solving f(x) = x^2 - 8, with f(x_n) = x_n^2 - 8.

Newton's formula for solving equations of form f(x) = 0 is given by the recurrence relation:
xn+1 = xn - f(xn)/f'(xn)
where xn is the nth approximation of the root of f(x) = 0, and f'(xn) is the derivative of f(x) evaluated at xn.

To write this formula as xn+1 = f(xn), we need to first rearrange the original formula to solve for xn+1:
xn+1 = xn - f(xn)/f'(xn)

Multiplying both sides by f'(xn) and adding f(xn) to both sides, we get:
xn+1*f'(xn) + f(xn) = xn*f'(xn)

Rearranging terms and dividing both sides by f'(xn), we get:
xn+1 = xn - f(xn)/f'(xn)

which is the same as:
xn+1 = f(xn) - xn*f'(xn)/f(xn)

Substituting f(x) = x^2 - 8 into this formula, we get:
xn+1 = (xn^2 - 8) - xn*(2*xn)/((xn^2 - 8))

Simplifying, we get:
xn+1 = xn - (xn^2 - 8)/(2*xn)

This is Newton's formula in form xn+1 = f(xn) for solving f(x) = 0, where f(x) = x^2 - 8.

Learn more about Derivative:
brainly.com/question/25324584

#SPJ11

Answer

967.1  squared cm, multiply area of base by two, and perimeter by 15.

The probability that at most 52 say that they drink coffee during exam week is 1.14%.

This is a binomial probability problem with n = 80, p = 0.67, and we want to find the probability that at most 52 students say they drink coffee during exam week. We can use the binomial probability formula:

P(X ≤ 52) = Σ P(X = k) for k = 0 to 52

where P(X = k) = (n choose k) p^k (1 - p)^(n - k)

Using a calculator or software, we can find that:

P(X ≤ 52) = 0.0114

This means that there is a 1.14% chance that at most 52 out of 80 college students surveyed say they drink more coffee during exam week, given that 67% of all college students prefer to do so.

In other words, the probability is very low that we would observe so few coffee-drinking students in our sample if the true proportion of coffee drinkers during exam week is indeed 67%.

To learn more about probability click on,

https://brainly.com/question/16184408

#SPJ4

The percentage of voters for each condition;

a. 24%

b. 42%

c. 31.43%

d. 47.83%

e.  0.46%

To determine the percentage, we have;

Percent of Independent but not swing voters = Percent of Independent - Percent of Independent and swing voters

= 35% - 11%

= 24%

b. Percent of voters who are neither Independent nor swing voters = 100% - Percent of Independent - Percent of swing voters

= 100% - 35% - 23%

= 42%

(c) Percent of Independent voters who are swing voters = Percent of Independent and swing voters / Percent of Independent

= 11% / 35%

= 31.43%

(d) Percent of swing voters who identify as Independents = Percent of Independent and swing voters / Percent of swing voters

= 11% / 23%

= 47.83%

(e)

Percent of Independent swing voters = Percent of Independent and swing voters / Total sample size

= 11% / 2,373

= 0.46%

The percentage of all swing voters is given as 23%.

Learn more about percentage at: https://brainly.com/question/24877689

#SPJ4

Answer:

\(\large \boxed{\sf \ \ \dfrac{5-\sqrt{3}}{2} \ \ }\)

Step-by-step explanation:

Hello,

\(\dfrac{1+2\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+2\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\ \text{... to eliminate the root in the denominator ...} \\\\=\dfrac{1-\sqrt{3}+2\sqrt{3}-2*3}{(1-3)}\\\\=-\dfrac{1+\sqrt{3}-6}{2}\\\\=-\dfrac{\sqrt{3}-5}{2}\\\\=\dfrac{5-\sqrt{3}}{2}\\\)

Do not hesitate if you have any question

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

Read more about angles at

https://brainly.com/question/28293784

#SPJ1

Answer:

A: 2 X 3/4= 1.5

B: 3 X 2/4= 1.5

C: 4 X 1/3= 4.3 (recurring)

D: 4 X 2/3= 2.66666667

5) (exact number) 2011.68

don't understand what number six is asking :/

Answer:

a = 50

50*2=100

Step-by-step explanation:

Sampled populations have equal variances.

The required condition for using an ANOVA procedure on data from several populations is that the sampled populations have equal variances.

When a researcher wants to compare the means of more than two groups, ANOVA is used. It compares the means of two or more populations to see whether they are significantly different.

The means of several groups may be compared using ANOVA, which stands for Analysis of Variance. ANOVA tests for differences in variances across multiple populations, with the null hypothesis being that they are equal.

Therefore, the correct option is c) sampled populations have equal variances.

The procedure may not yield valid results if the assumptions of ANOVA are violated. This is why it is critical to verify that all of the assumptions have been met before using ANOVA.

The assumptions of ANOVA are as follows: All groups come from populations with a normal distribution. All groups have equal variances. Researchers use a statistical test to see if the assumptions of ANOVA are met. They conduct an F test to determine whether the variances of the groups are equal.

To learn about normal distribution here:

https://brainly.com/question/4079902

#SPJ11

Answer: 110% of 120 minutes is equal to 132 minutes.

Step-by-step explanation:

To calculate percentiles:

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

Learn more about ratios here:

https://brainly.com/question/19220252

#SPJ1

True. Marginal cost refers to the additional cost incurred by producing one more unit of output.

Since the production of one more unit requires the use of additional variable factors of production (such as labor or raw materials), marginal cost always reflects the cost of those variable factors. Fixed costs, on the other hand, do not change with changes in output and are not included in marginal cost calculations. Therefore, marginal cost only reflects the change in cost associated with variable factors of production.

Learn more about Marginal cost here

https://brainly.com/question/3200587

#SPJ11

Fixing a UCL (Upper Control Limit) and LCL (Lower Control Limit) at 3 standard deviations, with an area of 99.73%, means that the probability of making a Type 1 error is approximately 0.27% for each tail (above or below the UCL and LCL, respectively).

When the UCL and LCL are set at 3 standard deviations, they encompass approximately 99.73% of the data under a normal distribution curve, leaving a small tail on each end. The probability of making a Type 1 error corresponds to the area under these tails. Since the distribution is symmetric, the probability is divided equally between the upper and lower tails.

Therefore, the correct answer is that the probability of making a Type 1 error is approximately 0.27% for each tail (above or below the UCL and LCL, respectively).

learn more about "standard deviations":- https://brainly.com/question/475676

#SPJ11

The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

To learn more about inequality refer to :

https://brainly.com/question/25275758

#SPJ1

Answer:

60%

Step-by-step explanation:

= fruit/total = 27/45 = 3/5 = 0.6 = 60%

Answer:

The equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:

Step-by-step explanation:

We know the slope-intercept form of the line equation

\(y=mx+b\)

where m is the slope and b is the y-intercept

Given the line

\(y=34x-8\)

comparing with the slope-intercept form of the line equation

The slope m = 34

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:  

slope = m = 34

Thus, the slope of the the new perpendicular line = – 1/m = -1/34 = -1/34

Using the point-slope form

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of slope = -1/35 and the point (12, 5)

\(y-y_1=m\left(x-x_1\right)\)

\(y-5=-\frac{1}{34}\left(x-12\right)\)

Add 5 to both sides

\(y-5+5=-\frac{1}{34}\left(x-12\right)+5\)

\(y=-\frac{1}{34}x+\frac{91}{17}\)

Therefore, the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:

Answer:

number 18 is Saturn number 19 is Mars

\(\huge\text{Hey there!}\)

\(\mathsf{6\%\ of\ 33.00}\)

\(\mathsf{= \dfrac{6}{100}\ of\ 33.00}\)

\(\mathsf{= \dfrac{6}{100}\times33.00}\)

\(\mathsf{= \dfrac{6}{100}\times 33}\)

\(\mathsf{= \dfrac{6}{100}\times \dfrac{33}{1}}\)

\(\mathsf{= \dfrac{6\div2}{100\div2}\times \dfrac{33}{1}}\)

\(\mathsf{= \dfrac{3}{50}\times\dfrac{33}{1}}\)

\(\mathsf{= \dfrac{3\times 33}{50 \times1}}\)

\(\mathsf{= \dfrac{99}{50}} \mathsf{\rightarrow 1 \dfrac{49}{50}}\)

\(\huge\text{Answer: }\)

\(\huge\boxed{\mathsf{\dfrac{99}{50} \ or\ 1\dfrac{49}{50}}}\huge\checkmark\)

\(\uparrow\large\text{Either those should work because they are equivalent to (equal to)}\\\large\text{each other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

\((f o g)(x) = f(g(x))\\ = f(x-6)\\ = (x-6)^{2} +4(x-6)-60\\ = x^{2} -12x+36+4x-24-60\\ = x^{2} -8x-48\\ = (x-12)(x+8)\)

Step-by-step explanation:

Answer:

1/243

Step-by-step explanation:

When you see this notation, it means plug in -1 for x in the function.

f(-1) = 3^((-1)-4)

f(-1) = 3^-5

f(-1) = 1/3^5

f(-1) = 1/243

Step-by-step explanation:

substitute (-1)

\( {3}^{x} - 4 \\ {3}^{ - 1} - 4 = \frac{1}{3} - 4 = - \frac{11}{3} = - 3.667\)

If Jamal wants to become a millionaire, then Jamal must wait for 19 years if he invests $22,108.44 at 21% today, Jamal must wait for 18 years if he invests $45,104.11 at 16% today, Jamal must wait for 22 years if he invests $152,814.56 at 8% today, and Jamal must wait for 24 years if he invests $276,434.51 at 6% today

To calculate the waiting period for Jamal, follow these steps:

Therefore, Jamal has to wait approximately 19, 18, 22, and 24 years respectively to become a millionaire by investing $22,108.44, $45,104.11, $152,814.56, and $276,434.51 respectively at 21%, 16%, 8%, and 6% interest rates.

Learn more about compound interest:

brainly.com/question/28020457

#SPJ11