What is the equation for the line that passes through the points (3, 4) and (5,8)?

Answer:

[tex]tn = {3 \times \sqrt{2} }^{n - 1} [/tex]

Step-by-step explanation:

since it is geometric sequence we will use the formula

[tex]tn = {ar}^{n - 1} [/tex]

n = 10

r = √2

a = 3

lets first see the result of the 10th term

[tex]t10 = {ar}^{10 - 1} [/tex]

[tex]t10 = {ar}^{9} [/tex]

[tex]t10 = {3 \times \sqrt{2} }^{9} [/tex]

t10 = 3 × 22.63

t10 = 67.89

approximately 68

t10 = 68

for the nth term

Tn = ar^n–1

[tex]tn = {3 \times (\sqrt{2} })^{n - 1} [/tex]

i hope this helps

Answer:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

[tex]a_{10}=48 \sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

To find the 10th term, substitute n = 10 into the equation:

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{10-1}[/tex]

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{9}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{\frac{9}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4+\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4} \cdot 2^{\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 16 \cdot \sqrt{2}[/tex]

[tex]\implies a_{10}=48 \sqrt{2}[/tex]

Answer:

y = x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = 1 , then

y = x + c ← is the partial equation

to find c substitute (2, 3 ) into the partial equation

3 = 2 + c ⇒ c = 3 - 2 = 1

y = x + 1 ← equation of line

Answer:No

Step-by-step explanation:

0+3 = 3, not zero

Answer: X= -1± √(-1)² - 4(7)(9)

2(7)

Step-by-step explanation: The correct equation for using the quadratic formula to solve 7x² = 9 + x for x is:

X= -1± √(-1)² - 4(7)(9)

2(7)

The quadratic formula is given by the equation X = -b ± √(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 7, b = 1, and c = 9, so plugging these values into the formula gives us the equation above.

The equation used to solve Quadratic Equation is -1 ± [√((-1)² - 4(7)(-9])/2(7)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

we have the Quadratic Equation as:

7x² = 9+ x

7x² -x -9= 0

Using Discriminant method

x = -b ± √(b² -4ac)/2a

x = 1 ± √(1² - 4(7)(-9)/2(7)

x = 1 ± √(1 + 196)/14

Thus, the formula used 1 ± [√(1² - 4(7)(-9])/2(7)

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ5

Answer:

11 inches

Step-by-step explanation:

If one inch represents 210 feet, then divide 2310 by 210 to get the number of inches in the scale drawing.

Answer:

11 inches

Step-by-step explanation:

2310/210 = 11

By using area of trapezium, it can be calculated that-

Length of fencing needed in 15.88m

What is area of trapezium?

Area of trapezium is the total space taken by the trapezium.

If the length of parallel sides be a and b and distance between the parallel sides are d,

Area of trapezium = [tex]\frac{1}{2}\times(a + b) \times (d)[/tex]

Length of the parallel sides = [tex]b_1[/tex] m and 5.28 m

Length of non parallel sides = 3.3 m and 3.3 m

Distance between parallel sides = 3m

Area of trapezium = [tex]\frac{1}{2} \times (b_1 + 5.28) \times 3[/tex]

By the problem,

[tex]\frac{1}{2} \times (b_1 + 5.28) \times 3 = 13.92[/tex]

[tex]b_1 + 5.28 = 13.92 \times \frac{2}{3}\\b_1 + 5.28 = 9.28\\b_1 = 9.28 - 5.28\\b_1 = 4 \m[/tex]

Length of fencing needed = 4 + 5.28 + 3.3 + 3.3 = 15.88 m

To learn more about area of trapezium, refer to the link-

https://brainly.com/question/1463152

#SPJ1

Answer:

5.85369.421.5 does not have a quotient because it is not a mathematical expression.

40.42 ÷ 4.3 = 9.4

15.48 ÷ 0.72 = 21.4

86.4 ÷ 2.4 = 36.0

50.31 ÷ 8.6 = 5.84

To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.

(a) The degree of freedom is 27

(b) The test statistic is -2.67

(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.

(d) |t| > 2.70

(1) The degree of freedom for the two-sample t-test is calculated as

(2) The test statistic for the two-sample t-test is calculated as:

Plugging in the values, we get:

(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.

(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.

Learn more about two-sample t-test here:

https://brainly.com/question/17438355

#SPJ4

By using algebra equation, the zeros of f(x)f(x) is ;

x = (-4 + 2i) and x = (-4 - 2i)

Given data :

This is a synthetic division shortcut. Write down the real root, then under a division symbol, the coefficients of the variables, 2, 18, 56, and 40. Drop down the 2 first, multiply by the root (-1) and add it to the next coefficient (18). 2*(-1) = -2, -2 + 18 = 16. Drop that one down. Next multiply 16 by the root, (-1) and add that to the next coefficient, 56 + (-16) = 40, drop down the 40, then lastly repeat this, multiply 40 by the root (-1) and add to the last coefficient 40 + (-40) = 0. If the remainder was not 0, then -1 would not have been a real root.

-1 | 2 18 56 40

......0 -2 -16 -40

--------------------

......2 16 40 0

Put these into another equation, (2x2 + 16x + 40)

Factoring out a 2 we get 2(x2 + 8x + 20)

The factors of 20 are 2*10 and 4*5. 2+10 = 12, 4+5 = 9, so we must use the quadratic equation to find our roots.

-8 ± √(64 - 4(20))/2 = -4 ± √(-16)/2 = -4 ± 4i/2 = -4 ± 2i

So the other two roots are x = (-4 + 2i) and x = (-4 - 2i)

Learn more about algebra equation refer to :

https://brainly.com/question/22399890

#SPJ1

Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

Answer: 8,000

Step-by-step explanation: So, to find how to round this to the nearest 1000, we need to look at the 3 digits being the 7. So, 899 is greater than 500, so we round up, so 7 + 1 is 8, and we change those 3 digits behind the zero to 0's, so we get 8,000. I hoped this helped.

Answer:

8000

7899 rounded to nearest thousand is 8000, because 7 is in thousand's place value, and the number after that is 8, which is more than 5, so 1 is added to 7, and it becomes 8. The rest of the numbers turn to 0.

so you get 8000.

hope it helps :)

Answer: 8k^2 - 19k + 12

Step-by-step explanation: The way we found this answer was by simplifying the expression.

Step 1 : We want to get (x-2) in the numerator so we could cross it out with the x-2 at the bottom to get our simplified expression.

(8k^3-19k^2+2k+10)/(k-2) = (x-2)(8k^2-17k+5)/(x-2)

You would need to factor out the (x-2)

Step 2: When you cross the (x-2) above with the (x-2) below you end up with 8K^2-17k+5 as the answer.

Answer:

[tex]8k^2-3k-4+\frac{2}{k-2}[/tex]

Step-by-step explanation:

⭐ See the image I attached to my answer to see the working.

⭐ I recommend you look at the image while following along with the steps to understand the steps.

1. See what multiplies with the first term in the divisor to get the first term in the dividend. Then, put that answer in the quotient space.

2. Under the first term in the dividend, write a - sign and open parentheses. Put the first term inside the parentheses.

3. Multiply what you put in the quotient space from step #1 with the second term in the divisor.

4. Put the product from step #3 inside of the parentheses.

5. Subtract the first two terms in the parentheses from the first two terms in the dividend.

. . . . . . . . . . . . . note: in polynomial division, you will not always subtract two terms. we are subtracting two terms here because there are two terms in the divisor.

6. Write the answer from #5 under the parentheses, and bring down another term from the dividend.

7. See what multiplies with the first term in the dividend to get the answer from #5. Then, put that answer in the quotient space.

8. Under step #6, write a - sign and open parentheses. Put the answer from #5 inside the parentheses.

9. Multiply the answer from #7 with the second term in the divisor.

10. Next to the answer from step #8, write the product of step #9.

11. Subtract the terms from step #10 from step #6.

12. Repeat until you have "brought down" all of the terms from the dividend.

After you are done, your remainder will not be 0. Instead, it will be +2. When you have a remainder that isn't 0, you cannot use the quotient as your answer. Instead, you have to write your answer in this format:

[tex]q(x)+\frac{r(x)}{d(x)}[/tex], where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

⇒ q(x) = [tex]8k^2-3k-4[/tex]

⇒ r(x) = +2

⇒ d(x) = k -2

⇒ [tex]8k^2-3k-4+\frac{2}{k-2}[/tex]

Answer:

y = -37

Step-by-step explanation:

y = -5 - 8x

y = -5 - 8(4)

y = -5 + ( - 8 x 4 )

y = -5 + ( - 32)

y = -37

Answer:

D.

Step-by-step explanation:

Thousandhts

Answer:

d. 7 thousandths

WHY?

0.007 places is a decimal representation of a number. In the decimal system, the value of a digit is determined by its position relative to the decimal point. In this case, the number 0.007 has three digits to the right of the decimal point, so it is said to have three decimal places. The value of each digit in this number is determined by its position: the first digit (0) is in the hundredths place, the second digit (0) is in the thousandths place, and the third digit (7) is in the ten-thousandths place.

1. The triangles are congruent based on the SSS congruence theorem.

2. The information is not enough.

3. Both are congruent by the HL congruence theorem.

If two triangles have a pair of congruent hypotenuses and a pair of congruent legs, then both triangles ae congruent to each other based on the HL congruence theorem.

The SSS Congruence Theorem states that if any two triangles have three pairs of corresponding sides that are congruent to each other, then the triangles are congruent.

1. Based on the SSS congruence theorem, the pair of angles in figure 1 are congruent.

2. There is no information available that shows the triangles have a pair of congruent hypotenuses, nor have three pairs of corresponding congruent sides. Th information given is not enough to prove that they are congruent by SSS or HL.

3. Based on the HL congruence theorem,, they are congruent to each other.

Learn more about the HL and SSS congruence theorem on:

https://brainly.com/question/2102943

#SPJ1

The measure of an angle m ∠YBA=47°.

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

Since,

ΔFBA=ΔYBA

The two triangles in the provided illustration are comparable.

So,

From the figure:

m ∠FBA=47°

So, m ∠YBA=47°

Therefore, the measure of angle  m ∠YBA=47°

To know more about angle, visit:

https://brainly.com/question/28451077

#SPJ1

The linear model that could be used to calculate cost of mailing a large envelope is L(x) = 0.88 + 0.2(x – 1) and used to calculate cost of mailing a package is P(x) = 1.71 + 0.17(x – 3). The weight at which the cost a large envelope and a package will cost the same amount to mail is 17 ounces.

Linear models are used to describe a continuous response variable as a function of one or more predictor variables. Let x be the weight in ounces and L be the cost of mailing a large envelope. Based on the provided information, the cost of mailing a large envelope increases with increasing weight. The cost of mailing one ounce is $0.88 and increased by $0.2 for each additional weight. Hence,

L(x) = 0.88 + 0.2(x – 1)

Let x be the weight in ounces and P be the cost of mailing a package. Based on the provided information, the cost of mailing a package remains the same for weight of 1 to 3 ounces at the cost of $1.71, and then increases by $0.17 for each additional weight. Hence,

P(x) = 1.71 + 0.17(x – 3)

The weight at which a large envelope and a package will cost the same amount to mail is determined by equating the two models.

L(x) = P(x)

0.88 + 0.2(x – 1) = 1.71 + 0.17(x – 3)

0.88 + 0.2x – 0.2 = 1.71 + 0.17x – 0.51

0.68 + 0.2 x = 0.17 x + 1.2

0.2x – 0.17x = 1.2 – 0.68

0.03x = 0.52

x = 17.33 ≈ 17 ounces

Note: The question is incomplete. The complete question probably is: Provided table indicates the U.S. Postal Rates for large envelopes and packages of different weights. a) Create a linear model that could be used to calculate the cost to mail a large envelope, given its weight in ounces. Use L to represent the cost to mail a large envelope and x to represent the envelope weight in ounces. Create a linear model that could be used to calculate the cost to mail a package, given its weight in ounces. Use P to represent the cost to mail a package and x to represent the package weight in ounces. Find the weight at which a large envelope and a package will cost the same amount to mail, assuming your linear models still apply to higher weights.

Learn more about Linear models:

https://brainly.com/question/28033207

#SPJ4

From the linear function, the rate of change is 35 and the unit cost is 35

A linear function is defined as a function that has either one or two variables without exponents.

In this problem, we have to write a linear function that models the table given. This will take the form of y = mx + c

m = slope or rate of change and c = constant or unit cost of the product.

The formula of slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table;

m = 215 - 180 / 5 - 4

m = 35

Using the slope of the line, we can find the y - intercept of the function.

y = mx + c

215 = 35(5) + c

215 = 175 + c

c = 215 - 175

c = 40

The linear function of the table is y = 35x + 40

Learn more on linear function here;

https://brainly.com/question/15602982

#SPJ1

Answer:

$2.75

Step-by-step explanation:

The difference in cost for 33 articles and 30 articles is

$57.40 - $49.15 = $8.25

From 30 to 33 articles, the difference is 3 articles.

3 articles cost $8.25.

Cost per article = $8.25/3 = $2.75

Answer:

5 [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

1 [tex]\frac{3}{5}[/tex] = 8/5

3 [tex]\frac{2}{3}[/tex] = 11/3

In order to add fractions, the denominators, or the bottom numbers, have to be the same. To make them the same, find the common denominator (the lowest number that both the numbers can be divisible by)

8/5+ 11/3  the common denominator would be 15 so multiply the appropriate numbers to the denominators and the numerators (the top number)

24/15 + 55/15 = 79/15

Now simplify

79/15 = 5 [tex]\frac{4}{15}[/tex]

The correct statement that assigns a random integer between 1 and 10, inclusive, to rn is (D).

int rn = (int) (Math.random() * 10) + 1.

The method Math.random() generates a random number between 0 and 1, inclusive. If we multiply this number by 10, we will get a random number between 0 and 10, exclusive. If we then add 1 to this number, we will get a random number between 1 and 11, exclusive. If we then take the integer part of this number using the (int) cast, we will get a random integer between 1 and 10, inclusive. This is exactly what statement (D) does.

Learn more about Math.random() here:

https://brainly.com/question/29644825

#SPJ4

Since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles.

To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles.

At α = 0.05, test the shipping firm's claim.

Under H0: μ 200  Vs H1: > 200  (Right tailed test)

n = 16, x bar = 205 , s = 14

Null Hypothesis;  H0:  μ = 35000  Vs  H1: < 35000

(Mean life of brand of tire less than 35000 miles).

Under H0 test statistic is

t = (x bar - μ) / (s / √n) ≈ [tex]t_n_-_1[/tex]

Now, n = 18, x bar = 34,200,  s = 12000

t = (34000 - 35000) / (1200 / √18) = -2.8284

t - critical value of α = 0.05 for left tailed at (18 - 1) df = -2.11

Therefore t calculated (= -2.8284) < -2.11

So, we do not reject H0.

Hence, since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

To know more about standard deviation, click on the link

https://brainly.com/question/475676

#SPJ1

Using proportions, the value of 3500 Yen on October 8, 1982 is 13.1 USD

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

On October 8, 1982;

267.38 Yen = 1US

The cost of 3500 Yen = ?

267.38 Yen = 1 USD

35000 Yen = x USD

Cross multiply both sides and solve for x

x * 267.38 = 3500 * 1

267.38x = 3500

Divide both sides by coefficient of x

267.38x / 267.38 = 3500 / 267.38

x = 13.1

The value of 3500 Yen is 13.1 USD

Learn more on proportions here;

https://brainly.com/question/870035

#SPJ1

Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.

We follow these steps in order to arrive at the answer:

Let the amount invested in bonds be x

Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.

The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x

The interest earned on bonds will be 0.06x0.06x

The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x

The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x

The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.

Hence total interest is:

1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x

Simplifying we get,

1000 -400 = 0.1x1000−400=0.1x

600 = 0.1x600=0.1x

\mathbf{x = 6,000}x=6,000

Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000

Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. The lateral line receptors are most likely is Mechanoreceptors.

Given that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it.

We have to find according to your understanding of sensory receptors, the lateral line receptors are most likely is.

We know that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. According to your understanding of sensory receptors, the lateral line receptors are most likely is Mechanoreceptors.

Mechanoreceptors, also known as Mechanoreceptors, are specialized neurons that react to pressure and deformation caused by mechanical forces. They are surrounded by sensory neurons, which translate external pressure into electrical signals that are sent to the brain.

To learn more about lines visit: https://brainly.com/question/2696693

#SPJ4

This question doesn't seem completed to me. Is there anything more after this?

Answer:

-3x+y=-5

Step-by-step explanation:

First, find the slope of the equation:

m=(y2-y1)/(x2-x1)  ==> m=slope of equation

(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)

m=(1-4)/(2-3)  ==> plugin x1=3, y1=4, x2=2, and y2=1

m=-3/(-1)

m=3

y=mx+b   ==> slope-intercept equation

1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1

1=6+b ==> solve for b

1-6=6-6+b

b=-5

y=3x+(-5)  ==> plugin -3 for m and -5 for b

y=3x-5 ==> simplify

Now, Isolate -5 since it is the only constant

y-3x=3x-3x-5  ==> isolate -5 by subtracting 3x on both sides

-3x+y=-5  ==> simplify and put in Ax+By=C form

y = 3x - 5

sorry can't help with step to step explanation......

Since, F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.

Here,

Null hypothesis,

[tex]H_{0}[/tex]: u1 = u2 =u3

u1,u2,u3 are means of stress  scale for group 1 , group 2 and group 3

Alternate hypothesis,

[tex]H_{A}[/tex] : u1≠u2

The F value is =19.056

Using F critical value α=0.05

df numerator =2 , df denominator = 27

F critical value =3.3541

Conclusion : F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

We, conclude that all three groups are equals in terms of mean.

To know more about  hypothesis , visit

https://brainly.com/question/27335001

#SPJ4