linear function passes through the points (2, 9) and (7, 34). What is the rate of change?

Answer:

a) 4d + 18

b) 38 inches

Step-by-step explanation:

a) The perimeter is simply the sum of all the exterior side lengths.

On the top, we've got d and d + 3.

On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.

The bottom is the same length as the top two lengths, so it's:

d + (d + 3) = 2d + 3

And, the right side is 6.

Adding these together, we have:

d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18

b) We just need to substitute 5 in for d:

4d + 18

4 * 5 + 18 = 20 + 18 = 38 inches

AnswerAnswer:

a) 4d + 18

b) 38 inches

Step-by-step explanation:

a) The perimeter is simply the sum of all the exterior side lengths.

On the top, we've got d and d + 3.

On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.

The bottom is the same length as the top two lengths, so it's:

d + (d + 3) = 2d + 3

And, the right side is 6.

Adding these together, we have:

d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18

b) We just need to substitute 5 in for d:

4d + 18

4 * 5 + 18 = 20 + 18 = 38 inches

Step-by-step explanation:

Answer:

It is 5.84 units away from the origin.

Step-by-step explanation:

[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2}} [/tex]

Therefore:

[tex]d = \sqrt{ {(5 - 0)}^{2} + {(3 - 0)}^{2} } \\ d = \sqrt{ {5}^{2} + {3}^{2} } = \sqrt{25 + 9} \\ d = \sqrt{34} = 5.83951...[/tex]

Final answer:

The distance from point E(5,3) to the origin is calculated using the Pythagorean theorem, resulting in \/34 units.

Explanation:

The question asks how far point E(5,3) is from the origin. To find the distance between a point and the origin in a Cartesian coordinate system, we use the Pythagorean theorem. Specifically, the distance ( extit{d}) can be calculated using the formula  extit{d} = \/((x_2 - x_1)² + (y_2 - y_1)²), where ( extit{x_1},  extit{y_1}) represents the coordinates of the first point (in this case, the origin (0,0)) and ( extit{x_2},  extit{y_2}) represents the coordinates of the second point (in this case, point E(5,3)).

Plugging in the values, we get  extit{d} = \/((5 - 0)² + (3 - 0)²) = \/(5² + 3²) = \/(25 + 9) = \/34. The exact distance between point E and the origin is \/34 units, which can also be approximated as a decimal if necessary.

Answer:

b

Step-by-step explanation:

Answer:

[tex]Fx=\frac{5\pm\sqrt{25+24} }{6}[/tex]

Step-by-step explanation:

A quadratic equation in one variable given by the general expression:

[tex]ax^2+bx+c[/tex]

Where:

[tex]a\neq 0[/tex]

The roots of this equation can be found using the quadratic formula, which is given by:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

So:

[tex]y(x)=3x^2-5x-2=0[/tex]

As you can see, in this case:

[tex]a=3\\b=-5\\c=-2[/tex]

Using the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(3)(-2)} }{2(3)}=\frac{5\pm\sqrt{25+24} }{6}[/tex]

Therefore, the answer is:

[tex]Fx=\frac{5\pm\sqrt{25+24} }{6}[/tex]

Answer:

- The price of a soccer ball is $14.5

- The price of a soccer bag is $5

Step-by-step explanation:

To solve this problem, we call:

s = the price of a single soccer ball

b = the price of a soccer bag

We have:

1) A soccer coach purchases 10 soccer balls and 2 soccers bags for $155: so we can write

[tex]10s+2b=155[/tex] (1)

2) Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189: so we can write

[tex]12s+3b=189[/tex] (2)

So we have a system of two equations in two unknown variables:

[tex]10s+2b=155\\12s+3b=189[/tex]

We solve it by multiplying eq.(1) by 3 and eq(2) by 2, and we get:

[tex]30s+6b=465\\24s+6b=378[/tex]

Now we substract eq(2) from eq(1) and we get:

[tex]6s=87[/tex]

So

[tex]s=\frac{87}{6}=14.5[/tex]

And by using eq(1) we also find the value of b:

[tex]10s+2b=155\\b=\frac{155-10s}{2}=\frac{155-10(14.5)}{2}=5[/tex]

So:

- The price of a soccer ball is $14.5

- The price of a soccer bag is $5

To solve this problem, we can set up a system of equations and use the elimination method to find the values of x and y. The cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.

To solve this problem, we can set up a system of equations. Let's use x to represent the cost of a soccer ball and y to represent the cost of a soccer bag.

From the first equation, we have 10x + 2y = 155. From the second equation, we have 12x + 3y = 189.

We can solve this system of equations using substitution or elimination method. I will use the elimination method.

Now we can substitute the value of x into one of the equations to find the value of y.

Therefore, the cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.

Answer:

C.

invest in a joint insurance and retirement plans

Step-by-step explanation:

this would be the obvious answers because there no risks that would compromise their future

Answer:

it's linear because the line doesn't go through the origin

Step-by-step explanation:

i know that bc it says. +1

hope this helps!

Answer: x^2 (x + 11) - 3 (x + 11)

Answer:

Answer: x^2 (x + 11) - 3 (x + 11)

Step-by-step explanation:

Edge

Answer:

34%

Step-by-step explanation:

The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F.

We want to find the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F.

The mean of the sampling distribution of the sample means is the same as the population mean,

[tex] \mu = 98.6 \degree[/tex]

The standard error of the mean becomes the standard deviation of the sampling distribution of the means.

[tex]SE= \frac{ \sigma}{ \sqrt{n} } [/tex]

[tex]SE= \frac{0.6}{ \sqrt{36} } = 0.1[/tex]

By the Central Limit Theorem, the distribution of mean of means is approximately normal

The z-score of 98.5° F

[tex] z= \frac{98.5 - 98.6}{0.1} = - 1[/tex]

By the empirical rule 68% of the distribution is within one standard deviation (-1 to 1).

Therefore from (-1 to 0), it will be approximately 34%

Final answer:

To calculate the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F, you'd use the z-score formula after finding the standard error. The final probability is found by subtracting the z-score probability corresponding to a score of -1 from 1. The correct distribution for calculation is the z-distribution due to the known standard deviation.

Explanation:

The question pertains to calculating the probability that the mean body temperature of a randomly selected sample of 36 adults is greater than 98.5° F. Given that the mean is 98.6° F and the standard deviation is 0.60° F, one would first calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation and n is the sample size. In this case, SE = 0.60/√36 = 0.10° F.

To find the probability, we can use the z-score formula, which is z = (X - μ) / SE, where X is the value we are finding the probability for, μ is the mean, and SE is the standard error. Plugging in the values, we get z = (98.5 - 98.6) / 0.10 = -1. When we look up the z-score of -1 in the z-tables or use a statistical software, we find the probability to the left of z=-1. However, since we want the probability that the mean temperature is greater than 98.5° F, we need to subtract this value from 1.

The final step will give us the probability that the mean of the selected sample is greater than 98.5° F. It's important to note that while the question hints at using the t-distribution due to not knowing the population standard deviation, since we're using the provided standard deviation of 0.60° F, we're actually using the z-distribution. If we were dealing with smaller sample sizes or truly didn't know the population standard deviation, we would use the t-distribution as suggested.

Answer:

b = y intercept

Step-by-step explanation:

y = mx +b

This is the slope intercept form of a line

The m is the slope and the b is the y intercept

Answer:

D

Step-by-step explanation:

The three-dimensional object formed when the shape is rotated about the axis is a cone.

A cone is a solid which tapers from a circular base to a point. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.

here, we have,

we know that,

When a right triangle is rotated about an axis, a cone is formed.

Find the attached figure to visualize the rotation.

Rotation of the base AB of the right triangle results in the circular base of the cone while rotation of hypotenuse AC results in the lateral surface of the cone.

Hence, The three-dimensional object is formed when the shape is rotated about the axis is a cone.

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Answer: B

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

1184.5

Step-by-step explanation:

150+400+180+300=1030

1030 × 15% = 154.5

(15% is also 0.15)

1030 + 154.5 = 1184.5

I hope this helps you :)

Answer:

mean = 9.3

median = 10

mode =13

Step-by-step explanation:

First put the data in order from smallest to largest

1,1,7,9,9,10,11,13,13,13,15

The mean is the sum of all the numbers divide by how many numbers we have

(1+1+7+9+9+10+11+13+13+13+15)/11102/11=9.272727=9.3

median is the middle number

11/2 = 5.5

The sixth number is the median= 10

mode is most often  13 appears the most

Answer:

The answer is 22 centimeters.

Step-by-step explanation:

Answer:

22 centimeters squared

Step-by-step explanation:

trust me just did it on EDG

Final answer:

The cartoon lasts 30 minutes, and the movie is six times longer, adding up to 210 minutes to watch both.

Explanation:

The subject at hand is the duration it takes to watch a cartoon and a movie. The cartoon lasts half an hour (30 minutes), while the movie is six times longer than the cartoon. To find the duration of the movie, we multiply its relative length by the duration of the cartoon. So, 6 times 30 minutes is 180 minutes. To calculate the total time to watch both the cartoon and the movie, we add the two durations together. Therefore, 30 minutes for the cartoon plus 180 minutes for the movie equals 210 minutes in total.

Answer:

D

Step-by-step explanation:

I interpret your problem as log49(7)=1/2

This would be the same as 49^1/2=7 because taking a number to the 1/2 power is the same as taking its square root [sqrt(49)=7].

Answer:

The greatest length she can cut to have equal length in all the cables, without a left over is 3 feet each

Step-by-step explanation:

in order to solve this, we treat the length of each cable as separate numbers for which we find the highest common factor, since we are told that they must all be of the same length. The highest common factor of two whole numbers, is the highest number which completely divides both number without a remainder. The highest common factor is found as follows:

Factors of 12 are : 1, 2, 3, 4, 6, and 12

factors of 15 are : 1, 3, 5, and 15

from the above, the highest factor that is common to both numbers is 3.

Therefore, if both cables are cut into 3 feet each, , a total of 9 pieces of cables (4 from the 12 feet cable and 5 from the 15 feet cable) of equal length will be obtained without any remainder.

Answer:

3 feet

Step-by-step explanation:

To solve this problem the heed to find the factors of 15 and 12

Factors of both numbers

12 : 1,2,3,4,6,12

15: :1.3,5,15

Then we find the highest common factor between them which is 3, 3 is a factor of both 12 and 15

remainder. The highest common factor is found as follows:

So, if both cables are cut into 3 feet each, you should have a total of 9 piecesa total of 9 pieces of cables.

From the 12 feet long cable you should have 3 feet x 4 meaning 4 pieces

From the 15 fert long cable you should have 3 feet x5 meaning 5 pieces

4+5 makes it 9 pieces without any remainder

Answer:

  x-intercept(s): ( 4, 0)

  y-intercept(s): ( 0, -14)

Answer: $29.10

Step-by-step explanation: 10.20 + 18.90 = $29.10

Answer:

uh my good sir whats your question we cant help if we dont know what the questions is.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

To solve the equations, subtract the given number from the sum on the left side of the equation to find the missing number. For the arithmetic expression, perform the operations in order.

In the first equation, you must find a number that, when added to 9, equals 10. To do this, subtract 9 from 10, which gives you 1. Therefore, the missing number is 1.

In the second equation, you need to find a number that, when added to 1, equals 10. Subtract 1 from 10 to get 9. So, the missing number is 9.

In the last equation, you simply need to perform the arithmetic operations in order: 200 + 500 = 700, 700 + 2000 = 2700, and finally 2700 - 3000 = -300. Therefore, the result of the expression 200 + 500 + 2000 - 3000 is -300.

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Answer:

False

$25,706.48

Step-by-step explanation:

The annual percentage rate (APR) is 4%, so the monthly rate is 4%/12 = ⅓%.

25 years = 300 months.

The monthly deposit (annuity) is $50.

The future value of the annuities is:

F = A [(1 + i)ⁿ − 1] / i

Given i = 1/300, A = 50, and n = 300:

F = 50 [(1 + 1/300)³⁰⁰ − 1] / (1/300)

F = 25,706.48

The statement is false.  The amount after 25 years is less than $30,000.

The statement doesn't make sense because if you make $50 monthly deposits at a 4% APR for 25 years, you will have approximately $41,981.86 in your retirement account, not only $30,000.

The statement does not make sense or is clearly false. Let's add up the total deposits over 25 years and calculate the interest gained using the given annual percentage rate (APR) of 4%.

Therefore, if you continue to make $50 monthly deposits with a 4% APR for 25 years, you will have just under $41,981.86 in your retirement account, not $30,000 as stated. So, the statement is inaccurate.

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Answer:

$1.85

Step-by-step explanation:

$7.00 is the price of 1 gallon of apple cider

Step 1

The first step would be to find how many ounces make a gallon

And 1 gallon of apple cider juice = 128 ounces

Therefore,

$7.00 makes 128 ounces of apple cider juice

Step 2

The second step is to find how many ounces make 1 packet or package boxes

Eight 4.23 ounces juice boxes = 1 packet

Therefore, 8 × 4.23 ounces = 33.84 ounces.

Step 3

To find cost per eight 4.23 ounce boxes of cider which is the cost per 33.84 ounces,

We used the proportion below.

If 128 ounces = $7

33.84 ounces = Y( we call this y because it is unknown)

We cross multiply

128 ounces × Y = $7 × 33.84 ounces

Y =($7 × 33.84 ounces) ÷ 128 ounces

Y = $1.85

Therefore, 33.84 ounces which is would cost us $1.85.

Therefore, the cost is $1.85 per eight 4.23 ounce boxes of cider.

The factor of the expression 12x³ – 9x² will be 3x² and (4x – 3).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ 12x³ – 9x²

Then the factor of the expression will be

⇒ 3x²(4x – 3)

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Answer:

neap tide

Step-by-step explanation:

Answer:neap tide is the correct one

Step-by-step explanation:

Answer:

1/2x units

Step-by-step explanation:

Answer:

1/2x units

Step-by-step explanation: