The math teachers can walk 76 miles in 4 days, the reading teachers can walk 63 miles in 7 days. Which group of teachers walked more miles per day?​

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

The radius of the given circle is 2 units.

Here, we are given an equation of a circle as follows-

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

The general form of the equation of a circles is -

\((x- h)^{2}+ (y-k)^{2} = r^{2}\)

where (h, k) are the coordinates of the center of the circle and r is the radius of the circle.

Let us convert the given equation into the general form by completing the squares as follows -

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

\(x^{2}+ (2*4)x+ y^{2} - (2*3)y + 21 = 0\)

\(x^{2}+ (2*4)x+ 16 -16+ y^{2} - (2*3)y + 9 - 9+ 21 = 0\)

\([x^{2}+ (2*4)x+ 16] -16+ [y^{2} - (2*3)y + 9] - 9+ 21 = 0\)

\((x+4)^{2} -16+ (y - 3)^{2} - 9+ 21 = 0\)

\((x+4)^{2} + (y - 3)^{2} = 16 + 9 - 21\)

\((x+4)^{2} + (y - 3)^{2} = 4\)

\((x+4)^{2} + (y - 3)^{2} = 2^{2}\)

Thus, we have obtained the equation of the circle in the general form. From this, we can observe that the center coordinates will be (-4, 3) and the radius of the circle will be 2 units.

Therefore, the radius of the given circle is 2 units.

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Answer:

I think C

Step-by-step explanation:

It has a whole number as numerator and denominator so it is rational and it is a real number, but it is not an integer because it is a fraction.

Answer:

Rational, and Real numbers.

Step-by-step explanation:

There's a certain overlapping sequence of categorizing:

Whole #, Integers, Rational, Real.

Fractions and decimals belong in Rational, so you could say they are real as well.

Hope this helps! (sorry about it being brief)

The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13

A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.

The possible polynomial in the question is; x³ + 5·x² - 11·x + 104

The factor of the polynomial is; (x + 8)

The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.

The other steps of synthetic division can then be presented, summarily as follows;

Therefore;

-8 | 1\({}\)   5     -11   104

   |   \({}\)   -8    24  104          

     1   -3    \({}\) 13      0

The factors of the polynomial

The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13

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The value of x is -3 and y is 7 for equilateral triangle having x+1, 2x+4 and 3x+y sides.

We can use the fact that an equilateral triangle has equal lengths on each of its three sides to determine the values of x and y.

Given:

First side=x+y

second side= 2x+4

third side=3x+y

An equilateral triangle has three equal sides, hence the following equations can be constructed:

x + 1 = 2x + 4

2x + 4 = 3x + y

Let's tackle each of these equations separately:

x + 1 = 2x + 4

We will subtract x from both sides and subtract 4 from both sides in order to solve this equation:

x + 1 - x = 2x + 4 - x

1 = x + 4

By taking 4 away from both sides, we arrive at:

1 - 4 = x + 4 - 4 , -3 = x

Therefore, x has been determined to be -3.

Now, substitute the value of x in the second equation:

2x + 4 = 3x + y

2(-3) + 4 = 3(-3) + y

-6 + 4 = -9 + y

-2 = -9 + y

y = -2 + 9

y = 7

So, we determined that y has a value of 7.

As a result, the values of x and y are, respectively, x=-3 and y=7

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Answer:

Step-by-step explanation:

In an equilateral triangle all sides are equal.

So each of these sides (and their equations are equal to each other.)

To find x - set the first two (as they only involve x) equal to each other and solve.

x + 1 = 2x + 4

x -x + 1 = 2x - x + 4

1 = x + 4

1- 4 = x + 4 - 4

-3 = x

Then substitute -3 for x in the last equation to find y, also setting it equal to one of the other equations.

3(x) + y = x + 1

3(-3) + y = -3 + 1

-9 + y = -2

-9 + 9 + y = -2 + 9

y = 7

so x = -3 and y equal 7

Complete question is;

Mr. Jenkins will purchase a riding lawnmower that costs $1,350 The store offers no interest if he uses the store credit card and the balance is paid in

full within one year. He has $1,500 in his checking account. Compare the

advantages and disadvantages to using either a debit card or a credit card.

Answer:

Advantages & disadvantages given below

Step-by-step explanation:

Advantages;

1. They have low fees; for example almost all store credit cards don't charge annual fees but instead they promote some very good offers.

2. Possibility of having discounts from retailers; because majority of retailers usually love promoting their credit cards because it helps them ensure they save more money and they hold on to this principle judiciously. For example there could be discounts upon first purchase or when you shop at target stores which they offer.

3) Majority of store credit cards offer a lot of benefits for members. For, owners of store credit cards could be offered the option of returning purchased items without presenting the receipt. There could also be I stances where they are giving free shipping of their products or they could be exposed to some good favorable payment plans.

Disadvantages;

1. Their credit limits are usually far lower than those of credit and debit cards.

2. Other cards give more flexible discount and reward system to its customers. This includes cash back or giving the incentive of earning more points when they spend beyond a certain amount.

Answer:

He will paint it 11 times. 8, 18, 28, 38, 48, 58, 68, 78, 88, 98

A should be the correct answer because it was selected randomly and the votes won't be fair.

Answer:

I'm pretty sure it's -4

Step-by-step explanation:

If you substitute in -2, you get e(-2)= -(-2)+ -6

which is equal to 2-6

2-6=-4

Answer:

e(-2)=-4

Step-by-step explanation:

e(-2)=-(-2)+-6

=2-6

=-4

Answer:

y

Step-by-step explanation:

Answer:

wth that's hard I can't answer that

Answer:

B

Step-by-step explanation:

∠ACE and ∠ECB form a straight angle whose sum = 180°, hence

2x + 2 + 5x + 3 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25 → C

1) The equation is true for n = $12.30

2) 24 fluid ounces is equivalent to 3 cups.

Here we want to see for which values of n is the equation:

3n = $36.90

true.

To get that,we need to isolate the variable n. To do so, we can divide both sides by 3.

n = $36.90/3

n = $12.30

That is the value of n.

We want to write 24 fluid ounces as cups, we know the relation:

1 fluid ounce = 0.125cups.

Then we can just do the change of units as follows:

24 fluid ounces = 24*(0.125 cups.) = 3 cups.

So there are 3 cups on 24 fluid ounces.

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Answer:

45° rotation clockwise

Step-by-step explanation:

When you plot these on the graph, the non prime ones are on quadrant 2 and when you plot the prime ones, it is on quadrant 1. This means that it is 45° to the right(clockwise)

⬇️red is prime blue is regular ⬇️

Answer:

2.221992

Step-by-step explanation:

can i have the crown pls ૮ ♡ﻌ♡ა

Answer:

2.221

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

Answer:

1.

d. (-14) + (-8)

2.

a. (-14) + 8

Step-by-step explanation:

(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.

(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.

Answer:

1. D  

2. A

Step-by-step explanation:

1.  It asks you what expression has the same value as (-14)-8.  All you need to do is find other equations that have the same value as that.  So the equation is -14-8.  IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5.  If it's both negative: -(-5), it will be +5.  If it is both positive: +(+5), it is going to be +5.  

IMPORTANT!

- and + = -

- and - = +

+ and + = +

What we are looking for: -14-8

So choice A is (-14)+8 which is simplified to -14+8.  So, this one isn't right.

Choice B: 14-(-8)= 14+8.  So, it's incorrect.

Choice C: 14+(-8)= 14-8.  Again, it's not -14-8 so it's not right.

Choice D: (-14)+(-8)= -14-8.  This equation matches the one we are looking for!  So it's correct!

2. Same thing as number 1.  Let's simplify the equation it wants us to find first.  

(-14)-(-8)= -14+8

So -14+8 is what we are looking for.

Choice A: (-14)+8= -14+8.  It matches!  So it is correct.  Let's look at the other options anyway.

Choice B: 14-(-8)= 14+8.  Nope.  Not right.

Choice C: 14+(-8)= 14-8 because - always beats +.  So, this one is also incorrect.

Choice D: (-14)+(-8)= -14-8.  Oops, this is also wrong.  So choice A is the right answer.

Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:

(When there is a number outside and inside a parentheses, multiply them.)

2(5)=10, CORRECT!    2+(5) is not 2 times 5.  It's whatever is closest to the parentheses, in this case being the positive sign.  So + and 5 is just 5!

IMPORTANT!

-2(-5)= - and - is positive, so positive (2 times 5).  Positive 10.

-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.

+2(+5)= + and + is positive, so positive (2 times 5).  Positive 10.

Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

Answer:

x=15

Step-by-step explanation:

6(5)=30

3(5)=15

The length of the missing side Triangle is 3

As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).

so

15/x=30/6 .................  the ratio of two sides of the triangle

x  =  15*6/30

x= 3

here the value of x is 3.

Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.

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Answer:

340

Step-by-step explanation:

10^3=1000 so 0.34 x 1000 is 340

Answer:

340

Step-by-step explanation:

If we use the rule PEMDAS then we do the exponent first.

0.34 x 10 x 10 x 10

0.34 x 1000

340

Answer:

-28

Step-by-step explanation:

math is math

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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She should spend 1 hour working on problems , 3 hour reading , Option B is the right answer.

The gain of the desired effect with respect to the previous gain is called margin gain

The marginal gain from 8:00 am to 9:00 am is

(40-0) = 40 problems

The marginal gain from 9:00 am to 10:00 am is

= 70-40 = 30 problems

The marginal gain from 10:00 am to 11:00 am is

(90-70) = 20 problems

As if she does more than one hour of problem solving her productivity decreases to 30 which is less than 1 hour of reading textbook

Therefore she should not spend more than 1 hour on problem solving.

Therefore Option B is the right answer.

1 hour working on problems , 3 hour reading

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer: he will be 14

Step-by-step explanation:

Anna is 14 and her brother is 10. Two years ago she was 12. 3/4 of 12 is 9. 9+5 more years is 14. :)))