Mathematics College

how do you know that the sum of (-2 3/4) and 5/9 is rational?


A.The sum is a terminating and repeating decimal
B.The sum is a non-terminating and a non-repeating decimal.
C.The sum is a fraction
D.The sum is an integer

Answers

Answer 1

Answer:

c

Step-by-step explanation:


Answer 2

Answer:

The sum is fraction therefore rational

Step-by-step explanation:

Given two numbers

[tex]-2\frac{3}{4}\text{ and }\frac{5}{9}[/tex]

we have to tell that how their sum is rational.

we add the above two number

[tex]-2\frac{3}{4}+\frac{5}{9}[/tex]

[tex]\frac{-11}{4}+\frac{5}{9}[/tex]

[tex]\frac{-99+20}{36}=\frac{-79}{36}=-2.194444...[/tex]

Hence, the sum is we can say fraction or non-terminating but repeating which is the definition of a rational number.

∴ from the given options answer C is correct.

The sum is fraction therefore rational.

Related Questions

write each percent as a fraction 13_1/3

Answers

13.33% is your answer

hope this helps :D

put the repeating sign over the last 3
13.33!!!!!

Mark brainiest! 

The skateboard that Jose wants costs $90 has a coupon for 1/5 off retail price. If Jose saves $18 a week, how long will it take to save enough to buy the skateboard?

Answers

1/5 of 90 is 18. So subtract 90 - 18 = 72. Then you would divide 72 by 18 to get 4

Answer:

4 weeks

Step-by-step explanation:

Kevin has three fourths yard of string he uses one third for a school project how many yards of string did he use on the project

                                                  _______
hint the answer is not 1/3 or 33.33333333%

Answers

3/4-1/3. Do that and tell me when your done

3/4 yard,

 he used 1/3

3/4 * 1/3 = 3/12 = 1/4

 he used 1/4 yard

Given f(x) = −9x5 − x4 + 3x3 − 8 and g(x) = −9x5 − 3x3 − 9x2 + 7, find and simplify f(x) − g(x)

Answers

f(x) − g(x) =  −9x^5 − x^4 + 3x^3 − 8 − (−9x^5 − 3x^3 − 9x^2 + 7)
f(x) − g(x) =  −9x^5 − x^4 + 3x^3 − 8 + 9x^5 +  3x^3 +  9x^2 −  7
f(x) − g(x) = − x^4 + 6x^3 +  9x^2 - 15
hope it helps

Robin's family breeds Great Danes. In the last litter, one of the puppies grew at an unusually consistent rate. At birth, he weighed two pounds. At eight months, he weighed 110 pounds.

Answers

Let's assume that you're being asked to write a formula for the dog's weight.

In this case, w = (weight after x months) = (initial weight) (1 + r)^x

We know the initial and final weights:  2 lb and 110 lb.  We also know that the time period involved is 8 months.  What is the "consistent" rate at which the dog gains weight?

110 lb = (2 lb) (1 + r)^8

Let's solve this for r.

Dividing both sides by 2 lb, 55 = (1 + r)^8

Finding the 8th root of both sides:  1.65 = 1 + r

Solving for r, r = 0.65

The dog gains weight at the consistent rate of 0.65 lb/month.

Check:  Does (2 lb) (1.65)^8 come out to 110 lb?

(2 lb)(54.94) = 109.9 lb (very close indeed to 110 lb).


Answer:

A. An additional month of growth is associated with an additional 13.5 pounds of weight.

Step-by-step explanation:

Jared used one whole number 2/5 of soil for his garden. He is digging another garden that will need 1/5 as much soil as the original. How much will he use total.

Answers

Assuming "one whole number 2/5 of soil for his garden" mean 1+2/5(equal to 7/5) then 1/5 of the original garden soil would be:
1/5 * 7/5 = 7/25

Then you need to add the first sum(7/5) with the second sum(7/25) to get the total soil. The calculation would look like this:
7/5 + 7/25= 35/25 + 7/25= 42/25= 1 + 17/25

9,032,504.75 in word form

Answers

Nine million thirty-two thousand five hundred four and seventy-five hundredths
nine million, thirty-two thousand, five hundred four and seventy-five hundredths

In 2001, the United States' oil consumption was 7,297.4 millions of barrels, while Japan's was 1,979.4 millions of barrels. How many more barrels did the United States consume than Japan?

Answers

the answer would be 5,318,000 more barrels were consumed by the U.S than Japan

The United states consumed 5,318 millions of barrels more then Japan.

what is the rule for solving proportions? A. The sum of the means is the product of the extremes. B. The product of the means is equal to the product of the extremes. C. The product of the extremes is twice the product of the means.

Answers

The rule is that :
B. The product of the means is equal to the product of the extremes
Final answer:

The rule for solving proportions is that the product of the means equals the product of the extremes. This method is used when dealing with categorical data in two categories.

Explanation:

The rule for solving proportions is this: The product of the means is equal to the product of the extremes (option B). When you have a proportion which is often written in the mathematically form 'a/b = c/d', you can use this rule. 'a' and 'd' are the extremes and 'b' and 'c' are the means. Therefore, the rule means that a*d (product of the extremes) is equal to b*c (product of the means).

In terms of identifying when you're dealing with a proportion problem, you're involved in this scenario when the data you're dealing with is of two categories like Yes or No, Success or Failure. This is typically when you're attempting to estimate a population proportion for example, the proportion of the population that smokes or will vote for candidate A.

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The observations you made in the unit circle can help you determine the x‑ and y‑coordinates of special points on the circle without memorizing the circle. Analyze some of the patterns by completing the parts below.
a. Look at all the ordered pairs whose angles are of the form k pi/4, where k is an integer. What do you notice?
b.Now look at the ordered pairs whose angles are of the form k pi/6 or k pi/3. What do you notice about their coordinates?
c.How can you determine if the coordinates of a point are positive or negative?

Answers

a. Look at all the ordered pairs whose angles are of the form k pi/4, where k is an integer. What do you notice?          These ordered pairs would be found along the lines that make 45 deg, 135 deg, 225 deg and 270 deg angles as measured from the positive x-axis.  Every such line is made up of an infinite number of dots representing such pairs.  And the x- and y-components of these pairs would be equal in magnitude (but could have different signs).

The table gives estimates of the world population, in millions, from 1750 to 2000. year population year population 1750 790 1900 1650 1800 980 1950 2560 1850 1260 2000 6080 (a) use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. compare with the actual figures

Answers

The exponential model provides a reasonable approximation for the world population growth between 1750 and 1800. However, it becomes less accurate for longer time periods due to various factors like technological advancements, medical breakthroughs, and changing social and economic conditions.

1. Define the model:

The general form of an exponential model is:

P(t) = a * b^(t)

where:

P(t) is the population at time t

a is the initial population (at t = 0)

b is the growth factor (greater than 1 for positive growth)

t is the time elapsed (in years, since the initial time)

2. Find the parameters:

We have data for 1750 (t = 0) and 1800 (t = 50):

P(0) = 790 million (initial population)

P(50) = 980 million (population after 50 years)

Using these values, we can solve for a and b:

b = (P(50) / P(0))^(1/t) = 980 / 790)^(1/50) ≈ 1.007

a = P(0) / b^0 = 790 / 1 ≈ 790

3. Predict the population in 1900 and 1950:

Now we can plug the values of a and b into the model to predict the population:

P(150) = 790 * 1.007^(150) ≈ 1912 million (predicted population in 1900)

P(200) = 790 * 1.007^(200) ≈ 3145 million (predicted population in 1950)

4. Comparison with actual data:

The actual population in 1900 was 1650 million and in 1950 was 2560 million. While the model overestimates the population in both cases, it still captures the general trend of growth.

Please help me with this Math question

Answers

Statements:
1.) angle 2 and angle 5 are supplementary
4.) l is parallel to m

Reasons:
1.) Given
2.) Vertical Angles Theorem
3.) Transitive Prop?- I'm not sure
4.) Converse of the Same-Side/Consecutive Interior Angles Theorem

A nationwide survey of college seniors by the university of michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in parade. if 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is
a. anywhere from 7 to 9;
b. at most 5;
c. not less than 8.

Answers

9 to 9 ration bro...7 to 9 is too little everyone be doing this research can’t support this because the researchers be doing it too tbh

emma siad "it is seventyfive hundredths of a mile to waterslide park." Charles said "it is seven and five-tenths miles to water slide park." whose statement makes sence?whose statement is nonsense? Explain your reasoning?

Answers

Emma: seventy-five hundredths of a mile
Charles: seven and five tenths of a mile
Distance: 0.75 miles
Emma: 75/100 miles
Emma: 0.75 miles, correct as this is the correct distance from the park
Charles: 7 and 5/10 miles
Charles: 7+ 0.5=7.5 miles, incorrect as this is far more than the distance to the park

Find the extreme values of f subject to both constraints f(x,y) = 2x^2+3y^2-4x-5, x^2 + y^2 <=16

Answers

[tex]f(x,y)=2x^2+3y^2-4x-5[/tex]
[tex]f_x=4x-4=0\implies x=1[/tex]
[tex]f_y=6y=0\implies y=0[/tex]

[tex]f(x,y)[/tex] has only one critical point at [tex](x,y)=(1,0)[/tex]. The function has Hessian

[tex]\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}4&0\\0&6\end{bmatrix}[/tex]

which is positive definite for all [tex](x,y)[/tex], which means [tex]f(x,y)[/tex] attains a minimum at the critical point with a value of [tex]f(1,0)=-7[/tex].

To find the extrema (if any) along the boundary, parameterize it by [tex]x=4\cos t[/tex] and [tex]y=4\sin t[/tex], with [tex]0\le t<2\pi[/tex]. On the boundary, we have

[tex]f(x(t),y(t))=F(t)=2(4\cos t)^2+3(4\sin t)^2-4(4\cos t)-5=32\cos^2t+48\sin^2t-16\cos t-5[/tex]
[tex]F(t)=35-16\cos t-8\cos2t[/tex]

Find the critical points along the boundary:

[tex]F'(t)=16\sin t+16\sin2t=16\sin t+32\sin t\cos t=16\sin t(1+2\cos t)=0[/tex]
[tex]\implies t=0,\dfrac{2\pi}3,\pi,\dfrac{4\pi}3[/tex]

Respectively, plugging these values into [tex]F(t)[/tex] gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when [tex]F(t)=47[/tex].

Now, solve for [tex]x,y[/tex] for both cases:

[tex]t=\dfrac{2\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=2\sqrt3\end{cases}[/tex]

[tex]t=\dfrac{4\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=-2\sqrt3\end{cases}[/tex]

so [tex]f(x,y)[/tex] has two absolute maxima at [tex](x,y)=(-2,\pm2\sqrt3)[/tex] with the same value of 47.

A square sheet of art paper has an area of 625 square inches. What is the minimum side length of an easel that supports the whole sheet of paper?

Answers

If the area of the paper is 625 sq in, the length of one side of this square is sqrt(625 sq in), or 25 inches.  That's the min. side length of an easel that is to support the whole sheet of paper along its lowest side.

area of a square = side^2

 to find the length of a side using area find the square root of the area

sqrt(625) = 25

so the easel has to be at least 25 inches

Simplify the expression
(-5)^3
Answers:
–125


125


–15


25

Answers

the answer youre looking for is -125
Okay since the power of 3 is an odd number, the answer will be a negative number.

Answer: A) -125

The total mileage they walked was 16 2/3 miles. If each kid contributed 4 1/6 miles to the hike, how many kids went on the hike?

Answers

Attached solution and work.

Answer:58

Step-by-step explanation:

another way to write (3x1000)+(3x10)+(3x1/100)+(3x1/1000)

Answers

That'd be 3000 + 30 + 0.03 + 0.003, or 3030.033

Expression after the simplification is 3030.033.

What is an expression?

Expression in mathematics is the combination of variables with the use of operations and predetermined rules. It could appear as an equation, a set of numbers, etc.

Given, expression

(3x1000)+(3x10)+(3x1/100)+(3x1/1000)

Simplifying,

(3x1000)+(3x10)+(3x1/100)+(3x1/1000)

= 3000 + 30  + 3/100 + 3/1000

= 3030033 / 1000

or, = 3030.033

Hence, the value of the expression is 3030.033.

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What is the product?

(4x)(-3x8) (-7x3)

Answers

Answer: [tex]84x^{12}[/tex]

Step-by-step explanation:

The given expression  : [tex](4x)(-3x^8) (-7x^3)[/tex]

Open brackets, we get

[tex]4x\cdot-3x^8\cdot-7x^3\\\\=4\cdot-3\cdot-7\cdot x\cdot x^8\cdot x^3[/tex]

Using law of exponents:-

[tex]a^m\cdot a^n=a^{m+n][/tex]

[tex]84\cdot x^{1+8+3}\\\\=84x^{12}[/tex]

Hence, the product [tex](4x)(-3x^8) (-7x^3)=84x^{12}[/tex]

Answer:

C. 84X^12

Step-by-step explanation:

edge 2021

Given f(x) = −9x5 − x4 + 3x3 − 8 and g(x) = −9x5 − 3x3 − 9x2 + 7, find and simplify f(x) − g(x)

Answers

f(x) − g(x) =  −9x^5 − x^4 + 3x^3 − 8 − (−9x^5 − 3x^3 − 9x^2 + 7)
f(x) − g(x) =  −9x^5 − x^4 + 3x^3 − 8 + 9x^5 +  3x^3 +  9x^2 −  7
f(x) − g(x) = − x^4 + 6x^3 +  9x^2 - 15
hope it helps

Suppose x and y vary together such that x is 7 times as large as y. write a formula that defines x in terms of y.

Answers

since y is less than x by 7 times [tex] \frac{x}{7}=y [/tex] so in terms of x we write
x=7y

what is 58/7 as a mixed number

Answers

58/7.......how many times does 7 go into 58 without going over....it goes in there 8 times....so 8 is ur whole number.....7 * 8 = 56....now take ur 58 and subtract 56 (58 - 56 = 2)....that is ur numerator, so basically, the remainder is ur numerator.....and the denominator, it stays the same.
so we end up with : 8 2/7

Answer:

[tex]8\frac{2}{7}[/tex]    and or  8 2/7

have an amazing day!

Step-by-step explanation:

What is the solution to 3/4(x+8)=9

Answers

Let's solve your equation step-by-step.34(x+8)=9Step 1: Simplify both sides of the equation.34(x+8)=9(34)(x)+(34)(8)=9(Distribute)34x+6=9Step 2: Subtract 6 from both sides.34x+6−6=9−634x=3Step 3: Multiply both sides by 4/3.(43)*(34x)=(43)*(3)x=4Answer:x=4
3/4(x+8)=9
distribute so:
3/4x + 3/4(8) = 9
3/4x + 6 = 9
3/4x = 9-6
3/4x = 3
4/3(3/4x) = (3) 4/3 
x=4

-4 4/5 divided by 4 please help!!!!!!

Answers

Your answer would be -1.2 or -1 1/5. I hope this helps love! :)

It takes 45 minutes for 4 people to paint 5 walls.
How many minutes does it take 6 people to paint 4 walls

Answers

4 people x 45 minutes = 180 minutes total to paint 5 walls

180/5 = 36 minutes of man work per wall

36 * 4 walls = 144 total minutes

144/6 people = 24 minutes total


A train is traveling from New Orleans to Memphis at a constant speed of 79 mph New Orleans and Tennessee are 395.1 miles apart how long will the train take to Tennessee

Answers

[tex]\bf \stackrel{distance}{d}=\stackrel{rate}{r}\cdot \stackrel{time}{t} \qquad \qquad 395.1=79t\implies \cfrac{395.1}{79}=t[/tex]

Answer:

About 5.0 hours

Step-by-step explanation:

Po is trying to solve the following equation by completing the square: 49x^2+56x-64 = 0.He successfully rewrites the above equation in the following form: (ax + b)^2 = c,where a, b, and c are integers and a > 0. What is the value of a + b + c?


Halp

Answers

(ax+b)² = c
(ax+b)(ax+b) = c

(ax+b)(ax+b) = a²x² + abx + abx + b² 

a²x² + 2abx + b² - c = 0
49x² + 56x - 64 = 0

a² = 49
a = 7 or -7
* given that a > 0 ; so a = 7

2ab = 56
ab = 56/2
ab = 28
b = 28/a
b = 4

- 64 = b² - c
- 64 = 16 - c
- 64 - 16 = - c
-80 = - c
80 = c

(7x + 4)² = 80

Check = (7x+4)(7x+4) - 80 = 0
49x² + 28x + 28x + 16 - 80 = 0
49x² + 56x + 64 = 0

Then; a + b + c 
7 + 4 + 80 = 91

Final answer:

To solve the equation 49x²+56x-64 = 0 by completing the square, we first convert it to the format (ax + b)² = c. It is found that a=1, b=4/7, and c=16/49. Hence, a+b+c = 381/147 or approximately 2.59183673469.

Explanation:

The equation to solve is 49x²+56x-64 = 0. By completing the square, we can rewrite the equation in the form (ax + b)² = c. To get to this form, Po first divided the entire equation by 49, giving x²+8/7x-64/49= 0. Following this, he then took half of the coefficient of x (which is 4/7), squared it (which is 16/49), and added it to both sides of the equation. This transforms the left-hand side of the equation into a perfect square giving us (x+4/7)²=16/49. Hence, we find that a=1, b=4/7, and c=16/49. Therefore a+b+c = 381/147 or approximately 2.59183673469.

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What reasoning and explanations can be used when solving radical equations?

Answers

A good thing to remember when solving radical equations is "get rid of radicals". If possible, square both sides of the equation or multiply by whatever order radicals you have. It is generally easier to solve equations when you don't have radicals

Answer:

The common reasoning that can be use while solving a radical equation are shown below.

Step-by-step explanation:

Radical equations are the equations which contains radical expressions like [tex]\sqrt{x}\text{ and }\sqrt{x+2}[/tex], etc.

If a radical expression is defined as [tex]\sqrt{x}[/tex], then the sign [tex]\sqrt{}[/tex] is the radical and x is radicand.

The common reasoning that can be use while solving a radical equation are:

1. Isolate or separate the radical expression.

2. To remove radical square both sides of the equation.

3. After that solve the equation to find the unknown variable

4. Check the answer for solution or extraneous solution.

For example:

[tex]\sqrt{x+1}+1=x[/tex]

subtract 1 from both sides.

[tex]\sqrt{x+1}=x-1[/tex]

Taking square on both sides.

[tex]x+1=(x-1)^2[/tex]

On simplification we get

[tex]x+1=x^2-2x+1[/tex]

[tex]0=x^2-2x+1-x-1[/tex]

[tex]0=x^2-3x[/tex]

[tex]0=x(x-3)[/tex]

Using zero product property,

[tex]x=0,x-3=0\Rightarrow x=3[/tex]

Check the equation for x=0,

[tex]LHS=\sqrt{0+1}+1=1+1=2\neq 0=RHS[/tex]

Since LHS is not equal to RHS, therefore 0 is an extraneous solution.

Check the equation for x=3,

[tex]LHS=\sqrt{3+1}+1=2+1=3=RHS[/tex]

Since LHS is equal to RHS, therefore 3 is an solution.

rounded to hundred how can I round to hundred

Answers

If you are talking about any number then.....
imagine a mountain, any number less than 5 is only the left and any number greater than 5 is on the right
      
Here, for example, let's try 13 

look at 13 on the pyramid .... since it's not a the top of the mountain so it falls back down to 10... it rounds down to 10
Now let's try 18 ...hmmm.... 18 is not at the top either so it falls as well. It falls down to 20 it rounds up to 20 

how about 15 u might be asking...it is at the top...15 is a little different ...make sure no one is looking and push it off the right side and falls to 20. Also rounding up to 20

              5
           4    6 
        3          7 
     2                8 
   1                      9 
0                           10
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