Consider the following system of equations:
-1/3x^2 = -5/6 + 1/3y^2 and
5y^2 = 25/2 - 5x^2
How many solutions does the system have?

Answer:

Step-by-step explanation:

There are 2 pints in one quart.

93 pints = 93/2 = 46 quarts and 1 pint left over.

Answer:

46.5 quarts

Step-by-step explanation:

There are 2 pints in 1 quart.

Hence,

93 pints     1 quart

------------ * ------------- = 46.5 quarts

      1           2 pints

For this case we have to:

[tex]x <-5:[/tex] Represents the solution of all strict minor numbers to -5.

[tex]x> 5:[/tex] Represents the solution of all strict major numbers to 5.

The global solution is given by the intersection of both sets. The symbol of intersection is denoted as: ∩

If we represent the solution in a numerical line, it gives us empty. do not intersect.

Answeer:

Empty set

Induction is the correct answer; when you use induction form general ideas and rules based on your experiences and observations. I hope this will help you! Have a wonderful day!

Answer:

d. induction

Step-by-step explanation:

When you use induction you form general ideas and rules based on your experiences and observations.

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

4(2x - 1) = (4)(2x) + (4)(-1) = 8x - 4

Put x = 6 to the expression:

8(6) - 4 = 48 - 4 = 44

The solution to the given expression is 44.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

By applying the distributive property of multiplication to the given expression, we have:

4(2x - 1) = 4(2x) - 4(1)

4(2x - 1) = 8x - 4

when x = 6, we have;

8x - 4

8(6) - 4

48 - 4 = 44.

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Answer:

A

Step-by-step explanation:

Work with the two points

Formula

m = (y2 - y1)/(x2 - x1)

Givens

y2 = 3

y1 = 1

x2 = - 2

x1 = - 5

Solution

m = (3 - 1) / (-2 - - 5)

m = 2 / (-2 + 5)

m = 2 / 3

Answer: A

Answer:

[tex]\large\boxed{\text{A.}\,2/3}[/tex]

Step-by-step explanation:

In this question ,we're trying to find the slope with the given points.

We would use the slope-formula to find the slope.

Slope-formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.

Your equation should look like this:

[tex]m=\frac{3-1}{-2-(-5)}[/tex]

Now we solve:

[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]

When you're done solving, you should get 2/3

This means that the slope is 2/3

Answer:

Step-by-step explanation:

Lets assume that a sphere with greater radius = R = 5cm

And a sphere with smaller radius = r = 4cm

Volume of a sphere = 4/3 π * r³

To find the volume of a sphere with radius 5.

Put the value in the formula.

=4/3π * r³

=4/3π *(5)³

5³ = 5*5*5=125

=4/3π * 125

=4/3 *3.14 *125

=1570/3

=523.3 cm³

Now find the volume of sphere with radius= 4

4/3π*r³

=4/3π * 4³

4³= 4*4*4=64

=4/3*3.14*64

=803.84/3

=267.9cm³

Now to find the space between the spheres subtract the volume of smaller sphere from the volume of larger sphere.

We can write it as:

Space between the spheres = Volume of larger sphere - Volume of smaller sphere

= 523.3 cm³ - 267.9cm³

= 255.4cm³ ....

Answer:

r equals 4- this is the value of r

hope this helps

Step-by-step explanation:

Answer:

[tex]\large\boxed{r=4}[/tex]

Step-by-step explanation:

In this question, we're going to need to solve the equation for r.

This means that we need to get the r by itself to see what it equals to.

Lets solve:

[tex]15r- 6r=36\\\\\text{Subtract 15r and -6r}\\\\9r=36\\\\\text{Now you will divide}\\\\r=4[/tex]

When you're done solving, you should get r = 4

This means that the value of r is 4 (or r = 4)

Answer:

The answer is

B. x =>z

They all equal the same.

Answer:

G'(0,5)

H'(4,-5)

F'(-2,-2)

Step-by-step explanation:

We need to identify the three vertices from the figure on the graph:

G(-3,5)

H(1,-5)

F(-5,-2).

If we translate these points 3 units to right, then that effects the x-coordinates.

So 3 more than -3, is 0.

3 more than 1 is 4.

3 more than -5 is -2.

So the new points are:

G'(0,5)

H'(4,-5)

F'(-2,-2).

Answer:

15 is your answer.

Step-by-step explanation:

Let "a number" = x

"Three times a number increase(d) by 4" = 3x + 4

"...is the same as" = "="

"four times that number decreased by 11" = 4x - 11

Set the equation:

3x + 4 = 4x - 11

Isolate the variable, x. Subtract 4x and 4 from both sides:

3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)

3x - 4x = -11 - 4

Simplify. Combine like terms:

-x = -15

Isolate the variable, x. Divide -1 from both sides:

(-x)/-1 = (-15)/-1

x = (-15)/(-1)

x = 15

15 is your answer.

~

Answer:

False

Step-by-step explanation:

I think this is a true or false question.

The statement is false.

Here is an example of it being false:

Choose the irrational number to be [tex]\sqrt{2}[/tex] and the rational to be 1.

The product of these numbers is [tex]\sqrt{2}[/tex] which is irrational, not rational.

Answer:

False

Step-by-step explanation:

Ight so any irrational number times a rational number is irrational. But keep in mind that If its 0 times an irrational number, its going to be 0, which is a rational number. So irrational x rational = irrational. Irrational x 0=rational 0.

Hope this helped

Answer:

0.2237

Step-by-step explanation:

Use the Table of Standard Normal Probabilities for Negative z-scores.

For z= -0.36 NORMSDIST(-0.36)=0.3594 (read value from the table)

For z= -1.10  NORMSDIST(-1.10)=0.1357 (value from the table)

You know P(-1.10<z<-0.36) = 0.3594-0.1357=0.2237

Answer:

D

Step-by-step explanation:

Plug in and see.

Check A: Lets plug in (0,3) into y<2/3 x+2.

3<2/3 (0)+2

3<2 is not true so not A

Check C: Lets plug in (3,5) into y<2/3 x+2.

5<2/3 (3)+2

5<2+2

5<4 is not true so not C

Check B: Lets plug in (-3,1) into y<2/3 x+2.

1<2/3 (-3)+2

1<0 is not true so not B

Check D: Lets plug in (1,2) into y<2/3 x+2.

2<2/3 (1)+2

2<2/3+2 is true so D

Answer:

Option D 74°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

The arcs that the outer angle encompasses are

254° and (360-254)=106°

therefore

∠x=(1/2)[254°-106°]

∠x=(1/2)[148°]

∠x=74°

Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

All die rolls have a 1 in 6 chance of landing on any specific number (because they have 6 equal sides). In probability, two independent events with probabilities a and b will occur concurrently [tex]a*b[/tex] of the time. In this case, [tex]a=b=\frac{1}{6} \to p=a*b=\frac{1}{6}*\frac{1}{6}=\frac{1}{36}[/tex]

Answer:

Required probability = 1/36

Step-by-step explanation:

It is given that,single die is rolled twice

The outcomes of rolling a die are

1, 2, 3, 4, 5, and 6

Total = 6

To find the probability

Probability of getting 2 = 1/6

Probability of getting 5 = 1/6

Therefore probability of rolling a 2 the first time and a 5 the second time. = 1/6 * 1/6 = 1/36

Answer:

37

Step-by-step explanation:

So this is probably not the correct mathematical way to do it, but it is really easy so you'll probably understand quicker. So a median is the middle number, so how do you find it. First, I counted how many numbers there were (17). Then I subtracted by one to get an even number (if you already have an even number skip this step, and just divide by 2). So now we have 16, so I divided it by 2 to get 8 and just added that 1 that we took out and got 9. So i counted from 24 and the 9th number was 37. To double check I did the same from 56 and got 37.

Answer:

Problem 3: H. 350 = r * 5

Problem 4: rate of speed = 70 miles per hour

Step-by-step explanation:

Problem 3:

speed = distance/time

Multiply both sides by time.

speed * time = distance/time * time

speed * time = distance

distance = speed * time

distance = 350

speed = r

times = 5

350 = r * 5

Answer: H. 350 = r * 5

Problem 4:

350 = r * 5

Divide both sides by 5.

350/5 = r * 5/5

70 = r

r = 7

rate of speed = 70 miles per hour

Answer:

H. 350 = r*5

Her average rate: 70 miles

Step-by-step explanation:

When finding average rate, you are always either multiplying or dividing so all the choices except for H, won't work.

Also, r represents the rate so its how many miles per hour. So you would multiply the miles per hour by the amount of hours you have.

So r*5.

To find her average you would solve for r in the equation.

So r*5 = 350

You would divide 5 by itself and then by 350, because whatever you do to one side of the equation, you do to the other.

So 5/5 = 1 or just r

350/5 = 70

r = 70

In the physics context of free fall, it would take an object approximately 7.67 seconds to fall from a 944-foot tower, neglecting air resistance. This is calculated using the formula for distance of a freely falling object s(t)=16t^2.

The question deals with the physics concept of free fall, specifically directed to the time it would take an object to fall from a certain height. Given that the distance s(t) of a freely falling object is given by the equation s(t)=16t^2, we can find the time t for an object to fall from a height of 944 feet, which is the height of the specific tower.

Setting s(t) equal to the height of the tower, we get: 944=16t^2. Solving this equation for t, we'll get the square root of 944/16 which is approximately 7.67 seconds. Therefore, it would take an object about 7.67 seconds to fall to the ground from the top of the 944-foot tower, neglecting air resistance.

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To determine how long it takes for an object to fall from a 944-foot tower, we use the formula s(t) = 16t^2. Solving for t, we find that it takes approximately 7.68 seconds. Thus, the object hits the ground after 7.68 seconds.

Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?

To solve this problem, we need to determine the time t it takes for the object to hit the ground. Given the height h = 944 feet, we'll use the formula for the distance fallen:

s(t) = 16t^2

We set s(t) equal to the height of the tower:

944 = 16t^2

Next, solve for t:

Divide both sides by 16:

944 / 16 = t^2

t^2 = 59

Take the square root of both sides:

t = √59

t ≈ 7.68 seconds

Therefore, it would take approximately 7.68 seconds for an object to fall to the ground from the top of the building.

Answer:

I believe it would be B

Step-by-step explanation:

take x and y values and figure it out what it is by itself

Answer:

3x-2

Step-by-step explanation:

[tex]9x^{2} -12x+4[/tex] can be factored using the perfect square rule into [tex](3x-2)^{2}[/tex]

and

[tex]9x^{2}-4[/tex] can be factored by using the difference of squares formula into [tex](3x+2)(3x-2)[/tex]

Both can be factored by (3x-2) so it is a common factor.

Hence, there are no common factors between the two equations.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

given equation is [tex]9x^2-4[/tex]

solving for x,

                     [tex]9x^2=4\\x^2=\frac{9}{4} \\x=\frac{3}{2}, -\frac{3}{2}[/tex]

putting values of x in equation 1,

x = [tex]\frac{3}{2}[/tex],

      [tex]\frac{81}{4}-12.\frac{3}{2}+4\\ \frac{25}{4}[/tex]Therefore, 3/2 is not a common factor

x=[tex]-\frac{3}{2}[/tex],

      [tex]\frac{81}{4}+12.\frac{3}{2}+4\\ \frac{169}{4}[/tex]Therefore, -3/2 is not a common factor

Hence, there are no common factors between the two equations.

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Answer:

option C

Step-by-step explanation:

We will call :

A=(-5, -1)    B=(-2, -1)   C=(-3, -4)   D= (-3, -4)

Perimeter= 2*AB+2BC

Where AB= [tex]\sqrt{(-5+2)^{2} +(-1+1)^{2} } = \sqrt{9} =3\\[/tex]

BC =[tex]\sqrt{(-2+3)^{2} +(-1+4)^{2} } = \sqrt{10} =3.16\\[/tex]

So We have:

Perimeter=2*3+2*3.16= 12.32  

Answer:

C.

Step-by-step explanation:

Answer:

[tex]\large\boxed{(f-g)(x)=-x^2+3x+7}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\(f-g)(x)=(3x+1)-(x^2-6)=3x+1-x^2+6=-x^2+3x+7[/tex]

Answer:

13 slices.

Step-by-step explanation:

To find your total amount of slices at the start, multiply your pizzas by your slices.

[tex]9*8=72[/tex]

Next, find the difference between your total amount of slices and the amount of slices which have been eaten.

[tex]72-59=13[/tex]

13 slices are left.

Detailed solution to math problems involving functions and mappings.

1. The function represented by the table:

Identify the pattern in the table to determine the function.

The cost increases by $1.95 for every 3 apples, so the function is C(a) = 0.65a (A).

2. Translating a function:

To shift f(x) = x^4 five units right and seven units down, the correct function is g(x) = (x+5)^4 - 7 (D).

3. Mapping the function:

Using the mapping provided, the correct values are: f(5) = 1, f(3) = 0, f(11) = 2, f(21) = 3 (A).

Answer:

12 miles

Step-by-step explanation:

Jay walks 0.75 miles in 15 minutes, or 1/4 hour, so his speed is:

0.75 mi / 0.25 hr = 3 mi/hr

Paul walks 2.5 miles in 30 minutes, or 1/2 hour, so his speed is:

2.5 mi / 0.50 hr = 5 mi/hr

After 1.5 hours, Jay has walked a distance of:

3 mi/hr × 1.5 hr = 4.5 mi

And Paul has walked a distance of:

5 mi/hr × 1.5 hr = 7.5 mi

So the total distance between them is:

4.5 mi + 7.5 mi = 12 mi

Answer:

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.

The y-intercept was (0,2) then it becomes (0,5) in the new line.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.

Both of these equations given are in this form.

y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.

Since b=2 then the y-intercept is 2.

y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.

Since b=5 then the y-intercept is 5.

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.