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Answer:

Option 3) (0.38,-2.85) and (2.62,3.85)

Step-by-step explanation:

The correct question is

The graphs of y=x^2-3 and y=3x-4 intersect at approximately...

we have

[tex]y=x^2-3[/tex] ----> equation A

[tex]y=3x-4[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

Equate equation A and equation B

[tex]x^2-3=3x-4[/tex]

[tex]x^2-3x-3+4=0[/tex]

[tex]x^2-3x+1=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

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

in this problem we have

[tex]x^2-3x+1=0[/tex]

so

[tex]a=1\\b=-3\\c=1[/tex]

substitute in the formula

[tex]x=\frac{-(-3)\pm\sqrt{-3^{2}-4(1)(1)}} {2(1)}[/tex]

[tex]x=\frac{3\pm\sqrt{5}} {2}[/tex]

so

[tex]x_1=\frac{3+\sqrt{5}} {2}=2.62[/tex]

[tex]x_2=\frac{3-\sqrt{5}} {2}=0.38[/tex]

Find the values of y (substitute the value of x in equation A or equation B)

For x=2.62 ----> [tex]y=(2.62)^2-3=3.85[/tex]

For x=0.38 ----> [tex]y=(0.38)^2-3=-2.85[/tex]

therefore

The intersection points are approximately  (0.38,-2.85) and (2.62,3.85)

[tex]T = \frac{-9}{2}x + 103[/tex] is the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.

Solution:

The linear equation in slope intercept form is given as:

T = cx + k ------ (i)

Where "t" is the temperature at an elevation x

And x is in thousands of feet

Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain

Given, when c = 6 thousand ft and [tex]T = 76^{\circ}[/tex] fahrenheit

This implies,

From (i)

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c  ----- (ii)

Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain

Given, when c = 12 thousand ft and [tex]T = 49^{\circ}[/tex] fahrenheit

This implies,

From (i)

49 = c(12) + k

49 = 12c + k

Substitute (ii) in above equation

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

[tex]c = \frac{-9}{2}[/tex]

Substituting the value of c in (ii) we get

[tex]k = 76 - 6( \frac{-9}{2})\\\\k = 76 + 27 = 103[/tex]

Substituting the value of c and k in (i)

[tex]T = \frac{-9}{2}x + 103[/tex]

Where "x" is in thousands of feet

Thus the required linear equation is found

The linear equation that represents the temperature T at an elevation x on the mountain (where x is in thousands of feet) is T = -4.5x + 103.

This is a problem involving linear equations in Mathematics. We are given two data points, (6, 76) and (12, 49) where the first value in each pair is an elevation (in thousands of feet) and the second value is the corresponding temperature in degrees Fahrenheit. We can use these points to derive a linear equation of the form T = mx + c where T is the temperature, m is the slope, x is the elevation, and c is the y-intercept. The slope of the line m can be calculated using the formula (y2-y1)/(x2-x1) = (49-76)/(12-6) = -27/6 = -4.5. Therefore, every thousand feet in elevation leads to a temperature drop of 4.5 degrees Fahrenheit. To calculate the y-intercept c we can substitute x and y values from one of our points into the linear equation. For instance, using point (6, 76) we get 76 = -4.5*6 + c, which gives c = 103. Therefore, the linear equation to find the temperature T at an elevation x (in thousands feet) is T = -4.5x + 103.

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Answer:The cost increases $3.99 for every additional movie rented.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this situation, the rate of change means the cost per movie.

Specifically, the cost is $3.99 per movie. In other words, the cost increases $3.99 when the number of movies increases by 1.

We could also say it like the cost increases $3.99 for every additional movie.

Therefore, among the options the second choice is correct, because specifies the right ratio of change that the table shows.

You can get this ratio of change by subtracting $7.98 - $3.99 = $3.99. Then, if you sum this difference to $7.98, you would get $11.97, and then $15.96, and so on. That means the ratio of change is $3.99 per movie.

Answer:

Given inequality:

[tex]y>3x-4[/tex]

To graph it.

Solution:

In order to graph the given inequality, we will first graph the equation of the line by replacing the inequality sign with equal to sign.

Thus, we will graph the line [tex]y=3x-4[/tex]

On comparing the line equation with standard equation [tex]y=mx+b[/tex] where [tex](0,b)[/tex] represents the y-intercept point of the line, we can conclude the y-intercept point for the given line is [tex](0,-4)[/tex]

We can find another point by plugging in [tex]x=1[/tex] in the equation.

So, we have:

[tex]y=3(1)-4[/tex]

[tex]y=3-4[/tex]

[tex]y=-1[/tex]

So, the other point is [tex](1,-1)[/tex]

Potting (0,-4) and (1,-1) on the graph.

We can joint the two points and extend it infinity in order to graph the equation of line.

Now, since the inequality sign is greater than,

1) so we make sure that the line of the equation is a broken line as the line is not included in the solution for the inequality.

2) The part of the graph lying above the line would be shaded as the solution for the inequality.

Answer:

It results -14 in either way

Step-by-step explanation:

Velocity As A Rate Of Change

The velocity of an object can be computed as the rate of change of its displacement (or position taken as a vector) over time. If we compute it as a derivative, it's called instantaneous velocity, and if computed as the slope of the function (difference quotient) at a certain point it's the average velocity

The position of the object as a function of time is

[tex]\displaystyle s(t)=6-14t[/tex]

Computing the derivative

[tex]\displaystyle s'(t)=-14[/tex]

We can see it's a constant value. If we use the slope or rate of change:

[tex]\displaystyle v=\frac{s_2-s_1}{t_2-t_1}[/tex]

Now let's fix two values for time  

[tex]\displaystyle t_1=5\ sec,\ t_2=8\ sec[/tex]

and compute the corresponding positions, by using the given function

[tex]\displaystyle s_1=6-14(5)=-64[/tex]

[tex]\displaystyle s_2=6-14(8)=-106[/tex]

Now we compute the average velocity

[tex]\displaystyle v=\frac{-106-(-64)}{8-5}[/tex]

[tex]\displaystyle v=\frac{-106+64}{3}=\frac{-42}{3}[/tex]

[tex]\displaystyle v=-14[/tex]

We get the very same result in both ways to compute v. It happens because the position is related with time as a linear function, it's called a constant velocity motion.

Answer:

[tex]A = 2(width*length) + 2(length*height)+2(width*height)\\=> 2(wl+lh+wh)\\where \ w = width,\  l=length \ and \ h = height[/tex]

l = 8, w = 5, h = 6

A = 2(5*8 + 8*6 + 5*6)

A = 236

[tex]Volume = width * length * height\\V = wlh[/tex]

V = 5*8*6

V = 240

Ratio of A to V = A / V

236/240 = 236:240

Step-by-step explanation:

The surface area of any object is the total area of each face of that object. Now, we have a rectangular prism with dimensions given. Considering a face of the prism, there is an opposite face and this is why the area of each face was multiplied by 2. That is how the formula for the surface area of an object is derived

For the volume, the formula is multiplying the height, width and length

When the area and volume is computed, we now take the ratio of the answers to arrive at 236/240 which in ratio form is 236:240

Answer:

C

Step-by-step explanation:

I just did the test

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a parallelogram.

The formula of an area of a parallelogram:

[tex]A=bh[/tex]

b - base

h - height

From the graph we have b = 21m and h = 33m.

Substitute:

[tex]A=(21)(33)=693\ m^3[/tex]

Answer:

√50 lies between 7.07 and 7.08.

Answer:

what is your question???????

Answer:

No it is not

Step-by-step explanation:

well if you see any number that is could be written as a  fraction is rational. square root of 9 is 3,  but in this case the square root of 2 is irrational, so it is a irrational number.

Yes, the fraction √ 2/9  is a rational number​

A rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number.

Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values.

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The student's homework question involves the calculation of a room's floor area for carpeting costs and then determining the wall area for papering costs, utilizing given ratios and costs per square meter.

The question involves calculating the area of a room's floor and using that to determine the cost of carpeting, followed by calculating the cost of papering the walls. To solve for this, we use the given ratio of the length being 3 times the breadth (let's say the breadth is 'b', then the length would be '3b'). When the carpeting cost of Rs. 60 per square meter totals Rs. 4500, we can find the area of the floor by dividing the total cost by the per square meter cost, which gives us an area of 75 square meters (i.e., 4500 / 60 = 75 m2).

Assuming the room to be a rectangle, the length and breadth can be determined from the area (since length times breadth = area), and given the relationship between length and breadth, we can solve for 'b' and then find '3b'. Once we have the dimensions of the floor, we can calculate the perimeter (2 times (length + breadth)) and use the given height to find the total area of the walls. The cost of papering is then determined by multiplying the wall area by the cost per square meter (Rs. 6 in this case).

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The sun is roughly 93,000,000 miles away from Earth

We can round this to 100,000,000

As a power of 10, this is [tex]10^{8}[/tex]

Have A Nice Day ❤  

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- Ally ✧  

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Answer:

There are an estimated 1 quadrillion ants living on earth. A quadrillion as a power of 10 would be [tex]10^{15}[/tex], because there are 15 zeros in a quadrillion.

Answer:

y=-5x+1

Step-by-step explanation:

The equation is: y=mx+b

m = the slope of the line

b = the y-intercept (0,b)

The y-intercept is (0,1) so b = (0,1)

So the equation would be y =mx+1

Now in order to calculate the slope, the equation is:

y₂-y₁    over

x₂-x₁

So we should use the points (-3,13) and (1,-7).

-7-13 over (over means a fraction symbol)

1+3

Simplify:

-20 over 4   =-5/1    = -5    

M=-5

So the equation is now:

y=-5x+1

Answer:

Step-by-step explanation:

You need to do some solving simultaneously to get these values.  Your quadratic equation is of the form

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

Use the coordinates you've been given to solve 3 equations.  It will be super simple if we start with the coordinate (0, 1).  Here's why (obvious after some substitution is done):

[tex]a(0)^2+b(0)+c=1[/tex] which gives us that

c = 1.  Now we have a variable to plug in for c to solve for a and b.  Again, we have coordinates that we can use to create 2 more equations:

[tex]a(-3)^2+b(-3)+1=13[/tex] and, simplified:

9a - 3b = 12

and the second equation is:

[tex]a(1)^2+b(1)+1=-7[/tex] and, simplified:

a + b = -8

Now combine the 2 bold equations and solve by elimination or substitution to find either a or b.  I chose elimination and multiplied the second equation by 3 to get a new equation:

3a + 3b = -24

Using the elimination method:

9a - 3b = 12

3a + 3b = -24

You can see that the b's subtract each other away, leaving us with

12a = -12 so

a = -1

Now plug -1 in for a to solve for b:

-1 + b = -8 so

b = -7 and the quadratic is

[tex]-x^2-7x+1=y[/tex]

Answer:

It's the first choice:  3x^2y(3x^2 - 2xy + y^2).

Step-by-step explanation:

9x4y − 6x3y2 + 3x2y3

We take the Greatest Common Factor which is  3x^2y:

= 3x^2y(3x^2 - 2xy + y^2).

Answer:

3x^2y(3x^2 - 2xy + y^2)

Step-by-step explanation:

You can give the guy above me a crown now lol 4 years later

Answer:

[tex]33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\66\dfrac{2}{3}\text{ quarts of sparkling water}[/tex]

Step-by-step explanation:

A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and 3/4 quart of grape juice.

The ratio of sparkling water to grape juice is

[tex]1.5\div \dfrac{3}{4}=\dfrac{3}{2}\div \dfrac{3}{4}=\dfrac{6}{4}\div \dfrac{3}{4}=6\div 3=2\div 1[/tex]

So, to make 100 quarts of punch you need x quarts of grape juice and 2x quarts of sparkling water.

Hence,

[tex]x+2x=100\\ \\3x=100\\ \\x=\dfrac{100}{3}=33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\2x=66\dfrac{2}{3}\text{ quarts of sparkling water}[/tex]

Answer:

66 1/3

Step-by-step explanation:

pleas mark me as brainliest

Answer:

5x^2+6x-1

Step-by-step explanation:

Remember that (f+g)(x)=f(x)+g(x).

(3x^2+7x)+(2x^2-x-1)

3x^2+2x^2+7x-x-1

5x^2+6x-1

The sum of the functions f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, represented by (f+g)(x), equals to 5x^2 + 6x -1.

In mathematics, particularly in algebra, the operation (f+g)(x) represents the sum of the two functions f(x) and g(x). In order to find the sum, you simply carry out the addition operation on the functions term by term. Given your functions f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, the sum (f+g)(x) is then calculated as follows:

Therefore, (f+g)(x) = 5x^2 + 6x -1.

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Answer:

13.333...

Step-by-step explanation:

20 divided by 6 = 3.33...

3.33 * 4 = 13.333

Answer: 5u/s

Step-by-step explanation:

the ball rolls a total of 5 units from x=-5 to x=0. It traveled  this total distance in one second. Therefore the ball goes 5 units per second.

Answer:10 people

Step-by-step explanation:

7 times less showed up so, 70 divided by 7 is 10. 10 guests attended.

The James family expected 70 guests for their party, but 7 times fewer showed up. By dividing the expected guest number by 7 (70 ÷ 7), we find that 10 guests attended the party.

The James family expected 70 guests to attend their independent day party. However, 7 times fewer guests showed up than expected. We can calculate this by dividing the expected number of guests by 7.

Step 1: Identify the total number of guests expected which is 70.

Step 2: Divide the expected number of guests by 7. This is because the actual number of attendees was 7 times fewer than the expected.

Step 3: Perform the division: 70 ÷ 7 = 10.

So, 10 guests attended the independent day party hosted by the James family.

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Answer:

yes

Step-by-step explanation:

rational numbers are

Fractions

Decimals

repeating decimals

decimals that stop and don't go forever

percent

perfect square and cube roots

whole numbers

Answer:

h(5) = - 22

Step-by-step explanation:

Given that h is a linear function say, h(x) = ax + b ......... (1)

Now, given that h(1) = 10 and h(3) = - 6  

Hence, we can write from equation (1), a(1) + b = 10, ⇒ a + b = 10 .......... (2)

And a(3) + b = - 6, ⇒ 3a + b = - 6 ........ (3)

Now, solving equations (2) and (3) we get (3a - a) = - 6 - 10

⇒ 2a = - 16

⇒ a = - 8

So, from equation (2), we get, b = 10 - a = 18  

Therefore, the linear function is

h(x) = - 8x + 18

Hence, h(5) = - 8(5) + 18 = - 22 (Answer)

Answer:

Zeros are [tex]x=-2\pi,-\pi,0,\pi,2\pi[/tex]

Step-by-step explanation:

[tex]f(x)=0\\-4\sin x=0\\\sin x=0\\[/tex]

[tex]\sin(-2\pi)=0\\\sin(-\pi)=0\\\sin(0)=0\\\sin(\pi)=0\\\sin(2\pi)=0[/tex]

It's B) 0, ±pi, ±2pi on edge

As it is proved that the equation has no solution, Derick is correct

Step-by-step explanation:

Given

[tex]-3(4n + 2) = -4n + -2 (4n - 6)[/tex]

We have to solve the equation in order to check if Derick was solved the equation correctly or not.

So,

Applying distributive property first

[tex]-12n -6 = -4n -8n +12\\-12n-6 = -12n+12\\-12n+12n-6 = 12\\-6 = 12[/tex]

As the variable is already cancelled in the equation there is no unique solution.

In order for an equation to have infinite solutions the constant on both sides of equation should be same which is not the case in the given equation

So,

As it is proved that the equation has no solution, Derick is correct

Keywords: Linear equations, variables

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Final answer:

Upon simplification, the equation results in a contradiction (-6 = 12), proving Derick's conclusion of no solution to be correct.

Explanation:

To determine if Derick's conclusion that the equation -3(4n + 2) = -4n + -2 (4n - 6) has no solution is correct, we first simplify the equation. Distributing the coefficients on both sides gives:

-12n - 6 = -4n - 8n + 12

Combining like terms on the right side leads to:

-12n - 6 = -12n + 12

Adding 12n to both sides and simplifying:

-6 = 12

This statement is a contradiction, implying that there is no value of n that can satisfy the original equation, meaning Derick's conclusion of no solution is correct.

Answer:

They traveling at [tex]0.37\ m/s[/tex] in backward direction.

Step-by-step explanation:

Given mass of Ammy [tex]m_1=55kg[/tex]

and velocity is forward at [tex]v_1=3m/s[/tex]

Also, mass of Jenny [tex]m_2=40kg[/tex]

Who is travelling in opposite direction [tex]v_2=-5m/s[/tex]

Let velocity in forward direction is positive and velocity in backward direction is negative.

Also, velocity after crash is [tex]v[/tex]

As they crashed into each other and they moved as one mass. We can apply principle of conservation of momentum.

Conservation of momentum says momentum before collision should equal to momentum after collision.

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex](55\times3)+(40\times(-5))=(55+40)v\\\\165-200=95v\\\\-35=95v\\\\v=\frac{-35}{95}=-0.368m/s[/tex]

So, velocity after collision [tex]v[/tex]≅[tex]-0.37m/s[/tex] is in opposite direction. That is the direction of Jenny.

Answer:

4.583 or 55/12

Step-by-step explanation:

A = 5, B = -22 and C = 4, D = -6. 5 multiplied by -22 is equal to -110, and 4 multiplied by -6 is equal to -24. Because a negative divided by a negative is a positive by the same rules of multiplication of negatives is a positive, just get rid of any negative signs in the equation. Now you have 110 / 24. 110/24 is equal to 4.583 or 55 / 12 in fraction form.

Answer:

Step-by-step explanation:

Here we need to use Ohm's Law, because we have electric current, voltage and resistances. This law state: [tex]V=IR[/tex]

So, first we need to calculate the total resistance to then find the voltage. The resistances can be placed in two ways: in parallel, in series.

The pair 4 and 8 ohms are parallel, so we solve:

[tex]R_{T}=\frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]

[tex]\frac{1}{R_{T}}=\frac{1}{4}+\frac{1}{8}=\frac{8+4}{32}=\frac{12}{32}=\frac{3}{8}[/tex]

Which is, [tex]R_{T}=frac{8}{3}[/tex]

Now, this total resistance of parallels ones is placed in series with the 3 ohm resistance, in this case we just sum, because they are in series:

[tex]R=3+\frac{8}{3}=\frac{9+8}{3}=\frac{17}{3}=5.67 ohm[/tex]

Now that we have the total resistance of the circuit, we use the Ohm's Law:

[tex]V=IR\\V=(0.6A)(5.67ohm)=3.4 Volt[/tex]

Therefore, the right answer is B.

The set of equations that represent this situation is:

[tex]y = \frac{1}{6}x + 3[/tex]

[tex]y = \frac{1}{2}x + 3[/tex]

Solution:

Let "x" represent the smaller number

Let "y" represent the larger number

Given that,

Six times a larger number is equal to the sum of a smaller number and 18

Here "times" represents multiplication

Six times a larger number = sum of a smaller number and 18

6 x larger number = smaller number + 18

6y = x + 18

Thus,

[tex]y = \frac{1}{6}(x + 18)\\\\y = \frac{1}{6}x + 3[/tex]

Also given that difference of twice the larger number and the  smaller number is 6

twice the larger number - smaller number = 6

2y - x = 6

Thus,

2y = x + 6

[tex]y = \frac{1}{2}(x + 6)\\\\y = \frac{1}{2}x + 3[/tex]

Thus the set of equations that represent this situation is:

[tex]y = \frac{1}{6}x + 3[/tex]

[tex]y = \frac{1}{2}x + 3[/tex]

Answer:

the correct answer is D

Step-by-step explanation: