jane and ben share a lottery win in the ratio 7:3, if Jane's share of the money is $5600, how much does ben recieve

Answer:

x = - 2, x = 1

Step-by-step explanation:

Given

4x² + 4x + 1 = 9 ( subtract 9 from both sides )

4x² + 4x - 8 = 0 ← in standard form

Divide through by 4

x² + x - 2 = 0

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Answer:

f(x) = 2(x - 5)² - 6

Step-by-step explanation:

Vertex Formula: y = a(x - h) + k; Vertex: [h, k]; there is a vertical stretch at 2 = a. The -h [phase shift (horizontal shift)] in parentheses gives you the OPPOSITE term of what it really is, so really, 5 = h. Now, k [vertical shift] is the ONLY normal term, so -6 = k.

Answer:

$5600

Step-by-step explanation:

Original Cost = x

Total Cost = $5824

Sales Tax = 4% or 0.04

Problem Setup

(Original Cost) + 4% (Original Cost) = Total Cost

x + 0.04x = 5824

1x+ 0.04x = 5824

1.04x = 5824

1.04x/1.04 = 5824/1.04

x=5600 Original Cost

To Check math multiply 5600 x 0.04 = 224.

Then add $5600 + $224 = $5824

The price of the car before sales tax is $5600.  

To determine the cost of the car before sales tax, we can use the equation provided:

[tex]x + 0.04x = 5824[/tex]

Here, [tex]x[/tex] represents the original price of the car before sales tax, and [tex]0.04x[/tex] represents the amount of sales tax, which is 4% of the car's price.

First, combine the terms on the left side of the equation:

[tex]1x + 0.04x = 1.04x[/tex]  

Therefore, the equation simplifies to:

[tex]1.04x = 5824[/tex]

Next, to solve for [tex]x[/tex], divide both sides of the equation by 1.04:

[tex]x = \frac{5824}{1.04}[/tex]

Calculating the right side:

[tex]x = 5600[/tex]

For this case we have the following functions:

[tex]f (x) = 2x ^ 2-8x + 6\\g (x) = 3x-1[/tex]

We must find f (x) + g (x):

We have to:

[tex]f (x) + g (x) = 2x ^ 2-8x + 6 + (3x-1)\\f (x) + g (x) = 2x ^ 2-8x + 6 + 3x-1[/tex]

We add similar terms:

[tex]f (x) + g (x) = 2x ^ 2-5x + 5[/tex]

Answer:

[tex]f (x) + g (x) = 2x ^ 2-5x + 5[/tex]

OPTION C

Answer:

She spent 25%

Hello There!

The girl spent 1/4 of her money. 12 is divisible by 3 and when we divide, we get a quotient of 3

If the girl spent $3, we subtract 3 from 12 and we see that 3 = 1/4 6=2/4 and 9=3/4 but if she spent $3 it would be 1/4

The Girl Spent 1/4 of her money. This is also known as 25%

The probability that a person will order dessert given that they ordered a steak for dinner, this is an example of conditional probability.

Given that another event (B) has previously occurred, the likelihood of an event (A) occurring.

Event A in Option(C) - A person will order dessert

Event B in Option(C) - A person will order steak for dinner

Event A will only occur if the event B has already completed, hence according to the definition this is an example of conditional probability.

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Answer:

The slope is m=-5

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

In this problem we have

y=-(2/3)-5x

so

the slope is equal to

m=-5

the y-intercept is equal to

b=-2/3

Answer:28

Step-by-step explanation:five numbers: 24, 25, 26, 27, 28

the largest is 28

The numbers are 24, 25, 26, 27, 28 and the largest will be 28.

Therefore, the numbers are 24, 25, 26, 27, 28 and the largest will be 28.

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Try to put in 9 and 10

Answer:

Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter, and is the longest chord.

Step-by-step explanation:

Answer:

Diameter

Step-by-step explanation:

Answer:

The total cost of the tent with the markup and then tax applied is $409.86

Step-by-step explanation:

230 is the original

the price is going to increase by 230(.65)=149.5

So the new price is 230+149.5=379.5 (this is before tax is applied)

The sales tax is 8% or .08

So the price is going to increase by .08(379.5)=30.36 (this is the tax to add in)

So the total cost is  379.5+30.36=409.86

Answer:

Cost of the tent: $517.86

Step-by-step explanation:

Since it's marked up by 65%, that means you add an additional $149.59 to $230. Now, you have $479.50. Now with 8% tax, you multiply $479.50 to 0.08 and we get $38.36. We add $38.36 to $479.50 and we get $517.86. I hope this helps and please mark me brainliest!

Answer:

y = (1/3)x

Step-by-step explanation:

If this is truly a line, then we can find its equation using any two of the three given points.  If we go from (3, 1) to (27, 9), x increases by 24 and y increases by 8.  Thus, the slope of this line is m = rise / run = 8 / 24, or m = 1/3.

Using the point (3, 1) and the slope m = 1/3, the slope-intercept form y = mx + b becomes 1 = (1/3)(3) + b.  Thus, b = 0, and the line is y = (1/3)x.

Answer:

y=[tex]\frac{1}{3}[/tex]x ~apex

Step-by-step explanation:

The problem involves creating and solving a system of equations based on a story problem. The three equations that represent the system are x + y + z = 120, x = y/2 + 35, and z = 2y - 20.

To complete the matrix equation that models this situation, we need to define the distances between the starting point, checkpoint 1, checkpoint 2, and the finish line. Let x represent the distance from the starting point to checkpoint 1, y represent the distance from checkpoint 1 to checkpoint 2, and z represent the distance from checkpoint 2 to the finish line. The matrix equation would look like this:

A * [x, y, z] = B

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Answer:

Step-by-step explanation:

No c

 as she was initially 300m away from the bridge (distance from bridge=300m)   (time=0) so it was her starting point.

      and after 6 minutes  (time=6min)  she reached the bridge.      (distance from bridge = 0m)

Answer:

C.Katy was initially 300 meters away from the bridge and it tooke her 6 minutes to reach the bridge.

Step-by-step explanation:

As you can see in the table when Katy had been walking for 0 minutes, she was 300 meters away, so initially Katy was 300 meters from the bridge.

When she reaches the bridge is when the distance is reduced to 0, since distances is reduced to 0 at 6 minutes, we can infer that it took her 6 minutes to reach the bridge, and that se was walking at a pace of 50 meters per minute.

The probability that the next post will have 0 comments is P = 4/9.

The probability will be equal to the quotient between the number of posts with no comments and the total number of posts.

We know that there are 9 posts, and by looking at the table, we can see that 4 out of these 9 posts have 0 coments.

Then the probability that the next post will have 0 comments is:

P = 4/9

So the correct option is B.

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Answer:

C) -4 degrees

Step-by-step explanation:

let's set Sunday Temp = 0°

Since Monday is 6° cooler than Sunday, we subtract 6° from 0 (Sunday's temp)

Monday's Temp -6 (0-6)

Since Tuesday's Temp is 4° higher than Monday, we add 4 to Monday's temp:

Tuesday's Temp -2 (-6+4)

Wednesday's Temp is cooler than Tuesday's but not as cool as Monday's, we assume that Wednesday's Temp is in-between -6 & -2

that makes

c. -4 a reasonable choice

Answer:

C) -4 degrees

Step-by-step explanation:

Let x be the temperature on sunday,

Then, according to the question,

The temperature on monday = x - 6,

On Tuesday = (x-6) + 4 = x - 2,

Now, Wednesday's temperature was cooler than Tuesday's, but not as cool as it was on Monday,

That is,  x - 6 < temperature on wednesday < x - 2

⇒ x- 6 - x < temperature on wednesday - x < x - 2 - x

⇒-6 < temperature on wednesday - temperature on sunday < -2

Since, -6 < -4 < -2

Hence, the possible difference between the temperature on Wednesday, as compared to the temperature on Sunday would be -4.

Option 'C' is correct.

Answer:

Step-by-step explanation:

Surface area is 2(πr²) + 2πrh.  The first includes the top and bottom; the second is the area of lateral sides of the cylinder (radius r and height h).

The volume of this cylinder is V = πr²h.

Answer:

2 pi r square + pi dh

Step-by-step explanation:

2 pi r square + pi dh

(2x^2)(3x^3)(4x)^2

=6x^5(16x^2)

=96X^7

Answer:

24 x^7

Step-by-step explanation:

(2 x^2)(3 x^3)(4 x)^2 = 2*3*4 * x² * x³ * x² = 24 x^7

Answer:

54.26

Step-by-step explanation:

0.4+0.86= 1.26

51+2= 53

53+1.26= 54.26

Answer:

54.26 i hope its right

Answer:

It is -373.

Step-by-step explanation:

Answer:

- x

Step-by-step explanation:

If we expand the product.

Each term in the second factor is multiplied by each term in the first factor

x(x - 4) + 3(x - 4) ← distribute both parenthesis

= x² - 4x + 3x - 12 ← collect like terms

= x² - x - 12

The middle term of the product is - x

Answer:

[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx}= x - \ln(1 + e^{x}) + C\end{aligned}[/tex].

Step-by-step explanation:

The first derivative of the denominator [tex]1 + e^{x}[/tex] is [tex]e^{x}[/tex]. Rewrite the fraction to obtain that expression on the numerator.

[tex]\begin{aligned}\frac{1}{1 + e^{x}} &= \frac{1 + e^{x}}{1 + e^{x}} - \frac{e^{x}}{1+e^{x}}\\&=1-\frac{e^{x}}{1+e^{x}}\end{aligned}[/tex].

In other words,

[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\end{aligned}[/tex].

Apply [tex]u[/tex]-substitution on the integral [tex]\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx}[/tex]:

Let [tex]u = 1 + e^{x}[/tex]. [tex]u > 1[/tex].

[tex]du = e^{x}\cdot dx[/tex].

[tex]\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx} = \int{\frac{du}{u}} = \ln{|u|} = \ln{u} +C = \ln{(1+e^{x})}+C[/tex].

Therefore

[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\\ & = x - \ln{(1 + e^{x})}+C\end{aligned}[/tex].

Answer:

-1,1,3

Step-by-step explanation:

The zeros,roots and the x-intercept are the same, so see where the graph touches the x axis and that or thosepoints is/are the zeros

Answer:

One solution

Step-by-step explanation:

We have the system

[tex]y=5x-1\\y=-3x+7[/tex]

To solve the system, equate both equations and solve for the variable x.

[tex]5x-1= -3x+7\\\\5x + 3x = 7 +1\\\\8x = 8\\\\x=1[/tex]

Now substitute the value of x in any of the two equations and solve for the variable y.

[tex]y=5(1)-1[/tex]

[tex]y=4[/tex]

Finally the system of equations has one solution

Answer:

30

Step-by-step explanation:

60% of the 50 students are 12 years old

60% * 50

Changing to decimal form

.60 * 50

30

30 of the students are 12

Answer:

Answer:

This question is based on the reasoning. Therefore, the negative slope of the line representing the data in the table.

Given;

A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.

We have to describe the slope of the line representing the data in the table.

Reasoning: The number of cards sold is represented by x-axis and the amount of money needed is represented  by the y-axis.

In general, as we sell more cards, we gain more money and then,  the amount of money needed goes down.

From the given graph terms, we start at the top of our graph with the amount of money needed and zero cards sold and then as we sell cards your slope of the line goes down and we need less and less money.

Therefore, the negative slope of the line representing the data in the table.

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Answer:

0.94

Step-by-step explanation:

5/6 +2 /3= 2 5/6 /3= 2.83/3= 0.94

Answer:

48 feet

Step-by-step explanation:

Distance = rate × time

d = 12 ft/min × 4 min

d = 48 ft

The diver will be 48 feet below the surface.

Answer:

-48 ft

Step-by-step explanation:

The unit rate of descent is

  -12 ft

-----------

  1 min

and so after 4 minutes, the diver will be 48 ft beneath the surface:

  -12 ft

----------- * 4 min = -48 ft

  1 min