Solve for x given BD = 4x+3 and AE = 4x+8. Assume B is the midpoint of segment AC and D is the midpoint of segment CE.

Answer:

The solution to the system would be (3, -1)

Step-by-step explanation:

You can find the solution to this system by using the elimination method. To do that, start by multiplying the top equation by -5 and then adding it through.

-5x + 20y = -35

5x + 9y = 6

-----------------

29y = -29

y = -1

Now that we have the value of y, we can plug it into either equation and find the x value.

x - 4y = 7

x - 4(-1) = 7

x + 4 = 7

x = 3

Final answer:

The solution to the given system of equations is the ordered pair (3, -1).

Explanation:

To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

1. Solve the first equation for x:

x = 7 + 4y

2. Substitute this value of x into the second equation:

5(7 + 4y) + 9y = 6

3. Simplify and solve for y:

35 + 20y + 9y = 6

29y = -29

y = -1

4. Substitute the value of y back into the first equation to find x:

x = 7 + 4(-1)

x = 3

Therefore, the solution to the system is the ordered pair (3, -1).

Answer:

46%  of Xander's friends prefer to stay home on Friday nights.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]

i.e

Zanders friends prefer to stay home on Friday night = 23

Total numbers of Zanders friends are 50.

Part value = 23

Total value = 50

Put in the formula

[tex]Percentage = \frac{23\times 100}{50}[/tex]

[tex]Percentage = \frac{2300}{50}[/tex]

Percentage = 46%

Therefore 46%  of Xander's friends prefer to stay home on Friday nights.

Answer:

wasdd ada

Step-by-step explanation:

Answer:

It is true

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

since y is inversely proportional to x the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportionality

to find k use the given condition when y = 7, x = 9

k = yx = 7 × 9 = 63

y = [tex]\frac{63}{x}[/tex] ← is the equation connecting them

when x = 21, then

y = [tex]\frac{63}{21}[/tex] = 3

The equation connecting y and x is y = 9 + 3x. When x = 21, y = 72.

The equation connecting y and x is given by y = 9 + 3x. In this equation, the constant term, also known as the y-intercept, is 9. The coefficient of x, also known as the slope, is 3. This means that for every increase of 1 in x, y increases by 3.

To calculate the value of y when x = 21, substitute x = 21 into the equation: y = 9 + 3(21) = 9 + 63 = 72. Therefore, when x = 21, y = 72.

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Answer: 15

Step-by-step explanation:

 Boys  :  Girls

    3x   +   1x    = 60

4x = 60

 x = 15

Girls (1x) = 1(15) = 15

Answer:

The answer is 15

Answer:

18.91 percent

Step-by-step explanation:

Percent error equation:     Difference       or    Difference/Actual

                                            Actual

The difference is the greater amount minus the smaller.

111 - 89 = 22

The actual is 111.

Now divide 22/111.

22/111 = 0.189 repeating

0.189 repeating = about 18.91 percent

Good Morning!

Distance = rate x time

1/2 mile = R x 2/5 hour

1/2=2/5R

/2/5 /2/5

R=1/2 x 5/2

R=1 1/4

She can swim 1 1/4 per hour.

I hope this helps! :)

Answer:

1 1/4

Step-by-step explanation:

Answer:

(x, y) = (- 3, - 2)

Step-by-step explanation:

given the 2 equations

5x + 7y = - 29 → (1)

y = x + 1 → (2)

substitute y = x + 1 into (1)

5x + 7(x + 1) = - 29 ( distribute and simplify left side )

5x + 7x + 7 = - 29

12x + 7 = - 29 ( subtract 7 from both sides )

12x = - 36 ( divide both sides by 12 )

x = - 3

substitute x = - 3 into (2)

y = - 3 + 1 = - 2

solution is (- 3, - 2 )

Answer:

(-3,-2)

Step-by-step explanation:

Answer:

C. 2x^2 - 85 / 13

Answer:

I am 99% sure the answer is f(x)= 4x + 5

Step-by-step explanation:

That is because the line intercepts y at 5 and every 4 cubes the line hits a corner...

Answer:

F(x)=4x +5

Step-by-step explanation:

Answer:

arc ≈ 25.13 feet

Step-by-step explanation:

arc length = circumference × fraction of circle

= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π

= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet

Answer:

The required simplest form is: [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

We have been given Kyle has 125 marbles.

And 50 out of total 125 are red and rest of them are other colours

that means other colour marble are 125-50=75

we need to find ratio of the number of red marbles to the total of marbles  

The rat io is: [tex]\frac{50}{125}=\frac{2}{5}[/tex]

The required simplest form is: [tex]\frac{2}{5}[/tex]

Answer:

Step-by-step explanation:

2/5

Answer:

Volume of a in z = 876 ounces

Step-by-step explanation:

For z, the ratio of x and y is 3 : 11

x : y = 3 : 11 , which means in 14 parts of solution z : x will be 3 parts and y will be 11 parts

So, in 2520 ounces solution of z ,

[tex]x=\frac{2520*3}{14}=540\\y=\frac{2520*11}{14}=1980[/tex]

Volume of a in z = { Volume of a in x + Volume of b in x }

Therefore,

[tex]Volume \thinspace of \thinspace a\thinspace in\thinspace x = 540\cdot \frac{2}{5} = 216\\Volume \thinspace of \thinspace b \thinspace in \thinspace x = 1980\cdot \frac{1}{3}=660[/tex]

So, Volume of a in z = 876 ounces

l - lenght

w - width

l - w = 5 → l = 5 + w

26 m - perimeter

l + l + w + w = 2l + 2w - perimeter

substitute l = 5 + w:

2(5 + w) + 2w = (2)(5) + (2)(w) + 2w = 10 + 2w + 2w = 10 + 4w

The equation:

10 + 4w = 26     subtract 10 from both sides

4w = 16    divide both sides by 4

w = 6

Answer:

f(t) = 451,400(0.968)^t

Step-by-step explanation:

Exponential Decay Function:

y = b (1-r) ^t

where

f(t)= 451,400 ( 1 - 0.032) ^t

f(t) = 451,400 (0.968) ^t

Answer:

This was the correct answer, I even provided proof from my own test. Hope this helps!

Step-by-step explanation:

The largest possible value for (a.bc + 0.d) is (10.56).

The largest possible value for (a.bc + 0.d) when (a), (b), (c), and (d) are replaced by four different digits from 1 to 9, inclusive, can be found by selecting the largest digits for (a), (b), and (c), and the smallest digit for (d).

This results in the number (9.86 + 0.7), which equals (10.56).

Therefore, the largest possible value for (a.bc + 0.d) is (10.56).

Complete question:

If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?

Answer:

a = 15, b = 7, c = 5, d = 10, e = 12

Step-by-step explanation:

You only need to find d.

22+d=32, d=10

Only one choice has d=10

Don't waste time checking the others.

Answer:

It’s B

Step-by-step explanation:

Answer:

a   -5/2 <=x

Step-by-step explanation:

5(x-2) <= 9x

Distribute the 5

5x -5*2 <= 9x

5x-10 <= 9x

Subtract 5x from each side

5x-5x-10 <= 9x-5x

-10 <= 4x

Divide by 4 on each side

-10/4 <=4x/4

-5/2 <=x

Answer:

all of the above

Step-by-step explanation:

Every one of these functions is defined for all values of x.

All the provided functions: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, have a domain of all real numbers. This means any real value can be input into these functions to get a real output.

The domain of a function is the set of all possible input values (usually represented by x) that will give an output value. In this case, we are asked to identify which of the provided functions have a domain of all real numbers. For the functions given: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, all of them have a domain of all real numbers. This is because no matter what value of x you choose, these functions will always provide a valid output of y. In other words, you can input any real number into these functions and get a real number out.

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Answer:

A.  F(x) = x^3+9x^2+27x+27

Step-by-step explanation:

I am not 100% sure but I think this is right.

I found the root for this equation: x=-3

Hope this helps!

Answer:

The correct option is D.

Step-by-step explanation:

In option A,

The given function is

[tex]F(x)=x^3+9x^2+27x+27[/tex]

[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]

[tex]F(x)=(x+3)^3[/tex]              [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]

The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.

In option B,

The given function is

[tex]F(x)=x^3+3x^2-9x-27[/tex]

[tex]F(x)=x^2(x+3)-9(x-3)[/tex]

[tex]F(x)=(x^2-9)(x+3)[/tex]

[tex]F(x)=(x+3)(x-3)(x+3)[/tex]         [tex][\because a^2-b^2=(a+b)(a-b)][/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]

Therefore, this function has 3 real roots.

In option C,

The given function is

[tex]F(x)=x^3-9x^2+27x-27[/tex]

[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]

[tex]F(x)=(x-3)^3[/tex]              [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]

Equate the function equal to zero, to find the roots.

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

The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.

In option D,

[tex]F(x)=x^3+3x^2+9x+27[/tex]

[tex]F(x)=x^2(x+3)+9(x+3)[/tex]

[tex]F(x)=(x+3)(x^2+9)[/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x^2+9)=0[/tex]

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

[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]

The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.

Answer:

Two real solutions

Step-by-step explanation:

z=-1.45

z=0.45

Answer:

ANSWER: Two real solutions

Step-by-step explanation:

its z=-1.45

its z=0.45

4.42×10^34 molecules/min

Multiply the various factors, along with the unit conversion (60 s/min).

... (3.35×10^25 molecules/L) × (2.2×10^7 L/s) × (60 s/min)

... = (3.35×2.2×60)×10^(25+7) molecules/min

... = 442.2×10^32 molecules/min

... ≈ 4.42×10^34 molecules/min

_____

Comment on scientific notation problems

Your scientific or graphing calculator will allow you to enter and display numbers in scientific notation.

Answer:

Number of​ restaurant-purchased meals eaten in a​ restaurant = 70

Number of​ restaurant-purchased meals eaten in a​ car = 22

Number of​ restaurant-purchased meals eaten in a​ home = 60

Step-by-step explanation:

Let the number of people that will eat in a restaurant be R.

Let the number of people that will eat in a car be C.

Let the number of people that will eat in a home be H.

From the information given in the problem we have,

R+C+H = 152 ____equation (1)

C+H-R = 12 ____equation (2)

R = H+10 ____equation (3)

1) Plugging in R=H+10 from equation 3 into the equation 2, we get

C+H-R=12

=> C+H-(H+10)=12

=> C+H-H-10=12

2) Cancelling out +H and -H, we get

C-10=12

3) Add 10 to both sides

C-10+10=12+10

4) Cancelling out -10 and +10, we get

C=22

5) Plugin C=22 in equation 1, we have

R+C+H = 152

=> R+22+H=152

Subtract 22 from both sides,

R+22+H-22=152-22

Cancelling out +22 and -22 from the left side, we get

R+H=130 ____let it be equation (4)

6) Plugin C=22 in equation 2, we have

C+H-R = 12

22+H-R = 12

Subtracting 22 from both the sides, we get

22+H-R-22 = 12-22

Cancelling out +22 and -22 from the left side,

H-R = -10 ____let it be equation (5)

7) Adding equation 4 and equation 5, we get

(R+H)+(H-R) = 130 + (-10)

=> R+H+H-R = 130-10

8) Cancelling out R and -R from the left side, we get

2H = 120

9) Dividing both sides by 2, we get

[tex]\frac{2H}{2} = \frac{120}{2}[/tex]

10) Cancelling out the 2's from the left side, we have

H=60

11) Plugging in C=22 and H=60 in the equation 1, we have

R+C+H = 152

=> R+22+60=152

=> R + 82 = 152

12) Subtracting 82 from both the sides, we get

R + 82 -82 = 152 -82

13) Cancelling out +82 and -82 from the left side, we get

R = 70

So, C=22, H=60, R=70

Answer:

35 + 5h = m

Step-by-step explanation:

Answer: 243, 729

Step-by-step explanation:

1, 3, 9, 27, 81    is a geometric sequence where r = 3

a₁ = 1

a₂ = 1 x 3 = 3

a₃ = 3 x 3 = 9

a₄ = 9 x 3 = 27

a₅ = 27 x 3 = 81

To find the next two terms, multiply the previous term by 3:

a₆ = 81 x 3 = 243

a₇ = 243 x 3 = 729

Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.

The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.

This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.

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Answer:

Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0 = tan θ = -1/5

Step-by-step explanation:

cos θ = 5/√26  

opposite side = s  

s^2 = 26-25 = 1  

s = -1  

tan θ = -1/5

Answer:

the bacteria's population is 120

Step-by-step explanation:

Answer:

After 40 hrs it is 213.333 bacterias

Approximately 213 bacterias

Step-by-step explanation:

Initial population of bacteria is 40

And it doubles every 15 hrs

If 15 hrs is double

1 hrs is 0.13333

Then 10 hrs is 1.3333

So the first 15 hrs

It multiplies to 40*2= 80

The second 15 hrs it multiplies by 80*2=160

The next 10 hrs it multiplies by

160*1.33333= 213.333

In a depreciation equation, you multiply the value of the car by the percent of depreciation minus 1.

In the given equation you are multiplying the value of the car by (.85)

This means the percent of depreciation would be 1 - 0.85 =0.15 which is 15%

The car depreciates by 15% every year.

Answer:

The car depreciates by 15% every year.

Step-by-step explanation: