PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A passenger and a freight train start toward each other at the same time from
two points 300 miles apart. If the rate of the passenger train exceeds the rate
of the freight train by 15 miles per hour, and they meet after 4 hours, what
must the rate of each be?

Answer:

43.

Step-by-step explanation:

Follow PEMDAS (Parentheses, exponents, multiply, divide, add, subtract). First you do 8-4 which is 4, then you multiply 4 by 4 which is 16 since you multiply next, then you add 27 to 16 which then gets you to 43.

Answer:

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]

Step-by-step explanation:

Given

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

[tex]g(x) = \sqrt{11 - 4x[/tex]

See attachment

Solving (a): (g + f)(2)

This is calculated as:

[tex](g + f)(2) = g(2) + f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g + f)(2) = g(2) + f(2)[/tex]

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

Solving (b): [tex](\frac{f}{g})(-1)[/tex]

This is calculated as:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

Calculate f(-1) and g(-1)

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = \frac{0}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

Solving (c): (g - f)(-1)

This is calculated as:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

Calculate g(-1) and f(-1)

[tex]g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}[/tex]

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

[tex](g + f)(-1) = \sqrt{15} - 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

Solving (d): (g * f)(2)

This is calculated as:

[tex](g * f)(2) = g(2) * f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g * f)(2) = g(2) * f(2)[/tex]

[tex](g * f)(2) = \sqrt 3 * -3[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]

Answer:

sub duplicate ratio of

hope it helps

Answer:

The mass of Element X will reach 62 grams in 7.0 years.

Step-by-step explanation:

We can find the time of decay of Element X by using the exponential decay equation:

[tex] \frac{dm}{dt} = -\lambda t [/tex]

The solution of the above equation is:

[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex]     (1)

Where:  

t: is the time =?

λ: is the decay constant                                                                                        

[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams

[tex]m_{0}[/tex]: is the initial mass = 90 grams

First, we need to calculate λ

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]   (2)    

Where [tex]t_{1/2}[/tex] is the half-life = 13 years

By entering equation (2) into (1) and solving for "t" we have:

[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]    

[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]      

[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]  

Therefore, the mass of Element X will reach 62 grams in 7.0 years.

I hope it helps you!

Answer:

The answer is D

......(don't mind this it's because it says that it needs to be 20 characters long) but the answer is D

[tex]1\frac{1}{2}[/tex] [tex]batches[/tex]

➛➛➛➛➛

[tex]\frac{1/2}{1} =\frac{3/4}{x}[/tex]

[tex]\frac{1}{2} =\frac{3}{4x}[/tex]

[tex]cross~multiply[/tex]

[tex]4x=2(3)[/tex]

[tex]\frac{4x}{4} =\frac{6}{4}[/tex]

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

Answer:

32 cartons

Step-by-step explanation:

Total sets needed

48 + 43 + 46 + 50 = 187

Cartons needed

187 / 6 = 31 1/6

need 32 cartons

Answer:

32 cartons

Step-by-step explanation:

add up all of the students = 187

divide by 6 = 187/6 = 31.16

round = 32 cartons

Answer:

95 square units

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 19

h = 10

Work:

A = 0.5bh

A = 0.5(19)(10)

A = 9.5(10)

A = 95

Hi there!

[tex]\large\boxed{x = -1}[/tex]

We can solve by multiplying each term to get a common denominator:

[tex]\frac{1}{x - 4} + \frac{x}{x - 2} = \frac{2}{x^2-6x+8}[/tex]

[tex]\frac{x -2}{(x - 4)(x - 2)} + \frac{x(x - 4)}{(x - 2)(x - 4)} = \frac{2}{x^2-6x+8}[/tex]

Since the denominators are all the same (x² - 6x + 8 factors to (x - 2)(x - 4)), we can ignore them temporarily and solve the numerator:

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

Simplify:

x - 2 + x² - 4x = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1) = 0

x = -1, 4

For the values of x to be a solution, they cannot cause the denominator to be equal to 0, so:

(x - 2)(x - 4) = 0

x = 2, 4. These values result in a denominator of 0, which is undefined.

Thus, the only solution is x = -1.

Answer:

∆ADE ≈ ∆ DCF

I hope this helps

Answer:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 divided by 10 = 5.5 around 5

Add all your numbers

Divide by the many numbers there are, go by the exact value or estimate if needed.

Answer:

c

Step-by-step explanation:

Interquartile range or IQR is the range of the "box" in the graph. So we have 54 and 36 so we subtract 54-36.

So we get 18.

Answer: 8 feet below sea level is higher

Step-by-step explanation:

Step-by-step explanation:

1*-2=-2, -2*-2=4, -2*4=-8, -8*-32=256

Answer:

I'm not 100% sure but I think its A

Answer: A would be your answer.

Step-by-step explanation: Internal conflict is when you have a problem with yourself and this means your not intercating with others.

Answer:

150.8 m³

48π m³

Step-by-step explanation:

V = πr²h/3

V = π · 4² · 9/3

150.8 m³

Answer:

4.5 cm

Step-by-step explanation:

KL = LM as triangle is isosceles

LM = KM as LF = FM = KN = NM, so the triangle is equilateral

EF ║ NM as LE⊥EF and LN⊥NM

EF is half the midsegment as ∠KLN ≅ ∠MLN, and LN is angle bisector of ∠KLM

Midsegment is half the side length, and all sides are 18 cm.

EF = 1/2(1/2*18) = 4.5 cm

Answer:

Step-by-step explanation:

n = 3

Answer: n= 3

Step-by-step explanation:

i hope this helped :))

Answer:

x=110˚

Step-by-step explanation:

We need to first find the other degree inside the triangle

first add 45˚ and 65˚

which is 110˚

subtract 110˚ with 180˚

which is 70˚

So we find x since a straight line is 180˚

subtract 70 and 180

which is 110˚

Hoped I helped!

Answer:

110 degrees

Step-by-step explanation:

A triangle is 180 degrees. So if the missing angle is 70, and 70+x=180 then x=110

Answer:

i think 11y

Step-by-step explanation:

Answer:

300 watermelons

Step-by-step explanation:

3:2 ratio

3 is water melons and 2 is mangoes.

200 mangoes were purchased.

200/2=100

The unit rate is 100, so multiply 3 by 100, which is 300.

So Jack bought 300 watermelons, and 298 of which will be devoured by yours truly.

---

hope it helps

Answer:

88

Step-by-step explanation:

10a-9=14a-25

10a-14a=-25+9

-4a=-16

a=4

10(4)-9+14(4)-25+6(4)+2

40-9+56-25+24+2

88

Answer:

AA

Step-by-step explanation:

AA

Answer:

15+ 8d

After d day,she has read 15 +8d pages

Answer:

The 1st step in evaluating the expression is doing the equation in the paranthesis. PEMDAS states we do the paranthesis 1st.

Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i

======================================================

Work Shown:

[tex]\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\[/tex]

Equating terms, we have this system

[tex]\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}[/tex]

Solve the second equation for b to get b = 5/a

Plug that into the first equation to solve for 'a'

[tex]24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\[/tex]

Setting each factor equal to zero would lead to...

We're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5

If a = 5, then,

b = 5/a = 5/5 = 1

So

[tex]\sqrt{24+10i} = a+bi = 5+1i = 5+i[/tex]

or in short,

[tex]\sqrt{24+10i} = 5+i[/tex]

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

If a = -5, then b = 5/a = 5/(-5) = -1

So it's very possible that we could also say

[tex]\sqrt{24+10i} = -5-i\\\\[/tex]

If you wanted to combine the two we would use the plus/minus notation like so

[tex]\sqrt{24+10i} = \pm(5+i)\\\\[/tex]

This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.

Answer:

24 area

18.80983669  perimeter

Step-by-step explanation:

1  (6*3/2)*2(1*3/2)+(4*3)

2 trust me

Answer: 13/4

Step-by-step explanation: it was 3.25 and that as a fraction is 13/4

3/4 + ( 1/3 × 6 ) + 1/2 =

3/4 + 2/4 + ( 2 ) =

3 + 2/4 + 8/4 =

5/4 + 8/4 =

5 + 8/4 =

13/4