Train a leaves station traveling at 40 mph. Eight hours later train b leaves the same station traveling in the same direction at 60mph. how long does it take for train b to catch up to train a?What would the formula look like to reach the desired answer?
Thank you! :)

Answers

Answer 1

Answer: $v_1=40\ mph\nv_2=60\ mph\nt_2=t_1-8\n\nv=(s)/(t)\to s=vt\n\ns_1=s_2\n\nv_1t_1=v_2t_2\n\nv_1t_1=v_2(t_1-8)$

$40t_1=60(t_1-8)\n\n40t_1=60t_1-480\n\n40t_1-60t_1=-480\n\n-20t_1=-480\ \ \ \ /:(-20)\n\nt_1=24\ (h)\n\nt_2=24-8=16\ (h)\n\nAnswer:16h.$

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Ryker is given the graph of the function y= 1/2x^2 - 4 . He wants to find the zeros of the function but is unable to read them exactly from the graph. Find the zeros give answer to nearest tenth

Answers

Answer:

x= 2.8 and x= -2.8

Step-by-step explanation:

$y=(1)/(2)x^2-4$

To find out the zeros, we replace x y with 0 and solve for x

$0=(1)/(2)x^2-4$

Add 4 on both sides

$4=(1)/(2)x^2$

Multiply by 2 on both sides

8= x^2

Now we take square root on both sides

x= +- $√(8)$

x=2.82843 and x=-2.82843

x= 2.8 and x= -2.8

$y=(1)/(2)x^2-4\n\nzeros\ when\ y=0\n\n(1)/(2)x^2-4=0\n\n(1)/(2)x^2=4\ \ \ \ /\cdot2\n\nx^2=8\n\nx=-\sqrt8\ and\ x=\sqrt8\n\n\underline{\underline{x\approx-2.8\ and\ x\approx2.8}}$

A rectangle has a perimeter of 80 feet. Its height is 5 feet shorter than 4 times its base. What are thedimensions (both base and height) of this rectangle?

Answers

Answer:

Let the height be x feet and the base be y feet

1st equation:

2(x+y)=80

x+y=40

2nd equation:

x=4y-5

x-4y=-5

Solution of the 1st and the 2nd equation:

x+y=40.1

x-4y=-5.-1

_________

x+y=40

-x+4y=5

_________

5y=45

y=9

x+y=40

x+9=40

x=40-9

x=31

. . The height is 31 feet and the base is 9 feet

Answer:

7 feet is the width, and 33 feet is the length.

Step-by-step explanation:

Brainliest would be great

Two angles are complementary. They have measures of (7x + 2)° and (3x – 2)°, respectively. What is the value of x?180
90
9
10

Answers

Answer:

Option (c) is correct.

The value of x is 9.

Step-by-step explanation:

Given : Two angles are complementary. They have measures of (7x + 2)° and (3x – 2)°, respectively.

We have to find the value of x.

Two angles are said to be complementary if the sum of measure of angle is 90°.

Given (7x + 2)° and (3x – 2)° are complementary angles.

That is sum of (7x + 2)° and (3x – 2)° is 90°

⇒ (7x + 2)° + (3x – 2)° = 90°

⇒ 7x + 2 + 3x - 2 = 90

⇒ 10x = 90

⇒ x = 9

Thus, the value of x is 9.

Hence, option (c) is correct.

$7x+2+3x-2=90\n 10x=90\n x=9$

1:2 = 4:8 The product of both the means and the extremes is

2
4
8
16

Answers

Answer:

Cross Products Property of Proportions states that the product of the means is equal to the product of extremes.

i,e $a : b : : c : d$

Also, in the proportion the first (a) and the last terms(d) are called the extremes, whereas the second(b) and the third terms(c) are called the means.

Given the proportion:

$1 : 2 = 4 : 8$

First term = 1

Second term = 2

Third term = 4

Fourth term = 8

By definition;

The product of means = $1 * 8 = 8$

The product of extremes = $2 * 4 = 8$

Therefore, the product of both the means and the extremes is, 8

lets say you have x:y=z:t
the means are y and z
the extremes are x and t
we have
1:2=4:8
means=2 and 4
extrememes=1 and 8
product of means=2 times 4=8
the product of extremes=1 times 8=8

the answer is 8

PLEASE HELP!! The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 195 grams of a radioactive isotope, how much will be left after 6 half-lives?
Use the calculator provided and round your answer to the nearest gram.

Answers

Answer:

3.047

Step-by-step explanation:

I'm not completely sure but i think its close

Final answer:

Applying the concept of half-life, if we start with 195 grams of a radioactive isotope, after 6 half-lives, we would be left with approximately 3 grams of the isotope.

Explanation:

The half-life concept is very important in Nuclear Physics, especially when we deal with Radioactive Isotopes. Regarding your question, if an isotope has a half-life, it means after each half-life, the quantity of the isotope decreases by half. So, to determine the remaining mass of a radioactive isotope after 6 half-lives, we have to consecutively halve the initial mass 6 times.

After the first half-life, 195 grams will become 97.5 grams.
After the second half-life, 97.5 grams will become 48.75 grams.
After the third half-life, 48.75 grams will become 24.375 grams.
After the fourth half-life, 24.375 grams will become 12.18 grams.
After the fifth half-life, 12.18 grams will become 6.09 grams.
After the sixth half-life, 6.09 grams will become around 3 grams (when rounded to the nearest gram).

So, after 6 half-lives, there will be approximately 3 grams of the isotope left.