help me with this math question

Velocity, distance and time:

This question is solved using the following formula:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

On the first day of travel, a driver was going at a speed of 40 mph.

Time [tex]t_1[/tex], distance of [tex]d_1[/tex], v = 40. So

[tex]v = \frac{d}{t}[/tex]

[tex]40 = \frac{d_1}{t_1}[/tex]

The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles

On the second day, the velocity is [tex]v = 60[/tex].

On the first day, he drove 2 more hours, which means that for the second day, the time is: [tex]t_1 - 2[/tex]

On the first day, he traveled 20 more miles, which means that for the second day, the distance is: [tex]d_1 - 20[/tex]

Thus

[tex]v = \frac{d}{t}[/tex]

[tex]60 = \frac{d_1 - 20}{t_1 - 2}[/tex]

System of equations:

Now, from the two equations, a system of equations can be built. So

[tex]40 = \frac{d_1}{t_1}[/tex]

[tex]60 = \frac{d_1 - 20}{t_1 - 2}[/tex]

Find the total distance traveled in the two days:

We solve the system of equation for [tex]d_1[/tex], which gets the distance on the first day. The distance on the second day is [tex]d_2 = d_1 - 20[/tex], and the total distance is:

[tex]T = d_1 + d_2 = d_1 + d_1 - 20 = 2d_1 - 20[/tex]

From the first equation:

[tex]d_1 = 40t_1[/tex]

[tex]t_1 = \frac{d_1}{40}[/tex]

Replacing in the second equation:

[tex]60 = \frac{d_1 - 20}{t_1 - 2}[/tex]

[tex]d_1 - 20 = 60t_1 - 120[/tex]

[tex]d_1 - 20 = 60\frac{d_1}{40} - 120[/tex]

[tex]d_1 = \frac{3d_1}{2} - 100[/tex]

[tex]d_1 - \frac{3d_1}{2} = -100[/tex]

[tex]-\frac{d_1}{2} = -100[/tex]

[tex]\frac{d_1}{2} = 100[/tex]

[tex]d_1 = 200[/tex]

Thus, the total distance is:

[tex]T = 2d_1 - 20 = 2(200) - 20 = 400 - 20 = 380[/tex]

The total distance traveled in two days was of 380 miles.

For the relation between velocity, distance and time, you can take a look here: https://brainly.com/question/14307500

Answer:

Total traveled distance is : 380 miles

Step-by-step explanation:

Let´s call variables of the first day of travel as:

v₁ = 40 mph

Time of travel  unknown but 2 hours more than the second day

Traveled distance ( unknown) but 20 miles more than the second day

And for the second day

v₂ = 60 mph

Time of travel t

Traveled distance s (unknown)

With that information, we can make a model of a two equations system as follows:

We know that s = v*t ( where s is the distance traveled, v the speed, and t the traveled time) then

First day  

Total distance traveled s + 20 is equal to:

s + 20 = 40 * ( t + 2 )

The second day:

s = 60*t

The system is:

s + 20 = 40 * ( t + 2 )

s = 60*t

By substitution

60*t + 20 = 40 * ( t + 2 )

60*t + 20 = 40*t + 80

60*t - 40*t = 80 - 20

20*t = 60

t = 3 hours

Now we can calculate the total distance traveled according to:

First day:  s₁ = 40 (m/h)* (t + 2) (h) = 40*5 miles      s₁ = 200 miles

Second day:

s = 60*t   =  60 (m/h)*3 (h)  =  180 miles

Total distance is : 380 miles

Answer:

it appears to be  FALSE....

f(g(x) = 3(13-2x) -7 = 39 - 6x - 7 = 32 - 6x

h(32-5x) = 6(32-6x)

= 192 - 36x

Step-by-step explanation:

Answer:

This gives us a pair of simple equations:

100percent =150(1). xpercent =114(2).

therefore, 114 is 76percent of 150

Step-by-step explanat:

Given:

Rate of interest = 8% compounded continuously.

Amount = 100,000

Time = 25 years

To find:

The principal value.

Solution:

Formula for amount after continuous compound interest:

[tex]A=Pe^{rt}[/tex]

Where, A is amount, P is principal, r is the rate of interest and t is the number of years.

Putting [tex]A=100000, r=0.08, t=25[/tex] in the above formula, we get

[tex]100000=Pe^{0.08(25)}[/tex]

[tex]100000=Pe^{2}[/tex]

[tex]\dfrac{100000}{e^{2}}=P[/tex]

[tex]\dfrac{100000}{7.389056}=P[/tex]

On further simplification, we get

[tex]P\approx 13533.528[/tex]

Therefore, the amount 13533.528 is invested.

Answer:

x = 18

Step-by-step explanation:

Since BD bisects ∠ ABC , then

∠ ABD = ∠ DBC = 79°

∠ ABC = ∠ ABD + ∠ DBC , that is

9x - 4 = 79 + 79 = 158 ( add 4 to both sides )

9x = 162 ( divide both sides by 9 )

x = 18

Answer:  Choice A

Explanation:

Notice how the numerators (2,4,6,8) are multiples of 2. So we can say that they are of the form 2k, where k is a whole number from 1 to 4.

If k = 1, then 2k = 2*1 = 2

If k = 2, then 2k = 2*2 = 4

and so on until we reach k = 4 and 2k = 8.

Similarly, the denominators are also multiples of 2. We shift things 1 spot to the right. So we start with 4 instead of 2. So we need to add on 2

If k = 1, then 2k+2 = 2*1+2 = 4

If k = 2, then 2k+2 = 2*2+2 = 6

and so on.

[tex]\displaystyle \sum_{k=1}^{4}\frac{2k}{2k+2} = \frac{2}{4}+\frac{4}{6}+\frac{6}{8}+\frac{8}{10}[/tex]

Taking into account the total amount of money spent on the games and the money that Tyrell had left after he bought the video games, Tyrell started with $541.

First you must know the total amount of money spent on the games. For that Tyrell bought 6 video games this summer and each game cost 27 dollars.

So to calculate the amount spent, the number of games purchased must be multiplied by the price of each one:

6 video games* 27 dollars each game= 162 dollars

So Tyrell spends 162 dollars.

On the other hand, you know that Tyrell had 379 dollars left after he bought the video games.

This indicates that after spending $ 162 on video games, there were $ 379 left over.

To know the amount of money that Tyrell had, you must add the amount spent on games and the money that was left over:

162 dollars + 379 dollars= 541 dollars

So, Tyrell started with $541.

Learn more with this similar examples:

Tyrell started with 541 $

There are two actions in the question.

First Tyrell bought 6 video games, each game cost 27 $.

Spent

According to that Tyrell spent

6 * 27 = 162 $

Keeps

The second fact is that after shopping Tyrell keeps 379 $.

If Tyrell spent 162 $ and still keeps 379 $, that means that the total amount of money Tyrell had is the sum of the money he spent plus the money he has

Now if we call "x" the quantity of money Tyrrel started with: Then

x  =  the money Tyrell spent on video games  plus the remaining 379 $

Then

x  =  162  + 379

x = 541 $

Answer:

To find the greatest common factor of two monomials, first find the prime factorization of each monomial, including all the variables (and a – 1 factor if necessary). Then take the product of all common factors. First, find the prime factorization of each monomial. So, the GCF is 3p2r3 .

Step-by-step explanation:

Answer:

you need 4 oz. to get the even 6 oz.

Answer:

z =   3 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

z = [tex]\frac{k}{x^{1/3} }[/tex]

5 = [tex]\frac{k}{4}[/tex]

k= 20

~~~~~~~~~~~~~~~

z = [tex]\frac{20}{6}[/tex]

z =  [tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]

Similar: yes

Similarity Statement: AB ~ TQ , BC ~ QR

Scale Factor: 4/3

Answer:

32/33

Step-by-step explanation:

We first need to find out how many square yards are vacuumed every one minute.

Let's set up a chart:

yards        minutes

8/11      -->    3/4

y          -->     1

Here, y is the number of yards it takes to vacuum in one minute. Next, we can use cross-multiplication to find out y.

1. Multiply 1 by 8/11 to get... 8/11

2. Multiply 3/4 by y to get... 3/4y

3. Equate them: 8/11 = 3/4y

4. Divide both sides of the equation by 3/4 OR multiply both sides of the equation by 4/3 to isolate y, the variable

5. This gives us 32/33 = y

Answer:

The volume of the figure is 905 cubic units.

Step-by-step explanation:

Rotation is a method of solid transformation which involve turning a given line, or object about a reference point. In the given question, rotating segment AB completely about the y-axis would form a 3 dimensional figure of a sphere.

volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius of the sphere.

Given that AB = 6, then the radius of the sphere = 6

volume of sphere = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](6)^{3}[/tex]

                              = [tex]\frac{88}{21}[/tex] x 216

                              = 905.14

volume of sphere = 905 cubic units

The volume of the figure is 905 cubic units.

Step-by-step explanation:

If it is a leap year =366

and if it is not a leap year=365

Answer:

365

Step-by-step explanation:

Answer:

3/16

Step-by-step explanation:

-3*-1=3, 4*4=16

Answer:

3/16

Step-by-step explanation:

Multiply both the numerators (top number) and denominators (bottom numbers) together

-3 x -1 = 3....bc negative times negative always equals positive

4 x 4 = 16

Answer:  Choice A

x = 19, RZ = 49, and RT = 98

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

How to get that answer:

Z is the midpoint of RT. This midpoint splits segment RT into two equal pieces RZ and ZT

RZ = ZT

4x-27 = 49

4x = 49+27

4x = 76

x = 76/4

x = 19

So far, we can see that the answer is either choice A or choice D.

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

If x = 19, then

RZ = 4x-27

RZ = 4*19-27

RZ = 76 - 27

RZ = 49

Which points us to Choice A as the final answer

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

We could skip the second section entirely because we initially set RZ equal to ZT, and ZT was 49. However, I showed that section to help confirm that we had the correct x value.

Also,

RT = RZ + ZT

RT = 49 + 49

RT = 98

Step-by-step explanation:

First, we may wonder, what does the term margin of error mean? Put simply, the margin of error is a measure of the degree to which research results do not reflect the views of the total studied population. In other words, it tells readers how much confidence they should have in the results presented.

It has often been suggested that a fundamentally and conceptually effective way that is always under the control of the researcher of making the margin of error smaller is to increase the sample size of the research. This basically involves collecting more sample data which thus leads to a closer estimate of the view of the entire population.

Answer:

you save $500 for 7 years at 6% compounding continuously

what is the final value...

A = $500 [tex]e^{.06(7)}[/tex]

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

KL + KJ = 17

2 + 3x + 5x - 1 = 17 add like terms

8x + 1 = 17 subtract 1 from both sides

8x = 16 divide both sides by 8

x = 2

KL = 5x - 1 replace x with 2

5*2 - 1 = 9

Answer:

y = -2x -3

Step-by-step explanation:

- the altitude trough F is a perpendicular line to the line DE

- find slope of line DE

D ( x2 = -5, y2 = -1); E (x1 = 3, y1 = 3)

slope m = (y2-y1) / (x2-x1) = (-1-3) / (-5-3) = -4/ -8 = 1/2

-find equation of the altitude trough F

lines that are perpendicular have the slope negative reciprocal (negative reciprocal of 1/2 is -2)

y= -2x +b , for point F(1, -5)

-5 = -2*1 +b, add 2 to both sides

-5 +2 = b, combine like terms

-3 =b

equation of the altitude trough F is y = -2x -3

Answer:

5:05

6

10

Step-by-step explanation:

3:30 + 1 hour = 4:30

4:30 + 35 mins = 5:05 pm

5 days per 1 gallon, 30 days for :

30/5 = 6

500/50 = 10

Answer:

The answer is "1.75".

Step-by-step explanation:

Given:

[tex]\to 4u + 10 =17[/tex]

Find:

[tex]\to u = ?[/tex]

Solution:

[tex]\to 4u + 10 =17\\\\\to 4u = 17-10\\\\\to 4u = 7\\\\\to u = \frac{7}{4}\\\\\to u=1.75[/tex]

Thank You! Hope it helps! Please mark me brainliest!

Answer:

The margin of error is of 1.5 milligrams.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Standard deviation of 9

This means that [tex]\sigma = 9[/tex]

Sample of 130

This means that [tex]n = 130[/tex]

Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content of all such eggs.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.96\frac{9}{\sqrt{130}}[/tex]

[tex]M = 1.5[/tex]

The margin of error is of 1.5 milligrams.

Answer:

D

Step-by-step explanation:

He needs to buy 6 items

6 bags of chips

6*2.25= $13.5 so not possible

6 candy bars

6*1.5= $9 so possible

These statements knock out B and C because the dark gray needs to be able to include 6 on the y-axis to show that he could buy 6 candy bars leaving D and A. However, in D it shows that he could actually buy more than 6 candy bars and buy 8 which leaves him with 0 dollars left

8*1.5=$12

Answer:

Step-by-step explanation:

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Step 1:  Add 79 to both sides

[tex]10x - 79 + 79 = 2x + 49 + 79[/tex]

[tex]10x = 2x + 128[/tex]

Step 2:  Subtract 2x from both sides

[tex]10x - 2x = 2x - 2x + 128[/tex]

[tex]8x = 128[/tex]

Step 3:  Divide 8 from both sides

[tex]\frac{8x}{8} = \frac{128}{8}[/tex]

[tex]x = 16[/tex]

Answer:  [tex]x = 16[/tex]

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Step-by-step explanation:

x=16

Answer:

Area= 2000 feet^2

Step-by-step explanation:

Know how to find the perimeter and the area of a rectangle

area=length*width

perimeter= 2*length + 2*width

Draw a rectangle

The question states that the pasture is 50 feet long

So the length of the rectangle pasture should be 50. We can label the 2 lengths of the rectangle to be 50 feet long

Since the farmer only has 160 feet of fence, we can say that because the pasture is a rectangle, we can label the width as 40 because 2*50+2*40=160

Now that we know the length and width, we can find the area by multiplying those 2 values together to get 2000

Answer:

[tex]\boxed{\sf Distance_{AB}= 8.24 \ units }[/tex]

Step-by-step explanation:

Here two points are given to us and we need to find the distance between the two points . The given points are , A(0,0) and B(8,2) . The distance between the two points can be found out using the Distance Formula , which is ,

Distance Formula:-

[tex]\sf\implies \green{ Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Therefore on substituting the respective values ,we can find the Distance as ,

[tex]\sf\longrightarrow Distance = \sqrt{ ( 0 - 8)^2 + (0-2)^2} [/tex]

Simplify the brackets ,

[tex]\sf\longrightarrow Distance =\sqrt{ (-8)^2+(-2)^2}[/tex]

Square the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance =\sqrt{ 64 + 4} [/tex]

Add the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance = \sqrt{68} [/tex]

Find the value of squareroot,

[tex]\sf\longrightarrow \boxed{\blue{\sf Distance = 8.24 \ units }}[/tex]

Hence the distance between the two points is 8.24 units .