Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark. How much shorter with their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead?

Answers

Answer 1

Answer:

If they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.

Step-by-step explanation:

Given that Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark, to determine how much shorter would their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead the following calculation must be performed, using the Pythagorean theorem:

14 ^ 2 + 48 ^ 2 = X ^ 2

196 + 2,304 = X ^ 2

√ 2500 = X

50 = X

14 + 48 - 50 = X

62 - 50 = X

Thus, if they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.


Related Questions

HELPPPPPPP
What is the value of x?

Answers

I.) 8
180 - 140 = 40.. divide that by 5 since it’s 5x, which’ ll leave you with 8.

Answer:

the angles are supplementary

so, 5x + 140 = 180

5x = 180 - 140

5x = 40

X = 40

5

X = 8

Which of the following relations is a function?
O A. {(2,- ), (-1, -1), (0,0), (1, 1)}
OB.{(2,0), (0, 3), (0, 1), (,1)
OC... {1-2, 1), (-1,0), (0, 1), (-2,2)}
OD. {(-2, 4), (-1, 1), (0,0), (1, 1)}
Reset
Next

Answers

Answer: D

Step-by-step explanation:

How many solutions does the function x^2+2x+2x=0

a. 0
b. 1
c. 2
d. 3​

Answers

Answer:

Equation is a quadratic equation (polynomial ax+by+c with highest degree 2), so it has two solutions.

Answer:

B. is correct because it only can go 1 way.

Step-by-step explanation:

The perimeter of a triangle is 44 inches. The length of one side is twice the length of the shortest side, and the length of the other side is eight inches longer than the length of the shortest side.
Choose a variable and tell what that variable represents.

Answers

Answer:

side a = Smallest = 9 inches

side b = 18 inches

side c = 17 inches

Step-by-step explanation:

The formula for the perimeter of a triangle = side a + side b + side c

side a = Smallest

The perimeter of a triangle is 44 inches.

The length of one side is twice the length of the shortest side

Hence:

b = 2a

The length of the other side is eight inches longer than the length of the shortest side.

Hence,

c = 8 + a

Hence, we substitute into the Intial formula

a + 2a + 8 + a = 44 inches

4a + 8 = 44

4a = 44 - 8

4a = 36

a = 36/4

a = 9 inches

Solving for b

b = 2a

b = 2 × 9 inches = 18 inches

Solving for c

c = a + 8

c = 9 inches + 8 = 17 inches

For a new study conducted by a fitness magazine, 265 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of 220 females was chosen Independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August perlod. During the September February period, participants consumed a mean of 23873 calories dally with a standard deviation of 192. During the March-August period, participants consumed a mean of 2412.7 calories daily with a standard deviation of 237.5. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a 90% confidence interval for the difference between the mean dolly calorie consumption of females in September-February and the mean dally calorie consumption Hy of females in March-August.

Answers

We can be 90% confident that the true difference between the mean daily calorie consumption of females in the September-February period and the mean daily calorie consumption of females in the March-August period falls within the range of 21460.3 to 23033.7 calories.

In this study conducted by a fitness magazine, two separate samples of females were chosen to investigate the difference in mean daily calorie consumption between two time periods: September-February and March-August. The first sample consisted of 265 females, and the second sample consisted of 220 females. The mean daily calorie consumption and standard deviations were calculated for each period. This information will be used to construct a confidence interval to estimate the difference between the mean daily calorie consumption of females in the two periods.

To construct a confidence interval for the difference between the mean daily calorie consumption of females in the September-February and March-August periods, we can use the formula:

Confidence Interval = (X₁ - X₂) ± (Z * SE)

Where:

X₁ and X₂ are the sample means of the two periods (September-February and March-August, respectively)

Z is the critical value associated with the desired confidence level (90% confidence level corresponds to Z = 1.645)

SE is the standard error of the difference between the means

First, let's calculate the sample means and standard deviations for each period:

For the September-February period: X₁ = 23873 calories, σ₁ = 192 (standard deviation), n₁ = 265 (sample size)

For the March-August period: X₂ = 2412.7 calories, σ₂ = 237.5 (standard deviation), n₂ = 220 (sample size)

Next, we calculate the standard error (SE) of the difference between the means using the formula:

SE = √((σ₁² / n₁) + (σ₂² / n₂))

Substituting the given values, we have:

SE = √((192² / 265) + (237.5² / 220))

Now, we can calculate the confidence interval using the formula mentioned earlier. With a 90% confidence level, the critical value Z is 1.645.

Substituting in the values, we get:

Confidence Interval = (23873 - 2412.7) ± (1.645 * SE)

Substituting the calculated value of SE, we can find the confidence interval:

Confidence Interval = (21460.3, 23033.7)

Therefore, we can be 90% confident that the true difference between the mean daily calorie consumption of females in the September-February period and the mean daily calorie consumption of females in the March-August period falls within the range of 21460.3 to 23033.7 calories.

Note: The confidence interval represents a range of values within which we believe the true difference lies, based on the given data and the selected confidence level.

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Simplify 2xy(4x+7-3y

Answers

Is it not just going to be distributed out into 8x^2+14xy-6xy^2

What single or double digit numbers make a SUM of 40?

Please help, I will award brainliest, rate, and thank. Please include all possible answers!!!

No links, no fake answers, you will be reported.

Answers

The sum numbers are 1, 2, 4, 5, 8, 10, 20, 40

calculate the power of the pump which can lift 400kg of water to be stored in a water tank at a height of 19m and 40s (take g=10/s2)​

Answers

Hi, here it is !
I hope this help...

Please help me! Only have about 10 minutes until I have to submit this assignment!

Answers

Answer:

626

Step-by-step explanation

The answer is 626 I think

state the equation of a line with slope m=2 and y intercept =3 then graph the line

Answers

Answer:

y=2x+3

The coefficient attached to x is the slope and the number being added to it is the y intercept.

Please see the attached image

How many solutions does the equation 5x + 3x – 4 = 10 have?
O Zero
O One
O TWO
O Infinitely many
be
????

Answers

Answer:

Step-by-step explanation:

Search...

1

cecewiliams23

08/12/2016

Mathematics

High School

answered

How many solutions does the equation 5x + 3x − 4 = 10 have

2

SEE ANSWERS

Answer

4.0/5

28

MathGeek289

Ambitious

236 answers

69.7K people helped

This Must Only Have One Solution, Because The Right Side Of The Equation Is Just Plainly Ten. Lets Solve This:

5x + 3x - 4 = 10

Add Four To Both Sides To Begin Simplifying.

5x + 3x = 14

Now, Combine Like Terms.

8x = 14

Divide:

8x/8 = 1X = X

14/8

X = 14/8

14/8 = 1.75

X = 1.75

Check:

(5 * 1.75) + (3*1.75) - 4 = 10

8.75 + 5.25 - 4 = 10

14 - 4 = 10

10 = 10.

This Is True, So X Does Equal 1.75

Drew needs to air up his teams 8 soccer balls. Each ball has a diameter of 70cm. In terms of pi, what is the total volume of air in all 8 soccer balls?

Answers

Answer:

1.44m^3

Step-by-step explanation:

Given data

Number of balls= 8

Diameter of ball = 70cm = 0.7m

Radius= 35cm= 0.35m

We know that a ball has a spherical shape

The volume of a sphere is

V= 4/3πr^3

substitute

V= 4/3*3.142*0.35^3

V= 0.18m^3

Hence if 1 ball has a volume of 0.18m^3

Then 8 balls will have a volume of

=0.18*8

=1.44m^3

ederal Government Employee E-mail Use It has been reported that 88% of federal government employees use e-mail. If a sample of 210 federal government employees is selected, find the mean, variance, and standard deviation of the number who use e-mail. Round your answers to three decimal places.

Answers

The mean, variance, and standard deviation of the number of federal government employees who use e-mail can be calculated using the binomial distribution formula.

Given that 88% of federal government employees use e-mail, we can define the probability of success (p) as 0.88 and the number of trials (n) as 210.

The mean of a binomial distribution is given by μ = np, where μ is the mean and n is the number of trials. Therefore, the mean of the number of federal government employees who use e-mail is μ = 210 * 0.88 = 184.8.

The variance of a binomial distribution is given by [tex]\sigma^2 = np(1-p)[/tex], where [tex]\sigma^2[/tex] is the variance and n is the number of trials. Therefore, the variance of the number of federal government employees who use e-mail is σ^2 = 210 * 0.88 * (1-0.88) = 21.504.

The standard deviation of a binomial distribution is the square root of the variance. Therefore, the standard deviation of the number of federal government employees who use e-mail is σ = sqrt(21.504) ≈ 4.637.

In summary, the mean of the number of federal government employees who use e-mail is 184.8, the variance is 21.504, and the standard deviation is approximately 4.637. These values represent the average, spread, and deviation from the mean, respectively, for the number of federal government employees who use e-mail in a sample of 210 individuals.

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how do you put this writing expression into a equation;

A number added to 13 all divided by 2

Answers

Answer:

Step-by-step explanation:

Let x be the number.

(x + 13)/2

Decide whether the given expression is a polynomial and tell why or why not.





5. 3x2 – 5x + 2

Answers

Answer:

3x² – 5x + 2 is a polynomial because:

Exponents are whole numbers, and the expression has at least 1 term.

Exponents other than whole numbers can take the form of variables in denominators, and roots which we don't want.

how do i find a unit rate​

Answers

Answer:

numerator divided by denominator

Step-by-step explanation:

numerator divided by denominator

1. What values of a, b, and c would you use in the quadratic formula for the following equation?
5x^2 +9x=4
A.a= -4, b = 9, c = 5
B.a=5, b= 9, c = -4
C.a=5, b= 4, c = 9
D.a= 5, b = 9, c=4​

Answers

Answer:

D

Step-by-step explanation:

because it is the answer that I think of

Write the equation of the
line that is parallel to
y = 1.5x – 6 and passes
through the point (4,2).

Answers

Heyoo. I hope this help! Feel free to ask me any questions if you need any more help. I also included a detailed explanation for the steps I did.

:)

The equation of the line is (y - 2) = 1.5(x - 4)

What is line ?

Euclid described a line as an "unextended length" that "stands equally with respect to its points"; he introduced the postulates as the main unprovable properties from which he constructed all of geometry, now called Euclidean geometry to avoid confusion with other geometries introduced from the late 19th century (such as non-Euclidean, projective and affine geometry).

In modern mathematics, given the multiplicity of geometries, the concept of line is closely related to the way geometry is described. For example, in analytic geometry, a plane line is often defined as a set of points whose coordinates correspond to a given linear equation, but in a more abstract setting, such as drop geometry, the line may be an object other than the set. of the points located on it.

When geometry is described by a set of axioms, the concept of line is usually left undefined (so-called primitive object). The properties of the lines are then determined by the axioms that refer to them. One of the advantages of this approach is the flexibility it gives users of the geometry. Thus, in differential geometry a line can be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and allows physicists, for example, to think of the path of a light ray as a line.

Given, [tex]y = 1.5x - 6....(1)[/tex]

We are comparing equation (1) with y = mx+c and get m = 1.5

It is also given required equation passes through the point (4,2)

We know, if slope of a equation m and the equation passes through (a,b) then equation of the line (y-b) = m (x-a)

Here,

[tex]m = 1.5 \\ a = 4 \\ b = 2[/tex]

So, required equation of the line [tex](y - 2) = 1.5(x - 4)[/tex]

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PLS PLE HELP IM BETYINY AND DONT GIVE ME THOSE LINKS THAT GIVE U A VIRUS

A small town is trying to establish a transportation system of large and small vans.
It can spend no more than $100,000 for purchasing both sizes of vehicles and no
more than $500 per month for maintenance. The town can purchase a small van for
$10,000 and maintain it for $100 per month. The large vans cost $20,000 each and
can be maintained for $75 per month. Each large van carries a maximum of 15
passengers
and each small van carries a maximum of 7 passengers. Find the
maximum number of passengers the transportation system can handle given the
constraints. How many large and small vans will they need to maximize the
number of passengers it can service?

Answers

i found this i hope it can help

Need someones help on this!

Answers

I think the answer is B hope this helps!

Find the values of x and y that make the quadrilateral a parallelogram.

Answers

Answer:

x= 114, y= 66

Step-by-step explanation:

Opposite angles of a parallelogram are equal

Help There are 7 red marbles and 5 blue marbles in a bag.
(a) What is the ratio of red marbles to blue marbles?
(b) What is the ratio of blue marbles to all marbles in the bag?

Answers

ratio of red to blue is : 7/5
ratio of blue to all is : 5/12
(a) 7:5 (red marbles to blue marbles)
(b) 7 + 5 = 12 total marbles
Ratio would be 5:12 (blue to total)







Find an equation of the plane tangent to the following surface at the given point. z=8-2x²-2y²; (5,3, – 60) Z=

Answers

z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).

Given the function is z=8-2x²-2y² and point is (5, 3, – 60).

We need to find the equation of the plane tangent to the given surface at the given point. The gradient vector of the function f(x, y, z) is given by(∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k∂f/∂x= -4x and ∂f/∂y= -4y

Therefore, the gradient vector is given by-4xi -4yj + k

Therefore, the equation of the tangent plane is given byz - z1=∇f(x1, y1) . (x - x1)i + ∇f(x1, y1) . (y - y1)j + (-1) [f(x1, y1, z1)]

where (x1, y1, z1) is the given pointWe have f(5, 3, – 60) = 8 – 2(5²) – 2(3²) = – 60

Therefore, the equation of the plane is given byz + 60= (-20i - 12j + k) . (x - 5) - (16i + 24j + k) . (y - 3)

Thus, z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).

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please explain clearly

Answers

The solution to the question

32 is 10% of what number?

Answers

32 is 10% of 320
To find the answer I multiplied 32 by 10
Brainliest would be nice

Mrs. Baxter deposits $2,000 in an account that earns 5% sample
interest, How much interest does Mrs Batter's investment en ter
8 years


The answer is $480!

Answers

Answer:

$800 in interest

Step-by-step explanation:

T = A(1 + rt)

T = 2,000(1 + .05(8))

T = 2,000(1.4)

T = 2800

2800 - 2000 = 800

What is the solution to this system

Answers

Answer:

the solution to the system is (1,3)

Step-by-step explanation:

x = 1 , y = 3

f(x) = = -X1 + X1X2 X2 – I1X2 Determine if this function is Lipschitz continuous (specify local or global). Note that this function is defined on R2.
Previous question

Answers

To determine if the function[tex]F(x) = -x1 + x1x2x2 - i1x2[/tex]is Lipschitz continuous, we need to examine its partial derivatives and check if they are bounded.

The function F(x) is defined on [tex]R^2,[/tex] so let's calculate its partial derivatives with respect to x1 and x2

∂F/∂x1 = [tex]-1 + x2^2[/tex]

∂F/∂x2 = [tex]x1x2 - i1[/tex]

Now, to determine Lipschitz continuity, we need to check if the partial derivatives are bounded on the given domain.

For ∂F/∂x1, we can see that it is not bounded because as x2 approaches positive or negative infinity, the value of ∂F/∂x1 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x1 is not bounded.

For ∂F/∂x2, we can also see that it is not bounded because as x1 approaches positive or negative infinity, the value of ∂F/∂x2 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x2 is not bounded.

Since both partial derivatives are not bounded, we can conclude that the function F(x) = -x1 + x1x2x2 - i1x2 is not Lipschitz continuous, neither locally nor globally, on the domain [tex]R^2.[/tex]

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Find the general solution for the differential equation
x sinθ dθ + (x3− 2x2cosθ) dx = 0

Answers

Therefore, x^2 - x^2cosθ + C = 0 is the general solution of the given differential equation.

General solution of the given differential equation is x^2 - x^2cosθ + C = 0, where C is the constant of integration.

To solve the differential equation, we have to integrate the given equation. Here, x sinθ dθ + (x^3 - 2x^2cosθ) dx = 0.

Let's integrate it using separation of variables.

x sinθ dθ = - (x^3 - 2x^2cosθ) dx

Dividing both sides by x^2, we get

sinθ dθ/x - (x - 2cosθ) dx/x^2 = 0

Now, integrate the above equation.

∫sinθ dθ/x - ∫(x - 2cosθ) dx/x^2 = ln|C|

Simplifying the above equation, we get

- cosθ/x + 1/x - x^(-1) sinθ = ln|C|

Multiplying both sides by -x, we get

cosθ - x + x^2 sinθ = -x ln|C|

Rearranging the terms, we get

x^2 - x^2cosθ + ln|C| = 0

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Helppp me please if u can thx .

Answers

$11.25 x 6 hours
= $67.5 x 6 Days
= $405.00
Other Questions
identify the values of coefficient a,b,and c in the quadrant equation 5x = 4x + 7a =b =C= Venice InLine, Inc., was founded by Russ Perez to produce a specialized in-line skate he had designed for doing aerial tricks. Up to this point, Russ has financed the company with his own savings and with cash generated by his business. However, Russ now faces a cash crisis. In the year just ended, an acute shortage of high-impact roller bearings developed just as the company was beginning production for the Christmas season. Russ had been assured by his suppliers that the roller bearings would be delivered in time to make Christmas shipments, but the suppliers were unable to fully deliver on this promise. As a consequence, Venice InLine had large stocks of unfinished skates at the end of the year and was unable to fill all of the orders that had come in from retailers for the Christmas season. Consequently, sales were below expectations for the year, and Russ does not have enough cash to pay his creditors.Well before the accounts payable were due, Russ visited a local bank and inquired about obtaining a loan. The loan officer at the bank assured Russ that there should not be any problem getting a loan to pay off his accounts payableproviding that on his most recent financial statements the current ratio was above 2.0, the acid-test ratio was above 1.0, and net operating income was at least four times the interest on the proposed loan. Russ promised to return later with a copy of his financial statements.Jurgen would like to apply for a $125,000 six-month loan bearing an interest rate of 8% per year. 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