You notice a hot air balloon descending. The elevation h
(in feet) of the balloon is modeled by the function h(x)=−8x+360,
where x
is the time (in seconds) since you first noticed the hot air balloon.

Graph the function and specify its domain and range. Then interpret the slope and intercepts of the graph.

Answer:

Make the -4 exponent in the denominator positive.

The information that would be included or entered into the application or online tool for personal budgeting should include but not be limited to:

The features that the tool will have are:

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If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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The absolute value equation which could be used to obtain the greatest and least possible temperature values when the temperature reading is 17°F is (17 ± 2)°F

The least possible value of temperature can be calculated thus :

The highest possible temperature can be calculated thus :

Hence, the absolute value equation which represents the scenario is (17 ± 2)°F

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Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

Answer:

b. 100 small squares forming a 10 by 10 pattern

Step-by-step explanation:

1 × 1 = 1

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

like this the 10th figure will be :

10 × 10 = 100

so, the answer is b.

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

The amount that will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% closed on April 12th is $9,457.19.

The APR represents the annual percentage rate.

The annual percentage rate is the interest rate for the year, including other finance charges.

To compute the interest, the annual percentage rate is multiplied by the loan amount and the period divided by 365 days.

Loan amount = $250,000

Annual percentage rate (APR) = 5.25%

Loan closing date = April 12th

April 12th to December 31st = 263 days

Interest for the year = $9,457.19 ($250,000 x 5.25% x 263/365)

Thus, for the year, the interest is $9,457.19.

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all the applications are true.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

Solution: Start by using:

2012 indicates that x=1

So A = 900 (1.05) = 900 × 1,05=945

B = 1100 (1.038) = 1100 × 1038 = 1141.8 \sC = 5000 (0,85) = 5000 x0.85 = 4250 \s4250 1141.8945

So, Ture is the first applicant.

Applying the second: 1.05-1=0.055% Ture

The third application is 1-0.85=0.15=15%. False

Applying the fourth: A 1.05+=0.05=5%

B: \s11038-1=0.038=3.8% \s5% > 3.8% Ture

Hence all the apply are true.

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Answer: x=4.7

Step-by-step explanation: 1. Subtract 3.9 to both sides to get 0.4x=1.88

2. Divide by 0.4 to both sides to get that x=4.7

Answer:

$29.40

Step-by-step explanation:

29.40 dollars as 100 - the sum of the cost = 29.4

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

103.67 in³

Step-by-step explanation:

given Volume of cone is 1/3 * π * r² * h

here given r = 6/2 = 3 , height = 11 inch

using the formula = 1/3 * π * 3² * 11

                              =103.67 in³ or 33π in³

Answer:

D

Step-by-step explanation:

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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It lies in first quadrant as it is in the form (+,+).

The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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The answers to the questions are in the picture

Answer:

2.57 yards longer

Step-by-step explanation:

Step one:

given data

We are told that the Jiaozhou Bay Bridge in China, spans 26.4 miles

Also, The longest sea bridge in the United States is the Lake Pontchartrain Causeway in Louisiana, which spans 41,940 yards

Required

Unit conversion from yards to miles

Step two:

let us convert 41,940 yards to miles

We know that 1 yard is 0.000568182 miles

hence 41,940 yards is x miles

cross multiply we have

x= 41,940*0.000568182

x=23.83 yards

Hence the difference in their lengths is

=26.4-23.83

=2.57 yards

Answer:

The 26% solution should she use is explained below in detailed explanation.

Step-by-step explanation:

Assumed there be 10 percent of x liters of acid solution

Assumed there be 26 percent of y liters of acid solution

provided Information

A chemist needed to combine a 10 percent acid solution with a 26 percent acid solution to obtain 16 liters of a 14 percent acid solution

So, ( 10 / 100 )*x + ( 26 / 100 )*y = ( 14 / 100 )*16

=> 0.1*x + 0.26*y = 0.14*16

=> 0.1*x + 0.26*y = 2.24 ....................... eq 1

x + y = 16 ......................... eq 2

Multiply ( 0.1 ) in both side in eq 2

=> 0.1*x + 0.1*y = 0.1*16

=> 0.1*x + 0.1*y = 1.6 ......................... eq 3

Subtract eq 3 from eq 1

0.1*x - 0.1*x + 0.26*y - 0.1*y = 2.24 - 1.6

=> 0.16*y = 0.64

=> x = 0.64 / 0.16

=> y = 4

So, 4 liters of 26% solution she should utilized

Q = 91°

Step-by-step explanation:

Note how the angles correspond to each of the shapes:

J ---> S

G ---> R

H ---> Q

I ----> P

Since J = 55°, we can see that S is also 55°. With H = 91°, this means that Q is also 91°

Answer:

2x+1

Step-by-step explanation:

The expression = (5x+3)-(3x+2) = 2x+1

The solution to the equation 2(x+1) = -8 is x = -5.

Given information:

The equation is 2(x+1)=-8.

In order to solve the equation 2(x+1)=-8, follow the process given below.

1. Distribute the 2 to the parentheses:

2x + 2 = -8

2. Subtract 2 from both sides to isolate the x term:

2x = -10

3. Divide both sides by 2 to solve for x:

x = -5

Therefore, the solution is x = -5.

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Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

It's the b graph

Step-by-step explanation:

Khan Academy.

Answer:

The line slightly curves.

Step-by-step explanation:

Got it right on Khan

Answer:

the first one is x=5 and then the second one is x=-2/3

Step-by-step explanation:

I hope this helps!

Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

An equation is an expression that shows the relationship between two or more numbers and variables.

A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains

Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains

Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

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