How do you solve for a side in right triangles?

The answer is:

The distance to over by Adam to get to the park is 108 miles.

To solve the problem, we need to write two equations using he given information about the times and his speed.

So,

For the first equation we have: Travel to Disney Park

[tex]time=4hours[/tex]

[tex]Distance=v*4hours[/tex]

For the second equation we have: Travel back from Disnery Park

[tex]time=4hours-2.5hours=1.5hours[/tex]

[tex]Speed=v+45mph[/tex]

[tex]Distance=(v+45mph)*1.5hours[/tex]

Then, if Adam covered the same distance going and coming back, we have:

[tex]v*4hours=(v+45mph)*1.5hours[/tex]

[tex]v*4hours=v*1.5hours+45mph*1.5hours[/tex]

[tex]v*4hours-v*1.5hours=45mph*1.5hours[/tex]

[tex]v*2.5hours=67.5miles[/tex]

[tex]v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph[/tex]

We have that the speed when he was going to Disney Park was 27 mph.

Now, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.

Therefore, substituting the speed into the second equation, we have:

[tex]Distance=(v+45mph)*1.5hours[/tex]

[tex]Distance=(27mph+45mph)*1.5hours=72mph*1.5hours=108miles[/tex]

Hence, we have that the distance that Adam should cover to get to the park is 108 miles.

Havea nice day!

Answer:

3. 2x - 1 = 4

4. x/6 = 1/2

The value of the solutions are,

3) x = 5/2

4) y = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One less than twice a number, x, is equal to four.''

And, ''A number divided by six is one-half.''

Now,

Since, The algebraic expression is,

''One less than twice a number, x, is equal to four.''

Hence, We can formulate;

⇒ 2x - 1 = 4

Solve for x;

⇒ 2x = 4 + 1

⇒ 2x = 5

⇒ x = 5/2

4) The algebraic expression is,

⇒ ''A number divided by six is one-half.''

Hence, We can formulate;

⇒ y/6 = 1/2

Solve for y as;

⇒ y = 6×1/2

⇒ y = 6/2

⇒ y = 3

Thus, The value of the solutions are,

3) x = 5/2

4) y = 3

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Answer:

The cost difference is $4.

Step-by-step explanation:

Consider the provided information.

I am paying $60 a month for my service.

I would like to upgrade to the $80.00 service package because my new employer offers a 20% discount with your company.

If i get 20% of discount that means i need to pay only 80% of the original amount.

80% of 80 can be calculated as:

[tex]\frac{80}{100}\times 80[/tex]

[tex]0.8\times 80=64[/tex]

Therefore, now i need to pay $4 extra for the upgrade service.

Hence, the cost difference is $4.

the cost difference would be $4 more per month if upgrade is done.

First, let's calculate the cost of the $80 service package with a 20% discount:

[tex]20\%\ of\ 80 = \frac{20}{100} \times 80 = 16[/tex]

Now we need to subtract the discount from the original price = [tex]\$80 - \$16 = \$64[/tex]

Now, let's find the cost difference between the current $60 service and the discounted $64 service. This can be done by subtracting 60 from 64 which gives:

[tex]\$64 - \$60 = \$4[/tex]

Therefore, the cost difference would be $4 more per month if upgrade is done.

Answer:

x = 5 and y = 2, or (5,2) (Whichever one you do in class)

Step-by-step explanation:

You should solve this problem using substitution!

First you want to solve for x on this equation, 3x + 2y = 19.

start by subtracting 2y on each side, 3x + 2y(-2y) = 19(-2y). 3x = -2y + 19

Then divide by 3, 3x/3 = (-2y + 19)/3, this would give you x = (-2y + 19)/3

Next you substitute (-2y + 19)/3 in for x in 4x + 3y = -14: 4(-2y/3 + 19/3) + 3y = -14

Then Solve: (See Math Papa Algebra Calculator if you want to know exactly how to solve.) This would give you y = 2

Then substitute the 2: giving you x = 5  

To solve the system of equations, use the method of elimination. Multiply both equations by suitable constants to eliminate one variable and then solve for the other variable. Substitute the value of one variable back into one of the original equations to solve for the other variable. The solution to the system of equations is obtained by finding the values of x and y that satisfy both equations.

The given question consists of a system of two linear equations:

3x + 2y = 19

-4x + 3y = -14

To solve this system, we can use the substitution or elimination method. Let's use the method of elimination:

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It’s a great way to write numbers that are very big numbers or very small numbers.

Have a great day!

Answer: [tex]x=11.47[/tex]

Step-by-step explanation:

Given the angle of 55 degrees, you know that the adjacent side is "x" and the length of the hypotenuse is 20.

Therefore, you need to remember the following identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

Then, knowing that:

[tex]\alpha=55\°\\adjacent=x\\hypotenuse=20[/tex]

 You need to substitute these values into[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]:

 [tex]cos(55\°)=\frac{x}{20}[/tex]

Now, you can solve for "x":

[tex]20*cos(55\°)=x\\x=11.471[/tex]

Rounded to the nearest hundreth:

[tex]x=11.47[/tex]

9^2 + B^2 = 18^2

81 + B^2 = 324

B^2 = 243

Square root 243

B =15.59

Answer:

6% tax

Step-by-step explanation:

6.89=6.5x

x=1.06

Answer

6%

Step-by-step explanation:

There are 8 pints in a gallon, so there are 16 pints in two gallons.

2 gallons = 16 Pints

Answer: 2 out of 14

Step-by-step explanation:

You have to do 2 plus 12 to get your total amount of shirts. Then since you only have 2 RED shirts the answer would be 2 out of 14.

Answer:

The measure of the length is [tex]23\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of rectangle

y-----> the width of rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(x+y)[/tex]

[tex]P=66\ ft[/tex]

so

[tex]66=2(x+y)[/tex]

Simplify

[tex]33=x+y[/tex] -----> equation A

[tex]x=2y+3[/tex] ----> equation B

Substitute equation B in equation A and solve for y

[tex]33=(2y+3)+y[/tex]

[tex]2y+y=33-3[/tex]

[tex]3y=30[/tex]

[tex]y=10\ ft[/tex]

Find the value of x

[tex]x=2(10)+3=23\ ft[/tex]

Answer:

The measure of the length is 23\ ft

Step-by-step explanation:

Answer: The answer is 12 units I remember this question from school.

The answer is 12 units.

Hope this helps!

The run is the horizontal change between two points along a line.

Answer:

The run is a HORIZONTAL change between two point son a line.

Step-by-step explanation:

This is because when your slope is a fraction, run is over rise, and run is when you go upwards to be able to plot a point. Therefore, the run is horizontal.

Since there is no number line below I’m going to do this.

_________ __________ __________

Just split it into three ,’:b

Answer:

1.57

it would be 1.57

Answer:

1.5651 to the nearest hundred would be 1.57

Step-by-step explanation:

9*3.14 = 28.26

(This solves for circumference)

300/28.26 = 10.6157

(This solves for rotations)

About 11 rotations.

Answer:

  66 g

Step-by-step explanation:

You want the combined mass of pebbles that are 4.5 grams or more, given the histogram of masses.

Each dot in the diagram represents one pebble, so the 5 dots above the mass of 4.5 g mean there were 5 pebbles with that mass.

The total mass of pebbles with mass 4.5 g or more will be the sum of the masses of each of the pebbles located in that column, and the columns to its right. Of course, we can use multiplication to simplify the repeated addition:

  5×(4.5 g) +4×(5 g) +3×(5.5 g) +1×(7 g) = 66 g

The combined mass of the pebbles 4.5 g or more is 66 g.

[tex]\bf \cfrac{4v+1}{6v^2-19v+10}\div \boxed{x}=\cfrac{4v-1}{3v-2}\implies \cfrac{~~\frac{4v+1}{6v^2-19v+10}~~}{x}=\cfrac{4v-1}{3v-2} \\\\\\ \stackrel{\textit{cross-multipying}}{\cfrac{~~\frac{4v+1}{6v^2-19v+10}~~}{\frac{4v-1}{3v-2}}=x}\implies \cfrac{4v+1}{6v^2-19v+10}\cdot \cfrac{3v-2}{4v-1}=x \\\\\\ \cfrac{4v+1}{(\underline{3v-2})(2v-5)}\cdot \cfrac{\underline{3v-2}}{4v-1}=x\implies \cfrac{4v+1}{(2v-5)(4v-1)}=x \\\\\\ \cfrac{4v+1}{8v^2-2v-20v+5}=x\implies \cfrac{4v+1}{8v^2-22v+5}=x[/tex]

The equivalent equation to 3x² + 24x + 15 = 0 is 3(x² + 8x + 5) = 0. It was found by factoring the given quadratic equation.

The equation you're asked to simplify is a quadratic equation, which has the form ax² + bx + c = 0. Here, a = 3, b = 24, and c = 15. The equivalent equation can be found by factoring the given equation.

The quadratic formula -b ± √b² - 4ac / 2a can be used to find the solutions of the equation, but we are asked to provide an equivalent form of the original equation. Factoring the original equation, we get: 3(x² + 8x + 5) = 0. That is the equivalent equation.

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The equation 3x^2 + 24x + 15 = 0 can be factored using the ac method. The factored form is (x + 3)(3x + 5) = 0. Solving the factored equations gives x = -3 and x = -5/3.

The equation 3x^2 + 24x + 15 = 0 can be factored.

Start by finding two numbers that multiply to give ac (a = 3, c = 15) and add to give b (b = 24).

In this case, the two numbers are 3 and 5. So we can factor the quadratic equation as (x + 3)(3x + 5) = 0.

Setting each factor equal to zero, we get x + 3 = 0 and 3x + 5 = 0.

Solving these equations gives x = -3 and x = -5/3.

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Answer:

- 11 - 6x + 2x^2 +8x^3

Step-by-step explanation:

Usually polynomials are written in descending order, with the highest exponent value going first. In this problem, you need to find the lowest exponent value, and go up from there. After looking at all the answers, you can conclude that - 11 - 6x + 2x^2 +8x^3 is correct.

I hope this helps!

Answer:

D

Step-by-step explanation:

A polynomial in ascending order means the term of lowest degree is first, followed by terms of increasing degree

A constant has degree zero

A term with x has degree 1

A term with x² has degree 2

A term with x³ has degree 3 ... and so on, thus

- 11 - 6x + 2x² + 8x³ ← is written in ascending order

Answer:

Driveway is 36.57 meters long.

Step-by-step explanation:

We are given the length of a driveway to be 40 yards and we are to find its length in meters.

We know that 1 yard is equal to 0.914 meter long. So we will simply multiply 40 by 0.914 to find the length of the driveway in the meters.

Length of driveway in meters = [tex]40 \times 0.914[/tex] = 36.57 meters

The required, driveway is approximately 36.576 meters long.

To convert yards to meters, we can use the conversion factor: 1 yard = 0.9144 meters.

Given that the driveway is 40 yards long, we can calculate its length in meters by multiplying 40 yards by the conversion factor:

40 yards * 0.9144 meters/yard = 36.576 meters.

Therefore, the driveway is approximately 36.576 meters long.

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Answer:

C. 0.26

Step-by-step explanation:

If the student selected was a sophomore at the jazz concert, we'd use the table to find the student being out of 35 students in the same situation. To get the correct answer you must take 35 divided by the total number of students attended (137). Therefore, 35/137= 0.255 rounded to the nearest tenth would be 0.26

Hope this helps! :)

Answer:

C) 0.26

Step-by-step explanation:

35 sophomores attended the jazz concert out of 137 total students.

Divide 35 by 137, which is roughly 0.25547445...

Round two decimal places and you will get 0.26.

Answer:

if the federal reserve sells 50,000 in treasury bonds to a bank at 6% interest, the immediate effect on the money supply would be; the money supply would decrease by $50,000

Step-by-step explanation:

if the federal reserve sells 50,000 in treasury bonds to a bank at 6% interest, the immediate effect on the money supply would be; the money supply would decrease by $50,000.

The $50,000 will be transferred to the federal reserves and thus not available to be borrowed by the public.

When the Federal Reserve sells Treasury bonds to a bank, the money supply decreases. This is because the bank, having bought the bonds, will have to reduce its loans to maintain requisite reserves. This is a product of open market operations, a monetary policy tool active within the central banking system.

The question you're asking pertains to the field of macroeconomics, specifically monetary policy. You're curious about the effects on the money supply if the Federal Reserve sells $50,000 in Treasury bonds to a bank at 6% interest.

When the Federal Reserve sells these bonds to a bank, it effectively reduces the amount the bank can loan out to customers. The financial institution has to hold a certain amount in reserves, hence, by buying the bonds, it has to reduce its loans to fulfill this requirement. This, therefore, results in an immediate decrease in the money supply.

It's important to note that the Federal Reserve sells bonds to control the flow of money in the economy. This selling of bonds is a type of monetary policy tool called open market operations, which is used to influence the quantity of bank reserves and the level of interest rates.

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Answer:

Subtract 9x from both sides.

Step-by-step explanation:

Answer:

Subtract 9x from both sides

Answer:

The first car travels at 60 mph and the second at 40 mph.

Step-by-step explanation:

Let's represent the speed of the first car as s1 and that of the second car as s1.  Then s1 = s2 + 20 reflects the fact that the speed of the first car is 20 mph faster than that of the second car.

The total distance traveled is 400 miles.  Since distance = rate times time,

time = distance / rate.

First car:  (s1*t) is the distance traveled;

Second car:  (s2*t) is the distance traveled.

Adding these two distances together results in 400 miles:

s1*t + s2*t = 400 miles, or

t(s1 + s2) = 400 miles.  Let's eliminate s1 by substituting s2+ 20 for it:

t(s2 + 20 + s2) = 400 miles.  But we know t:  the cars both travel 4 hours.

Thus,

(4 hr)(2s2 + 20) = 400 miles, or

(after dividing both sides by 4 hr)

(2s2 + 20) = 100 miles/hr

Subtracting 20 from both sides:

2s2 = 80, so that s2 = 40 mph.

If s2 = 40 mph, then s1 = s2 + 20 = 60 mph

The first car travels at 60 mph and the second at 40 mph.

Answer:

The first car travels at 60 mph and the second at 40 mph.

Step-by-step explanation:

hope this helps... :)

Answer: 2 2/5

Step-by-step explanation:

You can do 6 * 2/5 = 2 2/5

OR

You can do 2 + 2 + 2/5

6/5 = 1 1/5 * 2 = 2 2/5

Answer:Answer is 2 and 3

Step-by-step explanation:trust me

x = 7

hope this helps!

Answer:

Step-by-step explanation:

Do you mean an isosceles triangle? If you do then the answer is yes because two of the angles cannot be more that 90o. If they are the sum of the angles are going to be more than 180.

For example, if both angles in the isosceles triangles are 100 then the two angles will add up to 100 + 100 = 200 degrees. No triangle has 200 degrees in it.

Well how about 90.? Could two angles in a triangle have 90 each?

No because 90 + 90 = 180. There's no room for another angle.

So two angles of an isosceles triangle must be acute.

If this is not what you mean, please leave a not.

Answer: 34

Step-by-step explanation: 34 answer

The answer is 35. This is because 62 - 27 = 35