Benjamin and Felix are 35 miles apart. At 3:00pm they start jogging towards each other. Benjamin jogs at a pace of 16 minutes per mile. Felix jogs at a pace of 10 minutes per mile. how many miles will Benjamin jog in 45 minutes

Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.

[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore

QR/NO = PQ/PN

⇒ 20/35 = PQ/PQ +12

This is because:

PN = PQ + NQ; which is also
PN = PQ +12

(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms

240= 35 PQ - 20 PQ

240 = 15PQ; Divide both sides by 15

⇒ 240/15 = 15PQ/15
⇒ 16 = PQ

Therefore, QP = PQ which is equal to 16.

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The new expression is -12/(x - y) and the domain is x ≠ y

From the question, we have the following parameters that can be used in our computation:

12/(y - x)

Multiply the fraction by 1

So, we have the following representation

12/(y - x) * 1

Express 1 as -1/-1

This gives

12/(y - x) * -1/-1

So, we have

-12/(x - y)

It should be noted that the domain remains the same

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When we evaluate the expression 8x² + 6x - 8 in x = 2, we will get the value 36.

Here we need to evaluate the following expression:

8x² + 6x - 8

in x = 2.

Evaluating means that we need to replace the variable by the given number. Replacing the "x" by 2, we will get:

8*2² + 6*2 - 8

8*4 + 12 - 8

8*3 + 12

24 + 12 = 36

When x = 2, the expression is equal to 36.

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Answer:

157[tex]ft^{3}[/tex]

Step-by-step explanation:

Volume =  the area of the base times the height.

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

a = [tex]\pi[/tex][tex](5^{2})[/tex]   I am going to use 3.14 for [tex]\pi[/tex]

a = 3.14(25)

a = 15.7

Volume = 15.7 x 10 = 157

Answer:

785 ft२

Step-by-step explanation:

volume =3.13*5२*10

=3.14*25*10

=785 ft२

Answer:

distributive property is your answer

Answer:

See below

Step-by-step explanation:

Absolute value is the positive distance from 0, so |-7| = 7 because -7 is 7 from 0, whereas 6 is 6 away from 0. Because 7>6, then -7 has a greater absolute value than 6

Answer:

[tex]S_{1000}=500500[/tex]

Step-by-step explanation:

[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]

The given statement can be written as expression given by -

y = 3 ÷ (4 - x)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the statement as -

"3 is divided by the difference of 4 and a number"

Assume the number to be {x}. Then, we can write the expression as -

3 ÷ (4 - x)

Let this expression is equivalent to {y}. We can write -

y = 3 ÷ (4 - x)

Therefore, the given statement can be written as expression given by -

y = 3 ÷ (4 - x)

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5/8

i convert to decinal then back to fraction, but you can do it however.

Exact Form: 21/8
Mixed number form: 2 5/8

Step-by-step explanation:

Answer:

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

Find the legs first:

Find the hypotenuse using Pythagorean:

Find the perimeter:

Correct choice is A.

Answer:

A)  24 units

Step-by-step explanation:

The perimeter of a triangle is the sum of its side lengths.

From inspection of the given right triangle:

As the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the length of the hypotenuse:

[tex]\implies c^2=a^2+b^2[/tex]

[tex]\implies c^2=8^2+6^2[/tex]

[tex]\implies c^2=64+36[/tex]

[tex]\implies c^2=100[/tex]

[tex]\implies c=\sqrt{100}[/tex]

[tex]\implies c=10[/tex]

Therefore, the perimeter of the given triangle is:

[tex]\implies 8+6+10=24 \; \rm units[/tex]

Ellie spend of $37.8 for  2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad

Two or more expressions with an Equal sign is called as Equation.

The amount is not given for each hot dog, hamburger and potatos.

But Ellie brought 2 packs of hot dogs ,

3 lbs of hamburger, and

2 lbs. of potato salad

Let us consider each hot dog is $6

Hamburger is $5.6 and potatoes is $4.5

Total amount is 2(6)+3(5.6)+2(4.5)

12+16.8+9

$37.8

Hence, Ellie spend of $37.8 for  2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad

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Answer:

A) Angle A. Angle EG.

B) Angle A and Angle F.

C) Angle EG and Angle D.

I hope this helped you!

Answer:

Elliot = 16 years old

Miya = 10 years old

Cara = 25 years old

Step-by-step explanation:

Define the variables:

The average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]

[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]

[tex]\implies 2x+2y+2z=3x+3y+24[/tex]

[tex]\implies 2z=x+y+24[/tex]

[tex]\implies x=2z-y-24[/tex]

Cara is 9 years older than Elliot:

[tex]\implies z = x + 9[/tex]

Four years ago, Elliot was double the age of Miya:

[tex]\implies (x - 4) = 2(y - 4)[/tex]

[tex]\implies x - 4 = 2y-8[/tex]

[tex]\implies x +4 = 2y[/tex]

[tex]\implies y=\dfrac{1}{2}x +2[/tex]

Substitute the equations for z and y into the equation for x and solve for x:

[tex]\implies x=2z-y-24[/tex]

[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]

[tex]\implies x=\dfrac{3}{2}x-8[/tex]

[tex]\implies \dfrac{1}{2}x=8[/tex]

[tex]\implies x=16[/tex]

Substitute the found value of x into the equation for z and solve for z:

[tex]\implies z = 16 + 9[/tex]

[tex]\implies z = 25[/tex]

Substitute the found value of x into the equation for y and solve for y:

[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]

[tex]\implies y=8+2[/tex]

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

Therefore, the ages of Elliot, Miya and Cara are:

Answer:

C

Step-by-step explanation:

1 pound sand for 1 2/3 pounds gravel.

1 pound gravel for 2/5 pound cement.

3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =

= 5 pounds gravel.

5 pounds gravel = 5 × 2/5 = 2 pounds of cement

Answer:yesb

Step-by-step explanation:

because u

Answer: 4t

Step-by-step explanation:

You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!

Also please tell me if I was unhelpful/incorrect, thanks!

The linear equation in this case is . The [tex]$3 x^2+4 x+4=0$[/tex] answer is [tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex] and [tex]$3 y^2+2 x+4=0: \quad$[/tex]: quadratic [tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex] , is the solution.

[tex]$3 x^2+4 x+4=0 \quad: \quad x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}$[/tex]

[tex]$3 x^2+4 x+4=0$[/tex]

Apply the quadratic formula to the problem. [tex]$x_{1,2}=\frac{-4 \pm \sqrt{4^2-4 \cdot 3 \cdot 4}}{2 \cdot 3}$[/tex]

Simplify [tex]$\sqrt{4^2-4 \cdot 3 \cdot 4}: \quad 4 \sqrt{2} i$\\[/tex]

[tex]$x_{1,2}=\frac{-4 \pm 4 \sqrt{2} i}{2 \cdot 3}$[/tex]

Distinguish the answers

[tex]x_1=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}, x_2=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}\\x=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}\\x=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]

The following are the quadratic equation's solutions:

[tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]

2) [tex]$3 y^2+2 x+4=0: \quad$[/tex] A parabola with a focal length of and a vertex at (h,k)=(-2, 0) [tex]$|p|=\frac{1}{6}$[/tex]

[tex]$3 y^2+2 x+4=0$[/tex]

[tex]$4 p(x-h)=(y-k)^2$[/tex] is the common formula for a right-to-left parabola with a vertex at (h, k) and a focal length of |p|.

Rewrite [tex]$3 y^2+2 x+4=0$[/tex]  using the proper form: [tex]$4\left(-\frac{1}{6}\right)(x-(-2))=(y-0)^2$[/tex]

The following are characteristics of parabolas:

[tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex]

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The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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Answer:

To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.

Step-by-step explanation:

The size of the crowd that is 5 feet deep on both sides of the street along a 2.7 -mile section of a parade route is 74,131 people.

The number of people that can fit comfortably in a 5 feet by 5 feet area = 13.

Therefore;

The ratio of the number of people per unit area = 13/(5 × 5) = 13/25

The area A occupied by the crowd = 5 feet × 2.7 mile × 2

2.7 miles = 14,256 feet

∴ A = 5 feet × 14,256 feet × 2 = 1,42,560ft²

We then have:

[tex]\frac{number\ of\ people}{1,42,560} = \frac{13}{25}[/tex]

∴Number of people = 13/25 × 1,42,560 = 74,131.2 ≈ 74,131 people

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Answer:

5/19

Step-by-step explanation:

Answer:

Step-by-step explanation:

i have no idea

Answer:

RM832.29

Step-by-step explanation:

Calculate PV Savings

To calculate the present value of the savings, we can use the formula:

PV = cash savings / (1 + r)^t

Where PV is the present value, r is the discount rate, and t is the number of years.

Plugging in the values given in the problem, we get:

PV = RM2,000 / (1 + 0.15)^20

= RM2,000 / 1.15^20

= RM832.29

So the present value of the savings is RM832.29.

Answer: RM25,919.89.

Step-by-step explanation:

The present value of the cash savings is the sum of the present value of each year's cash savings.

To calculate this, the formula for the present value of a single cash flow is used:

Present Value = Future Value / (1 + r)^n

Where r is the discount rate, and n is the number of years.

So, for the first year's cash savings, the present value would be:

PV = 2000 / (1 + 0.15)^1 = 1739.13

For the second year's cash savings, the present value would be:

PV = 2000 / (1 + 0.15)^2 = 1510.71

This can be repeated for the remaining 18 years, and the sum of all the present values is the total present value of the cash savings over 20 years:

Total PV = 1739.13 + 1510.71 + .... + 437.66 = RM25,919.89

Therefore, the present value of the cash savings over 20 years with a 15% discount rate is RM25,919.89.

Answer:

I can't please the question is sooo hard but can you give steps

After conquering indigenous civilizations in Mexico and South America, Spanish Colonial Rule became wealthy thanks to the gold and silver it discovered.

The objectives of Spanish Colonial Rule were to take gold and silver from the Americas, to boost the Spanish economy, and to increase Spain's might. Additionally, Spain sought to evangelize Native Americans.

Further Spanish conquistadors, who were mostly poor nobility from Spain's destitute west and south, were able to conquer the vast empires of the New World with the aid of sickness (which reduced native resistance), superior military equipment, and tactical strategies such as surprise attacks and strong.

However, it was challenging to convince immigrants to colonize there due to friction with the local Indian population and the absence of significant silver or gold discoveries.

Thus these are the most leading factors that prevent to become more successful for Spanish Colonial Rule.

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Answer:

  d.  45°

Step-by-step explanation:

You want to know which from your list is a standard elbow angle.

An elbow is a pipe fitting that is used to change the direction of piping. Elbows can be used together to produce an offset and/or a change in the plane of the piping.

Standard elbow angles commonly are 90°, 45°, and, less commonly, 22.5°. The greater the angle, and/or the smaller the bend radius, the more resistance to flow it has.

The best choice of answer here is 45°.

__

Additional comment

The typical elbow has the same kind of threads on both sides. A "street elbow" has male threads on one side and female threads on the other side.

Elbow joints are not necessarily threaded. They may also be soldered, welded, or compression joints.

Answer:316.8

Step-by-step explanation:

Answer:316.8

Step-by-step explanation:

Answer: x = 13 and x = –29

Step-by-step explanation:i hope i help you

Answer:

To find the values of x that make the equation (x – 7)^2 = 36 true, you can start by undoing the square on the left side of the equation. Since (x – 7)^2 = (x – 7)(x – 7) = x^2 - 14x + 49. Then we know that x^2 - 14x + 49 = 36.

Now, you can add 14x and 49 to both sides to get x^2 = 50.

To find the values of x that make this equation true, we need to find the square root of both sides. So x = ±sqrt(50).

And the two values of x that will make the equation true are x = ±sqrt(50) = ±7sqrt(2). And it is not in the options given, which are x = 13, x = 1, x = -29, x = 42.

Step-by-step explanation:

The cost of the Bike wholesale after the markup is $236.25

From the question, we have the following parameters that can be used in our computation:

Bike wholesale = $189

Markup = 25%

The cost of the bike wholesale after the markup is then calculated as

Cost = Bike wholesale * (1 + markup)

Substitute the known values in the above equation, so, we have the following representation

Cost = 189 * (1 + 25%)

Evaluate the products

Cost = 236.25

Hence, the cost is $236.25

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