Jason and Jeremy work together at a juggling-ball factory. Jason lives 25 miles away from the factory and drives at 60 miles per hour. Jeremy lives 35 miles away from the factory and drives at 70 miles per hour. If they leave their houses at the same time, then
(a) who arrives at the factory first ?
(b) how long is it until the other person arrives?

Answer:

15×w

Step-by-step explanation:

15 times w is a number bigger 15 times or added up again and again 15 times:

w+w+w+w+w+w+w+w+w+w+w+w+w+w+w or 15×w

The expression to represent "15 times a number w" is written as 15w. Substituting ½ for w would lead to the multiplication 15 × ½, resulting in 7.5.

To represent the phrase "15 times a number w," you would write the algebraic expression 15w. This is accomplished by using the coefficient 15 to indicate that the number w is being multiplied by 15. So, if you were to substitute the value ½ for w into this expression, you would perform the multiplication 15 × ½ to get the result, which simplifies to 7.5.

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Answer:

a

Step-by-step explanation:

The quotient of the given expression is -2/5.

The number we obtain when we divide one number by another is the quotient

Given is the expression as -

- (4/5) ÷ 2

The given expression is -

- (4/5) ÷ 2

- (4/5) x 1/2

- 2/5

Therefore, the quotient of the given expression is -2/5.

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Answer:

the sum of the 2 expressions is -11+2i.

Step-by-step explanation:

-1-10=-11

-i+3i=2i

-11+2i

Answer:

x=-248 3/5

Step-by-step explanation:

13-9-x/11=3x/22+121/2

4-x/11=3x/22+121/2

4-121/2=3x/22+x/11

8/2-121/2=3x/22+2x/22

-113/2=5x/22

5x/22=-113/2

5x=(-113/2)*22

5x=-113*22/2

5x=-113*11

x=-1243/5

x=-248 3/5

Answer:

11,600

Step-by-step exp

the 4 in the tens place means the 6 stays the same

Answer:

11,600

Step-by-step explanation:

think of 100... that 1 is in the hundred place.  when rounding you look to the number to the right of that place. if that number is less than 5 you dont round up.  if the number is 5 or greater you round up.  in this case 11,647 the number 6 is in the hundred place.  look to the right of it. in this case it is 4.  4 is less than five so you don't round up.  your number 11,647 rounded to the hundred place is 11,600.

Cost of each book is $ 8 and cost of each pencil is $ 6

Solution:

Let "a" be the cost of 1 book

Let "b" be the cost of 1 pencil

John paid $34 for 2 books and 3 pencils

Therefore,

2 books x cost of 1 book + 3 pencil x cost of 1 pencil = 34

[tex]2 \times a + 3 \times b = 34[/tex]

2a + 3b = 34 ----------- eqn 1

He paid $36 for 3 books and 2 pencils

3 books x cost of 1 book + 2 pencil x cost of 1 pencil = 36

[tex]3 \times a + 2 \times b = 36[/tex]

3a + 2b = 36 -------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

4a + 6b = 68 ---------- eqn 3

Multiply eqn 2 by 3

9a + 6b = 108 --------- eqn 4

Subtract eqn 3 from eqn 4

9a + 6b = 108

4a + 6b = 68

( - ) -------------

5a = 40

a = 8

Substitute a = 8 in eqn 1

2(8) + 3b = 34

16 + 3b = 34

3b = 34 - 16

3b = 18

b = 6

Thus cost of each book is $ 8 and cost of each pencil is $ 6

Answer:

Step-by-step explanation:

400-65=335

Check the picture below.

the idea being, that if we run an altitude segment from a right-angle in a triangle, and parallel to the opposite side, like in thise case, we end up with 3 similar triangles, a Large one, containing the other smaller ones, a Medium and a Small.

now, let's simply use proportions for those similar triangles.

[tex]\bf \stackrel{Large}{\cfrac{12}{4+x}}=\stackrel{Small}{\cfrac{4}{12}}\implies \cfrac{12}{4+x}=\cfrac{1}{3}\implies 36=4+x\implies \boxed{32=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Small}{\cfrac{4}{y}}=\stackrel{Medium}{\cfrac{y}{x}}\implies 4x=y^2\implies 4(32)=y^2\implies 128=y^2\implies \sqrt{128}=y \\\\\\ \sqrt{64\cdot 2}=y\implies \sqrt{8^2\cdot 2}=y\implies \boxed{8\sqrt{2}=y} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{Large}{\cfrac{z}{4+x}}=\stackrel{Medium}{\cfrac{x}{z}}\implies z^2=(4+x)x\implies z^2=4x+x^2\implies z = \sqrt{4x+x^2} \\\\\\ z = \sqrt{4(32)+32^2}\implies z = \sqrt{128+1024}\implies z = \sqrt{1152} \\\\\\ z = \sqrt{576\cdot 2}\implies z = \sqrt{24^2\cdot 2}\implies \boxed{z = 24\sqrt{2}}[/tex]

The actual length of the garden is 2175 cm.

To find the actual length of the garden, we can use the scale. The scale indicates that 1 cm on the diagram represents 150 cm in real life. Since the length on the diagram is 14.5 cm, we can multiply this length by the scale factor to find the actual length.

Actual Length = Length on Diagram × Scale Factor = 14.5 cm × 150 = 2175 cm

Therefore, the actual length of the garden is 2175 cm.

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Answer:

19.9

Step-by-step explanation:

divide 199000 by 10000

=19.9

Answer:

19.9

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

P = (0,4) Q = (2,0)

Step-by-step explanation:

Incomplete Question Consider here NS = SQ then we may solve for NQ

Answer:

Therefore,

[tex]NQ=54\ units[/tex]

Step-by-step explanation:

Consider N -S -Q as a Straight line as shown in the figure below such that,

[tex]NS = 2x + 7[/tex]

[tex]SQ = 5x -23[/tex]

[tex]NS =SQ[/tex] ..............Consideration

To Find:

NQ = ?

Solution:

[tex]NS =SQ[/tex]   .....Given Consideration

Substituting the values we get

[tex]2x+7=5x-23\\\\3x=30\\\\x=\dfrac{30}{3}=10[/tex]

Therefore,

[tex]NS = 2\times 10 + 7 = 27[/tex]

[tex]SQ = 5\times 10 -23=27[/tex]

N -S-Q is a Straight Line,

Then BY Line Addition Postulate,

[tex]NQ=NS+SQ[/tex]       ...............N-S-Q

Substituting the values we get

[tex]NQ=27+27=54\ units[/tex]

Therefore,

[tex]NQ=54\ units[/tex]

Answer:

d = distance

(x_1, y_1) = coordinates of the first point

(x_2, y_2) = coordinates of the second point

Step-by-step explanation:

Answer:

The distance formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2

Step-by-step explanation:

Answer:

25.12 feet

Step-by-step explanation:

To find the circumference of the round wading pool with an 8-foot diameter using 3.14 for pi, the formula C = πd is used, resulting in a circumference of 25.12 feet.

The question is asking to find the circumference of a round wading pool with a diameter of 8 feet using 3.14 for pi. The formula for the circumference of a circle is C = πd, where C represents the circumference, π (pi) is approximately 3.14, and d is the diameter of the circle. Given that the diameter (d) of the pool is 8 feet, we substitute the values into the formula to get:

C = 3.14 × 8 feet = 25.12 feet

Therefore, the circumference of the wading pool is 25.12 feet.

Answer:

A. 2.3km

Step-by-step explanation:

Since 2cm = 1km

4.6cm = xkm

xkm = 4.6 x 1 / 2

= 2.3km

Answer:

I would believe that the answer is A. 2.3 km

Step-by-step explanation:

If 2cm=1km

then 4cm=2km

not to mention the km is 1/2 or the cm

so i would believe that .6cm would be .3km

therefore the answer must be 2.3km

Final answer:

The number halfway between 0.2 and 0.3 is 0.25, which is found by adding the two numbers and dividing the total by 2.

Explanation:

The number halfway between 0.2 and 0.3 can be found by calculating the average of the two numbers. To find the average, you add the two numbers together and then divide by 2.

To show the steps:

Therefore, the number that is halfway between 0.2 and 0.3 is 0.25.

The number halfway between 0.2 and 0.3 is 0.25.

To find the number halfway between 0.2 and 0.3, you calculate the average of the two numbers. Here's the step-by-step process:

So, the number halfway between 0.2 and 0.3 is 0.25. This method ensures that you find the exact midpoint between two values.

Answer:

[tex]\text{Inverse property of multiplication: For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

Explanation:

These are the examples given to illustrate the inverse property of multiplication:

         [tex]1/5\cdot 5=1\\\\ \sqrt{2}\cdot (1/\sqrt{2})=1[/tex]

And you must complete the statement to describe the property.

In the first example, 1/5 and 5 are reciprocal numbers of each other, also known as multiplicative inverses. And the example is showing that the product of 1/5 and its reciprocal is 1.

In the second example,    [tex]\sqrt{2}\text{ and }(1/\sqrt{2})[/tex]    are reciprocal of each other. Again, the example is showing that the product of those a number at its reciprocal is 1.

That is a general property, that can be written as:

             [tex]a\cdot 1/a=1[/tex]

That property is satisfied by any number except 0, because the reciprocal of    [tex]0[/tex]  , i.e.    [tex]1/0[/tex]    is not defined.

Then, the statemen is:

[tex]\text{For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

The statement that best describes the inverse property of multiplication is: Inverse property of multiplication: For all real numbers except 0, a * a⁻¹ = 1.

This means that if you multiply a number by its reciprocal, you will always get 1.

The examples you provided illustrate this property nicely:

5 * 1/5 = 1

√2 * 1/√2 = 1

Note that the inverse property of multiplication does not hold for the number 0, because the reciprocal of 0 is undefined.

Here is another example of the inverse property of multiplication:

3 * 1/3 = 1

You can check any other real number and its reciprocal, and you will always find that the product is 1.

The inverse property of multiplication is a useful property in mathematics, and it is used in many different areas, such as algebra, calculus, and physics.

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Answer:

20

Step-by-step explanation:

There are about 124.29 acres in this parcel woods

Step-by-step explanation:

The given is:

We need to find how many acres are in this parcel of woods

∵ The population density = 3.5 deer per acre

- That means 1 acre for every 3 dears

∵ There are a total of 435 deer

∴ [tex]\frac{3.5}{1}=\frac{435}{x}[/tex] , where x is the number of acres

- By using cross multiplication

∴ 3.5 × x = 1 × 435

∴ 3.5 x = 435

- Divide both sides by 3.5

∴ x = 124.29

There are about 124.29 acres in this parcel woods

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Answer:

Therefore the value of p is -3.

Step-by-step explanation:

Given a line has a slope of [tex]-\frac{1}{7}[/tex] and passes through (4,-2)and (p,-1)

The slope of a line which passes through [tex](x_1,y_1)[/tex]   and   [tex](x_2,y_2)[/tex] is

[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here [tex]x_1= 4,y_1=-2, x_2=p[/tex] and [tex]y_2= -1[/tex]

Therefore the slope of the line which passes through the given points is

[tex]=\frac{-1+2}{p-4}[/tex]

According to the problem,

 [tex]\frac{-1+2}{p-4}= -\frac{1}{7}[/tex]

[tex]\Leftrightarrow \frac{1}{p-4} =-\frac{1}{7}[/tex]

[tex]\Leftrightarrow p-4=-7[/tex]

[tex]\Leftrightarrow p = -7+4[/tex]

[tex]\Leftrightarrow p = -3[/tex]

Therefore the value of p is -3.

Answer: Y = 9

Step-by-step explanation:

Y & X

Y = KX

K = Y / X = - 15 / - 5 = 3

X = 3

K= 3

Y=?

Y = KX = 3 x 3 = 9

Therefore, when X = 3, Y = 9

Use the distance formula: sqrt((x2-x1)^2+(y2-y1)^2)

Plug in variables:

sqrt((-3-2)^2+(5-8)^2)

sqrt((-5)^2+(-3)^2)

sqrt(25+9)

sqrt(34)

Rounded to the nearest tenth is 5.8 units

Hope this helped.

Answer: if I am correct it is 39%

Step-by-step explanation:

Answer:

Senior citizen tickets = $9

Student tickets = $11

Step-by-step explanation:

We begin by converting these into simultaneous linear equation;

Senior citizen tickets = a

Student tickets = b

5a + 9b = 144

14a + 6b = 192

5a = 144 - 9b

a = 144/5 - 9b/5

a = 28.8 - 1.8b

We now substitute this into the first equation

14(28.8 - 1.8b) + 6b = 192

403.2 - 25.2b +6b = 192

-19.2b = 192 - 403.2

b = -211.2/-19.2

b = 11

Put the value of b into either equation

5a + 9b = 144

5a + 9(11) = 144

5a +99 = 144

5a = 144-99

5a = 45

a = 9

To find 20% of 950, first convert the percentage to a decimal (20% becomes 0.20) and then multiply that value by 950. The mathematical expression representing this calculation is 0.20 x 950, which yields the result: 190.

The question is asking about how to find 20% of 950 in mathematics. Here's how you do that:

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To find 20% of 950, convert 20% to decimal form as 0.20 and multiply it by 950. The result of this calculation is 190, which represents 20% of 950.

The expression to find 20% of 950 is obtained by multiplying 950 by the percentage in decimal form. Since 20% as a decimal is 0.20, you multiply 950 by 0.20 to find the answer. The calculation is as follows:

So, 20% of 950 is 190.

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Answer:

y = - 4

Step-by-step explanation:

The output is the value of y for a given input x

For an input of - 1, substitute x = - 1 into the equation.

y = (- 1)² - 5 = 1 - 5 = - 4 ← output

Answer:637kgms-2

Step-by-step explanation:the force acting on him will be Made X acceleration due to gravity. Then since the mass is 65, multiply it with 9.8, then you will get the force which is 637kgms-2

Answer:

p and q are both equal to 20.

Step-by-step explanation:

40 / 2 = p, so p = 20

100 / 5 = q, so q = 20

Answer:

Sally need  [tex]5\frac{1}{3}[/tex]  cups of orange juice.

Step-by-step explanation:

Given:

Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice.

If she uses 2 cups of pineapple juice.

Now, to find the cups of orange juice.

So, to solve by using unitary method:

As, ¼ of a cup of pineapple juice is needed for orange juice of = ⅔ cup.

So, 1 cup of pineapple juice is needed for orange juice of = [tex]\frac{2}{3}\div \frac{1}{4}[/tex]

[tex]=\frac{2}{3}\times \frac{4}{1}[/tex]

[tex]=\frac{8}{3}[/tex]  cups.

Thus, 2 cups of pineapple juice is needed for orange juice  of  = [tex]\frac{8}{3} \times 2[/tex]

= [tex]\frac{16}{3}[/tex]

= [tex]5\frac{1}{3}[/tex] cups.

Therefore, Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.