Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour; the other is headed west at a constant speed of 40 miles per hour. What is the distance between the cars in 30 minutes?

There are 21 nickels in carol bank

Solution:

Given that Carol's piggy bank consists of quarters and nickels

There are $ 4.55 in total

Let "a" be the number of nickels in bank

Let "b" be the number of quarters in bank

We know that,

1 quarter = $ 0.25

1 nickel = $ 0.05

Given that there are seven more nickels than quarters

Number of nickels = number of quarters + 7

a = b + 7 ---- eqn 1

From given question,

number of nickels in bank x value of 1 nickel + number of quarters in bank x value of 1 quarter = $ 4.55

[tex]a \times 0.05 + b \times 0.25 = 4.55\\\\(b + 7) \times 0.05 + b \times 0.25 = 4.55\\\\0.05b + 0.35 + 0.25b = 4.55\\\\0.3b = 4.55 - 0.35\\\\0.3b = 4.2\\\\b = 14[/tex]

Therefore from eqn 1

a = b + 7 = 14 + 7 = 21

a = 21

Thus there are 21 nickels in carol bank

Answer:

Both answer shown

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7 [/tex]

Step-by-step explanation:

Given: Little confusion is in the question

e^ln7 x1

i.e [tex]e^{ln 7x}[/tex]

To Find:

[tex]e^{ln 7x}= ?[/tex]

Solution:

We know Logarithmic identity as

1. [tex]\ln e = 1[/tex]

2. [tex]\ln e^{x} = x[/tex]

Similarly,

3. [tex]e^{\ln x}=x[/tex]

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7\times 1=7 [/tex]

Answer:

7x

Step-by-step explanation:

Answer:

The points each have scored are Susie 45.5 points and jack 40.5 points.

Step-by-step explanation:

Given:

Susie and jack are on a basketball team.

The total amount of points scored was 86.

Susie has 5 more than as many points as jack.

Now, to find the points they each have:

Let the points of jack be [tex]x[/tex].

Then the points of Susie be [tex]5+x[/tex].

There total points scored =  86.

According to question:

[tex]x+(x+5)=86.[/tex]

⇒ [tex]x+x+5=86.[/tex]

⇒ [tex]2x+5=86.[/tex]

Subtracting both sides by 5 we get:

⇒ [tex]2x=81.[/tex]

Dividing both sides by 2 we get:

⇒ [tex]x=40.5.[/tex]

Jack scored = 40.5 points.

Putting the value of [tex]x[/tex] to get the points of Susie:

[tex]x+5[/tex]

⇒ [tex]40.5+5 = 45.5[/tex]

Susie scored = 45.5 points.

Therefore, the points each have scored are Susie 45.5 points and jack 40.5 points.

Answer:

6.32

Step-by-step explanation:

There's an easy trick for this. Move the decimal point once to the left, and then multiply by 2.

31.60 turns into 3.16 (which is 10% btw)

Multiply 3.16 by 2 and you get 6.32, or 20% of 31.60. Hope this helped!

Answer: The inequality symbol is reversed

Step-by-step explanation:

Given : 3 > -6

If we we multiply both side by -3 , we will have

-3(3) < -6(-3)

-9 < 18

the inequality symbol  changes because , in the rule of inequalities , anytime we multiply or divide through by negative , the inequality symbol must change

Let x = the number of songs you can buy.

If you use company A at 0.79 dollars per song, your variable is 0.79x. If you use company B at 0.99 dollars per song, your variable is 0.99x. You are going to set both equal to 30.

Company A: 0.79x = 30

Company B: 0.99x = 30

When solving (though I know you didn't ask), do note that you cannot buy part of a song so you would need to round down to the nearest whole number.

So if you use company A, you divide both sides by 0.79 to isolate the variable x and satisfy the division principle of equality:

x = 30/0.79.

Simplify and your answer is 37.97, round down to 37 songs; you'd have 37 songs with company A and 77 cents left over in your account just sitting there because what really can you do with 77 cents on the App Store?

To model the song downloading situation with a budget of $30, we use the equations 0.79x <= 30 for Company A and 0.99x <= 30 for Company B, where x is the number of songs.

To model the situation where a student has $30 to spend on downloading songs, we can write two separate linear equations, one for each company. For Company A, which charges $0.79 per song, the equation will be:

0.79x ≤ 30

Where x represents the number of songs the student can download from Company A. For Company B, which charges $0.99 per song, the equation will be:

0.99x ≤ 30

Again, x represents the number of songs the student can download from Company B, but the cost per song is different, hence a different equation.

These equations are used to determine the maximum number of songs the student can download from each company without exceeding the $30 budget.

Answer:

420cal = 2 cups

Step-by-step explanation:

140cal = 2/3 cup

xcal= 2 cups

Divide 2/(2/3) = 3

Multiply both sides by 3 (answer)

140cal= 2/3 cups (3)

420cal = 2 cups

The 2 cups Contain 420 Cal.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/3 Cup contain = 140 Cal

So, 1 cup contain = 140 ÷ ( 2/3)

                             = 140 x 3/2

                             = 70 x 3

                             = 210

Then, In 2 cups = 210 x 2

                          = 420 Cal

Hence, 2 cups Contain 420 Cal.

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Answer:

$25.5 per hour.

Step-by-step explanation:

The function C(x) = 25.50x + 50 ........ (1)  models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house.

Now, from the linear equation it is clear that the change in cost of cleaning from 3 hours and 9 hours are respectively  {From equation (1)}

C(3) = 25.5 × 3 + 50 = $126.5 and

C(9) = 25.5 × 9 + 50 = $279.5

Therefore, the average rate of change of the function between 3 hours and 9 hours will be = [tex]\frac{\textrm {Change in price of cleaning}}{\textrm {Change in hours}}[/tex]

= [tex]\frac{279.5 - 126.5}{9 - 3}[/tex]

= $25.5 per hour. (Answer)

Answer:

180° rotation

Step-by-step explanation:

sign changes when we rotate a point to 180 degrees. so 9 became -9 and -1 became 1, which gave us the clue that it's 180° rotation

The given situation described 180° rotation

Andrew's rotation maps point M(9, -1) to M'(-9, 1).

Since signing is changed when we rotate a point to 180 degrees. So here 9 became -9 and -1 became 1, which provides us the clue that its 180° rotation.

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Answer: Search it up

Step-by-step explanation:

It shows you all the steps and will help you

The true statements are : A, E & F

Step-by-step explanation:

In geometry symbols, ≅ means congruent to, equivalence of geometric shapes and size thus ∠B≅∠X

The symbol ~ means similarity, same shape not same size. Line segment AB~WX and line segment ZW ~ DA

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Keywords :statements, true, similar, isosceles trapezoids

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Answer:

the first one and the last 2 are correct 8D

Step-by-step explanation:

1.0  0.91  0.3  0.07

descending

largest to smallest

Answer:

1.0, 0.91, 0.3, 0.07

Step-by-step explanation:

first take the decimal number(s) in front and put then first.

then take the ones closest to one

then thanks the ones closer to half

then, finally take the ones closer to zero

Answer:

y=-2x-2

Step-by-step explanation:

y+4=-2(x-1)

y+4=-2x+2

y=-2x+2-4

y=-2x-2

Answer:

D

Step-by-step explanation:

Because B can be simplified to 3-4 ( which is the ratio needed)

therefor we know that Dis the answer

Answer:D.It is greater than the ratio of trumpets to clarinets.

First, you have to find the ratio flutes to violins. That is 9:12. Simplified, it is 3:4. Now, lets go down the list of options we have to pick

First option is A.It is the same ratio of violas to oboes. The ratio violas to oboes is 4:3. That is not the same as 3:4, so eliminate that option.

Second option is B.It is greater than the ratio of oboes to violas. The ratio oboes to violas is 3:4. This is the same as 3:4, so eliminate that option.

Third option is C.It is the same as the ratio of clarinets to trumpets. The ratio clarinets to trumpets is 6:2. That simplified is 3:1. This is not the same as 3:4. So lets eliminate that option. The only option left is option D, but how to check is down below.

Finally, the last option is D. It is greater than the ratio of trumpets to clarinets. The ratio trumpets to clarinets is 2:6. That simplified is 1:3. 3:4 is greater than 1:3, so D is the correct answer.

Answer:

165

Step-by-step explanation:

55* 3 = = 165

Answer:

I think I know this one. H is the answer. H is a reflection of A over the x-axis.

Answer:

The answer is EF

Step-by-step explanation:

Im smart

Answer:

[tex]6x + 4x - 3x = 10x - 3x = 7x[/tex]

Weight of wire of 8.7 meters is 24.36 ounces

Solution:

Given that cable repair person has 8.7 meters of wire

Each meter of the wire weighs 2.8 ounces

To find: Weight of wire

From given information,

weight of 1 meter of wire = 2.8 ounces

Therefore weight of 8.7 meters of wire is found by multiplying weight of 1 meter of wire by 8.7

weight of 8.7 meter of wire = weight of 1 meter of wire x 8.7

weight of 8.7 meter of wire = 2.8 x 8.7 = 24.36

Therefore weight of wire of 8.7 meters is 24.36 ounces

The weight of the 8.7 meters of wire is 24.36 ounces.

To find the weight of the wire, we need to multiply the length of the wire by its weight per unit length. The student has 8.7 meters of wire, and each meter weighs 2.8 ounces.

Multiply the length of the wire in meters (8.7) by the weight per meter in ounces (2.8).

8.7 meters * 2.8 ounces/meter = 24.36 ounces.

Therefore, the total weight of the wire is 24.36 ounces.

The length of one edge of a cube with a volume of 1331 cm³ is 11 cm, derived by taking the cube root of the volume.

To calculate the length of one edge of a cube when the volume is given, we use the formula for the volume of a cube: Volume = side³, where 'side' is the length of one edge of the cube.

The cube in question has a volume of 1331 cm³. To find the length of one edge of the cube, we need to take the cube root of the volume. The cube root of 1331 cm³ is 11 cm, meaning each side of the cube measures 11 cm.

The cube root is calculated because raising a number to the third power cubes it, and taking the cube root is the inverse operation. This process allows us to determine the original value that was cubed to get the volume.

Answer:

Step-by-step explanation:

Supplementary angles add up to 180°.

m∠VST = m∠VSW + m∠TSW

m∠VST = 180° → m∠VSW + m∠TSW = 180°

Answer:

supplementary

Step-by-step explanation:

acute= less then 90 degrees

straight=180 degrees

complementary= 2 angles that equal 90 degrees

supplementary=2 angles that equal 180 degrees

Answer:

as illustrated

Step-by-step explanation:

X-4y= - 18

find 2 points on the line

x = 0     y = 4.5      (0, 4.5)

x = 4   y = 5.5         (4, 5.5)

Answer:

Please Check the image for the answer to your question hope this helps!

Step-by-step explanation:

DCF is 90°

so to find BCE

BCE+64+90=180

BCE=26°

CBE is (180-3x)

taking triangle BEC

(180-3x)+x+26=180

180-3x+x+26=180

-2x+26=0

-2x=-26

x=13

For this case we have the following inequality:

[tex]0.4 + y\geq 7[/tex]

If we subtract 0.4 from both sides of the inequality we have:

[tex]y \geq7-0.4\\y \geq6.6[/tex]

Thus, the solution is given by all the values of "y" greater than or equal to 6.6.

The graph of the solution is attached.

Answer:

[tex]y\geq6.6[/tex]

5(x - 3) +6 = 5x - 9​ has infinitely many solutions

Given equation is 5(x - 3) +6 = 5x - 9​

We have to find whether the given equation has one, zero, or infinitely many solutions

Let us solve the given equation

5(x - 3) + 6 = 5x - 9​

Let us use BODMAS rule to solve the given equation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

So let us first solve for brackets in given equation

5x - 15 + 6 = 5x - 9

5x - 9 = 5x - 9

0 = 0

Since the statement is true, there are infinitely many solutions

Answer:

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

Step-by-step explanation:

Let

x ----> the number of jars of nuts worth $4

y ----> the number of jars of nuts worth $6

we know that

[tex]x+y=50[/tex] ----> equation A

[tex]4x+6y=4.80(50)[/tex]

[tex]4x+6y=240[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (30,20)

see the attached figure

therefore

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

The student has to mix 20 jars of $4 nuts with 30 jars of $6 nuts to end up with 50 jars of nuts each worth $4.80.

This question falls under a mathematical concept known as linear equations. Let's denote the number of $4 jars as X and the number of $6 jars as Y. According to the question, X + Y = 50 because the total number of jars is 50. We can also write another equation, which is 4X + 6Y = 50 * 4.8 ($4.80 is the average price of a jar, and there are 50 jars). Solving this system of linear equations gives us X = 20 and Y = 30. So, the student has to mix 20 jars of nuts worth $4 per jar with 30 jars of nuts worth $6 per jar to get 50 jars of nuts worth $4.80 per jar.

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Answer:

16

Step-by-step explanation:

Quotient means the answer to a division problem.

80 ÷ 5 = 16

In long division:

   16 R0

5∫80

   5  

   30

Answer:

15 sec.

Step-by-step explanation:

Given: Object travels 1/20 of the length of the path in 3/4 seconds.

Let the entire length of the path be "x".

Now, solving to find the total time taken to travel entire length.

First step, Object travel= [tex]\frac{1}{20}\times x = \frac{x}{20}[/tex]

Next putting the value in the ratio of Length: time.

[tex]\frac{\frac{x}{20} }{\frac{3}{4} }[/tex]

And another ratio of entire length and total time

[tex]\frac{x}{Total\ time}[/tex]

Now, using scissor method fractioning to solve the ratio or fraction

⇒[tex]\frac{\frac{x}{20} }{\frac{3}{4} }= \frac{x}{Total\ time}[/tex]

To divide fraction, take reciprocal of the divisor and multiply the dividend.

⇒ [tex]\frac{x}{20} \times \frac{4}{3} = \frac{x}{Total\ time}[/tex]

⇒[tex]\frac{4x}{20\times 3} = \frac{x}{Total\ time}[/tex]

Cross multiplying both side.

⇒ [tex]Total\ time= \frac{20x\times 3}{4x}[/tex]

⇒ [tex]Total\ time= \frac{20\times 3}{4}[/tex]

⇒[tex]Total\ time= 5\times 3= 15\ sec[/tex]

∴ Total time taken by Object to travel entire length is 15 sec.

The length of the line segment that connects vertex A and vertex B is 5 units

Step-by-step explanation:

Let us revise some facts about the horizontal and vertical segments

In Δ ABC

∵ A = (1 , -1)

∵ B = (1 , 4)

∵ C = (8 , 4)

∵ The x-coordinate of point A = 1

∵ The x-coordinate of point B = 1

∴ The x-coordinates of points A and B are equal

- The x-coordinates of A and B are equal, then the line AB is a

  vertical segment

∴ The length of AB is the difference between the y-coordinates

   of points A and B

∵ The y-coordinate of point A = -1

∵ The y-coordinate ob point B = 4

∴ The length of AB = 4 - (-1)

∴ The length of AB = 4 + 1

∴ The length of AB = 5 units

The length of the line segment that connects vertex A and vertex B is 5 units

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Answer:

5 units

Step-by-step explanation: