Write an algebraic expression for each word phrase.
3. 14 less than the quotient of 63 and a number h.

Answer:

A. The pattern is you multiply by 5

B. All 6 prizes are 25,000 and 5,000 and 1,000 and 200 and 40 and 8

C. ??

Step-by-step explanation:

The cash prize values in the game show reduce by a multiple of 5 each time from $25,000 to $5,000, $1,000, $200, $40, and $8. This forms a declining sequence and can be represented in a tabular form.

Contestants on a popular game show have six containers from which to select a hidden cash prize. The pattern of the prize values seems to exist in multiples of 5, with each prize being 5 times smaller than the previous one.

a. 25,000 is the highest cash prize. The next highest prize is 5,000, which is 5 times smaller than 25,000. The third prize, 1,000, is again 5 times smaller than 5,000. Thus, there seems to be a pattern where each subsequent prize is 1/5th of the preceding one.

b. Continuing this pattern, the prize values in the remaining containers would be 200, 40, and 8. Each of these values is 1/5th of the preceding value.

c. We can represent the values in a numeric sequence as follows: 25,000, 5,000, 1,000, 200, 40, 8. Our table representation would look as follows:

ContainerPrize Value125,00025,00031,000420054068

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Answer:

First choice.

Step-by-step explanation:

You could plug in the choices to see which would make all the 3 equations true.

Let's start with (x=2,y=-6,z=1):

2x+y-z=-3

2(2)+-6-1=-3

4-6-1=-3

-2-1=-3

-3=-3 is true so the first choice satisfies the first equation.

5x-2y+2z=24

5(2)-2(-6)+2(1)=24

10+12+2=24

24=24 is true so the first choice satisfies the second equation.

3x-z=5

3(2)-1=5

6-1=5

5=5 is true so the first choice satisfies the third equation.

We don't have to go any further since we found the solution.

---------Another way.

Multiply the first equation by 2 and add equation 1 and equation 2  together.

2(2x+y-z=-3)

4x+2y-2z=-6 is the first equation multiplied by 2.

5x-2y+2z=24

----------------------Add the equations together:

9x+0+0=18

9x=18

Divide both sides by 9:

x=18/9

x=2

Using the third equation along with x=2 we can find z.

3x-z=5 with x=2:

3(2)-z=5

6-z=5

Add z on both sides:

6=5+z

Subtract 5 on both sides:

1=z

Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:

2(2)+y-1=-3

4+y-1=-3

3+y=-3

Subtract 3 on both sides:

y=-6

So the solution is (x=2,y=-6,z=1).

Answer:

y = ¼x + 2

Step-by-step explanation:

x - 4y = -8

-x - x

__________

-4y = -x - 8

___ _____

-4 -4

y = ¼x + 2

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Answer:

Width of rectangle is 15 ft !

Step-by-step explanation:

Given :-

• Area of rectangle = 375 ft²

• Length of rectangle = 25 ft

• Let width of the rectangle be b ft

Formula for area of rectangle

= ( lenght ) ( width )

Substituting the value ,

375 ft² = 25ft ( b ft )

[tex] \frac{375 {ft}^{2} }{25ft} = bft[/tex]

15 = b

So, the width of rectangle is 15 ft

The required width of the rectangle is  15 feet which is 25 feet long and the area is 375 square feet.

Given that,
A rectangle is 25 feet long. Its area is 375 square feet. What is the width of the rectangle is to be determined.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

Here,
The area of the rectangle = length * width
                                     25 =  375 * width
                                      width = 375 / 25
                                      width = 15

Thus the required width of the rectangle is  15 feet.

Learn more about rectangles here:

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Answer is  24 divided by 2/3

Answer:

24 ÷ 2/3

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

isolate the variable by dividing each side by factors that dont contain the variable

Answer:

the answer is C (2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm not sure if the right side is [tex]\frac{a + b}{2}[/tex] or [tex]a + \frac{b}{2}[/tex], so I'll provide an answer for both:

[tex]A = \frac{a + b}{2}[/tex]

[tex]2A = a + b[/tex]

[tex]2A - a = b[/tex]

[tex]A = a + \frac{b}{2}[/tex]

[tex]A - a = \frac{b}{2}[/tex]

[tex]2(A - a) = b[/tex]

[tex]2A - 2a = b[/tex]

Answer:

4.45

Step-by-step explanation:

4 9/20

4 + 9/20

1/20 = 0.05

so 9/20 = 9 × 0.05

9/20 = 0.45

4 9/20 = 4 + 0.45

4 9/20 = 4.45

Answer:

x= 31 degrees

Step-by-step explanation:

A triangle's angles add up to 180 degrees. Look at the 123, it's not part of the triangle. Subtract it from 180. You should get 57 degrees. Now, make an equation. You know it equals 180, so you add up all the sides like this: 57+92+x=180. After solving the equation, you should get 31 degrees.

Answer:

The number is 200.

Step-by-step explanation:

12% of a number = 24

Let the number be x.

[tex]\frac{12}{100}[/tex] of x = 24

0.12x = 24

x = [tex]\frac{24}{0.12}[/tex] = 200

So the number (x) is 200.

Answer:

slope = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 9, - 3) and (x₂, y₂ ) = (7, - 7)

m = [tex]\frac{-7+3}{7+9}[/tex] = [tex]\frac{-4}{16}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

-¼

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{3 - 7}{9 + 7} = - \frac{4}{16} = -\frac{1}{4} [/tex]

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

Alexis spent 2 hours and 45 minutes away from home, which is equivalent to 2.75 hours.

To calculate how long Alexis spent away from home, we need to find the difference between the time she left and the time she returned. She left her house at 7:45 p.m. and returned at 10:30 p.m.

First, we'll convert both times to a 24-hour format to make it easier to compute the time difference. The time Alexis left remains the same as 19:45 (since p.m. times are already in the second half of a 24-hour day), and the time she came back is 22:30.

Next, we subtract the time Alexis left from the time she returned:

22:30
-19:45
______

The difference in the minutes column is 30 - 45, which would be negative, so we need to borrow an hour from the hours column.

22:30
-19:45
______

Convert the borrowed hour into 60 minutes and add to the 30 minutes: 60 + 30 = 90 minutes.

21:90
-19:45
______

Now we can subtract the minutes:

90 - 45 = 45 minutes.

And subtract the hours:

21 - 19 = 2 hours.

Therefore, Alexis spent 2 hours and 45 minutes away from home.

To express this time purely in hours, we convert 45 minutes into hours by dividing by 60:

45 minutes ÷ 60 minutes per hour = 0.75 hours.

Adding this to the 2 hours, we find that Alexis was away from home for 2.75 hours.

Final answer:

Alexis was away from home for 2 hours and 45 minutes, which is equivalent to 2.75 hours. The calculation involves subtracting the time she left from the time she returned and converting minutes to hours for an accurate measure.

Explanation:

The student is asking how to calculate the time Alexis spent away from home while she went shopping for clothes. To solve this, we need to calculate the difference in time between when she left and when she returned.

Alexis left her house at 7:45 p.m. and returned at 10:30 p.m.. To find the number of hours she spent away from home, we can follow these steps:

Convert the times into a 24-hour format if necessary, but here it's not required as both times are in the p.m.

Subtract the start time from the end time.

In this case, 10:30 p.m. is the same as 22:30 in a 24-hour format, and 7:45 p.m. is the same as 19:45. So,

22:30 (End Time)
- 19:45 (Start Time)
----

We have a difference of 2 hours and 45 minutes. To express this time purely in hours, we convert 45 minutes to a decimal by dividing by 60 (since there are 60 minutes in an hour).

45 minutes / 60 = 0.75 hours

Therefore, Alexis was away for 2.75 hours.

Answer:

The distance she walks is 5 km

Step-by-step explanation:

Let

x -----> the distance in kilometers

y ----> the time in hours

we know that the speed is equal to divide the distance by the time

Average speed of 5 km/h

[tex]5=\frac{x}{y}[/tex]

[tex]y=\frac{x}{5}[/tex] -----> equation A

Average speed of 6 km/h

convert 10 minutes to hours

[tex]10\ min=10/60=1/6\ h[/tex]

[tex]6=\frac{x}{y-\frac{1}{6}}[/tex] ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (5,1)

see the attached figure

therefore

The distance she walks is 5 km

Verify

Average speed of 5 km/h

[tex]y=\frac{5}{5}=1\ h=(1)*60=60\ min[/tex]

Average speed of 6 km/h

[tex]y=\frac{5}{6}\ h=\frac{5}{6}*60=50\ min[/tex]

The difference is the time she will save

[tex]60\ min-50\ min=10\ min[/tex] ----> is correct

To find the distance Ms. Handler walks, we can set up a proportion and solve for the variable d. The distance is found to be 5 kilometers.

To solve this problem, we can set up a proportion between the distance Ms. Handler walks and the time it takes her at each speed.

Let's say the distance she walks is d kilometers. At a speed of 5 km/h, the time it takes her to walk the distance is d/5 hours. At a speed of 6 km/h, the time it takes her is d/6 hours.

We can then set up the following proportion:

d/5 = d/6 + 10/60

To simplify the equation, we can multiply both sides by 30 to get rid of the denominators:

6d = 5d + 5

Simplifying further, we get:

d = 5

Therefore, the distance Ms. Handler walks is 5 kilometers.

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Answer: The answer is 2 10/27

Answer:5n

Step-by-step explanation:

Final answer:

The weight of a 500g parcel, with a gravitational field strength of 10 N/kg, can be calculated using the formula w = mg, giving a weight of 5 N.

Explanation:

To calculate the weight of a parcel with a mass of 500g (0.5 kg), we will use the formula for weight, which is w = mg, where w is the weight in newtons (N), m is the mass in kilograms (kg), and g is the gravitational field strength in newtons per kilogram (N/kg). Given that the gravitational field strength is 10 N/kg, the weight of the parcel can be calculated as follows:

Therefore, the weight of the parcel is 5 N.

Sophie earns $8.00 per hour. To find this, dividends of $18 by 2.25, representing the total hours worked, result in the per-hour earning.

To calculate how much Sophie earns per hour, we need to divide her total earnings by the total number of hours she worked. Sophie earns $18 over 2 1/4 hours.

First, we express the hours worked as an improper fraction or a decimal for ease of calculation. Since 1/4 hour is equivalent to 15 minutes, and 2 1/4 hours are the same as 2 + 0.25 which equals 2.25 hours. Now we divide $18 by 2.25 hours to find the hourly wage:

Hourly Wage = Total Earnings / Total Hours Worked

Hourly Wage = $18 / 2.25 hours

Hourly Wage = $8.00 per hour

So, Sophie earns $8.00 per hour.

Answer:

EF =58

Step-by-step explanation:

from the illustration,

EF =DF - DE

given that DF =9x-39 , DE =47 EF=3x +10

substitute them into the formula,

3x +10=9x-39 - 47

solving for x

3x +10 =9x -86

grouping like terms

3x - 9x =-86 -10

-6x=-96

dividing through by -6

[tex] \frac{ - 6x}{ - 6} = \frac{ - 96}{ - 6} [/tex]

[tex]x = \frac{96}{6} [/tex]

[tex]x = 16[/tex]

but EF=3x+10

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

[tex]\huge\boxed{58}[/tex]

First of all, we know that [tex]DE+EF=DF[/tex], because these are two segments that make up one larger segment.

Write this as an equation.

[tex]DE+EF=DF[/tex]

[tex]47+(3x+10)=9x-39[/tex]

Remove the parentheses. [tex]47+3x+10=9x-39[/tex]

Combine the like terms. [tex]3x+57=9x-39[/tex]

Subtract [tex]9x[/tex] from both sides. [tex]-6x+57=-39[/tex]

Subtract [tex]57[/tex] from both sides. [tex]-6x=-96[/tex]

Divide both sides by [tex]-6[/tex]. [tex]x=16[/tex]

Now, find [tex]EF[/tex].

[tex]3x+10[/tex]

[tex]3(16)+10[/tex]

Multiply. [tex]48+10[/tex]

Add. [tex]\boxed{58}[/tex]

Answer:1/4

Step-by-step explanation: divide both numbers by 4

[tex]\huge\boxed{\frac{1}{4}}[/tex]

You can simplify a fraction by dividing its numerator and denominator both by a factor from both of the numbers.

In this case, [tex]4[/tex] is a factor of the numerator and the denominator.

Divide both the numerator and the denominator by [tex]4[/tex].

[tex]\dfrac{4}{16} \div \dfrac{4}{4} = \dfrac{4 \div 4}{16 \div 4} = \boxed{\dfrac{1}{4}}[/tex]

Answer:

15

Step-by-step explanation:

THE Answer is 67

Step-by-step explanation:

Answer:

The Correct Answer Is 57

Step-by-step explanation:

According To Research

=113+(-56)

=113-56

=57

Answer:

-262

Step-by-step explanation:

Evaluate Subtraction & Addition from right to left [or left to right, as long as you know what you are doing]:

38 + 16 - 12 - 2 - 302

|_______||____________|

[tex]44 - 316 = -262[/tex]

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Answer:

[tex]\large\boxed{\dfrac{7}{20}=0.35}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\dfrac{7}{20}=7:20=0.35\\\\\text{Use a calculator or long division}\\\\.\qquad\underline{0.35}\\.\ \ 20|7\\.\ \ \ \ \ \underline{\ 0}\\.\qquad70\\.\ \ \ \ \ \underline{\ 60}\\.\qquad100\\.\qquad\underline{100}\\.\qquad==[/tex]

[tex]\bold{METHOD\ 2}\\\\\dfrac{7}{20}=\dfrac{7\cdot5}{20\cdot5}=\dfrac{35}{100}=0.35[/tex]

Answer:

45°

Step-by-step explanation:

Complementary angles sum to 90°, thus

90° - 45° = 45° ← is the complement of 45°

Answer:

The answer would be B.

Step-by-step explanation:

Answer:

93

Step-by-step explanation:

PEMDAS

parenthesis, exponents, multiplication, division, addition, subtraction

34 x 3 - 9

102 - 9

93

Answer:

93

Step-by-step explanation:

First we have to use pemdas

so we multiply

34*3=102

the we subtract

102-9=93

so 93 is your answer.

Answer:

X=79

Step-by-step explanation:

The answer can be found by finding the difference of 67 and 55 which would be 12, then adding 12 and 67 to get 79. I can do this because if 2 numbers are split equally between them, then adding an number to get one will get you the other. It may seem confusing, comment if you still need help.

Answer:

4,320 dollars. Expression is 60 × 12(6)

Answer:The trip will cost 132$

can i get brainlyest

Step-by-step explanation:60(to join) + 12(per hike)x6(hikes)

12 x 6 = 72 + 60 =132