How to write z times 5 as an algebraic expression

Answer:

y = 5 × [tex]2^{x}[/tex]

Step-by-step explanation:

Exponential growth equations are usually in the form y = a × [tex]b^{x}[/tex].

So, y = 5 × [tex]2^{x}[/tex] is the best fit for that format.

Have a great day!

The exponential growth:

[tex]y=a\cdot b^x[/tex]

Therfore your answer is [tex]y=5\times2^x[/tex]

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

y = 2x + 5    it's a linear function in slope-intercept form

y - x = 4 → -x + y = 4   it's a linear function in standard form

x = 3   it's a vertical line

Answer:

Eleanor's net proceeds would be $1340.16.  

Step-by-step explanation:

If Eleanor purchased $2568 worth of stock and paid a 0.5% broker fee, she would have to pay $12.84 for the service, which is what we get when we multiply her initial purchase by the percentage (0.005).  When Eleanor sold the stock at $3928, she had to pay a flat fee of $7 for the trade, decreasing her overall profit by $7, or $3921.  Subtracting her initial investment from the overall profit gives Eleanor a net proceed of $1340.16.  

Eleanor's net proceeds from her stock sale, after accounting for both the original broker's fee and the online trading fee, are $3908.16.

To calculate Eleanor's net proceeds, we first need to calculate the fee she paid to her first broker. At 0.5% of $2568, that comes to $2568 * 0.005 = $12.84.

Next, she sold her stocks for $3928 using an online broker that charges a flat rate of $7 per trade. So, she paid another $7 in fees.

Therefore, the total fees she paid are $12.84 (first broker) + $7 (second broker) = $19.84.

Finally, to find her net proceeds, we subtract the total fees from the amount she sold her stocks for: $3928 - $19.84 = $3908.16.

So, Eleanor's net proceeds from selling her stocks are $3908.16.

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Answer:

Total surface area =61.23 in ^2

Step-by-step explanation:

To find the total surface area of a cylinder, we use the formula

T . S . A . = 2 π r h + 2 π r^ 2

where r is the radius and h is the height

We know the radius is 1.5 and the height is 5

Substituting the values into the equation

T . S . A . = 2 π (1.5)(5) + 2 π (1.5) ^2

                  = 15  π +4.5  π

                   = 19.5  π

Using 3.14 for  π

                   = 19.5 * (3.14)

                  =61.23 in ^2

Answer:

61.23 square inches

.............................................................................................................

Step-by-step explanation:

Answer:

2 and 3/4 lbs

Step-by-step explanation:

4 and 1/2 is equal to 9/2. If you multiply 4 by 2 and then add 1, you get 9, and put it over 2 because that is the denominator in the mixed number. Using the same method, we can find that 1 and 3/4 is equal to 7/4. However, the denominators are different, so we need to change that so they will be common. We can change 9/2 to 18/4 by multiplying both the numerator and the denominator by 2. This is technically the same as multiplying by 2/2, which is equal to 1, so the fraction will be equivalent, since anything multiplied by 1 is itself. Now we have 18/4 for the large carton and 7/4 for the small carton. Since the denominators are the same, they do not change. Just subtract the numerators to get 11, and then put it over 4 to get 11/4. In mixed number form, this is 2 and 3/4 lbs because 4 goes into 11 twice (8) and then you will have 3 left over. 8+3 = 11

Answer:

23/4pounds.

Step-by-step explanation:

41/2 take away 1 3/4 = 2 3/4.

Answer:

The answer is 7.21

Answer:

Step-by-step explanation:

Answer:

3.

Step-by-step explanation:

To find the GCF of two numbers:

List the prime factors of each number.

Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Hope This Helps!

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                     - Innverted

Answer:

3

Step-by-step explanation:

Answer:

A. −19z − 77

Step-by-step explanation:

−9(z + 3) − 5(2z + 10)

The first step is to distribute

-9*z -9*3  -5*2z -5*10

-9z-27 -10z-50

-19z -77

Answer

The correct answer is A

Step-by-step explana

Answer:

The area of figure is 304 square unit.

Step-by-step explanation:

The figure divided into 2 equal trapezoids.The height of each is 8. The basis of each trapezoid are 14 and 24. It means the length of the parallel sides are 14 and 24.

Area of a trapezoid is

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

Where, a and b are length of parallel sides and h is the height of trapezoid.

Area of a trapezoid is

[tex]A_1=\frac{24+14}{2}\times 8[/tex]

[tex]A_1=19\times 8[/tex]

[tex]A_1=152[/tex]

Therefore area of a trapezoid is 152.

The area of figure is twice of area of a trapezoid.

[tex]A=2\times A_1=2\times 152=304[/tex]

Therefore the area of figure is 304 square unit.

Answer:

304

Step-by-step explanation:

Hope this helps! :)

Answer:

Jacket A would be $86 and

Jacket B would be $12.. You would add them together and get the $98..

Step-by-step explanation:

Answer:

Equation:

xᵃ + xᵇ= 98

xᵃ=xᵇ-12

Jacket A costs $43

Jacket B costs $55

Step-by-step explanation:

We have 2 equations

Knowing

xᵃ= cost of jacket A

xᵇ= cost of jacket A

xᵃ + xᵇ= 98

xᵃ=xᵇ-12

If we replace xᵃ in the first equation

xᵇ-12 + xᵇ= 98

2xᵇ-12= 98

2xᵇ=98+12=110

xᵇ=110/2=55

xᵇ=55

xᵃ=xᵇ-12

xᵃ=43

Answer: 4. 7 unit

5. 20 unit

Step-by-step explanation:

4. Since, A≡ (-7,0) and B≡ (5,0)

Thus, By the distance formula,

[tex]AB = \sqrt{(5-(-2))^2+ (0-0)^2}[/tex]

⇒ [tex]AB = \sqrt{(5+2)^2+ (0)^2}[/tex]

⇒ [tex]AB = \sqrt{(7)^2+ (0)^2}[/tex]

⇒ [tex]AB = \sqrt{49+0}[/tex]

⇒ [tex]AB = \sqrt{49}[/tex]

⇒ AB = 7 unit

5. Here EF = 9x + 14, FG = 56 and EG= 250

But, According to the given diagram,

EF + FG = EG ( because G divides the line EG )

⇒ 9x + 14 + 56 = 250

⇒ 9x + 70 = 250

⇒ 9x = 250 - 70 ( By subtracting both sides by 70)

⇒ 9x = 180

⇒ x = 20  ( by dividing both sides by 9 )

Thus, the value of x is 20.

Answer:

C) 5 weeks

Step-by-step explanation:

Given :- Cost of bicycle = $80,

             Current Savings = $35 and

             Saves $10 per week

Additional money that is required to buy the bicycle =  $80 - $35

                                                                                           = $45

If she saves $10 per week then the best number of weeks to save $45 is 5 weeks

(Savings in 5 weeks = $10 × 5 =  $50)

Answer:x=-14y=174

y=3x+5,y=-x+4

3x+5=-x+4

There are infinite number of solutions!

Move all terms containing

x

x to the left side of the equation.

Tap for more steps...

4

x

+

5

=

4

4x+5=4

y

=

−

x

+

4

y=-x+4

Move all terms not containing

x

x to the right side of the equation.

Tap for more steps...

4

x

=

−

1

4x=-1

y

=

−

x

+

4

y=-x+4

Divide each term by

4

4 and simplify.

Tap for more steps...

x

=

−

1

4

x=-14

y

=

−

x

+

4

y=-x+4

Replace all occurrences of

x

x with the solution found by solving the last equation for

x

x. In this case, the value substituted is

−

1

4

-14.

x

=

−

1

4

x=-14

y

=

−

(

−

1

4

)

+

4

y=-(-14)+4

Simplify the right side.

Tap for more steps...

x

=

−

1

4

x=-14

y

=

17

4

y=174

The solution can be shown in both point and equation forms.

Point Form:

(

−

1

4

,

17

4

)

(-14,174)

Equation Form:

x

=

−

1

4

y

=

17

4

x=-14y=174

Answer:

1. LI=18

2. x=10

3. Yes (Y)

4. Yes (Y)

5. x=15

6. x=18

7. x=8

8. x=6

   y=6.5

Step-by-step explanation:

1. LI/JL=KH/JK

Replacing the given values:

LI/6=21/7

Dividing on the right side of the equation:

LI/6=3

Solving for LI: Multiplying both sides of the equation by 6:

6(LI/6)=6(3)

LI=18

2.TV/VS=RU/US

Replacing the given values:

x/17.5=8/14

Simplifying the fraction on the right side of the equation: Dividing numerator and denominator by 2:

x/17.5=(8/2) / (14/2)

x/17.5=4/7

Solving for x: Multiplying both sides of the equation by 17.5:

17.5(x/17.5)=17.5(4/7)=(17.5/1)(4/7)

Multiplying:

x=(17.5 x 4) / (1 x 7)

x=70/7

Dividing:

x=10

3. BC is parallel to DE if AD/DB is equal to AE/EC:

AD/DB=15/12=(15/3) / (12/3)→AD/DB=5/4

AE/EC=10/8=(10/2) / (8/2)→AE/EC=5/4

Like AD/DB=5/4=AE/EC → BC is parallel to DE

4. BC is parallel to DE if AD/DB is equal to AE/EC:

AD/DB= 2DB / DB→AD/DB=2

AE/EC=30 / (AC-AE)=30 / (45-30)=30/15→AE/EC=2

Like AD/DB=2=AE/EC → BC is parallel to DE

5. If JH is a midsegment of triangle KLM:

x=(1/2)(30)

x=15

6. If JH is a midsegment of triangle KLM:

x=2(9)

x=18

7. If JH is a midsegment of triangle KLM: x=8

8. 2x+1=x+7

Solving for x. Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:

2x+1-x=x+7-x

Subtracting:

x+1=7

Subtracting 1 both sides of the equation:

x+1-1=7-1

Subtracting:

x=6

2x+1=2(6)+1=12+1→2x+1=13

x+7=6+7→x+7=13

(3y-8)/(y+5)=(2x+1)/(x+7)

(3y-8)/(y+5)=13/13

(3y-8)/(y+5)=1

3y-8=y+5

Solving for y. Grouping the y's on the left side of the equation: Subtracting y both sides of the equation:

3y-8-y=y+5-y

Subtracting:

2y-8=5

Adding 8 both sides of the equation:

2y-8+8=5+8

Subtracting:

2y=13

Dividing both sides of the equation by 2:

2y/2=13/2

Dividing:

y=6.5

Final answer:

To find the quotient of 3 ÷ 2 1/3, convert the mixed number to an improper fraction (7/3), find the reciprocal (3/7), and multiply it by 3 to get 9/7, which is the answer in lowest terms.

Explanation:

The quotient of 3 ÷ 2 1/3 can be found by first converting the mixed number 2 1/3 to an improper fraction. The mixed number 2 1/3 is equal to ⅔, which when summed (2 * 3 + 1), gives us 7/3. To divide by a fraction, you multiply by its reciprocal. Thus, we have 3 × ⅓ (which is 3/7). Multiplying these we get 9/7, which cannot be further simplified. Therefore, the quotient in lowest terms is 9/7.

The quotient of 3 ÷ 2 1/3 is found by converting 2 1/3 to an improper fraction (7/3), taking the reciprocal (3/7), and multiplying it with 3. The result is the fraction 9/7, which is already in lowest terms.

To find the quotient of 3 ÷ 2 1/3, we first convert the mixed number to an improper fraction. The mixed number 2 1/3 is equivalent to 7/3 (because 2 × 3 + 1 = 7). To divide by a fraction, we multiply by its reciprocal. Therefore, we need to multiply 3 by the reciprocal of 7/3, which is 3/7.

The multiplication is straightforward: 3 × 3/7. We multiply the numerators (3 × 3) to get 9, and the denominators (1 × 7) to get 7, so we have 9/7. Since 9 and 7 have no common factors other than 1, 9/7 is already in its lowest terms. Thus, the quotient is 9/7 or 1 2/7 when expressed as a mixed number.

Answer:

Option  A) Only graph A represents a proportional relationship

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

therefore

Graph A represent a proportional relationship, because the line passes through the origin

Answer: GRAPH B

Step-by-step explanation: i got it right

Answer:

sum

Step-by-step explanation:

We know that, 'multiplication of two or more quantities can be expressed as the SUM of the same quantities'.

This means that 'multiplication of two or more terms is equal to adding as many copies of one of them'.

i.e. a × b = a + a + .... ( 'b' number of times ) = b + b + ... ( 'a' number of times )

Let us consider few examples,

A.  2 × 4 = 8

So, we can have that,  

2 × 4 = 2 + 2 + 2 + 2 = 8 i.e. we add the number 2 four times.

2 × 4 =  4 + 4 = 8 i.e. we add the number 4 two times.

B. 3 × 7 = 21

3 × 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 i.e. we add the number 3 seven times.

3 × 7 = 7 + 7 + 7 = 21 i.e. we add the number 7 three times.

Hence, 'The multiplication of two or more quantities may be expressed as the SUM of the same quantities'.

Answer:

3/4(6,-1)

Step-by-step explanation:

(6,6)*-(-6,1)

/by answer

Answer:

[tex]y = \frac{5}{12}x + \frac{21}{6}[/tex]      

Step-by-step explanation:

We are given the following information in the question.

The line passes through the point (6,6) and (-6,1).

We have to find the point slope form of the equation.

The point slope form of equation is given by:

[tex]y-y_1 = m(x-x_1)\\\text{where}\\m = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\\text{Putting}\\(6,6) = (x_1,y_1), (-6,1) = (x_2,y_2)\\\\y - 6 = \frac{1-6}{-6-6}(x - 6)\\\\y-6 = \frac{-5}{-12}(x-6)\\\\12(y-6) = 5(x-6)\\12y - 72 = 5x - 30\\12y = 5x -30 + 72\\12y = 5x +42\\\\y = \frac{5}{12}x + \frac{42}{12}\\\\y = \frac{5}{12}x + \frac{21}{6}[/tex]

The above equation is the required slope intercept form of equation passing through the given points.

For a 30 second flight, the airplane will travel 4.5 miles. To cover a distance of 12.75 miles, it will take 85 seconds.

The relationship between the distance an airplane travels and the time it takes is given by the equation [tex]d=0.15t[/tex].

Here, d stands for distance in miles and t for time in seconds. The coefficient 0.15 in this equation represents the speed of the airplane in miles per second.

To find how fast the airplane is flying, we must convert this speed to a more familiar unit, such as miles per hour.

Since there are 3600 seconds in one hour, the airplane's speed in miles per hour (mph) is

[tex]0.15 miles/second \times 3600 seconds/hour = 540 mph[/tex]

Now, to determine how far the airplane will travel in 30 seconds, we substitute t with 30 in the original equation:

[tex]d = 0.15 \times 30[/tex], yielding a distance of 4.5 miles.

To calculate how long it will take the airplane to go 12.75 miles, we use the original equation but solve for t:

[tex]t = \frac{d}{0.15} t = \frac{12.75}{0.15}[/tex]

which simplifies to 85 seconds.

Answer:

1. Yes

∆RST ~ ∆WSX

by SAS

2. Yes

∆ABC ~ ∆PQR

by SSS

3. Yes

∆STU ~ ∆JPM

by SAS

4. Yes

∆DJK ~ ∆PZR

by SAS

5. Yes

∆RTU ~ ∆STL

by SAS

5. Yes

∆JKL ~ ∆XYW

by SAS

6. No

7. Yes

∆BEF ~ ∆NML

by SAS

8. Yes

∆GHI ~ ∆QRS

by SSS

9. x=22

10. x=12

Step-by-step explanation:

1. RS/WS=ST/SX and m<RST=m<WSX

2. AB/PQ=8/6=4/3

BC/QR=AC/PR=12/9=4/3

AB/PQ=BC/QR=AC/PR

3. ST/JP=10/15=2/3

SU/JM=14/21=2/3

ST/JP=2/3=SU/JM

and m<TSU=70°=m<PJM

4. DK/PR=8/4=2

JK/ZR=18/9=2

DK/PR=2=JK/ZR

and m<DKJ=65°=m<PRZ

5. RT/ST=UT/LT

and m<RTU=m<STL

6. KL/YW=20/18=10/9

JL/XW=36/24=3/2

KL/YW=10/9≠3/2=JL/XW

7. BF/NL=24/16=3/2

BE/NM=39/26=3/2

BF/NL=3/2=BE/NM

and m<EBF=m<MNL

8. GH/QR=32/20=8/5

HI/RS=40/25=8/5

GI/QS=24/15=8/5

GH/QR=HI/RS=GI/QS=8/5

9. x/33=18/27

Simplifying the fraction on the right side of the equation:

x/33=2/3

Solving for x: Multiplying both sides of the equation by 33:

33(x/33)=33(2/3)

x=11(2)

x=22

10. x/16=9/12

Simplifying the fraction on the right side of the equation:

x/16=3/4

Solving for x: Multiplying both sides of the equation by 16:

16(x/16)=16(3/4)

x=4(3)

x=12

Answer: x = 2  11/36

Step-by-step explanation:

x-2 1/4 = 1/18

Isolate x: x - 2 1/4 + 2 1/4 = 1/18 + 2 1/4

x = 4/72 + 2 18/72

x = 2 22/72

x = 2 11/36

Check:

2 11/36 - 2 1/4 = 1/18

2 11/36 - 2 9/36 = 1/18

2/36 = 1/18

1/18 = 1/18

The new width of the photo is 2 inches.

To find the new width of the photo, we can use the concept of proportions. Let's set up the proportion:

Original Height / Original Width = Reduced Height / New Width

Plugging in the given values, we have:

16 in / 8 in = 4 in / x

Cross multiplying, we get:

16x = 32

Dividing both sides by 16, we find:

x = 2

So the new width of the photo is 2 inches.

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Answer:

Step-by-step explanation:

The Ratio of y : x equals to 7 : 2. Multyplying both number by three, y equals 21 and x equals 6

Answer:

x=6

Step-by-step explanation:

We can use ratios to solve this.  The ratio has to stay constant if they are proportional.  Put y in the numerator and x in the denominator.

         7         21

        ----- = ----

        2          x

We can solve using cross products.

7*x =2 *21

7x = 42

Divide each side by 7

7x/7 = 42/7

x =6

Answer:

x=175/3

Step-by-step explanation:

700/1200=x/100

Simplify to 7/12

7/12=x/100

Multiply both sides by 100

7/12×100=x

Simplify 7/12 ×100 to 700/12

700/12=x

Simplify 700/12 to 175/3

175/3=x

Switch Sides x=175/3

hope that helps you

To determine the percentage of boys in Roosevelt Middle School, divide the number of boys by the total number of students and multiply by 100. The result is about 58.3% when rounded to the nearest tenth.

In order to find the percentage of boys in Roosevelt Middle School, you'll need to take the number of boys and divide it by the total number of students, and then multiply by 100 to get the percentage. So the calculation is as follows:

Number of Boys ÷ Total number of Students × 100 = Percentage of Boys

Substituting the given values:

700 ÷ 1200 × 100 = 58.33

Rounding to the nearest tenth of a percent, we get 58.3%.

Therefore, the percentage of boys at Roosevelt Middle School is approximately 58.3%.

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Answer:

24 liters of 20% alcohol

Step-by-step explanation:

Answer:

Density is usually expressed as grams per cubic centimeter.

Volume = 55 * 25 * 20 = 27,500 cc

Density = Mass / Volume = 4,000 grams / 27,500 cc

= 0.1454545455 grams/cc

which is an extremely low density

Step-by-step explanation:

The density of the box is found by dividing its mass (4000 grams) by its volume (27500 cubic centimeters), resulting in a density of approximately 0.1455 grams per cubic centimeter.

To calculate the density of the box, you must find the mass per unit volume. The mass given is 4 kg, which is equivalent to 4000 grams since 1 kg = 1000 grams. To find the volume, multiply the length by the width by the height of the box:

Volume = Length × Width × Height = 55 cm × 25 cm × 20 cm = 27500 cm³

Now, divide the mass of the box by the volume to get the density:

Density = Mass / Volume = 4000 g / 27500 cm³ ≈ 0.1455 g/cm³

Therefore, the density of the box is approximately 0.1455 grams per cubic centimeter (g/cm³).

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Answer:

b

Step-by-step explanation:

to determine which value gives a solution, substitute the given values into the left side of the inequality and check the validity

a

- 6(10 - 2) = - 6 × 8 = - 48 < 4 → 2 is not a solution

b

9(10 + 3) = 9 × 13 = 117 > 4 → - 3 is a solution

c

- 3(10 - 1) = - 3 × 9 = - 27 < 4 → 1 is not a solution

d

0(10 - 0) = 0 × 10 = 0 < 4 → 0 is not a solution

The answer is 71 when simplified

Answer:

71

Step-by-step explanation:

One way of doing this problem is to remove the fractions.  If we move both decimal points two places to the right, we get 639/9.

Routine division results in a quotient of 71.