The length of a picture frame is 8 inches more than the width. For what values of x is the perimeter of the picture frame greater than 152 inches.

Answer:

  ≈ 58

Step-by-step explanation:

Estimation usually means you want an answer good to one or maybe two significant figures. That usually means you want to round the numbers involved to one or two significant figures.

Doing that here transforms the problem to 180/3 = 60, an answer with one significant figure.

You can improve the estimate a bit by recognizing that it is a little high (the numerator is higher than 175.32, but the denominator is the same). Since the numerator is high by about 5, the estimate is high by about 5/3 or a little less than 2. A closer estimate will be 60 - 2 = 58.

_____

The degree to which you refine the estimate will depend on the error requirements you have. Certainly an estimate of 60 is within 10% of the true value, so is "close enough" for many purposes.

To estimate 175.32 by 3, round 175.32 to 175, and divide by 3 to get 58. Since 175 is just under 180, which divides evenly by 3 to give 60, an estimate of 58 is reasonable.

To estimate the division of 175.32 by 3, we can round the numbers to make the calculation easier. First, we round 175.32 to 175 which is very close in value, and 3 remains as it is because it is already a whole number. So, our estimation becomes 175 / 3.

Dividing 175 by 3 gives us 58 as 3 times 58 is 174. We can see that this approximation is just 1 less than our rounded number, so it is a reasonable estimate. Therefore, 175.32 / 3 is approximately 58 when we estimate it without a calculator.

To check our estimation, we can compare it to similar, simple calculations. For example, if we divide 180 by 3, we get 60. Since 175 is slightly less than 180, our estimation of 58 is likely a good approximation for the division of 175.32 by 3.

Answer:

-1(7x-9)(x-2)

Step-by-step explanation:

Because I'm right you're wrong, I'm big, you're small, and there's nothing you can do about it!!!

Question:

Which scenario best matches the linear relationship expressed in the equation y = –14x + 1,700?

1) Kent has $1,700 in his bank account and spends $14 each week.

2) Kent has $1,700 in his bank account and deposits $14 each week.

3) Kent had $1,700 in his bank account and deposited another $14.

4) Kent has $14 in his bank account and spent $1,700.

Answer:

Option  1) Kent has $1,700 in his bank account and spends $14 each week.

Step-by-step explanation:

Let x denote the number of weeks.

Option 1: Kent has $1,700 in his bank account and -14x as the negative sign denotes how much amount he spend each week.

Thus, Option 1 is the correct answer.

Option 2: Kent has $1,700 in his bank account and deposits $14 each week.

Writing it as equation, we have, [tex]y=14x+1700[/tex] which is not the expressed linear equation.

Hence,  Option 2 is not the correct answer.

Option 3: Kent had $1,700 in his bank account and deposited another $14.

Writing it as equation, we have, [tex]y=14+1700[/tex] which is not the expressed linear equation.

Hence,  Option 3 is not the correct answer.

Option 4: Kent has $14 in his bank account and spent $1,700.

Writing it as equation, we have, [tex]y=14-1700[/tex] which is not the expressed linear equation.

Hence,  Option 4 is not the correct answer.

Thus, the scenario that matches the linear equation relationship expressed in the equation is Option 1.

The answer is Kent has $1,700 in his bank account and spends $14 each week.

Answer:

A

Step-by-step explanation:

Answer: 10 , 11 , 12

Step-by-step explanation:

Let the integers be : x , x + 1 and x + 2

the smallest multiplied by 3 implies 3x

From the first statement

3x = 18 + (x+2)

3x = 18 + x + 2

3x - x = 18 + 2

2x = 20

x = 10

Therefore : the numbers are : 10 , 10 + 1 and  10 + 2

the numbers are : 10 , 11 , 12

Answer:

10,11,12

Step-by-step explanation:

3 consecutive integers...x and x + 1 and x + 2

3x = x + 2 + 18

3x = x + 20

3x - x = 20

2x = 20

x = 20/2

x = 10

x + 1 = 10 + 1 = 11

x + 2 = 10 + 2 = 12

ur numbers are 10, 11, and 12

If Justin saves $8 every week, and x represents the number of weeks, this can be set up as 8x. We are trying to find the amount of money Justin has after x weeks, so y = 8x.

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Step-by-step explanation:

Let,

x be the number of candles sold by Julio in first week.

According to given statement;

Candles sold in first week = x

He sold twice the number of candles the second week as he did the first week.

Candles sold in second week = 2x

In the third week, Julio sold 4 less than the number he sold the first week.

Candles sold in third week = x-4

Total candles sold = First week + Second week + Third week

Total candles sold = x+2x+(x-4)

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Keywords: addition, variable

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Answer:

d^2 - π(d/2)^2

Step-by-step explanation:

Since the diameter of the circle is equal to the side of a square (d), that means that we have a circle inscribed in square.

If we draw a square and inscribe a circle in it, all parts of the square outside the circle will be waste, in this particular case.

If we want to find the area of the wasted material we need to subtract the area of the circle from the area of the square.

Area of the circle is:

P1 = πr^2, r being the radius

Since radius is half the diameter, that means that:

P1 = π • (d/2)^2

Area of the square whose side is d is:

P2 = d^2

So, the area of wasted material is:

P = P2 - P1

P = d^2 - π(d/2)^2

Answer:

No Solution

Step-by-step explanation:

4x-2y=8

y=2x+1

Make the first equation into where it says y=.

-2y=-4x+8

y=2x-4

Substitute either equation into the other as y=.

2x+1=2x-4   or    2x-4=2x+1

Switch terms around so they're with their like terms. Make sure it becomes the opposite when switching.

2x-2x=-1-4    or    2x-2x=4+1

0=-5                     0=5

Since x did not come back to equal an answer, this problem is not workable. There is no solution to it. If you were to do it a different way, there still would not be a solution to it.

Answer:

Option C) 144 centimeters squared.

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The surface area of a prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the base of the prism

P is the perimeter of the  base

L is the length or height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ cm^2[/tex] ---> the base is a right triangle

Find the perimeter of the base P

[tex]P=3+4+5=12\ cm[/tex] ---> is the perimeter of a triangle

we have

[tex]L=11\ cm[/tex]

Find the surface area SA

[tex]SA=2(6)+12(11)=144\ cm^2[/tex]

Answer:

144

Step-by-step explanation:

Answer:

.45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

If you divide 45 by 100, the decimal point will move two times to the left because there is two 0's in 100, making it 0.45

Answer:

a

Step-by-step explanation:

if f(x)=y then when x is 1 2(3)^X= 6

Answer:

first graph

Step-by-step explanation:

given: [tex]f(x) = 2(3)^{x}[/tex]

substitute some values for x and see which curves accurately reflect the corresponding y-values:

when x = 0, f(0) = 2(3)^0 = 2(1) = 2

hence the graph must pass through the point (0,2)

We can see from the choices that the 2nd and 4th graphs do not pass through (0,2), so we can eliminate these 2 from consideration

when x = 1, f(1) = 2(3)^1= 2(3) = 6

hence the graph must pass through the point (1,6)

We can see that the 3rd graph does not pass through this point so we can eliminate the 3rd graph also.

Only the 1st graph gives points consistent with the 2 cases above.

Answer:

  3.25

Step-by-step explanation:

The slope of the line is ∆y/∆x = (-2-1)/(7-3) = -3/4.

The point-slope form of the line with slope m through (h, k) is ...

  y -k = m(x -h) . . . . . . . . . . we have m=-3/4, (h, k) = (3, 1)

  y -1 = -3/4(x -3)

The y-intercept is the point on the line where x=0. For x=0, the value of y is ...

  y = -3/4(-3) +1 = 9/4 +4/4

  y = 13/4 = 3 1/4

The y-intercept is 3 1/4.

Answer:

  C  1

Step-by-step explanation:

BC is perpendicular to AB, so has a slope that is the negative reciprocal of that of AB:

  BC slope = -1/(AB slope) = -1/-1 = 1

Dilating the triangle has no effect on the slope.

The slope of B'C' is 1.

Answer: 90

Step-by-step explanation:

The formula for calculating the nth term of a sequence is given as :

[tex]t_{n}[/tex] = a + ( n - d )

Where a is the first term

d is the common difference and

n is the number of terms

This means that the 4th term of an arithmetic sequence will have the formula :

[tex]t_{4}[/tex] = a + 3d

And the 4th term has been given to be , 12 ,substituting into the formula we have

12 = a + 3d .............................. equation 1

Also substituting for the 8th term , we have

36 = a + 7d .............................. equation 2

Combining the two equations , we have

a + 3d = 12  ................... equation 1

a + 7d = 36 ------------ equation 2

Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is

a = 12 - 3d ................... equation 3

substitute a = 12 - 3d into equation  2 , equation 2 then becomes

12 - 3d + 7d = 36

12 + 4d = 36

subtract 12 from both sides

4d = 36 - 12

4d = 24

divide through by 4

d = 6

substitute d = 6 into equation 3 to find the value of a, we have

a = 12 - 3d

a = 12 - 3 ( 6)

a = 12 - 18

a = -6

Therefore , the 17th term of the sequence will be :

[tex]t_{17}[/tex] = a + 16d

[tex]t_{17}[/tex] = -6 + 16 (6)

[tex]t_{17}[/tex] = -6 + 96

[tex]t_{17}[/tex] = 90

Therefore : the 17th term of the sequence is 90

Answer:

The number is 40

Step-by-step explanation:

Step 1:  To find the number, multiply all of the numbers together

2 * 2 * 2 * 5

40

Answer:  The number is 40

Answer:

40

Step-by-step explanation:

2×2×2×5 = 40

The premium of the policy is approximately $64,198.32.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To calculate the premium of the policy, we need to take into account the probability of the person dying in the next 20 years and the payout of the policy.

Let P be the probability of the person dying in the next 20 years, and let A be the administrative costs of the policy.

Then the expected value of the payout of the policy is:

E(payout) = P x $60,000

And the expected value of the cost of the policy (including administrative costs) is:

E(cost) = P x premium + A

We want to find the premium of the policy, so we can rearrange this equation to solve for the premium:

premium = (E(cost) - A) / P

Substituting the given values, we get:

P = 0.072698

A = $75

E(payout)

= P x $60,000

= 0.072698 x $60,000

= $4,361.88

Now we need to calculate the expected value of the cost of the policy.

The cost of the policy includes both the payout (if the person dies) and the administrative costs (whether or not the person dies).

So we can write:

E(cost) = E(payout) + A x (1 - P)

where (1 - P) is the probability that the person will not die in the next 20 years.

Substituting the given values, we get:

E(cost) = $4,361.88 + $75 x (1 - 0.072698) = $4,746.88

Finally, we can calculate the premium of the policy:

premium = ($4,746.88 - $75) / 0.072698 = $64,198.32

Therefore,

The premium of the policy is approximately $64,198.32.

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hope it helps I just did it

Answer:

Students= 6

Teachers= 2

Step-by-step explanation:

Given: Art museum trip:

           Cost of ticket= $5.5 per teacher and $3 per student.

           Total amount paid= $29.

           Science trip:

           Cost of ticket= $22 per teacher and $11.5 per student.

           Total amount paid= $113.

Lets assume number of teacher be "x" and number of students be "y".

Now, forming an equation for cost of each trip.

we know, total cost= [tex]cost\ of \ each\ ticket \times numbers\ of\ tickets[/tex]

∴Art museum trip, [tex]5.5x+3y= 29[/tex] ---- 1st equation

Science museum trip, [tex]22x+11.5y= 113[/tex] ---- 2nd equation

Next using elimination method to find number teacher and students

[tex]5.5x+3y= 29\\22x+11.5y= 113[/tex]

Multiplying both side of 1st equation by 4

∴ [tex]22x+12y= 116\\22x+11.5y= 113[/tex]

changing sign of 2nd equation on both side and solving it.

∴ [tex]0.5y= 3[/tex]

Dividing both side by 0.5

[tex]y= \frac{3}{0.5}= 6[/tex]

Hence, number of students on field trip was 6.

Subtituting the value of y in 1st equation to find the number of teachers in field trip.

[tex]5.5x+3y= 29[/tex]

⇒ [tex]5.5x+3\times 6= 29[/tex]

⇒ [tex]5.5x+18= 29[/tex]

Subtracting both side by 18

⇒ [tex]5.5x= 11[/tex]

Dividing both side by 5.5

⇒ [tex]x= \frac{11}{5.5}= 2[/tex]

Hence, there were 2 teachers on field trips.

Answer:

4<5<6

4<5<7

4<6<7

5<6<7

since there are 4 pieces of wood, you will have 4 combinations.  since the sum of the 2 shortest sides need to be more than the longest side the inequalities above are valid.

Hope this helps!!

Final answer:

Out of the four lengths of wood provided, there are three valid combinations that can form triangles: 4 cm, 5 cm, 6 cm; 4 cm, 6 cm, 7 cm; and 5 cm, 6 cm, 7 cm. These combinations satisfy the Triangle Inequality Theorem, which is necessary for forming triangles.

Explanation:

To determine how many different combinations of 3 pieces of balsa wood can be used to make triangles, we must recall the Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For the pieces of lengths 4 cm, 5 cm, 6 cm, and 7 cm, we can form the following combinations that satisfy the Triangle Inequality Theorem:

4 cm, 5 cm, 6 cm

4 cm, 6 cm, 7 cm

5 cm, 6 cm, 7 cm

The inequalities for these combinations are as follows:

4 cm + 5 cm > 6 cm

4 cm + 6 cm > 5 cm

5 cm + 6 cm > 4 cm

4 cm + 7 cm > 6 cm

6 cm + 7 cm > 4 cm

5 cm + 7 cm > 6 cm

Each of these combinations is valid as the sum of the lengths of any two pieces is greater than the length of the third piece.

The medication reach half of its highest concentration in the patient's bloodstream in 3 hours 45 minutes, the correct option is D.

Concentration of a solution is the milligrams of the solvent dissolved in a liter of solution.

The graph shows the variation of the concentration of the solution with time.

The highest concentration of the medicine is 2.5 mg/L.

The half of the highest concentration is 1.25 mg/L.

The graph can be seen for the time corresponding to the concentration 1.25 mg/ L.

The time taken is 3.75 hours = 3 hours 45 minutes.

The missing diagram is attached with the answer.

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Answer:

D on Edge

Step-by-step explanation:

Just got it right.

Answer:

Step-by-step explanation:

in order to be like terms, they have to have the same variable (and exponent, if there is any).....or be just a constant with no variables (just a number)

like terms in 12a - 7 + 7a + 12b are :

12a and 7a....because they have the exact same variable (a)

12b....no like terms

-7...no like terms

so ur answer is : 12a and 7a

Answer:

The total area of the shape = 4 + 4 + 2 = 10 square units

Step-by-step explanation:

This shape consists of three shape parts.

So, the total area of this shape is the sum of the areas of these shape parts.

1st Part) Finding the area of Right Triangle with base 4 units and perpendicular 2 units

A right triangle with base 4 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 4 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(4)(2)}{(2)}[/tex] = 4 square units

2nd Part) Finding the area of Square with the equal length and width i.e. 2 units

Let  a be the length of any side = 2 units

As the area of square

[tex]A=a^{2} }[/tex]

[tex]A = (2)^{2}=4[/tex] square units

3rd Part) Finding the area of Right Triangle with base 2 units and perpendicular 2 units

A right triangle with base 2 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 2 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(2)(2)}{(2)}[/tex]= 2 square units

Therefore the total area of the shape will be the sum of area of Right Triangle with base 4 units and perpendicular 2 units, area of Square with the equal length and width i.e. 2 and area of Right Triangle with base 2 units and perpendicular 2 units

So,

The total area of the shape = 4 + 4 + 2 = 10 square units

Keywords: area of a shape, area of triangle, area of square

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an example of an equivalent inequality is

5+(-m) is greater than or equal to 20

Answer: 1/4 ( 12x + 24 ) -9x=−6x+6

The premiums indicated in the chart below on $30,000 policies are $240.00, $122.40, $62.40, $21.60, $652.50, $332.775, $169.50, $58.725 , $945.00, $482.475, $245.70, $85.05, $1,346.10, $686.761, $350.286  and $121.15.

To calculate the premiums for a $30,000 policy, first, we need to find the appropriate premium amount based on the given percentages for different payment frequencies (annual, semiannual, quarterly, and monthly).

**10-year Term Policy:**

- Annual premium: $240.00

- Semiannual premium (51% of annual): $240.00 * 51% = $122.40

- Quarterly premium (26% of annual): $240.00 * 26% = $62.40

- Monthly premium (9% of annual): $240.00 * 9% = $21.60

**Whole Life Policy:**

- Annual premium: $652.50

- Semiannual premium (51% of annual): $652.50 * 51% = $332.775 (approximately $332.78)

- Quarterly premium (26% of annual): $652.50 * 26% = $169.50

- Monthly premium (9% of annual): $652.50 * 9% = $58.725 (approximately $58.73)

**20-Payment Life Policy:**

- Annual premium: $945.00

- Semiannual premium (51% of annual): $945.00 * 51% = $482.475 (approximately $482.48)

- Quarterly premium (26% of annual): $945.00 * 26% = $245.70

- Monthly premium (9% of annual): $945.00 * 9% = $85.05

**20-year Endowment Policy:**

- Annual premium: $1,346.10

- Semiannual premium (51% of annual): $1,346.10 * 51% = $686.761 (approximately $686.76)

- Quarterly premium (26% of annual): $1,346.10 * 26% = $350.286 (approximately $350.29)

- Monthly premium (9% of annual): $1,346.10 * 9% = $121.15

Please note that the semiannual, quarterly, and monthly premiums are rounded to the nearest cent.

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Answer:

3000 inches cubed

Step-by-step explanation:

I hope this help sorry if I'm wrong

Answer:

it's 1480

Step-by-step explanation:

I just did it on imagine math :)

Answer:

The value of A in the given graph of the equation is 1

That is A=1

Step-by-step explanation:

Given graph of the equation is Ax+2y=-2

Given that the equation of line Ax+2y=-2 passes through the point (2,-2)

Let (x,y) br the point (2,-2)

Therefore we have that

A(2)+2(-2)=-2

2A-4=-2

2A-4+2=-2+2

2A-2=0

2A=2

[tex]A=\frac{2}{2}[/tex]

Therefore A=1

Therefore the value of A in the given graph of the equation is 1

The average speed is 135.26 miles per hour

Solution:

Given that, woman traveled 2445.9 miles in 18 hours five minutes

To find: Average speed of her flight in miles per hour

Let us first convert 18 hours 5 minutes to hours

We know that,

[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]

Therefore,

[tex]5 \text{ minute } = \frac{5}{60} \text{ hour } = 0.083 \text{ hour }[/tex]

Thus we get,

18 hours five minutes = 18 hour + 0.083 hour = 18.083 hour

Given that, distance = 2445.9 miles

Average speed is given by formula:

[tex]Average\ speed = \frac{distance}{time}\\\\Average\ speed = \frac{2445.9}{18.083}\\\\Average\ speed = 135.26[/tex]

Thus average speed is 135.26 miles per hour

Answer:

Step-by-step explanation:

5x - y = 3.......(1)

2y = 10x+2.....(2)

Rearranging (2)

-10x + 2y = 2......(3)

Multiply equation (1) by 2

10x - 2y = 6..........(4)

Adding (3) and (4)

-10x + 10x + 2y - 2y = 2 + 6

No solution since both x and y are eliminated.

The domain and the range of the functions is real numbers. Hence, option A is correct.

We need to determine the domain and range of the function  [tex]\bold{f(x)=-35x^3}[/tex].

Let us define the domain and the range of the function:

Domain:

When all the possible values of an independent variable for which we get the real value of a dependent variable then the values of the independent variables is called domain of the function.

Range:

All the possible values of the function is called the range of the function. Range is the sub-set of co-domain.

Now,

For the given function [tex]f(x)=-35x^3[/tex].

No value of x can restrict the above function hence its domain is real number that is [tex](-\infty, +\infty)[/tex].

And, range of the function is also the same [tex](-\infty, +\infty)[/tex].

Thus, the domain and the range of the functions is real numbers. Hence, option A is correct.

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The domain and range of the cubic function f(x) = -35x^3 are both all real numbers, because there are no restrictions on x and the function's output covers all real values.

The function described is f(x) = −35x^3. The domain of a polynomial function, which includes cubic functions like this one, is all real numbers because there are no restrictions on the values that x can take. Therefore, the domain is (−∞, ∞). Since the leading coefficient of the cubic term is negative, the ends of the graph will go towards negative infinity as x goes to positive and negative infinity. Therefore, the range of the function is also all real numbers, which we write as (−∞, ∞).

Answer:

When solving equations you goal is to get x by itself so

18-6.3x=49.5 (first step would be to minus 18 from each side)

-6.3x=31.5 (18-18=0, 49.5-18=31.5) (now you want to divide each side by -6.3)

x=-5 (-6.3/-6.3=1, 31.5/-6.3=-5)

Your final answer is

x=-5

Hope this helps ;)