How much longer is her guinea pig than her fish

8+1/82, 882/100 so you get 8 and 1/82

Answer:

The difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Step-by-step explanation:

The given expression is

[tex]\frac{2x+5}{x^2-3x}-\frac{3x+5}{x^3-9x}-\frac{x+1}{x^2-9}[/tex]

Find factors of denominators.

[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^2-9)}-\frac{x+1}{x^2-9}[/tex]

Use [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x-3)(x+3)}-\frac{x+1}{(x-3)(x+3)}[/tex]

Take  [tex]x(x+3)(x-3)[/tex] as LCD.

[tex]\frac{(x+3)(2x+5)-(3x+5)-x(x+1)}{x(x+3)(x-3)}[/tex]

[tex]\frac{(2x^2+5x+6x+15)-3x-5-x^2-x}{x(x^2-3^2)}[/tex]

[tex]\frac{2x^2+5x+6x+15-4x-5-x^2}{x(x^2-9)}[/tex]

[tex]\frac{x^2+7x+10}{x^3-9x}[/tex]

Therefore the difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Answer:

(x+5)(x+2)/x^3-9x

Step-by-step explanation:

For short if taking on edgen then option A is correct.

Answer:

1915/22

Step-by-step explanation:

5745 / 66

Factor the numbers:

5745 = 3 * 1915

66 = 3 * 22

(3 * 1915) / (3 * 22)

Cancel the common factor:

1915/22

To divide 5,745 by 66, first determine how many times 66 fits into 574, then bring down the next digit and repeat. The result is 87 with a remainder of 3 or 87.068 as a decimal. The answer to 5,745 ÷ 66 is 87.068.

To find the result of 5,745 ÷ 66, follow these steps:

The answer to 5,745 ÷ 66 is 87.068.

Answer:

The median is four.

Step-by-step explanation:

First you put the numbers in order from least to greatest and write the number as many times as indicated.

2 2 2 3 4 4 4 4 6 6 7 7 7 8 9

then start from one side then go to the other crossing out numbers. So cross out a two, then nine, then another two, then eight, then the last two, then the first seven and so on. When your done you should be left with one middle number, in this case it's four.

Answer is provided in the image attached

To find the side length of Rachael's square patio with an area of 290 square feet, you have to take the square root of the area. The square root of 290 is approximately 17. So, the side length of the patio is approximately 17 feet.

The subject at hand pertains to the geometry and area calculation of a square. In a square, all sides are equal. Thus, to find the side length when only given the area, you can simply take the square root of the area. The square root of 290 is approximately 17. Therefore, Rachael's patio has a side length of approximately 17 feet, making option C the correct answer.

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Answer:

x=3

Step-by-step explanation:

Basically the question is asking what value of x gives the same value for y

(or where do the 2 lines cross)

the input is x=3, the out put is y =-1

Answer:

x = 3

Step-by-step explanation:

X - LINE: Horizontal

Y - LINE: VERTICAL

The reason why it's x = 3 is because it's where both line up to, where they both intersect.

Input (x) is 3 & output (y) is -1

Hope this helps you!!! :)

Answer:

The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

Step-by-step explanation:

The student's question involves choosing between a flat rate of $500 or an hourly rate of $20 for a contractor's job. The better option depends on the number of hours worked compared to the flat rate. Calculations must be made to determine which method yields a higher payment.

The student's question is related to making a decision on a contractor's billing method.

The decision involves choosing between a flat rate of $500 or billing at an hourly rate of $20 per hour for a completed job. To determine which option is more advantageous, the contractor would need to calculate the total earnings based on the number of hours worked and compare it against the flat rate.

For instance, if the contractor works 10 hours, the payment at the hourly rate would be 10 hours × $20/hour = $200. Since $200 is less than the flat rate of $500, the hourly rate would be the better choice in this case. However, if the contractor works for 30 hours, the payment at the hourly rate would be 30 hours × $20/hour = $600, which is more than the flat rate, making the flat rate the better option.

The equation for the amount of money that Morgan has now is 16.31+m = 40

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, Morgan needs to earn $16.31 more to have $40.00, we need to establish an equation to find the amount of money Morgan need,

Let the required money be m,

So, the equation will be

16.31+m = 40

m = 40-16.31

m = 23.69

Hence the  equation for the amount of money that Morgan has now is 16.31+m = 40

Learn more about equations, click;

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Morgan currently has $23.69. An equation m + 16.31 = 40.00 is set up and solved by subtracting $16.31 from $40.00 to find the value of m.

We can set up the equation m + 16.31 = 40.00. This equation translates the fact that Morgan needs $16.31 more to have $40.00. Therefore, by performing a basic subtraction (40.00 - 16.31), we can solve for m.

Step 1: Write the equation: m + 16.31 = 40.00.
Step 2: Subtract 16.31 from both sides of the equation to isolate m: m = 40.00 - 16.31.
Step 3: Perform the subtraction to find m: m = 23.69.

This method is a straightforward way to solve for the current amount of money that Morgan has.

Final Answer:

The difference in the unit price per ounce for the laundry detergent Mr. and Mrs. O’Brien purchased is $0.045 per ounce, with Mr. O’Brien's detergent being the more cost-effective option.

Explanation:

To find the unit price per ounce for each type of laundry detergent, we first determine the cost per ounce by dividing the total cost by the total weight. For Mrs. O’Brien's detergent, which is 112 ounces for $13.44, the unit price per ounce is $13.44/112 = $0.12 per ounce. For Mr. O’Brien's detergent, which is 17.5 pounds for $19.60, we convert pounds to ounces (1 pound = 16 ounces) and calculate the unit price per ounce as $19.60/(17.5 * 16) = $0.165 per ounce.

The difference in unit price per ounce is then found by subtracting Mrs. O’Brien's unit price from Mr. O’Brien's unit price, resulting in $0.165 - $0.12 = $0.045 per ounce. The positive value indicates that Mr. O’Brien's detergent is more cost-effective on a per-ounce basis.

This mathematical approach provides a clear comparison of the unit prices, allowing consumers to make informed decisions based on cost-effectiveness. The calculated difference highlights the savings per ounce associated with Mr. O’Brien's laundry detergent.

Answer:

AC= 6 cm

Step-by-step explanation:

It is given that ABCD is a trapezoid

Also AC divides the trapezoid into two similar triangles

ΔABC≈ΔDCA

The ratio of corresponding sides of similar triangles are equal, so we have

[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]

now we can take

[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]

[tex]\frac{4}{AC} =\frac{AC}{9}[/tex]     ( since BC=4 and AD= 9)

now we cross multiply

[tex]4(9)=AC^{2}[/tex]

[tex]AC^{2}=36[/tex]

[tex]AC=\sqrt{36}[/tex]    (taking square root )

AC= 6 cm

The formula of a volume of a cylinder:

[tex]V_{cylinder}=\pi r^2H[/tex]

r - radius

H - height

We have the diameter d = 8 in and height H = 9 in.

[tex]d=2r\to r=d:2\to r=8\ in:2=4in[/tex]

Substitute:

[tex]V_{cylinder}=\pi(4^2)(9)=\pi(16)(9)=144\pi\approx144\cdot3.14=452.16\ in^3[/tex]

The formula of a volume of a cone:

[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have the diameter d = 8 in → r = 4 in and the height H = 18 in.

Substitute:

[tex]V_{cone}=\dfrac{1}{3}\pi(4^2)(18)=\pi(16)(6)=96\pi\approx96\cdot3.14=301.44\ in^3[/tex]

[tex]\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{452.16}{301.44}=1.5[/tex]

The volume of the cylinder is one and a half times larger than the volume of the cone.

If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.

[tex]V_{cone}=\pi r^2H\\\\V_{cylinder}=\dfrac{1}{3}\pi r^2H\\\\\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{\pi r^2H}{\frac{1}{3}\pi r^2H}=\dfrac{1}{\frac{1}{3}}=3[/tex]

The formula of a volume of a cylinder:

r - radius

H - height

We have the diameter d = 8 in and height H = 9 in.

Substitute:

The formula of a volume of a cone:

r - radius

H - height

We have the diameter d = 8 in → r = 4 in and the height H = 18 in.

Substitute:

The volume of the cylinder is one and a half times larger than the volume of the cone.

If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.

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Answer:

Equation of the line with m=3  and b = 8.25 is y=3 x+8.25

Step-by-step explanation:

m = 3 and b = 8.25

To get equation of line we use y=mx+b

Where m represents the slope = 3

b represents the y intercept = 8.25

Plug in the values in y=mx+b

y= 3x + 8.25

Equation of the line with m=3  and b = 8.25 is y=3 x+8.25

Answer:

y = 3x + 8.25

Step-by-step explanation:

y = mx + b

y = 3x + 8.25

Answer:

Angle x = 60.1 degrees

Step-by-step explanation:

Given : height of the ladder is 15 ft that is the hypotenuse

The top of the ladder is  13ft off the ground.

That is the oppposite side of angle x

Since this forms a right angle triangle we use trigonometric ratios to find x

We know the opposite side and the hypotenuse

sin(x) = opposite / hypotenuse

[tex]sin(x) = \frac{13}{15}[/tex]

[tex]x = sin^{-1}(\frac{13}{15})[/tex]

x= 60.073565

Angle x = 60.1 degrees

check the picture below.

make sure your calculator is in Degree mode.

Answer:

[tex]4x^2+34x-28=0[/tex]

x = 0.76

Step-by-step explanation:

We can write the area of steel before it is cut as:

Area = [tex](11+2x)*(6+2x)cm^2[/tex]

Expanding it by multiplying the brackets to get:

Area = [tex]4x^2+22x+12x+66[/tex]

Area  area of steel before cutting = [tex]4x^2+34x+66[/tex]

Then we need the area of steel after 11*6 inside dimensions are cut out:

[tex]4x^2+34x+66-(11*6)=4x^2+34x[/tex]

This area should be close to 28 cm[tex]^2[/tex], hence the equation becomes:

[tex]4x^2+34x-28=0[/tex]

Moreover, plotting the graph gives us a value of x = 0.76.

Answer:

Step-by-step explanation:

4x2+34x-28

0.76cm

plato

Answer:

slope = - [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

note that BC is perpendicular to AB, hence the slope of BC is the negative reciprocal of the slope of AB

[tex]m_{BC}[/tex] = - [tex]\frac{1}{2/3}[/tex] = - [tex]\frac{3}{2}[/tex]

Answer:the last one, 25 tenths

Step-by-step explanation:

Answer:

Cameron will make 15 baskets out of 50 tries.

Step-by-step explanation:

Since Annie can take out 18 baskets out of 30 and her brother can take out half as much, then we know that 18:2 is 9, so we know that Cameron can take out 9 baskets out of 30. Since this is our proportion( 9:30 ), we can simplify it which brings us to 3:10. And since we must find how much he will take out in 50 tries, We multiply the proportion by 5 which is 15:50, meaning he will make 15 baskets.

Final answer:

Cameron can make 15 baskets out of 50 attempts based on his success rate, which is half of his sister Annie's success rate of 60%.

Explanation:

Annie can make 18 baskets out of 30 attempts, which means her success rate is 60% (since 18 is 60% of 30). Her younger brother Cameron can make half as many baskets in the same number of attempts, so Cameron's success rate is 30% because half of 18 is 9, and 9 is 30% of 30. If Cameron were to attempt 50 shots, we would calculate the number of baskets he can make by applying his success rate to these 50 attempts. Therefore, 30% of 50 is 15. This means Cameron can make 15 baskets out of 50 attempts.

3x-5y=n

3x-5y=1

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

There are a few ways to solve this, the simplest of which is probably factoring. Start by finding factors of C (10) that add up to be B (-2).

fac(10) { -10, 1 ; -5, 2 }

Well, there are no factors of 10 that can add to b - so we will use the quadratic formula.

(-b +- sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -2, c = 10

b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36

-b +- sqrt(-36) / 2a

(2 +- sqrt(-36)) / 2

sqrt(-36)

sqrt(-1 * 36)

sqrt(-1) * sqrt(36)

i * 6

6i

2 + 6i / 2 ; 1 + 3i

2 - 6i / 2 ; 1 - 3i

Solutions: 1 + 3i, 1 - 3i

Answer:

x = 1± 3i

Step-by-step explanation:

x^2-2x+10=0

We can complete the square to solve by subtracting 10 from each side

x^2-2x+10-10=-10

x^2 -2x = -10

We need to add (2/2) ^2  to each side or 1

x^2 -2x+1 = -10 +1

x^2 -2x+1 = -9

The left side factors into (x- (2/2) ) ^2

(x-1) ^2 = -9

Take the square root of each side

sqrt((x-1) ^2 =± sqrt(-9)

x-1 = ±sqrt(-1) sqrt(3)

Remember the sqrt(-1) = i

x-1 = ± 3i

Add 1 to each side

x-1+1 = 1± 3i

x = 1± 3i

(x, y) = (-7, 2)

Divide the second equation by 4 and add it to the first.

... (-x) +(4)/4 = (-6y+19) +(-4x -12y)/4

... -x +1 = -9y -x +19 . . . . simplify

... 9y = 18 . . . . . . . add 9y +x -1

... y = 2 . . . . . . . . . divide by 9

... -x = -6·2 +19 = 7

... x = -7

The solution is (x, y) = (-7, 2).

Answer:

-.37

Step-by-step explanation:

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Answer:

-.37

Step-by-step explanation:

that 3 /1 is 3 that

Answer: y = 0

Step-by-step explanation: Since the degree of the numerator is lower than the degree of the denominator, the horzontal asymptote is 0.

Answer:

1: 6

2: 1,2,3

3: 4m-1>5m-4

4: Not enough data

5: n = 11

6: The ceiling is lower than 3m

7: G = 7

8: C = 18

9: p + 18 = 41; p = 23

10: D = 100t

Step-by-step explanation:

Question 1:

5*2+x/2-7

5*2+6/2-7

10+6/2-7

10+3-7

13-7

6

Question 2:

4*2<16

8<16 True

4*1<16

4<16 True

4*3<16

12<16 True

4*4<16

16<16 False

Question 3:

Let's plug in 1 for m

4*1-1____5*1-4

4-1_____5-4

3_____1

3>1

Question 4:

You did not give an equation, so I cannot answer.

Question 5:

2*11 + 5 =27

22 + 5 = 27

27 = 27

So n = 11

Question 6:

x<3

The ceiling is lower than 3m because x<3

Question 7:

5.1g = 35.7

5.1g/5.1=35.7/5.1

g = 7

Check: 5.1 * 7 = 35.7

Question 8:

36 + c = 54

36 + c -36 = 54 - 36

c = 18

Check: 36 + 18 = 54

Question 9:

p + 18 = 41; p = 23 is correct because the number of paperback books plus the number of hardcover books would equal the total number of books sold. Check: 23 + 18 = 41

Question 10:

d=100t is correct because each time t goes up one it goes up 100. Example: if it is at one hour, than it is 100, if it is at 3 hours, than d = 100*3 = 300, which is the same pattern as the table.

Hope this helps!

The expression 5x² + x - 7 is calculated by substituting x with 6. Inequality and equation solving techniques are used to find the solutions to 4n < 16, 4m - 1 compared to 5m - 4, and other given problems, resulting in specific numerical solutions and identifying suitable real-world scenarios like a ceiling height represented by x < 3.

To solve the expression 5x² + x
- 7 where x equals 6, we substitute and get 5(3)² + (3) - 7 = 45 + 3 - 7 = 41.

The solutions to the inequality 4n < 16 from the set {1,2,3,4} are 1, 2, and 3, since 4 times each of these is less than 16.

Comparing the expressions when m = 3, we get 4m - 1 and 5m - 4. Substituting we have 12 - 1 < 15 - 4, thus 11 < 11, which is false, so 4m - 1 = 5m - 4.

The inequality 15 > w is only true for w = 14. Values w = 15 and w = 21 do not satisfy the inequality.

In the equation 2n + 5 = 27, solving for n within the replacement set gives n = 11 as the correct solution.

The inequality x < 3 represents a situation where The ceiling is lower than 3 m.

To solve 5.1g = 35.7, divide both sides by 5.1 to find g = 7.

For the equation 36 + c = 54, subtract 36 from both sides to get c = 18.

Cassandra's situation is best represented by the equation p + 18 = 41, resulting in p = 23 paperback books sold.

The relationship between the distance d and time t from the truck table is d = 100t, since distance is increasing by 100 kilometers every hour.

Answer:

B 12

Step-by-step explanation:

Since f(6)  means we want to evaluate the function when x=6

We will want to use f(x) =2x  because  5<= 6 <10

f(6) = 2*6

f(6)=12

f(x) = x   when 2 ≤ x < 5

So you can use this function if "x" is greater than or equal to 2 and less than 5

f(x) = 2x   when 5 ≤ x < 10

You can use this function if "x" is greater than or equal to 5 and less than 10

f(6) This means that x is 6, so you can plug in 6 for "x" in the equation.

You use the second function because 6 is greater than 5 and less than 10

f(x) = 2x

f(6) = 2(6)

f(6) = 12     Your answer is B

[tex]Similar:\\\\\triangle STU\sim\triangle QPR\qquad \boxed{SAS}\to side-angle-side\\\\m\angle SUT=m\angle QRP\\\\\dfrac{10}{4}=\dfrac{20}{8}\\\\L_s=\dfrac{10}{4}=\dfrac{10\cdot2}{4\cdot2}=\dfrac{20}{8}=R_s\\-------------------------------[/tex]

[tex]\text{Not similar or not necessarily similar}\\\\180^o-(90^o+30^o)=180^o-120^o=60^o\neq50^o\\\\\text{different angles}\\-------------------------------[/tex]

[tex]Similar:\\\\\triangle ABC\sim\triangle FED\qquad\boxed{SSS}\to side-side-side\\\\\dfrac{15}{5}=\dfrac{12}{4}=\dfrac{9}{3}\\\\3=3=3\\-------------------------------[/tex]

Answer:

Correct answer is C.

Step-by-step explanation:

Note that graph in the diagram has period [tex]\pi.[/tex]

Consider the function [tex]y=-2\cos (2(x+\pi ))-1.[/tex]

This function has a period [tex]T=\dfrac{2\pi}{2}=\pi.[/tex] Functions in another options have period that differes from [tex]\pi.[/tex]

The graph of this function passes through the point (0,-3), because

[tex]y(0)=-2\cos (2(0+\pi ))-1=-2\cos 2\pi-1=-2\cdot 1-1=-3.[/tex]

Answer:

[tex]y=-2cos (2(x+\pi ))-1[/tex]

Step-by-step explanation:

We are a given a graph from which we can clearly see that y = -1 when x  = 0.

Next, we will find out which of the options is the equation of the given graph and for that we need to set our calculator to the radian mode and then put the value of x to be 0.

1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1  = 3

2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1

3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3

We get y = -1 when x = 0 in equation number 3, y = -2 cos (2(x + pi)) - 1, so that is the equation of the given graph.

Answer:

$0.13 (this is a rounded answer)

Step-by-step explanation:

The unit cost is the cost of a 1 ounce bottle so you would divide the cost by the total number of ounces:

$2.00 divided by 16 is 0.125 but you would round because you need a cost not a decimal.

So your final answer would be $0.13 per ounce.

Answer:

$.13 per fl oz

Step-by-step explanation:

To find the unit cost, we take the cost and divide by the number of units

$2.00/16

$.125 per fl oz

Since this is money we round to the nearest cent.

$.13 per fl oz