The bottom of Ignacio's desktop is 74.5\,\text{cm}74.5cm74, point, 5, space, c, m from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are 49.3\,\text{cm}49.3cm49, point, 3, space, c, m from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8\,\text{cm}4.8cm4, point, 8, space, c, m.
Write an inequality to determine the number of clockwise rotations, rrr, Ignacio could make with the knob without his legs touching the desk.

Answer:

y = 3x + 9

Step-by-step explanation:

9 = 3[0] + b

0

9 = b

y = 3x + 9

This would be considered a parallel line, so 3 remains the way it is.

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Answer:

all work is shown and pictured

Answer:

.25x+1.75=15 and x=53

Step-by-step explanation:

first subtract 1.75 from both sides

then divide by .25 on both sides

and you will get x=53

Answer:

6

Step-by-step explanation:

5*6=30

7*6=42

Hey!

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

Solution:

30 / 5 = 6

42 / 7 = 6

5 x 6 = 30

7 x 6 = 42

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

Answer:

Multiplier is 6!

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Hope This Helped! Good Luck!

Answer:

Step-by-step explanation:

f(x)= x-4/√x

f  exist for : x  >  0

so the domain is : D= ]0 ; + ∞[

The number of calories by a 37​-member platoon of​ soldiers will be 6,48,24000 calories.

A calorie is a unit of energy. Energy is defined as the capacity to do work.

Now it is given that,

Calories contain in 1 MRE = 1,600

Number of MREs taken by a soldier per day = 3

Therefore, number of calories taken by soldier per day = 3*1600

                                                                                            = 4800 calories

Therefore, number of calories taken by 37 soldier per day = 37*4800

                                                                                           = 1,77,600 calories

Now since, 12 months = 365 days

⇒Number of calories taken by 37 soldier in 12 months = 365*1,77,600

⇒Number of calories taken by 37 soldier in 12 months =6,48,24000 calories.

Hence,The number of calories by a 37​-member platoon of​ soldiers will be 6,48,24000 calories.

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Answer:

4x^2 + 28x - 80=0

Step-by-step explanation:

(2x+4)(2x+10) = 120

1. Use FOIL (Distribute):

4x^2 + 20x +8x + 40 = 120

2. Group like terms:

4x^2 + 28x+ 40 = 120

3. Subtract 120 from both sides:

4x^2 + 28x - 80 = 0

Answer:

Option 3 - [tex]4x^2+28x-80=0[/tex]

Step-by-step explanation:

We have given,

The length of a rectangular frame is represented by the expression L=2x+4.

The width of the rectangular frame is represented by the expression B=2x+10.

The total area of a rectangular frame is A=120 square inches.

To find : Write an equation to solve for the width of a rectangular frame ?

Solution :

The area of the rectangle is given by,

[tex]\text{Area}=\text{Length}\times \text{Breadth}[/tex]

Substitute the values,

[tex]120=(2x+4)\times(2x+10)[/tex]

[tex]120=4x^2+20x+8x+40[/tex]

[tex]4x^2+28x+40-120=0[/tex]

[tex]4x^2+28x-80=0[/tex]

The required equation is [tex]4x^2+28x-80=0[/tex]

Therefore, option 3 is correct.

Answer:

Option A k=5

Step-by-step explanation:

step 1

Find the equation of f(x)

we have the points

(-10,-6) and (0,4)

Find the slope m

[tex]m=(4+6)/(0+10)=1[/tex]

The function in slope intercept form is equal to

[tex]f(x)=mx+b[/tex]

we have

[tex]m=1[/tex]

[tex]b=4[/tex] -----> the point (0,4) is the y-intercept

substitute

[tex]f(x)=x+4[/tex]

step 2

Find the equation of g(x)

we have the points

(-2,-6) and (0,4)

Find the slope m

[tex]m=(4+6)/(0+2)=5[/tex]

The function in slope intercept form is equal to

[tex]g(x)=mx+b[/tex]

we have

[tex]m=5[/tex]

[tex]b=4[/tex] -----> the point (0,4) is the y-intercept

substitute

[tex]g(x)=5x+4[/tex]

step 3

Find the value of k

we have

[tex]f(x)=x+4[/tex]

[tex]g(x)=5x+4[/tex] -----> equation A

[tex]g(x)=f(kx)[/tex] -----> equation B

[tex]f(kx)=kx+4[/tex] ----> equation C

substitute equation A and equation C in equation B and solve for k

[tex]kx+4=5x+4[/tex]

[tex]kx-5x=0\\kx=5x\\k=5[/tex]

The value of k in the equation g(x) = f(k*x), where g(x) and f(x) are graphs, signifies a horizontal compression, expansion, or reflection of the f(x) graph. It depends on the given graph to determine the exact value of k.

Without the graphical representation, it's difficult to provide a definite value for k. However, understanding the relationship between f(x) and g(x) can help us make an educated guess. If g(x) is a horizontal compression of f(x) by a factor of k, then k is positive and larger than 1. If g(x) is a horizontal expansion of f(x), then k is positive and less than 1. If g(x) is a reflection of f(x) across the y-axis and has a horizontal compression or expansion, then k is negative. For example, if g(x) completes one cycle in a space where f(x) would complete 5 cycles, then k is 5. If g(x) completes 5 cycles in a space where f(x) would complete one cycle, then k equals 1/5.

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Answer:x= -2

Step-by-step explanation:

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}[/tex]

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}[/tex]

AC must be the diameter of the circle.

What is Circle?

A circle is a closed two dimensional figure in which the set of all the points in the plane is equidistance from a center.

Given that;

A circle passes through points A(7, 4), B(10, 6), C(12, 3).

Now,

If AC is diameter of the circle then half the distance of AC is its radius and midpoint of AC is the center of the circle.

Since, B is also on the circle , then distance from B to the center must be same radius distance.

Midpoint of AC is calculated as;

= (7 + 12 / 2 , 4 + 3/2)

= (19/2 , 7/2)

= (9.5 , 3.5)

Now, Distance from A to the center and check the distance of B to the center as;

AM = √(9.5 - 7)² + (3.5 - 4)²

AM = 2.5495

And,

BM = √(9.5 - 7)² + (3.5 - 6)²

BM = 2.5495

So,  Distance from A to the center and the distance of B to the center is same.

Thus, AC must be the diameter of the circle.

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Answer:

12:8

Step-by-step explanation:

The ratio of biographies to histories is 1.5, or more simply as a whole number ratio, 3:2. This means that for every 3 biographies, there are 2 history books.

The question wants us to calculate the ratio of the number of biographies to the number of histories in the book display. To do this, simply divide the number of biographies by the number of histories. The problem provides the number of biographies as 12 and the number of histories as 8. Thus, the ratio is: 12 (biographies) / 8 (histories) = 1.5.

In other words, for every 1.5 biographies, there is 1 history book on the display. However, since ratios are commonly expressed as whole numbers, we can multiply both sides by 2 to get the ratio as 3:2, meaning for every 3 biographies, there are 2 history books. This provides a cleaner and more interpretable ratio.

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There are 52 legs and they all belong to hamsters. so 13 Hamsters are there​.

Total No. of legs = 52

Each hamsters have 4 legs.

No. of Hamster = 52/4 =13 Hamsters

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If two coins are tossed simultaneously, you will have one of the possible results

[tex]HH,\ HT,\ TH,\ TT[/tex]

with probability 1/4 each.

So, you'll have at least one head if you have HH, HT or TH, i.e. with probability 3/4.

Similarly, you have at most one tail if you get HH, HT or TH, so the probability will be the same.

In fact, both claims (at least one head and at most one tail) are verified by the same set of outputs HH, TH, HT, since they're not satisfied only by the output HH.

So, if those claims are not satisfied with probability 1/4, they're satisfied with probability 3/4.

Final answer:

The probability of getting at least one head when tossing two coins is 0.75.

When two coins are tossed simultaneously, the sample space consists of the following possible outcomes: {HH, HT, TH, TT}. To find the probability of getting at least one head, we can count the favorable outcomes which include at least one head: these are HH, HT, and TH. Thus, there are 3 favorable outcomes.

The total number of possible outcomes is 4. Therefore, the probability is 3 out of 4, or
0.75.

To find the probability of getting at most one tail, we consider the favorable outcomes: these are HH, HT, and TH. Again, we can see there are 3 favorable outcomes.

Since the total number of outcomes is the same, the probability remains
0.75.

Answer:

D.) -3x = 4y

Step-by-step explanation:

[tex] -3(-4) ≠ 4(-3) \\ \\ 12 ≠ -12[/tex]

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The point (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y. This is determined by substituting x with -4 and y with -3 in each equation and checking if the equation is balanced.

To find which equation (-4,-3) is not a solution to, we substitute x with -4 and y with -3 into each equation, then see if both sides of the equation are equal.

So, (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y.

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Answer:

No solution

Step-by-step explanation:

Subtract 5k from both sides

Simplify

No solution

Event A = rolling a 4 on a single die

Event B = rolling a number divisible by 3 (3 or 6) on a single die

There are three outcomes possible in total if either event A happens or event B happens. This is out of six outcomes total.

Divide the values and reduce: 3/6 = 1/2

Final Answer: 1/2

Answer:

Its Brand 2 :) also do you do connexus?

if so whats ur name :)

Step-by-step explanation:

Answer:

brand 4

Step-by-step explanation:

Answer:  454

Step-by-step explanation:

The first three digits will be the significant digits.  Round the third digit.

454.12

the digit and the 4 is 1 so 454.12 is rounded to 454

Answer:

Step-by-step explanation:

| n+2 | = 7    : n+2 = 7   or  n+2 = -7

n=5  or n = - 9

Answer:

20 apple pies

Step-by-step explanation:

On Saturday they sold 16, while on Sunday they sold 4 more.

16+4 = 20.

20 apple pies.

Let P = perimeter

P = 3x + 5

Let x = 10

P = 3(10) + 5

P = 30 + 5

P = 35

Given that Henry can write 5 pages in 3 hours, his rate is 5/3 pages per hour. Multiplying this rate by 8 hours, we get approximately 13.33 pages. Therefore, Henry can write approximately 13 to 14 pages in 8 hours at the given rate.

The subject of this question is mathematics, specifically, it is dealing with the concept of rates. Given that Henry can write 5 pages in 3 hours, we can set up a rate, which is simply a ratio that compares quantities in different units. So, Henry's rate of writing is 5/3 pages per hour.

To find out how many pages Henry can write in 8 hours at this rate, we multiply his rate (5/3) by the number of hours (8 hours). So, (5/3) x 8 = 40/3 = 13.33. However, since we cannot have a fraction of a page, we can round this to 13 pages for a conservative estimate or to 14 pages for a liberal estimate.

So, at the rate given, Henry can write approximately 13 to 14 pages in 8 hours.

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Henry can write approximately 13.33 pages in 8 hours.

To find out how many pages Henry can write in 8 hours, we can set up a proportion using the given information.

Since Henry can write 5 pages in 3 hours, we can write the proportion as 5/3 = x/8.

To solve for x, we can cross multiply and then divide to find that x = 40/3.

So, Henry can write approximately 13.33 pages in 8 hours.

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Answer:

19 1/4 hours

Step-by-step explanation:

19 h 15 min = 19 hours + 15 minutes

                   = 19  hours + (15/60)  hours

                   = 19 + 1/4

                   = 19 1/4 hours

Answer:

Step-by-step explanation:

Start train 1 at 6 pm an train 2 at 9pm

Answer:

-4 10/13

Step-by-step explanation:

-52-8m = 10 + 5m

-8m = 62 +5m

-13m = 62

-m = 62/13

m = - 62/13

m = -4 10/13

Answer:

When there is not a constant rate of change

Step-by-step explanation:

A linear model shows a continuous response variable as a function of one or more predictor variables.

A linear model is a good fit for a set of data when the plotted points show a constant rate of change.

When a plot of values form a scatter plot, it is difficult to identify a linear model because the points will not appear to follow a trend.

To come up with a linear function in this case will require you to identify the line of best fit then extending the line to y-axis intercept so as to be able to find the slope.

Answer:

5x10⁸

Step-by-step explanation:

Cell = 200 cubic micrometers.

Te question is, how many 200 cubic micrometers are there in a cubic centimeter. 1st, we have to convert 200 cubic centimeter into cubic centimeter:

1cm = 1x10⁴micro, which is the same to:

1x10⁻⁴ cm = 1micro

Now, we have to cube both sides, to "equal the volumes"

(1x10⁻⁴cm)³ = (1micro)³

1x10⁻¹²cm = 1micro³

Multiple both sides by 200:

200 x 1x10⁻¹²cm = 1micro³ x 200

2x10⁻¹⁰cm³ = 200micro³

Finally, 1 cubic cm / 2x10⁻¹⁰cm³ = 5x10⁸

Final answer:

Explaining the number of cells in a cubic centimeter based on the volume of a 10 μm cell.

Explanation:

For a 10 μm cell:

Calculate the volume: V = (4/3)πr³

Convert diameter to radius: r = 5 μm

Substitute and calculate volume: V = (4/3)π(5)³ = 524 μm³

Convert to cubic centimeters: 1 μm³ = 10^-9 cm³, so 524 μm³ = 5.24 x 10^-7 cm³

Calculate the number of cells in 1 cm³: 1 cm³ / 5.24 x 10^-7 cm³ = 1.91 x 10^6 cells

Answer:

300

Step-by-step explanation:

Divide 3000 by 10 by striking out each zero one-by-one [300 ÷ 1] to get 300. This is one of the fastest ways to solve with zeros.

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The result would be 300 units and 320 units respectively.

3 thousand divided by 10 in unit and standard form:

To divide 3,000 by 10 in unit form: 3,000 ÷ 10 = 300 units.

To divide 3,000 by 10 in standard form: 3.2 × 10³ ÷ 10¹ = 3.2 × 10² = 320 units.