LaTanya says that the growth factor of f(x) = 100(1.25) is 25%. What mistake did LaTanya make?

Option D:

160 plastic cubes can fit into the box.

Solution:

Convert mixed fraction into improper fraction.

Length of the box = 4 ft

Width of the box = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] ft

Height of the box = 2 ft

Volume of the box = length × width × height

                                 [tex]$=4\times\frac{5}{2} \times2[/tex]

                                 = 20 ft³

Volume of the box = 20 ft³

Length of the plastic cube = [tex]\frac{1}{2}[/tex] ft

Volume of the cube = length × length × length

                                 [tex]$=\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2}[/tex]

                                 [tex]$=\frac{1}{8} \ \text{ft}^3[/tex]

Volume of the cube = 0.125 ft³

[tex]$\text{Number of plastic cubes}=\frac{\text{Volume of box}}{\text{Volume of cube}}[/tex]      

                                        [tex]$=\frac{20}{0.125}[/tex]

                                        = 160

Number of plastic cubes = 160

Hence 160 plastic cubes can fit into the box.

Option D is the correct answer.

For the graph, the image of triangle ABC after a reflection across the x-axis, the vertices of the image will be called A” B” , and C” are respectively,  (-3, 4),  (-3, 1),  (-1, 1)

Reflection about the axis is a transformation in geometry where a figure is flipped across a line or plane, producing a mirror image of the original figure. The line or plane across which the figure is reflected is called the axis of reflection.

Given that,

A graph, having triangle ABC

The reflection points, A', B', C'  = ?

All the vertices and their mirror image will be at equal distance from the x-axis

So, y-coordinate will be equal in magnitude but different in sign for all the vertices and their mirror image

x-axis is axis of reflection,

there will be no change in x-coordinates

So, x-coordinates will be same in magnitude and in sign as well

Now, Mirror image points can be written as,

A' = (-3, 4)

B' = (-3, 1)

C' =  (-1, 1)

Hence, the points are  (-3, 4),  (-3, 1),  (-1, 1)

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Solution:

Given equation of circle is:

[tex]x^{2} +y^{2} -12x-2y+12=0[/tex]

Move the constant to other side

[tex]x^{2} +y^{2} -12x-2y = -12[/tex]

Group the equation

[tex](x^{2} -12x)+(y^{2}-2y)=-12[/tex]

Add 36 and 1 from both sides

[tex](x^{2} -12x +36)+(y^{2}-2y + 1)=-12 + 36 + 1\\\\(x^{2} -12x + 36)+(y^{2}-2y + 1)= 25[/tex]

Which is simplified as:

[tex](x - 6)^2 + (y-1)^2 = 25[/tex] --------- eqn 1

The equation of circle is given as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where, r is radius and (h, k) is center

Compare eqn 1 with above general equation

(h, k) = (6, 1)

Thus the center of a circle is (6, 1)

Answer:

the center the circle is (6,1)  

Step-by-step explanation:

Answer:

The integer values of x are 5 and 6

Step-by-step explanation:

we have

Inequality A

[tex]4x-2>17[/tex]

solve for x

adds 2 both sides

[tex]4x>19[/tex]

divide by 4 both sides

[tex]x> 4.75[/tex]

solution A is the interval (4.75,∞)

Inequality B

[tex]3x+5<24[/tex]

solve for x

subtract 5 both sides

[tex]3x<19[/tex]

divide by 3 both sides

[tex]x<6.33[/tex]

solution B is the interval (-∞,6.33)

The solution of the inequality A and the inequality B is

(4.75,∞) ∩  (-∞,6.33)=(4.75,6.33)

The integer values of x are 5 and 6

Final answer:

The integer value of x for which both inequalities 4x - 2 > 17 and 3x + 5 < 24 are true is x = 5.

Explanation:

To find the integer value of x for which the inequalities 4x – 2 > 17 and 3x + 5 < 24 are both true, we solve each inequality step by step.

Answer:

7.9

4.2

9.3

17.8

Step-by-step explanation:

8. √63

the square of 8 is 64 √63 is close to 64 so we can say it's 7.9 approximately

9. √18

the square of 4 is 16, √18 is greater than 16 so we can say it's 4.2 approximately

10. √87

the square of 9 is 81, √87 is greater than 81 so we can say the value of it is approximately 9.3

11. √319

the square of 18 is 324, √319 is smaller than 324 so we can say it's 17.8

Answer:

3x - 24

Step-by-step explanation:

9x - 6x - 24

3x - 24

Answer:

48

Step-by-step explanation:

Step 1:  Convert words into an expression

What is 6 multiplied by 8

6 * 8

Step 2:  Multiply

6 * 8

48

Answer:  48

Answer:

45.6

Step-by-step explanation:

0.60 x 76 = 45.6

Answer:45.6

Step-by-step explanation:

60/100*76

0.6*76

45.6

Answer:

y=3x

Step-by-step explanation:

If y is the total distance from the shore and it increases by 3 miles every hour, then by plugging in the amount of hours that have passed into x we will find the distance they have traveled. For example, if they have been out for 5 hours then you would do y=3(5) which would be 15 miles from the shore.

The correct equation to represent the relationship between Mary's distance from shore and time is y=3x. This is a linear equation, with 3 representing the rate of increase in distance for each time unit (each hour).

In this case, Mary is moving at a constant rate, which means we are dealing with a linear relationship. The problem states that her distance from shore, y, increases by 3 miles for each hour, x. Therefore, the correct equation to model this scenario would be y=3x.

This is an equation of a line where 3 is the slope, signifying the change in distance for each time unit (in this case, an hour), and x is the time in hours. So, as time increases, the distance from the shore also increases at a rate of 3 miles per hour.

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3 km per minute is approximately equal to 111.8 miles per hour.

To convert 3 km per minute to miles per hour, we can use the conversion factors:

1 kilometer = 0.621371 miles 1 hour = 60 minutes

First, let's convert 3 km per minute to km per hour:

3 km/min * 60 min/hour = 180 km/hour

Now, let's convert km per hour to miles per hour:

180 km/hour * 0.621371 miles/km = 111.84757 miles/hour

Rounding to the nearest tenth, we get:

3 km per minute is approximately equal to 111.8 miles per hour.

Answer:

9

Step-by-step explanation:

because diameter never change or if it is radius the first half is 9 so, the second half would be 9 too.

so, x=9

Answer:

G x 3 = 48

Step-by-step explanation:

let G be Greg's score

And product means multiplication.

so G x 3 = 48.

finding Greg's score means 3g = 48.

g = 48/3

g = 16.

Answer:

266.5y

Step-by-step explanation:

120.5y+80.5y+65.5y

201y+65.5y

266.5y

y = ([tex]\frac{3}{2}[/tex])x -2 is the equation of the required line

Step-by-step explanation:

Step 1 :

Equation of the given line is 3x-2y=14

Re writing this in the form y = mx + c , we have

-2y = -3x +14

 y = ([tex]\frac{3}{2}[/tex])x - 7

The co efficient of x , m is the slope of the line. So for the given line the slope is  [tex]\frac{3}{2}[/tex]

Step 2 :

We have to find  equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of [tex]\frac{3}{2}[/tex].

Step 3 :

Equation of line with slope m and passing through a point ([tex]x_{1} ,y_{1}[/tex]) is

(y-[tex]y_{1}[/tex]) = m((x-[tex]x_{1}[/tex])

So equation of line passing through (-6,-11) and with a slope of  [tex]\frac{3}{2}[/tex] is

(y-(-11)) = [tex]\frac{3}{2}[/tex] ( x - (-6))

y + 11 = [tex]\frac{3}{2}[/tex] ( x + 6)

y = ([tex]\frac{3}{2}[/tex])x + 9 - 11

y = ([tex]\frac{3}{2}[/tex])x -2

Step 4 :

Answer  :

y = ([tex]\frac{3}{2}[/tex])x -2 is the required equation

The given equation has the slope 3/2 after converting to the slope-intercept form. Because parallel lines share the same slope, the equation for the line parallel to the given line, passing through the point (-6,-11), is found to be y = (3/2)x - 9 using the point-slope form.

To find an equation that is parallel to a given equation, we must first find the slope of the given line. The equation provided is in the form Ax + By = C. To convert this into slope-intercept form (y = mx + b), where m is the slope, we rearrange the equation to get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2.

Parallel lines share the same slope, the equation of the line parallel to the given one that passes through point (-6,-11) will also have the slope 3/2. We stick this and our point into the point-slope form of a line (y - y1 = m(x - x1)) to get: y + 11 = 3/2(x + 6). Simplifying, we get y = (3/2)x - 9 which is the equation of the line parallel to the given equation that passes through the point (-6,-11).

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The volume of a conical pile of dirt with an 11-meter radius and a 6-meter height is approximately 754.24 cubic meters.

The question is asking for help in calculating the volume of a conical pile of dirt.

The formula for finding the volume of a cone is  [tex]V = (1/3) \pi r^2h[/tex], where V is the volume, r is the radius, and h is the height of the cone.

Substituting the given values, the radius r is 11 meters, the height h is 6 meters, and using 3.14 for
π, the calculation would be -

V = (1/3) * 3.14 * 112 * 6.

To find the volume: V = (1/3) * 3.14 * 121 * 6

= 3.14 * 40.333333 * 6  

= 754.24 cubic meters.

So, there are approximately 754.24 cubic meters of material in the conical pile of dirt.

Answer:

453

Step-by-step explanation:

Since Brandon spent 47 % of his money you Will subtract 500-47.

Answer:

Step-by-step explanation:

Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...

  (10 +c)/(10 -c) = 3/2

  2(10 +c) = 3(10 -c) . . . . . . "cross multiply"

  20 +2c = 30 -3c . . . . . . . eliminate parentheses

  5c = 10 . . . . . . . . . . . . . . . add 3c -20

  c = 2 . . . . . . . . . . . . . . . . . divide by 5

The speed of the current is 2 miles per hour.

__

The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...

  (12 mi/h)(2 h) = 24 mi

The one-way distance of the trip is 24 miles.

Answer:

957.62

Step-by-step explanation:

Given the house price, P=$197,000, [tex]n=12\times 30=360, i=0.0415/12[/tex], the monthly payments, M, can be calculated as:

[tex]M=P[\frac{i(1+i)^n}{(1+i)^{360}-1}]\\\\M=[\frac{\frac{0.0415}{12}(1+\frac{0.0415}{12})^360}{(1+\frac{0.0415}{12})^{360}-1}]\\\\M=957.62[/tex]

Hence, the monthly payment of the baloon mortgage is $957.62

Answer:

116.3

Step-by-step explanation:

Supplementary angles add to 180

One angle is 63.7, the other is x

63.7+x = 180

Subtract 63.7 from each side

63.7-63.7+x = 180-63.7

x = 116.3

Answer:

0

Step-by-step explanation:

78/17 gives 4.588

In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.

In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588

This number is between 0 and 10.

The whole number there is 4. Therefore, 4 will be rounded up to Zero.

If the question and us to round up to the nearest whole number, as we have 4.588

The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.

4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0

g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x = [tex]\frac {4}{3}[/tex].

Step-by-step explanation:

We have a function f(x) = [tex]x^{2}[/tex] and another function , g(x) = [tex]\frac{3}{4} x^{2}[/tex]. In the graph of y = [tex]x^{2}[/tex] , the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.

Graphing y = (x - h)2 + k , where h = 0 & k = 0

Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.

Step-by-step explanation:

(a)

[tex] In\: \triangle ABC \& \triangle DEF \\\\

\frac {AB} {DE} = \frac {40} {48} = \frac {5} {6}...(1)\\\\

\angle ABC \cong \angle DEF... (each\: 90°)...(2)\\\\

\frac {BC} {EF} = \frac {30} {36} = \frac {5} {6}...(3)\\\\[/tex]

From equations (1), (2) & (3)

[tex] \triangle ABC \sim \triangle DEF[/tex]

(By SAS Postulate)

Hence both of the triangles are similar.

(b)

Prism DEF will have greater volume, because length of its sides are larger than that of prism ABC.

6/5 = 1.2 times greater.

Answer:

[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]

Step-by-step explanation:

If you are talking about radical expressions, then the two equations should be something like

[tex] \sqrt{x + 1} + \frac{2}{ \sqrt{x} } [/tex]

Assuming this is the intended expression, then:

[tex] \frac{ \sqrt{x \times } \sqrt{x + 1} + 2}{ \sqrt{x} } [/tex]

We then simplify by collecting LCM to obtain:

[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]

Answer: No

Step-by-step explanation:

10x + 11 when x= 1 is equal to 21

While 5x + 11, when x=1 is equal to 16

Answer:

252

Step-by-step explanation:

Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:

72/100 = 0.72

Then multiply 350 by 0.72:

350 x 0.72 = 252

I hope this helps!

Answer: -72√3

Step-by-step explanation:

(-9√2)(4√6)

−9√2*4√6

-9*4√2*6

-9*4√12

-9*4*2√3

-72√3

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)  

- Cutiepatutie ☺❀❤

Final answer:

To simplify (-9√2)(4√6), we multiply numerical coefficients (-9) and (4), and the square roots √2 and √6, simplifying to get -72√3 which is option B.

Explanation:

To simplify the expression (-9√2)(4√6), we need to follow the rules of algebraic multiplication for square roots. Here are the steps to simplify the expression:

The correct option from the given choices is thus B. -72√3.

Answer:

Find 6.75% of 260

Step-by-step explanation:

Hi

To find the volume of a cone, you use the formula 1/3πr²h, substituting in the radius for r and the height for h. For an example cone with a radius of 4 and a height of 9, the volume would be 48π or approximately 150.72 after rounding to the nearest hundredth.

The student is asked to find the volume of a cone. The formula to find the volume of a cone is 1/3πr²h, where r is the radius of the base of the cone and h is the height of the cone.

If the student is given the radius and the height, they would just need to substitute the values into the formula. For example, if the radius of the cone is 4 and the height is 9, the volume would be 1/3 * π * (4)² * 9 = 48π. If the student prefers a decimal approximation, they can substitute pi with 3.14 to get 150.72, rounded to the nearest hundredth.

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Answer:

x > 2/7

Step-by-step explanation:

Step 1:  Make an inequality

3/14 + x > 1/2

Step 2:  Solve for x

3/14 + x - 3/14 > 1/2 - 3/14

x > 2/7

Answer:  x > 2/7