Write 5.269 and 5.038 as mixed numbers

The garden club is planting fruit trees in their school's garden, and they have two types of trees: one large tree that needs a lot of fertilizer and several newly planted trees that need a much smaller amount of fertilizer. The large tree requires 5 pounds of fertilizer.

which is a significant amount compared to the smaller trees, which only need 0.5 pounds of fertilizer each.

The reason for the difference in fertilizer requirements is due to the size and age of the trees. The large tree is likely fully grown and mature, and therefore requires a substantial amount of fertilizer to support its growth and fruit production. The younger and smaller newly planted trees, on the other hand, need much less fertilizer since they are still growing and developing.

Providing the proper amount of fertilizer is crucial to ensuring healthy tree growth and fruit production, which is why the garden club is treating the larger tree differently than the smaller ones. By giving each tree the proper amount of fertilizer necessary for their growth stage, the garden club is helping ensure the success of their fruit tree planting project and ultimately helping to contribute to the schools' educational and environmental goals.

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Answer:

See attachment for graph

Step-by-step explanation:

Given

\(y = x^2 - 3\)

Required

The graph of the equation

First, we determine the range of y

\(x = -3\)

\(y = x^2 - 3 \to y = (-3)^2 - 3 = 6\)

\((-3,6)\)

\(x = -2\)

\(y = (-2)^2 - 3 = 1\)

\((-2,1)\)

\(x = -1\)

\(y = (-1)^2 - 3 = -2\)

\((-1,-2)\)

\(x=0\)

\(y = 0^2 - 3 = -3\)

\((0,-3)\)

\(x = 1\)

\(y= 1^2 - 3 = -2\)

\((1,-2)\)

\(x = 2\)

\(y =2^2 - 3 = 1\)

\((2,1)\)

\(x = 3\)

\(y = 3^2 - 3 = 6\)

\((3,6)\)

See attachment for graph

To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.

Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).

From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:

P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =

Therefore, the probability of selecting a student from the given information is .

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The small radius =5 cm; and the Long radius =5+4=9 cm.

Area (a + b) = 106 * pi cm^2 (given)

radius of a = x : radius of b = (x + 4)

Area a =\(pi * r^2 = pi * x^2\\\)

Area b = \(pi * r^2 = pi * (x + 4)^2\)

Area (a + b) = \(pi * x^2 + pi * (x + 4)^2\) = 106 * pi cm^2

Area (a + b) =\(pi * x^2 + pi * (x^2 + 8x + 16)\) = 106 * pi cm^2

Area (a + b) = pi * (\(2x^2\)+ 8x + 16) = 106 * pi cm^2

Area (a + b) = \(2x^2 + 8x - 90 = 0\)

2x^2 + 8x - 90 = x^2 + 4x - 45 = 0

x^2 + 4x - 45 = (x + 9)(x -5) = 0

x = 5 or x = -9

Therefore: radius a = 5 cm and radius b = 9 cm

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The question is incomplete

The sum of the areas of the two circles is 106pi cm^2 and the radius of the larger circle is 4cm longer than the radius Of the smaller circle. How could I find the length of the radii?

The fraction of magazines that were delivered to families who were home written as a decimal is 0.4

Difference between fraction and decimal?

Total number of families = 25

Number of families in home = 10

Then, number of families away = 25 - 10 = 15

Fraction of magazines that were delivered to families who were home

= Number of families in home/ Total number of families

= 10 / 25

= 0.4

Hence, the fraction of magazines that were delivered to families who

were home written as a decimal is 0.4

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

blue graph

Step-by-step explanation:

that graph looks similar to e^x

so f(-x) will be similar to e^-x

so it will be a reflection over y axis

see the picture below

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer + Step-by-step explanation:

let x be the time that Eric spends running

    y be the time that Eric spends walking

a) the statement “Eric runs and walks for a total of 12 minutes to reach his goal” is equivalent to the equation: x + y = 12

b) the coordinates of the intersection point are (5.333...  ,  6.666...)

Interpretation:

the time that Eric spends running is 5.333... minutes  

the time that Eric spends walking  is 6.666... minutes

Answer:

Given equation:

\(200x+80y=1600\)

where:

If Eric runs and walks for a total of 12 minutes, then:

\(x+y=12\)

To graph:

\(200x+80y=1600 \implies y=20-\dfrac{5}{2}x\)

\(\textsf{x-intercept}: \quad 20-\dfrac{5}{2}x=0 \implies x=8 \implies (8,0)\)

\(\textsf{y-intercept}: \quad 20-\dfrac{5}{2}(0)=20 \implies (0,20)\)

\(x+y=12 \implies y=12-x\)

\(\textsf{x-intercept}: \quad 12-x=0 \implies x=12 \implies (12,0)\)

\(\textsf{y-intercept}: \quad 12-0=12 \implies (0,12)\)

Point of intersection (equate equations):

\(\begin{aligned}20-\dfrac{5}{2}x &=12-x\\20-12 &=\dfrac{5}{2}x-x\\8&=\dfrac{3}{2}x\\16 &=3x\\x &=\dfrac{16}{3}\end{aligned}\)

\(y=12-\dfrac{16}{3}=\dfrac{20}{3}\)

\(\implies \left(\dfrac{16}{3},\dfrac{20}{3}\right)\)

The point of intersection tells us that Eric runs for 16/3 mins and walks for 20/3 minutes.

Answer:

2/7

Step-by-step explanation:

All I did was just simplify the fraction 4/14

4/14=2/7

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Answer:

3x° = 60°

2x° = 40°

Step-by-step explanation:

3x + 80 +2x = 180° (Linear Pair)

5x + 80 = 180

5x = 180 - 80

5x = 100

x = 20

Substituting the value for x,

3x° = 3 × 20 = 60°

2x° = 2 × 20 = 40°

Answer:

0.128rad/sec

Step-by-step explanation:

Let x represent the between the man and the point on the path

θ = the angle

dx/dt = 4 ft/s

dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

tan θ = x/20 ft

Cross Multiply

20tan θ = x

dx/dt = 20sec² θ dθ/dt

dθ/dt = 1/20 × cos² θ dx/dt

dθ/dt= 1/20 × cos² θ × 4

dθ/dt = 1/5 × cos² θ

Note : cos θ = 4/5

dθ/dt = 1/5 × (4/5)²

dθ/dt = 16/125

dθ/dt = 0.128rad/sec

Answer:

you can't square root with negative numbers the answer will be math error and you cant simplify it unless it has no negative in it.

Answer:  x= 21 =0.500

​

x= 8−2− −12 = 4−1−i 3

​ =−0.2500−0.4330i

x= 8−2+ −12 = 4−1+i 3

​ =−0.2500+0.4330ix= 21 =0.500

​

Step-by-step explanation:I hope this helped, if not HMU and I will get you a better answer

-Have a great day! :)

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

If two figures are similar, all of their pairs of corresponding sides have the same ratio:

To prove if the given figures are similar find the ratio between corresponding sides (to identify corresponding sides start with the smaller side in both figures and follow this logic):

Transformations from ABC to YZX: ABC (preimage) is dilated to get YZX (Image)

Find the factor of dilation:

Answer:

Nothing further can be done with this topic. Please check the expression entered or try another topi

Step-by-step explanation:

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Answer:

D is Permutation with repetition right

Step-by-step explanation:

Answer:

Step-by-step explanation:

there are 6-10

The interest that Jimmy's account has earned is $35.95.

Interest is the total increase in excess of the amount deposited in the account. Interest earned can be determined by subtracting the amount deposited from the current balance.

Interest = current balance - amount deposited

$3,485.95 - $3,450.00 = $35.95

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Answer:

(A) The lines L1 and L2 are NOT parallel

(B) The lines DON'T intersect

(C) The lines ARE skew

Step-by-step explanation:

L1: x=26+7t; y=8+3t; z=18+5t

L2: x=-11+8t; y=-11+5t; z=-13+8t

TEST FOR PARALLEL

The direction vector for L1 is (7,3,5)

The direction vector for L2 is (8,5,8)

Since 8 is not a multiple of 7,

5 is not a multiple of 3,

and 8 is not a multiple of 5; both direction vectors are NOT propositional.

The lines are hence unparallel lines. They do not move in the same direction.

TEST FOR INTERSECTION

We equate the functions of X, the functions of Y or the functions of Z, and substitute the value of t gotten, into another equation herein.

26 + 7t = -11 + 8t

7t - 8t = -11 - 26

-t = -37

t = 37

Substituting 37 for t in equation 3, we have

18+5(37) = -13+8(37)

18+185 = -13+296

203 = 283

Obviously, 203 is not equal to 283

These 3 equations aren't consistent, so the lines don't intersect or cross paths. Lines L1 and L2 are skew.

Answer:

(181,264,245) or x=181 y=264 z=245

Step-by-step explanation:

a) Clearly define your variables.

x=section a

y=section b

z=section c  

b) Write a system of equations.

x+y+z=690

20x+15y+10z=10,030

x+328=y+z ---> x-y-z=-328

c) We can solve using a matrix.

The numbers in parenthesis are what go in the matrix.

x(1)+y(1)+z(1)=690(690)

20x(20)+15x(15)+10x(10)=10,030(10,030)

x(1)-y(-1)-z(-1)=-328(-328)

(Pretend that the lines are not broken and look like this [])

       (⎡ 1   1   1      690    ⎤)  

rref (⎢20 15 10  10,030 ⎥)

      (⎣ 1  -1  -1     -328    ⎦)

Answer(Matrix): ⎡1 0 0   181 ⎤

                          ⎢0 1 0  264⎥

                          ⎣0 0 1  245⎦

Or you could solve without using a matrix:

(x + 8)(x - 6)

to factorise consider the factors of - 48 which sum to + 2

These are + 8 and - 6 thus

x² + 2x - 48 = (x + 8)(x - 6)

Answer:

D) x + 8

Step-by-step explanation:

factor. Find factors of x² & -48, in that, when combined, it will give 2x.

x² + 2x - 48

x             -6

x               8

(x - 6)(x + 8)

Check. Follow FOIL method. Combine the first, outside, Inside, & Last terms:

(x * x) = x²

(x * 8) = 8x

(x * -6) = -6x

(-6 * 8) = -48

x² + 8x - 6x - 48

x² + 2x - 48 (√)

Your answer choices:

(x - 6) & (x + 8)

x + 8 shows up as a choice, so D) x + 8 is your answer.

~

Answer:

principles of accounting are the rules and guidelines that companies must follow when reporting financial data. 

Revenue Recognition Principle,

Historical Cost Principle,

Matching Principle,

Full Disclosure Principle,

Objectivity Principle.