Show how 2/5 + 4/10 is the same as 4/5

The plants which are growing at the same rate are Plant 1 and Plant 4.

Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.

If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.

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Answer:

B. 1 and 4

Step-by-step explanation:

Edge 2023

Answer:

1a. -( x + 1)² + 4

1b. y-intercept at y = 3

1c. x-intercepts at x = -3 and x = 1

Derivation of 1b and 1c below

Step-by-step explanation:

Question 1a

The vertex equation form of a parabola is given by

y = a(x-h)²  + k where (h, k) are the coordinates of the vertex

If a > 0 then the parabola is facing up(vertex is at a minimum)  and if a < 0 then parabola is facing down (vertex at a maximum)

From the graph we see that the parabola is facing down so a = -1

The vertex is at (-1, 4) so h = -1 and k = 4

Therefore the equation of the parabola is

y = -1(x - h)² + k = -1(x- (-1))² + 4 = -1(x + 1)² + 4

y = -( x + 1)² + 4   (Answer 1a)

Question 1b

The y-intercept is the y-value where the parabola crosses the y-axis. From the graph we see that the parabola crosses the y-axis at y = 3 and x = 0

So y-intercept from the graph is 3

To solve algebraically, set x = 0 in the parabola equation and solve for y

We get, for x = 0,

y = - (0 + 1)² + 4

y = -(1²) + 4 = -1 + 4 = 3

Hence verified

Question 1c

There will be two x-intercepts for a parabola. Looking at the graph we see that the parabola intersects the x-axis at two points (-3, 0) and (1, 0). So the two x-intercepts are -3 and 1

Algebraically we can determine the x-intercepts by setting y = 0 and solving for the two values of x

Setting y = 0 in the parabolic equation, we get
y = 0 = -(x + 1)² + 4

Switch sides
-(x + 1)² + 4 = 0

-(x + 1)² = -(x² + 2x + 1) = -x² -2x - 1

-(x + 1)² + 4 = 0
==> -x² -2x - 1 + 4 = 0

==> -x² - 2x +3 = 0

Multiply by -1 both sides
==> x² + 2x - 3 = 0

Solve this quadratic equation by factoring

x² + 2x - 3 = (x - 1)(x + 3) = 0

The solutions are
x - 1 = 0   ==> x = 1

x + 3 = 0 ==> x = -3

Hence verified

Answer:

8

Step-by-step explanation:

I attached my answer........

Answer:

A. 52 is your answer

Step-by-step explanation:

Explained below

Answer:

Ans is a

First you solve the inside of the bracket u will get 4(13)

which will give u 52

As Deanna is sitting farther from the center she is travelling at a faster rate.

Circumference of a circle is the distance around the circle.

We know that merry-go-round covers distance in form of circles and we also know that circumference of a circle is 2πr.

As Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride it can thought of as the radius.

∴ In one rotation Denna will cover (2πr) feet which is

= (2π×10 feet.

= 62.8 feet in 15 seconds.

Now if we do the previous calculation for Raquel with r taken as 8 she will cover:

= 50.24 feet in 15 seconds.

Therefore Deanna is spinning at a faster speed.

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Step-by-step explanation:

the point is (2, -5).

the origin is (0, 0).

the distance between 2 points is calculated via Pythagoras due right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.

the direct distance is the Hypotenuse, and the x coordinate and y coordinate differences are the legs.

so,

distance² = (2 - 0)² + (-5 - 0)² = 2² + (-5)² = 4 + 25 = 29

distance = sqrt(29) = 5.385164807...

so, the second answer option is correct.

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

we have to solve the following sentence

[tex]\sqrt{17}[/tex] --- 4     ( insert <,>, = to make the following sentence true)

what is square root ?

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is  [tex]\sqrt{}[/tex] .

we know that

square root of 17 is 4.12310563

which is 4+ 0.12310563

that is if we add 4+0.12310563 we get 4.12310563

therefore square root of 17 is greater than 4

that is [tex]\sqrt{17}[/tex] > 4  

since 4.12310563 > 4

hence,   we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

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Answer: n>=10

Step-by-step explanation:

n=number

2(n-2)>=16

2n-4>=16

2n>=20

n>=10

Answer:

[tex]2(x-2)\geq 16[/tex]

[tex]2x-4\geq 16[/tex]

[tex]2x\geq 20[/tex]

[tex]x\geq 10[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter of the sandbox is 2x+2y.

Therefore, the inequality is

[tex]\boxed{2x+2y \leq 20}[/tex]

Answer:

The first answer is correct

Step-by-step explanation:

y = mx + b is the slope intercept form of a line

15x - 5y = 30  Subtract 15x from both sides

-5y = -15x + 60  Divide both sides by -5

y = 3x -6  The -6 is your y-intercept.  It is the point (0.-6)  We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.

The x-intercept is when y = 0

y = 3x -6

0 = 3x - 6 Add 6 to both sides

6 = 3x  Divide both side by 3

2 = x This is the point (2,0)

We could have taken the original equation and set x=0 and y=0

15x - 5y = 30

15(0) - 5y = 30

-5y = 30  Divide both sides by -5

y = -6

15x -5y = 30

15x - 5(0) = 30

15x = 30  Divide both sides by 15

x = 2

-

The total number of students chosen is 4, 13, 22, and 31.

To determine the students who will be going to the board:

Now, using the following term formula, a + d (n - 1).

The second student is up next.

The third student will:

The fourth student will:

Therefore, the total number of students chosen is 4, 13, 22, and 31.

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Answer:

Exact Form:

51/2

Decimal Form:

25.5

Mixed Number Form:

25 1/2

Step-by-step explanation:

The greatest number of identical arrangements that can be made is 6 arrangements of 7 tulips and 9 roses.

The above problem we can use the greatest common factor, we are provided with the information that there are a total of 42 tulips and 54 roses. Now, we will find the greatest common factor of 54 and 42.

42- 54|2

21- 27 | 3

7 - 9

So the greatest common factor of 54 and 42 is 6, here we are left with 7 and 9 which indicates the number of tulips and roses

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The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

[tex](x - 8)^{2} = 144[/tex]

The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -

[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]

[tex]x^{2} + 64 + 16x = 144[/tex]

[tex]x^{2} + 16x + 64 - 144 = 0[/tex]

[tex]x^{2} + 16x - 80 = 0[/tex]

[tex]x^{2} + 20x - 4x - 80 = 0[/tex]

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

d. 20 feet by 20 feet

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[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]

Let us assume the given number is x.

If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

= (x-5) × 2

Formation of equation:

The number decreased by 5 can be written as: x - 5

Now, to double it, we will multiply it by 2 = (x-5) × 2

Therefore, we have the algebraic form of the given condition as :

= (x-5) × 2

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Answer:

Step-by-step explanation:

speed = distance/time

however speed is a compound measure

distance to school = speed x time

                               = 30mph x 1/3hr

                               = 10m

time =  10m / 45mph

       = 13.3 (recurring)

       = 13 mins

According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

Answer:

y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Step-by-step explanation:

Look at (-3,3) and (2,7)

So the line rises 4 units and runs 5 units, then slope is 4/5

using m = 4/5, y = 3, x = -3

y = mx + b

3 = 4/5(-3) + b

3 = -12/5 + b

b = 15/5 + 12/5 = 27/5

so y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Answer:

(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and  Tcritical = 3.143

In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds

we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas

Mean, xbar = 1.01

Standard deviation, s = 0.29

Sample size, n = 7

Confidence interval  : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 7 - 1 = 6

Hence Tcritical = 3.143

Margin of Error = 3.143 * 0.29/sqrt(6)

Margin of error = 0.37211

Lower boundary = (1.01 - 0.37211) = 0.63789

Upper boundary = (1.01 + 0.37211) = 1.38211

(0.63789 ; 1.38211 )

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Answer:

Step-by-step explanation:

Answer is in the pic.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]

Use the trigonometric identities to prove the given equation:

[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]

                 [tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]

The number of each ticket sold was:

Given Information:

The steps below can be used to calculate the total number of seats in each section:

Step 1 - In the lower section, enter 'x' as the total number of seats.

Step 2 - The linear equation that represents total ticket revenue.

Step 3 - The linear equation representing the total number of tickets is as follows:

Step 4: Change the value of y in the equation (1).

Step 5: Change the value of 'x' in equation (2).

Therefore, the number of each ticket sold was:

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The correct question is given below:
A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets. There are three times the amount of seats in the upper section as the lower section. The revenue from selling all 24,200 tickets is $1,140,000. write a system to represent the situation. How many seats are in each section

Answer:

$448.766754 per week or $448

Step-by-step explanation:

i gotchu

theres 52.1429 weeks

divide 23,400 by 52.1429

u get $448.766754 per week

hi

1/3 =2 /6

so 1/6 +2/6 = 3/6

as 3/6 is half if his income, then he remains the other half

Answer:

2.7

Step-by-step explanation:

When you subtract a negative number, you are actually adding because the negatives cancel out. So, it will be -3.3+0.6, which is -2.7

hope this helps! ibrahim

Hi there! Your answer is 2.7

Step-by-step explanation:

Add: -3.3+-0.6 = 2.7

When subtracting two negative numbers, this will result in a positive number since the negatives cancel each other out.

Hope this helps! :)

Answer:

16 inches

Step-by-step explanation:

Multiply 120 by 2 to start reversing the triangle area equation.

120*2 = 240.

Now divide by 15

240/15=

16

The length is 16 inches