Diagonals of a parallelogram bisect each other true or false

Answer:

Step-by-step explanation:

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

Let's say that the very first figure is x and the next is y.

x - y = 3 -----> y=x-3 .........(i)

xy=88 .......(ii)

Substitute (i) to (ii)

xy=88

x(x-3)=88

x\(x^{2} - 3x = 88\\x^{2} - 3x - 88 = 0\)

(x+8)(x-11)=0

x+8=0 or x-11=0

x=-8 or x=11

Substitute x=-8 to (i)

y=x-3

y=-8-3=-11

Substitute x=11 to (i)

y=x-3

y=11-3=8

Thus, x = -8 and y =- 11 or x = 11 and y = 8

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

A 2nd equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0.  For instance, if school administration decides to build a chapel with a floor size of 400 sq metres and a length that is two meters longer than its width, we will need the aid of a quadratic equation to determine the length and breadth. 

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Answer:

2π or 6.2831 (I don't know which since I don't know what to round to or if it is supposed to be in terms of π soooo)

Step-by-step explanation:

\(2\pi(1) = 2\pi = 6.2831\)

Answer:

Step-by-step explanation:

width of the window is W

height of the window is 1.75 x W

perimeter of the window is 5.5w

33 ÷ 5.5 = 6

W = 6

ATQ

\(\\ \tt\Rrightarrow Perimeter=33\)

\(\\ \tt\Rrightarrow 2(L+W)=33\)

\(\\ \tt\Rrightarrow 2(x+1.75x)=33\)

\(\\ \tt\Rrightarrow 2x+3.5x=33\)

\(\\ \tt\Rrightarrow 5.5x=33\)

\(\\ \tt\Rrightarrow x=\dfrac{33}{5.5}\)

\(\\ \tt\Rrightarrow x=6\)

The area of the field in square meters is approximately 679.2431 m².Given: Width (W) of rectangular field in a park = 66.5ftLength (L) of rectangular field in a park = 110ftArea

(A) of rectangular field in a park in square meters.We can solve this question using the following steps;Convert the measurements from feet to meters.Use the formula of the area of a rectangle to find out the answer.1. Converting from feet to meters1ft = 0.3048m

Now we can convert W and L to meters

W = 66.5ft × 0.3048 m/ft ≈ 20.27 m

L = 110ft × 0.3048 m/ft ≈ 33.53 m2. Find the area of the rectangle

The formula for the area of the rectangle is given as;A = L × W

Substituting the known values, we have;

A = 33.53 m × 20.27 mA = 679.2431 m²

Therefore, the area of the field in square meters is approximately 679.2431 m².

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Answer:

12

Step-by-step explanation:

Sum means addition. 3 + 3 + 6 = 12

Answer:

12

Step-by-step explanation:

i hope this is what you meant

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Check the picture below.

3(6 - x) + 2x = 15

18 - 3

-3x+2x = 15

18 - x = 15

-x = 15 - 18

-x =- 3

x = 3

easy - peasy

Answer:

x=3

Step-by-step explanation:

PEMDAS

Or parenthesis, exponent, multiply, divide, addition, and subtraction. (Order of operations)

3(6-x) + 2x = 15

    Start with multiplying

18 - 3x + 2x = 15

    then combine like terms

18 - x = 15

    subtract 18 from each side

-x = -3

    times each side by -1 to remove the negative

x = 3

Answer:

Step-by-step explanation:

Fact: sum of angles in a triangle is 180° so add all angles and find x

x+2x+2x+15 =180 ; subtract 15 from both sides

5x = 180-15; divide by 5 both sides

x= 33

Answer:

Step-by-step explanation:

Answer and Step-by-step explanation:

Yes. x = 4 is a solution for 3x + 6 = 18.

All you have to do to check is plug it into the equation.

3(4) + 6 = 18

12 + 6 = 18

18 = 18

Correct!!

#teamtrees #WAP (Water And Plant)

Answer:

o resultado é 961

foi mal se erei

The maximum number of air hockey games that can be played out of the $100 game card at Dave & Buster's is 50.

With a $100 game card, the maximum amount of times to play air hockey is found thus;

After 2 rounds of ski-ball at the cost of $2 per game = $4

After 3 rounds of Dance Dance Revolution at the cost of  $2.50 per game = $7.50

If air hockey costs $1.75 per game, then;

$4 + $7.50 = $11.50

$100 - $11.50 = $88.50

Therefore $88.50/$1.75 = 50.5 approximately 50 times.

It will take 50 times to use up the rest of the $88.50 left from the $100 game card if air hockey costs $1.75.

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Answer:

4

Step-by-step explanation:

y÷x

12÷3=4 and 20÷5=4

The median of list of numbers is-2.

Given the list of numbers is 13,15,6,8,-16,2,-12,3,-18,-18.

The median is the median of a sorted list of numbers. To find the median of a sequence of numbers, the numbers must be sorted in order from lowest to highest or highest to lowest.

Firstly, we will arrange the number from ascending to descending, we get

-18,-18,-16,-12,-6,2,3,8,13,15.

Now, we will find the middle term of the sequence, we get

The middle terms are -6 and 2.

Further, we will find the median of it.

n=(-6+2)/2

n=-4/2

n=-2

Hence, the median of the list of numbers 13, 15, -6, 8, -16, 2, -12 ,3 ,-18 ,-18 is -2.

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4 (1/16)  =  4/16   =  1/4

(1/4) / 4    =   1/16  each day

Answer:

\(\frac{5}{24}\) of the book each day

\(83\frac{1}{3}\) % of the book each day

Step-by-step explanation:

1 - ⅙

⅚

⅚ ÷ 4

\(\frac{5}{24}\)

thissssssssssssssssssssssssss:

A melting sphere of ice with volume and surface area formulas of V=(4/3)πr³ and A=4πr² respectively, is melting at 5 in³/min. With the differentiation of the volume and surface area formulas and a given radius of 4 inches.

We will consider a piece of ice in the shape of a sphere that is melting at the rate of 5 in³/min. We will model the volume of ice by a function of the radius 'r'. We will differentiate the formula for the volume and surface area of a sphere. We will find dr/dt when radius is 4 inches.
1: Write the formula for the volume and surface area of a sphere.
Volume (V) = (4/3)πr³
Surface area (A) = 4πr²
2: Differentiate both formulas with respect to time 't'.
dV/dt = (4/3)π(3r²)(dr/dt)

=> dV/dt = 4πr²(dr/dt)
dA/dt = 4π(2r)(dr/dt)

=> dA/dt = 8πr(dr/dt)
3: Given that the ice is melting at the rate of 5 in³/min, we have dV/dt = -5 (since the volume is decreasing).
4: Find dr/dt when the radius is 4 inches.
-5 = 4π(4²) (dr/dt)
Solve for dr/dt:
dr/dt = -5 / (4π(16))
dr/dt = -5 / 64π
So, the radius is changing at the rate of -5/(64π) inches/min when the radius is 4 inches.
5: Find dA/dt when the radius is 4 inches.
dA/dt = 8π(4)(-5/64π)
Simplify the expression:
dA/dt = -40/16π
dA/dt = -5/2π
So, the surface area is changing at the rate of -5/2π in²/min when the radius is 4 inches.
In conclusion, when the radius of the melting ice sphere is 4 inches, the radius is changing at a rate of -5/(64π) inches/min and the surface area is changing at a rate of -5/2π in²/min.

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The electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.

The electric field a distance y above the midpoint between two equal and opposite charges, q and −q, that are a distance d apart as shown in Fig. 1 above can be found as follows:

Since, the distance between the charges is d, the distance from the midpoint to either of the charges would be d/2. According to the principle of superposition, the electric field due to the two charges would be the vector sum of the electric fields due to the charges q and -q at point P. Let's consider the electric field due to the charge q at point P and the electric field due to the charge -q at point P.

Electric field due to the charge q: Using Coulomb's law, we can write the electric field due to the charge q at point P as:

E1 = kq/r1²,

where k is Coulomb's constant, q is the charge, and r1 is the distance between the charge q and point P.

The distance r1 can be calculated as:

r1 = [(d/2)² + y²]^1/2

Since the electric field is a vector quantity, we can represent it in terms of unit vector i as follows:

E1 ˉ= kq/[(d/2)² + y²]^1/2 iˉ

Electric field due to the charge -q:

Similarly, the electric field due to the charge -q at point P can be written as:

E2 ˉ= - kq/[(d/2)² + y²]^1/2 iˉ (because the charge is negative)

Therefore, the net electric field at point P can be obtained by taking the vector sum of the electric fields due to the two charges:

E ˉ= E1 ˉ + E2 ˉ= [kq/[(d/2)² + y²]^1/2 - kq/[(d/2)² + y²]^1/2] iˉ= 0

Thus, the electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.

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Step-by-step explanation:

let's just write it down in mathematical notation :

length = 2×width - 1

the perimeter is the way all around an object.

so, for a rectangle that is

2×length + 2×width

for our rectangle here

2×length + 2×width = 70

now we use the original identity of length via width and get

2×(2×width - 1) + 2×width = 70

4×width - 2 + 2×width = 70

6×width - 2 = 70

6×width = 72

width = 12

FYI

length = 2×width - 1 = 2×12 - 1 = 24 - 1 = 23

Answer:

Step-by-step explanation:

ajns

The standard deviation of the sampling distribution of \(\hat{p}\) is 0.0315

The correct answer is an option (c)

We know that the formula for the standard deviation in terms of true probability and sample size:

SD = \(\sqrt{\frac{p(1-p)}{n} }\)

where, SD = standard deviation

p = true proportion

and n = total sample

Here, we have a sample of 250 people who work in Washington with proportion of 0.45

This means p = 0.45 and n = 250

Substitute these values in above formula to find the standard deviation.

⇒ SD = \(\sqrt{\frac{p(1-p)}{n} }\)

⇒ SD = \(\sqrt{\frac{0.45(1-0.45)}{250} }\)

⇒ SD = 0.0315

Therefore, the standard deviation of the sampling distribution = 0.0315

The correct answer is an option (c)

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Find the complete question below.

The οrdered pair that is a sοlutiοn οf the equatiοn is (-5, 0).

A value οr grοup οf values that satisfy an equatiοn οr an inequality are referred tο as sοlutiοns in mathematics. Fοr instance, if we have the equatiοn 2x + 3 = 7, the answer is x = 2 since we get the cοrrect answer when we replace x with 2: 2(2) + 3 = 7.

Similar tο the last example, if we had an inequality like x + 4 > 10 then the sοlutiοn is x > 6, meaning any value οf x greater than 6 wοuld make the inequality true.

Tο find which οrdered pair is a sοlutiοn οf the equatiοn -5x - 3y = 25, we need tο substitute values οf x and y intο the equatiοn and see if it hοlds true.

Let's try the ordered pairs one by one:

a) (-5, 0)

Substituting x = -5 and y = 0 in the equation, we get:

-5(-5) - 3(0) = 25

25 = 25

This equation is true, so (-5, 0) is a solution of the equation.

b) (0, -8)

Substituting x = 0 and y = -8 in the equation, we get:

-5(0) - 3(-8) = 25

24 = 25

This equation is not true, so (0, -8) is not a solution of the equation.

Therefore, the ordered pair that is a solution of the equation is (-5, 0).

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Complete question:

Which ordered pair is a solution of this equation?

-5x - 3y = 25

a) (-5, 0)

b) (0, -8)

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &10250\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &9\\ \end{cases} \\\\\\ A=10250(1 - 0.05)^{9}\implies A=10250(0.95)^9\implies A\approx 6460\)

The rate of change of the function and the value of the function when x = 24 is: rate of change: -2/3, value: 22​.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (26 - 34)/(18 - 6)

Slope (m) = -8/12

Slope (m) = -2/3.

At data point (6, 34) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 34 = -2/3(x - 6)  

y = -2x/3 + 38

When x = 24, we have;

y = -2(24)/3 + 38

y = 22

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For the given system of equations:

x = 42 / (25 - M)

y = (208 - 10M) / (25 - M)

Where M is a value less than 25, different values of M can be substituted to find corresponding values of x and y.

Let's assume that x vans were used and y buses were used for the field trip.

Since each van holds M students and each bus holds 25 students, the total number of students can be expressed as:

M * x + 25 * y = 208   (Equation 1)

We also know that there were a total of 10 vehicles used:

x + y = 10   (Equation 2)

To solve this system of equations, we can use substitution or elimination.

Let's use elimination to solve the system of equations:

Multiply Equation 2 by M to match the coefficients of x:

M * (x + y) = M * 10

Mx + My = 10M   (Equation 3)

Now we can subtract Equation 3 from Equation 1 to eliminate x:

(M * x + 25 * y) - (Mx + My) = 208 - 10M

25y - My = 208 - 10M

(25 - M)y = 208 - 10M

y = (208 - 10M) / (25 - M)   (Equation 4)

Substitute the value of y in Equation 4 back into Equation 2 to solve for x:

x + (208 - 10M) / (25 - M) = 10

x(25 - M) + 208 - 10M = 10(25 - M)

25x - Mx + 208 - 10M = 250 - 10M

25x - Mx = 250 - 208

(25 - M)x = 42

x = 42 / (25 - M)   (Equation 5)

Now we have expressions for x and y in terms of M. Since the number of vehicles cannot be negative, x and y must be positive integers.

By trying different values of M, we can find the suitable values of x and y. Keep in mind that M must be less than 25 since each bus holds a maximum of 25 students.

For example, if we let M = 20:

x = 42 / (25 - 20) = 8

y = (208 - 10 * 20) / (25 - 20) = 8

Therefore, if M = 20, there would be 8 vans and 8 buses used for the field trip.

By trying different values of M, we can find other valid combinations of vans and buses that satisfy the given conditions.

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the length of side x = 12.5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, we have,

From the given figure, we get.

These two figures are similar.

so, we have,

8/x=y/5 ............(1)

10/15=4/z ......(2)

8/15=y/z .....(3)

Solving we get,

x=12.5

Hence,  the length of side x = 12.5.

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