AC and BE intersect at point P. If m∠APE = 70°, then what is the measure of m∠EPD?

Answer:

The slope: 4

Y-intercept: 9

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

In this case y = 4x + 9

m = 4

b = 9

So,

The slope: 4

Y-intercept: 9

Answer:

Slope: 4/1 or 4

Y-Intercept: 9

Step-by-step explanation:

y = mx + b is the Slope Intercept Formula. 'm' in the formula stands for rate of change in y/x, which is practically slope. 'b' in the formula is where the line crossed the y line. It's where it intercepts with y.

Answer: 20 children in total.

Step-by-step explanation: If you do 20% of 20 you get 4.

20

let the total children be x

therefore 20/100 × x =4

x = 400/10

x =20

Answer: S=V cubed

Step-by-step explanation:

Answer: A. S = cube of V

Step-by-step explanation:

Cube both sides of the equation to single s out

If the outlier is removed, the following measures will change:

mean

range

a) Mean: Mean is the average of a set of numerical values. It is calculated by summing up all the values in the set and then dividing the sum by the number of values. The mean is a measure of central tendency and represents the typical value of a set of data.

b) Range: Range is a measure of dispersion and represents the difference between the largest and smallest values in a set of numerical data. It provides a quick and simple way to understand the spread of the data, and the difference between the extreme values. The range is calculated by subtracting the smallest value in the set from the largest value.

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The three consecutive positive integers satisfying the statement are

9, 10, and 11.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The three numbers be n, (n + 1), and (n + 2).

Therefore, the numerical expression of the given statement is,

2(n)(n + 2) + 2 = 20(n + 1)

2n² + 4n + 2 = 20n + 20.

2n² - 16n - 18 = 0.

n² - 8n - 9 = 0.

n² - 9n + n - 9 = 0.

n(n - 9) + 1 (n - 9) = 0.

(n - 9)(n + 1) = 0.

n = 9 is the positive integer.

So, The numbers are 9, 10, and 11.

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$20

there is two ways to solve this.

ratio form:

80% / 100% = X / $25

---> 2000 / 100 = X

---> X = 20

Decimal form:

80% --- move decimal two places to the left.

80% = 0.8 --- now multiply decimal by total value

0.8 x 25 = 20

$20.

The greatest possible sum of two number is 6.7. Naomi's statement is false.

The least possible difference between two number is -10 Naomi's statement is false

The greatest product of two number in the set is 30.6. Naomi's statement is false

The least possible quotient of two numbers from the set is -6. Naomi statement is false

In mathematics, an operation is a function which takes zero or more input values to a well-defined output value. The number of operands is the arity of the operation.

The greatest possible sum = 4+2.7 = 6.7

The least possible difference = -6-4 = -10

The greatest possible product = -6×-5.1 = 30.6

The least possible quotient = 4÷ -2/3 = -12/2 = -6

Therefore all Naomi's statement are false.

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The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.

One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.

In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.

To start, we'll find a common denominator for all the terms in the expression.

The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.

Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.

96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.

Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.

So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.

Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.

The final equivalent expression is

=> 104/120a + 107/120b + 15/120 - 90/120

=> (104 + 107 + 15 - 90)/120a + (107/120)b

=> 136/120a + 107/120b.

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Answer:

(10, 24)

Step-by-step explanation:

First equate both the equations,

2(x+2) = 4(x-4)

Then expand the brackets,

2x + 4 = 4x - 16

Collect like terms in each sides,

4 + 16 = 4x - 2x

Simplify and solve,

20 = 2x

20 ÷ 2 = x

x = 10

Then substitute 10 for x in one of the equations,

y = 2(x + 2)

y = 2(10 + 2)

y = 24

Therefore, the point of interssection is (10, 24).

you can solve this using the simultaneous equation

so y = y

4(x-4) = 2( x + 2)

4x - 16 = 2x +4

4x - 2x = 4+16

2x/2=20/2

therefore x=10

y=2 (x+2)

y=2(10+2)

y=2(12)

y=24

[tex]2x+2y=-8 \implies x+y=-4 \implies y=-4-x[/tex]

We can substitufe this result into the second equation.

[tex]-10x-5(-4-x)=-5 \\ \\ -10x+20+5x=5 \\ \\ -5x+20=5 \\ \\ -5x=-15 \\ \\ x=3 \implies y=-4-3=-7[/tex]

[tex]\therefore[/tex] The solution is [tex](3,-7)[/tex].

Answer:

Step-by-step explanation:

if the bars are similar, they are proportional.

make a proportion: length  =  30    =  10

                                width       12         x

cross multiply:     12 times 10 = 120

divide by the number that ids left - 120 ÷ 30  = 4 cm

The width of the smaller bar is 4 cm.

The largest value of success probability p with zero as most likely number of success with n independent trials is equal to 1 / ( n + 1 ).

Probability of success is equal to p

Probability of failure is equal to ( 1 - p)

Number of trials is positive integer n

Condition for 'n' independent trials :

Zero is most likely number of success

⇒ P(0) ≥ P(1)

⇒ ⁿC₀ p⁰ ( 1 - p )ⁿ⁻⁰  ≥ ⁿC₁ p¹ ( 1 - p )ⁿ⁻¹

⇒ ( 1 - p )ⁿ ≥ np ( 1 - p )ⁿ⁻¹

⇒( 1 - p ) ≥ np

⇒ np + p ≤ 1

⇒ p ≤  1 / ( n + 1 )

Largest value of p is equal to 1 / ( n + 1 ).

Therefore, the largest value of success probability p with n independent trials is equal to 1 / ( n + 1 ).

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Answer:

9

Step-by-step explanation:

this is the explanation 6×3=18 18÷2=9

Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Explaining quadrilaterals?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.

What is quadrilateral formula?

When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.

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The complete question is -

Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.

Answer:

6

Step-by-step explanation:

The number completes the sequence is 6

The area of the triangle is 1 square foot.

Remember that the area of a triangle of base B and height H is:

A =B*H/2

Here we can see that:

B = 3ft

H = (2/3) ft

Replacing that in the area formula we will get:

A = (3ft)*(2/3)ft/2 = 1 ft²

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Answer:

248

Step-by-step explanation:

Find the volume of each box, then add them up.

Volume = l x w x h

Top:  5 x 2 x 5 = 50

Middle:  6 x 4 x 3 = 72

Bottom:  9 x 7 x 2 =126

Total = 50 + 72 + 126 = 248 cubic feet

Answer:

Step-by-step explanation:

90

By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

It primarily consists of a variable, sometimes with a numerical constant in addition.

Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

So, we know that the ration is 6:11 and the perimeter is 510 units.

Then, form and solve the equation as follows:

510 = 2(6x + 11x)

510 = 12x + 22x

510 = 34x

x = 510/34

x = 15

Then, the length will be:
6x

6(15)

90 units

Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

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Answer:

B.

Step-by-step explanation:

The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the segment.

The midpoint of segment AB can be found as follows:

Midpoint of AB = ((-7/2 + -7)/2, (3/2 + 3)/2) = (-7, 3)

Since the midpoint of AB is the same as point B, we can conclude that the midpoint of segment AB is (-7, 3).

Answer and Step-by-step explanation:

Let's call the angle between the roads on the south side "y" for simplicity. Since the two roads intersect, the sum of the two adjacent angles on one side must add up to 180 degrees. Therefore, we can set up an equation:

y + 69 = 180

Solving for y, we get:

y = 180 - 69 = 111

We also know that y is equal to 3x, so we can set up another equation:

3x = 111

Solving for x, we get:

x = 37

Therefore, the value of x is 37.

Answer:  b=6

Step-by-step explanation:

Step-by-step explanation:

cubing on both sides,

(-4)³= ³√(9x-1)³

-64=9x-1

-64+1=9x

-63=9x

-63/9=x

x=-7

Answer:

Below

Step-by-step explanation:

You need to find the LCD of 12 16 and 20

Using Prime Factorization:

     12 = 2 * 2          * 3

     16 = 2 * 2 * 2 * 2

    20 = 2 * 2               * 5      

            2    2   2   2  3   5                  so LCD will be 2 * 2 * 2 * 2 * 3 * 5= 240

so she will need    240 / 12 = 20 packs of pencils

                               240 / 16 = 15  packs of notebooks

                                240 / 20 = 12 packs of pens

The numeric value of the inverse function at x = 4096 is given as follows:

f-¹ (4096) = 6.

To find the inverse function, we exchange x and y in the original function, then isolate y.

The transformation rule for each point on the inverse function, compared to the original function, is given as follows:

(x,y) -> (y,x).

f(6) = 4096, hence the point on the function is:

(6, 4096).

Then the point on the inverse will be of:

(4096, 6).

Meaning that:

f-¹ (4096) = 6.

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The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

Let x(t) and y(t) be the solution of the linear system of differential equations:

[tex]$\frac{dx}{dt} = ax + by$[/tex]

[tex]$\frac{dy}{dt} = cx + dy$[/tex]

with initial conditions x(0)=5 and y(0)=3.

The general solution of the system of differential equations can be written as:

[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]

where X0 = 5 and Y0 = 3.

Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

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Answer: C

Step-by-step explanation:

Just look for the less than or equal to sign

The best estimate for the owl population is 2,378.

The population of the owl can be estimated using the concept of proportion. Proportion refers to a mathematical comparison between two numbers. According to the concept, if two sets of given numbers are increasing or decreasing in the same ratio, hence the ratios are said to be directly proportional to each other.

Based on the provided information, 29 owls are tagged and released as part of a research project. Assume that the total number of owl populations is x. At the later time, researchers counted 902 owls and found the 11 were tag. Hence, there are 18 tagged owls which are not accounted for. Assuming that the proportional of tagged owls to number of owls counted applies to the remaining population, the total number of owls can be best estimated as:

x = (902/11)*29 = 2,378

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