Given: ​ ​△ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯​ ​ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason ​△ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯​ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles ​CA=CB+BACE=CD+DE​ Segment Addition Postulate ​CB+BACB=CD+DECD​ Substitution Property of Equality ​CBCB+BACB=CDCD+DECD​ ​ Addition of fractions ​1+BACB=1+DECD​ Simplification of fractions Response area Subtraction Property of Equality

Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

Answer:

Step-by-step explanation: 2.922

Answer: 2.922

Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.

Answer:

C

Step-by-step explanation:

Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

Answer:

see explanation

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2

this indicates the sequence is geometric

the nth term of a geometric sequence is

f(n) = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 6 and r = 2 , then

f(n) = 6 [tex](2)^{n-1}[/tex]

Step-by-step explanation:

6(8x+5)

Use the distributive property to multiply 6 by 8x+5.

48x+30

Hope it Helps!

The maximal number of consecutive integers by using the expression [tex]2*sqrt(n*|a|).[/tex]

Let f(x) = ax^n + bx^{n-1} + ... + z be a polynomial with integer coefficients and degree n>1. According to the theorem of Tchebychev, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is bounded by the expression 2*sqrt(n*|a|), where a is the coefficient of the highest degree term of f(x).

For example, let f(x) = 3x^3 + 4x^2 - 5. The coefficient of the highest degree term is 3, and the degree of the polynomial is 3. Therefore, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is 2*sqrt(3*|3|) = 6.

To calculate this maximal number, we can follow these steps:

Identify the degree of the polynomial, n.

Identify the coefficient of the highest degree term, a.

Calculate the maximal number of consecutive integers by using the expression 2*sqrt(n*|a|).

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The diameter of the circle is 30 feet

To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.

So, we can write the equation:

diameter^2 = radius^2 + (distance between chord and center)^2

We know the radius is half the diameter, so we can substitute that in:

diameter^2 = (diameter/2)^2 + (15)^2

And we can solve for the diameter:

diameter^2 = diameter^2/4 + 225

diameter^2 = diameter^2/4 + 225

4diameter^2 = diameter^2 + 900

3diameter^2 = 900

diameter^2 = 900/3

diameter = sqrt(900/3)

So the diameter of the circle is 30 feet.

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The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.

What is upper and lower bound of a function?

A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.

Given,

 [tex]f(h) = \frac{48-h}{48}[/tex]

where    f(h) = Percentage of battery left

              h = Hours of cell phone use

Lower Bound of parameter h,

h = 0 ( When percentage is 100%)

f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1

Upper bound of parameter h,

h = 48 (When percentage is 0%)

f(h) = [tex]\frac{48-48}{48}[/tex] = 0

Therefore the upper bound of h is 0 and lower bound of h is 1.

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To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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The probability of each of your three friends having an ace is 32%.

The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).

Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.

This means that the probability of each of your three friends having an ace is 32%.

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The radius of a sphere whose surface area is  324*pi cm² is:

R = 9 cm.

We know that the surface of a sphere of radius R is given by:

S = 4*pi*R^2

Where pi = 3.14

Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:

S =  324*pi cm² = 4*pi*R^2

We can divide both sides by pi, so we get:

324 cm^2 = 4*R^2

Now we can solve that equation for R, we will get:

R^2=  (324 cm^2)/4 = 81cm^2

R = √(81 cm^2)

R = 9cm

The radius of the sphere is 9cm.

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The point at a graph where the graph cuts the x-axis is known as the x-intercept. Therefore, the x-intercept is a point.

A graph is made up of four quadrants in which two are positive and two are negative quadrant.

There are two types of axis which are x-axis and y-axis two negative and two positive.

The y-intercept is the point where the graph cuts the y-axis .Graph Theory is the study of graphs which comes under discrete mathematics.

It is defined as a mathematical structure that connects a group of points to express a specific function.

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Answer:

24 students are in the class

Step-by-step explanation:

Let x represent the total number of students in the class. We have the equation:

(2/3)x = 16

x = 24 students

So, there are 24 students in the class.

Answer:

24 students

Step-by-step explanation:

16/2=8

8*3=24

Answer:

Step-by-step explanation:

y=2x-5+2

then you do minus 2 on both sides

Hope this helped!

5 half-dozens he should buy to make enough cookies.

What is an average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.

Here, we have

If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.

There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.

However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.

1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.

Since there are 6 eggs in a half dozen,

we need 30/6 = 5 half-dozens of eggs.

Hence, 5 half-dozens he should buy to make enough cookies.

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The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

No solution equation:

5x + 5 = 5x - 5

To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.

5x + 5 = 5x - 5

Subtract 5x from both sides:

5 + 5 = - 5

Simplify:

10 = -5

At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

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Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.

The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6

The price of a Kaiser roll  = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5

$6 - $5 = 1

Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

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The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.

The given inequality is 3(2m - 1) ≤ 4m + 7

Remove the brackets by multiplying 3 with each term inside it:

6m - 3 ≤ 4m + 7

Subtract 4m from both sides of the equation.

6m - 3 - 4m ≤ 4m + 7 - 4m

2m -3 ≤ 7

Add 3 to both sides of the equation.

2m - 3 + 3 ≤ 7 + 3

2m ≤ 10

Divide both sides of the equation with 2.

2m/2 ≤ 10/2

m ≤ 5

Hence the solution of the equation is m ≤ 5, that is option A.

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The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.

Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10

= 73

Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.

There are on one event is where 5 athletes are, that is 8th grade baseball players.

So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

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Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

Answer:

hhhhhhhhhhhhhhhh hhhhhhhhhhh

Step-by-step explanation:

hhhhhhhhh hhhhhhhhh hhhhhhh hhhhhh

If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years then he has to pay 3009.6 back.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.

A=P(1+rt)

Where, A is final amount, P is principal amount, r is rate of interest, t is time period.

P=3000, r=0.16%=0.16/100=0.0016, t=2

A=3000(1+(0.0016)2)

=3000(1+0.0032)

=3000(1.0032)

=3009.6

Hence, Canon needs to pay back 3009.6

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Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

Answer:

The answer is (4x² - 36x + 81)

Step-by-step explanation:

So,

(2x - 9)² = (2x)² - 2(2x)(9) + (9)²

(2x - 9)² = 4x² - 36x + 81

Thus, The product of (2x - 9)² is (4x² - 36x + 81)

No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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Answer: Marissa divided the marked section of the wall into 3 equal parts. If she painted one of these parts blue, then the part that she painted blue is 1 out of the 3 equal parts. So, the fraction of the wall that is blue is 1/3.

Another way of understanding this is that if the wall is divided into 3 equal parts and Marissa painted 1 part, then the fraction of the wall that is painted is 1/3.

So the fraction of the whole wall that is blue is 1/3.

Step-by-step explanation:

The price of the sales tax on the elephant could be 0.75$

What is percentage ?

percentage can be defined as the product of ratio of given value and total value and hundred.

Given

he sells a stuffed elephant for $14.95,

the sales tax is 5% of the sale price .

So,

as the tax is 5% of the given value.

so we are here multiplying the given value to the 5/100

we get,

The amount of the tax could be

 = 14.95*5/100

 = 0.7475

≈ 0.75 (rounded)

Hence the  price of the sales tax on the elephant could be 0.75$

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