In parallelogram ABCD, diagonals AC and BD intersect at point E, BE=x+21, and DE=4x.
What is BD?
Enter your answer in the box.

Answer:

4:2 and 14:7

Step-by-step explanation:

The ratios equivalent to 8:4 would be:

4:2

14:7

5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.

:D

Answer:

They are all equivalent except for 5:10

Step-by-step explanation:

You can write ratios as fractions

[tex]\frac{8}4}[/tex]   [tex]\frac{4}{2}[/tex]  [tex]\frac{14}{7}[/tex]   [tex]\frac{5}{10}[/tex]  If I simplify each fraction, I can see that they all equal 2 expect for the the last one.

2   2   2   1/2

Answer:

Length in inches → 11

1 inch = 2.5 centimeters

Length in Centimetres → 11 × 2.5 → 27.5 cm

Answer:

k = ± [tex]\sqrt{\frac{2A-3t\p}{\pi } }[/tex]

Step-by-step explanation:

2A = πk² + 3t ( subtract 3t from both sides )

2A - 3t = πk² ( isolate k² by dividing both sides by π )

[tex]\frac{2A-3t}{\pi }[/tex] = k² ( take square root of both sides )

± [tex]\sqrt{\frac{2A-3t}{\pi } }[/tex] = k

Answer:

Step-by-step explanation:

Substitute and calculate:

The equations of the lines are:

7. y = 3/2x - 3/2

8. y = -1/3x - 8/3

The equation that represents a line, in slope-intercept form is, y = mx + b.

7. Find the slope (m) between (5, 6) and (1, 0):

Slope (m) = (6 - 0)/(5 - 1) = 6/4

Slope (m) = 3/2

Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:

0 = 3/2(1) + b

-3/2 = b

b = -3/2

To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:

y = 3/2x - 3/2

8. Find the slope (m) between (-5, -1) and (1, -3):

Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6

Slope (m) = -1/3

Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:

-3 = -1/3(1) + b

-3 = -1/3 + b

-3 + 1/3 = b

-8/3 = b

b = -8/3

To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:

y = -1/3x - 8/3

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Answer:

6.5625 gal per hour

Step-by-step explanation:

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.

Answer:

x intercept is -3

Step-by-step explanation:

We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1)     = (2- -4)/(6- -3)     = (2+4)/(6+3)     =6/9     = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x  Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3  

Answer:

y = 5

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

AB = CD , that is

7y = 3y + 20  ( subtract 3y from both sides )

4y = 20 ( divide both sides by 4 )

y = 5

Answer:

d. y= 2x³

Step-by-step explanation:

All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.

The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).

Linear equation:

Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.

Given,

Here we have the following system of linear equations.

2x + 3y = 6

-3x + 5y = 10

Now, we need to find the solution for the equations.

Here we have to use the substitution method to solve this one,

To do the substitution method we have to follow the following steps:

Step 1) Solve anyone of the equations either for the variable x or y

Step 2) Now, substitute the value obtained from step 1 to the other equation

Step 3) Finally, solve the equation to find the value of the remaining variable.

Here we have to take the equation (2), and we have to solve it for the value of y,

For that we have to rewrite the equation as,

5y = 10 + 3x

y = (10 + 3x)/5

Apply the value of y on the equation (1), in order to get the value of x,

So,

2x + 3(10 +3x)/5 = 6

2x + (30 + 9x)/5 = 6

(10x + 9x + 30)/5 = 6

19x + 30 = 30

19x = 0

x = 0

Now, apply the value of x on the equation in order to get the value of y,

y = (10 + 3(0))/5

y = 10/5

y = 2.

Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).

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Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34

+7x

4x - 6 = 34

+6

4x = 40

/4

x = 10

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34  Add 7x to both sides

4x - 6 = 34  Add 6 to both sides

4x = 40  Divide both sides by 4

x = 10

Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.

According to the question,

We have the following information:

Amira is younger than Marques.

Their ages are consecutive integers.

The sum of Amira's age and 2 times Marques's age is 38.

Now, let's take Amira's age to be x years.

Then, Marques's age will be (x+1) years.

So, we have:

x + 2(x+1) = 38

x + 2x + 2 = 38

3x+2 = 38

3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)

3x = 36

x = 36/3

x = 12 years

Hence, Amira's age is 12 years.

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Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

Answer:

There is no dot plot below

Step-by-step explanation:

Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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$128,000 represents 100%

To find how much is 4% we can use the next proportion:

Solving for x:

Her commission is $5,120

Answer: 93°

Step-by-step explanation:

[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]

Answer:

-16

Step-by-step explanation:

fog(18)=f(g(18))

g(18)=[tex]\sqrt{18-9} =\sqrt{9} =3[/tex]

f(3)=-8(3)+8

=-16

The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.

For the given question;

The function is given as;

y=4ˣ

Interchange the variables of the function.

x = 4∧y

Taking log both side.

㏑ x =  ㏑(4∧y)

Using the power rule of log function.

㏑ x =  y㏑(4)

y = ㏑ x/㏑(4)

Now, replace y with f⁻¹(x).

f⁻¹(x) = ㏑ x/㏑(4)

Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.

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The correct question is-

Evaluate the inverse when y=4ˣ. Show all of your work.

The distance between the translated points C and D is 5 units

From the question, the coordinates are given as

A (-2,3) , B (3,3) , C (4,6) , and D (-1 , 6)

The sequence of transformations is given as

The above sequence of transformations are rigid transformations.

This means that the lengths are preserved

In other words,

CD = C'D'

So, we have the distance to be

Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]

Where

(x, y) = C (4,6) , and D (-1 , 6)

So, we have

Distance = √[(4 + 1)² + (6 - 6)²]

Evaluate

Distance = 5

Hence, the distance is 5 units

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the answer would be (0,5)

If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

Total number of registered voters in Central city = 29791 voters

Total number of voting centers = 93 voting centers

The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers

Substitute the values in the equation

The number of population serves by each center = 29791/93

= 320.33

≈ 320

Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

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The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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The sum of 12 and P can be written as 12 + P

Then, f decreased by the sum of 12 and P can be written as:

f - (12 + P)

Answer: it isn't correct, the correct answer is f - (12 + P)

Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.

AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2

Order of operations:

Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.

The order using PEMDAS:

Parentheses,

Exponents,

Multiplication and Division (from left to right),

Addition and Subtraction (from left to right).

Given,

Here we have the expression. 3.2+2(-1.5)-3.4

Now, we have to use the order of operations concept in order to solve it.

The highest priority for the order of operation is brackets and the next priority is for division and multiplication,

So, here we have to solve those things first, then we get,

=> 3.2 + (-3) - 3.4

We know that (+) x (-) = -, so, the expression is rewritten as,

=> 3.2 - 3 - 3.4

The next priority is for addition and subtraction,

So, the result is,

=> 3.2 - 6.4

=> -3.2

Therefore, the resulting number is -3.2

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