Given: m<4 + m<7 = 180 degrees
Prove: c || d

The measure of ∠B is 60°

The measure of ∠H is 135°

The length of AB is 2cm

From the question, we are to determine the measure of the angles and the length of line AB.

From the given information, we have that

Quad ABCD. is similar to Quad, EFGH

In the diagram,

Measure of ∠F = 60°

But, ∠B ≅ ∠F

∴ The measure of ∠B = 60°

Measure of ∠H

∠E + ∠F + ∠G + ∠H = 360° (Sum of angles in a quadrilateral)

From the diagram,

m ∠E = 90°

m ∠F = 60°

∠G ≅ ∠C

m ∠C = 75°

∴ m ∠G = 75°

Thus,

90° + 60° + 75° + ∠H = 360°

225° + ∠H = 360°

∠H = 360° - 225°

∠H = 135°

Hence, the measure of ∠H is 135°

Length of AB

The length of HE is twice the length of DA,

Thus,

The length of EF will be twice the length of AB

From the diagram,

EF = 4cm

∴ AB = 4/2 cm

AB = 2 cm

Hence, the length of AB is 2cm

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Answer:

35ºy^2+252yº

Step-by-step explanation:

If Henry and Emma want to buy a total of 0.5 yds of fabric and the fabric costs $8.72 per yard then the amount each will pay if they want to split the cost evenly is equal to $2.18.

The amount Henry and Emma will have to pay if they want to split the cost can be calculated by using division.

First, we calculate the cost of 0.5 yards of fabric.

1 yard of fabric cost = $8.72

0.5 yards of fabric cost = x

Here x is the cost of 0.5 yards of fabric

8.72 × 0.5 = x

x = $4.36

As the cost of 0.5 yards of fabric is calculated to be $4.36, the amount each will pay if they want to split the cost evenly can be found by dividing the cost of 0.5 yards by 2.

cost of 0.5 yards of fabric / 2 = 4.36 / 2 = $2.18.

Hence each one of them will pay $2.18 if they want to split the cost evenly.

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The goals of the vision statement for vision 2030 include:

The creation of a climate that opens up business opportunities, broadens the economic base, and generates jobs for all Saudis is a primary objective of Vision 2030. By utilizing the country's special position and potential, luring the top talent, and boosting international investment, we will be able to accomplish this.

It should be noted that the vision is to bring about an economy that's prosperous. Therefore, goals of the vision statement for vision 2030 include:

a vibrant society,

a thriving economy

an ambitious nation.

secure environment

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Using the together rate, it will take more 3.45 days to complete the work.

The together rate is given by the sum of each separate rate.

For this problem, the rates are given as follows:

Hence the amount completed in 2 days is:

2 x (0.1 + 0.0833) = 0.3666.

The amount it would take them to complete 100% of the project working together is found by the together rate as follows:

[tex]\frac{1}{x} = \frac{1}{10} + \frac{1}{12}[/tex]

[tex]\frac{1}{x} = \frac{6 + 5}{60}[/tex]

x = 60/11

x = 5.45 days.

The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is:

0.6334 x 5.45 = 3.45 days.

It will take more 3.45 days to complete the work.

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The length of the actual hotdog is 15 cm

The graph that completes the question is added as an attachment

The length of the hotdog in the figure is given as

Length = 9 units

The scale is given as

Scale: 6 units = 10 cm

So, we have

6 * 9 units = 10 * 9 cm

Divide both sides by 6

So, we have

9 units = 15 cm

Substitute 9 units = 15 cm in Length = 9 units

Length = 15 cm

Hence, the length of the actual hotdog is 15 cm

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The amount invested in the bond with 5% simple interest is $16,666.67

The amount invested in the bond with 6.5% simple interest is $33,333.33  

What is simple interest?

The interest earned under a simple interest arrangement is determined as the amount invested multiplied by the interest rate and the time the investment lasts

I=PRT

let us assume that x was invested in the bond with 5%

interest on x=5%*x=0.05x

amount invested in other bond=50000-x

interest earned on 6.5%=(50000-x)*6.5%

interest earned on 6.5%=3250-0.065x

total interest=0.05x+3250-0.065x

total interest=3250-0.015x

total interest=3000

3000=3250-0.015x

0.015x=3250-3000

0.015x=250

x=250/0.015

x=$16,666.67

amount invested at 6.5%=$50,000-$16,666.67

amount invested at 6.5%=$33,333.33

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It would take 16 days for the number of magical coins to exceed 50,000.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of magical coins available after x days. this can be represented by:

y = 1(2)ˣ

To exceed 50000 coins:

50000 = 1(2)ˣ

x = 15.6

It would take 16 days for the number of magical coins to exceed 50,000.

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After solving, the factors of equation 4x²+17x+15 are:

So,

Given the equation: 4x²+17x+15

Then,

Factors are: (x+3) and (4x+5)

Therefore, after solving, the factors of equation 4x²+17x+15 are:

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The result of simplifying the expression (x²/x⁻¹¹)¹/₃ using the exponent rules is [tex]\sqrt[3]{}[/tex](x¹³)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(x²/x⁻¹¹)¹/₃

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

(x⁽²⁻⁽⁻¹¹⁾)¹/₃

(x⁽²⁺¹¹⁾)¹/₃

(x¹³)¹/₃

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these powers, we have:

x⁽¹³*¹/₃⁾

x⁽¹³/₃⁾

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt[3]{}[/tex](x¹³)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

If you are just combining like terms then the answer is just 4x + 2y

Hope this helps :)

The required solution of the given system of equation is y=2-9x and y=x/2-1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The is given system of equation

2-9x=x/2-1

According to given question we have

The equation is

2-9x=x/2-1

We have to split into different system of equation to find the solution of the problem we have

So,

y=2-9x

and

y=x/2-1

Therefore, the required solution of the given system of equation is y=2-9x and y=x/2-1.

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If a function is onto, then its domain can be a set of all non negative real numbers if the function is defined as y = √ x.

It is not necessary that function that is onto should have the domain as non negative real numbers only.
It can also have negative real numbers in its domain.

If the function is of the form:

y = √ x

Then the function will have a domain that is non negative real numbers.

But if function is of the form:

y = x²

Then it can have the domain as all real numbers.

Therefore, we get that, if a function is onto, then its domain can be a set of all non negative real numbers if the function is defined as y = √ x.

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Answer:

The equation has infinitely many solutions.

Step-by-step explanation:

6(2y + 6) = 4(9+3y)

2y + 36 = 36 + 12y     ---->   should be 12y + 36 = 36 + 12y

12y = 12y correct

0 = 0  correct

The equation has no solution.   --->   should read "The equation has infinitely many solutions."​

2.4645×10⁴ gallons of milk do United States dairy cows produce each year.

We need scientific notation reason is large number can be written in compact form.

According to the given question There are approximately 9.3 x 106 dairy cows in the United States.

Which is 985.8 cows in the united states.

Also given each cow produces 2.5×10 = 25 gallons of milk per year.

∴ United state cows will produce (985.8×25) gallons of milk each year which is = 24645 gallons of milk per year.

Now 24645 can be represented as 2.4645×10⁴ gallons of milk.

We have raised it to the 4th power of 10 because we have moved the decimal 4 digits before to balance the number and we know that in scientific notation base should be greater than 1 and less than 4 so moving the decimal to some other place is not valid.

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The distance between two points (2,-2) and (-3,-1) is √26 units.

Given points are (2,-2) and (-3,-1)

Let A(2,-2), B(-3,-1)

We need to calculate the distance between two points.

We know that distance between two points means the length of the line segment that connects two points in the 2D plane.

The formula for finding the distance between the two points A(x₁, y₁),

B(x₂, y₂) in a plane is given by

                                D = √((x₂ - x₁)² + (y₂ - y₁)²)

Now we have two points A(2,-2), B(-3,-1)

By using the above formula we get the distance as

D = √((-3 - 2)² + (-1 - (-2))²)

D = √((-5)² + (-1+2)²)

D = √(25 + (1)²

D = √(25+1)

D = √26 units

∴ The distance between two points (2,-2) and (-3,-1) is √26 units.

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Answer:

Step-by-step explanation:

1: 500,000 cm

500,000cm can also be written as 5000m or 5 km

So it becomes 1:5km

the 1 represents 1cm on the map so every centimeter in the map is 5 kilometers in real life

If we want to get what 7 cm would be in kilometers then we have to multiply both sides by 7.

So it would be 1 x 7 and 5x 7

it would end up being 7 : 35 km

The answer is: 35km

The total capacity of pool in gallons is 1625.

Let us assume the water in the pool be x liters. Forming the equation according as per the statement in question -

x + 300 = 80% of total volume - Equation 1

Forming the equation according to second statement -

30% × x = 300

30/100 × x = 300 - Equation 2

Finding the initial volume of water using equation 2-

x = 300×100/30

Cancelling zero and performing division and multiplication to find the initial volume of water

x = 1000 gallons

Now finding the total volume or capacity of pool by keeping the value of x in first equation -

1000 + 300 = 80/100 × total volume

Total volume = 1300×100/80

Performing multiplication and division to find the total capacity of pool

Total capacity of pool = 1625 gallons

Hence, the total capacity of pool in gallons is 1625.

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The rate at which Riya is applying mulch in m³/m² is 0.25m³/m²

From the question, we are to determine the rate at which Riya is applying mulch in m³/m²

From the given information, we have that

Riya is applying mulch to her garden at a rate of 250,000 cm³ of mulch for every m² of the garden space

That is,

The rate at which she is applying mulch is 250,000 cm³/m²

Now, to determine the rate in m³/m², we will convert 250,000 cm³ to m³

Converting 250,000 cm³ to m³

250,000 cm³  = 250000 × (10⁻²)³ m³

= 250000 × 10⁻⁶ m³

=  0.25 m³

Hence, the rate at which Riya is applying mulch in m³/m² is 0.25m³/m²

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The transformations that would guarantee triangles JOY and PEP are congruent are

The given parameters are:

Triangles JOY and PEP

From the question, we understand that:

The triangles are congruent after being transformed

The transformations that ensure congruency are rigid transformation

The rigid transformations are:

Using the above as a guide, we have the true options to be:

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Answer:

A and c

Step-by-step explanation:

The value of z in the given inverse variation is,  z= 1 / 9

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

In the question given,

first of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.

z = k / (x) (y)

0.5 = k / (2) (4)

k = 4

now write the function equation again by putting value of k,

⇒ z = 4 / (x) (y)

put x = 4 and y = 9 to find the value of z.

z = 4 / 36

z = 1 /9

Thus, z = 1/9

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The required function following the given conditions is z = 180 / (x × y).

What is a function?

A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.

Writing the function satisfying the given conditions

Given, x = 3, y = 2, z = 30

Let the function satisfying the given conditions be z = k / (x.y)         —--- 1

Putting all the values, we get,

k = 3 × 2 × 30

= 180

Using the value of k in equation 1, we have,

z = 180 / (x × y)

Hence, the required function is z = 180 / (x × y).

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Answer:

The population of a species that grows exponentially over time can be modeled by P(t)=Pe^(kt), where P(t) is the population after time t, P is the original population when t=0, and k is the growth constant.

Step-by-step explanation:

this is from my science

i hope it helped!!!!!!

Answer: 454.5

Step-by-step explanation:

-2, 20, -200, 2,000 ==> 4 numbers

Mean: (-2+20+(-200)+2000)/4=

(18-200+2000)/4=

(-182+2000)/4

1818/4=454.5

Answer:

Step-by-step explanation:

In order to cancel the coefficient of P you have to divide both sides by the coefficient not add the coefficient to both sides.

-2/3p = 4

-2/3p / -2/3 = 4 / -2/3    (Multiply both sides by -2/3 to isolate p)

p = 4 / 2/3     ([tex]\frac{4}{1} (-\frac{2}{3} ) = -\frac{8}{3}[/tex])(keep change reciprocate)

p = -8/3

The expression that means the same as the given expression is w ÷ 5

From the question, we are to determine which of the given expressions means the same as w/5

To do this, we will simplify each of the given expressions if possible

This expression cannot be simplified further

This expression cannot be simplified further

This expression can be written as w/5

This expression can be written as 5w

This expression cannot be simplified further

This expression can be written as 5/w

Hence, the expression is w ÷ 5

Here is the complete question:

Which Of the expressions below means same as w/5

w + 5

w - 5

w ÷ 5

5 × w

5 - w

5 ÷ w

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