Shade ______ line
for greater than (>).

Answer:

See proof below

Step-by-step explanation:

We will use the SAS condition for congruency of two triangles

SAS (Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

In the two triangles ΔHIK and ΔJIK we have
m∠4 = m∠3  (given)

HK ≅ KJ

IK is the common side

So the two sides HK and IK are equal and the included angles ∠4 and ∠3 are also equal

So by SAS, the two triangles are equal

So m∠2 = m∠1

which means IK bisects ∠HIK

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables.

Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

From the given options, the system of equations

2x + 6y = 18 and x + 5y = 13  

4x + 7y = 10 and -3x + y = -1    

Can be solved using the Elimination method  

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

From the given options, the system of equations  

y = x + 8 and y = 4x + 2

y = 3x + 3 and y = x + 7

Can be solved by using the Substitution method

Therefore,

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

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Answer:

Step-by-step explanation:

$7.75/6= $1.29

$8.33/7= $1.19

$10.45/9= $1.16

The better deal in the 9 candy bars for $10.45 because its only $1.16 PER candy bar.

For all n that is higher than or equal to 4, this statement is true.

By taking the cubes of both sides of the inequality, we can demonstrate this.

log2(n3) = [tex]3\sqrt{n}[/tex]

n^(3/2) <= 3 * log2(n) (n)

Since log2(n) > 2 for n >= 4, we can write:

3 * 2 * (log2(n)) = 3 * n where n(3/2) = 3 * log2(n)

This suggests that:

[tex]\sqrt{n} =( \frac{3}{n{log 2}} + n) (n)[/tex]

We come to the conclusion that the square root of n will eventually be less than or equal to log2(n3) for all n higher than or equal to 4 since the right-hand side of this inequality approaches zero as n goes to infinity. The assertion is accurate as a result.

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The student must she score on the fourth test in order to raise her test average 4 points is 4 points.

An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,

Let the required point be x,

According to question,

x+4×3 / (3+1) = 4

x+12 = 16

x = 4

Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.

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Answer:

-16x² + 10x - 14.

Step-by-step explanation:

To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).

So, let's first evaluate g(x):

g(x) = 8x² - 5x + 7

Next, substitute g(x) into f(x):

(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14

Therefore, (f g)(x) = -16x² + 10x - 14.

Answer:[tex]\sqrt{6}[/tex]

Step-by-step explanation:

The distance between 2 points is given by:

[tex]\sqrt{(x2-x1)+(y2-y1)}[/tex]

Let (6,3) be (x1, y1) and (8,7) (x2,y2).

=[tex]\sqrt{(8-6)+(7-3)}[/tex]

=[tex]\sqrt{2+4}[/tex]

=[tex]\sqrt{6}[/tex]

Hope this helps :)

[tex]\sqrt{p^1^2-16p^6+80}[/tex]

A pic down below is given:

Surface area of a rectangular prism is 444 square unit.

A rectangular prism is a three-dimensional shape with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.

The sides of a rectangular prism is 5, 4, 3, 3.7.

This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.

Surface area of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)

Surface area of a rectangular prism = 2 × 222

Surface area of a rectangular prism = 444 square unit

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Answer: 6x - 3

Step-by-step explanation:

I believe this question is asking you to expand the equation

Distribute the 3 to both terms on the inside to get: 3(2x -1) = 6x-3

Answer:

Step-by-step explanation:

i believe its 5x?

sorry if im wrong but i times 3 x 2 then 6 -1 or you can do 3 x 2 then 3 x -1 to get 6x and -3

Answer:

Option C

Step-by-step explanation:

First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.

A. x = 63, and z = 104 and together they equal 170, so not A

B. x = 76 and z = 63 and together they equal 139 so not B

C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.

D. x = 63 and z = 76 and together they equal 139 so not D.

From all of this it must be option C

Step-by-step explanation:

Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.

The surface area of the solid is the sum of all of the areas of its faces.

The area of a right triangle is a well-known formula. You should already know this.

The scientist poured 17 ounces of chemical out of the beaker, calculated from the total and remaining amount of chemical.

We are aware of the conversion unit that 1 pint is equal to 16 fluid ounces. So, total amount of chemical in the beaker is -

Chemical in beaker in points = 5/4

Chemical in beaker in ounces = 16×1/14

Chemical in beaker = 20 ounces

Now, the expression to calculate poured amount of chemical will be -

Total amount = poured chemical + remaining chemical

20 = poured chemical + 3

Poured chemical = 20 - 3

Performing subtraction on Right Hand Side of the equation

Poured chemical = 17 ounces

Therefore, 17 ounces of chemical was poured.

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The correct question is -

A beaker contains 1 1/4 pints of a chemical. A scientist pours the chemical out of the beaker until only 3 fluid ounces remain. How many fluid ounces of the chemical did the scientist pour out of the beaker?

the first choice is the right answer

please check my working for guidance

Answer:

Step-by-step explanation:

Given room looks like a rectangular room.Let w be the wide and l be long of the rectangular room respectively.Given,w=10 feet and l=24 feet.

we know area of the rectangular room= l*w

So,area=10*23

area=230 sq.feet

Given,cost of trim=$0.85 per foot

So,total cost =230* 0.85

=195.5

So,Jennifer charges $195.5 to buy enough

The one who types the fastest is Morgan. hence, the correct option is A.

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation , the instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We have been given that equation y=39x

Which models the total number of words Alexa can type, where y is the number of words typed and x is the time in minutes.

The data shows the relationship for Morgan.

Then we can conclude that Morgan types the fastest.

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Answer:B

Step-by-step explanation:

R^2=Q^2-P^2

R^2=2025

R=45

Answer:

b) 45cm

Step-by-step explanation:

by pythagoras theorem:

R² = P² - Q²

R² = 53² - 28² = 2809 - 784

R² = 2025

R = √2025

R = 45cm

Hope this helps!

The formula (D) f(n) = 65 − 9(n − 1) represents the arithmetic sequence for 65, 56, 47, 38, 29 ….

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.

In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.

For instance, a1 = 25 and a(n) = a(n-1) + 5.

Each word in an arithmetic sequence increases by adding or subtracting a certain constant, k.

As opposed to a geometric sequence, where each term is increased by dividing or multiplying a certain constant k, this one does not.

For instance, a(n) = a(n-1) + 5 and a1 = 25.

So, we have the sequence:

65, 56, 47, 38, 29 …

Now, the difference is 65 - 56 = -9

Now, the first term is 65.

Then, the equation which represents its formula is f(n) = 65 − 9(n − 1).

Therefore, the formula (D) f(n) = 65 − 9(n − 1) represents the arithmetic sequence for 65, 56, 47, 38, 29 ….

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Complete question:

An arithmetic sequence begins with 65, 56, 47, 38, 29 … Which option below represents the formula for the sequence?

(A) f(n) = 56 − 9(n)

(B) f(n) = 56 + 9(n −1 )

(C)  f(n) = 65 + 9(n −1 )

(D) f(n) = 65 − 9(n − 1)

The volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

The volume of a right circular cylinder can be calculated using the formula:

V = π * r² * h

Where r is the radius and h is the height of the cylinder.

Plugging in the values for r and h, we get:

V = π * 7² * 1.5

V = π * 49 * 1.5

V = 73.5 * 1.5

Therefore, V = 110.25

So the volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

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If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.

Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:

Area = length x width = 75 meters x 50 meters = 3750 square meters

Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:

Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter

Multiplying the area by the cost per square meter gives us:

Total cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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The solution of the system of equation y - 10 = 2x and 1/2 y = x + 5 is

The simultaneous equation is solved by substitution method as follows

y - 10 = 2x and

1/2 y = x + 5

Isolate y in the first equation to get

y = 2x + 10

substitute y in 1/2 y = x + 5

1/2 (2x + 10) = x + 5

x + 5 = x + 5

x = 0

substitute x = 0 into y = 2x + 10

y = 2(0) + 10

y = 10

hence the solution is (0, 10)

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The requried solutions are as follows,
(1) the original price is $450.   (2)  the original price is $172.40.

Sale price is defined as the price of a product marked including of various price cut such as discounts.

Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)

Sale price = Original price - Discount

$90 = x - 0.8x

Simplifying the right-hand side:

$90 = 0.2x

x = $450

Therefore, the original price is $450.

If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:

Sale price = Original price - Discount

$146.54 = x - 0.15x

Simplifying the right-hand side:

$146.54 = 0.85x

x = $172.40

Therefore, the original price is $172.40.

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It will take 20 pounds for both charges to be the same.

An equation containing variables with its highest power as one is called linear equation.

To ship a package,

UPS charges $4 for the first pound and $0.50 for each additional pound.

FedEx charges $6 for the first pound and $0.40 for each additional pound.

These can be written in the linear equation form as,

Let p be the pound charges by both UPS and FedEx,

then, 4+0.50p-------(1)

6+0.40p-----(2)

When the charges are same, (1)=(2)

4+0.50p = 6+0.40p

⇒0.10p=2

⇒p=20

Hence, this means that, it will take 20 pounds for both charges to be the same.

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Figure E has more area than Figure D. Figure E has an area of 26 square units, while Figure D has an area of 22 square units. The difference in area is 4 square units, which is the area of the 4 squares added to the bottom of Figure E.

If the side length of each square in the figures is doubled, the area of each square will be quadrupled since the area is proportional to the square of the length of the side.

In Figure D, each square has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure D will be 15 x 4 = 60 square units.

In Figure E, each square also has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure E will be 12.5 x 4 = 50 square units.

The new ratio of their areas would be:

New ratio of areas = (Area of Figure D) / (Area of Figure E) = 60 / 50 = 6/5

So the new ratio of their areas would be 6:5.

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The correct answer is 178 bottles of water sold on Sunday.

Vendor is a person or a company that sells goods or services. The term is commonly used to refer to individuals who sell items at events, markets, or street stalls. Vendors may sell a variety of products, including food, drinks, clothing, accessories, and more

If the vendor sold 405 bottles of water on Saturday, and sold 127 fewer bottles on Sunday, then on Sunday she sold 405 - 127 = 278 bottles of water.

However, the question states that she actually sold 178 bottles of water on Sunday, so the number of bottles she sold on Sunday was incorrect.

The correct answer is 178 bottles of water sold on Sunday.

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Answer:

Step-by-step explanation:

Since M is the point of intersection of the diagonals of the square, it is also the midpoint of both diagonals. This means that AM is equal to half the length of a side of the square and also bisects the angle formed by the two sides that it connects.

Let's call the length of a side of the square s. Then, the distance AM can be found using the Pythagorean theorem:

AM = sqrt((5 - 2)^2 + (1 - 1)^2) = sqrt(3^2 + 0^2) = sqrt(9) = 3

So, the length of a side of the square is 2 * AM = 2 * 3 = 6.

Next, we can use the length of a side and the coordinates of A to find the coordinates of B. Since AB is a side of the square and is 6 units long, we can find B by moving 6 units to the right of A:

B = (2 + 6, 1) = (8, 1)

We can also find the coordinates of C by moving 6 units up and 6 units to the left of A:

C = (2 - 6, 1 + 6) = (-4, 7)

Finally, we can find the coordinates of D by moving 6 units down and 6 units to the right of A:

D = (2 + 6, 1 - 6) = (8, -5)

So, the coordinates of the other vertices of the square are B = (8, 1), C = (-4, 7), and D = (8, -5).

Answer: 4(9a-4) and x = 18

Step-by-step explanation:

36a - 16 a common factor in this is 4 so if we factor out 4 we would get

4(9a-4)

1/2x - 7 = 1/3(x-12) we would distribute out the 1/3 so 1/3x and 1/3 x - 12 which would simply into 4

1/2x - 7 = 1/3x - 4 get the x's into one side so subtract 1/3x and add 7 on both sides

1/2x - 1/3x = 3 --- multiply 1/2x with 3/3 and 1/3x with 2/2

3/6x - 2/6x = 3

1/6x = 3 --- isolate x by multiplying 6 on both sides

x = 18

Given:-

By using formula:-

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

О m³   (cubic meters)

Step-by-step explanation:

The volume formula is length * width * height

Example:

volume = 3m * 5m * 4m

volume = 60m³

The solution is, О m³   (cubic meters), is the correct label to show volume.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

to find the correct label to show volume.

now, we know that,

The volume formula is length * width * height

as we know that,

the standard unit for length is meter (m).

now, we have,

length has unit m

width (= length) has unit m

and, height (=length)  has unit m

so, we get,

Volume = length * width * height

             = m * m* m  (as unit)

             = m³

Example:

volume = 3m * 5m * 4m

volume = 60m³

Hence, The solution is, О m³   (cubic meters), is the correct label to show volume.

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