Determine whether the pair of figures is similar. If so, find the scale factor. Explain your reasoning.
OA) no; ZBCD # ZFCG
OB) no; BD #CO
OC) Yes: A BDC-A FGC because ZB
OD) Yes: A BDC-A FGC because ZB
4
LO
ZF. ZD
ZF. ZD
5
D 3
C
25
5
20
BD
ZG. ZBCD ZFCG, and C=
FG
ZG, ZBCD = ZFCG, and
BD
=
DC
CB

Answer:

Step-by-step explanation:  (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient

Hope it helps =}

Answer:

b

Step-by-step explanation:

Given:-

By using formula:-

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

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:

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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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

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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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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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

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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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

The soap used by the machine last year is 5399.76 gallons.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Let the soap used last year = x.

Then, according to the given condition:

4,508.8 = x (1 - 16.5%)

4,508.8 = x (83.5/100)

x = 4,508.8(100) / 83.5

x = 5399.76

Hence, the soap used by the machine last year is 5399.76 gallons.

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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 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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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

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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Answer:

13 square units

Step-by-step explanation:

The composite figure can be decomposed into

2 semicircles each of diameter 3

1 rectangle of height 1 and length 5

1 square of side 1

Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle

So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07

= 7 square units rounded to nearest whole number

Area of the rectangle = width x length = 1 x 5 = 5 square units

Area of square of side 1 = 1 x 1 = 1 square unit

Total area of shaded area = 7 + 5 + 1 = 13 square units

Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

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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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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.

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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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 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?

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.

Check the picture below.

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

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.

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).