someone help me with both of these geometry problems

When two lines intersect the vertically opposite angles so formed are equal in measure.

When two lines intersect each other, then the opposite angles, created due to the intersection are called vertical angles or vertically opposite angles.

We can see in the figure two lines intersect each other at a point. Therefore the two pairs of vertically opposite angles are ∠1 and ∠3, ∠2 and ∠4.

From the figure, ∠1 + ∠2 = 180°  [Linear pair]     eqn(1)

∠2 + ∠3 = 180°  [Linear pair]   eqn(2)

From eqn(1) and eqn(2), we get

∠1 + ∠2 = ∠2 + ∠3

∴ ∠1 = ∠3

Similarly, we can prove ∠2 = ∠4 also.

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36 square units make up the larger circle's surface area.

We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.

We know that the area of a circle is given by the formula A = πr^2.

We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the area of the larger circle is 36 square units

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The coordinates of the center of the circle and the radius length of the specified circle are (-3,2) and 6 units, respectively.

A circle is a shape formed by all points in a plane that are at a particular distance from the center. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant. A circle is a closed two-dimensional object in which the set of all the points in the plane is equidistant from a particular point called "centre". The line of reflection symmetry is formed by every line that travels through the circle. It also features rotational symmetry around the center for all angles.

Here,

x²+6x+9-9+y²-4y+4-4=23

(x+3)²-9+(y-2)²-4=23

(x+3)²+(y-2)²=36

(x+3)²+(y-2)²=6²

center=(-3,2)

radius=6

The coordinates of the center of the center and the length of the radius of the given circle is (-3,2) and 6 units.

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Answer: We start by distributing the -6 to the terms inside the parentheses:

8f - 6(-5) - 6(7f)

Then we simplify each term inside the parentheses:

8f + 30 + 42f

Now we combine like terms:

8f + 30 + 42f = 50f + 30

So the simplified expression is 50f + 30

Step-by-step explanation:

Alex has five cups of strawberries and wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Alex has enough strawberries to make both recipes.

To check if Alex has enough strawberries, we add the amount of strawberries needed for the fruit salad (1 3/4 cups) and the amount needed for the jam (3 1/2 cups)

1 3/4 cups + 3 1/5 cups

= 1 + 3/4 + 3 + 1/5

Multiplying 3/4 with 5/5 and 1/5 with 4/4 to make denominator equal

= 1 + 15/20 + 3 + 4/20

= 4 + 19/20

= 4 19/20 cups

4 19/20 is less than 5 cups. So Alex has enough strawberries for both recipes.

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The short leg of a 30-60-90 triangle is 1/2 the length of the hypotenuse. 30-60-90 triangle is the half of an equilateral triangle.

Right triangles with 30-60-90 interior angles are called special right triangles.

A 30-60-90-degree triangle is a special right triangle and its side lengths are always consistent with each other. The ratio of the sides follows the 30-60-90 triangle ratio: 1: 2: [tex]\sqrt{3}[/tex] .

Short side (opposite the 30° angle) = x

Hypotenuse (opposite the 90° angle) = 2x

Long side (opposite the 60° angle) = x√3

30-60-90 Triangle Theorem:

These three properties can be examined by the 30-60-90 triangle theorem and are unique to these special right triangles:

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Answer: I can't answer that because it's not a question

Step-by-step explanation:

The distance from Alberto's house to the school is 4 units and from Alberto's house to the library is 6 units

Consider the following diagram.

From given coordinate grid we can observe that Alberto's school is located at point (-1, 4)

Alberto's house is at (3, 4).

And the library is located at the reflection of (3, 4) across the y-axis.

This means, the libarary is located at point (-3, 4)

We know that the absolute value is nothing but the distance between a number and zero on a number line.

The distance from Alberto's house to the school would be,

= distance between points (3, 4) and (-1, 4)

= |3 - (-1)|

= |3 + 1|

= |4|

= 4 units

And the distance between Alberto's house to the library would be,

= distance between points (3, 4) and (-3, 4)

= |3 - (-3)|

= |3 + 3|

= |6|

= 6 units

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The complete question is:

This coordinate grid shows where Alberto’s school is located. Each unit represents one block. Alberto's house is at (3, 4). The library is located at the reflection of (3, 4) across the y-axis. What are the coordinates of the library?

The area of a right-angled triangle is represented by the expression

x(x + 2) = 24 having area 24 square feet.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a right-angled triangle is (1/2)×base×height.

Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.

Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).

Therefore, The area of the triangle is,

(1/2)×x(x + 2) = 24.

x(x + 2) = 24.

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When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].

Given is the statement -

"8[tex]\frac{1}{4}[/tex] divided by 2/11"

We can write it as -

x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}

x = 33/4 x 11/2

x = 363/8

x = 45[tex]\frac{3}{8}[/tex]

Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].

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Answer:

Its the second image

Step-by-step explanation:

Step-by-step explanation:

so, clearly, the triangles BCF and DCF are congruent.

that makes the line CF a bisector of the kite figure.

and so, both angles are identical halves of the total angle at C.

therefore,

3x + 13 = 13x - 7

13 = 10x - 7

20 = 10x

x = 20/10 = 2

Answer:

Step-by-step explanation:

Answer is choice A

Both functions are decreasing at a rate of -2. You can find this by finding the slope.

The expression for area of the rectangles are obtained as x² + 10x + 21 and  x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The dimension of both the rectangles are given as,

First rectangle : (x + 3) and (x + 7)

Second rectangle : (x - 1) and (x - 8)

Since, the area of a rectangle is product of its dimensions.

It can be obtained as,

Area of first rectangle is given as,

⇒ (x + 3) × (x + 7)

⇒ x² + 10x + 21

Area of second rectangle is given as,

⇒ (x - 1) × (x - 8)

⇒ x² - 9x + 8

Hence, the area of both the rectangles are obtained as  x² + 10x + 21 and  x² - 9x + 8 respectively.

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Total 400 calories is expected to have a meal has 300 calories from fat  the relationship between the total calories a meal has and the number of calories from fat .

A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables). There are points on a scatter (XY) plot that depict the connection between two sets of data. The sample illustrates the weight and height of one person for each dot. Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another. The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.

given

300 calories from fat

total = 100 + 100 + 200

= 400 calories

Total 400 calories is expected to have a meal has 300 calories from fat  the relationship between the total calories a meal has and the number of calories from fat .

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In one min Charlie can read is [tex]2\frac{1}{7}[/tex] pages at a constant rate.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.

In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.

In [tex]\frac{2}{3}[/tex] min Charlie can read [tex]1\frac{3}{7} = \frac{10}{7}[/tex] pages

In one min Charlie can read is: [tex]\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}[/tex]

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Answer:

For this example they are all the same thing.  

530:1 or 530 mph

Step-by-step explanation:

A unit rate is when the denominator is 1.  In this case, the denominator is already 1 hour.

$164.86 more is needed to reach the goal of $1,200.00.

First, we need to find out how much money Mrs LeBlanc's class has raised since they have raised 50% of the total needed. We can do this by multiplying the total needed by 50%:

$1,200.00 * 50% = $600.00

Next, we need to find out how much money Ms Warner's class has raised since they have raised one-third as much as Mrs LeBlanc's class. We can do this by multiplying the amount raised by Mrs LeBlanc's class by one-third:

$600.00 * 1/3 = $200.00

Now we can add up the amount raised by all three classes to see how much has been raised in total:

$600.00 (Mrs. LeBlanc's class) + $235.14 (Mr. Patel's class) + $200.00 (Ms. Warner's class) = $1035.14

Finally, we can subtract the total amount raised from the goal amount to find out how much more is needed:

$1,200.00 - $1,035.14 = $164.86

So $164.86 more is needed to reach the goal of $1,200.00.

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Answer:

y=7/2 and x=6

Step-by-step explanation:

2x−6y=−2y−2 can be turned into x=2y−1.

Now you can substitute the equations.

−6x−4y=−2x−38

−6(2y−1)−4y=−2(2y−1)−38

Then you can simplify.

−12y+6=−36

−12y=−42

y=7/2

Then you can substitute y to find x.

x=2y−1

x=2(7/2)-1

x=6

And then our answers are y=7/2 and x=6.

Hope this helped! :)

Step-by-step explanation:

the given ratio is

8 / 20/10 = 8 / 2 = 4

for x mathletes we need to keep the same ratio :

x / 30/5 = 4

x / 6 = 4

x = 4×6 = 24

24 mathletes.

Answer:

90 cups

Step-by-step explanation:

Number of cups needed = 30 / (1/3) cups

                                          = 90 cups

Thought process:

1 cup -> 1/3 ounce

3 cups -> 1 ounce

? cups -> 30 ounce

Hence, ? = 30 x 3

                = 90

Answer:

Its 22:40

Step-by-step explanation:

Answer: 22:40
Pretty simple

Step-by-step explanation:

Answer:

c) 16 cm²

Step-by-step explanation:

Given information,

→ Base = 4 cm

→ Height = 8 cm

Area of triangle formula,

→ Area = ½ × b × h

Now the area of triangle is,

→ ½ × b × h

→ ½ × 4 × 8

→ 2 × 8

→ 16 cm²

Hence, the area is 16 cm².

The area of the floor in the scale drawing is 60 inches²

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Actual rectangular floor.

Length = 24 feet

Width = 40 feet

Scale rectangular floor.

Length = 6 inches

Width = 40/4 = 10 inches

The area of the scale rectangular floor.

= Length x Width

= 6 x 10

= 60 icnhes²

Thus.,

The area of the floor is 60 inches².

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Surface Area : Volume = 6 : s

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Surface Area of a Cube = 6a² in a square units

Volume of cube = a³ cubic units

where a is the side length of the cube.

Given length of the cube = s

Surface Area of cube A = 6s²

Volume of cube V = s³

Ratio between Surface Area and volume:

Surface Area / Volume = 6s² / s³

Surface Area / Volume = 6 / s

Surface Area : Volume = 6 : s

Hence the ratio between Surface area and volume of cube is 6 : s.

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Answer:

y = [tex]\frac{1}{3}[/tex] x - 6

Step-by-step explanation:

9y - 3x = -54

We want in the form

y = mx + b

9y - 3x = -54  Add 3x to both sides

9y - 3x + 3x =  3x - 54

9y = 3x - 54   Divide all the way through by 9

[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]

y = [tex]\frac{3}{9}[/tex] x - 6

We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x - 6

The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.

What is median ?

The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.

A. IQR  for male dataset

The IQR is calculated as follows:

IQR = Q3 - Q1

      =

For the male's data:

IQR = Q3 - Q1

      = 25 - 1

      = 24

Hence, the IQR of the male dataset is 24.

B. Difference in median values

We have:

median = 20 ----- Male dataset                                                    

median = 6  ----- Female dataset

So, the difference (d) is:

d = 20 - 6

  = 14

Hence, the difference in median of both dataset is 14.

C. Best measure of center

The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.

The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot

D. Reason for outlier

There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.

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The degree of the polynomial 2x² 5x³ 7 is 5.

The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of the variable is 5, which appears in the term 5x³. The degree of a polynomial is a whole number that tells us how many times the variable is multiplied by itself. The degree of the polynomial is 5.

It's worth noting that polynomials can be constant or non-constant, meaning they don't have to have a variable in them, in that case the degree is 0. And also a polynomial with only one term, the degree of that polynomial is the exponent of that term.

In this case, we only have one term with variable x in it, 5x³, and the degree is the exponent of that term which is 5.

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Solving for x in the angle bisector which resulted to the proportion  x over 18 = 45 over 20 results to x = 40.5

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.

By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The division from angle bisectors gave rise to the proportion which is given by

x / 18 = 45 / 20

cross multiplying

x = 18 * 45 / 20

x = 40.5

hence x is solved to get 40.5

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