During a person's commute to school, she spends 20 minutes driving 45 mph and 5 minutes stopped at red lights. What is the person's average speed during her commute

Side HG of ΔIHG is congruent to side CD of ΔBCD.

The correct option is A.

Two triangles are said to be congruent if the three sides and the three angles of both the triangles are equal in any orientation.

Given,

ΔIHG ≅ ΔBCD

By the given figure,

HG ≅ CD

Hence, side HG is congruent to side CD.

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The remainder of the table for the given function rule should be completed as follows;

x      -2    -1      0    1       2    

y      -7    -8    -9   -10    -11    

Based on the information provided, we have the following function rule:

Function, f(x) = y = -x - 9

When the domain x = -2, the range (y) of this function is given by;

Range, y = -x - 9

Range, y = -(-2) - 9

Range, y = 2 - 9

Range, y = -7.

When the domain x = -1, the range (y) of this function is given by;

Range, y = -x - 9

Range, y = -(-1) - 9

Range, y = 1 - 9

Range, y = -8.

When the domain x = 0, the range (y) of this function is given by;

Range, y = -x - 9

Range, y = -(0) - 9

Range, y = 0 - 9

Range, y = -9.

When the domain x = 1, the range (y) of this function is given by;

Range, y = -x - 9

Range, y = -(1) - 9

Range, y = -1 - 9

Range, y = -10.

When the domain x = 2, the range (y) of this function is given by;

Range, y = -x - 9

Range, y = -(2) - 9

Range, y = -2 - 9

Range, y = -11.

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The given figure is a composite figure which consists of a rectangle BECF and a triangle ABD.

In the above figure,

(1)  BECF is a rectangle

(2) ABD is a triangle

Area of the given composite figure

= Area of rectangle BECF + Area of triangle ABD

Area of rectangle BECF :

length CF = 18 cm and width BC = 10 cm

= length x width

=  18 x 10

=  180 cm2 ----(1)

Area of triangle ABD :

Base BD  =  BE - DE  =>  18 - 6 => 12 cm

Height AB = AC - BC => 8 - 10 => 2

Area of triangle ABD = (1/2) x b x h

 =  (1/2) x 12 x 2

= 12 cm2 ----(2)

(1) + (2) :

Area of the given composite figure is

=  180 + 12

=  192 cm2

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Answer:

$13,511

Step-by-step explanation:

Year 1: $22,000×.85=$18,700

Year 2: $18,700×.85=$15,895

Year 3: $15,895×.85=$13,510.75

($13,511 to nearest dollar)

The angles formed by lines a, c, and d are 90 degrees, 90 degrees, 90 degrees, 90 degrees.The angles formed by lines b and c are 80 degrees, 80 degrees, 80 degrees, 80 degrees.

In order for two lines to be parallel, the angles formed by the lines and any transversal must be equal. In this case, the angles formed by lines a, c, and d must be equal to 90 degrees, and the angles formed by lines b and c must be equal to 80 degrees.

For two lines to be parallel, the angles formed by the lines and any transversal crossing them must be equal. In this particular case, the angles formed by lines a, c, and d must be equal to 90 degrees, and the angles formed by lines b and c must be equal to 80 degrees. This means that the angles formed by lines a, c, and d must be 90 degrees, 90 degrees, 90 degrees, and 90 degrees, clockwise from top left. Similarly, the angles formed by lines b and c must be 80 degrees, 80 degrees, 80 degrees, and 80 degrees. Finally, the angles formed by lines b and d must be 58 degrees, 80 degrees, 80 degrees and 80 degrees. All these conditions must be met for lines a and b to be parallel.

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Answer:

see explanation

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

E (0, 7 ) → E' (0, - 7 )

F (- 5, - 1 ) → F' (- 5, - (- 1) ) → F' (- 5, 1 )

G (3, 0 ) → G' (3, 0 ) ← unchanged as G is on the x- axis

This means that an earthquake of magnitude 7.9 is 10^4 (or 10,000) times more intense than an earthquake of magnitude 3.5.

An earthquake is a sudden shaking of the ground caused by the shifting and breaking of large pieces of rock beneath the Earth's surface. Earthquakes can be caused by a variety of factors including the shifting of tectonic plates, volcanic activity, and underground explosions.

An earthquake of magnitude 7.9 is significantly more intense than an earthquake of magnitude 3.5 on the Richter scale. The Richter scale is logarithmic, meaning that each whole number increase in magnitude corresponds to an increase in shaking intensity by a factor of 10. This means that an earthquake of magnitude 7.9 is 10^4 (or 10,000) times more intense than an earthquake of magnitude 3.5.

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The proportion of people who approved of both leaders exists 40%.

The logical connections between two or more sets of objects are shown by a Venn diagram, which uses circles or other forms that overlap. They frequently act as a visual organization tool, showcasing how things are alike and different.

A Venn diagram is a type of visual organizer that examines the connections among a variety of items. It consists of overlapping circles. To organize things, numbers, and shapes, they are frequently utilized. An instruction or label that relates in some way to the data is given to each circle.

As stated in the title. 60% of individuals favored leader B, and 65% favored leader A. If 15% of the population remained closed to the leaders,

The proportion of people who approved of both leaders

= 60 % - 20 % = 40 %

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Answer:

Hello!

Your answer follows below:

Step-by-step explanation:

X5 -3x3 -x2 +2x +2 ÷ x2 -2 = Please view attached file.

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HCF of 32 and 24 is 8 (eight)

What is HCF?

HCF stands for the highest common factor - it is the greatest factor that divides the given number.

For example, 2 is the HCF of 4 and 6.

Given numbers are 32 and 24

prime factor of 32 is 2*2*2*2*2

prime factors of 24 are 2*2*2*3

HCF will be the product of a common number which is 2*2*2 =8

therefore, the HCF of 32 and 24 should be 8

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the complete question should be as follow

what is the HCF of 32 and 24?

The length of the rectangular garden is 12 m and the breadth is 5 m.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. In the above example, the area of the rectangle whose length is 4 inches and the width is 3 inches is 12 square inches. We have 4 × 3 = 12. The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".

Area of a Rectangle = (Length × Breadth) square units

Let us assume that the length of the rectangular garden is x and the breadth is y.

We are given that The perimeter of a rectangular garden is 38m and its area is 60sq.

Perimeter = 2(length + breadth) = 2(x +y)

∴ 2 (x+y) = 38 ⇒ x+ y = 17 ⇒ y = 17 -x

Area = length×breadth = xy

∴ xy = 60

Substitute y from above equation:

x(17 - x) = 60

⇒ 17x - x² = 60

⇒ x² - 17x + 60 = 0

Solving this quadratic equation, we get

x = 12 , 5

Thus, the length of the rectangular garden is 12 m and the breadth is 5 m.

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The length of the base of an isosceles triangle is 7

as given in the question,

the length of base be x

the length of the leg is 3x+2

the perimeter of the isosceles triangle is 39

Therefore, an isosceles triangle which has two equal sides or legs as well as two equal angles. The Greek words iso means same and skelos are the source of the name leg. An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

If the length of

In an isosceles triangle,

The length of the two legs or sides is the same. The other leg is therefore 3x+2 if one leg is the other is also  3x+2.

The triangle's three sides add up to its perimeter

that is

=> x + (3x+2) + (3x+2) = 39

=> 7x + 4 = 39

=> 7x = 35

=> x = 5

the  value of x is 7

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The length of the base of an isosceles triangle is x = 7

Yes, there is enough information to solve for x. The perimeter of an isosceles triangle is the sum of all its sides. Since the perimeter is given and two sides are known, it can be expressed as follows:

x + (3x +2) + (3x +2) = 39

Solving for x,

5x + 4 = 39

5x = 35

x = 7

Therefore, the length of the base is 7. This can be verified by substituting the value of x into the equation for the perimeter, which would yield a result of 39.

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The coefficient of the given expression 4x+17 is 4 and the constant is [tex]4[/tex].The coefficient is a number or variable that is multiplied by another variable in the expression. Think about [tex]4a^{2}[/tex]. In this instance, the literal coefficient of [tex]4[/tex] is [tex]a^{2}[/tex] and the numerical coefficient of [tex]a^{2}[/tex] is [tex]4[/tex]. The numerical coefficient of n is [tex]12[/tex] in the expression [tex]12n[/tex]; if there is no number, the coefficient is assumed to be [tex]1[/tex].

The numerical coefficient of both [tex]a^{2}[/tex] and [tex]b[/tex] in the expression [tex]a^{2}[/tex] + b is [tex]1[/tex]. Terms with similar literal coefficients are called like terms, while terms with different literal coefficients are called unlike terms. A value or number that never changes in its expression is called a constant. It is always the same. For instance, the values [tex]36[/tex] and [tex]82[/tex] in the preceding figure are constant because they have the same face value. It never loses value.

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The value of function H(x) at x = -4 is 16, at x  = -3 is -13, at x = 2 is 2, at x = 3 is 5, and at x = 5 is 11.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output.

Given:

H(x) = 3x - 4

Calculate the value of the function when x = -4 as shown below,

H(x) = 3 × (-4) - 4

H(x) = -12 - 4

H(x) = 16

Calculate the value of the function when x = -3 as shown below,

H(x) = 3 × (-3) - 4

H(x) = -9 - 4

H(x) = -13

Calculate the value of the function when x = 2 as shown below,

H(x) = 3 × 2 - 4

H(x) = 6 - 4

H(x) = 2

Calculate the value of the function when x = 3 as shown below,

H(x) = 3 × 3 - 4

H(x) = 5

Calculate the value of the function when x = 5 as shown below,

H(x) = 3 × 5 - 4

H(x) = 11

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Answer: k = 32

Step-by-step explanation:

k/8 - 1 = 3         We add 1 on both sides

+1          +1

k/8 = 4          Now we have to multiply by both sides to isolate the k

x8     x8

k = 32

The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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The number of As that are needed for 12Bs will be 6 and the ratio is 1:2.

It should be noted that ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

It was Illustrated that the rate relating A to B is 1/2 and we want to use the rate to find how many As are needed for 12Bs.

From the information, the rate relating A to B is 1/2. The number of As that are needed for 12Bs will be:

= 1/2 × 12.

= 6

Therefore, there'll be 6 As that are needed.

The ratio is:

= 6 / 12.

= 1 / 2

= 1:2.

The ratio is 1 / 2.

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Complete question

The rate relating A to B is 1/2. Use the rate to find how many As are needed for 12Bs, then write the ratio.

Answer:

с.0

Step-by-step explanation:

The y-intercept of a graph is the point where the graph crosses the y-axis. This means that when x=0, the value of y is equal to the y-intercept. In the equation y = 2.5x, when x=0, y=2.5 * 0 = 0. So the y-intercept of this graph is 0

Answer:

0.7

Step-by-step explanation:

30% off a price means you pay 70% of the tag price.  So multiply the tag price by 0.70

Example:

A $75 pair of sneakers is 30% off. You pay $75 x 0.7 = $52.50

To prove this is right, 30% off $75 is:

$75 x 0.30 = $22.50

$75 - $22.50 = $52.50

Answer:48

Step-by-step explanation:jjjhdwjhwed

Answer:

start by defining some extremes:

the absolute maximum for a/b would be at the maximum a and minimum b. This is 4/4 = 1. The minimum for a/b is 3/5

Are these both allowed values? NO! Each case is a limit which cannot be reached, because the a and b values must stop short of the limits. The answer appears to be: 3/5 < a/b < 1 (0.6 < a/b < 1)

Answer:

Set x equal to zero and then simplify

Area of the shaded sectors and segment are 1. 51.3 cm², 2. 30.1 cm² and 3. 14.14 cm².

Circles are two dimensional figure which are set of all points which are equal distance from a common point.

Area of the sector = (θ/360°) π r², where θ is the sector angle.

1. r = 7 cm

  θ = 120°

  Area of the sector DEF = (120/360)  π 7²

                                          = [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × 7²

                                          = 51.3 cm²

2. We have to find the area of the segment DF.

   Area of the segment DF = Area of the sector DEF - Area of ΔDEF

   From 1. Area of sector DEF = 51.3 cm²

   To find area of ΔDEF, make two triangles by drawing a perpendicular       bisector from E to line DF. Let O be the point on the line DF where the perpendicular line touches..

Then we get two triangles and they are congruent by RHS congruency rule. [ Both have hypotenuse = 7 cm, both have right angles and a common side which is the perpendicular drawn.

Let's find base and height of ΔDEF.

Let x be the base. Then x/2 is the base of one triangle.

Sin 60° = base / hypotenuse

√3 / 2 = (x/2) / 7

x/2 = (√3 / 2) × 7

x = 7[tex]\sqrt{3}[/tex] cm

Base = 7[tex]\sqrt{3}[/tex] cm

Cos 60° = Height / hypotenuse

1 / 2 = Height / 7

Height = (1/2) × 7

           = 3.5 cm

Area of  ΔDEF = [tex]\frac{1}{2}[/tex] × base × height

                        = [tex]\frac{1}{2}[/tex] × 7[tex]\sqrt{3}[/tex] × 3.5

                        = 21.2 cm²

Area of the segment DF = Area of the sector DEF - Area of ΔDEF

                                        = 51.3 cm² - 21.2 cm²

                                        = 30.1 cm²

3. r = 6 cm

   θ = 45°

   Area of sector KLM = (45/360)  π 6²

                                    =  [tex]\frac{1}{8}[/tex] × [tex]\frac{22}{7}[/tex] × 6²

                                    = 14.14 cm²

Hence the area of shaded portions are calculated as above.

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keeping in mind that the mid-segment of a trapezoid is simply half the sum of the parallel sides or "bases", Check the picture below.

[tex]B E=\cfrac{C D+A F}{2}\implies 2x+10=\cfrac{18~~ + ~~(6x-12)}{2}\implies 4x+20=6x+6 \\\\\\ 20=2x+6\implies 14=2x\implies \cfrac{14}{2}=x\implies 7=x[/tex]

Answer:

A square or cube....

Step-by-step explanation:

Who keep spamming random questions????

The new images has vertices Q´ (-12, 0), R´  (0, 0), P´(-12, -8),  and the type of dilation is contraction.

Dilation is the process of modifying the dimensions of an object or shape by varying some scale variables. For instance, a circle with a radius of 10 units gets shrunk to a circle with a radius of 5 units. This technique is applied in photography, fine art, logo design, and other fields.

When we dilate the points of a given figure, we simply multiply each x-coordinate and y-coordinate by the scale factor.

Here the points are P(-3,-2),Q(-3,0), and R(0, 0) and the scale factor is

k = 4

Therefore,

⇒ Q (-3,0) → Q´ (-3 × 4,0 × 4) = (-12, 0)

⇒ R (0, 0) → R´  (0, 0)

⇒ P (-3, -2) →  T´  (-3 × 4, -2 × 4) = (-12, -8)

Thus, the new images has vertices Q´ (-12, 0), R´  (0, 0), P´(-12, -8),

Also, the type of dilation is contraction.

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Answer:

C. 0≤x≤12

Step-by-step explanation:

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs) (Input, Output). In algebra, relationship and function are crucial ideas. Both in real life and in mathematics, they are often utilized. To further comprehend the significance of each of these relational and functional concepts, let's describe them.

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs). In algebra, relationship and function are crucial ideas. Both in real life and in mathematics, they are often utilized. To further comprehend the significance of each of these relational and functional concepts, let's describe them.

If each element x∈R has a distinct R-relative, resulting in R[x] consisting of a single element, then the relation R is referred to be a mapping (map), a function, or a transformation. This distinct component is known as the function value at x and is indicated by the symbol R(x) (under R). R[x] therefore only has one member, R(x).

Let us consider a domain for x ∈ N

The R ⇒ R is defined for f(x) = 2x ; x≤ 5

f(x) = 2x

will have a domain of 1, 2, 3,4, 5 and The value of the function will be

f(x) = 2, 4, 6, 8, 10 .

So, the 5 coordinates of the relation is {(1,2), (2,4), (3, 6), (4,8), (5, 10)}

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

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The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

What is meant by map?

Let us consider a domain for x ∈ N

The R ⇒ R is defined for f(x) = 2x ; x≤ 5

f(x) = 2x

will have a domain of 1, 2, 3,4, 5 and The value of the function will be

f(x) = 2, 4, 6, 8, 10 .

So, the 5 coordinates of the relation is {(1,2), (2,4), (3, 6), (4,8), (5, 10)}

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

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The insurance expense for the year ending December 31 would be $2,200.

If the insurance policy has benefits beginning on April 1 and the annual income statement is for the year ending December 31, then the insurance expense for the year would be a prorated portion of the $3,300 premium.

To determine the prorated amount, we need to calculate the number of months in the year covered by the policy. From April 1 to December 31, there are 9 months. The insurance expense for the year would be $3,300 divided by 3 (the number of years of the policy) and multiplied by 9/12 (the number of months in the year covered by the policy). This would be $3,300 / 3 * 9/12 = $2,200.

Therefore, the insurance expense for the year ending December 31 would be $2,200.

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Total $825 amount of insurance expense will be reported on the annual income statement for the year ended December 31.

In the given question, on April 1, a company paid the $3,300 premium on a three-year insurance policy with benefits beginning on that date.

We have to find amount of insurance expense will be reported on the annual income statement for the year ended December 31.

The total months between April 1 and December 31 is 9.

Insurance expense for 9 months (from 1 April to 31 Dec) = ($3300/3) *9/12

Insurance expense for 9 months (from 1 April to 31 Dec) = $1100 * 3/4

Insurance expense for 9 months (from 1 April to 31 Dec) = $3300/4

Insurance expense for 9 months (from 1 April to 31 Dec) = $825

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The explanation regarding the given values is given below.

An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, also, |5| will give 5 as well.

Given that x is on the right side of 1 therefore will be a positive quantity, while y is of the left side of 0 therefore will be always negative.
Also, y is more close to 0 while x is far from 1. Thus, we can write |x|>|y|.

Now, the two values are +x and -y let consider the given expressions,

2.1)
x + (-y)

= x - y
Since x is positive and greater than y while y is negative therefore, the result of this expression will be always positive and the value of the sum will be the absolute difference between x and y.

2.2)
(-y) - x
Since x is positive and greater than y while y is negative, therefore,

= -y + (-x)

= -y - x

The result of this expression will be always negative because y and x both will be negative and the value of the sum will be the numerical combined value of x and y.

2.3)
x - (-y)
Since x is positive and greater than y while y is negative, therefore,

= x + y

= x + y

The result of this expression will be always negative. therefore, the result of this expression will be always negative and the value of the sum will be the absolute sum of x and y.

2.4)
-y + x
Since x is positive and greater than y while y is negative, therefore,

= x - y

Since x is positive and greater than y while y is negative therefore, the result of this expression will be always positive and the value of the sum will be the absolute difference between x and y.

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