How do I simplify this?

4) m∠BAD=30° (angle subtraction postulate)

5) m∠B=45° (sum of angles in a triangle)

The top rung of a ladder is 18 inches long, lengths of the rungs increase one-half inch uniformly from the top to the bottom. The length of the ladder after 10th rung from the top is 33inches.

A ladder is a piece of gear used for climbing up or down objects that consists of repeating bars or steps (rungs) between two upright lengths of metal, wood, or rope.

In the industry, step ladders are most frequently used. This ladder is unique since it may be used in any location. This is due to the fact that it may be utilized without needing to lean against any kind of support because it is self-supportable. This ladder can therefore be used in the middle of a room or in other places without support.

Step ladders are incredibly practical to have throughout the house, particularly in the kitchen. Simply said, this ladder is a miniature ladder that you can use to access higher objects. When purchasing this ladder, storage space is not a concern because step stools are made to fold up.

Given,

Top rung =18 inches

Length increases = 1.5inches

Therefore, after 10th rung length= (1.5*10)+18 inches= 33 inches

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Answer:

x = 2/3

Step-by-step explanation:

If f(x) = -3x + 4, f(x) = g(x), and g(x) = 2, by the Transitive Property, -3x + 4 = 2

From here we can solve for x.

-3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
3x = 2
3x/3 = 2/3
x = 2/3

Answer: it's A.12 \ 3 =4  if worrg do D.16\4=4  i hop this help's you

i did this one long time ago it was ether one so ya i forgotten it sorry

The shapes which are similar to shape A are the shape in pink color, the shape in blue color inside the square and the shape in voilet color inside the square.

From the given figure, we can find the similar shapes

From shape A to shape in pink color, the  translation is rotation about the origin at 90° counterclockwise.

From shape A to shape  the shape in blue color inside the square, the translation is diminishment with the scale factor 0.5 and opposite rotation about an origin 90° clockwise.

From shape A to the shape in voilet color inside the square, the translation is enlargement with the scale factor 1.5 and opposite.

Shapes in various dimensions are scaled using the scale factor. In geometry, we study a variety of two- and three-dimensional geometrical shapes. A measurement for similar figures that appear the same but have distinct scales or measures is the scale factor.

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Answer:

r = 26

Step-by-step explanation:

Let's solve the problem,

→ 0.5r + 5 = r - 8

→ r - 0.5r = 5 + 8

→ 0.5r = 13

→ r = 13/0.5

→ [ r = 26 ]

So, the value of r is 26.

Answer:

24 +16÷4=00

(24+16)÷4=00

24÷(4+2)=42

Answer:

6/14,9/21

Step-by-step explanation:

those two are equavalent to 3/7

An amount of 2 liters of the 30 % vinegar solution to obtain a 20 % vinegar solution.

According to the statement, a vinegar solution with a given concentration must be prepared by using two vinegar solutions with different concentrations. We can find the required addition of the 30 % vinegar solution by weighted averages, whose respective formula is:

(20 / 100) · (4 + x) = (30 / 100) · x + (15 / 100) · 4

0.2 · (4 + x) = 0.3 · x + 0.15 · 4

0.8 + 0.2 · x = 0.3 · x + 0.6

0.1 · x = 0.2

x = 2

An amount of 2 liters of the 30 % vinegar solution to obtain a 20 % vinegar solution.

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Answer:

y = 2

Please go through my explanation.

Step-by-step explanation:

If y = 3x + 2

then y intercept is the value of y  when x = 0

At x = 0

y = 3 x 0 + 2

y = 0 + 2

y = 2

I have attached a graph to prove this

Note

It does not fit any of the answer choices. Maybe the answer choices are incorrect or the equation is incorrect.

The y intercept from the answer choices should be either (0, 9) or (0, -9) since x has to be 0 to get the y intercept

If y-intercept is to be 9, the equation should be y = 3x + 9

If y-intercept is to be -9, the equation should be y = 3x -9

You may wish to explain to the teacher about this if you are absolutely sure that the equation and answer choices are correct

Hope that helps in some small way

A point on the y-axis known as an intercept is where the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.

A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively.

We have,

f(x) = 3x + 2

To find the y intercept put x= 0 we get

y = 3x  +2

y= 3(0)+ 2

y= 0+ 2

y= 2

Thus, the y intercept is (0, 2).

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The conversions to standard and scientific notation will result into-

D (Jupiter) = 143000 Km

λ (Wavelength) = 4.39 x [tex]10^{-4}[/tex] meters.

We have diameter of Jupiter and radiation of a wavelength.

We have to write them in standard notation and scientific notation.

Scientific notation is a way of writing very large or very small numbers in the powers of 10.

According to the question -

D = 1.43 x [tex]10^{5}[/tex] Km

In standard notation -

D = 143000 Km

and

λ = 0.000439

In scientific notation -

λ = 4.39 x [tex]10^{-4}[/tex] meters

Hence, the conversions to standard and scientific notation will result into-

D (Jupiter) = 143000 Km

λ (Wavelength) = 4.39 x [tex]10^{-4}[/tex] meters

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If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.

Given:

k=0.12

Original or initial temperature=190 degrees Fahrenheit

Freezer temperature = 0 degrees Fahrenheit

Using Newton's Law of cooling to find the temperature of the hot chocolate

Temperature (t)= Temperature of surrounding environment T1 +(initial temperature of object T0-Temperature of surrounding environment T1)e-^kt

Hence,

T(t)=0+(190-0)e^-0.12t

T(t)=190e^-0.12t

Where t=4

T(t)=190e^-0.12(4)

T(t)=190e^-0.48

T(t)=117.5688

T(t)=117.57 (Approximately)

Therefore if the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.

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Answer:

See explanation

Step-by-step explanation:

The inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].

As per the question statement, Layla has a budget of $680 to spend at a bicycle store for some new gear and biking outfits, and she buys a new bicycle for $319.28, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94.

We are required to express the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget if a new biking outfit costs $77.02

First, let us calculate the total spending Layla has already done before going for new biking outfits, which is $319.28 on bicycle, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94, summed up as [tex][319.28+(4.90*3)+37.94]=(319.28+14.7+37.94)=371.92[/tex]

And supposing that she buys "x" new biking outfits, of $77.02 each, the total spending has to be equal to, or less than $680, i.e.,

[tex][680\geq (371.90+77.02x)][/tex]

Hence, the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].

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The number of minutes it takes Darius to reach the shipwreck is 8.75 minutes

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Initial position = -5 feet

Rate = -8 feet per minute

Final position = - 75 feet

The linear equation of this situation is

Final position (y) = Initial position + Rate * Time (x)

So, we have

-75 = -5 -8x

This gives

-8x = -70

Divide both sides by -8

x = 8.75

Hence. the number of minutes it takes Darius to reach the shipwreck is 8.75 minutes

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Answer: -1<x<7

Step-by-step explanation:

4|x-3|-6<10

4|x-3|-6+6<10+6

4|x-3|<16

4|x-3|/4<16/4

|x-3|<4

x-3<4

x<7

x-3>-4

x>-1

-1<x<7

Answer:

this is since the decimal point moves

Step-by-step explanation:

forget about the decimal point for right now

025

04

-------

0

8

20

0

0

0

+

-----

100

now there are 3 numbers behind the decimal points (2,5,and 4) so put the decimal point where 3 numbers are behind it.

.100 or .1

The area of the pre-image is 300 square units

A triangle is a 2D shape that has a 3 sides and angles. The formula for calculating the area is expressed as;

Area= 1/2 * bh

where

b is the base of the triangle

h is the height of the triangle

Given the following parameters

Area of triangle = 75 square inches

If the area is increased with with a scale factor of 1 to 4, then

Area of pre-image = 4 * 75

Area of pre-image = 300 square units

Hence the area of the pre-image is 300 square units

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Sum of their ages= 53

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away,

a-b = c (c may be a positive or negative value it may be 0 too)

given that, total of the ages of andrew, caren and barbara is 68 years

asked about their total 5 years back so we have to subtract five years from three of them then we will get,

3x5=15

subtract 15 from 68 to get total of their ages five years ago

68-15=53

this gives the total age of  andrew , caren and barbara  5 years ago

which is equal to 53

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Answer:

Ages together equal 53.

Step-by-step explanation:

An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. For instance, the adjacent image shows 5 2 peaches, or 5 peaches with 2 subtracted.

a-b = c (c may have a positive, negative, or even zero value.)

Given that, Andrew, Caren, and Barbara's combined age is 68 years.

asked them how many years back in total they had, so we had to take away five years from three of them to get,

3x5=15

In order to calculate their ages five years ago, take 15 out of 68.

68-15=53

this reveals Andrew, Caren, and Barbara's combined ages. five years ago

which is equal to 53.

For the given kite DCBA, the value of AD as 22 units and CB as 30 units.

We know that the two longer sides and the two shorter sides of the kite are equal to each other.

So, we get that:

AD = CD

Substituting the values, we get that:

11 y - 22 = 7 y - 6

11 y - 7 y = 22 - 6

4 y = 16

y = 16 / 4

y = 4

AD = 11 y - 22 = 44 - 22 = 22 units

AB = BC

Substituting the values, we get that:

3 x + 12 = 5 x

5 x - 3 x = 12

2 x = 12

x = 12 / 2

x = 6

CB = 5 x = 30 units

Therefore, we get that, for the given kite DCBA, the value of AD as 22 units and CB as 30 units.

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The length of the rectangle is 82.4 inches and the width of the rectangle is 21.6 inches.

Let the length of the rectangle be x inches.

So, the width of the rectangle will be:

Width = 1 / 4 x + 1 inches.

Now, the perimeter = 52 inches.

Now, the formula for the perimeter is:

P = 2 (l + b)

Substituting the values in the formula, we get that:

52 = 2 ( x + 1 / 4 x + 1)

104 = 5 / 4 x + 1

103 = 5 / 4 x

x = 103 × 4 / 5

x = 82.4 inches.

Length = 82.4 inches

Width = 1 / 4 x + 1 = 21.6 inches.

Therefore, we get that, the length of the rectangle is 82.4 inches and the width of the rectangle is 21.6 inches.

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Answer:

In equation 8p-1-2q+7q, 1 is the constant

Step-by-step explanation:

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Example: in "8p-1-2q+7q", 1 is the constants.

Let's simplify step-by-step.

8p−1−2q+7q

=8p+−1+−2q+7q

Combine Like Terms:

=8p+−1+−2q+7q

=(8p)+(−2q+7q)+(−1)

=8p+5q+−1

=8p+5q−1

The equivalent expression of 24 over 80 is 3/10

The expression is given as

24 over 80

Rewrite the expression properly

So, we have

24/80

Divide the numerator and the denominator by 8

So, we have

3/10

Hence, the equivalent expression of 24 over 80 is 3/10

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Answer:

2.42

Step-by-step explanation:

3 - 4/7 = 2.42

3 - 8/14 = 2.42

3 - 0.57 = 2.42

3 - 57.1 = 2.42

Breaking things down like this will make it easier to solve and get you answers faster!

there are  a total of 7983360 way of arrangements of the pies.

As we are provided we  three pieces of apple pie, five pieces of cherry pie, and four pieces of pumpkin pie, in total 12 pies

So total combination will be

12! = 1*2*3*4*5*6*7*8*9*10*11*12

   = 479001600

In the event that there was 1 pie, at that point it would be fair 1 in its line. If we had 2 pies A and B, at that point we have 2 combinations AB and BA. Adding a 3rd pie C would multiply those combinations by 3, ABC, ACB, BAC, BCA, CAB, and CBA. If each pie piece may be a unique work of craftsmanship at that point 12! is the proper amount of combinations. On the off chance that you need combinations that disregard setups where for illustration two cherry pie pieces are compatible, meaning you want uniqueness at that point you divide 12! by 5 at that point by 3 and after that by 4.

Usually 12! / (5*3*4) = 7983360 exceptionally interesting combinations.

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Answer: 308.0006

Step-by-step explanation: