solve the following 4x-1/2 = x + 7 and 3x + 2 = 2x+13/3

Answer:

a=15, b=14

Step-by-step explanation:

We know all angles must add up to 360, so lets add all angles and set them equal to 360.

[tex]7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360[/tex]

We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.

[tex]3b=6b-42[/tex]

Now solve for b in both equations

[tex]3b=6b-42\\-3b=-42\\b=14[/tex]

[tex]17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=\frac{381-17a}{9}[/tex]

Now we set the two equations equal to each other to solve for a:

[tex]14=\frac{381-17a}{9} \\126=381-17a\\-255=-17a\\15=a[/tex]

This gives a=15, b=14.

If two hikers are 11 miles apart and walking towards each other and they meet in 2 hours, then if one hiker walks 0.3mph faster than the other, then the rate at which the slow hiker and fast hiker walk towards each other is equal to 2.6 and 2.9 mph respectively.

Consider, the speed of the slow hiker = s

Then, the speed of the fast hiker = s + 0.3

The distance covered by both the hikers in 1 hour = 2s + 0.3 miles

The distance covered by both the hikers in 2 hours = 2(2s + 0.3) = 4s + 0.6 miles

We can find the value of s by forming an algebraic expression as follows,

4s + 0.6 = 11

4s = 11 - 0.6

4s = 10.4

s = 10.4 / 4

s = 2.6

Speed of the slow hiker = s = 2.6 mph

Speed of the fast hiker = s + 0.3 = 2.6 + 0.3 = 2.9 mph

Hence, the rate at which the slow hiker and the fast hiker walk toward each other is equal to 2.6 and 2.9 mph respectively.

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The correct representation of x + 5 using algebra tiles is one green rectangle box and one small yellow box.

Algebra tiles are the tiles or square or rectangular boxes which are use to represent the polynomial expression whether of linear , monomial or quadratic.

There are three types of algebra tiles :

All of these tiles has different color to represent positive and negative value :

Square Type                      Positive color                      Negative Color

Small squares                     Yellow                                 Red

Rectangles                          Green                                  Red

Large Squares                     Blue                                    Red

For the given question, Expression is x + 5

that means, there is one Green rectangle and one Yellow small square.

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Yes, the given expressions i.e., 3m^2+2m^2 and 5m^2 are equivalent expression.

An expression is defined as a combination of various terms or numbers that are combined by using mathematical operations in addition, subtraction, multiplication, and division.

Equivalent expressions are expressions that have similar value or worth but do not look the same. When considering if the expressions given are equivalent, at least two expressions are must.

A) Yes, by considering the above definitions we can conclude that 3m^2+2m^2 and 5m^2 are equivalent expressions.

B) Given, 3m^2+2m^2 and 5m^2

Now, solve 3m^2+2m^2 we simply get the value which is similar to other expression given to us in the question i.e., 5m^2.

Hence, 3m^2+2m^2 and 5m^2 are similar or equivalent expression.

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Answer:

85%

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

85% because, $40 X .85 = $34 which means, $34 is 85% of $40

The margin of error at 90% confidence and its interpretation is 0.085. 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion.

The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.

Given, random sample of 92 .

The formula for margin of error is;

[tex]E = z(\sqrt{(p(1 - p)/n} )[/tex]

The parameters are given as;

Sample size; n = 92

Sample of success; x = 51

Sample proportion:

p = 51/92

= 0.554

z at 90% CL = 1.645

Thus;

[tex]E = 1.645(\sqrt{(0.554(1 - 0.554)/92} )[/tex]

[tex]E = 0.085[/tex]

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Answer:

3d-4

Step-by-step Explanation:

2d+1+d-5 Combine like terms 2d and d together which is 3d. That leaves you with 1-5 which is -4. so then you end up with 3d-4 as your answer.

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

for i in range(4):

  bill = float(input("Enter bill for quarter " + str (i+1) + ": "))

  total += bill

average = total / (4 * 3)

if average > 75:

  print("Average monthly bill is $" + str(average) + ". Too much water is being used")

if 25 <= average < 75:

  print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")

if average < 25:

  print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

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Answer:

1.7 kilograms

Step-by-step explanation:

750 + 450 + 0.5kg ( 1kg = 1000) so 0.5 would be 500g.

=1,700g (1.7kg) :)

Answer:

4x^3 (3)_/x + 10x^3 (3)_/x

Step-by-step explanation:

First lets solve the first term

When you multiply exponents you add them, so x^10 can be split into:

x^3 * x^3 * x^3 * x^1

We can then take it out.

4x^3 (3)_/x

Then for the other part we can also factor it.

2*2*2 is 8 so we can take that out and multiply it by 5 =10

You can keep x in there since you can factor it into smaller pieces.

The final answer you get when you add all of it together is :
4x^3 (3)_/x + 10x^3 (3)_/x

The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.

In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:

V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)

V' = 1018791.667 ft³

V'' = (1 / 3) · (34.5)² · 55.5

V'' = 22019.625 ft³

Second, calculate the volume of the obelisc:

V = V' + V''

V = 1018791.667 ft³ + 22019.625 ft³

V = 1040811.292 ft³

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Answer:

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

Therefore A+B+C = 180

This means 4x+34+7x-10+5x+12 = 180

Simplies down to 16x+36 = 180

Rearrange to have 16x = 144

Divide by 16 on both side to get x = 9

Substitue the value of x back into the equation of A

A = 4(9)+34 = 70 degrees

Answer: A. [tex]3\sqrt{5}[/tex]

B. l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

A. A=l*w

l=2w

A=2w*w

90=2w*w

w*w=45

w=[tex]\sqrt{45}[/tex]

w=[tex]\sqrt{9*5}[/tex]

w=[tex]3\sqrt{5}[/tex] ==> Square length and the rectangle width

B. 90=l*w

90=l*[tex]3\sqrt{5}[/tex]

30=l[tex]\sqrt{5}[/tex]

l=[tex]\frac{30}{\sqrt{5} }[/tex]

l=[tex]\frac{30\sqrt{5} }{5}[/tex]

l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]

highest common factor (HCF) of 32, 48 and 72= 8

HCF - Highest Common Factor

The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely. The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).

There are many ways to find the HCF of two numbers. One of the quickest ways to find the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its various aspects and properties. Find answers to questions like what is the highest common factor for a group of numbers, easy ways to calculate HCF, HCF by division method, its relation with LCM, and discover more interesting facts around them.

HCF by Prime Factorization

In order to find the HCF of numbers by the prime factorization method, we use the following steps. Let us understand this method using the example given below.

Step 1: Find the common prime factors of the given numbers.

Step 2: Then, multiply these common prime factors to obtain the HCF of those numbers.

highest common factor (HCF) of 32, 48 and 72

32 = 2x2x2x2x2

48= 2x2x2x2x3

72= 2x2x2x3x3

highest common factor (HCF) of 32, 48 and 72 = 2x2x2= 8

highest common factor (HCF) of 32, 48 and 72= 8

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Answer:

12 cm

Step-by-step explanation:

Volume of total shape = Volume of big rectangle - Volume of small rectangle

Volume of big rectangle = L×B×H

Volume of big rectangle = 10 cm×3 cm×2 cm

Volume of big rectangle = 60 cm

Volume of small rectangle = l×b×h

l = 10 cm - 6 cm = 4cm

Volume of small rectangle = 4 cm×3 cm×4 cm

Volume of small rectangle = 48cm³

Volume of total shape = 60cm³ - 48cm³

Volume of total shape = 12cm³

Answer:

A. 25°

Step-by-step explanation:

In triangle ABC:

<A + <B + <C = 180°

=> 45° + (2x - 15)° + 4x° = 180°

=> 6x° + 30° = 180°

=> 6x° = 150°

=> x° = 25°

Choose A.25°

Answer:

A. 25 degrees

x = 20

2(20) - 15 = 25 degrees

A local maximum occurs over the interval (-2,0).

A local minimum occurs over the interval (0,2).

If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.

Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.  

Here the given x and f(x) values for the continuous function f(x) are:

x        f(x)

-3       -16

-2        -1

-1         2

0         -1

1          -4

2          -1

As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).

The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).

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Answer:

3

Step-by-step explanation:

y=mx+b

m is the slope

Answer:

(30.00)

Step-by-step explanation:

(30.00) is the correct answer for your question/ statement you have asked. the answer is (30.00) again.

Answer:

See picture below

Step-by-step explanation:

Answer:

7. 2^-5= 1/2^5= 1/32

8. (4/5)^-3= (5/4)^3=125/64

9. 8^-4/8^-7=8^-4+(-7)=8^11=216

10. (1/3)^-2 x (1/3)^2=(1/3)^-2+2=(1/3)^0=1

Answer:

Step-by-step explanation:

1) Use multiplication distributive property [tex](xy)^a=x^ay^a[/tex]

= [tex]\frac{(x^4)^2y^2}{3}[/tex]

2) Use Power rule [tex](x^a)^b = x^{ab}[/tex]

= [tex]\frac{x^8y^2}{3}[/tex]

Answer:

[tex]volume = 653.71 {cm}^{3} [/tex]

Step-by-step explanation:

Volume = πr^2h

=

[tex] \frac{22}{7} \times {4}^{2} \times 13 \: c {m}^{3} [/tex]

= 22*16*13/7 cm^3

= 653.714cm^3

Rounding off = 653.71 cm^3

Answer:

653.45

Step-by-step explanation:

it told me the answer

The standard form for given values is 12416.

A number has two form . First is standard form and another is expended form of numbers.

It is a form in which we write number as a whole without describing the places for the numbers.

The numbers such as 456, 17817, 9009, 32 etc all are the standard form of the numbers.

In the case of expended form we generally write number with its describe places of value or with the plus (+) symbol between them.

For example, 16 ones 24 tens 1 hundred is the expended form of numbers.

In the given question the form given is :

16 ones 24 tens 1 hundred

so, we have to place 16 at ones place , 24 at tens place and 1 at hunderedth place value .

Therefore, the standard form becomes : 12416.

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The complete question is:

Convert to standard form

16 ones 24 tens 1 hundred

The approximation of -8 plus the square root of 20 is given by:

-3.5.

To round a number to the nearest tenth, it will have only one decimal digit, and the rule is as follows:

The square root of 20 is given by:

sqrt(20) = 4.47.

7 > 5, hence, rounded to the nearest tenth:

sqrt(20) = 4.5.

Then:

-8 + 4.5 = -3.5.

Which is the approximation.

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Each side of the triangle should contain four numbers whose sum is 28.

3+5+9+11=28

3+10+8+7=28

11+6+9+7=28

The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.

We use special terminology to define the sides of right triangles.

The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.

The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is across from another at a particular angle.

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Yes, figure B is a scale copy of figure A.

As per the question statement and its reference diagram attached thereby, we are provided with two geometrical figures of same shape but different sizes.

We are required to determine if figure B is a scale copy of figure A or not.

To solve this question, we need to carefully compare the lengths of the corresponding sides from both the figures.

We can clearly see that, the dimension of every side of figure B is twice that of the corresponding side of Figure A, i.e.,

[tex](1*2)=2\\(2*2)=4\\(3*2)=6\\(4*2)=8[/tex]

Hence, it is proved that figure B is a scale copy of figure A.

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Answer:

the tetrahedron, octahedron and icosahedron

Answer:

tetrahedron, octahedron, icosahedron