8.121 Round 8.121 to the nearest tenth.

For figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

What is the Basic Proportionality Theorem?

The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

Figure 2)

By using the Basic Proportionality Theorem, we can write

                        [tex]\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14[/tex]

Now for figure 3)

            By using Pythagoras' theorem, we can write

                        [tex]24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1[/tex]

Hence, for figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

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Answer:

The point on the segment connecting A and B that is 4 times as far from B as it is from A is (-8, 8).

Answer:

or the distance to be 4 times the distance from B as A   the segment must be divided into (4+1) = 5 segments

  so we want the point that is 1/5 of the way from A to B

x    from A   to B   is     2   to   - 6   =   -8 units       1/5 * -8    +  2  =    0.4

y    from A   to B   is     7 to    -3    =   -10 units      1/5 * -10  +  7    = 5    

Answer:

60

Step-by-step explanation1

135 = 2x+15 => corresponding angles

2x= 135-15

2x= 120

x= 60

The inequality that can be used to determine the number of books, b, Erin must sell in order to meet her goal of making more than $180 in book sales is 12b ≥ 180.

2. The solution to the inequality 12b ≥ 180 is that b ≥ 15.

Inequality is a mathematical statement that two or more mathematical expressions are unequal because their solutions are not equivalent in value.

Inequalities are depicted as less than (<), more than (>), not equal to (≠), less than or equal to (≤), and more than or equal to (≥).

The selling price per book = $12

The total sales revenue expected is ≥ $180

The number of books = b

Inequality describing the situation = 12b ≥ 180

b ≥ 180 ÷ 12

b ≥ 15

Thus, we can conclude that Erin needs to sell 15 or more books to earn $180 or more from the book sales.

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32 more blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles.

we need to find the numbar of blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

Let the number of blue marbles added be n,

required probability P = 3/4

Total marbles = 10 + 7 + 3

                      = 20

Number of blue marbles=7

Using definition of probability,

(7 + n)/(20+n) = 3/4

4(7+n)=3(20+n)

28+4n=60+3n

n = 32

Therefore, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.

What is speed ?

The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.

144/r= t

144/(r-4)-144/r = 3

LCM r(r-4)

144r-144(r-4)/r(r-4)=3

Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]

[tex]\frac{576}{r(r-4)}=3[/tex]

Multiply both sides by r(r-4)

[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]

Simplify

576=3 r(r-4)

Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]

r=16, r=-12

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The expression that shows how many sweatshirts were not adult sizes is  s - 19 .

Given :

the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes.

Expression :

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Expression = number of sold sweatshirts - number of adult sizes.

= s - 19.

This gives the number of sweatshirts that are not adult sizes

if s = 25

then not adult sizes sweatshirts = s - 19

= 25 - 19

= 6

Hence the expression is s - 19.

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Y= 2.5x equation represent their relationship .

An equation is a formula that is express the equality of two expressions ,by the connecting them with the equal sign .

The process of equting one thing with another is called the equation of science with objective .

The equation is representing direct proportion is, by the connecting them with in the equal sign.

y = kx ← k is the constant of proportion

Here k = 2.5 , thus

y = 2.5x ← equation of proportion.

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Answer:

<

A

Step-by-step explanation:

There are 45 different ways in which two of them can be selected as the best students in the class.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).

A k-combination of a set S is officially defined as a subset of S's k unique elements.

Total number of students = 10

Number of students to be selected = 2

No. of ways = 10C2

                   = (10*9)/2

                   = 5*9

                   = 45

Hence, there are 45 different ways in which two of them can be selected as the best students in the class.

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The transformation from f(x) = -7|x| + 7 to  g(x) =  7|x|- 7 is-

The graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)

What is rotation?

The mathematical transformation which turns a geometrical figure about a fixed point is called rotation. The fixed point is called center of rotation.

f(x)= –7|x|+7

g(x) =  7|x|- 7

At first the graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)

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Answer:

u > -11/10

Step-by-step explanation:

The cyclist takes 0.36 hours to travel 4.5 miles.

Here given that,

The distance travelled by the cyclist 3.75 miles.

Time = 0.3 hour

Distance / Time = Speed

By substituting,

3.75 / 0.3

= 12.5 miles per hour is the speed.

2) Distance = 4.5 miles, speed = 12.5 miles per hour.

Distance / Speed = Time

Time = 4.5 / 12.5

=0.36 hours

Therefore it takes 0.36 hours to travel 4.5 miles.

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Answer: 39 crackers

Step-by-step explanation:

There are seven days a week

Only Friday, he eats half, so 6 left

6 times 6 = 36

36+ 3= 39

The swimming pool was on sale for $1206.2, which is 18.5% less than its initial $1429.35 cost.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Here,

Sale price after discount=$1206.2

Discount percent=18.5%

Original price=1206.2+18.5%*1206.2

=$1429.35

The original price of the swimming pool was $1429.35 as It was at sale price of $1206.2 with the discount of 18.5%.

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The simplest form of the ratio r:h:u is 5 : 8 : 14.

What is the ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

We have,

r : h  = 5 : 8   .........(i)

h : u =  4:7    ........(ii)

Multiplying the (i) and (ii) by numbers that will make 'h' have the same value in the ratios

Multiplying (i) by 1

(r : h)*1  = (5 : 8)*1

= r : h  = 5 : 8  

Multiplying (ii) by 2

(h : u)*2 =  (4:7) *2

= 8 : 14

the ratio r : h : u in the simplest form = 5 : 8 : 14.

Hence, the simplest form of the ratio r:h:u is 5 : 8 : 14.

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Answer:

0

Step-by-step explanation:

10x + 12 = 2(5x+6)

or, 10x + 12 = 10x + 12

or, 10x - 10x = 12 - 12

or, 0 = 0

.

. . so, 0 is the answer.

Step-by-step explanation:

10x + 12 = 2(5x + 6)

10x + 12 = 10x + 12

10x + 12 = 10x + 12

10x + 12 - 12 = 10x + 12 - 12

10x = 10x

10x - 10x = 10x - 10x

____________________________________________

Answer:

7 cm ; 10 cm ; 14 cm

Step-by-step explanation:

x = y + 3

z = 2y

x + y + z = 31

y + 3 + y + 2y = 31

4y = 31 -3

4y = 28

4/4 y = 28/4

y = 7

z = 7(2) = 14

x = 7 + 3 = 10

Answer:

A. Imaginary Square is 1 so ye ignore

Answer:

5

Step-by-step explanation:

[tex] {x}^{3} - {2xy}^{2} + {y}^{3} \\ {( - 2)}^{3} - 2( - 2)(3) {}^{2} + {3}^{3} \\ - 8 + 4 - 18 + 27 \\ 31 - 26 = 5[/tex]

Answer:

55

Step-by-step explanation:

1. Substitute in the values

  -2^3 - ( 2 * -2 * 3^2 ) + 3^3

2. Simplify the powers

  -8 - ( 2 * -2 * 9 ) + 27

3. Solve the brackets

  -8 - ( -4 * 9 ) + 27

  -8 - ( -36 ) + 27

  -8 + 36 + 27

4. Solve

  -8 + 63

  55

If a car is traveling at 50 mph due south at a point 1 mile north of an intersection. the radar gun register at -62.6 mph.

Distance can be defined as how far an object is from another object.

Distance of the first car north of the intersection point =y

Distance of the police car west of the intersection  =x

Distance between the cars =s

s² =x² +y²

x=1.4 miles or 0.25 miles

y =1/2 miles or 0.50 miles

Pythagoreans theorem

Distance between cars

s =√x²+y²

s=√(0.25 miles)² +(0.50 miles)²

s =0.559 miles

Hence,

ds/dt = [0.25 miles/ 0.559 miles (-40 mph)] + [0.50 miles/0.559 miles (-50 mph)

ds/dt = -17.89 + -44.7

ds/dt = - 62.59mph

ds/dt =- 62.6 mph (Approximately)

Therefore the distance is 62.6 mph.

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Converting 7π/21 to degrees will be 60°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.

Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.

It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.

This will be illustrated as:

= 7π / 21 × 180 / π

= 7/21 × 180

= 60°

The value is 60°.

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Answer:

Step-by-step explanation:

The answer is 12

Answer:

x=12

Step-by-step explanation:

[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]

Answer: A) y = 5x – 13

Step-by-step explanation:

The equation is y=mx + b

We know the slope is 5 and the y-intercept is at ( 0, -13)

So our equation is y = 5x - 13

So, the answer is A

Answer:

A

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent.

Δ PQR  congruent to Δ PNM

PR and PM are corresponding sides , then

PM = PR = b

a) The probability of rolling a total of 5 is 1/9.

b) If a pair of fair dice 360 times, then 40 times you will get a total of 5.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The number of 5 in the table is 4.

The total number of outcomes is 6 × 6 = 36

The number of outcomes of favorable event is 4.

Total number of outcomes is 36.

The probability getting total of 5 after rolling the pair of dice is

=4/36

Divide the denominator and numerator by 4:

= 1/9

If 360 time the pair of dice rolled, the number of times to get total 5 is

360 × (1/9)

= 40.

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Answer:

8, 0

Step-by-step explanation:

Answer:  Just add them up. 5 1/20

Step-by-step explanation:

1+1+2=4. For the fractions, find the LCM. The LCM is 20 so you make all the fractions denominator 20. 2/20, 4/20, 15/20. Now you get 5 1/20 in the end

Answer: 40%

Step-by-step explanation:

Take 10 divided by 25; then times 100 = 40%

Answer:

f(x)=7

Step-by-step explanation:

f(x)= 1/2x+5 ; x=4

f(4)= 1/2(4)+5

f(4)= 2+5

f(x)=7

Hope this helps, because I just did this lesson and I was confused at first, but with practice you will get it!