ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)

Answer: 3/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 12 and 16 is 4

Divide both the numerator and denominator by the GCD

12 ÷ 4

16 ÷ 4

Reduced fraction: 3/4

Therefore, 12/16 simplified to lowest terms is 3/4.

Answer:.

Step-by-step explanation:

If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of  different random samples of four accounts that are possible is 230,300.

Given data:

Number of population of bank account = 50

Random sample = 4 accounts

Now let find the different random samples of four account that are possible

Different random sample = 50! / (50 -4)! × 4!

Different random sample = 50! / 46! × 4!

Different random sample = 230,300

Therefore the different random samples is 230,300.

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a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.

b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 3x² - 18x + 56.

Giving the temperature in degrees Fahrenheit in x days after Sunday.

The day that represents Thursday is given by:

x = 4.

Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:

f(4) = 3(4)² - 18(4) + 56 = 32 ºF.

Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.

The numeric value is of 35 when:

3x² - 18x + 56 = 35

The solutions to the quadratic equation are:

x = 1.6, x = 4.4.

Hence the days are:

Monday and Thursday.

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Answer: (f+g)(x) = 6x²- 4x + 6

Step-by-step explanation:

We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)

Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)

We are left with (f+g)(x) = 6x²- 4x + 6

The value of WV is 9x - 10

A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.

From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.

We have;

This is represented as;

WV + VY = WY

Then;

WV = WY - VY

substitute the values

WV = 5x + 19 - (29 - 4x)

expand the bracket

WV = 5x + 19 - 29 + 4x

collect like terms

WV = 9x - 10

Hence, the value is  9x - 10

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Answer:

x+5

Step-by-step explanation:

there are no like terms

The equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following statement - "4 less than a number is given w".

Assume the number to be [x].

We can write the equation representing the statement -

"4 less than a number is given w" as a mathematical expression as -

[w] = x     where x ∈ (- ∞, 4)

Therefore, the equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

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The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph

The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.

From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(bench press weight, squat weight).

From the table given by the first image at the end of the answer, the points are listed as follows:

(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).

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The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways

The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:

nCr = n!/(r!(n - r)!)

The total number of cards that we have in a deck of cards = 52.

There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways

After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).

Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:

Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card

Plugging in the relevant values gives;

Number of ways = (13 × 6) × 48 × 44 × 40

= 6,589,440 ways

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The expressions are:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

15 x squared minus 18 end quantity over 6.

= 15x² - 18 / 6

= 3(5x² - 6)/ 6

= (5x² - 6)/ 2

and, 5 x squared minus 18 end quantity over 2

= 5x² - 18/2

and, 5 x squared minus 6 end quantity over 2

= 5x² -6 /2

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The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

According to the question,

We have the following information:

Cost of 1 pound of grapes = $3.75

Cost of 1 pound of apples = $4

Total cost made by selling = $251.75

And the weight of the apples and grapes sold = 64

Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.

So, we have:

x+y = 64

x = 64-y ....(1)

3.75x+4y = 251.75

Putting the value of x in this equation:

3.75(64-y)+4y = 251.75

3.75*64-3.75y+4y = 251.75

240+0.25y = 251.75

0.25y = 251.75-240

0.25y = 11.75

y = 11.75/0.25

y = 47 pounds

Now, putting this value of y in equation 1:

x = 64-y

x = 64-47

x = 17 pounds

Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

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The percent that Desmond average speed increase is 25%.

From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.

It should be noted that the percentage increase in speed will be:

= Change in speed / Initial speed × 100

= (30 - 24) / 24 × 100

= 6/24 × 100

= 25%

The percentage is 25%.

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The flowchart that is used to prove GR ║ F_K is presented as follows;

∠RND and ∠FDP are supplementary  ⇒    ∠RND + ∠FDP = 180°

Given                            [tex]{}[/tex]                                 Definition of supplementary

∠KDN  ≅ ∠FDP                 [tex]{}[/tex]                    ⇒    ∠KDN = ∠FDP

Vertical angles are congruent[tex]{}[/tex]                    Definition of congruent angles

∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°    

Definition of same side interior angles[tex]{}[/tex]                    Substitution property

[tex]{}[/tex]                                           GR ║ F_K

The relationships between the angles formed by a transversal and two parallel lines are;

Definition of congruency;

Two lines, shape or figure are said to be congruent if they have the same size and shape.

Supplementary angles;

Supplementary angles are angles that have a sum of 180°

Substitution property of equality

The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.

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Answer:

A. REFLECTION

Please guys do some research i know you're not that stu p id-_-

Answer:

6 and - 18

Step-by-step explanation:

let the 2 integers be a and b , then

a + b = - 12 → (1)

[tex]\frac{a}{b}[/tex] = - 3 → (2)

multiply both sides by b ( b ≠ 0 )

a = - 3b

substitute a = - 3b into (1)

- 3b + b = - 12

- 2b = - 12 ( divide both sides by - 2 )

b = 6

substitute b = 6 into (1) and solve for a

a + 6 = - 12 ( subtract 6 from both sides )

a = - 18

the two integers are - 18 and 6

The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question.,

x ≥ 9 and,

y > 3

The equation is,

650 x + 1400 y ≤ 1

[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]

x/23.07 + y/10.71 ≤ 1

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if we take 25 to be the 100%, what is 100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]

Answer:

25

Step-by-step explanation:

25/100=.25x100=25

The mean score of all the students is 79.5 and it is round off into one decimal place.

Mean

Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given,

In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.

Here we need to find the mean score of all students.

In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,

=> 30 x 87.7 = 2631

Similarly, the total score for 21 students is,

=> 21 x 67.7 = 1421.7

So, the 51 students, cumulative score is

=> 2631 + 1421. 7 = 4052.7

Therefore, the mean score is calculated as,

=> 4052.7/51

=> 79.464

When we round off the value into one decimal place then we get

=> 79.5

Therefore, the mean value of all the students is 79.5.

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The circumference of the circle is 25.1 inches.

The length of the arc ACB is 4.2 inches.

The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of a circle = 2 × 3.14 × 4

circumference of a circle = 8 × 3.14

circumference of a circle = 25.1 inches

The length of the arc ACB can be found as follows:

length of arc = ∅/ 360 × 2πr

length of the arc = 60 / 360 ×  2 × 3.14 × 4

length of the arc = 60 / 360 ×  25.12

length of the arc = 1507.2 / 360

length of the arc = 4.18666666667

length of the arc = 4.2 inches

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The y-intercept of the graph as shown is 2.

The equation of a line can be represented as follows:

y = mx + b

where

The y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .

Therefore, let's trace the value of y when x  = 0 on the graph.

Hence, when x = 0, y = 2

Therefore,

b =  y-intercept = 2

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Answer:b=2b

b=−2b

b=−3b

b=3b

Step-by-step explanation: because I tought myself i know

The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]

The interior angles of a triangle are the angles formed by the sides sides of the triangle.

The question can be solved by making use of the known properties of a triangle.

The angle sum property of the interior angles in a triangle gives;

The sum of the interior angles of a triangle is 180°

Therefore; x + 2·x + 70 = 180

3·x = 180° - 70° = 110°

[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]

The measure of angle A is 2·x

Which gives;

[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]

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If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2

Let coordinates

P = (2, 7) and Q = (2, -3)

PR = QR

(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2

(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y

or Y^2 - 14Y + 49 = Y^2 + 6Y + 9

20Y = 40

Y=2

coordinates of R if triangle PQR is isosceles ;

Hence any point R on the line Y = 2 will make PQR a isosceles triangle

with PR = QR.

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The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)

From the question, we have the following inequality that can be used in our computation:

2x+5y<1

Solving further, we need to collect the like terms

Since there are no like terms in the expression, it remains unchanged

So, the inequality becomes

2x + 5y < 1

Subtract 5y from both sides of the inequality

This gives

2x < 1 - 5y

Divide both sides by 2

The expression becomes

x < 1/2 - 5/2y

Evaluate

x < 0.5 - 2.5y

At this point, we assume any value for y and then solve for x

Assume that the value of y is 4

So, we have the following representation

x < 0.5 - 2.5 * 4

Evaluate the products

x < -9.5

This means that x is less than -9.5 when y is 4

-10 is less than -9.5

So, we have

x = -10 and y = 4

Express as ordered pairs (i.e. coordinates)

(x, y) = (-10, 4)

Hence, the coordinates of the solution is (-10, 4)

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The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°

We have different trigonometric ratios such as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.

This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;

tan θ = 10/50

where θ is the true bearing angle. Thus;

tan θ = 0.2

θ = tan⁻¹0.2

θ = 11.31°

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