Use the number line diagram below to answer the following questions.1.What is the length of each segment on the number line?

We need to find the midpoint of a segment HX given the endpoints:

H = (4.5, -4.25) and X = (3.25, -2.75)

where we have written the coordinates (initially in mixed number form) in decimal form for ease of handling operations.

4 1/2 = 4.5

-4 1/4 = -4.25

etc.

Now we apply the formula for the midpoint (in the x and y coordinates separately):

x coordinate of midpoint = (4.5 - 3.25)/2 + 3.25 = 3.875

y coordinate of midpoint = (-2.75 - (-4.25))/2 + (-4.25) = -3.5

So we can write the coordinates of themidpoint as:

(3.875, -3.5) or in mixed number form as: (3 7/8, -3 1/2)

Let's denote by x = the number of events.

and let's denote by y = the dollars raised.

Because the dollars raised to depend on the number of events, we can say that the dependent variable is y, and the independent variable is x. Now, we have the following data:

first event: 1, and the dollars raised is 230. That is, our first point is:

second event: 2, and the dollars raised is 230 + 30. That is, our second point is

Now, let's calculate the slope of the graph:

that is equivalent to say:

The equation for a line is y = mx + b. Now, let's calculate b

y = mx + b

so

b = y- mx

but m = 15, so the previous equation is equivalent:

b = y - 15x

if we choose the point (x,y) =(1,230) and we replace it in the previous equation we have:

b = 230- 15(1) = 230 - 15 = 215.

So, our equation of the line is :

y = 15x + 215

if x = 10 events we have :

y = 15(10) + 215 = 365 dollars

then, to the question: how much money will be raised after 10 events?, the answer is 365 dollars.

To find:

The graph of quadrilateral ABCD and its translation.

Solution:

Plot the points A(−4,1) B(−3,3) C(0,1) D(−2, 0) on the graph and join the points.

The translation is (x,y)→(x+4, y−2). So, the image after translation is given below:

We have to the ratio between the dried fruit and the sunflower seeds.

We know that the recipe requires 1/2 cup of dried fruit, and 1/8 of sunflower seeds. The ratio would be

If we triple the recipe, the ratio won't change, because ratios are constant, that way no matter if you do ten times more of the recipe, the result will be the same, because the ratios is the same too.

Take into account that the scores are three even consecutive numbers. Being x a missing value we can write:

2x, 2(x+1), 2(x+2), 2(x+3)

where each of the previous expressions corresponds to the score of Velasquez, Migule, Juan and Pablo respectivelly.

Now, due to the sum of all scores are 36 point, we can write:

2x + 2(x+1) + 2(x+2) + 2(x+3) = 36

By applying distribution property left side and by ordering like terms we get:

2x + 2x + 2x + 2x + 2 + 4 + 6 = 36

8x + 12 = 36

Now, by subtracting 12 both sides, simplifying and dividing by 8 we obtain:

8x = 36 - 12

8x = 24

x = 24/8

x = 3

Then, we can replace the previous value into the expression which represents Juan score:

2(x + 2) = 2(3 + 2) = 2(5) = 10

Hence, Juan scored 10 points (option D)

Given the following question:

It tells us that these pizzas are the same size

We are trying to find out which one of these pizza's have the greatest number of equal pieces.

For first pizza

It's cut up in four different pieces and these four pieces are equal

For the second pizza it is cut up in three different pieces and these three pieces are equal.

For the third pizza it is cut up in two pieces, these pieces are indeed equal.

Again the question is asking us which one has the GREATEST NUMBER of equal pieces

4, 3, 2

4 > 3

4 > 2

= 4

Your answer is the first pizza.

4(x + 2)(x + 9)

4x² + 44x +72​

a = 4, b = 44, c = 72

a(c) = 4(72) = 288

The factors of 288 whose sum gives 44 are 36 and 8

4x² + 36x + 8x +72​

4x(x + 9) + 8(x + 9)

(4x + 8)(x + 9)

To factorise completely, 4 is common to the first parenthesis:

(4x + 8) = 4(x + 2)

The factorisation of 4x² + 44x +72​:

4(x + 2)(x + 9)

moved from (1, - 3) to (-2, -1)

x'= x -3

y=

Explanation

A simple event is one that can only happen in one way - in other words, it has a single outcome.

A compound event is more complex than a simple event, as it involves the probability of more than one outcome.

Getting a spade card is a simple event

Also, Getting a numbered card is a simple event

Getting an ace

24 days

1) Consider that Bob reads at a regular pace. So, we can write out a pair of ratios. Note that if Bob reads half of a 200 pages book so he does 100 pages in 4 days

2) So writing out a pair of ratios we have:

Now, we can cross multiply them:

The only valid pair is B.

To determine this we need to remember that the input is the value of x and the output is the value of y.

For the input 4, that is x=4, the graph passes through the output is 5, that is y=5. This means that the graph passes through the point (4,5).

We want to know the measure of the angle ADB on the circle D.

For doing so, we remember that:

• The measure of an inscribed angle is ,half ,of the measure of the arcs it intercepts.

• The measure of an arc is ,equal ,to the measure of the central angle it generates (whose vertex is the center of the circle).

In the graph, we see that the angle ACB is inscribed, and thus, the measure of the arc AB is given by:

But, the arc AB is equal to the central angle it generates, this is:

This means that the measure of ∠ADB is 114°.

Definiendo como x al número desconocido.

la suma de ocho y un numero: 8 + x

cuatro multiplicado por la suma de ocho y un numero: 4(8 + x)

la suma de nueve y el numero: 9 +x

la suma de estas dos cantidades es igual a: 4(8 + x) + (9 + x)

Explanation:

0.001×4:

Explanation

Step 1

add 14 in both sides,

Step 2

divide both sides by -2

I Hope this helps you

Down Payment = 3900

Loan Amount - 15,300 - 3900 = $11,400

Total Paid on Loan = $252.34 (monthly) for 4 years (4 x 12 = 48 months).

So, he paid

So, total amount Tony paid for the car is "downpayment (3900) + loan amount with interest (12,112.32)".

So,

Answer: $16,012.32

The interest is the excess amount on the loan.

Loan amount = $11,400

Loan + Interest amount = $12,112.32

Thus, the interest amount is 12,112.32 - 11,400 = $712.32

Answer: $712.32

Surface Area of a Sphere

For a sphere of radius r, the surface area can be calculated as:

A frog's egg has a diameter of d = 1.2 mm. The radius is half the diameter, thus:

r = 1.2 mm/2 = 0.6 mm

Calculating the surface area:

Choice D

We can write the quotient as:

We can use the fact that:

to transform the quotient into a multiplication.

If b=1/3, then 1/b=3/1.

Then the expression becomes:

The fraction 5/2 can be expressed as mixed number as:

Answer: the result is 2 1/2 or 2.5.

The quotient becomes the multiplication 5/6 * 3.

[Option A]

Answer:

  D.  All real numbers are either rational or irrational.

Step-by-step explanation:

You want to know the true statement about the sets of rational, irrational, integer, and whole numbers.

A rational number is one that can be written as the ratio of two integers. All integers and whole numbers are rational, but not all rational numbers are integers.

  3 = 3/1 . . . . an integer that is written as a rational number

  1/2 . . . . . . . a rational number that is not an integer

An irrational number is a number that cannot be written as a ratio of two integers. √2 is an example of an irrational number. Its decimal representation has a fractional part that is never-ending and never-repeating.

The decimal part of any real number either terminates, repeats, or neither. If the number terminates or repeats, it is a rational number. If it doesn't, then it is an irrational number.

  D.  All real numbers are either rational or irrational.

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Answer:

Explanation:

Based on the given figure, the two angles ( 54° and x) are supplementary.

So, they add up to 180°.

54 + x =180

We subtract 54 from 180 to get the value of x:

x=180-54

Calculate

x= 126°

Therefore, the value of x is 126°.

From the given diagram, notice that DE is congruent to AB, EC is congruent to BC and the angles ABC and DEC are congruent.

Since two sides of the triangles and the included angle are congruent, we know from the SAS congruence theorem that ABC and DEC are congruent.

Therefore, the answer is: yes, the triangles ABC and DEF are congruent due to the SAS theorem.

Answer:

13.3

Explanation:

To calculate the mean number of movies, use the formula below:

Substituting the data gives:

The mean number of movies that the students saw is 13.3 (correct to the nearest tenth).

Answer:

Assuming the scale of the graph is 1, the range would be just -1

Step-by-step explanation:

The graph is just a single horizontal line, so the range (what y can be) will always be that one constant. It appears that the scale of the graph is by 1s, so the Range would be -1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Step 02:

We must apply algebraic properties.

x = 168 / 14

x = 12

The answer is:

x = 12

Using the distance(d) formula to obtain the length AB,BC,CA.

The distance formula is,

Given

Therefore,

Therefore,

Using Heron's formula to solve for the area

where,

Therefore, the area is

blank A: a^2 + b^2 = c^2

blank B: Definition of unit circle

blank C: sin θ = y/1 = y

Explanation:

In order to prove the identity given, we first start with Pythagoras's theorem

which is blank a.

Next, we apply the theorem to the circle to get

then we make the substitutions.

Since it is a unit circle r = 1 (blank B) and using trigonometry gives

and

which is blank C.

With the value of x, y and r in hand, we now have

Hence, the identity is proved.

Explanation

Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;

Therefore, we can say

We will substitute the above in equation 2

Since the width must be shorter than the length therefore the width will be 5 inches.

Hence;

Answers:

The dimensions are:

Length = 7 inches

Width = 5 inches

By using the distribution property in the following algebraic expressions, you obtain:

6) -4(e + 6) = (-4)(e) + (-4)(6) = -4e - 24

7) (b + 3)(-7) = (b)(-7) + (3)(-7) = -7b - 21

8) (2n + 3)6 = (2n)(6) + (3)(6) = 12n + 18

9) 5(c + d) = (5)(c) + (5)(d) = 5c + 5d

10) 27(3x - 1) = (27)(3x) + (27)(-1) = 81x - 27

11) (e - f)(3) = (e)(3) + (-f)(3) = 3e - 3f

where you have taken into account, that each term inside a parenthesis must be multiplied by all terms of the other facto. Furthermore, you took into account the signs multiplcation rule (+ x + = +, - x - = +, - x + = -, + x - = -), and also you mulitiplied coefficients by coefficients for cases in which you have numbers and variables.

Explanation

Step 1

set the equations:

we have three rectangles triangles,so

Let

triangle STR and triangle RTQ

so,

a) for triangle STR

let

so, we can use the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)

so

b) for triangle RTQ

again, let's use the P.T.

c)

we know the triangles STR and SQR are similar, so

also,

finally, we can set a new equation with triangle SQR

d)again, let's use the P.T.

Step 2

solve the equations

solution:

a)

b) now using equation (4) and equation(5) we can set system of 2 equations and 2 unknown values, so

so

RQ=20

now, replace in equation (5) to find RS

RS=15

finally, replace RS in equation (1) to find x

therefore, the answer is

I hope this helps yuo

The area of a parallelogram can be determined by multiplying its height by its base following the formula:

If you know the area and the height of the parallelogram you can determine the length of the base. To do so, you have to divide the area by the height:

We know that the area of the window is A=31ft² and the height is h=33ft, you can calculate the length of the base as follows: