John owes $25.20 to his mom. He borrowed $27.60 from his dad. Howmuch does he owe in all? Write your answer as a rational number *

We are given a mid-point for segments AD and BC, we have the following:

segments AE and DE are congruent, that is:

By definition of mid-point.

Segments BE and CE are congruent, that is:

By definition of mid-point.

We also have that angles AEB and DEC are congruent, that is:

By the vertical angles theorem, which states that when two lines intercept their vertical or opposite angles are equal or congruent.

Now we can conclude that triangles AEB and DEC are congruent, that is:

Due to the Side-Angle-Side Theorem, which states that when two triangles have two congruent sides and the angle between the congruent sides also congruent, then the triangles are congruent.

In a parallelogram, the opposite sides are parallel.

This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:

Now, we need to find x.

Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.

The x distance from O to R is

The x distance from T to S is

Since these x distances are equal, then:

Then, the coordinates of S are:

Which corresponds to option B.

Triangles' resemblance is reflected by their congruence. If the matching sides and angles of two triangles match, the triangles are said to be congruent.

For triangles, there are five primary congruency rules: Side-Side-Side is an SSS criterion. The side-angle-side SAS criterion. Angle, Side, Angle is an ASA criterion. Angle-Angle-Side is an AAS criterion.

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

An isosceles triangle in geometry is one with at least two equal-length sides. It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter version adding the equilateral triangle as one of the possible configurations.

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We have the following:

We know that 100% is the value of the purchase of $ 75, therefore, if we add 5%, it would be 105%, that is equal to 1.05, so we multiply the value of 75 by 1.05, and we are left with the following

Total value is $78.75 and taxes are 3.75

If we spin the spinner once, we can get two possible outcomes (red or blue).

If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.

Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.

Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.

Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is

There are 768 possible outcomes in the sample space.

SOLUTION

Let us use a diagram to illustrate the information, we have

Now, from the diagram, let the length of the uniform strip of floor around the rug be x, So, this means the length and width of the rug is

Now, since she can afford to buy a rug of 264 square feet for carpeting, this means that the area of the rug is 264, hence we have that

Solving for x, we have

Dividing through by 4 we have

So from our calculation, we go for x = 3, because 20 is large look at this

length cannot be negative, so we go for x = 3.

Hence the dimensions of the rug becomes

So the dimension of the rug should be 22 x 12 feet

To find:

We need to find two points on the linear equation y-1=0 and to plot those points on graph.

Step by step solution:

We know that:

General coordinate of any two points on line y = 1:

= (x, 1)

So let us assume any two random points on the line:

= (1,1) and (2,1)

We will now mark them on the graph:

We have to identify the intervals where the function is concave upwards and where is concave downward.

We can differentiate them in a graph as:

We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.

Then, we can write all the intervals as:

The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.

From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.

It should be noted that the requirements is 250kcal per kilograms.

Therefore, the calories will be:

= Weight × Required calories

= 250 × 25

= 6250 kcaloriies

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To get x, we will use the equation below:

open the inner paremthesis

open the parenthesis

180 - x = 94

collect like term

180 - 94 = x

86 = x

The given ratio is 9/5

This ratio is already in the simplified form. To find equivalent ratios, we would multiply the numerator and denominator by constant numbers. We have

If we multiply by 2, it becomes

9 * 2/5 * 2 = 18/10

If we multiply by 3, it becomes

9 * 3/5 * 3 = 27/15

If we multiply by 4, it becomes

9 * 4/5 * 4 = 36/20

Thus, three equivalent ratios are

18/10, 27/15 and 36/20

Recall than a direct variation implies the following type of relationship between y and x:

y = k * x

where k is a constant value

Then you have (by dividing by x, the following:

y / x = k (the constant)

then, we are told that when y = 90 , x = 15, so we have:

90 / 15 = k

6 = k

so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?

so we write:

y = k * x

y = 6 * 4

y = 24

This is the value of y when x is 4 since the constant k is 6 as we found above.

Another example:

We need to find the variation relationship for a case that when y = 6, x = 12

We think the same way we did before, starting with the fact that a direct variation is of the form:

y = k * x

given the info that when x = 12, y = 6, we can find the constant k:

6 = k * 12

divide by 12 both sides:

6/12 = k

1/2 = k

So k is 1/2 (one half)

Then we can write the variation as:

y = (1/2) x

(the product of 1/2 times x)

the answer is associative property of multiplicaction

because

A*(B*C)=(A*B)*C

The mathematical sentences that can be found in the sentence are:

A mathematical sentence  can be described as the statement that comprises the  two expressions nor more than two expression.

It should be noted that these two expressions  can make use of the  numbers as well as the variables and in some of the cases combination of them however the  mathematical sentence do encompass the symbols  which could be inform of equals, greater than, as well as  less than.

Therefore, the options that are examples of mathematical sentences are option B C D E F.

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The mathematical sentences which can be found in the sentence are;

B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1

A mathematical sentence can be described as a statement that comprises two expressions or more than two expressions.

Expression can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Remember that these two expressions can make use of the numbers as well as the variables and in some cases a combination of them however the mathematical sentence does encompass the symbols which could be in form of equals, greater than, as well as less than.

Hence, the options that are examples of mathematical sentences are ; B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1

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From the table it can be observed that rate expense for a month is -$1,120.00. The negative value means that amount is reduced.

So rent expense is -$1,120.00, where negative sign is for decrease in amount.

Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.

Given the expression f/g

Which is a rational expression.

The domain is all real numbers of (x) except the zeros of the denominators

The zeros of the denominators can be calculated using the equation g(x)=0

So, the answer will be as follows:

The domain of f/g consists of numbers (x) for which g(x) ≠ 0 that are in the domains of both f and g

L: Length

W: Width

The perimeter of a rectangle is:

The area of a rectangle is:

A bus travels 8.4 miles east and then 14.7 miles north.

What is the angle of the bus resultant vector?

see the figure below to better understand the problem

The angle of the bus resultant vector R is equal to

tan(x)=14.7/8.4

mm

The equation is -2n - 7.3 = 16 1/2

The value of the variable n = -11.9

STEP - BY - STEP EXPLANATION

What to find?

• Write the equation of the given statement.

• The value of n.

Given:

find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?​

To solve follow the steps below:

Step 1

Translate the given statement into equation.

Let n be the number.

-2n - 7.3 = 16 1/2

Step 2

Convert 16 1/2 to decimal.

-2n - 7.3 = 16.5

Step 3

Add 7.3 to both-side of the equation.

-2n = 16.5 + 7.3

Step 4

Simplify the right-hand side of the equation.

-2n =23.8

Step 5

Divide both-side of the equation by -2.

n = -11.9

Therefore, the value of the variable n = -11.9

Given that the required linepasses through the points (15, 5)and (5, 15).

Find the slope of the line using teo-point formula.

Substitute the value of m into theslope-intercept form y = mx+c.

Plug in the point (5, 15)to find c, the y-intercept.

Thus, y = -x + 20, which is the required equation of line.

From the rectangle TUVW, the coordinates of the points are shown below:

T(-5, -5), U(-1, -5), V(-1, 4), and W(-5, 4)

If TUVW is translated 5 units right and 4 units up, the coordinates of the new rectangle are in the form (x+5, y+4):

T'(0, -1), U'(4, -1), V'(4, 8), and W'(0, 8)

To find a slope of a line we need two points, so we will do it as follows.

Therefore it is (a) the slope is 3.

Answer:

a.3

Step-by-step explanation:

To find the slope, use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 10-4)/(7-5)

   = 6/2

   = 3

From the information available, the mixture will test negative if all 6 samples are negative.

The probability of each is independent of the other for all 6 samples.

The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be

However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;

Therefore if we have the probability of the mixture testing negative as

The probability of the mixture testing positive would be;

ANSWER:

The probability that the mixture will test positive is 0.5031

Rounded to 2 decimal places,

Answer:

[tex]y-45=5(x-9)[/tex]

Step-by-step explanation:

Definition of the variables:

Given information:

As the rate of change is constant and linear, the rate of change is the slope of the line.  Therefore, the slope is 5.

At hour 9 (x-value) the company had produced 45 (y-value) goods.  Therefore, this can be represented by the point (9, 45).

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-45=5(x-9)[/tex]

Therefore, the equation that correctly represents the goods produced by the company after x hours is:

[tex]\boxed{y-45=5(x-9)}[/tex]



Let

x ------> number of switch type A

y -----> number of switch type B

so

Remember that

1 hour=60 min

32 hours=32*60=1,920 minutes

4x+5y=1,920 -------> equation 1

3x+5y=1,740 ------> equation 2

Solve the system of equations

Solve by graphing

using a graphing tool

see the attached figure

Solution is

x=180

y=240

therefore

When a=2, b=3, x=4, and y=5,

evaluate:

Let's replace b, x and y by the appropriate values:

now let's solve what is inside the parenthesis:

again more solving inside the second parenthesis:

and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:

You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.

Like:

and then evaluate:

Answer: the probability that at least two have seen a ghost or felt its presence is 0.527

Explanation:

In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as

P(x) = nCx * p^x * q^(n - x)

where

p = probability of success

q = 1 - p = probability of failure

n = sample size

x = number of successes

From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,

p = 17% = 17/100 = 0.17

q = 1 - 0.17 = 0.83

n = 10

x = 2

We want to find P(x ≥ 2)

P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)

P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552

P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178

P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473

P(x ≥ 2) = 0.527

the probability that at least two have seen a ghost or felt its presence is 0.527

Given

Eliza had $14

Emma had $64 more than Eliza

Find

how much did Emma have

Explanation

as we have given

Eliza has $14

so , Emma = $64 + $14 = $78

Final Answer

Therefore , the Emma had $78

Answer:

A(-1,4) and B(2,0)

Step-by-step explanation:

The quadratic parabola equation is represented as;

Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':

Hence, the equation for the parabola:

Now, for the line since it is a horizontal line, the equation would be:

Then, for (f+g)(x):

Then, the graph for the composite function and the points that lie on the graph:

A(-1,4) and B(2,0)