The perimeter of the rectangle is 42 inches. Find the value of x.

Answer/Step-by-step explanation:

Length of AC:

Given that AB = x + 2, and BC = 7x - 3, therefore,

\( (x + 2) + (7x - 3) = AC \) (segment addition postulate)

Simply the expression for the length of segment AC

\( x + 2 + 7x - 3 = AC \)

Collect like terms

\( x + 7x + 2 - 3 = AC \)

\( 8x - 1 = AC \)

Length of QR:

Given that PQ = 8y + 5, and PR = 13y + 25, therefore,

QR = (13y + 25) - (8y + 5) (PQ + QR = PR)

Simplify the expression to for the length of segment QR

QR = 13y + 25 - 8y - 5

Collect like terms

QR = 13y - 8y + 25 - 5

QR = 5y + 20

Answer:

A) y = -5/2x - 2

Step-by-step explanation:

y = slope + y-intercept

The slope is negative and the y-int is -2, thus the first option.

Answer:

96,000 people

Step-by-step explanation:

convert the length from miles to feet.

2.5 miles = 13,200 feet

Area = 13,200× 8

Area = 105,600 square feet

but the fans will be on both sides of the sidewalk,hence,

the area will be twice.

105,600 square feet ×2= 211,200 square feet.

1 fan = 2.2 square feet

x = 211,200 square feet

therefore number of fans will be = 96,000 people.

The total number of groups in the study of one way ANOVA with the given condition of variable and levels is four different groups and number of different factors in one-way ANOVA is equal to one.

In a one-way ANOVA with one independent variable with four levels, there are four different groups in the study.

Each group represents a level of the independent variable.

There is only one factor in a one-way ANOVA.

The factor is the independent variable with the four levels, which is used to classify the groups in the study.

The factor is what the researcher is interested in studying.

And the ANOVA is used to determine if there are any statistically significant differences in the mean scores between the groups.

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Answer:

C) \(m =\frac{-8}{5}\)

The slope of the perpendicular line \(m =\frac{-8}{5}\)

Step-by-step explanation:

Explanation:-

Given that the slope of the given line is

    \(m =\frac{5}{8}\)

The slope of the perpendicular line

 = \(\frac{-1}{m}\)

The slope of the perpendicular line

 = \(\frac{-1}{\frac{5}{8} }\)

Final answer

The slope of the perpendicular line

                                          \(m =\frac{-8}{5}\)

The y-intercept of a line is the point where the line crosses the y-axis. In other words, it is the point at which the line has an x-coordinate of 0.

To find the y-intercept of the line y = –10x + 1/9, we can set x = 0 in the equation and solve for y:

y = –10x + 1/9

= –10*0 + 1/9

= 1/9

Therefore, the y-intercept of the line is 1/9.

The probability of event F, P(F), is 2/3. This means that given event E has occurred, there is a 2/3 chance of event F occurring.

To calculate the probability of event F, we can use conditional probability.

Conditional probability measures the likelihood of an event occurring given that another event has already occurred.

In this case, we are given the probabilities of events E and F, as well as the probability of their intersection.

The formula for conditional probability is P(F | E) = P(E ∩ F) / P(E), where P(F | E) represents the probability of event F given event E, P(E ∩ F) represents the probability of events E and F occurring together, and P(E) represents the probability of event E.

Using the given values, we have P(E ∩ F) = 1/6 and P(E) = 1/4. Substituting these values into the formula, we get P(F | E) = (1/6) / (1/4) = (1/6) * (4/1) = 4/6 = 2/3.

Hence, the probability of event F, P(F), is 2/3. This means that given event E has occurred, there is a 2/3 chance of event F occurring.

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Exact Area = pi square units

Approximate Area = 3.14 square units

=========================================

Work Shown:

The full circle area is pi*r^2 = pi*2^2 = 4pi

This quarter circle has area (4pi)/4 = pi  square units

This is approximately equal to pi = 3.14

Answer:15

Step-by-step explanation:

Answer:

2y = 10 is an equation

An equation is a statement that shows that the values of two mathematical expressions are equal (indicated by the sign =)

Answer:

Hope it help you

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Explanation

NOTE - ANSWER IN PHOTO

Answer:

  (3.75, 3.5)

Step-by-step explanation:

The weighting factors for the weighted average of the end points are the reverse of the length ratios.

For a 1 : 3 split, the first point is weighted by a factor of 3; the second point is weighted by a factor of 1. The weighted sum is divided by the total of the weights.

  (3(3, 2) +1(6, 8))/(3+1) = (9+6, 6+8)/4 = (3.75, 3.5)

Answer:

\(\fbox{\begin{minipage}{9em}Option d is correct\end{minipage}}\)

Step-by-step explanation:

Given:

Point A(3, 2)

Point B(6, 8)

Point C lies on segment line AB and divides AB into a ratio of 1 : 3

Solve for:

Coordinate of C

Solution:

Denote the coordinate of origin O(0, 0)

Point A(3, 2) => Vector OA(3 - 0, 2 - 0) or OA(3, 2)

Point B(6, 8) => Vector OB(6 - 0, 8 - 0) or OB(6, 8)

=> Vector AB = Vector OB - Vector OA = (6 - 3, 8 - 2) or vector AB(3, 6)

Point C lies on segment line AB and divides AB into a ratio of 1 : 3

=> Vector AC = (1/3) Vector CB, or

    AC/CB = 1/3

=> AC/(AC + CB) = 1/(1 + 3)

=> AC/AB = 1/4

=> AC = AB/4

=>  Vector AC = (1/4) Vector AB  = ((1/4)*3, (1/4)*6) = (0.75, 1.5)

=> Vector OC = Vector OA + Vector AC = (3 + 0.75, 2 + 1.5) = (3.75, 3.5)

=> C(3.75, 3.5)

Option d is correct!

Answer:

correct

Step-by-step explanation:

The perimeter is the sum of the sides.

Rectangle ( opposite sides are congruent ), thus

perimeter = 2x + 2(x + 18) = 2x + 2x + 36 = 4x + 36

Square ( sides are congruent ), thus

perimeter = 4(x + 9) = 4x + 36

The perimeters are the same, so the student is correct

There are a total of 2,184 different ways a person can order one ice cream cone with three different flavors if there are 14 flavors to choose from, and the order of stacking matters.

To calculate the number of ways to order the ice cream cone, we need to consider the choices for each position: the top, middle, and bottom.

For the top flavor, there are 14 options available since there are 14 flavors to choose from. After selecting the top flavor, there are 13 remaining flavors to choose from for the middle position. Finally, for the bottom flavor, there are 12 remaining choices.

To find the total number of ways, we multiply the number of choices for each position: 14 choices for the top flavor, 13 choices for the middle flavor, and 12 choices for the bottom flavor. Therefore, the total number of ways to order the ice cream cone is 14 x 13 x 12 = 2,184.

In conclusion, there are 2,184 possible ways to order one ice cream cone with three different flavors if there are 14 flavors to choose from, and the order of stacking matters.

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Answer:

134.375

Step-by-step explanation:

43 is 32% of what number

32% = 0.32

43/0.32 = 134.375

All the inequalities that represent the situation are as follows;

A. 0.5x + 0.25y ≤ 20.

C. 2x + 3y ≤ 120.

A combinations of necklaces and key chains you can make given the situation include the following:

A. 30 necklaces and 20 key chains.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of necklaces and number of key chains respectively, and then translate the word problem into algebraic equation as follows:

Based on the table of values (see attachment) and given x ≥ 0 and y ≥ 0, a system of linear inequalities to describe this situation include the following:

0.5x + 0.25y ≤ 20.

2x + 3y ≤ 120.

Next, we would use an online graphing calculator to plot the above system of linear inequalities in order to determine its solution as shown in the graph attached below.

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Slack represents the buffer or flexibility available in the project schedule, allowing for adjustments and potential delays without affecting the project's critical path.

In project network analysis, slack refers to the difference between the latest start and earliest start times of an activity. It represents the amount of time that an activity can be delayed without affecting the overall project duration.

The latest start time (LS) is the latest point in time an activity can start without delaying the project completion. It is determined by considering the dependencies and constraints of the project schedule. The earliest start time (ES) is the earliest possible point in time an activity can start based on its dependencies and the project schedule.

By subtracting the earliest start time from the latest start time, we calculate the slack or float of an activity. If an activity has positive slack, it means there is flexibility in its start time, and it can be delayed without impacting the project's critical path or completion date. On the other hand, if the slack is zero or negative, it indicates that any delay in the activity will affect the project's overall duration, making it critical.

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ANSWER

EXPLANATION

Given that;

Let U(x) = 2x and V(x) = x^2 + 1

Apply the quotient rule to find the derivative of f(x)

Differentiate U and V with respect to x

Hence, we have

Answer:

The true statements are

3/5 is the base

3 is the exponent

(3/5)³ = 3/5 × 3/5 × 3/5

(3/5)³ = 27/125

Step-by-step explanation:

Let a and b be any integer, given the expression;

\(a^b\)

a is the base

b is the exponent

Similarly if we have;

\(a^3\)

This means we can multiply a in three places as shown;

\(a^3 = a \times a \times a\)

Applying this to the given expression

\((\frac{3}{5} )^3 = \frac{3}{5} \times \frac{3}{5} \times \frac{3}{5} \\Also\\(\frac{3}{5} )^3 = \frac{3 \times 3 \times 3}{5 \times 5 \times 5} \\(\frac{3}{5} )^3 = \frac{27}{125}\)

The base value will be 3/5 and the exponent is 3

Answer:

a) 1/2 x - 3/2

Step-by-step explanation:

y = 2x +3

y-3 = 2x

x = (y - 3 )/2

x= 1/2 - 3/2

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

12 2/8

Step-by-step explanation:

split 11 5/8 into 11 and 5/8

add 3/8 and 5/8 to make 1

add 11 to make 12

then and the 2/8

the complete answer is 12 and 2/8

Your answer is 12.25.

\(11\frac{5}{8} +\frac{3}{8} =12\\12+\frac{2}{8} =12.25\)

Answer:

a) y=|(1\2)x-2| + 4

b)y=|(1/2)x-2|+2

c)y=|(1/2)x-1|+3

d)y=|(1/2)x-3|+3

Step-by-step explanation:

Translating up and down is done outside of the absolute value and is intuitive in that up is added to the original value and down is negative.  Left and right is shown within the absolute value and is the opposite of what you would think it to be in that left is added and right is subtracted.

Answer:

therefore = 8: 20 a.m

Step-by-step explanation:

The time will they back at the bus depot together is shown below:

The factors of 20 minutes and 35 minutes are 5, 4 and 5, 7

So here the LCM is 5

Now

= 5 ×  4 × 7

= 140 mins later

As the bus took off at 6 am

So,  

Hours       Mins

6               0

+ 2            20    (140 mins = 2 hrs 20 mins)

= 8            20      

therefore = 8: 20 a.m

Answer:

3(2x + 1)(3x - 5)

Step-by-step explanation:

Given

18x² - 21x - 15 ← factor out 3 from each term

= 3(6x² - 7x - 5 ) ← factor the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 5 = - 30 and sum = - 7

The factors are + 3 and - 10

Use these factors to split the x- term

6x² + 3x - 10x - 5 ( factor the first/second and third/fourth terms )

3x(2x + 1) - 5(2x + 1) ← factor out (2x + 1) from each term

(2x + 1)(3x - 5)

Then

18x² - 21x - 15 = 3(2x + 1)(3x - 5)

Answer:

A

Step-by-step explanation:

u = -v, which means they are parallel but in opposite directions. Therefore, the given vectors are neither orthogonal nor parallel.

To find U.V, we use the dot product formula:

U.V= (-8)(8)+(4)(4)+(-6)(-1)= 64+16+6=86

Since the dot product of u and v is not zero, i.e. U.V = 86, the vectors are not orthogonal.

To determine if the vectors are parallel, we can compare their direction or compute the angle between them. One way to check if they are parallel is to divide one vector by the other and see if they are scalar multiples of each other.

If u and v are parallel, then there exists some scalar k such that u = kv or v = ku.

Let's take u = (-8, 4, -6) and v = (8, 4, -1)

We can see that u = -v, which means they are parallel but in opposite directions. Therefore, the given vectors are neither orthogonal nor parallel.

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Answer:

36. \(\frac{a^{7} }{b^{8} }\)  | 37. 1 ( anything raise to 0 equal 1 ) | 38. \(g^{4}\)

Step-by-step explanation: Just flip the exponent degree to negative when you move it down and positive when you move it up. You will be able to solve the rest. :)