please help me with questions 1 and 2 (with explanations and calculation) thank you so much

The completed statement are:

Part A:

Angle UZT is congruent to angle TZY.

Using the image attached figure, we can see that:

∠UZT = 54°

∠TZY = 54°

Hence one can say that ∠TZY = ∠UZT are both congruent angles.

Part B:

Angle VZW is congruent to angle YZX.

Using the image attached attached, we can see that:

∠VZW = 71°

∠YZX = 71°

Hence, ∠YZX = ∠VZW are both  regarded as congruent angles .

Therefore, The completed statement are:

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Answer: a, c

Step-by-step explanation:

Based on the fact that the road sign's distance to Beaston is rounded to the nearest unit, the actual range of possible miles to Beaston is 9.50 ≤ x ≤ 10.49.

Based on the fact that the miles to Beaston are rounded to the nearest mile, the first thing to do is to find the lowest and highest numbers that can be rounded to 10 miles.

The lowest number that you can round to 10 miles is:

= 9.5 miles

Because of the 0.5 attached to the 9 miles, you will round up to 10 instead of down to 9.

The highest number that you can round to 10 miles at two decimal places is 10.49 miles.

The reason this is the highest is that the 0.4 is the tenths number just before 0.5. This means that you round the whole number down to 10.

Assuming the distance to Beaston is x, the interval would then be:

9.50 ≤ x ≤ 10.49.

In conclusion, the range of miles of Beaston is  9.50 ≤ x ≤ 10.49.

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The graph for the given system of equations is shown below

From the question, we are to determine the graph that describes the given system equations

First, we will graph the given system of linear equations.

The given equations are

Y equals four over X +3

and

Y equals negative 2X subtract four

That is,

y = 4/(x+3)

y = -2x -4

The graph for the given system of equations is shown below

The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below

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Step-by-step explanation:

we have

B = J + 2

as the number of laps Bill ran.

to get the number of laps Jill ran we need to transform this equation, so that we get

J = ...

or

... = J

J has to be on one side, and the rest on the other (just as it is with B = ...).

so,

B = J + 2

B - 2 = J

or

J = B - 2

hey ! we are finished already !

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes

The volume of the composite cylinder is expressed as shown below;

V = πr²h

where

r is the radius

h is the height

According to the given diagram;

V = Vl - Vs

V = π(10)²*15 -  π(5)²*15

V = 1500π - 375π

V = 1125π cubic inches

If the value of π is 3.14, hence;

V = 1125(3.14) cubic inches

V = 3532.5 cubic inches

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

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The missing number in the given series is 24.

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.

Given the series,

4, ?, 144, 864, 5184, 31104

Multiplying with 6 in each term in the given sequence.

4×6 = 24

24×6 = 144

144×6 = 864

864×6 = 5184

5184×6 = 31104

Following the above sequence, we get the 2nd term is 24.

Hence the missing number is 24.

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Answer: A

Step-by-step explanation:

[tex]WX=\sqrt{(-1-3)^2 +(1-4)^2}=5[/tex]

Since WXYZ must be a square, all the sides must have a length of 5.

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

Explanation:

Replace x with 4 and y with 5.

Then use the order of operations (PEMDAS) to simplify until you get a single number.

Something like 9x means "9 times x", and a similar situation happens with the 8y term as well.

---------

Here's what the steps look like:

9x + 8y

9*4 + 8*5

36 + 40

76

Therefore, 9x+8y = 76 when x = 4 and y = 5.

The point (4,5) is located on the line 9x+8y = 76

Isolate y

Compare to slope intercept form y=mx+b

Slope=m=5/3

Answer:

[tex]\dfrac{5}{3}[/tex]

Step-by-step explanation:

To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:

Given relation:

[tex]3y-5x=10[/tex]

Add 5x to both sides:

[tex]\implies 3y-5x+5x=10+5x[/tex]

[tex]\implies 3y=5x+10[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]

[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]

Slope-intercept form of a linear equation

[tex]y = mx+b[/tex]

where:

Comparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.

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Answer:

x= 5/2

Step-by-step explanation:

Answer:

-4 =x

Step-by-step explanation:

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The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).

We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.

Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.

We are also given that EC (a part of diagonal AC) is 8 units long.

As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).

Now, we are told that DB (a part of diagonal BD) is x - 1 units long.

To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is

(x - 1) units + (x - 1) units = 2x - 2 units.

The area of a rhombus is given by the formula:

Area = 1/2 × Product of Diagonals.

Substituting the given values, we have:

72 = 1/2 × 16 × (2x - 2).

Now, we can simplify the equation:

72 = 8x - 8.

Move the constant term to the right side:

8x = 72 + 8.

Combine the constants:

8x = 80.

Finally, solve for x by dividing both sides by 8:

x = 80 / 8 = 10.

So, the value of x is 10 units. The correct answer is B).

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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9

10

14

16 "--

    Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.

The choice of buying the item affected your choices available on your trip.  

Answer:

dependent events

Step-by-step explanation:

Answer:

blank = inheritance

Step-by-step explanation:

Hope that helps

The price x which will maximize the company's revenue is 904

The price x which will maximize the company's revenue is 240

Let

Price of the good = x

Number of goods sold = 2712- 3x

The formula for revenue is given as;

Revenue = Price × Quantity

= x( 2712 - 3x)

Expand the bracket

2712x - 3x^2

Therefore, the price x which will maximize the company's revenue will be:

2712x - 3x^2 =0

Collect like terms

3x² = 2712x

3x =  2712

Divide both side by 3

3x/3 = 2712/3

x = 904

Hence, the price x which will maximize the company's revenue is 904

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The length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft

Area of square = Length ²

Area of square = Length ²

24 = length ²

√24 = √length²

√24 = length

length = 4.898979485566356196394568149411782783

Approximately,

length = 4.9 ft

In radical form

length = √24

= 2√6

Therefore, the length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft

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The value of A such that cos A = 0.7715 is 39.5 degrees

The equation is given as:

cos A = 0.7715

Where the angle is in degrees

There are several ways to solve this equation, some of which include:

In this case, we make use of the first option; using a scientific calculator

Recall that the equation is represented as:

cos A = 0.7715

Next, we take the arccos (or anti cosine) of the above equation.

This is represented as

arccos(cos A) = arccos(0.7715)

Evaluate the expression on the left-hand side

A = arccos(0.7715)

Evaluate the expression on the left-hand side using the scientific calculator

A = 39.5112207183

Approximate the above expression

A = 39.5

Hence, the value of A such that cos A = 0.7715 is 39.5 degrees

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Answer:

  (a)  h^-1(x) = (x+6)/6

Step-by-step explanation:

The inverse relation can be found by solving for y: x = h(y).

  x = h(y) . . . . . the inverse relation

  x = 6y -6 . . . . . use the function definition

  x +6 = 6y . . . . add 6

  (x +6)/6 = y . . . . divide by 6

The inverse function is ...

  [tex]\boxed{h^{-1}(x)=\dfrac{x+6}{6}}[/tex]

Using the permutation formula, the number of different options for the top three finishers is given as follows:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

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Slope-Intercept Form: y = mx + b

---Where m is the slope and b is the y-intercept

Correct Answer: y = -5/4x + 2

---Option A

Hope this helps!

Answer:

We multiply by 2 and add 4

Step-by-step explanation:

To find the pattern,  we find the slope

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

m = ( 10-6)/(3-1)

m = 4/2

m =2

We are multiplying by 2

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Using the point (1,6)

6 = 2(1)+b

6 = 2+b

The y intercept is 4

y = 2x+4

We multiply by 2 and add 4

The solutions using the relevant theorems are:

13. x = −3 or x = 4

14. x = 12

15. x = 12

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6

The midsegment of a triangle that joins two sides of a triangle divides the two sides proportionally based on the triangle midsegment theorem.

The angle bisector of a triangle, according to the angle bisector theorem divides the opposite angles sides in a proportional manner.

The theorem states that when three or more lines that are parallel is cut across by two transversals, they are divided by the transversal proportionally.

13. Apply the angle bisector theorem:

x/3 = (x + 4)/(x + 2)

Cross multiply

x(x + 2) = 3(x + 4)

x² + 2x = 3x + 12

x² + 2x - 3x - 12 = 0

x² - x - 12 = 0

Factorize

x = −3 or x = 4

14. Apply the angle bisector theorem:

16/x = 12/9

x(12) = (16)(9)

12x = 144

x = 12

15. Apply the angle bisector theorem:

(x - 4)/6 = x/9

9(x - 4) = 6x

9x - 36 = 6x

9x - 6x = 36

3x = 36

x = 12

16. Apply the triangle midsegment theorem:

3x/(x + 4) = (x - 1)/(x - 2)

Cross multiply

3x/(x + 4) = (x - 1)/(x - 2)

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² + 3x - 4 - 3x² + 6x = 0

-2x² + 9x - 4 = 0

Factorize

x = 1/2 or x = 4

17. Apply the Parallel Lines and Proportionality Theorem:

(x + 3)/(2x + 2) = (2x + 2)/(4x - 2)

Cross multiply

4x² + 10x - 6 = 4x² + 8x + 4

4x² + 10x - 6 - 4x² - 8x - 4 = 0

2x - 10 = 0

2x = 10

x = 5

18. Apply the angle bisector theorem:

(2x + 3)/x = (x + 4)/(x - 2)

Cross multiply

(2x + 3)(x - 2) = x(x + 4)

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize

x = −1 or x = 6

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Answer:

a(1) = 2

a(n) = a(n-1)+4

Step-by-step explanation:

Using the given arithmetic sequence,

a1 is 2

a2 is 6

a3 is 10

a4 is 14

a5 is 18

and to get from a1 to a2 you have to +4, to get from a2 to a3 you have to +4 and so on.

In a reclusive formula you need to find two pieces of information:

1. The first term of the sequence

2. The pattern rule to get any term from the term that comes before it

Using the given sequence, the first term is 2 and the rule to get any term from its previous term is +4.

So, putting that information in the form of a recursive formula will read as the following:

an+1 = an+4

a1 = 2, n is greater or equal to 1 (n is an interger)

Which can be rearranged to

a(1) = 2

a(n) = a(n-1)+4

If we suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. Her next step would be administering the treatment again.

Reason Behind the Next Step of the Study

It is given the the researcher conducts an A-B-A-B study.

Her first step was recording the baseline observations.

Hence, first A indicates the first step here that is, recording the observations

In the next step of the study, she administers a treatment.

Thus, B denotes the administering treatment step.

Again, for the third step of the study, she again records behavior during the treatment.

This is again denoted by A.

Hence, we can conclude that in the A-B-A-B study, A denotes recording observation or behavior, B denotes administering a treatment.

Now, since, A, B, and A steps of the study have already been followed, the next phase is B which is concerned with reintroducing or re-administering the treatment.

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Answer:

The first choice.  

Step-by-step explanation:

The second choice is a translation and the third choice is a reflection.

Answer:

Step-by-step explanation:

1. yes

2. 0.048955

3. equal, not equal, less than and equal to, less than, greater than and equal to, greater than

4. 9 51/250

5. 387.5%

Answer:

not linear since all first differences are not equal

Step-by-step explanation:

To find the first differences, subtract each y value from the next y value.

Use only y values.

here are the 4 first differences you need to calculate.

1 - 0 = 1

4 - 1 = 3

9 - 4 = 5

16 - 9 = 7

Now you place them in the appropriate column in the table.

x   y      first difference

0   0       1

1   1         3

2   4       5

3   9       7

4   16

If the first differences were all equal, the function would be a linear function.

In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.

Answer:

N = 2.1

M = 4.5

Step-by-step explanation:

<p is 25 degrees.  I know this because the exterior angle of p corresponds with 155.  Since this is a straight angle, angle p must be 25 (180-155).  Now I can use the cos and the sin of 25 to find M and N

sin 25 = N/5  multiply both sides by 5 to get

5 sin 25 = N  Use your calculator put in 5 sin 25

2.1 rounded to the nearest tenth.

cos 25 = M/5  Multiply both sides by

5 cos 25 = M Use your calculator

4.5