Given that segment AD is congruent to segment BC, and angle DAB is congruent to CBA; Prove: triangle ABE is isosceles

We will solve as follows:

From the information given we can deduce that the triangle is Isosceles. We also have from theorem that angles that are opposite to congruent sides are also congruent, therefore angle

Using this, and the fact that the sum o all internal angles of a triangle add to 180°, the following is true:

Now, we replace the values we know:

So, the value of angle

6 square box, each of length 3.5 inches:

Area of the original box = 6 x area of the smaller box = 6 x L x L

Area of the original box = 6 (3.5 x 3.5) = 6 (12.25) = 73.5 square inches

We have the next polynomial function

In order to find the zero we punt the function equal to zero

We have a given zero that is 1-i

x=1-i

than means that we need the conjugate of the zero given is also a zero

x=1+i

and then we need a third zero because the polynomial has third-degree it can be calculated if we factorize the polynomial given

Therefore the zeros are

x=-1

x=1-i

x=1+i

Part (A):

The value of 3/5 in the decimal form is 0.6 which is less than 1.

Thus, one of the factors of the should be less than 3/5 and other greater than 3/5.

Part (B):

For example take,

2 and 3/10.

The product of 2 and 3/10 is 3/5.

2 is greater than 3/5 and 3/10 is smaller than 3/5.

The base equation of a parabola is F(X) = X^2 + C

if we make F(X+2) it means the chart will move 2 units to the left

on the other hand, if the make F(X) + 5, it means the chart will displace 5 units upwards

As a result, from the given chart, our equation would be: y = 3(x+2)^2 + 5

The two triangles are not similar

Here, we want to check the if the given triangles are similar

From the diagrams given, we can see that the only similarity between the two is the presence of an angle 100 at the top vertex

This does not give any other proof of similarity between the two triangles

Thus, we have it that the triangles cannot be similar based on the given point

Hence, we can conclude that the two triangles are not similar

In order to calculate the distance between A and C, we can use the Pythagorean Theorem, since we have a right triangle:

So the distance between A and C is 13 meters.

From the figure given;

Observe that, side AB is congruent to EF.

Side AC is congruenct ED

side BC is congruent to FD

From the above, we can deduce that Δ ABC ≅ Δ EFD

Remember that the average or mean is the ratio between the sum of all numbers involve and the total number of items there.

In this case, the total is 28 degrees, and the total number of days is 7, we just have to divide.

The probability P of an event e can be found using the formula:

Required: The probability that the next respondent will be between 18 and 25

Number of respondents between the ages of 18 and 25 = 25

Total number of respondents :

Hence, the probability of a selecting a respondents in the age range 18 to 25 is:

Answer: 0.1256

SOLUTION

Tom wants to get to the playground at 2:30 p.m

if it take him 2

Answer:

[tex]\sqrt{122}\approx{11.05}[/tex]

Step-by-step explanation:

In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation [tex]a^2+b^2=c^2[/tex].

In the triangle on the left:

[tex]a^2+b^2=c^2[/tex]

[tex]5^2+9^2=c^2[/tex]

[tex]25+81=c^2[/tex]

[tex]106=c^2[/tex]

[tex]\sqrt{106}=c[/tex]

The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:

[tex]a^2+b^2=c^2[/tex]

[tex]4^2+(\sqrt{106})^2=c^2[/tex]

[tex]16+106=c^2[/tex]

[tex]122=c^2[/tex]

[tex]\sqrt{122}=c[/tex]

[tex]c\approx{11.05}[/tex]

Problem

The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services . can u please just do C (graph the function using six values of it's domain​

Solution

Part a

For this case a linear function is given by: y = mx+b

If we compare the function y =30 +5x we can see that we have the sam efunctional form and we can conclude that yes is a linear function with m = 5 and b =30

Part b

For this part since we have a linear function the domain is given by:

D= [0,1,2,3,4,5}

Then the domain is discrete

Part c

For this case we have the following solution:

Given:

a.) Solution A is 65% salt

b.) Solution B is 90% salt

c.) She wants to obtain 140 ounces of a mixture that is 85% salt.

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 140

y = 140 - x (Eq. 1)

0.65x + 0.90y = 0.85(140)

0.65x + 0.90y = 119

(0.65x + 0.90y = 119) x 100

65x + 90y = 11,900 (Eq. 2)

Substitute Eq. 1 to Eq. 2

65x + 90y = 11,900

65x + 90(140 - x) = 11,900

65x + 12,600 - 90x = 11,900

65x - 90x = 11,900 - 12,600

-25x = -700

-25x/-25 = -700/-25

x = 28 ounces

y = 140 - x

y = 140 - 28

y = 112 ounces

Therefore, you will be needing 28 ounces of Solution A and 112 ounces of Solution B.

Apr = 2.5% every 6 months

Use formula

N = N1 ( 1+ 2.5/100)^ 2

APY= (1 + r/2) ^2 - 1

. = ( 1 + 2.5/2) ^2 - 1

. = (2.25)^2 - 1

. = 4.0625

Then answer is

Annual percentage yield

APY = 4.06 %

Answer:

Febuary -2.25

Explanation:

We are told that the negative values indicate the amount of data that was under the plan. Therefore, the more negative the value, the less of the data Emmanuel used.

With this in mind, looking at the table we note that in the month of febuary Emmnuel used -2..25 of data (2.25 untis less than his plan ) which is the least amount of data used in any month.

We are given the expression

and are asked to evaluate it when x=5 and z=7. For this, we simply replace the given values on the original expression, like this:

And now we simplify it as much as possible:

Solution

- We are told that dog treats, Barker and DogYum cost $1.95 for 3 oz and $2.10 for 3.25 oz respectively and we are required to find out which is more expensive per ounce.

- In order to find the more expensive dog treat, we need to find the cost per ounce for each item. The cost per ounce is given by the formula below:

- The dog treat with the larger cost per oz is the more expensive item.

- Thus, let us calculate the cost per oz for both items.

DogYum:

Barker:

- We can observe that Barker is marginally more expensive than DogYum. We can confirm this by simply subtracting the cost per oz for both treats.

Final Answer

The answer is:

DogYum is less expensive, per ounce

Let's complete the transformation from ABCD to EHGF.

Let's first determine the coordinates of the two figures.

Figure ABCD:

A : -5, 2

B : -3, 4

C : -2, 4

D : -1, 2

Figure EHGF:

E : 4, 1

H : 2, 3

G : 1, 3

F : 0, 1

Reflecting ABCD over the y - axis, we get:

P (x, y) = P' (-x, y)

For ABCD:

A : -5, 2 = A' : 5, 2

B : -3, 4 = B' : 3, 4

C: -2, 4 = C' : 2, 4

D: -1, 2 = D' : 1, 2

Let's now complete the translation,

(x + S), (y + T)

Where,

S = translation at x-axis

T = translation at y-axis

We get,

A' : 5, 2 = E : 4, 1 → S, T = 4 - 5, 1 - 2 = -1, -1

B' : 3, 4 = H : 2, 3 → S, T = 3 - 4, 3 - 4 = -1, -1

C' : 2, 4 = G : 1, 3 → S, T = 1 - 2, 3 - 4 = -1, -1

D' : 1, 2 = F: 0, 1 → S, T = 0 - 1, 1 - 2 = -1, -1

Therefore, we can say that the translation is (x + _, y + _) = (x + (-1), y + (-1)) = x - 1, y - 1

On the graph, the x axis represents rainfall while the y axis represents number of umbrella sold. We can see that as the amount of rainfall is increasing, the number of umbrellas sold is increasing. This is shown by the line moving upwards in the positive direction. the relationship between the amount of rainfall and the number of a umbrellas sold is a positive association.

Answer

C. The shape of both data distributions are non-symmetric

Step-by-step explanation

Ordering both data sets from least to greatest, we get:

R's sleep log:7.5 8 8.58.5 99.5

B's sleep log: 6.5 6.577.57.512

We can see that B's data is concentrated at the lower values (12, the maximum, is an outlier). Then, the shape of B's data distribution is non-symmetric. But, in R's data every value is equidistant from the other ones, in consequence, the shape of R's data distribution is symmetric.

from Least likely to Most likely

Event 3,

Event 1,

Event 4,

Event 2

STEP-BY-STEP EXPLANATION

BAG A contains:

no of white marbles = 11

no of blue marbles = 9

Total marbles in Bag A

= 11 + 9 = 20

Prob. of choosing a white marble in Bag A

= 11 / 20

Prob. of choosing a blue marble in Bag A

= 9 / 20

BAG B contains:

no of white marbles = 6

no of blue marbles = 2

Total marbles in Bag B

= 6 + 2 = 8

Prob. of choosing a white marble in Bag B

= 6 / 8

Prob. of choosing a blue marble in Bag B

= 2 / 8.

Event 1: Choosing blue marble from Bag B

= 2 / 8 = 0.25

Event 2: Choosing white marble from Bag B

= 6 / 8 = 0.75

Event 3: Choosing purple marble from Bag A

= 0 / 20 = 0

Event 4: Choosing white marble from Bag A

= 11 / 20 = 0.55.

Hence, from Least likely to Most likely we have Event 3, Event 1, Event 4, Event 2.

We are required to find both the recursive rule and the Explicit rule for the values given in the table.

Recursive rule:

To get the recursive rule, we need to find the common ratio.

The common ratio (r) is found by dividing the 2nd term by the 1st term, or the 3rd term by the 2nd term, or the 4th term by the 3rd term, and so on.

We can generalize and say the common ratio is also the division of the nth term by the (n-1)th term.

Let us put these facts into mathematical expressions:

Thus, we can now write the recursive formula as:

Explicit rule:

To get the rule, we need to recognize the pattern:

We can see a pattern developing and from that, we can generalize:

Thus, the explicit rule is:

We and a problem with a constant of variation of 4.

We can think as following:

Kate wants to make a party and make candies for her guests. She intent to make at least 15 candies and an additional of 4 candies for each guest. Thetermine the total number of candies, c, that Kate must make according to the total numer of guests, g.

Answer: c = 4g + 15

Given data:

Amount of money invested, P = $1000

Interest rate, r = 0.0625

Total money in the account, A = 5500

Now, to find the years use simple interest rate formula that is

Therefore, t will become

Putting the values we get,

Thus, it will take 72 years for the account to reach 5500.

A biologist studying the growth of a particular species of algae and later designed a model equation for the growth

F(d) = 11(1.01)d

Where, f(d) is in mm and d is days

QUESTION A

F(d) = 11(1.01)d

f(d) = 11.79 mm

Substitute f(d) = 11.79 mm into the model equation

11.79 = 11(1.01)d

11.79 = 11 * 1.01 * d

11 .79 = 11.11 x d

11.79 = 11.11d

Divide both sides by 11.11

11.79/11.11 = 11.11d/11.11

d = 11.79/11.11

d = 1.061

Thde reasonable domain to plot the growth function is 1.061 < d > 1.061

notice that we have one factor of the complete expression, then, we can make the following division:

therefore, the missing factor is 7y+4

Clare is going to need 50 minutes to label 750 books

1) Gathering the data

750 books

15 books per minute

2) Let's set a proportion for that, considering the fact that her speed is constant

15 books ----------------------1 minute

750 -------------------------------x

15x = 750

x= 50 books

3) Clare is going to need 50 minutes to label 750 books.

Given the equation of the line :

To find the slope, solve the equation for y:

Divide both sides by -3 :

So, the slope of the given line = 4/3

And the slope of the line parallel to the given line = 4/3

Because the parallel line have the same slopes

So, the answer is : slope = 4/3