Find the sides of a triangle if two of its sides are equal, the third side is 1 1 3 cm longer than the others, and its perimeter is 5 2 5 cm.

Answer:

[tex]a\approx 31[/tex]

[tex]b\approx 72[/tex]

Step-by-step explanation:

Please find the attachment.

We have been given that in triangle ABC, A=25, C=55 and AB=60. We are asked to find the approximate measures of the remaining side lengths of the triangle.

We will use Law of Sines to solve for side lengths of given triangle.

[tex]\frac{\text{sin}(A)}{a}=\frac{\text{sin}(B)}{b}=\frac{\text{sin}(C)}{c}[/tex], where a, b and c are opposite sides corresponding to angles A, b and C respectively.

Upon substituting our given values, we will get:

[tex]\frac{\text{sin}(25)}{a}=\frac{\text{sin}(55)}{60}[/tex]

[tex]a=\frac{60\text{sin}(25)}{\text{sin}(55)}[/tex]

[tex]a=\frac{60*0.422618261741}{0.819152044289}[/tex]

[tex]a=\frac{25.35709570446}{0.819152044289}[/tex]

[tex]a=30.9552980807967304[/tex]

[tex]a\approx 31[/tex]

Therefore, the measure of side 'a' is approximately 31 units.

We can find measure of angle B using angle sum property as:

[tex]m\angle A+m\angle B+m\angle C=180[/tex]

[tex]25+m\angle B+55=180[/tex]

[tex]m\angle B+80=180[/tex]

[tex]m\angle B=100[/tex]

[tex]\frac{\text{sin}(100)}{b}=\frac{\text{sin}(55)}{60}[/tex]

[tex]b=\frac{60\text{sin}(100)}{\text{sin}(55)}[/tex]

[tex]b=\frac{60*0.984807753012}{0.819152044289}[/tex]

[tex]b=\frac{59.08846518072}{0.819152044289}[/tex]

[tex]b=72.1336967815383509[/tex]

[tex]b\approx 72[/tex]

Therefore, the measure of side 'b' is approximately 72 units.

Answer:

Current balance in Marcelo's account = $132.63

Step-by-step explanation:

Given:

Initial amount in Marcelo's bank account = $49.13

Amount paid in two fees = $32.50 each

Amount added by two deposits = $74.25 each

To find balance in dollars in Marcelo's account.

Solution:

Total amount paid in fees = [tex]2\times \$32.50=\$65[/tex]

Total amount deposited = [tex]2\times \$74.25=\$148.50[/tex]

The balance in Marcelo's account can be represented as:

⇒ Initial balance - Amount given in fees + Amount deposited

⇒ [tex]\$49.13-\$65+\$148.50[/tex]

⇒ [tex]\$132.63[/tex]

Thus, balance in Marcelo's account now = $132.63

Answer: 132.63

Step-by-step explanation:

I copied the other guy lol thanks for the points

Answer:

a.

Option 1

Option 2

b. Sample statistics

Step-by-step explanation:

a.

The set that includes the list of all possible individual in the interested area of study is termed as population while the portion or a part of population is termed as sample. The given scenario indicates that population is all elderly people from which 949 elderly people are selected for study and so, 949 elderly people are included in sample. So, option 1 and option 2 are correct for indicated scenario.

b.

The percentages 22% and 17% are calculated from 949 elderly people that are indicated as sample. Hence, the percentages 22% and 17% are the measure of sample and so, they represents sample statistics.

Final answer:

The relevant population is all elderly people, and the sample consists of 949 elderly people. The numbers 22% and 17% represent sample statistics.

Explanation:

a. The relevant population is all elderly people, so options 2 and 3 are correct. The sample consists of 949 elderly people, so option 1 is also correct.

b. The numbers 22% and 17% represent sample statistics. The sample statistics are calculated from the data collected in the sample, which in this case is the proportion of elderly persons with depression who went on to develop dementia.

Answer:

Estimated Average Requirement (EAR)

Step-by-step explanation:

The Estimated Average Requirement (EAR) is the average amount of daily intake value which is estimated to meet the needs of 50% of the healthy individuals.

The EAR is estimated on the basis of specific conditions of adequacy, and are derived from a careful study of the literature.

The major parameters which is selected for the criterion are reduction of disease risk.

Answer:

-6

Step-by-step explanation:

The survey question 'Do you eat at least five servings a day of fruits and vegetables?' is designed to collect categorical data, as it classifies respondents into groups based on their affirmative or negative answer, rather than providing a numerical value.

The question "Do you eat at least five servings a day of fruits and vegetables?" is designed to collect categorical data. This is because the answers to the question will classify respondents into different categories, specifically those who do eat at least five servings of fruits and vegetables per day and those who do not. As such, the data obtained will be qualitative in nature, allowing us to compare and organize individuals based on their dietary habits.

For a more comprehensive understanding, let's compare data types. In contrast to categorical data, a quantitative variable is numeric and can be measured or counted. It can further be subdivided into discrete or continuous data. Quantitative discrete data involve counts of items or occurrences (e.g., the number of classes you take per school year), while quantitative continuous data involve measurements that can take on any value within a given range (e.g., the weights of soups measured in ounces).

Returning to the student's survey question about fruit and vegetable consumption, it is evident that the data collected does not involve counting or measuring numerical values, but rather involves placing respondents into categories based on their dietary habits. Therefore, the variable in question is indeed categorical.

Answer:

Therefore, we conclude that  R is an equivalence relation.

Step-by-step explanation:

We know that  a relation on a set  is called an equivalence relation if it is reflexive, symmetric, and transitive.

R is refleksive because we have that   a+b = a+b.

R is symmetric because we have that a+d =b+c equivalent with   b+c =a+d.

R is transitive because we have that:

((a, b), (c, d)) ∈ R ; ((c, d), (e, f)) ∈ R

a+d =b+c ⇒ a-b=c-d

c+f =d+e ⇒ c-d =e-f

we get

a-b=e-f ⇒  a+f=b+e ⇒((a, b), (e, f)) ∈ R.

Therefore, we conclude that  R is an equivalence relation.

Answer: This is an reduction.

Step-by-step explanation:

Given : A street is drawn by dilating segment [tex]\overline{FG}[/tex] about center A with a scale factor greater than 0 but less than 1.

Then by using (2.) , we can say that this is an reduction.

Answer:

Step-by-step explanation:

Check the attachment the solution of the work is given there

Answer: 0.74

Step-by-step explanation:

Let h = rhombus' height

Looking at the attachment, we see that the circle has an area of [tex]\pi *(\frac{h}{2}) ^{2}[/tex]

The rhombus has an area of [tex]\frac{h^2}{sin(70°)}[/tex]

because the base is [tex]\frac{b}{sin(90)} = \frac{h}{sin(70)}[/tex]

due to the law of sines

Thus, Area Circle / Area Rhombus is

[tex]\frac{(\pi(\frac{h}{2})^2)}{(\frac{h^2}{sin(70)}) } = 0.74[/tex]

- We´re gonna work with two separate triangles:

-The first one is the larger triangle (40º angle) and a vertical side that represents the ENTIRE height, b, of the tower.

Larger triangle with height b: tan 40°= [tex]\frac{b}{87}[/tex] ; .8390996312 = [tex]\frac{b}{87}[/tex];  b≈73.00166791

-The second one the smaller triangle (25º angle) and a vertical side, a, that represents the height of the first (bottom) section of the tower.

Smaller triangle with height a: tan 25°= [tex]\frac{a}{87}[/tex] ; ..4663076582 = [tex]\frac{a}{87}[/tex];  a≈40.56876626

-Then you need to solve for the vertical heights (b and a) in the two separate triangles.

-The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract.

In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem.

Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 ≈ 32 feet

The answer is

[tex]f(x) = \begin{cases}x-2 \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

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

Here's how I got that answer:

Start with the piecewise definition for y = |x|.

[tex]g(x) = \begin{cases}x \text{ if }x \ge 0 \\ -x \text{ if }x < 0\end{cases}[/tex]

Everywhere you see an 'x', replace it with x+2

[tex]g(x+2) = \begin{cases}x+2  \text{ if }x+2 \ge 0 \\ -(x+2) \text{ if }x+2 < 0\end{cases}[/tex]

[tex]g(x+2) = \begin{cases}x+2  \text{ if }x \ge -2 \\ -x-2 \text{ if }x < -2\end{cases}[/tex]

Now tack on "-4" at the end of each piece so that we shift the function down 4 units

[tex]g(x+2)-4 = \begin{cases}x+2-4  \text{ if }x \ge -2 \\ -x-2-4 \text{ if }x < -2\end{cases}[/tex]

[tex]g(x+2)-4 = \begin{cases}x-2  \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

[tex]f(x) = \begin{cases}x-2  \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

Check out the attached images below. In figure 1, I graph y = x-2 and y = -x-6 as separate equations on the same xy coordinate system. Then in figure 2, I combine them to form the familiar V shape you see with any absolute value graph.

Answer:

After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].

Step-by-step explanation:

Given:

[tex]3x^2-x[/tex]

We need to factorize the given expression using GCF.

Solution:

[tex]3x^2-x[/tex]

Now GCF means Greatest common factor.

From the given 2 numbers we need to find the greatest common factor.

[tex]3\times x\times x- 1 \times x[/tex]

In the given expression GCF is 'x'.

Hence we can say that;

[tex]x(3x-1)[/tex]

Hence After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].

Answer:

The perimeter of Roxanne's right triangular garden is 79 feet.

Step-by-step explanation:

Given,

Length of 1 side = 19 feet

Hypotenuse = 33 feet

We have to find out the perimeter of the triangular garden.

Solution,

Since the garden is in shape of right triangle.

So we apply the Pythagoras theorem to find the third side.

"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides".

So framing in equation form, we get;

[tex]33^2=19^2+(third\ side)^2\\\\1089=361+(third\ side)^2\\\\(third\ side)^2=1089-361\\\\(third\ side)^2=728[/tex]

Now taking square root on both side, we get;

[tex]\sqrt{(third\ side)^2} =\sqrt{728} \\\\third\ side=26.98\approx27\ ft[/tex]

Now we know that the perimeter is equal to sum of all the three side of a triangle.

Perimeter = [tex]19+27+33=79\ ft[/tex]

Hence The perimeter of Roxanne's right triangular garden is 79 feet.

Question is Incomplete; Complete question is given below;

Roger is having a picnic for 78 guests. He plans to  serve each guest at least one hot dog. If each  package, p, contains eight hot dogs, which  inequality could be used to determine how many  packages of hot dogs Roger will need to buy?

1) [tex]p \geq 78[/tex]

2) [tex]8p \geq 78[/tex]

3) [tex]8 +p \geq 78[/tex]

4) [tex]78 + p \geq 8[/tex]

Answer:

2) [tex]8p \geq 78[/tex]

Step-by-step explanation:

Given:

Number of guest in the picnic = 78 guest

Number of hot dog each guest will have = 1

Number of hot dogs in each package = 8 hot dogs.

We need to write the In equality used to determine the number of packages of hot dogs roger must buy

Solution:

Let the number of packages be 'p'.

First we will find the total number of hot dogs required.

so we can say that;

total number of hot dogs required is equal Number of guest in the picnic multiplied by Number of hot dog each guest will have.

framing in equation form we get;

total number of hot dogs required = [tex]78\times 1 =78[/tex]

Now we can say that;

Number of hot dogs in each package multiplied by number of packages should be greater than or equal to total number of hot dogs required.

framing in equation form we get;

[tex]8p\geq 78[/tex]

Hence The In equality used to determine the number of packages of hot dogs roger must buy is [tex]8p\geq 78[/tex].

Answer: she has 30 pages left to read.

Step-by-step explanation:

Let x represent the total number of pages in the book which Lilla is reading.

Lilla read 1/5 of her book last week. This means that the number of pages that she read last week is

1/5 × x = x/5

This week she read 3 times as much as she read last week. This means that the number of pages that she read this week is

3 × x/5 = 3x/5

The number of pages that she has left to read would be

x - 3x/5

= (5x - 3x)/5 = 2x/5

b. There are 75 pages in Lilla's book. It means that the number of pages that she has left to read would be

(2 × 75)/5 = 150/5

= 30

Final answer:

Lilla read 4/5 of her book after two weeks and has 1/5, or 15 pages, left to read of her 75-page book.

Explanation:

Lilla read 1/5 of her book last week. This week she read 3 times as much as she read last week. To express how much of her book Lilla has left to read, let us denote the total amount of the book as 1 (or 100%).

a. The amount she read this week would be 3 times 1/5, which is 3/5. Thus, the total amount Lilla read over the two weeks is 1/5 + 3/5, which simplifies to 4/5 of the book. Therefore, the expression for the amount of the book Lilla has left to read is 1 - 4/5, which simplifies to 1/5 of the book.

b. Lilla's book has 75 pages. To find out how many pages she has left to read, we calculate 1/5 of 75. This is done by multiplying 75 by 1/5:

75  imes 1/5 = 75/5 = 15 pages

Therefore, Lilla has 15 pages left to read.

Answer:

The code is attached. I used python to define the function and matplotlib library to plot the histogram.

Step-by-step explanation:

Answer:

Option 3)  Closer to 0      

Step-by-step explanation:

Correlation:

Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.

Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.

Thus, for the given situation, if there is no relationship between two quantitative variables then the value of the correlation coefficient, r, is close to 0

Answer:

B.

Step-by-step explanation:

Find the total profit.

P=7300-5500

P=1800

Since each shovel makes up 50 of the profit.

50N=1800

N=1800%2F50

N=36

36 shovels were sold.

Answer:

24.2%  students received grades with z-scores between 0.15 and 0.85

Step-by-step explanation:

We are given the following in the question:

The grades of a benchmark test for North High School were normally distributed.

WE have to find the percentage of students that  received grades with z-scores between 0.15 and 0.85.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(score between 0.15 < z < 0.85)

[tex]P(0.15 \leq z \leq 0.85)\\\\= P(z \leq 0.85) - P(z \leq 0.15)\\\\\text{Calculating the value from standard normal z-table}\\\\= 0.802 - 0.560 = 0.242 = 24.2\%[/tex]

24.2%  students received grades with z-scores between 0.15 and 0.85

The asymptotes are found using the rational function ax^n/ bx^m where n is the degree of the numerator and m is the degree of the denominator.

In the given equation the numerator isn’t raised to any power so n is considered equal to 1. The Demi actor has x raised to the 2nd power so m equals 2.

If n < m then the c axis, y= 0 is the horizontal asymptote.

Also because n is less than m there are no vertical asymptote.

The domain is any real number so the domain would be (-infinity, infinity)

Answer:

No because if the Rays meet at a point other than Q the angles will change

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

First statement

[a b c | d][x]

[a b c]x=d

ax+bx+cx=d

Second statement

Ax=d

Given that A = [a b c]

[a b c]x=d

ax+bx+cx=d

ax+bx+cx=d

Then, they are going to have the same solutions

The statement is false. The solution sets for the augmented matrix [a, b, c, d] and the matrix equation Ax = d (where A = [a, b, c]) are not the same unless 'd' is consistently a column vector with 'a', 'b', 'c'.

The statement presented in the question is false. When we talk about a linear system, an augmented matrix generally pairs a coefficient matrix with an answer matrix. This would look like [A|d], where 'A' would be a matrix, and 'd' is the constants column vector.

Conversely, Ax = d is a matrix equation where 'A' is again the coefficient matrix, 'x' is the variable matrix, and 'd' is the constants column vector.

In your provided augmented matrix, [a b c d], unless 'd' is a consistent column vector with the other column vectors, it can't be virtually the same as the matrix system Ax = d where A = [a b c] because the augmented matrix [a b c d] would mean that A = [a b c] and d = [d].

Unless 'd' is mathematically consistent with the column vectors 'a', 'b', and 'c', the solution sets would not be the same.

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The drag force can be mathematically expressed as Fd = 0.5 × ρ × v^2 × A × Cd, where Fd is the drag force, ρ is the density of the fluid, v is the velocity of the object, A is the reference area, and Cd is the drag coefficient.

The drag force can be mathematically expressed as:

Fd = 0.5 × ρ × v2 × A × Cd

Where:

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Answer:

Therefore,

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\cot B =\dfrac{1}{2}[/tex]

[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given:

Right △ABC has its right angle at C,

BC=4 , and AC=8 .

To Find:

Cos A = ?

Cot B = ?

Csc B = ?

Solution:

Right △ABC has its right angle at C, Then by Pythagoras theorem we have

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the values we get

[tex](AB)^{2}=4^{2}+8^{2}=80\\AB=\sqrt{80}\\AB=4\sqrt{5}[/tex]

Now by Cosine identity

[tex]\cos A = \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\[/tex]

Substituting the values we get

[tex]\cos A = \dfrac{AC}{AB}=\dfrac{8}{4\sqrt{5}}=\dfrac{2}{\sqrt{5}}\\\\Ratinalizing\\\cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

Now by Cot identity

[tex]\cot B = \dfrac{\textrm{side adjacent to angle B}}{\textrm{side opposite to angle B}}[/tex]

Substituting the values we get

[tex]\cot B = \dfrac{BC}{AC}=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

Now by Cosec identity

[tex]\csc B = \dfrac{Hypotenuse}{\textrm{side opposite to angle B}}\\[/tex]

Substituting the values we get

[tex]\csc B = \dfrac{AB}{AC}=\dfrac{4\sqrt{5}}{8}=\dfrac{\sqrt{5}}{2}[/tex]

Therefore,

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\cot B =\dfrac{1}{2}[/tex]

[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]

Final answer:

To solve for q in the equation 3(q + 4/3) = 23, we distribute the 3, subtract 4 from both sides, and then divide by 3 to find that q is approximately 6.33.

Explanation:

To solve for q in the equation 3(q + \dfrac{4}{3}) = 23, we need to apply some basic algebra principles. First, we distribute the 3 into the parentheses.

3q + 3 \times \dfrac{4}{3} = 23

3q + 4 = 23

Now, subtract 4 from both sides to get 3q alone on one side.

3q = 23 - 4

3q = 19

Last, divide both sides by 3 to solve for q.

q = \dfrac{19}{3}

q = 6.333...

Thus, q is approximately equal to 6.33 when rounded to two decimal places.

The value of q is q= 19 / 3.

Let's solve for q in the equation:

3(q+ 3 / 4)=23

We can solve the equation by distributing the terms, adding/subtracting to both sides, dividing both sides by the same factor, and simplifying.

Steps to solve:

1. Distribute the terms:

3q+4=23

2. Add/subtract to both sides:

3q+4−4=23−4

3q=19

3. Divide both sides by the same factor:

3q / 3 = 19 / 3

4. Simplify:

q= 19 / 3

Therefore, the value of q is q= 19 / 3.

Answer: Zoey needs 168 square feet if carpet squares.

Step-by-step explanation:

Zoey wants to cover her bedroom floor with carpet squares. Each square has an area of 1 square foot.

The formula for determining the area of a rectangle is expressed as

Area = length × width

Her bedroom measures 12 feet by 14 feet. Therefore, the area of her bedroom would be

12 × 14 = 168 square feet.

Therefore, the number of carpet squares that Zoey needs would be

168/1 = 168 square feet

Answer:

  168 squares

Step-by-step explanation:

Each square is 1 foot on a side, so along the 14-foot wall, Zoey will need 14 squares. Altogether, Zoey will need 12 rows of 14 squares, so 12×14 = 168 squares.

The maximum weight of boxes that can be placed into the elevator is:

[tex]\to 2000 - 200 = 1800 \ lbs[/tex]  

It should be noted that Y must be an even integer for the equivalence to hold, whereas X might be odd or even because 40X is always even.

Learn more:

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Answer:

Step-by-step explanation:

The absolute value of z is the distance between the point graphed from the complex number and the origin on a complex plane.  In a complex plane, the x axis is replaced by R, real numbers, and the y axis is replaced by i, the complex part of the complex number.  Our real number is positive 3 and the complex number is -5, so we go to the right 3 and then down 5 and make a point.  Connect that point to the origin and then connect the point to the x axis at 3 to construct a right triangle that has a base of 3 and a length of -5.  To find the distance of the point to the origin is to find the length of the hypotenuse of that right triangle using Pythagorean's Theorem.  Therefore:

[tex]|z|=\sqrt{(3)^2+(-5)^2}[/tex] and

[tex]|z|=\sqrt{9+25}[/tex] and

[tex]|z|=\sqrt{34}[/tex]

Answer:

Step-by-step explanation:

The equation used to represent the height of the ball, h in feet after t seconds is expressed as

h = -16t^2 + 48t + 4

A) The height of the ball after 2 seconds would be

h = - 16 × 2² + 48 × 2 + 4

h = - 64 + 96 + 4

h = 36 feet

B)The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -16

b = 48

Vertex = - - 48/32= 1.5

So the ball will attain maximum height at 1.5 seconds.

C) The maximum height of the ball would be

h = -16 × 1.5² + 48 × 1.5 + 4

h = - 36 + 72 + 4

h = 40 feet

Final answer:

The ball will be at a height of 64 feet after 2 seconds. It will reach its maximum height of 58 feet after 1.5 seconds.

Explanation:

To solve the problem, we need to use the given quadratic equation for the ball's height h(t) = -16t2 + 48t + 4. This equation models the motion of the ball thrown into the air with an initial upward velocity.

A: Height After 2 Seconds

To find the height of the ball after 2 seconds, we substitute t = 2 into the equation:

h(2) = -16(2)2 + 48(2) + 4

h(2) = -16(4) + 96 + 4 = 64 feet

B: Time to Reach Maximum Height

To determine when the ball reaches its maximum height, we need to find the vertex of the parabola, which occurs at t = -b/(2a) where a=-16 and b=48. So t = -48/(2(-16)) = 1.5 seconds.

C: Ball's Maximum Height

To find the ball's maximum height, we substitute t = 1.5 into the height equation:

h(1.5) = -16(1.5)2 + 48(1.5) + 4

h(1.5) = -16(2.25) + 72 + 4 = 58 feet

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The tangent of an angle is the ratio of the opposite over adjacent sides.

tan(angle) = opposite/adjacent

tan(theta) = 4/3

This means that

opposite = 4 and adjacent = 3

This only happens when angle P is the reference angle. In other words,

tan(P) = 4/3