the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base. find the altitude.

Answer:

AD is Congruent to BC and it's given, (given just means that it was already said or stated, and you don't need to do the work to find it) Angle DAC would be congruent to angle BAC (if that doesn't work, rearrange them to look like angle CAB). AC would be congruent to DB. Triangle ADC would be congruent to triangle BCD by (since i don't know exactly which way the letters are arranged is would either be SAS or SSA) and that's because you know two of the sides are congruent to each other and one angle.

I tried hard to sketch out what the shape looked like based on the information given, and that's because I need a visual of what the shape looks like. Sorry, this took so long to answer.

The blanks are filled in below and completed the proof.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

AD is congruent to BC.

AD is parallel to BC.

Now,

Since AD is parallel to BC, alternate interior angles AD and BC are congruent.

AC is congruent to AC since segments are congruent to themselves.

Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence theorem.

Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to angle BAC.

Since those alternate interior angles are congruent. AB must be parallel to CD.

Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.

Thus,

The blanks are filled in above.

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Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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Answer:

x= [tex]5\frac{1}{7} or \frac{36}{7}[/tex]

y=7

Step-by-step explanation:

we use comparing fractions for this since we know the bottom sides for both triangles we will use that

4/7=x/9

cross multiply

4(9)=7x

36=7x

/7.  /7

36/7=x

5 1/7=x

now to find y we do same thing

4/7=4/y

cross multiply

4y=7(4)

4y=28

/4.  /4

y=7

hopes this helps please mark brainliest

Answer: The amount of money needed to be given to the server is $30 and 23 cents.

Since tax is 6%, hence:

Total bill including tax = $28.52 + 6% of $28.52 = $30.23

The amount of money needed to be given to the server is $30 and 23 cents.

Therefore the denominations needed for this is one $20 bill, two $10 bills and 23 pennies.

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Step-by-step explanation:

Symptoms of an allergic reactions:

Allergies cause your body to react to normally harmless things like pollen, dust, and animal dander. Symptoms can be mild, but can be very serious for some people.

allergen he can enter the body in four different ways.

Allergy symptoms vary from person to person, and the substances that trigger the allergic reaction may also be different.

If you have a runny or stuffy nose after a few minutes of walking, you may have allergic rhinitis. This is our reaction to tiny particles in the air we breathe.

Sneezing doesn't seem to be a big deal. However, it can be a mild early sign of a serious allergy, even the foods you eat.Your sneezing can also be quickly replaced by more serious symptoms.

Occasional itchy or watery eyes can occur for many reasons. But it could be something more serious, like a drug allergy.

Strange changes can be signs of a severe allergic reaction to food or drugs. You may notice sudden wheezing. Or you just feel like you can't breathe.

Rash may be itchy, painful, warm, bumpy, or blistered. They are a common result of allergic reactions to pet dander, chemicals, foods, drugs, or cosmetics.

A sudden drop in blood pressure can make you feel like you're going to pass out. The whole body may become weak or confused. this is a serious situation.

If your mouth, lips, or tongue are swollen for no apparent reason, this may be angioedema, a sign of an allergic reaction. It's not necessarily serious.

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The values for the highlighted variables is a=-1,b=-9,c=9,d=3,e=3,f=2 and g=3/2.

Given:

3x/2x-6 + 9/6-2x

Rewrite 6-2x as 2x-6 by taking (-1) as common factor:

= 3x/2x-6 + 9/(-1)(2x-6)

so a = -1

= 3x/2x+6 + -9/2x-6

so b = -9

The LCM of 2x - 6 and 2x - 6 is 2x -6.

= 1*3x + 1*-9 / 2x-6

= 3x - 9 / 2x -6

so c = 9

(3x - 9) = 3(x-3)

(2x - 6) = 2(x - 3)

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

so d =3,e=3 and f=2 , g = 3/2.

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Full question:

Enter the values for the highlighted variables to complete the steps to find the sum:

3x/2x-6 + 9/6-2x = 3x/2x-6 + 9/a(2x-6) = 3x(2x-6)+6(2x-6)=3x-c 2x-6 =d(x-x) f(x-3) = g

A- -1

B= -9

C= 9

D= 3

E= 3

F= 2

G= 1.5

The exclusive right to distribute, exhibit, perform, or reproduce an original work in copies, as well as the right to create derivative works based on the original work, is known as copyright. This assertion is true.

A bundle of legal privileges known as copyrights automatically belongs to everyone who produces an original work of authorship, such as a piece of literature, film, music, or software. These privileges include the ability to copy, create derivative works from, distribute, perform, and show the work in public.

The following exclusive rights belong to copyright owners exclusively, according American copyright law: Create phonorecords or duplicates of the material. Make works based on the original work. distribute copies or phonorecords of the work to the public by selling, transferring ownership, leasing, renting, or borrowing.

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The method of least squares of residuals is commonly used to get the best fit with linear regression. The reason why the absolute value of residual's (|y- ypred|) is not used is as follows :

Although least squares purposefully square the error in the belief that it will respond better when values deviate from your projected value, you could run something similar if you so desired.

Consider the following scenario: You plot your data's real values on a graph, and you observe a straight line of numbers with a few outliers that have greater values than you would expect. You could be tempted to believe that the best fit is a straight line along the values. Because the real pattern must take into account all the values that occurred, least squares adapt more to the outliers than other values and purposefully squares values, sort of assuming that the straight line of actual values was a coincidence.

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The graph of the function is given in attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is f(x) = x² + 3

f of x equal to x square plus three

f(x) = x² + 3

y= x² + 3

Select a few x values, and plug them into the equation to find the corresponding  y values.

x       0      1       2       3       4

y        3      4      7      12      19

Hence, the graph of the function is given in attachment.

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Step-by-step explanation:

just like with every equation. we move things around by applying the same operations to both sides.

-4(y + 3) + 35 > 4(6 - y)

-4y - 12 + 35 > 24 - 4y

23 > 24

that is always false (23 is never larger than 24).

so, there is no solution.

Answer:

The equation for this is:

n(g) + 49 - 3

Step-by-step explanation:

The term "Product" means "multiplication." And "number" can be reduced to the term "n," like "g" is. The word "and" means "addition." And, "3 less" means - 3:

n(g) + 49 - 3

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

49g -3

Step-by-step explanation:

3 less than the product of a number g and 49

Writing an algebraic expression

less than means it comes after

the product of a number g and 49

49g

3 less than

49g -3

The number of applications Jen can expect from the self-tanner is 22.5.

What is applications?
Mathematical Applications focuses on developing students' mathematical expertise in both established and novel contexts. Financial modelling, matrix, network analysis, route as well as project planning, decision-making, as well as discrete growth and decay are a few of these contexts.

What is an advertising claim?

An advertising claim is a statement made in advertising about the advantages, features, and performance of a good or service with the intention of convincing the consumer to buy it.

First, to determine how many applications 1 -oz of the bottle can provide.

Number of applications 1 -oz of the bottle can provide = 3/2 = 1.5

Second, to determine the number of applications 15 oz of the bottle can provide = 15 x 1.5 = 22.5 applications

Hence, the total number of applications expected is 22.5

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The equation that represents the function g , the result of the transformation is g(x) = -(1/2)tanx     .

In the question ,

the parent function is given to be tangent ,

let the the parent function be denoted by "f" ,

So , f(x) = tanx,

given that the function is horizontally compressed by a factor of 1/2 ,

that means the function is multiplied by 1/2 ,

So ,g(x) = (1/2)tanx

also given that it is reflected over the x axis ,

reflection over x axis means , multiplying it by -1,

So , g(x) = -(1/2)tanx .

Therefore , the function g is g(x) = -(1/2)tanx  .

The given question is incomplete , the complete question is

The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis. Write an equation to represent function g, the result of this transformation ?

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Answer:

g(x)=-tan(2x)

Step-by-step explanation:

The maximum speed is 3667 m/s if the engine can impart a force of 4522 N on the road.

What is Drag coefficient?

The aerodynamic drag coefficient is a measure of the effectiveness of a streamline aerodynamic body shape in reducing the air resistance to the forward motion of a vehicle.

Given that,

mass of a car(ρ) = 1834 kg

drag coefficient (c) = 0.342 kg/m

Force(F) = 4522 N

and we have to find maximum speed.

We know the formula for Drag coefficient,

c = 2F/ ρu^2

⇒ u^2 = 2F/ ρc

          = 2(4522)/1834×0.342

          = 9044 / 672.2

   u^2 = 13.454

       u = 3.667

       u = 3667 m/s

Therefore maximum speed is 3667 m/s.

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The area of the Rectangle is 70 units², So option (C) is the correct answer.

Let,

     Length of Rectangle = 10 units

     Width of Rectangle = 7 units

Area of rectangle =  length × Width

Putting the Length and Width of the rectangle in the last equation.

So,

Area of rectangle = 10 × 7 units²

Area of rectangle = 70 units²

Hence, The area of the rectangle is 70 units².

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If 4 in has a force of 50 applied. The pressure is 12.5N/m².

Using this formula to find the pressure

Pressure = Force /Area

Where:

Force = 50

Area =4

Let plug in the formula

Pressure = 50/4

Pressure = 12.5 N/m²

Therefore the pressure is  12.5 N/m².

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The required three additional points that the line have slope (-7, -7) and m=2 passes through are (0,7), (2,11) and (1,9).

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

we are given with the point (-7,-7) and m = 2(which is not given in this question so this question is incomplete)

now

first construct a linear equation using point(-7,-7) and m=2

(y−y1)=m(x−x1)

and we have

x1=-7, y1=-7

(y+7)=2(x+7)

(y+7)=2x+14

y=2x+7

Now, we can substitute values for x and y to find 3 additional points that lie on this line.

and after drawing graph we'll get the points:

(0,7), (2,11) and (1,9)

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The statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.

K-means Clustering is a vector quantization technique that seeks to split "n" observations into "k" clusters, with each observation referring to the cluster with the closest mean, which reflects a model of the cluster.

This means that the K-means algorithm recognizes the "k" number of centroids and then allocates every data point to the cluster with the fewest centroids.

Thus, the statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.

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Answer:

[tex]z\leq 16.1[/tex]

Step-by-step explanation:

-4z>=-64.4

/-4.    /-4

z>=16.1

And when we switch the signs we switch which was the alligator points

z<=16.1

Hopes this helps please mark brainliest

Answer:

z ≤ 16.1

Step-by-step explanation:

Given inequation,

→ -4z ≥ -64.4

Now the value of z will be,

→ -4z ≥ -64.4

→ z ≤ -64.4/-4

→ z ≤ 64.4/4

→ [ z ≤ 16.1 ]

Hence, the value of z is 16.1.

(a) The number of people expected to have blood type O+ among 40 randomly selected people  is 14 .

(b) the standard deviation of number of people who have blood type O+ among 40 people is 3.0166 .

In the question ,

it is given that ,

probability that the person has blood group of type O+ is (p) = 0.35

the number of people randomly selected is (n) = 40 people ,

So , Number of people expected to have blood type O+ among 40 randomly selected people = Mean of the binomial distribution .

= n × p

= 40 × 0.35
= 14

So ,The standard deviation of the number of people expected to have blood type O+ among 40 randomly selected people = √(n × p × q)

= √(40 × 0.35 × (1-0.35))

= √(40 × 0.35 × 0.65)

= 3.0166

Therefore , (a) The number of people expected to have blood type O+ among 40 randomly selected people  is 14 .

(b) the standard deviation of number of people who have blood type O+ among 40 people is 3.0166 .

The given question  is incomplete , the complete question is

If the probability that a person has blood type O+ is 0.35 and you have 40 randomly selected people ,

(a) About how many would you expect to have blood type O+ ?

(b) What is the standard deviation of the number of people who would have blood type O+ among the 40 people ?

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Since the number of roots of a polynomial function is equal to the highest degree of the polynomial function, the total number of roots of the given polynomial functions are 6 and 2 respectively.

We have two polynomial functions given by -

[tex]F(x) = 3x^{6}+2x^{5}+x^{4}-2x^{3}[/tex] ----- (1)

[tex]G(x)=5x-12x^{2} +3[/tex] ---- (2)

We have to find out the total number of roots of each polynomial function.

We know that, the number of roots of a polynomial function is equal to the highest degree of the polynomial function.

In equation (1), we have

[tex]F(x) = 3x^{6}+2x^{5}+x^{4}-2x^{3}[/tex]

Here, we can see that the highest degree of the polynomial function F(x) is 6 which is the highest degree of x in the polynomial.

So, the total number of roots of the polynomial function F(x) is 6.

Similarly, in equation (2), we have

[tex]G(x)=5x-12x^{2} +3[/tex]

Here, we can see that the highest degree of the polynomial function G(x) is 2 which is the highest degree of x in the polynomial.

So, the total number of roots of the polynomial function G(x) is 2.

Therefore, the total number of roots of the given polynomial functions are 6 and 2 respectively.

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Expectancy theory would best provide perspective on the question 'if i study for 12 hours, what is the probability that i'll get an on the exam?".

 Expectancy theory (expectancy theory of motivation) was put forward by Victor Vroom in 1964. Vroom put more emphasis on outcome factors, rather than needs as proposed by Maslow and Herzberg.

This theory states that the intensity of the tendency to perform in a certain way depends on the intensity of the expectation that performance will be followed by a definite outcome and on the attractiveness of the result to the individual.

Vroom argues that people will be motivated to do certain things to achieve goals if they believe that their actions will lead to the achievement of these goals.

There are three main assumptions of Vroom in expectancy theory.  These assumptions are as follows:

-Every individual believes that if he behaves in a certain way, he will get certain things.  This is called an outcome expectancy as a person's subjective assessment of the likelihood that a certain outcome will arise from that person's actions.

-Each outcome has value, or appeal to a particular person.  This is called valence (valence) as the value that people give to an expected result.

-Each outcome is associated with a perception of how difficult it is to achieve that outcome.  This is called effort expectancy as the possibility that one's efforts will result in the attainment of a certain goal.

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The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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For the non negative number, the first number of rows of pascal's triangle is attached below.

Non negative number:

Non negative number means the number which is either zero or a positive number.

Given,

Here we have a non-negative integer number of rows, And we have to generate the first number of rows of pascal's triangle And in pascal's triangle, each number is the sum of the two numbers directly above it.

Before make the pascal's triangle,

We know that the given condition is each number is the sum of the two numbers directly above it.

Based on these condition, we have plotted the following pascal's triangle.

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The  expression whose value is twice the value of the element in the 3rd row and the 2nd column will be x [2][1] × 2

Given,

In the question:

A two-dimensional array x of doubles

Write an expression whose value is twice the value of the element in the 3rd row and the 2nd column.

Now, According to the question:

A two-dimensional array x of doubles

The value of the element in the 3rd row and the 2nd column.

Also, Value is twice of an element.

The expression will be :

=> x [2][1] × 2

Hence, The  expression whose value is twice the value of the element in the 3rd row and the 2nd column will be x [2][1] × 2

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Answer:

-0.5

Step-by-step explanation:

To find the middle of two numbers you can add them together then divide by two. Here you would do -7 + 6 which equals -1

The divide by 2 which equals -0.5

The correct answer is 0.75x + 0.15y = 90 is the equation that describes the quantity of pens and pencils the glee club can purchase.

The maximum number of pens the club can purchase is 120.

The maximum number of pencils the club can purchase is 600.

Each pen costs $0.75.

Total number of pens = x

Each pencil costs $0.15

y = number of pencils

(Cost of each pen) x (Number of pens) + (Cost of each pencil) x (Number of pencils) = $90 which equals the total cost for pens and pencils.

The formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

When 0.75x = 90

x = 90/0.75

x = 120, the club purchases the most pens.

The maximum number of pens the club can purchase is 120.

When the club purchases the most pens, 0.15x = 90

x = 90/0.15

x = 600

Hence, the maximum number of pencils the club can purchase is 600 and the formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

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Examples of complex fraction are [tex]\frac{\frac{1}{4}}{\frac{3}{8}}[/tex], [tex]\frac{\frac{1}{3}}{9}[/tex], [tex]\frac{4}{\frac{2}{5}}[/tex] etc.

The first and most common way to represent a fraction is with [tex]\frac{a}{b}[/tex]

Where 'a' is the numerator and 'b' is the denominator.. A horizontal bar separates the numerator and denominator.

A complex fraction is one that contains fractions in the numerator, denominator, or both.

some examples of complex fractions are:

[tex]\frac{\frac{1}{4}}{\frac{3}{8}}[/tex] , [tex]\frac{\frac{1}{3}}{9}[/tex] , [tex]\frac{4}{\frac{2}{5}}[/tex] etc.

Thus, an example of complex fraction is [tex]\frac{4}{\frac{2}{5}}[/tex].

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The pattern will be attached in the figure attached, in the matrix form.

What is the matrix?

The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.

We can arrange it as A = (0 0 0 0 1 1 0 0 1)

We know A*TA = 0

If A has an entry 9 then, the sum of all the diagonal elements.

So the T will be the form of the matrix attached below.

Hence the Pattern will be attached in the figure attached.

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The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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