The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?

Answers

Answer 1
a^2 = x^2 - 5^2     where a = altitude, x=shorter leg and y=longer leg.

a^2 = y^2 + 11^2

x^2  - 5^2 = y^2 - 11^2.......... (1)

Also consider the  whole triangle:

x^2 + y^2 = 16^2..........(2)

x^2 - y^2 =   -96  .........(3)                 (from  equation (1))


adding   2 x^2 =   256 + -96 =  160

x^2 = 80 

x = sqrt80

   =  8.94 to nearest hundredth

Related Questions

HELP ME PLEASE !! IM SO CONFUSED

Answers

1. 2.0 x 10^-2
2. 2.2 x10^6
3. 2.0 x 10^4


Just covert each until you reach the end, like you know that there are 356 days in a year and 100 years in a century.

PS They're in scientific notation





The odds that you will pick a heart from a standard deck of 52 cards is 13:39. TRUE or FALSE

Answers

the odds of picking a heart is 13:39.

the statement is TRUE.

To determine whether the statement is true or false, we need to calculate the odds of picking a heart from a standard deck of 52 cards and compare it to the given odds of 13:39.

Step 1: Calculate the number of hearts in a standard deck.

A standard deck of 52 cards contains 13 hearts.

Step 2: Calculate the total number of cards in the deck.

A standard deck of 52 cards contains 52 cards.

Step 3: Calculate the odds of picking a heart.

The odds of picking a heart can be expressed as the ratio of the number of favorable outcomes (hearts) to the number of unfavorable outcomes (non-hearts).

Number of hearts: 13

Number of non-hearts: 52 - 13 = 39

So, the odds of picking a heart is 13:39.

Now, let's compare the calculated odds (13:39) with the given odds (13:39).

Since the calculated odds match the given odds, the statement is TRUE.

If you were to add all odd numbers between 1 and 11 (both inclusive), the result would be

Answers

The sequence of all odd numbers between 1 and 11 (both inclusive) is
1,3,5,7,9,11

This is an arithmetic sequence with common difference of d=2
The first term is a₁=1.

The number of the term 11 (without counting) is found from
1 + (n-1)*2 = 11
1 + 2n - 2 = 11
2n -1 = 11
2n = 12
n = 6

The sum of the first n terms of an arithmetic sequence is
[tex]S_{n} = \frac{n(a_{1}+a_{n})}{2} [/tex]

Therefore, the sum of the sequence is
S₆ = [6*(1 + 11)]/2
    = (6*12)/2
    = 36

Answer:  36

Final answer:

By adding all the odd numbers from 1 to 11 inclusive (1, 3, 5, 7, 9, 11), the sum is 36.

Explanation:

If you were to add all odd numbers between 1 and 11 (both inclusive), the odd numbers are: 1, 3, 5, 7, 9, and 11. To find the result of adding these numbers together, you simply add each one sequentially:

1 + 3 = 4

4 + 5 = 9

9 + 7 = 16

16 + 9 = 25

25 + 11 = 36

So, the result of adding all the odd numbers from 1 to 11 inclusive is 36.

what is the exact solutions of x2=5x+2

Answers

Move all terms to the left of equal with changed sign

x²-5x-2 = 0

Solve with x₁,₂ = (-b±√Δ)/2a

Δ = b²-4ac

call a (1)x², b -5 and c -2

x1,2 = (-(-5)±√(-5)²-4*1*(-2))/2*1

x1,2 = (5±√25+8)/2

x1,2 = (5±√33)/2

x1 = (5+√33)/2

x2 = (5-√33)/2

Answer:

The answer has a positive 5 and 33.

Step-by-step explanation:

I used a calculator.

Why is sin(20) = sin(160) = -sin(200) = -sin(340)?

Answers

Because they're all the same distance from the x axis on a coordinate plane. Also, remember that in quadrant I, all trig values are positive. In Q II, only sine and cosecant are positive. In Q III, only tangent and cotangent are positive. In Q IV, only cosine and secant are positive. Think of it as All Students Take Calculus.

Answer:

see.

Step-by-step explanation:

The value of sin is the same at the same distance from the cuadrant limit of the point. For the case of 20°, we have that the sin is the same in the following case:

As 20 is positive we use the limit cuadrant at 90°. The distance of 20 to 90 is 70. So, sin(20)=sin(90+70)=sin(160).

Also we have that sin(x) is a odd function, so sin(-x)=-sin(x), so

sin(-20°)= -sin(20°)

-sin(-20°)=sin(20°)

-sin(340°)=sin(20°).

and,

sin(-160°)=-sin(160°)

-sin(-160°)=sin(160°)

-sin(200°)=sin(160°)=sin(20°).

Tuna provides 30 calories per ounce . On a graph representing the relationship between the number of ounces of tuna a person consumes and the number of calories the tuna provides which quantity should be graphed on the x-axis

Answers

Ounces of tuna will go on the x axis and calories on the y axis.  This is because the relationship between the number of ounces a person eats and the calories he consumes then is a positive correlation (a line with a positive slope which goes from lower left to upper right) with x being the independent variable. As x increases, y increases. In other words you can ONLY change the amount of calories you consume WHEN you change the amount of ounces you eat.  You can't change the number of calories independent of the number of ounces. The independent variable goes along the x axis, cuz the x variable always represents the independent variable.

Answer:

Ounces of tuna will go on the x axis and calories on the y axis.  This is because the relationship between the number of ounces a person eats and the calories he consumes then is a positive correlation (a line with a positive slope which goes from lower left to upper right) with x being the independent variable. As x increases, y increases. In other words you can ONLY change the amount of calories you consume WHEN you change the amount of ounces you eat.  You can't change the number of calories independent of the number of ounces. The independent variable goes along the x axis, cuz the x variable always represents the independent variable.

Step-by-step explanation:

PLEASEEEEE HELPPPP ASAP NEED TO GET RIGHT!!!! WILL GIVE THANKS

Answers

You are given the function sin θ = 3/√34. You are asked to find the possible coordinates of point Pp on the terminal arm of θ in the first quadrant. The sine function is equal to the opposite side over the hypotenuse side. Let us assign variables as x, y and r where x is the distance of the line to the x - axis, y is the distance of the line to the y - axis and r is the distance of the hypotenuse line. Apply pythagoreas theorem

r² = x² + y²
(√34)² = x² + 3²
34 = x² + 9
x² = 25
x = 5

the coordinates is placed as (x,y) and you already solved these values and so (5, 3) 




Bao Yu is completing the square to solve the polynomial equation.

x2 – x – 3 = 0



What should be her first step?


adding –x to both sides of the equation

adding –3 to both sides of the equation

isolating the first term, x2

isolating the constant, –3

Answers

Solution:

The square of the given equation can be completed as below:

Here we will make the terms on left hand side such that it gets the form of [tex]a^2\pm2ab+b^2=(a\pm b)^2[/tex]

[tex]x^2-x-3=0\\\\\text{Isolate the constant}\\\\x^2-x=3\\\\x^2-2\times\frac{1}{2}\times x +\frac{1}{2}^2=3+ \frac{1}{2}^2\\\\(x-\frac{1}{2})^2=\frac{13}{4}\\[/tex]

Hence the correct option is isolating the constant , -3.

The polynomial equation x^2 – x – 3 = 0 is a quadratic equation, and the first step in completing the square is (d) isolating the constant, –3

What are polynomials?

Polynomials are expressions that are represented with variables and coefficients

Below are the steps taken to determine Bao Yu's first step

The equation is given as:

x^2 – x – 3 = 0

Isolate the constant -3 in the equation.

So, we have:

x^2 – x = 3

Hence, the first step in completing the square is (d) isolating the constant, –3

Read more about polynomials at:

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Simplify 7x + (x – 4)(x + 5) – 5x.

Answers

7x+(x-4)(X+5)-5x
7x+(X*2+ 5x-4x-20)-5x
7x+(X*2+ x-20)-5x
X*2+3x-20

Answer:

x^2 + 3x – 20

Step-by-step explanation:

I just did the assignment

Choose the point on the terminal side of -45°. (-3, -3) (4, -4) (5, 5) (-2, 2)

Answers

(4, -4) is the answer

-45° is in quadrant IV and the point (4, -4) is the only point out of the points given that is also in quadrant IV
The angle of -45 its terminal side lies in the fourth quadrant, i.e. the x-coordinates is *positive* and y-coordinates is *negative*

The point (4,-4) is the only one that satisfies that condition


hope that helps

The product of three and a number is thirty-three. What is the number? N = 11 N = 30 N = 36

Answers

Answer:

Step-by-step explanation:

N=11

Christine buys 7 hamburgers and 3 sodas for $27.95. Laura buys 5 hamburgers and 4 sodas for $23.40. How much does a hamburger cost?

A. 1 .85
B. $3.20
C. $6.80
D. $6.55
E. $3.50

Answers

7h+3s=27.95 subtract 7h from both sides

3s=27.95-7h  divide both sides by 3

s=(27.95-7h)/3

Then we are told:

5h+4s=23.4,  using s found above makes this equation become:

5h+4(27.95-7h)/3=23.4  multiply both sides by 3

15h+4(27.95-7h=70.2  perform indicated multiplication on left side

15h+111.8-28h=70.2 combine like terms on left side

-13h+111.8=70.2 subtract 111.8 from both sides

-13h=-41.6  divide both sides by -13

h=$3.20

Is it possible for one point to be in two different planes?

Answers

Yes, it is possible for one point to be in two different planes. Imagine this: take the point in the corner of a room. That point is part of 3 planes (both walls and the floor).

 

To add, in mathematics, a plane is a flat, two-dimensional surface. 

Answer:

Yes, it is possible for one point to be in two different Planes.

This can be explained in following way.

The Intersection of two plane is a line.And on a line infinite number of point lies.

So,"yes" one point or Infinite number of points can be common between two different planes.

A company performs linear regressions to compare data sets of two similar products. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, what can be concluded?

A. Brand A's data are probably linear, while brand B's data are probably not. B.Neither data is likely to be linear.
C.Both data sets are probably linear.
D.Brand B's data are probably linear, while brand A's data are probably not.

Answers

I think the correct answer would be B. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, then neither of the data is likely to be linear. In order to be linear, the residuals of both data set should be, more or less, linear or approaching linearity in nature. Therefore, the linear regression that was done would not give good results since it is only applicable to linear data sets. Also, you can say that the relation of the data sets of the products are not linear. It would be best to do a curve fitting for both sets by using different functions like parabolic functions.

Brand A's data are probably linear, while brand B's data are probably not.

What can be concluded from a graph?

A graph shows how much a set of data fits into a pattern. This data is defined by the regression line.

Now, when we have the graph for brand A as an increasing curve, and the residuals for brand B form a U-shaped pattern, we can conclude that Brand A's data are probably linear, while brand B's data are probably not.

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Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F + G) (2) =

Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F - G) (6) =


Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F  G) (2) =



Answers

Answer with Step-by-step explanation:

F = {(0, 1), (2, 4), (4, 6), (6, 8)}  

G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F+G)(2)=F(2)+G(2)

            = 4+5

            = 9

F = {(0, 1), (2, 4), (4, 6), (6, 8)}  

G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F - G) (6) =F(6)-G(6)

               =8-9

               =-1

F = {(0, 1), (2, 4), (4, 6), (6, 8)}

G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F.G) (2) =F(2).G(2)

             = 4×5

            = 20

-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step

Answers

-10 - 2v < 6                   6v + 12 < -6
-2v < 6 + 10                  6v < -6 - 12
-2v < 16                        6v < -18
v > -16/2                       v < -18/6
v > -8                            v < -3

solution is : -8 < v < -3

Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?

Answers

We are given a line with the following data:

r-value = 0.657 (r)
standard deviation of x-coordinates = 2.445 (Sx)
standard deviation of y-coordinates = 9.902 (Sy)

We are asked to find the slope of the line up to 3 decimal places.

To find the slope of the line, based on the data that we have, we can use this formula:

slope, b = r * (Sy / Sx) 

substitute the values to the formula:

b = 0.657 * ( 9.902 / 2.445 )

Solve for the b.

Therefore, the slope of the line is 

b = 2.66078, round off to three decimal places:

b = 2.661 is the slope of the line. 

Answer: 2.661

Step-by-step explanation:

A P E X

a pizza delivery shop averages 21 minutes per delivery with a standard deviation of 3 minutes. what is the probability that a pizza takes less than 15 minutes to be delivered?

Answers

We have the mean, μ = 21 and the standard deviation, σ = 3

We want P(X<15)

Standardizing gives:

P(X<15) = P(Z<(15-21)/3)
P(X<15) = P(Z< -2) ⇒ When the value of the z-score is negative, we will read the value of z<2 on the z-table then subtract the answer from 1

P(X<15) = 1 - P(Z<2)
P(X<15) = 1 - 0.9772
P(X<15) = 0.0228

the probability that pizza takes less than 15 minutes to be delivered is 0.0228 = 2.28%

 Round answer as needed


simplify 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³

a) -4m³ + 8p²

b) 8p² - 4

c) 4m³ - 13p³ + 5p

d) -4m³ + 13p³ - 5p

Answers

7p³ + 2m³ - 6m³ + 4p - 9p + 6p³
= 13p³ - 4m³ - 5p
= -4m³ + 13p³ - 5p

answer
d) -4m³ + 13p³ - 5p

Final answer:

The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).

Explanation:

To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.

Like terms have the same variable raised to the same power.

In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.

Combine terms with p³: 7p³ + 6p³ = 13p³.Combine terms with m³: 2m³ - 6m³ = -4m³.Combine terms with p: 4p - 9p = -5p.

Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).

anna owes home antiques Whose value is 160000 today assuming normal growth. however anna believes the value will grow at 16% per year for the next three years she wants to take this rapis growth ibto consideration when valuing the buisness for potential sale find the future value of the buisness in three years then use that future value to find the present value at a rate 8% compounded annually

Answers

The formula is
A=p (1+r)^t
A future value?
P present value 160000
R interest rate 0.16
T time 3years
A=160,000×(1+0.16)^(3)
A=249,743.36

Use that future value to find the present value at a rate 8% compounded annually
To find p (present value) solve the formula for p
P=A÷ (1+r)^t
Where r is 0.08
P=249,743.36÷(1+0.08)^(3)
p=198,254.33

Which statement is true about the equations –3x + 4y = 12 and x – y = 1? The system of the equations has exactly one solution at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.

Answers

Final answer:

The system of equations has exactly one solution, but it is located at (16,15), not (–8, 3), (–4, 3) or any other points. So, none of the provided options are true.

Explanation:

The task is to identify the statement that is correct about the system of equations –3x + 4y = 12 and x – y = 1. To discover this, we must solve the system which consists of these two linear equations. Adjust equation two to be in the same format as equation one by adding y to both sides which gives x = y + 1. Substitute it into the first equation: -3(y + 1) + 4y = 12, which simplifies to -3y - 3 + 4y = 12, giving y = 15. Substitute y = 15 to the second equation, it gives us x = 16. Hence, none of the provided solutions is correct, because the system has exactly one solution at (16,15).

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Are the two triangles below similar?

Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional

Answers

Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.

Explanation:-

In Δ ABC

∠A=30° , ∠C=65 °

By angle sum property of triangle

∠A + ∠B + ∠C= 180°

⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°

⇒∠B=85°

Now in ΔABC and ΔDEF

∠A=∠D=30° and ∠B=∠E=85°

⇒ there are two pairs of congruent corresponding angles.

So by AA-similarity criteria

ΔABC ≈ ΔDEF




Answer:

Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

Two triangles ABC and DEF are given .

The measure of angles in triangle ABC are:

m<A=30°,m< C=65°,

m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)

In triangle DEF the measure of the angles are :

m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)

In triangles ABC and DEF,

< A=<D=30°

<B=<E=85°

<C=<F=65°

The two triangles are similar by AAA property.

Which expression represents the area of the shaded triangle?

Answers

Answer:

B. [tex]\frac{1}{2}\times (5.7)\times (1.9)[/tex]

Step-by-step explanation:

We have been given an image of a triangle. We are asked to choose the correct option that represents the area of the shaded region.

We know that the area of a triangle is half the product of its height and base.

Upon looking at our given diagram we can that shaded region is in form of triangle and the height of both triangles is 5.7 meters. We can also see that the base of shaded triangle is 1.9 meters.

[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Height *Base})[/tex]

[tex]\text{Area of shaded region}=\frac{1}{2}\times (5.7)\times (1.9)[/tex]

Therefore, option B is the correct choice.

Answer:

b.

Step-by-step explanation:

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)

Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.

Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.

Step 4: x equals negative 8 plus or minus six all over two.


Step 1

Step 2

Step 3

Step 4

Answers

To solve for the roots of a quadratic equation, you use the equation

[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]

The parameters a, b and c represent the coefficients of the standard form of the quadratic equation: y = ax^2 + bx + c. Thus, for the equation y = x2 − 8x + 7,

a = 1
b = -8
c = 7

The mistake Joyce made was in Step 1. Because Step 1 is wrong, the rest of the equation is wrong consequently. The mistake was made by Joyce when she assigned b = 8. She forgot to include the negative sign of -8x. 

Her mistake is in the first step, she wrote the equation incorrectly.

Solving quadratic equations:

A general quadratic equation:

ax^2 + bx + c = 0

has the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, the equation is:

y = x^2 - 8x + 7

And what Joyce writes in each step is:

Step 1:

x = (-8 ± √(8^2 - 4*1*7))/(2*1)

Then we can already see the mistake.

Notice that in the given equation, we have:

b = -8

And the general solution has:

x = (-b ± √(b^2 - 4ac))/(2a)

-b would be equal to 8, then what Joyce must have written here is:

x = (8 ± √((-8)^2 - 4*1*7))/(2*1)

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(06.02)The graph shows the number of weeks a movie has been in theaters and the number of tickets sold each week
Which statement best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold?

As the number of weeks increases, the number of tickets sold decreases.
As the number of weeks increases, the number of tickets sold increases.
As the number of weeks decreases, the number of tickets sold decreases.
No relationship can be determined.

Answers

Looking at the graph, you can see that as more weeks pass, the amount of tickets sold are slowly decreasing. 

Therefore, A) As the number of weeks increases, the number of tickets sold decreases would be the correct answer.

As the number of weeks increases, the number of tickets sold decreases so option (A) will be correct.

What is a graph?

The link between lines and points is described by a graph, which is a diagrammatic representation of a network. A graph is made up of some points and the distance between two.

In another word, graph is geometrical relation of the analytical variable.

For example to draw the equation y = 6x +8 this will draw a straight line in the coordinate geometry.

In the given question it is clearly visible that as the weeks in theater are increasing the points are going down on the y-axis which is tickets sold.

As the number of weeks increases, the number of tickets sold decreases hence option (A) will be correct.

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Merlin industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.

Answers

This is exponential growth/decay function, in this case decay, of the form:

f=ir^t, f=final value, i=initial value, r=common ratio or "rate", and t=times rate is applied or "time".

In this case i=2100 and r=(100-14)/100=0.86 so the equation is:

f=2100(0.86^t)  and in five years...

f(5)=2100(0.86^5)

f(5)≈$987.90  (to nearest whole cent)

Susie and Amelia solved the same equation using two separate methods. Their work is shown in the table below:

Answers

Susie made the error when she subtracted 2

Answer:

(C)

Step-by-step explanation:

Explanation of Susie's method:

The given equation is:

[tex]2x-3=4x-2[/tex]

[tex]2x-2x-3=4x-2x-2[/tex]

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

[tex]-3+2=2x[/tex]      ( she made a mistake when she subtracted 2)

[tex]-1=2x[/tex]

[tex]x=-\frac{1}{2}[/tex]

Susie made a mistake in step 4 when she subtracted 2,

Thus, option C is correct.

Calculate each unit rate
$11.49 for 3 packages

Answers

For the total it would be like $34.47 and so the unit rate might be $3.83

Eduardo bought a refrigerator with a sticker price of $2400. If he paid $35 a week for two years, what was the approximate markup rate on the refrigerator?
A. 65.9%
B. 51.7%
C. 34.1%
D. 75.8%

Answers

There are 52 weeks a year
In 2 years there are 104 weeks

Total paid
35×104=3,640

markup rate
((3,640−2,400)÷2,400)×100=51.7%

It's b

Answer:

The correct answer is option B

Step-by-step explanation:

Payment done per week [tex]= 35 dollar\\[/tex]

Total number of weeks in a  year [tex]= 52 weeks\\[/tex]

Total number of weeks in two  year [tex]= 104 weeks\\[/tex]

Total amount paid in two weeks

[tex]= 35 * 104\\=3,640\\[/tex]

The make up rate is basically the amount paid over and above $2400

[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]

Find the center and radius of a circle defined by the equation x^2+yy^2+4x-8y+13=0

Answers

hello : 
x²+y²+4x-8y +13 = 0
(x² +4x) +(y² -8y )+13 = 0
(x²+4x+4) -4 +(y-8y +16) -16 +13 = 0
(x+2)² +(y -4)² = 7
the center is : (-2 , 4) and radius √7
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