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The hypotenuse of a right triangle is 4 meters more than three times the length of the shorter . The length of the longer leg is less than that of the hypotenuse. Find the length of the shorter leg of the triangle .

Answers

Answer 1

Answer:

The hypotenuse of a right triangle is 4m longer than the shorter leg and 2m longer than the longer leg. What are the lengths of the sides?

Just for variety, consider the hypotenuse = h, the short leg h-4 and the long leg h-2.

c^2 = a^2 + b^2; so h^2 = (h-4)^2 + (h-2)^2; h^2 = h^2 - 8h + 16 +h^2 -4h +4;

h^2 -12h +20 = 0 factors to (h - 10)(h - 2) = 0 so h = 2 or h = 10

Since (h - 2) = (2 - 2) = 0 and a triangle cannot have a side of zero length, 10 is the length of the hypotenuse.

h^2 = (h-4)^2 + (h-2); 10^2 = (10-4)^2 + (10-2); (10)^2 = (6)^2 + (8)

The hypotenuse is 10 cm, short leg 6 cm and long leg 8 cm.


Related Questions

Help this needs to be answered

Answers

The equation of the linear function in slope-intercept form is  [tex]f(x) = \frac{1}{2}x - 5[/tex]

The equation of a linear function can be written in the slope intercept form as:

f(x) = mx + b,

where,

m represents the slope of the linear function

b represents the point on the y-axis where the line intercepts the y-axis. (at this point, x = 0)

we need to find the value of m and b to be able to write the equation of the linear function.

Find slope (m):

From the image attached, the red line represents the rise (3 units) while the blue line represents the run (6 units).

Slope (m) = rise/run

Substitute:

Slope (m) = 3/6

m = 1/2

Find the y-intercept (b):

From the graph, the line cuts the y-axis at y = -5.

Therefore,

b = -5

Next is to substitute m = 1/2 and b = -5 into f(x) = mx + b. Thus:

[tex]f(x) = \frac{1}{2}x - 5[/tex]

The equation of the linear function is: [tex]f(x) = \frac{1}{2}x - 5[/tex]

Learn more about how to write the equation of a linear function here:

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PLEASE PLEASE HELP I HAVE SCHOOL TMRW AND I HAVE TO FINISH THIS BY TONIGHT level two :brain teasers puzzle 15

Answers

Answer:

add each fraction together to make a whooe number

Step-by-step explanation:

for example 6/1+6/5=1 so add each fractiin together to make a whole number

factorize 3x²-11x-20​

Answers

Hello this is the answer, hope it helped :)

What effect will replacing x with (x - 4) have on the graph of the equation y = (x - 3) ^ 2 ?

a. slides the graph 7 units down
b. slides the graph 4 units up
c. slides the graph 1 unit right
d. slides the graph 4 units right

Answers

Answer:

d. slides the graph 4 units right

Step-by-step explanation:

When you replace x with x - h, the graph shifts h units horizontally.

Here, the replacement is x - 4.

Compare x - 4 to x - h.

h = 4

The shift is 4 units right.

Answer: d. slides the graph 4 units right

Solve for X. Geometry

Answers

Answer:

x=12

Step-by-step explanation:

QS=QR+RS

2x-11=7+x-6

x=12

Find the distance between (3, −7)
and (4, 1). Write your answer using a radical sign.

Answers

Answer:

sqrt(65)

Step-by-step explanation:

To find the distance between the two points

d = sqrt(  (x2-x1)^2+ (y2-y1)^2)

   = sqrt( (4-3)^2 +(1 - -7)^2)

    = sqrt( 1^2 + (1+7)^2)

    = sqrt( 1+8^2)

    = sqrt(1+64)

sqrt(65)

Given Points

( 3 , -7 ) x = 3 and y = -7( 4 , 1 ) x = 4 and y= 1

Using Formula

[tex] \large\begin{gathered} {\underbrace{\boxed{ \bf {\red{Distance \: = \: \sqrt{(x_2 \: - \: x_1) ^{2} \: + \: (y_2 \: - \: y_1) ^{2} } }}}}}\end{gathered}[/tex]

Substuting the values

[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ \bigg(4 \: - \: 3 \bigg) ^{2} \: + \: \bigg(1 \: - \: [ - 7 ]\bigg) ^{2} }[/tex]

[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ (1) ^{2} \: + \: (1 \: + \: 7 ) ^{2} }[/tex]

[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 1 \: + \: (8 ) ^{2} }[/tex]

[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 65 }[/tex]

[tex]\Large \purple \diamond \: \: \underbrace {\rm {{{\color{blue}{Distance \: = \: \sqrt{65} }}}}} \: \: \purple \diamond[/tex]

By increasing the list price of a book by ₹10 a person can buy a 10 books less for ₹1200 Find the original list price of the book. ( form Quadratic equation for the question) ​

Answers

Answer:

cwbmwl2h2h2jl2bcek2k3cgwkel

If LM = x + 3, MN = 2x and LN = 24, what does x equal

Answers

Answer:

[tex]\displaystyle 7 = x[/tex]

Step-by-step explanation:

[tex]\displaystyle 24 = [3 + x] + 2x → 24 = 3 + 3x → \frac{21}{3} = \frac{3x}{3} \\ \\ 7 = x[/tex]

I am joyous to assist you at any time.

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
There are 31 pink beads and 15 purple beads on Violet's necklace. What is the ratio of the number of beads to the number of pink beads?
A. 15:31
B. 46:31
C. 31:15
D. 31:46

Answers

Answer:

B. 46:31

Step-by-step explanation:

Answer:

46:31

Step-by-step explanation:

There are 46 beads in total (31 pink and 15 purple).

So, the ratio of the total number of beads to the number of pink beads is 46:31.

Hope this helps :)

Jason counted by 6's aloud and Lawton counted by 4's aloud. What is the first number they will both say?​

Answers

Answer:

12

Step-by-step explanation:

The first number they will both say = L.C.M of (6,4)

=> L.C.M of (6,4) is 12

The first number they will both say is 12

Heyo random person scrolling.Please help me?

Answers

Let's do

[tex]\\ \sf\longmapsto 2sin^260cos60tan^245[/tex]

[tex]\\ \sf\longmapsto 2\left(\dfrac{\sqrt{3}}{2}\right)^2\times \dfrac{1}{2}\times (1)^2[/tex]

[tex]\\ \sf\longmapsto 2\times \dfrac{(\sqrt{3})^2}{2^2}\times \dfrac{1}{2}\times 1[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{2}\times \dfrac{1}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{4}[/tex]

Trigonometric values

[tex]\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}[/tex]

Please answer this and simplify

Answers

Answer:

volume = x(x+2)(2x+1) = 2x^3+5x^2+2x

a = 2

b = 3

c = 5

d = 2

e = 2

f = 1

Volume=x(x+2)(2x+1)=2x3+5x2+2x

A=2.

B=3

C=5

D=2

E=2

F=1

WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART PLEASE GOVE EXPLANATION?

Answers

Answer:

0.249

Step-by-step explanation:

tan(theta) = opposite / adjacent (according to the SOH CAH TOA rule), which effectively means y/x in this case.

So -0.242 / -.970 ≈ 0.249

Other explanation:

On a unit circle,

y = sin(θ)

and

x = cos(θ).

And since, tan = sin/cos, tan(θ) = y/x. You y and x are given, so calculating tan is a matter of dividing them.

can someone pls help me on number 4

Answers

Answer:

Step-by-step explanation:

Do this by converting the numbers to decimals

9 1/4 inches / 12 inches / foot = .770833 feet to 6 decimal places.

9.770833 feet is the length of the given board.

11.25 inches = 11.25 / 12 = 0.9375 feet

So the amount of board used is 9.770833/0.9375 = 10. 42222 feet used in cutting up the board.

Therefore there is 10.42222187 board cut up. The decimal is the remainder.

0.42222187 * 12 = 5.066 inches or rounded to 5 inches.

Help please, area of a triangle

Answers

Answer:

84 ft^2.

Step-by-step explanation:

Use Pythagoras to find the value of h:

25^2 = h^2 + 7^2

h^2 = (25-7)(25+7)

h^2 = 576

h = √576 = 24

Area  = 1/2 * 7 * 24

= 84.

I need help finding the domain and range of y+9x=15

Answers

Answer:

domain) all real numbers

range) all real numbers

Step-by-step explanation:

y=15-9x

there are no illegal values for x that would make the equation invalid so domain is all real numbers

this line is not flat so range is also all real numbers

Verizon charges a $40 sign up fee and $60 a month for their new hotspot. T-Mobile charges a $100 sign up fee and then $40 per month for their new hotspot. After how many months of service will the two company's fees be the same?

Answers

It will take 3 months for both company's fees be the same

Let

y = total charges

x = number of months

Verizon:

y = 40 + 60x

T-Mobile:

y = 100 + 40x

Number of months it will take both companies to charge the same fee

Equate the total charges of both companies

40 + 60x = 100 + 40x

40 - 100 = 40x - 60x

-60 = - 20x

x = -60 / -20

x = 3 months

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Write the equation of the line in slope-intercept form. m=5/9 y-intercept (0,2) 2 The equation of the line in slope-intercept form is (Type an equation. Use integers or fractions for any numbers in the equation. Simplify your answer.​

Answers

Answer:

y = (5/9)x + 2

Step-by-step explanation:

Slope intercept form is

y = mx + b then plug in the values

y = (5/9)x + 2

If n = 4, the value of the expression 28 – 12 + vñ : 2 is
0 15
021
O
017

Answers

Answer:

17

Step-by-step explanation:

[tex] 28 - 12 + \sqrt{n} \div 2 = [/tex]

n = 4

[tex] = 28 - 12 + \sqrt{4} \div 2 [/tex]

[tex] = 16 + 2 \div 2 [/tex]

[tex] = 16 + 1 [/tex]

[tex] = 17 [/tex]

I really need this answered. I need to find the area ​

Answers

Answer:

I think 5

Step-by-step explanation:

5u^2

just count the no. of squares

if they allocate sides or an area for the small square then:

sides

(side^2 • 5)

eg.  the side is equal to 2cm, then

(2^2 • 5) = 4(5)

              = 20 cm^2

allocated area for small square

square area • 5

eg. one square has an area of 4 cm^2

4 • 5 = 20 cm^2

A 3cm x 2cm rectangle sits inside a circle with a radius of 4cm
What is the area of the shaded region
round your final answer to the nearest hundredth

Answers

The area of the shaded region is 44.24\ cm^{2}44.24 cm2

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

step 1

Find the area of circle

The area of the circle is equal to

A=\pi r^{2}A=πr2

we have

r=4\ cmr=4 cm

substitute

A=\pi (4)^{2}A=π(4)2

A=16\pi\ cm^{2}A=16π cm2

step 2

Find the area of rectangle

The area of rectangle is equal to

A=(3)(2)=6\ cm^{2}A=(3)(2)=6 cm2

step 3

Find the difference

16\pi\ cm^{2}-6\ cm^{2}16π cm2−6 cm2

assume

\pi=3.14π=3.14

16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}16(3.14) cm2−6 cm2=44.24 cm2

Correct answer gets brainliest and 5 stars

Answers

Answer:

Does the answer help you?

The sum and product of two numbers x and y are 3 and 1.25 respectively. Form two
equations involving x and y and solve them to obtain the possible values of x and of y.


Please solve thissss pleaseee I have test tomorrow

Answers

Answer:

X+Y=3........(1)

X×Y=1.25........(2)

i) In (1):X+Y=3

X=3-Y.......(3)

ii)Subt (3) in (2)

XY=1.25

(3-Y)Y=1.25

3Y -Y²=1.25

0=Y²-3Y+1.25

[tex] \frac{ - ( - 3) + \sqrt{( - 3) { }^{2} - 4(1)(1.25) } }{2(1)} [/tex]

Y=2.5 OR Y=0.5(when you substitute a minus -)

iii)Substitute the Y values in (3)

what is the equation in slope intercept form 3 y - 9= 12x
Please help I need to turn it in.

Answers

Answer:

y=4x+3

Step-by-step explanation:

3y-9=12x

+9      +9

3y=12x+9

/3      /3

y=4x+3

Answer: y = 4x + 3

Explanation:

3y = 12x + 9 (i moved the constant to the right-hand side and change its sign.)

y = 4x + 3 (i divided both sides of the equation by 3 and got y = 4x + 3)

What set of number does the following number belongs to? (1.1A.1a) -√5​

Answers

Answer:

irrational

Step-by-step explanation:

See the image for a Venn diagram illustrating relationships among the various subsets of real numbers.

Find the arc length of the partial circle.

Answers

Answer:

● 23.55 units

Step-by-step explanation:

Arc length = 5( 270 π/ 180)

= 7.5 π units

= 7.5 (3.14)

= 23.55 units

OAmalOHopeO.

Answer:  Approximately 23.55 units

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

Explanation:

For now, we'll just find the perimeter of the full circle. The term "circumference" is the same as the perimeter of the circle.

Use the circumference formula to get

C = 2*pi*r

C = 2*3.14*5

C = 31.4

The distance around the full circle is approximately 31.4 units. It's approximate because pi = 3.14 is approximate.

We don't want the full distance around the circle. Instead, we want just the length of the green arc shown in the drawing. This is exactly 3/4 of the full circle, aka 3/4 = 0.75 = 75% of the full perimeter.

The length of the green arc is about 0.75*C = 0.75*31.4 = 23.55 units long. Imagine using a cloth ruler (used in tailoring clothes) as one way to confirm that this arc length is roughly 23.55 units long. Or you could imagine unwrapping this curved portion to lay it completely straight and flat against a ruler.

An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?
x3 feet
5 + 11x2 feet
5x2 + 11 feet
5x3 + 11x5 feet

Answers

Answer:

the answer is 5×3+11×5 feet

Answer:

4th option

Step-by-step explanation:

An equilateral triangle has 3 congruent sides

Divide the perimeter by 3 for length of side

[tex]\frac{15x^3+33x^5}{3}[/tex]

= [tex]\frac{15x^3}{3}[/tex] + [tex]\frac{33x^5}{3}[/tex]

= 5x³ + 11[tex]x^{5}[/tex] ← length of 1 side

Calculate the mass of 245 mL of benzene if the density of benzene is 0.8765 g/mL.

Answers

Answer: 214.7425g

Step-by-step explanation:

Total benzene = 245mL

Density of benzene = 0.8765g/mL

Which means there is 0.8765g benzene per mL

Mass = 245×0.8765

= 214.7425g

Therefore there is 214.7425g of mass in 245mL benzene

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If the density of benzene is 0.8765 g/mL, the mass of benzene is 214.74 grams.

Given the following data:

Density of benzene = 0.8765 g/mL Volume of benzene = 245 mL

To find the mass of benzene:

Density is mass all over the volume of a substance or an object.

Mathematically, the density of a substance is given by the formula;

[tex]Density = \frac{Mass}{Volume}[/tex]

Making mass the subject of formula, we have;

[tex]Mass = Density[/tex] × [tex]Volume[/tex]

[tex]Mass = 0.8765[/tex] × [tex]245[/tex]

Mass = 214.74 grams.

Therefore, the mass of benzene is 214.74 grams.

Read more: https://brainly.com/question/18320053

Refer to Table 20-3.A
3. Accofding to the table, what percent of families in Edgerton have income levels below $69,000?

Select one:
O a. 60 percent.
O b. 80 percent.
O C. 40 percent.
O d. 20 percent.

Answers

Answer:

A. 60 Percent

Step-by-step explanation:

Quintle means 5.

Below $69,000 covers three of the five quntiles (bottom, second, and middle).

3/5 equals .6 or 60%

inverse proportion
it takes 3 hrs for two people to clean six identical rooms.
how long would it take 5 people to clean 20 of the same rooms at the same k rate

Answers

Answer:

4 hours per each room for 5 people

Step-by-step explanation:

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